Yield gap analysis

41
Yield gap analysis
of field crops
Methods and case studies

Cover photograph: ©FAO/Daniel Hayduk
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Yield gap analysis
of field crops:
FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS
Rome, 2015
FAO
WATER
REPORTS
41
VO Sadras
South Australian Research & Development Institute, Australia
KG Cassman and P Grassini
University of Nebraska, USA
AJ Hall
IFEVA, University of Buenos Aires, Argentina
WGM Bastiaanssen
Delft University of Technology, The Netherlands
AG Laborte
International Rice Research Institute, The Philippines
AE Milne
Rothamsted Research, UK
G Sileshi
World Agroforestry Centre, Malawi
P Steduto
FAO, Italy

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ISBN 978-92-5-108813-5 (FAO)
Recommended citation:
FAO and DWFI. 2015. Yield gap analysis of field crops – Methods and case studies, by Sadras, V.O.,
Cassman, K.G.G., Grassini, P., Hall, A.J., Bastiaanssen, W.G.M., Laborte, A.G., Milne, A.E., Sileshi , G.,
Steduto, P. FAO Water Reports No. 41, Rome, Italy.
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© FAO and DWFI, 2015

iii
Contents
List of figures v
List of boxes viii
List of tables viii
Foreword ix
Acknowledgements x
Preface xi
Summary xii
1. Introduction 1
2. Definitions of crop yield 4
2.1. Evolution of yield criteria 4
2.2. Yield definitions 5
3. Scales, data sources and overview of methods 10
3.1. Actual yield data: spatial scales and accuracy 10
3.2. Temporal scales 15
3.2.1. Removing the dynamic components of environment and technology 15
3.2.2. Capturing the dynamic components of environment and technology 15
3.3. Modelled yield 18
3.3.1. Desirable attributes of models in yield gap studies 18
3.3.2. Weather data for modelling crop yield 19
3.3.3. Modelling yield within the context of a cropping system 22
4. Approaches to benchmark yield and quantify yield gaps 23
4.1. Approach 1: high-yielding fields, experimental stations and 23
growers contests
4.1.1. Sunflower in rainfed systems of Argentina 23

iv
4.1.2. Maize in sub-Saharan Africa 24
4.1.3. Grain legumes in India 26
4.1.4. Wheat-maize double crop in the Hebei plain of China 26
4.2. Approach 2: boundary functions accounting for resources 27
and constraints
4.2.1. Yield and water productivity gaps 27
4.2.1.1. Wheat in rainfed systems 27
4.2.1.2. Millet in low-input systems of Africa 31
4.2.1.3. Sunflower in rainfed systems of Argentina 32
4.2.1.4. Maize in irrigated systems of USA 33
4.2.1.5. Yield vs water availability in a critical period of yield determination 34
4.2.2. Yield gaps and nitrogen uptake 35
4.2.3. Yield gaps and soil constraints 36
4.2.4. Water productivity as a function of yield 37
4.3. Approach 3: modelling 38
4.3.1. Maize (USA, Kenya) and wheat (Australia) 38
4.3.2. Rice in Southeast Asia 41
4.3.3. Maize in Zimbabwe 42
4.3.4. Quinoa in Bolivia 42
4.3.5. Estimating yield potential with climate indices 42
4.3.6. FAO’s Agro-Ecological Zones system 44
4.4. Approach 4: remote sensing 44
4.4.1. Benchmarking crop yield and yield gaps with remote sensing 46
4.4.2. Benchmarking water productivity with remote sensing 46
5. Conclusions and recommendations 48
Glossary 50

v
List of figures
1. Time trends in FAO’s Net Production Index (2004-2006 = 100) 2
2. Decreasing rate of improvement of soybean yield in Kentucky (USA) with 5
increasing cropping intensity, Measured
3. Definitions of yield relevant to yield gap analysis; arrows illustrate some 5
yield gaps
4. County-level average (2004-2008) yields for rainfed and irrigated maize in 11
Nebraska and Kansas
5. Sub-national (district, region, province) data coverage in Sub-Saharan 11
Africa
6. Comparison between average farmer-reported Natural Resource District 12
(NRD) in Nebraska, USA, and USDA-NASS county-level average maize and
soybean yields (upper and bottom panels, respectively)
7. Box-plots of farmer-reported maize yield, applied irrigation, and N fertiliser 13
during the 2004-2011 interval in the Lower Platte North Natural Resource
District in Nebraska (USA) for irrigated (I) and rainfed (R) maize
8. Dynamics of nitrogen fertilisation in France according to three sources: 14
AGRESTE (Statistical Service of the French Ministry of Agriculture), ONIGC
(French National Office of Arable Crops), and ARVALIS (French Technical
Institute for Cereal Crops)
9. Dynamics of rizhoctonia root rot in direct-drilled wheat crops in South 14
Australia. Wheat was grown in rotation with volunteer pasture
(closed square), pea (closed circle), medicago (open circle) or in monoculture
(open square). Error bars are lowest significant difference (P=0.05).
10. Trends in grain yields of (a) irrigated and rainfed maize in Nebraska, (b) 16
wheat in The Netherlands and wheat in Wimmera (South-east Australia).
Sequential average yields in (c) Nebraska, (d) The Netherlands and
Wimmera, and associated coefficients of variation for (e) Nebraska, and (f)
Wimmera and The Netherlands as calculated based on 1, 2, 3 ... n years of
yield data starting from the most recent year (2011 for Nebraska and 2009
for The Netherlands and Wimmera) and going backwards.
11. (a) The rate of rice yield improvement between 1966 and 1979 in Central 17
Luzon (Philippines) was much larger for growers in the top quantiles than
for those in the lower quantiles As a consequence the gap between the
yield of best and average farmers (b) almost doubled during this period In
(a) the red lines represent the ordinary least squares estimate and the 90%
confidence interval of the estimate. The gray area refers to the 90% confidence
band for the quantile regression estimates.

vi
12. Time trends in actual and modelled yield, and yield gap of wheat in the 17
irrigated Yaqui Valley of northwest Mexico between 1968 and 1990.
Modelled yields are estimates with CERES-Wheat, assuming no change in
cultivar or management, thus accounting for weather-based potential yield.
13. Time trend in the area planted to sugarcane in the state of São Paulo, 18
Brazil, where the yield gap was ≤20%. Yield gap is the difference between
actual and water-limited yield.
14. With increasing model complexity, parameter error increases and structure 19
error decreases towards a limit of irreducible error (dotted line).
15. Simulated rainfed maize water-limited yield (Yw) across four sites in the 21
USA Corn using weather data from (a) NOAA weather stations (Tmax, Tmin,
precipitation, and humidity) coupled with gridded solar radiation data from NASA-
POWER database, (b) gridded NCEP data, (c) gridded CRU data and
(d) gridded NASA plotted against simulated Yw based on high-quality
weather data from meteorological stations of the High Plains Regional
Climate Center (HPRCC) network.
16. Variation in maize mean yield with fertiliser and yield gap on various soil 25
types in sub-Saharan Africa. Vertical bars indicate 95 percent confidence
bands.
17. Comparison of average, minimum and maximum yield of peanuts 26
measured in experimental stations and in whole-districts of India. The
lines are y = x.
18. Yield gap analysis of wheat-maize double cropping and its components 27
in the Hebei plain of China. Yields are potential, calculated with models;
experimental, measured in researcher designed trials in growers’ fields,
and maximum, average and minimum yield from surveys.
19. Crop growth and yield depend on the capture and efficiency in the use of 30
resources (CO2, radiation, water and nutrients) and environmental factors
modulating the development, morphology and physiology of the crop.
20. a boundary function with slope = 20 kg grain ha-1 mm-1 and x-intercept 30
= 110 mm (solid line) for a particular set of crops comprising South
Australian environments and cultivars and management of the 1960-70s
(circles). (b) The original concept, with an updated slope = 22 kg grain
ha-1 mm-1 and x-intercept = 60 mm, applied to a large (n=691) data set
of crops in four dry environments of the world.
21. (a) Frequency distribution of millet yield per unit seasonal 31
evapotranspiration in Western Sahel and (b) relationship between grain
yield and evapotranspiration for crops in Western Sahel; data from Egypt
and USA are included for comparison. The solid line has a slope = 16.7 kg
grain ha-1 mm-1 and an x-intercept = 158 mm, both derived from
Rockström et al. (1998).
22. (a) Relationship between sunflower grain yield and seasonal water supply 32
in farmers’ fields (open symbols; n = 169) and small-plot fertilizer trials
(closed symbols; n = 231) in the Western Pampas. Water supply is available
soil water at sowing plus sowing-tomaturity rainfall. (b) Relationship
between yield and evapotranspiration for sunflower crops in Australia,
Lebanon, Spain, Turkey, and United States.

vii
23. a) Relationship between grain yield and seasonal water supply (available 33
soil water at sowing plus sowing-to-maturity rainfall and applied irrigation)
for maize crops grown under near-optimal management in the Western
US Corn Belt. The database included a wide range of environments and irrigation
schedules; none of the fields had obvious nutrient limitations, diseases, insect
damage, weeds, or hail. (b) Farmers’ irrigated yields in the Tri-Basin NRD as a
function of seasonal water supply (+). Tri-Basin county-level average rainfed
yields are also shown for comparison (•).
24. Relationship between attainable soybean yield and rainfall during the 34
period of pod and grain set in (a) deep and shallow soils at Tandil, (b) deep soil at
Pergamino, (c) combined data for Tandil and Pergamino. Curves are: (a) deep soil,
y = 0.25 + 2.79 (1- e –0.0258 x); shallow soil, y = -1.15 + 3.81 (1-e-0.0240x); (b) y =
-0.56 + 4.7 (1-e-0.0259x), (b) y = -0.059 + 1.02 (1- e-0.0242x)
25. Attainable yield of maize as a function of rainfall in the critical period 35
of grain yield determination for deep Typic Argiudolls and shallow
Petrocalcic paleudolls (0.5-0.7m). The critical period is 20 d before to
30 d after anthesis. Double-headed arrows indicate yield gap due to soil.
26. Actual wheat yield as a function of seasonal nitrogen uptake in 36
Mediterranean (closed symbols) and non-Mediterranean environments
(open symbols). The figure in the left shows a complete data set compiled
from papers published in SCI journals (n = 630). The figure in the right
shows the five highest yields in each of 50 kg/ha intervals of nitrogen uptake.
27. Normalised relationship between yield and nitrogen input for 334 wheat 36
crops in Australia. The solid line is a nitrogen-response curve representing
the upper limit of the relationship
28. Relationship between water productivity (yield per unit evapotranspiration) and 37
yield of maize in the Doukkala Irrigation Scheme, Morocco. The red line is the
boundary function fitted by calculating the 90th percentile of water productivity
for yield split in 1000 kg/ha intervals. Both yield and water productivity were
derived with methods combining remote sensing and modelling.
29. Simulated potential yield (Yp) or water-limited yield (Yw) based on site-specific 39
weather, soil properties, and management data collected from farmer’s fields in
three cropping systems: rainfed maize in west Kenya, irrigated maize in Nebraska
(USA), and rainfed wheat in Victoria (Australia) (n = 54, 123, and 129 field-year
cases, respectively). Each bar corresponds to an individual field-year case. The
yellow and red portions of the bars indicate actual farmer’s yield (Ya) and yield
gap (Yg), respectively. Horizontal lines indicate average Yp (or Yw) and Ya (solid
and dashed lines, respectively) for the region. Means and coefficients of variations
(CV) for Yp (or Yw) and Yg are shown. Fields were sorted from highest to lowest
Yp or Yw. Note that Ya>Yw for some site-years in Victoria which reflects incorrect
specification of model inputs , actual yields, and/or inability of crop models to
portray specific genotype x environment x management interactions.
30. Median (a) actual yield (t ha-1), (b) modelled water use (mm), (c) water use 43
efficiency, i.e. (a)/(b), (d) normalised photothermal coefficient (MJ m-2d-1 kPa-1
oC-1), and (e) normalised water use efficiency, i.e. (c)/(d). Data corresponds to the
period 1975-2000. Note water use efficiency decreases from south to north in the
eastern region (c) but this gradient is largely accounted for the climate variables
in the normalised photothermal coefficient (e)

viii
31. Spatial distribution of the ratio between actual and attainable crop 47
yield in the irrigation scheme Doukkala in Morocco. The attainable
yield is estimated as the 98% percentile of the crop yield for various
crop types grown in the region

List of boxes
1. THEORETICAL YIELD 6

2. MAXIMISING YIELD AND WATER PRODUCTIVITY – DOES IT MAKE SENSE? 7

3. BOUNDARY FUNCTIONS 28

4. REMOTE SENSING: APPROACHES TO ESTIMATE CROP YIELD 44

List of tables
1. Classification of global weather databases used to understand current and future 20
agricultural productivity. Weather databases used in the present study have been
underlined
2. Basic statistics and robust parameter estimates (Winsorized means and coefficients 24
of variation) of maize grain yield (t ha-1) from various soil fertility management
inputs.
3. Actual average farmer yield (Ya) and estimates of average potential yield (Yp) or 40
water-limited yield (Yw), yield gaps (Yg), and Yg-to-Ya ratio (Yg:Ya) for three
cropping systems based on four different methods: crop simulation models, upper
percentiles of farmer Ya, and maximum yields. Values are means for one single
year (rainfed maize in western Kenya) or 3 years for irrigated maize in Nebraska
and rainfed wheat in Victoria.

ix
Foreword
A world population that will exceed 9 billion by 2050 will require an estimated 60 percent more
food. This increase means we need a major boost in current primary agricultural productivity. It is
estimated that 80% of the required increase can stem from intensification. Achieving this produc-
tion target without further large-scale conversion of land to agriculture requires higher crop inten-
sification and greater annual crop productivity. However, crop productivity varies greatly from
place to place, depending on environment, inputs and practices. Assessing the yield gap of existing
cropped lands will indicate the possible extent of yield increase from actual values.
The authors of this publication provide a wide-ranging and well-referenced analysis of literature
on current methods to assess productivity and productivity gaps of crops and cropping systems.
“Potential” and “water-limited” yield are used to define current best attainable yields under irri-
gated and rain fed conditions, respectively, whereas “theoretical” yield represents the maximum
yield that can be achieved according to current understanding of physiological principles of crop
productivity, providing a guide to future increases in crop yield.
The methods for benchmarking yields and identifying yield-gaps are presented through a number
of case studies, grouped into four approaches covering a range of applications. First, where actual
levels of yield can be compared with attainable yields, there can be an immediate benefit to increase
farm yield. Second, analysis of actual yields against environmental drivers provides insight into
management possibilities to increase yield. It has particular application in rain fed systems where
frontier analysis can identify seasons and conditions that support greatest water-limited yield and
suggest management strategies and tactics to maximise water-productivity under the range of envi-
ronmental conditions analysed. Third, crop models of various types, when used to provide inde-
pendent benchmarks for potential and water-limited yield, can be extrapolated to areas of limited
data availability, as it is currently the case for developing countries where the largest increases in
food demand will occur. Fourth, large scale comparisons made by combining actual yield data with
model estimates and remotely sensed information of crops and environment can inform about
priority assessments and policy planning at regional and national scales.
Much work is needed to meet the challenge for greater food supply in the coming decades. The
methods described here will form a basis for that work.
Moujahed Achouri
Director, Land and Water Division

x
Acknowledgements
This publication has benefited from the support and input of a number of experts coming from
different institutions who participated in the “Expert Consultation on Crop yield and water
productivity gaps” organized by FAO, the Daugherty Water for Food Institute at the University
of Nebraska (DWFI), the Stockholm Environmental Institute (SEI) and the Swedish International
Agricultural Network Initiative (SIANI) in October 2013.
Therefore, special thanks go to Roberto Lenton (DWFI), Johan Kuylenstierna (SEI) and Matthew
Fielding (SIANI) for their institutional and financial contribution to the consultation.
High appreciation goes to the participants to the expert consultation for their active and valuable
contribution in the debate: Prof. Víctor Sadras of the South Australian Research & Development
Institute, Australia; DWFI Faculty Fellows Kenneth Cassman and Patricio Grassini of the
University of Nebraska, USA; Prof Antonio Hall of the University of Buenos Aires, Argentina;
Dr. Wim Bastiaanssen of the Delft University of Technology, The Netherlands; Dr Sileshi G
Weldesemayat of the World Agroforestry Centre, Malawi; Pablo Tittonel of the Wageningen
University, the Netherlands; Elias Fereres of Cordoba University, Spain; Jennie Barron of the
Stockholm Environmental Institute and affiliated to Stockholm Resilience Centre, Sweden;
Christopher Neale, Director of Research for the Robert B. Daugherty Water for Food Institute
and Professor in the Department of Biological Systems Engineering, Nebraska, USA; Lenny van
Bussel, Crop Science and Resource Conservation, University of Bonn, Germany and member
of the Plant Production Systems Group, Wageningen University, the Netherlands; Genesis T.
Yengoh, Lund University Center for Sustainability Studies, Sweden; and Shulan Zhang, College of
Natural Resources and Environment, Northwest A&F University, China.
The support of colleagues at FAO has been indispensable for this publication. We wish to acknowl-
edge the critical inputs from Barbara Herren (Agriculture production and Protection Division),
John Latham and Roberto Cumani (Land and Water Division) and Chung Te Tzou (Regional
Office for Asia and Pacific). Special thanks go to Jippe Hoogeveen, Patricia Mejias Moreno and
Michela Marinelli (Land and Water Division), not only for their valuable interventions during the
discussion, but also for their kind assistance in organizing the event, in collaboration with Deborah
Welcomme, and in the editing of the manuscript.
We are also particularly grateful to Professors Elias Fereres and David Connor (Emeritus Professor
of Agronomy, University of Melbourne, Australia) for their insightful comments on the structure
and content of the publication.
Finally, we wish to acknowledge with thanks the generous financial support received from the
Robert B. Daugherty Foundation and the Bill & Melinda Gates Foundation for the work on the
yield gap analysis.

xi
Preface
On behalf of the Food and Agriculture Organization of the United Nations (FAO) and the Robert
B, Daugherty Water for Food Institute at the University of Nebraska (DWFI), we are delighted
to present this joint publication on “Yield gap analysis of field crops: Methods and case studies”.
The publication reviews methods for yield gap analysis, clarifying definitions and techniques to
measure and model actual, attainable and potential yield at different scales in space and time and
uses case studies to illustrate different approaches. We see this publication as a significant contribu-
tion towards our respective efforts to advance global water and food security through improve-
ments in water and land productivity.
Importantly, the publication provided critical input to, and benefitted from, the Expert
Consultation on “Crop yield and water-productivity gaps: method, problems and solutions”
that was co-hosted by FAO, DWFI and the Stockholm Environment Institute (SEI) in Rome on
3-4 October 2013. The Consultation brought together leading professionals to discuss methods
to measure the gaps, as well as ways to diagnose the root causes of yield and water productivity
gaps and the actions that will be needed to close yield gaps in both small and large scale cropping
systems, including management options and policies to provide incentives for the adoption of
gap-closing technologies.
This joint publication and the Expert Consultation are among the first results of a far-reaching
agreement between FAO and DWFI signed by University of Nebraska President James Milliken
and FAO Director General Jose Graziano da Silva in July 2012. The agreement calls for a collab-
orative program with three areas of focus: sustainably increasing crop yields and water productiv-
ity using modeling, remote sensing and information systems; improving drought management and
climate adaptation; and improving sustainable production under drought, stress and water-limited
conditions. The work on yield gap analysis is part of the first area of focus, and builds on the activi-
ties of FAO and the DWFI to develop tools and knowledge-delivery systems to inform and guide
policymakers in managing water and agriculture and to identify areas with the greatest potential to
increase food supply on a sustainable basis. In particular, it builds on two major initiatives: (i) the
work of a team at the University of Nebraska and partner institutions to build a global Yield Gap
Atlas; and (ii) the Regional Initiative on Water Scarcity for the Near East and North Africa Region
providing tools and methods to increase water productivity in irrigated and rainfed systems.
Pasquale Steduto
Deputy Regional Representative for
the Near East and North Africa
FAO Representative in Egypt
Food and Agriculture Organization
of the United Nations (FAO)
Cairo, Egypt
Roberto Lenton
Founding Executive Director
and Robert B. Daugherty Chair
Water for Food Institute at the
University of Nebraska
Lincoln, Nebraska, USA

xii
Summary
The challenges of global agriculture have been analysed exhaustively and the need has
been established for sustainable improvement in agricultural production aimed at food
security in a context of increasing pressure on natural resources.
Whereas the importance of R&D investment in agriculture is increasingly recog-
nised, better allocation of limited funding is essential to improve food production.
In this context, the common and often large gap between actual and attainable yield
is a critical target.
Realistic solutions are required to close yield gaps in both small and large scale crop-
ping systems worldwide; to make progress in this direction, we need (1) definitions
and techniques to measure and model yield at different levels (actual, attainable,
potential) and different scales in space (field, farm, region, global) and time (short,
long term); (2) identification of the causes of gaps between yield levels; (3) manage-
ment options to reduce the gaps where feasible and (4) policies to favour adoption of
gap-closing technologies.
The aim of this publication is to review the methods for yield gap analysis, and to
use case studies to illustrate different approaches, hence addressing the first of these
four requirements.
Theoretical, potential, water-limited, and actual yield are defined. Yield gap is the
difference between two levels of yield in this series. Depending on the objectives of the
study, different yield gaps are relevant. The exploitable yield gap accounts for both the
unlikely alignment of all factors required for achievement of potential or water limited
yield and the economic, management and environmental constraints that preclude, for
example, the use of fertiliser rates that maximise yield, when growers’ aim is often a
compromise between maximising profit and minimising risk at the whole-farm scale,
rather than maximising yield of individual crops. The gap between potential and water
limited yield is an indication of yield gap that can be removed with irrigation.
Spatial and temporal scales for the determination of yield gaps are discussed. Spatially,
yield gaps have been quantified at levels of field, region, national or mega-environment
and globally. Remote sensing techniques describes the spatial variability of crop yield,
even up to individual plots. Time scales can be defined in order to either remove or
capture the dynamic components of the environment (soil, climate, biotic components
of ecosystems) and technology. Criteria to define scales in both space and time need to
be made explicit, and should be consistent with the objectives of the analysis. Satellite
measurements can complement in situ measurements.
The accuracy of estimating yield gaps is determined by the weakest link, which in many
cases is good quality, sub-national scale data on actual yields that farmers achieve. In
addition, calculation and interpretation of yield gaps requires reliable weather data,
additional agronomic information and transparent assumptions.
The main types of methods used in yield benchmarking and gap analysis are outlined
using selected case studies. The diversity of benchmarking methods outlined in this

xiii
publication reflects the diversity of spatial and temporal scales, the questions asked, and
the resources available to answer them. We grouped methods in four broad approaches.
Approach 1 compares actual yield with the best yield achieved in comparable envi-
ronmental conditions, e.g. between neighbours with similar topography and soils.
Comparisons of this type are spatially constrained by definition, and are an approxima-
tion to the gap between actual and attainable yield. With minimum input and greatest
simplicity, this allows for limited but useful benchmarks; yield gaps can be primarily
attributed to differences in management. This approach can be biased, however, where
best management practices are not feasible; modelled yields provide more relevant
benchmarks in these cases.
Approach 2 is a variation of approach 1, i.e. it is based on comparisons of actual yield,
but instead of a single yield benchmark, yield is expressed as a function of one or few
environmental drivers in simple models. In common with Approach 1, these methods
do not necessarily capture best management practices. The French and Schultz model
is the archetype in this approach; this method plots actual yield against seasonal water
use, fits a boundary function representing the best yield for a given water use, and
calculates yield gaps as the departure between actual yields and the boundary func-
tion. A boundary model fitted to the data provides a scaled benchmark, thus partially
accounting for seasonal conditions. Boundary functions can be estimated with different
statistical methods but it is recommended that the shape and parameters of boundary
functions are also assessed on the basis of their biophysical meaning. Variants of this
approach use nitrogen uptake or soil properties instead of water.
Approach 3 is based on modelling which may range from simple climatic indices to
models of intermediate (e.g. AquaCrop) or high complexity (e.g. CERES-type models).
More complex models are valuable agronomically because they capture some genetic
features of the specific cultivar, and the critical interaction between water and nitrogen.
On the other hand, more complex models have requirements of parameters and inputs
that are not always available. “Best practice” approaches to model yield in gap analysis
are outlined. Importantly, models to estimate potential yield require parameters that
capture the physiology of unstressed crops.
Approach 4 benchmarking involves a range of approaches combining actual data,
remote sensing, GIS and models of varying complexity. This approach is important for
benchmarking at and above the regional scale. At these large scales, particular atten-
tion needs to be paid to weather data used in modelling yield because significant bias
can accrue from inappropriate data sources. Studies that have used gridded weather
databases to simulate potential and water-limited yields for a grid are rarely validated
against simulated yields based on actual weather station data from locations within
the same grid. This should be standard practice, particularly where global scale yield
gaps are used for policy decisions or investment in R&D. Alternatively, point-based
simulations of potential and water-limited yields, complemented with an appropriate
up-scaling method, may be more appropriate for large scale yield gap analysis. Remote
sensing applied to yield gap analysis has improved over the last years, mainly through
pixel-based biomass production models. Site-specific yield validation, disaggregated in
biomass radiation-use-efficiency and harvest index, remains necessary and need to be
carried out every 5 to 10 years.

11. Introduction
1. Introduction
Progress in crop production derives from advances in breeding and agronomy,
including improvements in the spatial and temporal arrangement of crops in farming
systems. The interaction between breeding and agronomy is widely acknowledged as
a major driver of enhanced production. For instance, dwarfing genes in cereals lead
to physiological improvement in grain/stem partitioning of dry matter with direct
consequences for yield, but also allowed higher rates of nitrogen fertiliser with reduced
risk of lodging in comparison with older, taller cultivars. Importantly, grass herbicides
were critical to capture the benefits of short-stature cereals in mechanised production
systems. The development and adoption of productivity enhancing technology can
be stimulated or hindered by political, economic, environmental and infrastructure
factors, as illustrated in Figure 1. Notwithstanding their importance, these factors are
outside the scope of this publication. Likewise, we do not discuss policies to deal with
yield gaps (Sumberg, 2012).
The challenges of global agriculture have been analysed exhaustively and the need
has been established for sustainable improvement in agricultural production aimed
at food security in a context of increasing pressure on natural resources (Cassman
2012; Connor and Mínguez 2012). Of a total global land area of 13,000 Mha, arable
land and permanent crops account for by 12%, permanent meadows and pastures for
26%, forests for 30% whereas 32% of this land is unsuitable for agriculture (FAO
2011). Analysis that accounts for suitability of remaining land for cropping and alter-
native land uses concludes that expansion of cropping land to 2050 is likely to be
small. Globally, 15% of arable land is irrigated and currently accounts for 42% of all
crop production; 7100 km3 of water are consumed annually to produce food globally
whereas feeding the world population of around 9 billion by 2050 would require an
additional 2100 km3 year (Sumberg 2012; Rockstrom et al. 2012).
Whereas the importance of R&D investment in agriculture is increasingly recognised,
better allocation of limited funding is essential to improve food production (Sumberg
2012; Connor and Mínguez 2012; Hall et al. 2013). In this context, the common and
often large gap between actual and attainable yield is a critical target. Realistic solutions
are required to close yield gaps in both small and large scale cropping systems world-
wide; to make progress in this direction, we need:
1. Definitions and techniques to measure and model yield at different levels (actual,
attainable, potential) and different scales in space (field, farm, region, global) and
time (short, long term).
2. Identification of the causes of gaps between yield levels.
3. Management options to reduce the gaps where feasible.
4. Policies to favour adoption of gap-closing technologies.
In this context, the aim of this publication is to review the methods for yield gap
analysis, and to use case studies to illustrate different approaches. Section 2 outlines
the evolution of yield to highlight historical changes in the meaning of this term; this

2 Yield gap analysis of field crops - Methods and case studies
Figure 1
(a) Time trends in FAO’s Net Production Index (2004-2006 = 100) highlighting the sustained
increase in productivity where infrastructure and policy favour development and adoption
of technology. Examples of disruption in productivity caused by (b) drought in south-
eastern Australia, where rainfall between 1997 and 2009 was 73 mm below average since
the start of the 20th century (CSIRO, 2011); (c) European policies combined with climate
and agronomic constraints; see for example Peltonen-Sainio et al. (2009) for a discussion
of the effect of European policies on adoption of agricultural technologies in Finland and
Brisson et al. (2010) for an account of recent yield stagnation in France; and (d) substantive
changes in production systems triggered by changes in political systems in eastern Europe.
(e) Highlights the sharp increase in total productivity against the slower improvement in
productivity per capita where rates of population growth remain high in India.
Source: FAO (http://faostat.fao.org/default.aspx); accessed 12 June 2012.
1960 1980 2000 2020
0
20
40
60
80
100
120
Argentina
Brazil
Canada
China
Egypt
Indonesia
Israel
Malaysia
Mexico
Morocco
South Africa
Turkey
USA
Uruguay
Australia
1960 1980 2000 2020
AgricultureNetProductionIndex(2004-06=100)
20
40
60
80
100
120
1960 1980 2000 2020
20
40
60
80
100
120
Denmark
Finland
France
Germany
Italy
Netherlands
Norway
Sweden
millennium
drought
(d)
Year
1960 1980 2000 2020
20
40
60
80
100
120
Hungary
Poland
Romania
India
1960 1980 2000 2020
20
40
60
80
100
120
Berlin Wall falls
per capita
0.71 ± 0.04 y-1
total
1.80 ± 0.052 y-1
(e)
(c)(b)
(a)

31. Introduction
leads to the definitions of yield used in this paper. Section 3 highlights the importance
of explicit definitions of spatial and temporal scales in yield gap analysis, and discusses
different data sources and their reliability. Desirable attributes of models in yield
gap studies are discussed, including aspects of model structure, complexity, calibra-
tion, validation and input requirements. Section 4 is the core of this publication. It
presents methods spanning a broad range of scales, complexities, input requirements
and associated errors. Case studies include irrigated and rainfed crops in diverse crop-
ping systems, from subsistence agriculture to high-input systems in North and South
America, Africa, Europe, Asia and Oceania. Section 5 presents a summary and recom-
mendations of methods for yield benchmarking and gap analysis.

2. Definitions of crop yield
2.1. Evolution of yield criteria
Before agriculture, our ancestors were not unlike other animals, for which “yield” was
the ratio between the energy derived from food and the energy invested in obtaining
it. Once the sowing of crops was established as a common practice, the definition of
yield shifted from an energy ratio to the ratio between the numbers of seed harvested
and seed sown (Evans 1993). This was particularly important in low-yielding seasons,
when early farmers had to make the hard decision of allocating seed for food or seed
for the next sowing. An important consequence of this measure of yield was that selec-
tion favoured highly competitive plant types, i.e. abundant tillering/branching, large
inflorescences, small grain and weak seed dormancy (Evans 1993). Only when avail-
ability of arable land came under pressure, mass of product per unit land area become
a more important criterion.
This shift in definition of yield had a dramatic impact on selective pressures, shifting
from the aggressive high-yielding plant (seeds per seed sown) to the less competitive
“communal plant” able to produce more yield per unit area (Donald 1981). Evans
(1993) envisaged the next measure of yield whereby the time dimension is consid-
ered explicitly, yield per ha per year. This measure is particularly important in the
comparison of systems with contrasting cropping intensity, i.e. number of crops per
year (Egli 2008; Cassman and Pingali 1995). Cassman and Pingali (1995) highlighted
that the green revolution in rice had as much to do with increased cropping intensity
as with increased harvest index and yield potential of semi-dwarf varieties. Thus,
IR-8, the first modern rice cultivar, was much faster to mature than traditional rice
land races it replaced (often by as much as 30–45 days) which allowed double rice
cropping on irrigated land -now the dominant land use in rice-growing regions of
South and Southeast Asia.
Increasing cropping intensity is widespread worldwide (Cassman and Pingali 1995;
Farahani et al. 1998; Caviglia et al. 2004; Sadras and Roget 2004). In environments
with favourable temperature and water availability, this involves a shift to multiple
crops per year. This applies not only to the tropics, but also to temperate environments
such as the Pampas of Argentina, where wheat-soybean double cropping is a dominant
feature. In environments where rainfall or temperature prevents multiple cropping,
such as dry environments of southern Australia, cropping intensity has been increas-
ing at the expense of pastures. Thus, the concept of yield progress based on kg per
ha will become inappropriate in some instances. Increasing cropping intensity could
contribute to either stabilisation or decline in yield per crop. This was illustrated by
Egli (2008), who reported an inverse relationship between rate of progress of yield of
soybean crops and intensity of cropping measured as % of double crops in the system
(Figure 2). Paradoxically, the best environments supporting higher cropping intensity
showed the lowest rate of improvement in yield of individual crops.
Yield of individual crops, in kg per ha, is also inappropriate for comparisons of main-
stream agriculture and organic production systems, as yield of individual crops does
not account for the additional land, time, labour, and water cost of organic nutrients
(Connor and Mínguez 2012). Meaningful comparisons of this kind must focus on the

whole production system, rather than
individual crops.
Explicitly measuring yield per unit
area and time is therefore of increasing
importance. Where multiple cropping
is prevalent, yield gap analysis should
target the system and its components;
Section 4.1.4 presents an example of
gap analysis in wheat-maize double
crops in China.
2.2. Yield definitions
This publication focuses on economic
yield of desired plant products; be they
grain, oilseed, tubers, corms, sugar,
fibre, forage, or energy content. Yields
of individual crops are in a contin-
uum from crop failure to potential and
several authors have proposed defini-
tions to account for this range (van
Ittersum and Rabbinge 1997; Evans
and Fischer 1999; Connor et al. 2011).
From these sources, here we list the
definitions of yield relevant for yield
gap analysis (Figure 3).
Theoretical yield is the maximum
crop yield as determined by biophysi-
cal limits to key process including
biomass production and partitioning.
It can be estimated with models with
sound physiological structure, and
parameters reflecting the biophysi-
cal boundaries of key processes. This
benchmark is perhaps more useful for
breeding (Box 1); given its agronomic
focus, this publication will not deal
with theoretical yield.
Potential yield (Yp) is the yield of a
current cultivar “when grown in envi-
ronments to which it is adapted; with nutrients and water non limiting; and with pests,
diseases, weeds, lodging, and other stresses effectively controlled” (Evans and Fischer
1999). Potential yield depends on location as it relates to weather but is independent
of soil, which is assumed to be physically and chemically favourable for crop growth.
The climate factors that influence potential yield are radiation, ambient CO2 concen-
tration and temperature (Evans and Fischer 1999; van Ittersum et al. 2013); photosyn-
thesis, growth and potential yield are also responsive to fraction of diffuse radiation
and vapour pressure deficit (Rodriguez and Sadras 2007). Potential yield is relevant to
benchmark crops where irrigation, the amount and distribution of rainfall, or a combi-
nation of irrigation and rainfall ensure that water deficits do not constrain yield.
Figure 2
Decreasing rate of improvement of soybean yield in
Kentucky (USA) with increasing cropping intensity,
measured as percentage of wheat-soybean double
cropping.
Source: Adapted from Egli (2008).
Figure 3
Definitions of yield relevant to yield gap analysis;
arrows illustrate some yield gaps.
Source: Multiple sources (Bingham 1967; van Ittersum & Rabbinge 1997;
Evans and Fischer 1999; Lobell et al. 2009; Connor et al. 2011).
3
Yield
theoretical potential actual actualwater-limited
irrigated rainfed
Figure 2
Cropping intensity (% of total area double-cropped)
0 20 40 60 80
Rateofyieldincrease(%year
-1
)
0.0
0.5
1.0
1.5
2.0
r2 = 0.61***

Water-limited yield (Yw) is similar to yield potential, except that yield is also limited
by water supply, and hence influenced by soil type (water holding capacity and
rooting depth) and field topography. This measure of yield is relevant to benchmark
rainfed crops.
Attainable yield is the best yield achieved through skilful use of the best available tech-
nology. Some studies use attainable yield as an approximation to either potential yield
or water-limited yield (Hall et al. 2013).
Actual (Ya) reflects the current state of soils and climate, average skills of the farmers,
and their average use of technology.
Box 1
THEORETICAL YIELD
The biophysical boundaries of yield are important, for example, when we ask
questions about the value of improved crop photosynthesis – What is the gap between
current photosynthesis and the biological limit of this trait? What is the expected
impact of enhanced photosynthesis on crop yield? (Parry et al. 2011).
Models like APSIM, CERES, CropSyst or SUCROS (Section 3.3) could be used to
estimate theoretical yield. However, these models are normally parameterised against
the actual crop phenotype (Lindquist et al. 2005), and therefore do not necessarily
capture the biophysical boundaries of important processes such as photosynthesis.
Thus, models to calculate theoretical yield need not only plausible physiological
and agronomic assumptions but also parameters that capture these boundaries; this
requires a theoretical approach.
Attempts have been made to establish an upper boundary for daily net production of
biomass from biophysical principles (Connor et al. 2011; Loomis and Amthor 1999)
and, separately, for the biological limit of harvest index (Foulkes et al 2009). The lack
of independence between production and partitioning of biomass (Körner 1991) and
trade-offs, for example between further increase in harvest index and lodging (Foulkes
et al. 2011), are some of the many constraints to scale up from low levels of organisation
and short time steps to seasonal growth and yield (Connor and Fereres 1999).
Theoretical yield can therefore be derived from basic principles in two ways: modelling
yield from the bottom up, or estimating the upper limit of key parameters such as
radiation use efficiency, and use these theoretical parameters in crop-level models.
Theoretical yield is constrained by genotypic (e.g. canopy architecture, harvest index)
and environmental drivers of crop development, growth and resource partitioning
in non-stress conditions. Recognised environmental factors include solar radiation,
ambient CO2 concentration, temperature and photoperiod, as they modulate
development and growth (Fischer 1985; Slafer et al. 2009). More recently, the list of
environmental factors has been expanded to include proportion of diffuse radiation
and vapour pressure deficit (Rodriguez 2007). For a given amount of radiation,
photosynthesis increases with the proportion of diffuse radiation, that depends on
atmospheric conditions and canopy traits (Spitters 1986; Sinclair and Shiraiwa 1993b;
Roderik and Farquhar 2003). Stomatal conductance and photosynthesis decline with
high vapour pressure deficit even in well-watered plants including irrigated rice and
wetland species (Otieno et al. 2012; Ohsumi et al. 2008). Latitudinal gradients of both
diffuse radiation and vapour pressure deficit have been described for the wheat-belt
of eastern Australia, which account for part of the latitudinal gradients of crop yield
potential (Rodriguez and Sadras, 2007).

Yield gap is the difference between two levels of yield. Depending on the objectives
of the study, different yield gaps are relevant (Figure 3). The exploitable yield gap
accounts for both the unlikely alignment of all factors required for achievement of
potential or water limited yield and the economic, management and environmental
constraints that preclude, for example, the use of fertiliser rates that maximise yield,
when growers’ aim is often a compromise between maximising profit and minimising
risk at the whole-farm scale, rather than maximising yield of individual crops (Box 2).
To account for this, a factor (< 1) is used to scale yield potential and water-limited yield.
A factor = 0.8 has been used in extensive production systems; higher factors may apply
for high-value horticultural crops, and smaller factors in other systems depending on
technological and economic (e.g. grain price) drivers.
Box 2
MAXIMISING YIELD AND WATER PRODUCTIVITY – DOES IT MAKE SENSE?
The notion that yield and water productivity can be “optimised” provides a sound
working hypothesis when we ask questions about the best combination of resources
(land, water, nutrients, radiation, labour, capital). In real production settings,
however, the maximum output (yield, water productivity) is rarely the best strategy
as it may require cropping practices that are economically unsound or too risky in
economic and environmental terms. To illustrate this point, we present two examples
of trade-offs: between the efficiency in the use of water and nitrogen, as related to
nitrogen supply in rice and maize, and between water productivity and yield of rice,
as related to water regime.
Nitrogen-driven trade-off between water productivity and the efficiency in the
use of nitrogen
High water productivity requires adequate nitrogen supply. However, the relationship
between yield and nitrogen supply conforms to the law of diminishing returns,
and therefore nitrogen use efficiency declines with increasing nitrogen supply. The
effect of individual inputs such as water and nitrogen on the carbon, water and
nitrogen budgets of crops thus determines a nitrogen-driven trade-off between
water productivity and nitrogen use efficiency (Sadras and Rodriguez 2010). This is
illustrated for aerobic and flooded rice in the Philippines and for rainfed and irrigated
maize in the USA (Fig. Box 2-1).
Thus, maximising water productivity in some farming systems may require nitrogen
rates that are too costly, too risky or environmentally unsound. This is particularly
important with high fertiliser-to-grain price ratio, in environments prone to nitrogen
leaching, or where biophysical, social, economic or infrastructure factors constraint
the use of fertiliser.
Water-regime driven trade-off between rice yield and water productivity
Bouman et al. (2006) and Farooq et al. (2009) reviewed the water productivity of rice,
of which about 90% is produced in irrigated or rain-fed lowland fields (“paddies”).
Water for lowland rice needs to account for land preparation requirements, seepage,
percolation, evaporation and transpiration. Combined seepage and percolation, for
example, range from 1-5 mm d-1 in heavy clay soils to a massive 25-30 mm d-1 in sandy
and sandy-loam soils (Bouman et al. 2006). In a context of water scarcity, water saving
technologies are being explored to reduce water use and improve water productivity,
including aerobic rice and alternate wetting and drying. The principle underlying these
techniques is the increase in water productivity associated with reduced water input.
However, water saving techniques can also reduce grain yield.

Comparison of rice crops grown under aerobic and flooded conditions in tropical
environments of the Philippines (14o N) showed a substantial increase in water
productivity at the expense of grain yield (Fig. Box 2-2). In relation to the flooded
regime, aerobic culture increased average water productivity from 5.7 to 7.4 kg grain
ha-1 mm-1 and reduced yield from 6.4 to 5.7 t ha-1. In contrast, aerobic rice crops in
temperate environments of Japan (34-35o N) outperformed their flooded counterparts
in terms of water productivity (average 8.3 vs. 3.4 kg grain ha-1 mm-1) and showed no
yield penalty (average 8.6 vs. 8.1 t ha-1) (Kato et al. 2009).
For a large number of crops in central-northern India and Philippines, alternate
wetting and drying improved water productivity of rice in comparison with the
flooded checks, but yield penalties up to 70% were recorded. Further studies in
lowland rice areas with heavy soils and shallow (0.1-0.4 m) groundwater tables in
China and Philippines showed that alternate wetting and drying outperformed their
flooded counterparts in terms of water productivity (Fig. 3c) with no associated yield
penalties (Fig. 3d). In all these cases, extremely shallow groundwater tables allowed
for ponded water depths that were typically within the root zone during the drying
periods (Bouman et al. 2006).
In summary, cultural practices to improve water productivity are obviously desirable,
but need to be seen in the broader context of agronomic, economic and environmental
trade-offs. Some trade-offs are inherent to the biophysical features of cropping
systems, and cannot be broken. The nitrogen-driven trade-off between water and
nitrogen productivity belongs to this category. This type of trade-off may lead to
practices that do not necessarily maximise water productivity, but rather account
for multiple objectives: lower rates of nitrogen fertiliser and associated low water
productivity may be justified in terms of reduced economic and environmental risk.
Figure Box 2-1.
Nitrogen driven trade-off between water productivity and nitrogen utilisation
efficiency in (a) flooded and (b) aerobic rice in the Philippines, and (c) rainfed
and irrigated maize in USA. Water productivity is yield per unit irrigation +
rainfall (a,b) or yield per unit evapotranspiration (c,d). In all cases nitrogen
utilisation efficiency is grain yield per unit nitrogen uptake (excluding root N).
Source: (Belder et al. 2005; Kim et al. 2008)
0 50 100 150
15
20
25
30
40
50
60
70
80
0 50 100 150
15
20
25
30
40
50
60
70
80
Waterproductivity(kgha-1
mm-1
)
0
2
4
6
50
55
60
65
WP
NUE
Fertiliser rate (kg N ha
-1
)
0 150
0
2
4
6
50
55
60
65
(a) flooded rice
(b) aerobic rice
(c) rainfed maize
(d) irrigated maize
WP
NUE
WP
NUE
WP
NUE
Nitrogenutilisationefficiency(kgkgN-1
)
Fig. Box 2-1

The trade-off between yield and water productivity associated with water saving
techniques can be broken in some instances, as illustrated in Fig. Box 2-2. Water
saving techniques that improve water productivity at the expense of grain yield can be
justified in some cases, but research should be encouraged to identify the conditions
where improved water productivity can be achieved with no yield penalties.
Figure Box 2-2.
(a) Aerobic rice had similar or greater water productivity and (b) lower yield
than rice grown under a flooded regime in the Philippines. (c) Alternate wetting
and drying improved rice water productivity and (d) caused no yield penalties in
comparison with the flooded checks in the Philippines and China.
Source: (Bouman et al. 2005; Bouman et al. 2006).
Yield flooded (t ha-1
)
0 2 4 6 8 10
Yieldaerobic(tha-1
)
0
2
4
6
8
10
0 4 8 12
Waterproductivityaerobic
(kgha-1
mm-1
)
0
4
8
12
Water productivity flooded (kg ha-1
mm-1
)
1:1
1:1
(b)(a)
Water productivity flooded (kg ha-1
mm-1
)
0 4 8 12
Waterproductivityalternatewetanddrying
(kgha-1
mm-1
)
0
4
8
12
1:1
(c)
Yield flooded (t ha-1
)
0 2 4 6 8 10
Yieldalternatewetanddrying(tha-1
)
0
2
4
6
8
10
1:1
(d)
Figure Box 2-2
The gap between potential and water limited yield is an indication of yield gap that
can be removed with irrigation. For example, modelling studies in cropping systems of
Bolivia compared yield of rainfed quinoa, from 0.2 to 1.1 t ha-1, with yield under irriga-
tion aimed at avoiding stomatal closure during all sensitive growth stages from 1.5 to
2.2 t ha-1, thus representing gaps around 1.2 t ha-1 (Geerts et al. 2009). Yield responses
to irrigation for major annual and perennial crops have been recently reviewed by FAO
(Steduto et al. 2012).
In addition to yield gaps outlined in Figure 3, other yield gaps can be defined that,
for example, compare different cropping technologies such as nutrient management
(Section 4.1.2) and irrigation regimes (Section 4.3.4).

3. Scales, data sources
and overview of methods
Yield gaps can be quantified at different scales in space and time (Hall et al. 2013).
Hence, the accuracy and precisiona of basic data for yield gap analysis need to be
considered in relation to the target spatial and temporal scale. Spatially, yield gaps have
been quantified at levels of field e.g. (French and Schultz 1984b), region e.g. (Casanova
et al.1999), national or mega-environment e.g. (Caldiz et al. 2002) and globally e.g.
(Licker et al. 2008). Variation of yield within fields is the focus of site-specific manage-
ment (Cassman 1999). No attempt has been made, however, to capture within-field
variation in yield gap analysis.
Some yield gap studies do not make explicit assumptions about time scale, some have
explicitly used time series that are long enough to span a wide weather range but short
enough to meet the assumption of constant technology, and some have explicitly used
time series to characterise time-trends in yield gaps. In addition to the accuracy of
yield data, reliable weather data, additional agronomic information and transparent
assumptions are essential for calculation and interpretation of yield gaps, as discussed
in the next Sections.
3.1. Actual yield data: spatial scales and accuracy
The accuracy of estimating yield gaps is determined by the weakest link, which in
many cases is good quality, sub-national scale data on actual yields that farmers achieve
(Van Ittersum et al. 2013). Monfreda et al. (2008) and You et al. (2009) comprehensively
reviewed yield data availability. There are three main levels of spatial resolution at
which actual yield data can be available:
(i) First-level administrative units: district, region, province, country.
(ii) Second-level administrative units: municipality, county, sub-district.
(iii) Farmer-reported data or data collected through surveys from relatively smaller
areas.
Current global yield databases are mostly based on data around year 2000 reported
in the Agro-Maps (FAO et al. 2006; FAO 2012) for the first and, sometimes second,
levels of administrative units complemented with interpolation methods to achieve
full spatial coverage (Monfreda et al. 2008; You et al. 2009). More accurate geospatial
distribution of current crop yields and their spatio-temporal variability are needed and
yields of irrigated and rainfed crops must be distinguished within administrative units
where both forms of production exist. An example of this kind is the USDA-NASS
database where long-term (30+ years) county-level yield data are available, separately
for each crop species, under each water supply regime, as illustrated for maize in
Figure 4. Importantly, a good understanding of local conditions is essential to avoid
data misinterpretation; e.g. owing to the “millennium drought”, yield maps around
year 2000 are a biased snapshot for production systems of Australia (Figure 1).
a See Glossary for definitions of this and other terms.

113. Scales, data sources and overview of methods
Many countries where yield-gap analysis is urgently needed have no data at the second,
or even first, spatial level (Monfreda et al. 2008; You et al. 2009). For example, You et al.
(2009) reported that only a few Sub-Saharan Africa countries (Benin, Cameroon, D.R.
Congo, Uganda, Zambia, Mozambique) have more than 10 crops with yields reported
at sub-national scale, that is, at the district, region, or province level (Figure 5). For other
countries (Angola, Republic of Congo,
Gabon, Ivory Coast) production data
are only available at the country level.
Cowpea, bean, maize and cassava have
the most complete sub-national data
coverage, with data for over 70% of
total sub-national units. Over all crops
and countries in Sub-Saharan Africa,
there is an approximately 40% coverage
of sub-national data. Sub-national data
(municipality, county, or sub-district)
are not currently available for most
Sub-Saharan Africa countries. Another
problem is that, in many countries,
average yields are not crop-specific, that
is, they are only reported for aggregate
crop categories such as ‘grain’, ‘fruit’,
‘pulses’, and ‘vegetables’ (Monfreda et
al. 2008). Some projects are currently
underway to achieve greater spatial
resolution and specificity with regard
to crop species; such as Global Futures
(http://globalfuturesproject.com/) and
Figure 4
County-level average (2004-2008) yields for rainfed and irrigated maize in Nebraska and
Kansas. Counties with negligible maize harvested area (<1500 ha) are shown in white.
Source: USDA-NASS data mapped by Patricio Grassini.
Yield (t ha-1) Yield (t ha-1)
IRRIGATEDRAINFED
Figure 5
Sub-national (district, region, province) data coverage
in Sub-Saharan Africa.
Source: You et al. (2009).
5
0 70 140 21035 Kilometers
NNIrrigated maizeRainfed maize
3.7 – 5.6
9.4 – 11.3
7.5 – 9.4
5.6 – 7.5
1.8 – 3.7
Rainfed yield (Mg/ha)
3.7 – 5.6
9.4 – 11.3
7.5 – 9.4
5.6 – 7.5
1.8 – 3.7
Rainfed yield (Mg/ha)
9.4 – 10.4
12.4- 13.4
11.4 – 12.4
10.4 – 11.4
8.4 – 9.4
Irrigated yield (Mg/ha)Yield (t ha-1) Yield (t ha-1)
IRRIGATEDRAINFED

construction of a number of household panel survey datasets are in progress at several
international agricultural research centres.
Because national and sub-national yield averages are based, in many countries, on esti-
mates and surveys, the accuracy of reported yield should be evaluated by comparison
against independently collected data and direct on-farm measurements and moni-
toring. For example, Wairegi et al. (2010) found the FAO-reported country-level
average banana yield for Uganda of 5.5 t ha-1 (by year 2007) underestimated measured
yield in control plots of a nationwide on-farm trail conducted in the same year, in
which yield averages ranged from 9.7 to 20
t ha-1 across major producing areas. In a
broader analysis, Tittonell and Giller (2013)
compared two sources of yield data for
several crops in eastern and southern Africa.
They concluded that, despite its wide cover-
age, FAO’s national average yield was close
to the mid-range yield reported in the scien-
tific literature for maize, sorghum, millet
and some grain legumes. In contrast, the
FAO average yield for cassava and highland
banana was closer to the lower end of the
yield range found in the literature.
KimandDale(2004)comparedyieldofcereals
and sugarcane from two sources, FAOSTATS
and national databases, for a number of coun-
tries between 1997 and 2001. The two sources
were in close agreement for all reported crops
in Canada and USA (difference below 1%).
Large mismatches were found for Mexico
(up to 33% for oats) and for rice in Japan,
Korea and Mexico (≥ 25%). Despite some
uncertainties, the FAO database provides
long-term time series for most crops and
countries that are otherwise unavailable or
difficult to obtain (Tittonell and Giller 2013;
Kim and Dale 2004).
Grassini et al. (unpublished) found good
agreement between county-average yield
for soybean and corn reported by USDA-
NASS and average yields estimated from
farmer-reported data in three Nebraska
Natural Resources Districts located in the
same counties, in the same years (Figure 6).
USDA-NASS average yields are based on
harvested yields, reported by a sample of
farmers within each county, verified with
independent yield samples taken by USDA
staff when the crop reaches maturity. For the
Natural Resources Districts in Nebraska, all
farmers within the reporting areas send their
crop yield reports to the local district office
together, in many cases, with yield maps
Figure 6
Comparison between average farmer-reported
Natural Resource District (NRD) in Nebraska, USA,
and USDA-NASS county-level average maize
and soybean yields (upper and bottom panels,
respectively).
Data include three NRDs: Tri-Basin (2005-2010),
Lower Platte (LP) North (2004-2011), and Lower Big
Blue (2000-2011). Irrigated and rainfed crops in the
LP North NRD are indicated with solid and open
symbols, respectively. Note that no data on rainfed
yields are available for the Tri-Basin and Lower Big
Blue NRDs. Dashed lines indicate 1-to-1 line.
Source: Grassini et al. (unpublished).
6
5
7
9
11
13
15
5 7 9 11 13 15
USDA reported yield (Mg/ha)
NRDreportedyield(Mg/ha)
Tri-Basin
Lower Big Blue
LP North (irrigated)
LP North (rainfed)
2
3
4
5
2 3 4 5
MAIZE
SOYBEAN
NRDreportedyield(tha-1)
USDA reported yield (t ha-1) 6
5
7
9
11
13
15
5 7 9 11 13 15
Tri-Basin
Lower Big Blue
LP North (rainfed)
2
3
4
5
2 3 4 5
MAIZE
SOYBEAN
USDA reported yield (t ha-1)
6
5
7
9
11
13
15
5 7 9 11 13 15
Tri-Basin
Lower Big Blue
LP North (rainfed)
2
3
4
5
2 3 4 5
MAIZE
SOYBEAN
USDA reported yield (t ha-1)

Figure 7
Box-plots of farmer-reported maize yield, applied
irrigation, and N fertiliser during the 2004-2011
interval in the Lower Platte North Natural Resource
District in Nebraska (USA) for irrigated (I) and
rainfed (R) maize.
Box plots indicate: median (horizontal lines), 25
and 75 percentiles (box), 10 and 90 percentiles
(bars), and 5 and 95 percentiles (solid circles).
Average number of observations, across years,
was 400 and 50 for irrigated and rainfed maize
crops, respectively.
Source: Grassini et al. (unpublished).
and elevator tickets. These independent quality-control checks can help identify prob-
lems and improve the method to estimate and report actual yields.
Comparisons of databases of wheat, soybean and maize acreages and yields estimated
by a pair of independent organisations in Argentina (Ministerio de Agricultura vs. BC,
Bolsa de Cereales de Buenos Aires) indicated a high degree of consistency between data
sources, as reflected in high correlation coefficients (i.e. high precision) (Sadras et al.
2013b). However, a significant mismatch between sources was found that was inversely
proportional to acreage. This means that for some applications, for example calcula-
tion of relative rate of progress in grain
production, both data sources would return
statistically equivalent results. This is not the
case for questions requiring accuracy, such as
estimates of actual regional production.
Local yield gap analysis can also benefit
from data collected through government and
industry organisations, including growers
marketing cooperatives. As regulatory
pressures on environmental performance
of agriculture increase (e.g., water quality,
endangered species, greenhouse gas emis-
sions), the standard and requirements for
farmer reporting is likely to increase. For
example, the national organisation of New
Zealand’s grape and wine sector requires
for all members to complete their annual
survey as a condition for accreditation for
the Sustainable Winegrowing New Zealand
program (Campbell 2013). This leads to
greater availability of high quality yield,
acreage and input data (fertilisers, irriga-
tion amount, pesticides, etc), which provides
opportunities to quantify impact of manage-
ment practices on yield and efficiencies of
water and nutrients as a complement to
high-cost, multi-year, multi-site field studies
e.g. (Grassini et al. 2011) . A pre-condition
is that on-farm yield data must be of suffi-
cient detail and quality (i.e. include field
location, water regime and other significant
agronomic information) and capture a repre-
sentative population of farmers over several
cropping seasons. Accuracy of farmer-
reported data can be assured when comple-
mented with yield maps, elevator tickets,
etc., and/or validated against other inde-
pendent sources of yield data for the same
region. The farmer-data reporting system of
the Nebraska Natural Resources Districts is
an example of a high-quality database that
includes field-specific information on yield
and inputs across many fields over many
years (Figure 7). Data reported by a popula-
Appliedirrigationwater(mm)
0
100
200
300
400
500
Grainyield(Mg/ha)
0
3
6
9
12
15
18
R I R I R I R I R I R I R I R I
Year
Nfertilizerrate(kgN/ha)
0
50
100
150
200
250
R I R I R I R I R I R I R I R I
2005 2006 2007 2008 2009 2010 20112004
Grainyield(tha-1)

tion of farmers allow analysis of variation in
yield and input-use efficiency across farms.
Furthermore, when these data are comple-
mented with more detailed data on crop,
soil, inputs and management practices (e.g.,
tillage, irrigation scheduling, sowing date),
they can help to identify region-specific sets
of management practices that give highest
yields and input-use efficiencies with lowest
risk (Grassini and Cassman 2012).
As with yield, the reliability of other impor-
tant data such as fertiliser use depends on
source and scale. Figure 8 illustrates the
discrepancy in nitrogen fertilisation rates in
France among three sources. Irrespective of
the source of data, a good understanding of
the farming system is important to reduce
likelihood of artefacts and misinterpretation
of data. To illustrate this point, Figure 9
shows the dynamics of rhizoctonia bare
patch caused by Rhizoctonia solani Kühn
AG-8 in wheat crops after the establishment of direct drill. Under South Australian
conditions, impact of the disease peaks after 5–6 years from implementation of
direct drill technology, and decreases afterwards with the development of disease-
suppressing microorganisms in the soil (Roget 1995). In this scenario, sampling for
yield in 1983-84 would have returned larger yield gaps than after 1988. The example
in Figure 9 applies to individual fields; at regional level, spread of adoption of direct
drill could lead to different patterns, highlighting again the importance of scale. The
Figure 8
Dynamics of nitrogen fertilisation in France
according to three sources: AGRESTE (Statistical
Service of the French Ministry of Agriculture),
ONIGC (French National Office of Arable Crops), and
ARVALIS (French Technical Institute for Cereal Crops).
Source: Brisson et al. (2010)
Figure 9
Dynamics of rizhoctonia root rot in direct-drilled wheat crops in South Australia. Wheat was
grown in rotation with volunteer pasture (closed square), pea (closed circle), medicago (open
circle) or in monoculture (open square). Error bars are lowest significant difference (P=0.05).
Source: Roget (1995)
Nitrogenfertilisation(kgha-1)
Year
9
Year
Rhizoctoniapatcharea(%)
9
Year
9
Year

next Section summarises approaches able to deal with this type of variation and Section
3.3.3 expands on the importance of cropping system context for modelling aspects of
yield gap analysis.
3.2. Temporal scales
The approach used to define time scale for yield gap analysis depends on the objec-
tives of the study, but the assumptions must be transparent and consistent with the
requirements for critical interpretation of results. Time scales can be defined that either
remove or capture the dynamic components of the environment (soil, climate, biotic
components of ecosystems) and technology. Over time for example, pathogens and
weeds can build up gradually, temperature can increase, rainfall decline and soil nutri-
ents can be depleted; all these trends could lead to increasing yield gaps. Changes in the
opposite direction, e.g. establishment of disease suppression microorganisms (Figure 9)
can contribute to narrowing gaps over time. We assume that effects of other drivers of
crop production, including shifts in markets and policy, are meditated by development
and adoption of technology (Figure 1).
3.2.1. Removing the dynamic compo-
nents of environment and technology
The number of years required to estimate actual yield is a compromise between a time
series that is long enough to capture variation in weather, and short enough to avoid
trends associated with technological and environmental change (van Ittersum et al.
2013; Calviño and Sadras 1999). van Ittersum et al. (2013) illustrate this balance for irri-
gated maize in Nebraska and a favourable environment for rainfed wheat production
in The Netherlands (Figure 10). In both cases, yields from the five most recent years
were enough to obtain estimates of the average yield and the coefficient of variation
that are similar to those obtained with yields from the last 10 years. In harsh environ-
ments for rainfed crop production, 10 years is needed for Nebraska and even more are
needed for Australia. Less than five years in these harsh production environments leads
to biased estimates of average yield and coefficient of variation through the influence of
years with exceptionally high or low seasonal rainfall. Finally, note that a longer time
interval (20 years) may bias the estimates of average yield and coefficient of variation
due to the technological change, i.e. improved varieties and agronomy, and to a lesser
extent changes in climate, as shown for irrigated and rainfed maize in Nebraska and
wheat in The Netherlands.
3.2.2. Capturing the dynamic compo-
nents of environment and technology
The second approach to deal with time series is to explicitly quantify the changes
in yield gaps over time. Laborte et al. (2012) presented a dynamic view of yield
gaps accounting for the differential rate of yield progress through time. It revealed
that Philippine rice growers in the upper quantiles improved yield much faster than
growers in the lower quantiles, hence broadening the yield gap with time (Figure 11).
Section 4.3.2 presents further details of this study.
Bell and Fischer (1994) compared actual and modelled wheat yield in the irrigated
Yaqui Valley of northwestern Mexico between 1968 and 1990 (Figure 12). Actual yield
increased linearly at a rate of 57 kg ha−1 y−1. Modelled yield accounting for weather-
based potential yield declined at 46 kg ha−1 y−1; this was putatively associated with a

mild warming trend over the period. The gap between actual and modelled yield thus
declined at 103 kg ha−1 y−1. Using this dynamic perspective, the authors concluded
that allowance for the temporal temperature change showed that the returns from
improved crop management and breeding were superior to those suggested by the
increase in actual yield.
Van den Berg and Singels (2012) compared actual yield records and simulated yield
potential of sugarcane in five agroclimatic regions of South Africa. The gap between
Figure 10
Trends in grain yields of (a) irrigated and rainfed maize in Nebraska, (b) wheat in The
Netherlands and wheat in Wimmera (South-east Australia). Sequential average yields in
(c) Nebraska, (d) The Netherlands and Wimmera, and associated coefficients of variation
for (e) Nebraska, and (f) Wimmera and The Netherlands as calculated based on 1, 2, 3 ... n
years of yield data starting from the most recent year (2011 for Nebraska and 2009 for
The Netherlands and Wimmera) and going backwards.
Yields are reported at standard moisture content of 0.155 and 0.145 kg water kg-1 grain
for maize and wheat, respectively. The vertical dashed lines indicate the most recent 5, 10
and 20 years included in the calculation of average yields and coefficients of variation.
Source: van Ittersum et al. (2012).
10
Years
1980 1985 1990 1995 2000 2005 2010
Grainyield(Mgha
-1
)
2
4
6
8
10
12
1980 1985 1990 1995 2000 2005 2010
0
1
2
3
6
8
10
Sequentialaverageyield(Mgha
-1
)
6
7
8
9
10
11
12
1.0
1.5
2.0
2.5
8.0
8.5
9.0
9.5
Number of years included in the calculation
0 5 10 15 20
CV(%)
0
5
10
15
20
25
30
0 5 10 15 20
0
5
10
15
40
50
60
(a) (b)
(c) (d)
(e) (f)
Irrigated maize,
Nebraska
Rainfed maize,
Nebraska
Rainfed wheat,
The Netherlands
Rainfed wheat,
Wimmera
CV(%)Sequentialaverageyield(tha-1)Grainyield(tha-1)

potential and actual yield averaged 33% for large scale growers and 53% for small scale
growers but periods of widening and narrowing gaps were identified in the 22–year
Figure 11
(a) The rate of rice yield improvement between 1966 and 1979 in Central Luzon
(Philippines) was much larger for growers in the top quantiles than for those in the lower
quantiles As a consequence the gap between the yield of best and average farmers (b)
almost doubled during this period In (a) the red lines represent the ordinary least squares
estimate and the 90% confidence interval of the estimate. The gray area refers to the
90% confidence band for the quantile regression estimates.
Source: Laborte et al. (2012).
Figure 12
Time trends in actual and modelled yield, and yield gap of wheat in the irrigated Yaqui
Valley of northwest Mexico between 1968 and 1990. Modelled yields are estimates
with CERES-Wheat, assuming no change in cultivar or management, thus accounting for
weather-based potential yield.
Source: Bell and Fischer (1994).
11
Year
1965 1970 1975 1980
Yieldgap(tha-1
)
1.0
1.5
2.0
2.5
3.0
wet season
dry season
Quantile
Rateofyieldimprovement(tha-1
y-1
)
0
0.1
0.2
0.3
0 0.40.2 0.6 0.8 1.0
(a) (b)
12
Year
1965 1970 1975 1980 1985 1990 1995
Yield(kgha-1
)
0
2000
4000
6000
8000
10000
actual
modelled
gap
57 ± 12.8 kg ha
-1
y
-1
-103 ± 14.8 kg ha
-1
y
-1
-46 ± 20.8 kg ha-1
y-1

time series of this study; biotic factors
such as stem borers possibly contributed
to the dynamics of these yield gaps.
Marin and de Carvalho (2012) mapped
the gap between actual and water-limited
yield of sugar cane in the state of São
Paulo (Brazil) and reported a reduction in
the gap from 58% in 1990/91 to 42% in
2005/06. The planted area where the yield
gap was 20% or less increased markedly
after the 2000s (Figure 13). Deployment
of improved management underlying the
narrowing of this gap was partially associ-
ated with higher gasoline-to-ethanol price
ratio since the beginning of the 2000s
and the availability of biofuel vehicles in
Brazil after 2002.
In contrast to the narrowing of yield gaps whereby improved technology over-rides
potentially negative factors such increasing insect pressure, Tittonell and Giller (2013)
present an example of increasing yield gap between fertilised and unfertilised maize in
association with depletion of soil nutrients over a 10-year time series in Ivory Coast.
Continuous cropping without sufficient input of nutrients and organic matter may lead
to significant soil degradation and increasing yield gaps with both technological (i.e.
lack of response to improved varieties) and social (i.e. chronic poverty) consequences.
In all the cases outlined in this Section, a dynamic perspective exposes a significant
dimension of yield gap.
3.3. Modelled yield
Credible assessment of the impact of technology, soils, current and future climate on
food production depends on our ability to estimate crop yields accurately in response
to these sources of variation. Crop simulation models, validated on their ability to
reproduce major interactions between genotype, environment and management, can
help estimate potential and water-limited yields. Here we outline desirable features of
models to use in yield gap analysis, and look critically at bias in modelled yield associ-
ated with the source of weather data.
3.3.1. Desirable attributes of models in yield gap studies
Van Ittersum et al. (2013) summarised desirable attributes for models to be used in
yield gap analysis. These include use of daily time step weather data, capacity to capture
management practices that influence yield (e.g. sowing date, plant density, cultivar
maturity), eco-physiological in structure, crop specificity, low requirement of cultivar-
specific parameters, proved performance through validation and peer-reviewed publi-
cations, full documentation of parameterisation, and user friendly interface. The study
of Rötter et al. (2012) further highlights the importance of local model calibration.
Crop simulation models estimate different yield levels, depending on the assump-
tions and modelling approach. Crop models with typically daily time-step and
Figure 13
Time trend in the area planted to sugarcane in the
state of São Paulo, Brazil, where the yield gap was
≤ 20%. Yield gap is the difference between actual
and water-limited yield.
Source: Marin and Carvalho (2012).
13
Year
1988 1992 1996 2000 2004
Area(km2
)
0
20000
40000
60000
80000
r
2
= 0.59
P = 0.003

sufficient detail of physiological prin-
ciples can be used to estimate yield
potential. This involves the assump-
tions of non-limiting water and nitro-
gen. Estimates using actual weather,
and consequently a certain frequency
and intensity of water stress, could
be considered closer to water-limited
yield. Indeed, modelled yield often
reproduces the upper boundary of
measured yield under water limiting
conditions (Angus & van Herwaarden
2001). Models such as CERES,
APSIM, CropSyst, ORYZA2000 and
AquaCrop are suitable for estimating
both yield potential and water-limited
yield (Bouman et al. 2001; Jones et al.
2003; Keating et al. 2003; Stöckle et al.
2003; Steduto et al. 2009).
There are two trade-offs to consider in selecting modelling methods. First, there is a
trade-off between error due to structure and error due parameters represented in Figure
14. In general, errors associated with structure are reduced when the realism, hence the
complexity, of the models increase. The downside of increasing model complexity is a
larger number of parameters to be quantified, with the consequent increase in error due
to parameters. Second, there is a trade-off between the convenience and likelihood of
model adoption and the requirements of data to parameterise and apply models.
3.3.2. Weather data for modelling crop yield
The models commonly used to simulate potential and water-limited yield require
a minimum data set of daily weather variables including incident solar radiation,
maximum and minimum temperature, precipitation, and some measure of humidity,
i.e. relative humidity, actual vapour pressure, dew point temperature. If measured solar
radiation is not available (which is often the case), then simulations can be based on the
NASA agroclimatology solar radiation data, except at sites with complex topography
(Bai et al. 2010) or atmospheric pollution (Stanhill and Cohen 2001).
More than 30 weather data sources have been used in agricultural research, but few
have been used for simulating yields (Ramirez-Villegas and Challinor 2012). The main
differences among sources of the weather databases used to simulate potential and
water-limited yields are: (i) observed site-specific vs. interpolated gridded data, (ii)
temporal resolution (daily vs. monthly), and (iii) spatial resolution (among gridded
databases) (Table 1). Gridded weather data are uniformly distributed within each
spatial cell. Values within cells are typically derived by interpolating weather data based
on coordinates of the sites within the grid and in nearest-neighbour grids, taking in
consideration distance from each other, elevation, and other variables. Gridded weather
data have the advantage of full geospatial coverage, but they are derived, not observed
data. Various authors have demonstrated that interpolated monthly observations may
lead to over-estimation of simulated yields in particular in locations with high day-
to-day variability in weather (Soltani and Hoogenboom 2007; van Bussel et al. 2011);
interpolation of monthly precipitation data in particular leads to substantial error an
should therefore be avoided in all cases.
Figure 14
With increasing model complexity, parameter error
increases and structure error decreases towards a limit
of irreducible error (dotted line).
Source: Passioura (1996).
14
Error Complexity
total
parameter
structure

Table1
Classificationofglobalweatherdatabasesusedtounderstandcurrentandfutureagriculturalproductivity.Weatherdatabasesusedinthepresentstudyhavebeenunderlined.
ClassificationSourceTimeStep
Referenceandtime
interval
GeospatialcoverageReportedvariables*Examples
Point-based
data
WeatherstationsDailyHPRCCa,CMAb,DWDc
(1983-2010)
RegionalTmin,Tmax,Precip,Windspeed,Tdew,RH,Vapor
Pressure,Radiation
Sinclair&Rawlins.(1993);
Grassinietal.(2009)
NOAAd
(1900-2010)
GlobalTmin,Tmax,Precip,Tdew,Windspeed,RH,Vapor
Pressure
GriddeddataInterpolatedand
generatedbasedon
datafromweather
stations,satellites,
oceanbuoys,etc.
DailyNCEP/DOEReanalysisIIe
(1979-2010)
Global
(2.5°x2.5°)(~70,000km2)
Tmin,Tmax,Windspeed,Precip,RH,Windspeed,
Radiation
Lobell&Asner.(2003);Twine&
Kucharik.(2009)
ERA-Interim
Reanalysis
(1989-2013)f
Global
(1.5°x1.5°)(~25,000km2)
Tmin,Tmax,Windspeed,Precip,RH,Windspeed,
Radiation
Rötter.(1993);deWitetal.
(2010)
Interpolatedfrom
weatherstations
MonthlyCRU05(3.10)g,Univ.
DelawareClimateDataset
(1961-2009)
Global
(0.5°x0.5°)(~3,000km2)
Tmin,Tmax,TotalPrecip,numberofwetdays,
VaporPressure
Bondeauetal.(2007);Lickeret
al.(2010)
Average
50-ymonth-
lymean
WorldClimh(1950-2000)Global
(1km2)
Tmin,Tmax,TotalPrecip,numberofwetdaysNelsonetal.(2010);Ortizet
al.,(2008)
SatelliteDailyNASA-Poweri(1983-2010)
exceptprecip(1997-2010)
Global1°x1°
(~12,000km2)
Tmin,Tmax,Precip,Tdew,Radiation,RHLobelletal.,(2010)
*Minimumtemperature(Tmin),maximumtemperature(Tmax),precipitation(precip),dewpointtemperature(Tdew),relativehumidity(RH),incidentsolarradiation(radiation)
aHighPlainsRegionalClimateCenter(HPRCC).http://www.cma.gov.cn/english/
bChinaMeteorologicalAdministration(CMA).http://www.cma.gov.cn/english/
cGermanWeatherService(DWD).http://www.dwd.de/
dNationalOceanicandAtmosphericAdministration(NOAA):http://www7.ncdc.noaa.gov/CDO/cdo
eNationalCenterforEnvironmentalPrediction/DepartmentofEnergy(NCEP).http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis2.html
fECMWFre-analysis(ERA):http://www.ecmwf.int/research/era/do/get/era-interim
gClimateResearchUnit(CRU).http://badc.nerc.ac.uk/data/cru/
hWorldClim.http://www.worldclim.org/
iNationalAeronauticsandSpaceAdministration(NASA).http://power.larc.nasa.gov/
Source:vanWartetal.(2013).

Observed daily weather data are unavailable in many cropping regions but gridded
global weather databases with complete terrestrial coverage are available. These are
typically derived from global circulation computer models, interpolated weather
station data, or remotely sensed surface data from satellites. Studies that have used
gridded weather databases to simulate yield potential and water-limited yield are rarely
validated against simulated yields based on actual weather station data from a location
within the same grid.
Van Wart et al. (2013) compared three gridded weather databases (CRU, NCEP/DOE,
and NASA POWER data) for simulation of water-limited maize yields in four loca-
Figure 15
Simulated rainfed maize water-limited yield (Yw) across four sites in the USA Corn using
weather data from (a) NOAA weather stations (Tmax, Tmin, precipitation, and humidity)
coupled with gridded solar radiation data from NASA-POWER database, (b) gridded NCEP
data, (c) gridded CRU data and (d) gridded NASA plotted against simulated Yw based
on high-quality weather data from meteorological stations of the High Plains Regional
Climate Center (HPRCC) network.
Insets show deviations of points from 1:1 line. RMSE and ME units are in t ha-1. Average
water deficit (in mm, estimated as the difference between sowing-to-maturity total rainfall
and reference evapotranspiration), as determined by simulations using control-data, was
-42 (Cedar Rapids, IA), -135 (Lincoln, NE), -149 (Grand Island, NE) and -238 (McCook, NE).
Table 1 shows detail of weather databases.
Source: van Wart et al. (submitted)
15
Simulated Yw-Control (t ha-1)
SimulatedYw(tha-1)
15
SimulatedYw(tha-1)
15
SimulatedYw(tha-1)

tions across the US Corn Belt (Figure 15). Simulations of water-limited yields based
on recorded daily data from well-maintained weather stations were taken as controls.
Agreement between simulations of water-limited maize yields based on control weather
and those based on gridded weather databases was poor with the latter having strong
bias and large root mean square error, 32% to 46% of absolute mean yield across loca-
tions and years. Of particular note was the average upward bias of about 4.0 t ha-1
estimated by CRU and NASA. Water deficit (estimated as the difference between
sowing-to-maturity total rainfall and reference evapotranspiration) and solar radiation
had a large influence on discrepancies between simulated water-limited maize yields
estimated by global and control weather databases. In contrast, simulated water-limited
yield using observed daily weather data from stations in the NOAA database combined
with solar radiation from the NASA-POWER database were in better agreement with
water-limited yields simulated with control weather data (i.e., little bias and an RMSE
of 16% of the absolute mean). These results highlight the likely bias of simulated agri-
cultural productivity under current and future weather conditions in studies relying on
gridded global weather databases. In contrast, point-based simulations of potential and
water-limited yields, complemented with an appropriate up-scaling method, perhaps
based on agro-ecological zones schemes, may be a more robust approach to achieve
full terrestrial coverage without losing accuracy on the estimates of yield potential and
water-limited yields (van Ittersum et al. 2013).
3.3.3. Modelling yield within the context of a cropping system
For a given region, potential and water-limited yield can be simulated for recom-
mended sowing dates, planting density and cultivar (which determines growing period
to maturity). However, sowing dates and cultivar maturity need to reflect the dominant
cropping system. The cropping system “context” is critically important in dictating
feasible growth duration, particularly in tropical and sub-tropical environments where
two or even three crops are produced each year on the same land. Farmers attempt to
maximise output of their entire cropping system rather than the yield or profit of indi-
vidual crops. Likewise, where machinery and labour are limiting or costly, achieving
recommended sowing dates may not be feasible for the entire farm. Hence, capturing
the spread of sowing dates and of season length is relevant to calculate potential yield
or water-limited yield. In all cases, the assumptions must be transparent and consistent
with the objectives for proper interpretation of results.
In this way, Grassini et al. (2011) simulated an average yield potential of 15.4 t ha-1 for
irrigated maize in south-central Nebraska (USA) using current average farmer manage-
ment practices. However, simulations indicated that use of longer maturity hybrids and
higher plant populations could increase average potential yield but trade-offs limited
their adoption by farmers, at least under current grain to input price ratios. Trade-offs
associated with longer maturity hybrids include higher risk of frost before physiologi-
cal maturity, difficulties in harvest operations due to wet weather and snow, and grain
drying costs. Likewise, yield and economic benefits from higher plant populations can
be reduced, or even eliminated, as a result of higher seed costs, higher plant-to-plant
variability if intra-row spacing is not uniform and greater incidence of lodging and
green snap. Therefore, simulated yield potential based on current dominant manage-
ment practices may be a more meaningful benchmark for farmers dealing with the
trade-off between maximising net return and minimising risk.

234. Approaches to benchmark yield and quantify yield gaps
4. Approaches to benchmark yield
and quantify yield gaps
Analysis of gaps between yield levels allows for identification of constraints, trade-offs
and opportunities for improvement. The exploitable yield gap has the greatest practical
interest in the context of improving agricultural production. In this Section, we outline
the main types of methods used in yield benchmarking and gap analysis using selected
case studies. The methods span a broad range of scales, complexities, input require-
ments and associated errors. We grouped methods in four broad approaches.
Approach 1 compares actual yields with maximum yields measured in high-yielding
farmer’s fields, experimental stations, or growers contests. Comparisons of this type
are spatially constrained by definition, and are an approximation to the gap between
actual and attainable yield. This approach can be biased, however, where best manage-
ment practices are not feasible; in these cases modelled yields provide more relevant
benchmarks. Approach 2 is based on comparisons of actual yield, but instead of a
single yield benchmark, yield is expressed as a function of one or few environmental
drivers in simple models, usually using boundary functions as reference. In common
with Approach 1, these methods do not necessarily capture best management practices.
Approach 3 is based on modelling which may range from simple climatic indices to
models of intermediate (e.g. AquaCrop) or high complexity (e.g. CERES). Approach 4
involves a range of methods combining remote sensing, actual data, GIS, and models
of varying complexity. This approach is mostly used at and above the regional scale.
4.1. Approach 1: high-yielding fields,
experimental stations and growers contests
Yields in farmer’s fields can be benchmarked against various references, including the
best performing crops in neighbouring fields, yield in experimental stations or yields in
growers contests where similar soil, topography, weather, and biotic conditions apply.
4.1.1. Sunflower in rainfed systems of Argentina
Hall et al. (2013) benchmarked yield of rainfed sunflower at the regional to national
level in Argentina. The 2.25 Mha sunflower-growing area was categorised, on the basis
of expert opinions, into eight regions. Within each region, reported yields for those
districts contributing most to total regional yield were used to estimate mean actual
yield on a yearly basis. Mean yields from comparative yield trials were used as an esti-
mate of attainable yields for each year and region combination. These attainable yields
approximate water-limited yields (Section 2.2). Years of suitable data varied across
regions from 5 to 9. The actual/attainable yield gap was significant in all regions, and
ranged between 20 and 77 % of mean actual yields, which – in turn - ranged from 1.52
to 2.25 t ha-1 across regions. At a whole-country level, the mean actual/attainable yield
gap was 0.75 t ha-1, equivalent to 41% of mean country yield of 1.85 t ha-1.
For five of the eight regions, yield data for individual fields were also available.
Mean individual field yields in these regions were significantly lower than attain-
able yield estimates derived from comparative yield trials, but the mean values for

the top deciles of commercial fields (an alternative estimate of attainable yield) were
indistinguishable (three regions) or slightly greater (two regions) than the estimates
of attainable yield derived from comparative yield trial estimates. A third estimate of
mean regional attainable yield, the 95th percentile of ranked reporting district yields
pooled across years and reporting districts within each region, was also calculated.
These estimates, which importantly do not allow calculation of yearly values of the
actual/attainable yield gaps, underestimated mean attainable yields derived from
comparative yield trials in four out of eight regions and attainable yields derived
from individual fields in all five regions for which this data was available. These
contrasts between estimates of attainable yield are useful as indicators of strengths
and weakness of the three approaches.
An important additional message arising from the whole analysis, and which bears
on the use of model-derived estimates of attainable yield, was the overriding impor-
tance of spatial and inter-annual variation in environmental (including management)
conditions on yield. This was evident in the databases for reporting districts, for
comparative yield trials, and for individual commercial fields. More effort is needed
to understand the causes of this variability and, especially, on the effects of spatial
scale on the values of actual/attainable yield gap estimates.
4.1.2. Maize in sub-Saharan Africa
Sileshi et al. (2010) compared actual maize yield obtained with inorganic and
organic nutrient inputs with control (no input) on experimental stations and farm
fields. The comparison also involved yield gaps with inorganic and organic fertilis-
ers, i.e. in situ green manure from sunhemp (Crotalaria spp.), velvetbean (Mucuna
spp.), sesbania (Sesbania spp.), tephrosia (Tephrosia spp.) and gliricidia (Gliricidia
sepium) on different site conditions. For each input tested at a given site or in a
particular season, there was a corresponding grain yield from maize grown continu-
ously without external nutrient input (control) thus constituting a pair of means
(treatment and control). The number of countries covered, number studies, pairs
of means extracted and robust parameter estimates of yield gaps for each treat-
ment are summarised in Table 2. This analysis did not apply the hierarchy of yields
commonly used for gap analysis (Section 2.2); instead, an ad hoc gap was defined as
the difference in grain yield between maize grown using a given nutrient input and
the control under a specific study condition.
Table 2
Basic statistics and robust parameter estimates (Winsorized means and coefficients of variation)
of maize grain yield (t ha-1) from various soil fertility management inputs.
Control Fertiliser Sunhemp Velvetbean Sesbania Tephrosia Gliricidia
Number of countries 12 13 11 12 7 9 5
Number of studies 110 71 39 45 42 28 14
Pairs of means# 473 346 214 242 262 177 114
Estimated mean 1.4 3.9 3.3 2.8 2.9 2.0 3.3
95% confidence band 1.3-1.4 3.7-4.1 3.0-3.6 2.6-3.1 2.6-3.1 1.6-2.2 3.0-3.6
CV (%) 69.3 46.3 54.4 59.4 67.2 67.3 43.0
# Total number of pairs of means (treatment and control) from all published studies.
Most studies reported means from more than one season and site, and more than one treatment with the same control.
Source: Sileshi et al. (2010).

Despite the genetic potential of maize to yield up to 10 t ha-1, actual yields did not
exceed 8 t ha-1 in the majority of cases. The probability of exceeding 8 t ha-1 was
<3% with the recommended rate of fertiliser, while in 75% of the cases yields were
<5 t ha-1 with all inputs. Inorganic fertiliser increased yield and reduced the coeffi-
cient of variation relative to both the unfertilised control and organic nitrogen treat-
ments. Yield gains were however lower and more variable on farmers’ fields than in
research stations. These differences may be caused by factors that are generally not
transferable, such as environmental conditions and management practices on research
stations where stricter attention is paid to sowing dates, spacing, weeding, fertiliser
doses and pest control than in farmers’ fields.
Refined statistical analyses also suggested variation in yield gaps with elevation,
mean annual precipitation and soil type, including clay content. Although yields
with the recommended rate of inorganic fertiliser were generally higher on Nitosols
than other soil types, yield gains over the control were the lowest (Figure 16). The
lower gain on Nitosols could be explained by the ‘saturated soil fertility’ effect.
Variability in yield gaps (indicated by the 95% confidence bands) was highest on
Acrisols and Nitosols and lowest on Lixisols. The high variability on Acrisols could
be attributed to their sensitivity to degradation (Stocking, 2003). Overall, the analy-
ses indicated that organic inputs from the legumes may have large impacts on more
sensitive and less resilient soils.
Variation in yield gaps with elevation, mean annual precipitation and the clay content
of the soil were also significant in some cases. For example, for maize grown with
inorganic fertiliser, the partial predictions of yield gap had a strong quadratic rela-
tionship with elevation and soil clay content. The 95% confidence bands also indi-
cated negative values on sites with elevations below 600 m or above 1300 m, and soil
clay content below 20% or above 40%. The 95% confidence bands also widened,
indicating increasing risks of using inorganic fertiliser outside this range. Similarly,
soil clay content significantly influenced yield gaps in the treatments that receive
organic nitrogen from sunhemp, sesbania and tephrosia.
Figure 16
Variation in maize mean yield with fertiliser and yield gap on various soil types
in sub-Saharan Africa. Vertical bars indicate 95 percent confidence bands.
Source: Sileshi et al. (2010).
1
Acrisols Lixisols Ferrasols Luvisols Nitosols Acrisols LixisolsFerrasols LuvisolsNitosols
Fig. 16
Meanyield(tha-1)
Yieldgap(tha-1)
3
0
6
3
0
6
Soil type
Treatment yield Yield gap

Yield gaps also varied with overall site
productivity indicated by the control
yield. Yield gains with inorganic fertiliser
were as high as 8 t ha-1 where the control
achieved <2 t ha-1, while they remained
below 4 t ha-1 where the control achieved
more than 2 t ha-1.
4.1.3. Grain legumes in India
Bathia et al. (2006) analysed regional-level
yield gaps of soybean, peanut, chickpea and
pigeonpea in India. They compared actual
yield in experimental stations, best farms,
and whole-districts. An interesting aspect
of this work is that mean, maximum and
minimum yields were derived for each yield
category and used for yield gap calculations
(Figure 17). The information from each
of these measures of yield gap is different,
and the distinction is particularly important
when identifying the putative causes of the
gaps. Nutrient supply for example is a much
more likely cause of gaps in maximum yield,
i.e. the yield achieved in more favourable
(wetter) seasons than in causing gaps when
yield is small. Efforts to identify specific
yield gaps in extreme seasons are important
for risk management, and to allow for the
capture of the benefits of better seasons.
4.1.4. Wheat-maize double crop
in the Hebei plain of China
Most benchmarking studies focus on single
crops. Liang et al. (2011) is one of few exam-
ples targeting double crops. The study was based on a survey of 362 farms in six coun-
ties of the Hebei Plain, where wheat–maize double crop is the most important compo-
nent of the system. Survey data from a single season were used to calculate maximum,
average and minimum yield. These yields were compared with (a) modelled yield, and
(b) experimental yield in growers’ fields during the same season; trials were designed
and managed by researchers using recommended practices seeking high yield. The
authors of the study defined modelled yield as the “climate-driven potential”, which
corresponds to the definitions of Yp or Yw depending on water supply (Section 2.2).
Best farmer yield of wheat, maize and aggregated wheat-maize was close to the experi-
mental yield, and about 78–89% of potential yield estimated with models (Figure
18), suggesting that there is no residual exploitable gap for the best farmers. The
gap between average and best yield was around 30% for both individual crops and
whole-system. Based on interviews and field observations, Liang et al. (2011) identi-
fied agronomic and socio-economic issues underlying yield gaps. For example, lack of
access to shared irrigation facilities precludes the adoption of wheat irrigation at stem
elongation, as recommended.
Figure 17
Comparison of average, minimum and maximum
yield of peanuts measured in experimental stations
and in whole-districts of India. The lines are y = x.
Source: Bathia et al. (2006). 17
0
1000
2000
3000
4000
5000
Average yield
Districtyield(kgha-1
)
0
1000
2000
3000
4000
5000
Minimum yield
0 1000 2000 3000 4000 5000
0
1000
2000
3000
4000
5000
Maximum yield
Yield in experimental station (kg ha-1
)

4.2. Approach 2: boundary
functions accounting for
resources and constraints
Crop yield is a function of capture and
efficiency in the use of resources, and
non-resource constraints modulating crop
development, morphology, and physiology
(Figure 19). To account for both resources
and non-resource environmental factors,
methods have been developed that are
based on the notion of boundary func-
tions (Box 3). Boundary functions have
been used to benchmark yield in rela-
tion to resources, mostly water (Section
4.2.1) and nitrogen (Section 4.2.2), and soil
constraints (Section 4.2.3).
4.2.1. Yield and water
productivity gaps
This approach was pioneered by French and
Schultz (1984a, 1984b) for rainfed wheat
in Australia and has been more recently
applied to a range of rainfed and irrigated
cropping systems worldwide. The method
can be applied to water use during the
whole season, or limited to crop-specific
critical periods.
4.2.1.1. Wheat in rainfed systems
French and Schultz (1984a, 1984b) bench-
marked wheat yield in south-eastern
Australia, and identified management and
environmental causes of the gap between
actual and attainable yield. Here we outline
the concept and update the benchmarking
of wheat in dryland systems.
These authors plotted grain yield against evapotranspiration (ET) of wheat crops, esti-
mated as soil water at sowing plus in-season rainfall, in diverse locations and seasons,
and fitted a boundary line with biophysically relevant parameters (Figure 20a):
Yw = TEY * (ET-E)
Where Yw is water-limited yield, the slope TEY can be interpreted as the maximum
transpiration efficiency for the production of grain, and the x-intercept E can be inter-
preted as non-productive water loss, primarily soil evaporation. The characteristic
slope in the original study was 20 kg grain ha-1 mm-1, and was supported by physi-
ological considerations. The authors recognised the x-intercept was dependent on envi-
ronmental conditions, chiefly rainfall and soil, and suggested a range between 30 and
170 mm for crops in eastern Australia. For instance, 30 mm would be more typical of
northern regions where water supply involves a large proportion of stored soil mois-
ture and relatively few, normally large rainfall events during the season. In southern
Figure 18
Yield gap analysis of wheat-maize double
cropping and its components in the Hebei plain
of China. Yields are potential, calculated with
models; experimental, measured in researcher-
designed trials in growers’ fields, and maximum,
average and minimum yield from surveys.
Source: Liang et al. (2011).
wheat
0
5000
10000
15000
maize
Yield(kgha-1
)
0
5000
10000
15000
wheat + maize
modelled experimental maximum average minimum
0
10000
20000
30000
Yield definition
22%
11%
16%
27%
33%
30%

Box 3
BOUNDARY FUNCTIONS
Yield gaps result because one or more factors (for example water and nutrient
availability) limit crop yield. This limiting effect in biophysical systems can sometimes
be estimated using boundary functions, first proposed by Webb (1972). While
evaluating fruit size in strawberry, he discovered that berry weight, when plotted
against achene number, always lay below or near a linearly increasing boundary. He
proposed that the boundary represented the limiting effect of achene number on
strawberry weight, and that the measurements lying below the boundary were limited
by other factors, for example water deficit. Since that time the boundary line has
become a popular model for limiting responses in biological data, including several
examples on crop yield (Casanova et al. 1999; French and Shultz 1984).
Most methods for fitting boundary lines have been somewhat ad-hoc. In some cases
a line is simply drawn by eye. Other methods rely on using an arbitrarily chosen
threshold to select a subset of the data to which the boundary line is fitted using the
least squares method (Webb, 1972). In some cases, the parameters of the boundary
function are derived from physiological or agronomic principles (Section 4.2.1.1).
These methods have been subject to criticism because they lack an underlying statistical
model. A second criticism is that boundary lines are often used inappropriately. For
example in cases where the boundary line model does not make biological sense (i.e.
when we would not expect the independent variable to limit the dependent variable)
or where there are simply insufficient data in the neighbourhood of the boundary to
estimate its location (i.e. when there are too few data or when other more limiting
factors are prevalent). Milne et al. (2006a, 2006b) addressed these issues by proposing
(i) an objective method of fitting boundaries, and (ii) methods for assessing whether
the models are appropriate for given sets of data.
The method of Milne et al. (2006a) assumes that the data follow a censored bivariate
normal distribution, where the boundary line defines the censor. Maximum likelihood
is used to estimate the distribution parameters. Unlike many other methods of fitting
a boundary line all of the data points are used, not just an arbitrarily selected subset.
The parameters for the censored distribution comprise those which describe the
bivariate normal part of the model, the parameters of the boundary line (e.g. for a
straight line boundary y = ax + b these are a and b); and a parameter which describes
the variation around the boundary (σB). The latter is attributed to measurement
error, and so σB, provides an indication of how certain we are of the position of the
boundary line. Confidence intervals for the parameter estimates are calculated from
the Fisher information matrix (Milne et al. 2006a). The equation of the boundary
line (e.g. straight line, parabola etc) is defined in the statistical model prior to fitting
the parameters. Visual inspection of the data and knowledge of the biological system
help decide which form of boundary line should be used. To assess the suitability
of the boundary line model (i.e. the censored distribution) to describe the data, the
analyst can compare its performance with a bivariate normal distribution (Milne et
al. 2006a). The latter model is the null hypothesis against which the evidence for the
boundary is assessed. The model with the censor has more parameters than the one
without. Typically goodness of fit improves with increasing number of parameters.
To account for this association, we compare the models using Akaike’s information
criterion (AIC) (1973) which measures performance based on a compromise between
parsimony and goodness of fit.

regions where initial soil water is generally low, and crops rely on winter rainfall,
the combination of small rainfall events and hard setting soils with poor infiltration,
surface ponding and run-off could lead to x-intercepts about 170 mm.
As with any empirical model, the parameters need local calibration, and extrapola-
tion beyond the range of tested applicability should be avoided. For example, the
slope representing attainable yield per unit transpiration is expected to be larger
The AIC is given by
AIC=−2lnM+2p
where M is the maximum likelihood value and p is the number of parameters in the
model. The smaller the AIC value the more appropriate the model.
Figure Box 3-1 shows an example of a boundary line model fitted to data relating
evapotranspiration and yield of wheat crops in dry environments worldwide. With
no previous assumptions, except for the linearity of the model, and using the whole
data set, Milne et al. (2006a) method returned a slope = 24.6 kg ha-1 mm-1, with 95
percent confidence interval (-3.412, -1.504). This compares with the 22 kg ha-1 mm-1
rate based on a combination of empirical line fitting informed by physiological
principles (Section 4.2.1.1).
Figure Box 3-1.
Example of linear boundary function fitted with the method of Milne et al.(2006a,
2006b). Data are actual wheat yield vs estimated evapotranspiration in China,
the Mediterranean region of Europe, North America and Australia compiled by
Sadras and Angus (2006). A boundary line of the form y y=ax+b was assumed.
The estimated parameter values were a=0.025 with 95 percent confidence interval
(0.020, 0.030) and b=−2.458 with 95 percent confidence interval (-3.412, -1.504). The
variation around the boundary, σB=0.971, with confidence interval (0.791, 1.151).
According to the AIC the boundary line model describes this data better than a
bivariate normal model.

under conditions that favour high
biomass per unit transpiration
and high harvest index, namely
low vapour pressure deficit, high
proportion of diffuse radiation,
high radiation-to-temperature
ratio, high atmospheric concen-
tration of CO2, and a high propor-
tion of water available around
and after flowering (Abbate et al
2004; Rodriguez and Sadras 2007;
Sadras and Rodriguez 2007).
The main environmental sources
of variation in the x-intercept are
soil characteristics (French and
Schultz 1984a,b; Ritchie 1972)
and the seasonality and size struc-
ture of rainfall, i.e. the x-intercept
is smaller for crops grown with
high stored water/seasonal rain
ratio, and with dominance of large
rainfall events during the growing
season (Sadras and Rodriguez
2007a). Other factors that affect
seasonal soil evaporation, chiefly
by changing the partitioning of
radiant energy between canopy
and soil, include tillage and stubble
management, row-spacing and
sowing density, the rate of canopy
expansion early in the season and
the rate of senescence as affected
by cultivar and management
(Cooper et al.1987; Monzon et al.
2006; Richards 2006).
Four elements reinforce the
notion that the model of French
and Schultz is robust and agro-
nomically relevant to benchmark
yield of rainfed wheat. First, a
line with slope = 22 kg grain
ha-1 mm-1 and x-intercept = 60
mm provided a reasonable upper
boundary for a large number of
crops from diverse regions of
the world (Figure 20b). Second,
the simpler boundary function
of French and Schultz generally
agrees with boundary functions
generated with more complex
simulation models involving
dozens of parameters and daily
Figure 20
(a) The original model of French and Schultz (1984) assumed
a boundary function with slope = 20 kg grain ha-1 mm-1 and
x-intercept = 110 mm (solid line) for a particular set of crops
comprising South Australian environments and cultivars and
management of the 1960-70s (circles). (b) The original concept,
with an updated slope = 22 kg grain ha-1 mm-1 and x-intercept
= 60 mm, applied to a large (n=691) data set of crops in four
dry environments of the world.
Source: Sadras and Angus 2006 .
20
0 200 400 600
0
2
4
6 (a)
Evapotranspiration (mm)
0 200 400 600
Yield(tha
-1
)
0
2
4
6 (b)
China Loess Plateau
Mediterranean Basin
North American Great Plains
SE Australia
Figure 19
Crop growth and yield depend on the capture and efficiency
in the use of resources (CO2, radiation, water and nutrients)
and environmental factors modulating the development,
morphology and physiology of the crop.
above-ground resources
CO2, radiation
soil resources
water, nutrients
environment
temperature
day-length
insects
environment
salinity, pH
compaction
pathogens

input of weather variables (O’Leary and Connor 1996; Angus and van Herwaarden
2001; Asseng et al. 2001; Sadras and Rodriguez 2007; Hochman et al. 2009). In fact,
the French and Schultz model is often considered a back-of-the-envelope check for
more refined models. Third, a close alignment between actual yield-to-transpiration
ratios corresponding to 150 years of wheat breeding in Australia, and the original
(20 kg grain ha-1 mm-1) and current (24 kg grain ha-1 mm-1) estimates of the model’s
slope reinforce our confidence in both the value and interpretation of this parameter
(Sadras and Lawson 2013a). Fourth, the method of Milne et al. (2006a; 2006b) applied
to the data set in Figure 20b returned parameters that, without a priori assumptions, is
consistent with the parameters in the model of French and Schultz (Box 3).
In summary, the approach of French and Schulz is solid, despite the lack of consid-
eration of seasonal dynamics of rainfall and water use. This method is attractive
for its simplicity, and results in estimates that are not necessarily worse than those
derived from more complex, daily-time step crop models, provided the parameters
are adjusted to local conditions. Of the two parameters, the slope can be considered
robust and taken as crop-specific constant in a first approach, whereas care should be
taken to derive sensible values for the x-intercept. The approach of French and Schultz
has been limited to Australia until
recently, but tests in other regions
of the world and crops suggest a
broader generality (Sections 4.2.1.2
to 4.2.1.4). This approach is useful to
benchmark attainable yield against
water use, with relatively low
demand of inputs, namely estimates
of initial and final soil content and
in-season rainfall to estimate evapo-
transpiration, and measured yield.
French and Shultz-type boundary
functions can also be derived using
models like CropSyst, CERES or
APSIM, or a combination of actual
data and modelling, e.g. actual yield
and modelled evapotranspiration.
4.2.1.2. Millet in low-input
systems of Africa
Sadras et al. (2012) compiled millet
grain yield and water-use data from
published sources, mostly from the
West African Sahel generally asso-
ciated with ICRISAT. Data from
Egypt, a more favourable African
environment, and the United States,
to represent higher-input cropping
systems, were included in the analy-
sis for comparison. For a collection
of 58 crops in the Sahel, millet yield
per unit water use averaged 3 kg
grain ha-1 mm-1 (Figure 21a). Yield
per unit transpiration of millet is
the lowest among C4 crops and is
primarily associated with low harvest
Figure 21
(a) Frequency distribution of millet yield per unit seasonal
evapotranspiration in Western Sahel and (b) relationship
between grain yield and evapotranspiration for crops in
Western Sahel; data from Egypt and USA are included for
comparison. The solid line has a slope = 16.7 kg grain ha-1
mm-1 and an x-intercept = 158 mm, both derived from
Rockström et al. (1998).
Source: Sadras et al. (2012).
Evapotranspiration (mm)
0 200 400 600 800
Yield(kgha-1
)
0
2000
4000
6000 Western Sahel
Egypt
USA
0
5
1 0
1 5
2 0
2 5
3 0
0 2 4 6 8 1 0 1 2
Frequency(%)
W ate r us e e fficie n cy (kg h a -1
m m -1
)
(a)
(b)
mean = 3.0 kg ha-1
mm-1
SE = 0.25 kg ha-1
mm-1
skewness = 2.0
kurtosis = 5.5
n = 58
Yield per unit evapotranspiration (kg ha
-1
mm
-1
)

index. However, millet’s low harvest index needs to be considered in the context of a
trade-off between grain production and valuable crop residues. For example, some
popular landrace millet varieties in India are over 3-m tall, and are valued for the large
amount of fodder they provide, even though grain yields are relatively low.
A boundary function with a slope of 16.7 kg grain ha-1 mm-1 captured the upper limit
of water productivity for millet crops (Figure 21b). This boundary function applied to
the stressful Sahel conditions, and to the more favourable environments of Egypt and
North America. Most millet crops in the Sahel were well below this boundary function.
Environmental, management and plant-related factors contributed to the low water
productivity of millet in the Sahel. Low soil fertility and sparsely sown crops mean
ground cover is typically low, i.e. peak leaf area indices are normally below 1, or below
2 in more intensive systems. This in turn favours unproductive soil evaporation. Sandy
soils, which are prone to crusting, favour episodic runoff and deep drainage. Indeed, a
series of experimental and modelling studies converge to conclude that production in
these environments is less limited by water than by soil fertility, agronomy and inputs, as
there is often residual water in the soil at maturity, large unproductive losses of water are
common, and nutrient stress is often more severe than water stress (Sadras et al. 2012).
4.2.1.3. Sunflower in rainfed systems of Argentina
Grassini et al. (2009a) explored the relationship between sunflower grain yield and
seasonal water supply using a 4-year database of commercial crops in the Western
Pampas (n = 169; paddock size between 21 and 130 ha). Only crops grown on deep
soils with no obvious physical or chemical constraints to rooting were included. Data
collected from small-plot (56 m2) fertilization studies were also included in the analy-
sis (n = 231). Water productivity for each field-year was calculated as the quotient
between grain yield and seasonal water supply, where water supply is initial soil water
plus seasonal rainfall.
The boundary function that delimits the maximum yield over the range of water supply
had a slope of 9.0 kg grain ha-1 mm-1 and an x-intercept of 75 mm (Figure 22a). Salient
features of this figure are: (i) many crops had water supplies greater than the maximum
expected cumulative evapotranspiration (630 mm) for the region, (ii) yield varied widely
Figure 22
(a) Relationship between sunflower grain yield and seasonal water supply in farmers’
fields (open symbols; n = 169) and small-plot fertilizer trials (closed symbols; n = 231)
in the Western Pampas. Water supply is available soil water at sowing plus sowing-to-
maturity rainfall. (b) Relationship between yield and evapotranspiration for sunflower
crops in Australia, Lebanon, Spain, Turkey, and United States.
Source: Grassini et al. (2009a).
0.0
1.0
2.0
3.0
4.0
5.0
0 250 500 750 1000 1250
Seasonal water supply (mm)
Grainyield(tha-1)
Boundary function:
slope = 9 kg ha-1 mm-1
x-intercept = 75 mm
n = 400
(a)
(b)
0 250 500 750 1000 1250
Seasonal evapotranspiration (mm)
Bekaa Valley, Lebanon
Bursa, Turkey
Cordoba, Spain
Great Plains, USA
Tatura, Australia
(c)
n = 154
Boundary function
as in (a)
15
20
25
30
uency(%)
Mean: 3.9 kg ha-1 mm-1
n = 169; CV: 43%
Skewness: 0.41
Kurtosis: -0.84
0.0
1.0
2.0
3.0
4.0
5.0
0 250 500 750 1000 1250
Grainyield(tha-1)
Boundary function:
slope = 9 kg ha-1 mm-1
x-intercept = 75 mm
n = 400
(a)
(b)
0 250 500 750 1000 1250
Seasonal evapotranspiration (mm)
Bekaa Valley, Lebanon
Bursa, Turkey
Cordoba, Spain
Great Plains, USA
Tatura, Australia
(c)
n = 154
Boundary function
as in (a)
15
20
25
30
uency(%)
Mean: 3.9 kg ha-1 mm-1
n = 169; CV: 43%
Skewness: 0.41
Kurtosis: -0.84
(b)(a)

for a given water availability, (iii) on average, farmers’ yields were 50 percent below
the boundary function, and (iv) maximum on-farm grain yields (4.9 t ha-1) approached
those reported for modern hybrids under potential conditions. Average on-farm yield
per unit water supply ranged from 1.1 to 8.0 kg grain ha-1 mm-1. The boundary func-
tion defined for the Western Pampas provided a reasonable upper limit for rainfed and
irrigated sunflower crops grown in other semi-arid environments in the Mediterranean
Basin (Lebanon, Spain, Turkey), the Great Plains of North America and Australia
(Figure 22b). Although crops were grown under good management practices, most of
the data points were below the boundary function. The gaps were associated with high
soil evaporation, high evaporative demand of the atmosphere, and untimely rainfall
during the growing cycle in relation to critical crop stages. Splitting crops in three cate-
gories depending on the range of water supply allowed for more refined identification of
agronomic and environmental factors underlying the yield gaps (Grassini et al. 2009a).
4.2.1.4. Maize in irrigated systems of USA
Grassini et al. (2009b) compiled data on
maize grain yield, applied irrigation, irri-
gation system and nitrogen fertiliser rate
during three years from commercial irri-
gated fields inside the Tri-Basin Natural
Resources Districts of Nebraska, USA
(n=777;paddockmeansize:46ha).Seasonal
water supply was calculated as available
soil water at sowing + sowing-to-maturity
rainfall + applied irrigation. Modelled yield
and water supply in 18 locations across the
Western U.S. Corn Belt were used to derive
(i) a boundary function (slope = 27.7 kg
grain ha-1 mm-1, x-intercept = 100 mm) and
(ii) a mean function (slope = 19.3 kg grain
ha-1 mm-1, x-intercept = 100 mm). The
boundary function defines the maximum
yield over the range of water supply, and
the mean function accounts for the vari-
ability in attainable yield at a given water
supply caused by year-to-year variation in
solar radiation, temperature, vapour pres-
sure deficit, and seasonal distribution of
water supply. When compared to reported
data on grain yield and water supply from
maize crops in the Western US Corn Belt
under good management, both the bound-
ary and mean functions proved to be robust
benchmarks (Figure 23a). On average,
farmers’ yields were 20 percent below the
mean benchmark function although ≈ 4
percent of the cases approached or even
exceeded this benchmark (Figure 23b).
Grain yield was not responsive to water
supply over 900 mm; an important fraction
of the total fields (55 percent) exceeded the
apparent 900 mm threshold required to
maximize yield. The apparent water excess
Figure 23
a) Relationship between grain yield and seasonal
water supply (available soil water at sowing plus
sowing-to-maturity rainfall and applied irrigation)
for maize crops grown under near-optimal
management in the Western US Corn Belt. The
database included a wide range of environments
and irrigation schedules; none of the fields had
obvious nutrient limitations, diseases, insect
damage, weeds, or hail. (b) Farmers’ irrigated yields
in the Tri-Basin NRD as a function of seasonal water
supply (+). Tri-Basin county-level average rainfed
yields are also shown for comparison (•).
Source: Grassini et al. (2011).
Grainyield(tha-1)
(b)
n = 777
0
6
12
15
18
0 400 800 1200 1600
3
9
n = 123
(a)
Rainfed
Irrigated -
Sprinkler
Irrigated -
Subsurface
drip irrigation
Boundary function:
slope = 27.7 kg ha-1
mm-1
Mean WUE function:
slope = 19.3 kg ha-1 mm-1
x-intercept = 100 mm 8
10
12
14
16
18
400 800
6
12
15
18
3
9
0
Tri-Basin NRD average
rainfed yields
0
5
10
15
20
25
Frequency(%)
Mean = 14.0 kg ha-1
n = 777, CV=13%
WUE
8 10 12
Rainfed crops
(8.8 kg ha-1
mm-1)
Grainyield(tha-1)
(b)
n = 777
0
6
12
15
18
0 400 800 1200 1600
3
9
n = 123
(a)
Rainfed
Irrigated -
Sprinkler
Irrigated -
Subsurface
drip irrigation
Boundary function:
slope = 27.7 kg ha-1
mm-1
Mean WUE function:
slope = 19.3 kg ha-1 mm-1
x-intercept = 100 mm 8
10
12
14
16
18
400 800
6
12
15
18
3
9
0
Tri-Basin NRD average
rainfed yields
0
5
10
15
20
25
Frequency(%)
Mean = 14.0 kg ha-1
n = 777, CV=13%
WUE
8 10 12
Rainfed crops
(8.8 kg ha-1
mm-1)
Yield per u
(kg
Mean function

was weakly related to available soil water at sowing and sowing-to-maturity rainfall but
strongly related to applied irrigation. Water productivity of irrigated crops ranged from
8.2 to 19.4 kg mm-1 ha-1 across field-years. Average water productivity was higher in
irrigated than in rainfed crops (14.0 vs 8.8 kg grain ha-1 mm-1).
Fields under centre pivot irrigation had higher water productivity (≈ 13 percent) than
their counterparts under gravity irrigation. Yield per unit irrigation averaged 44, 62,
and 77 kg grain ha-1 mm-1 under pivot and 28, 36, and 42 kg grain ha-1 mm-1 under
gravity in 2005, 2006, and 2007, respectively. When these values were corrected by the
average rainfed yield on each year (5.1, 5.2, and 7.5 tonnes ha-1), the resulting water
productivity became relatively stable across years: 27, 37, and 32 kg grain ha-1 mm-1
under pivot and 18, 21, and 18 kg grain ha-1 mm-1 under gravity in 2005, 2006, and
2007, respectively. High ΔY per unit irrigation reflects not only the response to increas-
ing water supply, but also differences in the agronomic management between irrigated
and rainfed crops (e.g. plant population, nutrient inputs). Consequently, rainfed crops
had lower attainable yield and water productivity than irrigated crops (Figure 23b).
4.2.1.5. Yield vs water availability in a critical period of yield determination
Calviño and Sadras (1999) benchmarked soybean yield in the Pampas of Argentina,
in a period of fast change and adoption of technology including the first generation
of transgenic (herbicide tolerant) varieties. Their aim was to produce a reference to
measure the impact of changing technology, including new varieties and management
practices, and to identify causes of gaps between actual and attainable yield. They gath-
ered yield and rainfall data from 30–35 crops per year in farmers’ fields during four
years. The period was long enough to span an important range of rainfall, and short
enough to meet the assumption of constant technology. To reinforce this assumption,
additional criteria were used to narrow the range of crops in the sample, e.g. fixed row
spacing, narrow sowing date window, narrow range of maturity groups. Using the
3-highest yielding crops each season as a measure of water-limited yield, they fitted the
boundary model (Figure 24):
Yw = a + b (1 – e-c W)
where a, b and c are empirical parameters, and W is rainfall in February plus a carry-
over of January rainfall; a estimates yield when W = 0, and a + b is the maximum
Deep soil
Rainfall during critical period (mm)
0 50 100 150 200
Yield(tha
-1
)
1
2
3
4
Shallow soil
(a) Tandil (37
o
S) (b) Pergamino (34o
S)
0 50 100 150 200 250 0 50 100 150 200 250
Yield
(fractionofmaximum)
0.4
0.6
0.8
1.0
(c) Tandil + Pergamino
Figure 24
Relationship between attainable soybean yield and rainfall during the period of pod and grain
set in (a) deep and shallow soils at Tandil, (b) deep soil at Pergamino, (c) combined data for Tandil
and Pergamino. Curves are: (a) deep soil, y = 0.25 + 2.79 (1- e –0.0258 x); shallow soil, y = -1.15 + 3.81
(1-e-0.0240x); (b) y = -0.56 + 4.7 (1-e-0.0259x), (b) y = -0.059 + 1.02 (1- e-0.0242x).
Source: Calviño and Sadras (1999).

attainable yield. Similar to the model of
French and Schulz, this model establishes
a boundary function in relation to water
availability. In contrast to the model of
French and Schulz, the parameters of this
model cannot be explained in terms of
biophysical processes except for the esti-
mate of attainable yield. Also unlike the
model of French and Schulz, this model
captures the physiological principle of a
most critical period for yield determina-
tion (Andrade et al. 2005), i.e. instead of
using seasonal water use, it constrains the
driving variable to the typical window of
pod and grain set in February.
A similar approach was used by Calviño
et al. (2003) to benchmark maize yield
in the Pampas. They collected yield data
from 216 commercial crops in Tandil (37
oS, 59 oW) from three-year time series to
meet the criterion of constant technol-
ogy, reinforced with specific criteria to
narrow the range of agronomic practices. A boundary function was fit that related
the yield of the 15% highest yielding crops and rainfall from 30 d before to 20
d after flowering, the critical period for grain yield determination in maize. The
boundary function was tested against independent data, and was used to estimate
the yield gap associated with shallow soils (Figure 25). The double-headed arrows
in Figure 25 highlight that the yield gap between shallow and deep soils is smaller
under both low and high rainfall conditions, when the storage capacity of soil is
less relevant; the largest gap is at intermediate rainfalls when storage capacity of soil
water buffers dry spells between rainfall events.
4.2.2. Yield gaps and nitrogen uptake
Benchmarks based on capture of nitrogen are agronomically, economically and envi-
ronmentally relevant in a context of increasing energy and fertiliser price and concerns
with nitrogen leaching and greenhouse emissions.
Savin et al. (2006) used the relationship between actual wheat yield and nitrogen uptake
to investigate putative differences in nitrogen use efficiency between Mediterranean and
non-Mediterranean environments (Figure 26). Boundary functions revealed a lower effi-
ciency in Mediterranean environments hypothetically associated with hotter conditions
during grain filling. The curves in Figure 26 are empirical, and similar to the approach
based on water use (Section 4.2.1.1 to 4.2.1.4), they account for the seasonal capture of
a major crop resource. A significant part of the gap between actual and attainable yield
is accounted for grain nitrogen concentration (Savin et al. 2006; Ciampitti & Vyn 2012),
which constrains the application of this approach to benchmarking.
Hochman et al. (2013) use a nitrogen-based benchmark to estimate yield gaps in
rainfed wheat crops in Australia. They compiled a data set of yield and nitrogen use,
calculated as the sum of crop nitrogen uptake and nitrogen lost to the root zone, and
derived a normalised boundary function based on a representative nitrogen response
Figure 25
Attainable yield of maize as a function of rainfall
in the critical period of grain yield determination
for deep Typic Argiudolls and shallow Petrocalcic
paleudolls (0.5-0.7m). The critical period is 20 d
before to 30 d after anthesis. Double-headed arrows
indicate yield gap due to soil.
Source: Calviño et al. (2003).
boundary in
deep soil
boundary in
shallow soil
Rain in critical period (mm)
5
50 150 250
2
4
6
8
10
Yield(tha-1)
Fig.
25
Thursday, May 8, 14

curve (Figure 27). The normalisation estimates the shortfall in nitrogen input of the
actual crop relative to the input required to reach yield potential. The analysis indi-
cated 64% of crops attained actual yields that was within 80% of the expected yield
as simulated using the actual input of nitrogen for each crop.
Ciampitti and Vyn (2012) fitted boundary functions to characterise the relationship
between yield and nitrogen uptake of maize in a comparison of old (1940 to 1990)
and new (1991 to 2011) technologies using a comprehensive, worldwide database.
The boundary functions were fitted with linear + plateau models with three param-
eters. All three parameters differed with technology: the rate of change in yield with
increasing nitrogen uptake increased from 74 kg grain per kg N with old technology
to 93 kg grain per kg N with new technology, the nitrogen required to maximise
yield was reduced from 181 kg N per ha
to 168 kg N per ha, and maximum yield
increased 13 to 16 t ha-1. These bound-
ary functions could be used for yield gap
analysis, although this was not the original
aim of this study, and shifts in parameters
highlight the importance of proper defini-
tions of technological background.
4.2.3. Yield gaps and
soil constraints
Casanova et al. (2002) measured yield gaps
of irrigated rice in the Ebro Delta of
Spain using a soil-focused approach. They
measured yield (y) and soil texture and
chemical properties (xi) in 50 fields. A
boundary line was defined for each xi vari-
able according to the following steps: (a)
each xi was categorised in 10 groups, (b)
Figure 27
Normalised relationship between yield and
nitrogen input for 334 wheat crops in Australia.
The solid line is a nitrogen-response curve
representing the upper limit of the relationship.
Source: Hochman et al. (2013).
Figure 26
Actual wheat yield as a function of seasonal nitrogen uptake in Mediterranean (closed
symbols) and non-Mediterranean environments (open symbols). The figure in the left shows
a complete data set compiled from papers published in SCI journals (n = 630). The figure in
the right shows the five highest yields in each of 50 kg/ha intervals of nitrogen uptake.
Source: Savin et al. (2006).
26
0
2
4
6
8
10
12
2
4
6
8
10
12
0 50 100 150 200 250 300 350
NABS (KgN ha-1)
Yield(Mgha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
0 50 100 150 200 250 300 350
NABS (KgN ha-1)
Yield(Mgha-1)
Figure 1. Yield plotted against the total amount of N
uptake by the crop when grown in Mediterranean
(closed circles) and in non Mediterranean conditions
(open circles)
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.18x
2
+ 73.38x
R
2
= 0.89
0 50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
NABS (KgN ha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
Yield(Mgha-1)
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.18x
2
+ 73.38x
R
2
= 0.89
0 50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
NABS (KgN ha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
Yield(Mgha-1)
Figure 2. Relationship between yield and N uptake
for the selected 5 highest yields within each interval
of N uptake for Mediterranean (n=25; closed circles)
and other regions (n=30; open circles). Curves were
fitted with a quadratic model forced through the
origin.
Yield(tha-1)
Nitrogen uptake (kg ha-1)
26
0
2
4
6
8
10
12
2
4
6
8
10
12
0 50 100 150 200 250 300 350
NABS (KgN ha-1)
Yield(Mgha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
0 50 100 150 200 250 300 350
NABS (KgN ha-1)
Yield(Mgha-1)
(open circles)
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.18x
2
+ 73.38x
R
2
= 0.89
0 50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
NABS (KgN ha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
Yield(Mgha-1)
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.18x
2
+ 73.38x
R
2
= 0.89
0 50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
NABS (KgN ha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
Yield(Mgha-1)
Figure 2. Relationship between yield and N u
for the selected 5 highest yields within each in
of N uptake for Mediterranean (n=25; closed c
and other regions (n=30; open circles). Curve
fitted with a quadratic model forced throu
origin.
Yield(tha-1)
Nitrogen uptake (kg ha-1)
1
0
2
4
6
8
10
12
2
4
6
8
10
12
0 50 100 150 200 250 300 350
NABS (KgN ha-1)
Yield(Mgha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
0 50 100 150 200 250 300 350
NABS (KgN ha-1)
Yield(Mgha-1)
(open circles)
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.18x
2
+ 73.38x
R
2
= 0.89
0 50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
NABS (KgN ha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
Yield(Mgha-1)
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
y = -0.18x
2
+ 73.38x
R
2
= 0.89
50 100 150 200 250 300 350
y = -0.18x
2
+ 73.38x
R
2
= 0.89
0 50 100 150 200 250 300 350
y = -0.14x
2
+ 67.11x
R
2
= 0.90
NABS (KgN ha-1)
0
2
4
6
8
10
12
2
4
6
8
10
12
Yield(Mgha-1)
Figure 2. Relationshi
for the selected 5 hig
of N uptake for Medi
and other regions (n=
fitted with a quadra
origin.
Yield(tha-1)
Nitrogen uptake (kg ha-1)Nitrogen uptake (kg ha-1)
Yield(tha-1)
Fig. 26

frequency distributions of yield for each xi were tested for normality, (c) for groups
passing the normality test the average xi and yield at 95% confidence are selected,
and (d) a linear regression is fitted using selected xi and yield. This approach gener-
ated boundary lines with positive slope for resource-type variables, such as cation
exchange capacity, and with negative slopes for constraint-type variables such as
salinity. Yield was estimated as:
y = Min [f (x1), f (x2)…f (xn)]
where f (xi) is the maximum yield for independent variable xi. This approach identi-
fied three main variables, namely topsoil cation exchange capacity, soil salinity and pH
which collectively accounted for a yield gap of 2.9 t ha-1 relative to attainable yield in
the region around 11 t ha-1. A residual gap of 0.8 t ha-1 corresponded to other, uniden-
tified factors. A variation of this method opened up the “black box” of yield into
numerical yield components (panicles per m2, spikelets per panicle, fraction of filled
panicles and individual grain mass) and accounted for crop status variables, i.e. crop
establishment, duration and nutrient status. This approach is particularly interesting
for local studies of soil constraints.
4.2.4. Water productivity as a function of yield
Water productivity increases non-linearly with grain yield, as shown for example in
rainfed and irrigated wheat crops in the USA (Musick et al. 1994). The analysis in
Figure 28 for maize in Doukkala Irrigation Scheme of Morocco illustrates how bound-
ary functions could be used to capture the upper limit of water productivity, identify
underperforming fields and calculating water productivity gaps; this approach has not
Figure 28
Relationship between water productivity (yield per unit evapotranspiration) and yield
of maize in the Doukkala Irrigation Scheme, Morocco. The red line is the boundary
function fitted by calculating the 90th percentile of water productivity for yield split in
1000 kg/ha intervals. Both yield and water productivity were derived with methods
combining remote sensing and modelling.
Source: Goudriaan and Bastiaanssen 2013.

been documented, but we suggest it could be useful for gap analysis where the focus
is water productivity.
4.3. Approach 3: modelling
Approach 1 and 2 underestimate maximum yield where best practice is not feasible;
for example, where policy or infrastructure limitations prevent the use of inputs such
as fertiliser. In this section we compile a series of case studies including a compari-
son of yield benchmarking and gap analysis using on-farm yields (Approach 1) and
modelled yield (Approach 3) with Maize in USA and Kenya, and wheat in Australia.
Other case studies deal with rice in Southeast Asia, maize in Zimbabwe, quinoa in
Bolivia. The use of climatic indices to estimate yield potential and FAO’s Agro-
Ecological Zones system are outlined.
4.3.1. Maize (USA, Kenya) and wheat (Australia)
Van Ittersum et al. (2013) assessed the implications of using different methods based
on simulated or actual yields for yield gap assessment at a local level. The following
methods were evaluated for their ability to estimate potential yield or water-limited
yield for irrigated and rainfed cropping systems, respectively, and their corresponding
yield gaps, across farmer’s fields over relatively small geographic areas:
• site-specific simulation of potential or water-limited yield using crop growth
models;
• derivation of potential or water-limited yield from upper percentiles of farmer
yield distributions;
• maximum yields measured in experimental stations, growers contests, or highest-
yielding farmer’s fields.
Three cropping systems of varying level of intensification were considered for the
analysis: rainfed maize in western Kenya, irrigated maize in Nebraska (USA), and
rainfed wheat in Victoria (Australia). Year-specific information about yield, manage-
ment, weather and soil properties were available for each farmer’s field from three years
for Nebraska and Victoria and one year for Kenya. Detailed descriptions of cropping
systems, structure and validation of crop models, and data inputs can be found in previ-
ously published studies (Grassini et al. 2011; Tittonell et al. 2006; Hochman et al. 2009).
Owing to the capacity to capture major interactions among weather, soils and manage-
ment, crop modelling appeared to be the most reliable way to estimate potential yield
and water-limited yield for each specific crop within the defined cropping system. The
attributes for a model to be useful in this type of study have been discussed in Section
3.3. Models allowed for probability distributions rather than single values of potential
and water-limited yield and yield gap (Figure 29). Variability in simulated potential
and water limited yield reflected not only differences in management practices among
fields, but also variability in weather across years and fields. Under such conditions,
farm managers face large uncertainty about yield-affecting conditions, and hence
appropriate level of inputs in the season ahead (Box 2). If inputs are applied in excess of
amounts needed for maximum profit in a year when potential or water limited yield is
below average, closing a small yield gap will likely not meet their economic goals. On
the other hand, if farmers invest too little inputs in a year with high potential or water-
limited yield, the yield gap will be large and they will miss the possibility of high profit.

This was the case for rainfed maize and wheat cropping system in Kenya and
Australia, although there are differences between these systems (Figure 29). While
Australian farmers face greater uncertainty about water limited yield, they are also
much better equipped to cope with this uncertainty, due to better access to informa-
tion and inputs, than Kenyan farmers who often also face labour constraints because
of manual ploughing. As a result, yield gaps were much smaller in rainfed wheat in
Australia compared to rainfed maize in Kenya (yield gap-to-actual yield ratio of 0.4
and 2.2, respectively) (Figure 29). In the case of irrigated maize in Nebraska, access
to irrigation water compensates for weather variability and associated risk, allowing
growers to fine tune their management and achieve small gaps (yield gap-to-actual
yield ratio of 0.1) (Figure 29).
Estimates of yield potential, water limited yield and yield gap based on maximum yields
or an upper yield percentile are static or non-spatially explicit, unless they are linked
with some environmental variable. A single estimate of potential or water limited yield
29
0
2
4
6
8
Grainyield(Mgha
-1
)
0
4
8
12
16
Field-year number
0
2
4
6
Yw = 2.4 Mg ha-1
(CV=70%); Ya = 1.7 Mg ha-1
(CV=77%); Yg = 0.8 Mg ha-1
(CV=95%)
Yp= 14.7 Mg ha-1
(CV=7%); Ya= 13.1 Mg ha-1
(CV=7%); Yg= 1.6 Mg ha-1
(CV=67%)
Yw= 5.4 Mg ha-1
(CV=26%); Ya= 1.7 Mg ha-1
(CV= 56%); Yg= 3.7 Mg ha-1
(CV=36%)
Yw
Ya
Yw
Ya
Ya
Yp
Rainfed maize, west Kenya
Irrigated maize, Nebraska, USA
Rainfed wheat, Victoria,
Australia
Grainyield(tha-1)
Figure 29
Simulated potential yield (Yp) or water-limited yield (Yw) based on site-specific weather, soil
properties, and management data collected from farmer’s fields in three cropping systems: rainfed
maize in west Kenya, irrigated maize in Nebraska (USA), and rainfed wheat in Victoria (Australia)
(n = 54, 123, and 129 field-year cases, respectively). Each bar corresponds to an individual field-year
case. The yellow and red portions of the bars indicate actual farmer’s yield (Ya) and yield gap (Yg),
respectively. Horizontal lines indicate average Yp (or Yw) and Ya (solid and dashed lines, respectively)
for the region. Means and coefficients of variations (CV) for Yp (or Yw) and Yg are shown. Fields were
sorted from highest to lowest Yp or Yw. Note that Ya>Yw for some site-years in Victoria which reflects
incorrect specification of model inputs , actual yields, and/or inability of crop models to portray specific
genotype x environment x management interactions.

used as a reference in gap analysis does not reflect the full range of conditions within
an agro-ecological zone and cropping system. The yield achieved by a contest winner
or in the highest-yielding fields in any region or season was unattainable by most
other farmers who did not benefit from the same climatic or soil conditions. Likewise,
measured yields in experimental stations can also be biased if soil and topography (i.e.
deep, fertile soils on flat land or on well terraced slopes) do not represent the surround-
ing production systems. Hence, maximum yields and upper yield percentiles provide
an estimate of the best G x E interaction across a large population of site-years, rather
than a measure of long-term average potential or water limited yield. Although all these
empirical methods are convenient when data are lacking to calibrate and validate a crop
model and to run it for a range of fields and years, they gave inconsistent estimates of
potential and water limited yield compared to those obtained from crop simulation. In
the case where actual yield was high, which indicates favourable growing conditions
and little stress (i.e. irrigated maize in Nebraska), there was relatively close agreement
among yield potential, water limited yield and yield gap estimates based on maximum
yields or upper percentiles and estimates based on crop simulation (Table 3). In
contrast, there was very poor agreement among these estimates in cases where farmers
did not (or could not) use best management practices and thus achieved low yields
(i.e., Kenya rainfed maize). Likewise, estimates of potential and water limited yield
based on maximum yield or upper percentiles can be biased by atypical years or farms
amongst the observations, but this cannot be defined without more detailed analysis
using simulation models. This problem played a role in the dataset for rainfed wheat
in Victoria in which the average maximum yield and the average 95 and 99 percentiles
Table 3
Actual average farmer yield (Ya) and estimates of average potential yield (Yp) or water-limited
yield (Yw), yield gaps (Yg), and Yg-to-Ya ratio (Yg:Ya) for three cropping systems based on four
different methods: crop simulation models, upper percentiles of farmer Ya, and maximum yields.
Values are means for one single year (rainfed maize in western Kenya) or 3 years for irrigated
maize in Nebraska and rainfed wheat in Victoria.
Yield (t ha-1)
Rainfed maize,
western Kenya
Irrigated maize,
Nebraska, USA
Rainfed wheat,
Victoria, Australia
Actual yield (Ya) 1.7 13.2 1.9
Yp or Yw based on: Yw Yp Yw
Simulation model 5.4 14.9 2.6
Upper percentiles Ya:
95th percentile 3.6 14.4 3.5
99th percentile 3.9 14.8 4.1
Maximum Ya a 6.0 17.6 4.3
Yg based on:
Simulation model b 3.7 (Yg:Ya = 2.2) 1.6 (Yg:Ya = 0.1) 0.8 (Yg:Ya = 0.4)
Upper percentiles Ya:
95th percentile 1.9 (Yg:Ya = 1.1) 1.1 (Yg:Ya = 0.1) 1.9 (Yg:Ya = 1.0)
99th percentile 2.2 (Yg:Ya = 1.3) 1.6 (Yg:Ya = 0.1) 2.2 (Yg:Ya = 1.2)
Maximum Ya 4.3 (Yg:Ya = 2.5) 4.5 (Yg:Ya = 0.3) 2.3 (Yg:Ya = 1.2)
a Maximum yields were derived from measured yields at: nearby experimental stations (rainfed maize in western
Kenya), National Corn Growers Association (NCGA) contest-winning irrigated fields in Nebraska (irrigated maize
in Nebraska), and highest-yielding farmer fields (rainfed wheat in Victoria).
b For Australia, when Ya>Yw, Yg=0 was assumed.

of farmers yields across three years was well above the average simulated water-limited
yield over the same period (Table 3). If the maximum yield and 95 and 99 percentiles
of farmers yields had been taken from the entire population of field-years, aggregated
across years, the difference between simulated Yw and the 95 and 99 percentiles would
be substantially higher as the best year would have been used as the benchmark.
4.3.2. Rice in Southeast Asia
Laborte et al. (2012) analysed farmers’ yields and yield gaps in the wet and dry
seasons in four intensively cropped rice areas in Southeast Asia: Central Luzon,
Philippines; West Java, Indonesia; Suphan Buri, Thailand; and Can Tho, Vietnam.
Yield gaps were estimated based on potential yield derived from the crop growth
model ORYZA2000 applying crop development rates calculated from observed
phenological stages, actual crop establishment methods and actual average planting
dates of farmers (Bouman 2011).
Exploitable yield gaps (Section 2.2) were estimated based on economic (80% of poten-
tial yield) and best farmers' yields (upper 10 percentile in each year, season, and site).
They found yield differences of 2.6–5.4 t ha−1 between average and potential yields,
1.0–3.6 t ha−1 between average and economic yields, and 1.1–2.3 t ha−1 between average
and best farmers’ yields. The gap between average and best yields was higher in rice-
importing countries (Indonesia and Philippines) compared with rice-exporting coun-
tries (Thailand and Vietnam).
Many yield gap studies consider a single year or period (Section 3.2.1). In addition
to looking at yields and yield gaps across sites, this study evaluated yield differences
across time using four decades of farm survey data (1966 to 2008) for Central Luzon,
Philippines. They used quantile regression to estimate annual increments in yields
that correspond to various percentage points of the distributions of farmers’ yields.
From 1966 to 1979, annual increases in rice yields for farmers in the upper quantiles
were much higher than those in the lower quantiles as yield increased with adoption
of higher-yielding modern rice varieties by some farmers. On the other hand, there
was no significant change in yields for the lowest 10 percentile despite more than a
decade since the introduction of modern rice varieties. Owing to the differential rate of
adoption of new technology between leading and average farmers during this period,
the gap between average and best yields increased with time (Figure 11). From 1982
onwards, the lower 30 percentile had slightly higher annual increments than others, as
farmers with low yields started to adopt modern rice varieties. However, the mean gap
between average and best yields for surveys conducted during the 2000s did not differ
much from that of the 1980s.
Closing the yield gap in farmers' fields in Southeast Asia remains a challenge. Best
farmers’ yields were already near to, or in some cases, even higher than their estimate
of economic yield. This implies that it will not be economically attractive for best-
yielding farmers to further increase yields, unless there is a change in the prices of rice
and/or production inputs to warrant more investment. On the other hand, the gap
between average and best yields could still be reduced, especially in the rice importing
countries, where the gap is larger. This study gave indications of some causal factors
by comparing some characteristics of and production inputs used by average and best
yielding farmers. To bridge the gap, production inputs such as fertiliser and labour
should be used more efficiently and intensive knowledge delivery and programs that
enhance farmers’ skills as well as institutional arrangements are vital.

4.3.3. Maize in Zimbabwe
Kahindae el al. (2007) used a simulation model (APSIM) to investigate alternative crop-
ping practices to close the yield gap of maize in semi-arid Zimbabwe. They estimated
two extreme yields, i.e. maximum with good supply of water or nitrogen, and a rainfed
control closer to standard practices with no fertiliser and no supplemental irriga-
tion. Within the boundaries of these extreme yields, a range of feasible options were
modelled, e.g. modest amounts of inorganic nitrogen or manure in combination with
locally developed rain water harvesting techniques. This modelling exercise showed the
synergy between water and nitrogen, which is consistent with theoretical and empirical
considerations (Sadras 2005; Cossani et al. 2010).
4.3.4. Quinoa in Bolivia
Geerts et al. (2009) used the AquaCrop model to examine the potential of closing
quinoa yield gaps using irrigation in the Bolivian Altiplano, where yields of rainfed
crops are low and unstable. Simulated scenarios included a rainfed control, a refer-
ence strategy avoiding stomatal closure during all sensitive growth stages and allowing
drought stress during the tolerant growth stages and various restrictive deficit irriga-
tion strategies representing cases when water resources are limited. From the scenario
analysis, probability curves were derived for three agro-climatic regions. The modelled
yields of rainfed quinoa during dry years ranged from 1.1 t ha-1 in the northern region
to 0.2 t ha-1 in the southern Altiplano and increased to 2.2-1.5 t ha-1 with the best
irrigation treatment, corresponding to yield gaps > 1 t ha-1. Minimum water avail-
ability required to significant reductions in yield gaps were identified, in the order of
600-700 m3 per ha for the central and southern regions.
4.3.5. Estimating yield potential with climate indices
Previous Sections illustrated yield gap analysis based on simulation models accounting
for environment, crop and management factors. Here we outline simpler methods to
account for major climate drivers in the definition of yield potential (Section 2) and
their application in benchmarking. Fischer (1985) defined a photothermal quotient
(PTQ) relating solar radiation (Rad) and mean temperature (T) above a base tempera-
ture (Tb) during a time window comprising the most critical period for grain set:
PTQ = Rad / (T- Tb)
This coefficient reflects four physiological principles, namely (a) grain number is
the main yield component (Sadras, 2007b), (b) grain number is proportional to total
growth during a species-specific critical window around flowering (Andrade et al.,
2005), (c) growth rate during this critical window is proportional to photosynthesis
and hence radiation, and (d) the duration of this period is inversely proportional to
temperature. On these principles, Fischer’s (1985) photothermal quotient and derived
indices usually capture a substantial part of the variation in grain yield of diverse annual
grain crops (Fischer 1985; Cantagallo et al. 1997). In the study of Bell and Fischer
(1994) outlined in Section 3.2.2, the rate of change of wheat yield in the Yaqui Valley
of Mexico calculated with the photothermal quotient was similar to the rate calculated
with CERES-wheat, although estimates were offset by approx. 0.8 t. Estimates of grain
number using a photothermal coefficient, and modelled (Menendez and Satorre 2007)
or actual (Calviño and Sadras 2002) kernel weight were used to generate location-
specific benchmarks of wheat yield in the Pampas.
Rodriguez and Sadras (2007) used a normalised photothermal coefficient (PTQn)
accounting for the effects of photosynthetically active radiation (PAR), mean tempera-

0 3 4 0 6 8 01 7 0 k m
0 . 5 3 - 1 . 2 8
1 . 2 8 - 1 . 5 8
1 . 5 8 - 1 . 8 3
1 . 8 3 - 2 . 0 3
2 . 0 3 - 2 . 8 6
a ) Y i e l d
1 0 6 - 1 9 2
1 9 2 - 2 2 4
2 2 4 - 2 6 1
2 6 1 - 3 2 2
3 2 2 - 6 2 3
b ) W a t e r u s e
V I C
0 . 1 9 - 0 . 3 7
0 . 3 7 - 0 . 4 6
0 . 4 6 - 0 . 5 2
0 . 5 2 - 0 . 6 1
0 . 6 1 - 0 . 9 3
d ) P T Q n
V I C
c ) W U E
3 . 0 - 5 . 4
5 . 4 - 6 . 1
6 . 1 - 6 . 8
6 . 8 - 7 . 8
7 . 8 - 1 1 . 7
V I C
3 . 9 - 1 0 . 2
1 0 . 2 - 1 2 . 2
1 2 . 2 - 1 4 . 1
1 4 . 1 - 1 7 . 5
1 7 . 5 - 3 7 . 1
e ) W U E n
ture (T), vapour pressure deficit (VPD) and fraction of diffuse radiation (FDR) to
benchmark wheat yield in eastern Australia
PTQn = PAR * FDR / VPD * T
Doherty et al. (2008) combined actual yield, modelled seasonal evapotranspiration and
the coefficient PTQn to produce a shire-level benchmark of attainable wheat water
Figure 30
Median (a) actual yield (t ha-1), (b) modelled water use (mm), (c) water use efficiency, i.e.
(a)/(b), (d) normalised photothermal coefficient (MJ m-2d-1 kPa-1 oC-1), and (e) normalised
water use efficiency, i.e. (c)/(d). Data corresponds to the period 1975-2000. Note water
use efficiency decreases from south to north in the eastern region (c) but this gradient is
largely accounted for the climate variables in the normalised photothermal coefficient (e).
Source: Doherty et al. (2008).

productivity (Figure 30). The rationale of this approach is that the boundary water-
limited yield, as determined with the French and Schultz model (Section 4.2.1.1), can be
improved by accounting for physiologically relevant (a) critical period and (b) climatic
drivers included in PTQn. This approach may be of interest to benchmark yield in
future climates where warming and increased VPD are likely to have significant impact
on water productivity (Potgieter et al. 2013).
4.3.6. FAO’s Agro-Ecological Zones system
GAEZ refers to the Agro-Ecological Zones system, developed by FAO and IIASA
(International Institute for Applied Systems Analysis). This tool enables land-use
planning based on an inventory of land resources and their biophysical limitations
and potential for crop production. The characterization of land resources accounts for
climate, soils and landform, which are basic for the supply of water, energy, nutrients
and physical support to crops. GAEZ models potential yield and downscales year 2000
statistics of main food and fiber crops to derive actual yield. The spatial resolution for
yield gap analysis, derived from potential and actual yield, is 5 arc-minute. Further
details can be found in: http://www.fao.org/nr/gaez/publications/en/
4.4. Approach 4: remote sensing
We emphasised the need for precision and accuracy of crop yield data for gap
analysis, and highlighted some of the limitations from actual measurements, surveys,
regional and national statistics and modelled yield. Indirect measurements via satel-
lites have a potential to measure fields and regions to complement and cross check
other sources of data (Box 4).
Lobell (2013) recently reviewed the application of remote sensing in yield gap analysis;
thus, this Section only presents a few examples.
Box 4
REMOTE SENSING: APPROACHES TO ESTIMATE CROP YIELD
Remote sensing is the technology of identifying, observing, and measuring an object
without coming into direct contact with it. The radiometers aboard dozens of polar
orbiting satellites measure the reflected, emitted and scattered radiance in small parts
of the electromagnetic spectrum (visible, red-edge, near-infrared, thermal infrared,
microwave, etc.). Spectral reflectance and spectral emittance measurements are combined
with algorithms that convert raw data into quantitative bio-physical information at
various scales, from small farm plots to large agro-holdings. The smallest scale is one
pixel, and for field scale applications the pixel size often ranges from 10 m x 10 m to
30 m x 30m. The second smallest scale is a combination of a number of pixels. A group
of pixels can form a soil or management unit on a farm, or can be an entire field. The
frequency at which data can be measured depends on the type of satellite; combinations
of different satellites are used to acquire most of these data with an interval of a few days
with a resolution of 30 m x 30 m or better, provided that cloud cover is not persistent.
Approaches
Remote sensing approaches to estimate crop yield can be based on (Lobell 2013): (1)
biomass production and partitioning, (2) empirical models relating spectral vegetation
index and yield, and (3) integration of remotely sensed data and crop growth models.

1. Biomass production and partitioning
Biomass production can be calculated as the product between absorbed
photosynthetically active radiation (APAR) and radiation use efficiency (Monteith
1977). APAR is the radiation (400 to 700 nm) absorbed by the crop and subsequently
used for photosynthesis; it depends on: (i) solar radiation at the top of the atmosphere,
(ii) cloud cover, (iii) atmospheric constituents that control the transmittance of
radiation through the atmosphere and (iv) the size, architecture and greenness of
canopies where chlorophyll captures photosynthetically active light. Cloud cover
can be acquired from geostationary satellites that measure cloud brightness with
small time intervals e.g. (Hammer et al. 2003). Remotely sensed vegetation indices
e.g. (Asrar et al. 1992) or leaf area index (Mynemi et al. 2002) describe the extent
of green leaves that intercept the photosynthetically active radiation. Hence, APAR
can be derived totally from satellite measurements see also Baret and Guyot (1991).
Various equations have been developed for the determination of radiation use
efficiency, for example Field et al. (1995) and Hilker et al. (2008). As radiation use
efficiency varies with crop stage, crop geometry and environmental and management
factors, the assumption of a fixed efficiency could be an important source of error
in estimating biomass and yield (Stockle and Kemanian 2009). The same conclusion
applies to deterministic crop production simulation models and this is therefore a
more general challenge in the modelling of crop yield.
Actual yield (Ya) can be computed as a function of cumulative biomass produced during
the season (ΣB), harvest index (HI) and the water content of the crop at harvest (moi):
Ya = (ƩB.HI)/(1-moi) Yact =
1-moi
Reviews on harvest index have been published by Hay (1995) and Unkovich et al.
(2010), who emphasised the variability of this trait. Various approaches have been
developed for the computation of harvest index (Sadras and Connor 1991; Ferreres
and Soriano 2007; Kemanian et al. 2007; Raes et al. 2010). It is common practice to
locally calibrate the harvest index and water content of the harvestable crop to ensure
that fresh crop yield estimation from satellite data matches local measurements. This
approach was applied by Zwart and Bastiaanssen (2007) in Mexico using harvest index
values published by Lobell et al. (2003b). This method was followed also by van
Dam and Malik (2003) in the Sirsa District of India using the official figures by the
Indian Bureau of Statistics. Bastiaanssen and Ali (2003) used a similar approach which
produced realistic results for wheat and sugarcane crops cultivated in the Indus Basin,
Pakistan. On average, an accuracy of over 90% was achieved in the yield estimations.
This can be improved further if local yield data are used in the calibration.
2. Empirical models relating spectral vegetation index and yield
Several studies used linear regression between spectral vegetation indices and crop
yield. The yield data can be taken from crop cutting experiments or from secondary
data sources. A single vegetation index measurement or the accumulated vegetation
index for crop- specific developmental phases can be selected. The USDA method is
based on the latter selection and applies essentially to cereals; it works particularly well
for wheat (Hatfield 1983b). Applications in other crops include Daughtry et al. (1992)
with maize and soybean and Steven et al. (1983) with sugarbeet.
3. Integration of remotely sensed data and crop growth models
Satellite measurements can be linked with crop simulation models. By comparison of
model and satellite-based variables, the model updates its state conditions, remaining
ƩB*HI

4.4.1. Benchmarking crop yield and yield gaps with remote sensing
The work of Lobell and Ortiz-Monasterio (2006) and Samarasinghe (2003) are exam-
ples of the multiple and varied combinations of modelling and remote sensing that
can be used in benchmarking crop yield. Lobell and Ortiz-Monasterio (2006) worked
with wheat in Mexico and Samarasinghe (2003) with rice, tea, rubber and coconut in
Sri Lanka. Both used a similar yield reference for gap calculations, i.e. highest yield in
farmer’s fields (Lobell and Ortiz-Monasterio 2006) or 95 percentile yield (Samarasinghe
2003). Lobell and Ortiz-Monasterio (2006) combined Landsat images with a tempera-
ture-based model of crop growth and Samarasinghe (2007) combined NOAA-AVHRR
images with a radiation-based model of crop growth based on SEBAL ET rates and
soil moisture values from Sri Lanka (Bastiaanssen and Chandrapala, 2003). Lobell and
Ortiz-Monasterio (2006) further crossed-linked remote sensing data with modelled
grain yield using CERES-wheat.
Figure 31 shows the estimated ratio between actual and attainable yield in the Doukkala
irrigation scheme in Morocco, where the attainable yield is defined as the 95% percen-
tile on the probability density function of actual crop yield. By considering this ratio
in single pixels within the same agro-ecological zone, the opportunity arises to define
the yield gap for all different crop types. The dominant crop types are wheat, maize,
soybean and sugarbeet. The areas with a ratio lower than 0.7 are either rainfed crops,
or partially irrigated crops. Indeed, the Doukkala irrigation scheme is located in the tail
end of the Uom R’bia river basin system, and the scheme is in competition with water
resources that are diverted to Casablanca.
4.4.2. Benchmarking water productivity with remote sensing
Remote sensing has also been used to estimate evapotranspiration with a number of
methods at different scales in space and time (Hatfield 1983a; Borchardt and Trauth
2012; Jian et al. 2012; Ma et al. 2012; Poblete-Echeverria and Ortega-Farias 2012; Yang
et al. 2012b; Yang et al. 2012a); details of these methods are beyond the scope of this
publication. Combined with estimates of yield based on remote sensing (Box 4), these
estimates of evapotranspiration allow for calculation of water productivity that is fully
derived from remote sensing.
more in line with the actual crop growing conditions. This complex mathematical
approach is meant to estimate the production of a representative field in a given region,
and is suitable for research more than to management applications. Currently, it is
not feasible to apply modelling of this complexity at the scale of individual pixels.
Examples of this approach can be found in Maas (1991) and Vazifedoust et al. (2009).
In summary, approach 1 requires standard computation procedures and is applicable
across a range of physiographical conditions; assumptions on both radiation use
efficiency and harvest index need local and crop specific calibration libraries that
could be valid for a number of 5 to 10 years. Approach 2 generates simple solutions
for particular crops provided satisfactory agreement can be found between spectral
vegetation indices and crop yield, but requires repeatedly local calibrations against
destructive crop yield measurements that constrain its application. Moreover, poor
regression results are often found (e.g. Lyle et al 2013). Approach 3 is more suitable
for scientific research than applications.

Methods have also been developed that directly estimate water productivity without
individual solutions to crop yield and evapotranspiration. Zwart et al. (2010) for
example, reduced the inputs of the equation of water productivity to four spatial
variables derived from routine satellite measurements: broadband surface albedo,
normalised difference vegetation index (NDVI), extraterrestrial radiation and air
temperature. The model of Zwart et al. (2010) was used to map wheat water produc-
tivity on a global scale. Their study was followed up by Bastiaanssen et al. (2010) for
wheat, rice and maize at global scale level and publications are under preparation.
Gonzalez-Dugo and Mateos (2008) benchmarked water productivity of irrigated
cotton and sugarbeet in an irrigation scheme comprising 15,000 ha in southern Spain.
They used published boundary functions, i.e. yield vs evapotranspiration, for each
crop and actual yield from local growers (Approach 2). To relate actual yield and actual
evapotranspiration, reference evapotranspiration was multiplied by robust crop coef-
ficients derived from multispectral vegetation indices, derived in turn from ground- or
satellite-based radiometric measurements.
Figure 31
31. Spatial distribution of the ratio between actual and attainable crop yield in the irrigation scheme
Doukkala in Morocco. The attainable yield is estimated as the 98% percentile of the crop yield for
various crop types grown in the region.
Source: Bastiaanssen et al. (under preparation).
31

5. Conclusions
and recommendations
The spatial scale selected for benchmarking should depend on the nature of the
problem. For the improvement of yield at the farm scale, for example, benchmarking
at the field level is required. Parallel to the spatial scale, the time scale needs consider-
ation. If the aim is to benchmark crops under current technology, the time scale needs
to be long enough to capture as much variation in seasonal conditions as possible, and
short enough to meet the assumption of constant technology. A dynamic perspective
allows for benchmarking that captures time trends associated with technological prog-
ress, rates of adoption and environmental change. Both static and dynamic approaches
to benchmarking yield of rainfed crops need to capture the large seasonal and intra-
seasonal variation of rainfall in dry environments. The diversity of benchmarking
methods outlined in this publication reflects the diversity of spatial and temporal
scales, the questions asked, and the resources available to answer them. We grouped
methods in four broad approaches. These approaches are not rigid, and combinations
of methods are common.
Approach 1 compares actual yield with the best yield achieved in comparable envi-
ronmental conditions, e.g. between neighbours with similar topography and soils
(Section 4.1). Comparisons of this type are spatially constrained by definition, and
are an approximation to the gap between actual and attainable yield. With minimum
input and greatest simplicity, this allows for limited but useful benchmarks; yield
gaps can be primarily attributed to differences in management. This approach can be
biased, however, where best management practices are not feasible as illustrated for
maize in Kenya; modelled yields provide more relevant benchmarks in these cases
(Section 4.1.3). On the other hand, current models are unsuitable to answer some
questions of local relevance. For example, generic crop models are unable to capture
the biophysical interactions between green manure and chemically and physically
contrasting soils; the question of maize yield gaps and risks associated with these
drivers in sub-Saharan Africa is thus answered with a combination of actual yield
data and various models (Section 4.1.2).
Approach 2 is a variation of approach 1, i.e. it is based on comparisons of actual yield,
but instead of a single yield benchmark, attainable yield is expressed as a function of
one or few environmental drivers such as actual evapotranspiration. In common with
Approach 1, these methods do not necessarily capture best management practices. The
French and Schultz model is the archetype in this approach, and other variants include
nitrogen uptake or soil properties instead of water. A boundary model fitted to the
data provides a scaled benchmark, thus partially accounting for seasonal conditions.
Parameters for boundary functions can be estimated with quantile regression, which
requires some arbitrary assumption on the fraction of data to be used. Inclusion of
remote sensing-based populations of crop yields is the way forward. A combination
of empirical curve fitting and physiologically informed parameterisation has also been
used. We recommend (i) using the method of Milne et al. as a statistically robust, objec-
tive approach to derive boundary functions (Box 3) and (ii) checking the shape and
parameters of boundary functions for physiological and agronomic meaning. Where
statistical and biophysical criteria conflict, we are inclined to favour biophysical criteria.

495. Conclusions and recommendations
Approach 3 is based on modelling which may range from simple climatic indices such
as Fischer’s photothermal coefficient to intermediate models such as AquaCrop and
the more complex CERES-type models. More complex models are valuable agronomi-
cally because they capture some genetic features of the specific cultivar, and the critical
interaction between water and nitrogen. “Best practice” to model yield in gap analysis
has been outlined (Section 3.3). Importantly, models to estimate potential yield require
parameters that capture the physiology of unstressed crops. Particular attention needs
to be paid to weather data used in modelling yield because significant bias can accrue
from inappropriate data sources; this is illustrated for gridded global weather databases
in Section 3.3.2. Studies that have used gridded weather databases to simulate potential
and water-limited yields for a grid are rarely validated against simulated yields based
on actual weather station data from locations within the same grid. This should be
standard practice, particularly where global scale yield gaps are used for policy deci-
sions or investment in R&D. Alternatively, point-based simulations of potential and
water-limited yields, complemented with an appropriate up-scaling method, may be
more appropriate for large scale yield gap analysis.
Approach 4 benchmarking involves a range of approaches combining remote sensing,
actual data, and models of varying complexity (Section 4.4). These models can be
applied to any pixl of 10 m x 10m or 30m x 30 m or assimilate basic remote sensing
vegetation data into complex mechanistic crop growth simulation models. This
approach is important for benchmarking at and above the regional scale. Remote
sensing applied to yield gap analysis has improved over the last years, but significant
constraints remain unsolved including the radiation use efficiency and harvest index,
which require a local calibration. The vantage point of remote sensing is the production
of actual yield data that facilitates the identification of local yield gaps.
Irrespective of the approach used to estimate yield and calculating yield gaps, a critical
assessment of data reliability (yield, weather, agronomy) and sound understanding of
the actual biophysical and agronomic background of the targeted system are essential
to reduce the likelihood of misinterpretation of data. Variation of yield within fields
remains a challenge for yield gap analysis.

Glossary
Precision: the extent to which a measurement procedure gives the same results each
time it is repeated under identical conditions.
Accuracy: the closeness of a measurement to the true value.
Boundary function: upper and/or lower limit to the value of the response variable at
any given value of the independent variable imposed by some biological mechanism
so that values larger/smaller than the upper/lower boundary, respectively, are not
possible (ignoring measurement error). Boundary functions are also called “enve-
lope” functions.
Benchmark: a point of reference that serves as a basis for evaluation or comparison.
Decile: one of nine actual or notional values of a variable dividing its distribution into
ten groups with equal frequencies. For example, the 9th decile is the value below
which 90% of the population lie.
Percentile: one of 99 actual or notional values of a variable dividing its distribution
into 100 groups with equal frequencies. For example, the 90th percentile is the value
below which 90% of the population lie.

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I4695E
Yield gap analysis
of field crops
To feed a world population that will exceed 9 billion by 2050
requires an estimated 60% increase over current primary
agricultural productivity. Closing the common and often large
gap between actual and attainable crop yield is critical to
achieve this goal.
To close yield gaps in both small and large scale cropping
systems worldwide we need (1) definitions and techniques to
measure and model yield at different levels (actual, attainable,
potential) and different scales in space (field, farm, region,
global) and time (short and long term); (2) identification of the
causes of gaps between yield levels; (3) management options to
reduce the gaps where feasible and (4) policies to favour
adoption of sustainable gap-closing solutions.
The aim of this publication is to critically review the methods
for yield gap analysis, hence addressing primarily the first of
these four requirements, reporting a wide-ranging and
well-referenced analysis of literature on current methods to
assess productivity of crops and cropping systems.
This work builds on the activities of FAO and the Dougherty
Water for Food Institute (DWFI) to develop tools and
knowledge delivery systems to inform and guide policymakers
in managing water and agriculture. Two major initiatives are at
the foundation of this publication: the Global Yield Gap Atlas
(led by DWFI) and the Regional Initiative on Water Scarcity for
Near East and North Africa (led by FAO).
41
I4695E/1/06.15
9 7 8 9 2 5 1 0 8 8 1 3 5
ISBN 978-92-5-108813-5 ISSN 1020-1203

Yield gap analysis

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