Time integration of evapotranspiration using a two source surface energy balance model using NARR reanalysis weather data and satellite based METRIC data

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Time Integration of Evapotranspiration
DATASET · AUGUST 2013
DOI: 10.13140/RG.2.1.1004.3045
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1 AUTHOR:
Ramesh Dhungel
University of California, Merced
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Retrieved on: 12 October 2015

Time integration of evapotranspiration using a
two source surface energy balance model
using NARR reanalysis weather and satellite
based METRIC data
Ramesh Dhungel
Major professor: Dr. Richard G. Allen
Committee Members:
Dr. Fritz Fiedler, Dr. Karen Humes, Dr. Ricardo Trezza
Department of Civil Engineering
University of Idaho
Developed methodologies and models
Dissertation defense

Outline
 Background and Motivation
 Problem statement
 Objectives
 Results and discussions
 Methodology
 Study Area
 Conclusions and Recommendations

Background and motivation
 Need of high spatial and temporal resolution ET maps
 Availability of weather based gridded data to complete and
close surface energy balance
 Need of ET in between the satellite overpass dates
 Unavailability of thermal based surface temperature and
satellite images for computing ET in-between the satellite
overpass dates
 Need of accurate ET for water rights issues, groundwater
recharge, irrigation management, crop water management etc.

Problem statement
1. Landsat satellite only overpass the same area once each 4-8 days,
only at about 11:am
2. Remote sensing models are able to compute relatively accurate ET
at 4-8 days
5. Problem with image timing. Precipitation event prior to the satellite
overpass can elevate the ET values so the image may not represent
the period, for example a month.
3. But the major problem is the cloudy images and these images can’t
be used to compute ET
4. Because of the clouds, computation of ET from satellite images can
be longer than a month

Problem statement
6. Challenge remains to extrapolate ET between the satellite overpass
dates
7. Currently, ET is extrapolated using
splined interpolation of ETrF
r
ET
ins
ET
FETr 
Reference ET from
Meteorological
station
HGRET nins 
Rn G H
Satellite based ET
Relative ETrF can be interpolated or
extrapolated over intervening time periods
between satellite overpasses

Objectives
Specific Objectives
1. Develop procedures to apply currently available gridded data to
compute ET during the extrapolating period
3. Compare the simple FAO 56 soil water balance model to a more
advanced Hydrus 1D soil water balance model
2. Develop a resistance based two source surface energy balance
model that incorporates soil water balance model
Extrapolation of ET between satellite overpass dates
Main Objective

Objectives
Specific Objectives
4. Develop a procedure to expedite the numerical iteration process
used in the surface energy balance
6. Develop a computational strategy to force simulated ET to
adequately target METRIC ET for next satellite overpass date
5. Develop a irrigation sub-model to incorporate the impacts of irrigation
events of ET form agricultural areas

Methodology
Three phases
Phase 1- Inversion of METRIC ET from NARR
reanalysis data and METRIC data
Phase 3- Adjustment of
of ET to agree with the next
METRIC image
Phase 2- Extrapolation of ET from NARR
reanalysis data and METRIC roughness
data

Phase 1,2,3
Papers
Paper 3
Comparisons between the FAO-56 soil water evaporation model and
HYDRUS 1D evaporation model over a range of soil textures
Paper 1 – Phase 1
Parameterization of soil moisture and vegetation characteristics with a
two source surface energy balance model using NARR and METRIC
data sets at satellite overpass time
Paper 2 – Phase 2 and 3
Extrapolation of ET with a two source surface energy balance model
using NARR reanalysis weather data and Landsat-based METRIC ET
data

Completion of study
 Literature Review
 Exploration of current available ET models and procedures (Single and multiple
sources)
– SEBAL (Bastiaanssen et al., 1998)
– SEBS (Su, 2002)
– ALEXI (Norman et al., 2003)
– METRIC (Allen et al., 2007)
– Raupach, 1989
– McNaughton and Van den Hurk, 1995
– Shuttleworth and Wallace, 1985
– Choudhury and Monteith, 1988
– Norman et al., 1995
– Li et al. 2005
– Colaizzi et al., 2012 etc.
 Development of a land surface model
 Testing the model
 Development of code

Time schedule
Year Work Done Remarks
1 Course work and research ( 2009 – 2010)
• Course work
• Gathered ideas for the dissertations
• Gathered data and finalization of procedure
Kimberly first
semester, Moscow
Campus second
semester
2 Course work and research (2010 – 2011)
• Course work
• Worked on comparison on Hydrus-1D to FAO- 56 model
• Worked on accuracy of the equations on METRIC model
• Understood the ET computation procedure from METRIC
• Processed METRIC images for generating data
Kimberly
3 Course work and Development of procedure ( 2011 – 2012)
• Course work
• Understood the currently available models
• Developed a model to extract NARR reanalysis data
• Developed different procedures of land surface model starting with a single source model
• Understood the possibility of using Penman Monteith equation and aerodynamic equation
• Develop a simple two source model for testing purpose
Kimberly
4 Development of model (2012-2013)
• Developed a detail two source model
• Incorporated soil water balance components
• Developed irrigation scheduling model, code the model
Kimberly
5 Running and testing (2013 – 2014)
• Developed the ET adjustment model
• Run the model for accuracy analysis
• Wrote papers
• Defend the work
Kimberly

Study area and data
NARR reanalysis data
METRIC data - At satellite overpass
Single pixel = 1024 km2
32 km resolution, every 3
hours
29 pressure level and surface
level data
UTC time zone, Lambert
conformal conic projection
Grib (Grided binary and netcdf
(network common data form)
format
Southern Idaho near American Falls
Study area near American Falls, ID overlaying Idaho map,
Landsat image and NARR pixel for May 17, 2008
30m resolution of all bands
60m-120m resolution of
thermal band

Data
uz(m/s), Ta(K), qa(kg/kg) Blending height
30m
RS↓(W/m2)
RL↓(W/m2)
P(mm/3hr)
Srun(mm/3hr)
α LAI, NDVI
εo
Zom(m)
NARR reanalysis METRIC Data

NARR reanalysis relook
Study area near American Falls, ID overlaying Idaho map
and NARR downward longwave radiation for north America
for May 17, 2008
North American Regional Reanalysis

Developed Land Surface model
Wind Speed, Air Temperature, Specific Humidity Blending Height
30m
Incoming Solar
Radiation
Incoming Longwave
Radiation Outgoing Longwave Radiation
from Soil
Outgoing Longwave Radiation
from Vegetation
Soil Evaporation
Canopy transpiration
Root Zone Soil Moisture
Soil Surface Soil Moisture
Precipitation
Sensible Heat Flux
from Soil
Sensible Heat Flux
from Vegetation
Surface Runoff
Drainage to Root Zone Layer
Deep Percolation from
Root Zone Layer
Irrigation
Overall process – Paper 1 and paper 2 (Phase 1,2,3)

Developed two source model
 Inversion model 1: Computes the canopy transpiration, soil
moisture at root zone and canopy resistance for the satellite
overpass date
 Inversion model 2: Computes the soil evaporation, soil moisture at
surface and soil surface resistance for the satellite overpass date
 Extrapolation model 3: Extraplates ET between the satellite
overpasses dates in conjunction with irrigation and soil
water balance using a three-hour timesteps
 Adjustment model 4: Adjusts the extrapolated ET between the
satellite overpass dates over all timesteps
The major four models are listed below:
 Python and ArcGis Script
 About 10 thousand lines code

Model description
 Uses unique and accurately calibrated METRIC ET to partition ET at
the start of the simulation and to adjust simulated ET
 Uses resistance based aerodynamic surface energy balance
approach to fluxes
 Not dependent on the thermal sensor based surface temperature to
extrapolate ET in the intervening time period
 Uses less meteorological data from the weather station
 Uses currently available gridded weather data to compute ET for
higher temporal resolution i.e. 3 hours
 Developed as an improvement and simplification of current
available models

Running the code
and Output
An example

Output variables and fluxes
0 1 2 3 4 5 6 7 8 9 10
i Date precip ssrun irrigation NDVI fc hc d n Zom
Index MDH-UTM mm/3hr mm/3hr m3/m3 - - m m - m
11 12 13 14 15 16 17 18 19 20
Z1 rac LAI In_short In_long Tair uz S_hum Albedo Albedo_soil
m s/m - W/m2 W/m2 K m/s kg/kg - -
21 22 23 24 25 26 27 28 29 30
Albedo_veg ea eosur Air_den u_fri rss kh ras_bare ras_full ras
- kPa kPa kg/m3 m/s s/m - s/m s/m s/m
31 32 33 34 35 36 37 38 39 40
rsc_final rah soilm_cur_final
H_Flux_rep_soi
l Ts outlwr_soil LE_soil Lambda_soil ETsoi_sec_pre ETsoil_hour
s/m s/m m3/m3 W/m2 K W/m2 W/m2 J/kg mm/sec mm/hr
41 42 43 44 45 46 47 48 49 50
G_Flux_ite_soil sheat_soil_final soilm_root_final H_Flux_rep_veg Tc outlwr_veg eoveg f F1 AWF
W/m2 W/m2 m3/m3 W/m2 K W/m2 kPa - - -
51 52 53 54 55 56 57 58 59 60
F4
ETveg_sec_pr
e ETveg_hour LE_veg sheat_veg_final netrad_veg netrad_soil T_com netrad sheat
- mm/sec mm/hr W/m2 W/m2 W/m2 W/m2 K W/m2 W/m2
61 62 63 64 65 66 67 68 69 70
gheat_com LE
EThour_co
m Ref_ET Pevap X_30m psi_m_30m psi_h_30m X_dzom psi_h_dzom
W/m2 W/m2 mm/hr mm/sec mm/3hr - - - - -
71 72 73 74
X_hd psi_h_hd L stat_img
- - m -
About 100 parameters, variables and fluxes

Variables
and fluxes
used in
models
Fluxes, Parameters and boundary
conditions
Symbol Min Max Units
Sensible heat flux H -50 500 W/m2
Sensible heat flux for soil portion Hs -50 500 W/m2
Sensible heat flux for canopy portion Hc -50 500 W/m2
Ground heat flux G -50 200 W/m2
Latent heat flux for soil (LEs) - - W/m2
Latent heat flux for canopy (LEc) - - W/m2
Incoming shortwave radiation Rs↓ - - W/m2
Incoming longwave radiation RL↓ - W/m2
Friction velocity u* 0.01 500 m/s
Aerodynamic resistance from canopy height to
blending height
rah 1 500 s/m
Albedo soil αs 0.15 0.28 -
Albedo canopy αc 0.15 0.24
Single area leaf equivalent bulk stomatal
resistance
rl 80 5000 s/m
Fraction of cover fc 0.05 1 -
Roughness length of momentum Zom 0.01 m
Bulk boundary layer resistance of the vegetative
elements in the canopy
rac 0 5000 s/m
Canopy resistance rsc 0 5000 s/m
Soil surface resistance rss 35 5000 s/m
Single area leaf equivalent bulk stomatal
resistance
rl 80 5000 s/m

Land surface model
Latent heat flux (LE ) model-the players
a p s a
s
ah ss as
C e e
LE
r r r


 
  
  
WindTemperature
a p c a
c
ah sc ac
C e e
LE
r r r


 
  
  
Aerodynamic eqn. of LE
es: saturation vapor at soil surface, d is zero plane displacement, zos : minimum value of roughness
length, cp : specific heat capacity of moist air , γ : psychrometric constant, ρa :
atmospheric density, fc : fraction of canopy cover
𝒇 𝐜 =
𝑵𝑫𝑽𝑰 − 𝑵𝑫𝑽𝑰 𝒎𝒊𝒏
𝑵𝑫𝑽𝑰 𝒎𝒂𝒙 − 𝑵𝑫𝑽𝑰 𝒎𝒊𝒏

Land Surface model
Sensible heat flux (H) model - the players
( )a p s a
s
ah as
C T T
H
r r
 


( )a p c a
c
ah ac
C T T
H
r r
 


Temperature Wind
Aerodynamic eqn. of H

Land Surface model
Latent heat flux (LE) model - integration of processes
rss = 3.5
θsat
θsur
2.3
+ 33.5
θsur (Soil moisture) controls
evaporation from soil through rss
a p s a
s
ah ss as
C e e
LE
r r r


 
  
  
Sun, 1982 (Loam soil)

Land surface model
Latent heat flux (LE) model - integration of processes
a p c a
c
ah sc ac
C e e
LE
r r r


 
  
  
rsc =
rl
LAI
fc
F1 F4
AWF =
θroot − θwp
θfc − θwp
F4 =
1
1 + 20 e(−8 AWF)
θroot (Soil moisture at root) controls
transpiration from soil through rsc

NOAH procedure to calculate F1
l min
l max
1
r
f
r
F
1 f



g
gl
c
R 2
f 0.55
R LAI
f
 
 
 
  
   
  
• r l is bulk stomatal resistance of the well-illuminated
leaf
• Rgl is minimum solar radiation necessary for
photosynthesis (transpiration) to occur
• Rg is incident solar radiation,
• F1 is functions representing the effects of plant stress
due to photosynthetically active radiation (PAR)
• rlmax and rlmin is maximum and minimum value of
single area leaf equivalent bulk stomatal resistance
respectively
l
sc
1 4
c
r
r
LAI
F F
f

Advancement of current
practice of canopy
resistance calculation
Concentrate the multiple
leaf into the canopy
Correction to standard LAI
calculation

Surface Energy balance
Soil Portion Vegetation Portion
_n s s s sR LE G H   _n c c cR LE H 
_max(0.4 ,0.15 )s s n sG H R
( )a p s a
s
ah as
C T T
H
r r
 


( )a p c a
c
ah ac
C T T
H
r r
 


a p s a
s
ah ss as
C e e
LE
r r r


 
  
  
a p c a
c
ah sc ac
C e e
LE
r r r


 
  
  
HGLERn The players
𝐑 𝐧_𝐬
= 𝐑 𝐬↓ − 𝛂 𝐬 𝐑 𝐬↓ + 𝐑 𝐋↓ − 𝐑 𝐋_𝐬↑ − 𝟏 − 𝛆 𝐨_𝐬 𝐑 𝐋↓
RL_s↑ = Ts
4
σ εo_s
𝐑 𝐧_𝐜
= 𝐑 𝐬↓ − 𝛂 𝐬 𝐑 𝐬↓ + 𝐑 𝐋↓ − 𝐑 𝐋_𝐜↑ − 𝟏 − 𝛆 𝐨_𝐜 𝐑 𝐋↓
RL_c↑ = Tc
4
σ εo_c
σ: Stefan-Boltzmann constant

Iteration procedure
of rah (Phase 1)
Backward averaged
H, G, u*
Initial H is taken from
METRIC in Phase 1
Two source surface
energy balance model
Computed soil and canopy
portion fluxes separately
METRIC ET
Convergence of rah makes
convergence of surface energy
balance fluxes

Iteration procedure
of rah (Phase 2)
No METRIC ET
Initial H is taken from previous
timesteps in Phase 2

Inputs from METRIC Model
ETins(mm/hr) NDVI fc
05/17/2008Phase 1

270
278
286
294
302
310
1
31
61
91
121
151
181
211
241
Temperature(K)
Time step number relative to May 17, 2008
Surface Temperature Air Temperature
270
280
290
300
310
320
1
31
61
91
121
151
181
211
241
Temperature(K)
Time step number relative to May 17, 2008
Surface Temperature Air Temperature
Results
A1: Irrigated agricultural pixel (Landuse: 82,
NDVI: 0.71 to 0.83 and fc: 0.86 to 1) from 05/17/2008 to 06/18/2008
A2: Irrigated agricultural pixel (Landuse 82, NDVI: 0.12 to
0.32 and fc: 0.05 to 0.27) from 05/17/2008 to 06/18/2008
Behavior of simulated surface temperature vs. air temperature input
Near neutral condition
Difference between Tb and Ta is larger
than A1

Models Coordinates
(m)
NLCD
Landuse
classes
fc Tb
(K)
H
(W/m2)
G
(W/m2)
Rn
(W/m2)
LE
(W/m2)
METRIC 2612097,
1330202
Agricultural 0.063 305 119 96 641 426
Simulated 303 92 84 603 427
METRIC 2606520,
1327977
Desert 0.28 321 278 111 519 130
Simulated 309 334 78 543 131
METRIC 2604335,
1326667
Grassland 0.19 324 275 110 499 114
Simulated 310 316 93 525 116
METRIC 2600245,
1328521
Agricultural 0.85 301 98 43 600 459
Simulated 303 138 12 609 459
METRIC 2609171,
1333273
Agricultural 0.05 320 250 100 445 95
Simulated 313 284 105 485 96
METRIC 2612312,
1329483
Agricultural 0.24 309 155 90 603 358
Simulated 305 160 64 583 359
Results and discussions
Surface energy fluxes for different landuse classes

30 thousand pixels
Two different dates
05/17/2008 and 06/18/2008
Phase 1 Next slide

Mismatch in Sensible heat flux (W/m2)
(06/18/2008)
H
Simulated
H
METRIC
Finer resolution

30 thousand pixels
Two different dates
05/17/2008 and 06/18/2008
Phase 1

Soil evaporation (Ess)
(mm/hr)
Canopy transpiration(T)
(mm/hr)
ETins(mm/hr)
(METRIC)
Phase 1
+ =

Soil surface evaporation(rss)
(s/m)
Canopy resistance(rsc)
(s/m)
Phase 1
Low rss
Low rsc
High rsc
High rss

Phase 1 – Inversion of METRIC ET
Parameterize of Soil moisture at surface and root zone
ET METRIC (mm/hr)
Soil moisture at
surface (θss)
(m3/m3)
Soil moisture at
rootzone (θroot)
(m3/m3)
θroot : (0.18-0.22 m3/m3
High θsur

Phase 2 and 3
 Extrapolation of ET
 Calibration of the Model
 Adjustment of ET

Soil water balance
𝛉 𝐬𝐮𝐫(𝐢) =
𝛉 𝐬𝐮𝐫(𝐢−𝟏) +
𝐏(𝐢) + 𝐈 𝐫𝐫(𝐢) − 𝐒 𝐫𝐮𝐧(𝐢) − 𝐄 𝐬𝐬(𝐢)
𝐝 𝐬𝐮𝐫
𝐢𝐟 𝛉𝐬𝐮𝐫𝐢 ≤ 𝛉𝐟𝐜
𝐢𝐟 𝛉𝐬𝐮𝐫𝐢 > 𝛉𝐟𝐜
𝛉𝐟𝐜
𝛉 𝐬𝐮𝐫(𝐢) = 𝛉 𝐬𝐮𝐫(𝐢−𝟏) +
𝐏(𝐢) + 𝐈 𝐫𝐫(𝐢) − 𝐒 𝐫𝐮𝐧(𝐢) − 𝐄 𝐬𝐬(𝐢) − 𝐓𝐞(𝐢)
𝐝 𝐬𝐮𝐫
− 𝐃𝐏𝐞(𝐢) + 𝐂𝐑 𝐞(𝐢)
Phase 2 - Soil surface layer (10cm)
• 3 layered soil water balance model
• 1st layer is evaporation layer
• 2nd layer is canopy transpiration layer
• 3rd layer deep percolation from root zone

Soil water balance
𝛉 𝐫𝐨𝐨𝐭(𝐢) =
𝛉 𝐫𝐨𝐨𝐭(𝐢−𝟏) +
𝐏(𝐢) + 𝐈 𝐫𝐫(𝐢) − 𝐒 𝐫𝐮𝐧(𝐢) − 𝐓(𝐢) − 𝐄 𝐬𝐬(𝐢)
𝐝 𝐫𝐨𝐨𝐭
𝐢𝐟 𝛉 𝐫𝐨𝐨𝐭(𝐢) ≤ 𝛉𝐟𝐜
𝛉𝐟𝐜 𝐢𝐟 𝛉 𝐫𝐨𝐨𝐭(𝐢) > 𝛉𝐟𝐜
𝛉 𝐫𝐨𝐨𝐭(𝐢) = 𝛉 𝐫𝐨𝐨𝐭(𝐢−𝟏) +
𝐏(𝐢) + 𝐈 𝐫𝐫(𝐢) − 𝐒 𝐫𝐮𝐧(𝐢) − 𝐓(𝐢) − 𝐄 𝐬𝐬(𝐢)
𝐝 𝐫𝐨𝐨𝐭
− 𝐃𝐏 𝐢 + 𝐂𝐑(𝐢)
Phase 2 - Root zone layer (1-2m)
• 1st (evaporation) layer is subset of 2nd layer
• Sub-setting allows track evaporation from soil surface
and transpiration from root zone simultaneously

Soil water balance
An illustration ( 3 hours time steps)
Index
no. Date
P Irr Srun Ess T Total water
(root zone)
Total water
(surface)
mm mm mm mm mm mm mm
1 5/17/08 14:00 0.0359 2.35 197.68 2.27
2 5/17/08 17:00 0.0170 1.26 196.40 2.25
3 5/17/08 20:00 0.0173 1.25 195.13 2.23
4 5/17/08 23:00 0.0158 0.06 195.06 2.22
5 5/18/08 2:00 0.0043 0.05 195.01 2.21
6 5/18/08 5:00 0.0043 0.04 194.96 2.21
7 5/18/08 8:00 0.0099 1.06 193.89 2.20
8 5/18/08 11:00 0.0217 2.21 191.66 2.18
9 5/18/08 14:00 0.0195 2.43 189.20 2.16
10 5/18/08 17:00 0.0137 2.04 187.15 2.14
11 5/18/08 20:00 0.0108 1.86 185.29 2.13
12 5/18/08 23:00 0.0095 0.05 185.23 2.12
13 5/19/08 2:00 0.0041 0.04 185.18 2.12
14 5/19/08 5:00 0.0041 0.03 185.15 2.11
15 5/19/08 8:00 0.0091 1.00 184.15 2.10
16 5/19/08 11:00 0.0203 2.05 182.07 2.08
17 5/19/08 14:00 0.0193 2.14 179.92 2.06
18 5/19/08 17:00 0.0107 1.31 178.60 2.05

Irrigation sub-model
Irr(i) =
( θfc−θroot i ) droot if θroot i < θt
0 if θroot(i) ≥ θt
θt = θfc − RAW
Phase 2
When soil moisture at root zone is below
threshold moisture content (θt), vegetation starts
to stress

Phase 2 – Extrapolation of ET (mm/hr)
Phase 2 - One day evaluation
Change in solar radiation Change in canopy resistance

Results and discussion
Phase 2 -Next satellite passing date (06/18/2008) (per. 05/17 – 06/18)
ET Simulated
(mm/hr)
ET METRIC
(mm/hr) NDVI
Mismatch
Mismatch: Irrigation timing, aerodynamic and radiometric temperature, zoh, partitioning of the fluxes

Results and discussions ET
ET hourly ET daily
Phase 2 (06/18/2008, before adjustment)
Daily ET is computed letting the extrapolation
model run beyond the satellite overpass time for a
full day without interrupting at a satellite overpass
time

Daily ET from 05/17/2008 to 06/18/2008
A1: Irrigated agricultural pixel (Landuse: 82, NDVI: 0.71 to 0.83 and fc: 0.86 to 1)
A2: Irrigated agricultural pixel (Landuse 82, NDVI : 0.12 to 0.32 and fc : 0.05 to 0.27)
D1: Desert pixel (Landuse 52, NDVI: 0.2 to 0.17, fc: 0.28)
Phase 2 (before adjustment)
0
2
4
6
8
10
12
136 141 146 151 156 161 166 171
ET(mm/day)
Day of the year
ET_A1 ET_A2 ET_D1 ETr
Follows very well the reference
ET

Fluxes METRIC
Results
(06/18/2008 11am.)
Simulated Results
(Extrapolation model)
(06/18/2008 11am.)
Simulated Results
(Inversion model)
(06/18/2008 11 am.)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ET Mean Standard
deviation
Mean Standard
Deviation
R2 Slope Intercept MAE RMSE E di Mean Standard
Deviation
(mm/hr) mm/hr) (mm/hr) (mm/hr) (mm/hr) (mm/hr) (mm/hr)
URA AOI 0.62 0.20 0.62 0.29 0.63 1.17 -0.11 0.13 0.18 0.16 0.67 0.62 0.2
BLA AOI 0.59 0.19 0.54 0.3 0.66 1.2 -0.20 0.15 0.19 0.04 0.66 0.59 0.19
MD AOI 0.16 0.04 0.18 0.04 0.61 0.66 0.7 0.02 0.03 0.44 0.65 0.16 0.05
Temperature
(Tb)
K K K K K
URA AOI 303.1 6.5 302.7 3.17 0.59 0.57 128.4 3.17 4.18 0.59 0.67 302.3 3.8
BLA AOI 304.0 5.8 304.0 4.6 0.52 0.90 28.7 3.2 4.09 0.51 0.65 303.2 3.2
MD AOI 322.1 0.87 309.5 0.54 0.00 -0.04 323.49 12.63 12.67 -206.5 0.05 309.0 0.7
Ground heat
flux
(G)
W/m2 W/m2 W/m2 W/m2 W/m2 W/m2 W/m2
URA AOI 57.3 24.51 39.05 45.8 0.85 1.73 -60.41 28.1 30.9 -0.59 0.58 31.47 35.81
BLA AOI 70.4 44.0 49.68 48.53 0.38 0.56 42.3 34.7 45.3 -0.06 0.53 36.2 34.9
MD AOI 115.2 11.2 75.3 17.9 0.83 1.4 -92.69 39.9 40.8 -12.2 0.19 68.3 19.5
Sensible
heat flux (H)
URA AOI 109.4 73.9 159.18 66.5 0.46 1.0 49.62 66.5 93.14 -0.58 0.54 177.62 67.4
BLA AOI 125.6 71.3 198.8 116.8 0.54 0.4 36.3 90.2 108.7 -1.3 0.49 195.6 75.3
MD AOI 288.0 28.1 369.55 8.5 0.24 -0.14 412.56 84.2 87.9 -8.7 0.18 383.84 11.4
Net radiation
(Rn)
URA AOI 590.51 49.7 623.2 57.4 0.55 0.85 116.6 43.49 50.95 -0.04 0.56 631.3 46.9
BLA AOI 592.0 45.6 614.36 56.1 0.47 0.56 246.6 37.7 47.0 -0.05 0.57 626.72 40.67
MD AOI 508.7 13.6 568.22 14.17 0.01 -0.1 621.4 59.6 62.9 -20.4 0.15 576.4 15.7
Phase 2 – projected model results vs. METRIC (06/18)

0
1
2
3
4
50.0
0.2
0.4
0.6
0.8
1.0
1.2
1
31
61
91
121
151
181
211
241
P(mm/3hr)
ET(mm/hr)
Index number (every 3 hours)
P ET_simulated Ess T NDVI
Irrigated agricultural pixel (Landuse: 82, NDVI: 0.71 to 0.83 and fc: 0.86 to 1) from 05/17/2008 to 06/18/2008
0
1
2
3
4
50.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
31
61
91
121
151
181
211
241
P(mm/3hr)
ET(mm/hr)
P ET_modeled Ess T NDVI
Irrigated agricultural ET (Landuse 82, NDVI : 0.12 to 0.32 and fc : 0.05 to 0.27) from 05/17/2008 to 06/18/2008
Phase 2 (before adjustment)

0
80
160
240
1
31
61
91
121
151
181
211
241
Cumulativewater(mm)
Index number (every 3 hours )
Cum_P Cum_ET Cum_Irri
Cum_Dep Cum_ETr
0
80
160
240
1
31
61
91
121
151
181
211
241
Cumulativewater(mm) Index number (every 3 hours )
Cum_P Cum_ET Cum_Irri
Cum_Dep Cum_ETr
0.32 and fc: 0.05 to 0.27) from 05/17/2008 to 06/18/2008
A1: Irrigated agricultural pixel (Landuse: 82, NDVI: 0.71 to
0.83 and fc: 0.86 to 1) from 05/17/2008 to 06/18/2008
Phase 2
High cumulative ET and near
reference level
Low cumulative ET compared
to pixel A1

0
1
2
3
4
50
800
1600
2400
3200
4000
4800
1
31
61
91
121
151
181
211
241
P(mm/3hr)
Resistance(s/m)
P rss rsc
D1 :Desert pixel (Landuse 52, NDVI: 0.2 to 0.17, fc: 0.28) from
05/17/2008 to 06/18/2008
0
1
2
3
4
50
800
1600
2400
3200
4000
4800
1
31
61
91
121
151
181
211
241
P(mm/3hr)
Resistances(s/m)
P rss rsc
A1: Agricultural pixel (Landuse 82, NDVI: 0.71to 0.83 and fc:
0.86 to 1) from 05/17/2008 to 06/18/2008
Phase 2
rss respond according to P rss respond according to P and
remained low as fc is near 1
rsc is low during daytime and elevate at night time because of no solar
radiation

0
1
2
3
4
50.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1
31
61
91
121
151
181
211
241
P(mm/3hr)
Moisturecontent(m3/m3)
P Soilm_root
0.83 and fc: 0.86 to 1) from 05/17/2008 to 06/18/2008
0
1
2
3
4
50.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1
31
61
91
121
151
181
211
241
P(mm/3hr)
Moisturecontent(m3/m3)
Precip Soilm_sur Soilm_root
0.32 and fc: 0.05 to 0.27) from 05/17/2008 to 06/18/2008
Phase 2
θroot decreased faster as T is high θsur responded rapidly with P as fc is low
θroot decreased slowly as fc is low

Correction of ET
ETC(i) = ETS(i) − Err
i − i(S)
i(E) − i(S) Error Map 06/18/2008 11am
Phase 3
𝐸𝑟𝑟= 𝐸𝑇𝑠 𝐸 - 𝐸𝑇 𝑀 𝐸ET is adjusted linearly assuming that error grows at the
same rate over the time

Correction of ET
0
1
2
3
4
50.0
0.2
0.4
0.6
0.8
1.0
1.2
1
31
61
91
121
151
181
211
241
P(mm)
ET(mm/hr)
P ET_simulated ET_cor
0
1
2
3
4
50.0
0.2
0.4
0.6
0.8
1
31
61
91
121
151
181
211
241
P(mm)
ET(mm/hr)
P ET_modeled ET_cor
A1: Irrigated agricultural pixel (Landuse: 82, NDVI: 0.71 to 0.83
and fc: 0.86 to 1) from 05/17/2008 to 06/18/2008
0.32 and fc: 0.05 to 0.27) from 05/17/2008 to 06/18/2008
Phase 3 ( Adjustment of ET)
Least correction
High correction

0
0.2
0.4
0.6
0.8
1
1.2
136 141 146 151 156 161 166 171 176
ETrF
Day of the year
ETrF_sim ETrF_METRIC ETrF_cor
A2: Irrigated agricultural pixel (Landuse 82, NDVI: 0.12 to 0.32
and fc: 0.05 to 0.27) from 05/17/2008 to 06/18/2008
Phase 3 (Adjustment of ETrF)
Simulated ETrF is low because of mismatch of Irr
2424 rETF
r
ETET 

Comparison of Hydrus 1D and FAO-56
Paper 3
𝜕θ
𝜕t
=
𝜕
𝜕x
K(h)
𝜕h
𝜕x
+ Cosθ − S
Hydrus-1D - Richards’ Equation
−K h
𝜕h
𝜕x
+ 1 ≤ Emax at z = L
θ is the angle between the flow direction and the
vertical axis (i.e., γ = 00 for vertical flow, 900 for
horizontal flow)
x is the spatial coordinate (positive upward) i.e. x = L at soil
surface and x = 0 at the bottom of the soil profile
h : pressure head
K(h): Unsaturated hydraulic conductivity
Hydrus 1D mode (Šimůnek, 2008)

FAO 56
FAO 56 – Mass balance of water
Kr is a soil evaporation reduction coefficient that is
multiplied by the potential evaporation rate
De is cumulative depth of evaporation (depletion)
Paper 3
Kr = min
TEW − De(i−1)
)
(TEW − REW)
,
1.0
0.0 ≤ Dei
= Dei−1
− 1 − fb Pi− ROi +
Ii
fw
+ fb Pi+1 − ROi+1 +
Ii+1
fw
+
Ei
few
+ Tei
≤ TEW
TEW : Total evaporable water
REW: Readily evaporable water
De = Depletion
fb : fraction of the precipitation and irritation occurring during a time step that contributes to evaporation during the same time step (fb =
0 to 1), few : wetted fraction of the soil surface layer, fw: fraction of soil surface that is wetted, Tei : depth of transpiration extracted from
the exposed and wetted fraction of the soil surface layer (few), Ei : evaporation during timestep
(Allen et al., 1998, Allen, 2011)

FAO 56
FAO 56 – Mass balance of water
Stage 1 : Energy limiting stage
Stage 2 : Falling stage
Evaporation is only limited by energy available, no
resistance from soil
Evaporation is limited by soil resistance
ET is in reference level
ET is smaller than reference level
E2 = Kr Ke maxETr
Kemax : potential rate of evaporation relative to the
reference ET
ETr: Reference ET based on alfalfa
E1 = Ke maxETr

Standard input for FAO-56 and Hydrus-1D
Soil Properties Symbol Units Silt Loam
Field Capacity water content θfc m3/m3 0.36
Wilting Point water content θwp m3/m3 0.22
Depth of Surface Soil Layer subjected to Drying by
Evaporation Ze m 0.1
Total Evaporable Water (calculated) TEW mm 25
Readily Evaporable Water REW mm 8
Soil Properties Symbol Units
Sandy
Clay Loam
Silt
Loam
Silt
Residual soil water content θr m3/m3 0.1 0.067 0.034
Saturated soil water content θs m3/m3 0.39 0.45 0.46
Parameter α in the soil water retention
function [L-1]
α
mm-1 0.0059 0.002 0.0016
Parameter n in the soil water retention
function
n
1.48 1.41 1.37
Saturated hydraulic conductivity, Ks [LT-1] Ks mm/day 314.5 108 60
Tortuosity parameter in the conductivity
function
Tr
0.5 0.5 0.5
FAO 56
Hydrus 1D
Paper 3

Comparison of FAO-56, Hydrus-1D and Lysimeter
0
25
50
75
1000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
8/5/1977
8/7/1977
8/9/1977
8/11/1977
8/13/1977
8/15/1977
8/17/1977
8/19/1977
8/21/1977
8/23/1977
8/25/1977
8/27/1977
8/29/1977
8/31/1977
9/2/1977
9/4/1977
9/6/1977
9/8/1977
9/10/1977
9/12/1977
9/14/1977
9/16/1977
9/18/1977
9/20/1977
9/22/1977
9/24/1977
Precip.+Irri.(mm/day)
Ke
Precip (mm) Ke (FAO-56 with skin evaporation) Ke (HYDRUS 1D -3m) Lysimeter Ke(FAO-56)
0
25
50
75
1000.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
8/5/1977
8/7/1977
8/9/1977
8/11/1977
8/13/1977
8/15/1977
8/17/1977
8/19/1977
8/21/1977
8/23/1977
8/25/1977
8/27/1977
8/29/1977
8/31/1977
9/2/1977
9/4/1977
9/6/1977
9/8/1977
9/10/1977
9/12/1977
9/14/1977
9/16/1977
9/18/1977
9/20/1977
9/22/1977
9/24/1977
Precipi+Irri.(mm/day)
Evaporation(mm/day)
Precip (mm) Es (FAO 56 with skin evaporation) Es (HYDRUS 1D -3m) Lysimeter FAO-56
Paper 3
Daily comparison

Comparison of Hydrus 1D and FAO-56
0
25
50
75
1000.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
8/5/1977
8/7/1977
8/9/1977
8/11/1977
8/13/1977
8/15/1977
8/17/1977
8/19/1977
8/21/1977
8/23/1977
8/25/1977
8/27/1977
8/29/1977
8/31/1977
9/2/1977
9/4/1977
9/6/1977
9/8/1977
9/10/1977
9/12/1977
9/14/1977
9/16/1977
9/18/1977
9/20/1977
9/22/1977
9/24/1977
Precip.+Irri.(mm/day)
Cum.ET(mm)
Precip (mm) Ke (FAO 56 with skin evaporation)
Ke (HYDRUS 1D -3m) Lysimeter
y = 0.97x - 0.57
R² = 0.83
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Evaporation(mm)FAO56
Evaporation (mm) Lysimeter
y = 1.03x - 0.38
R² = 0.88
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Evaporation(mm)FAO56-
skin
Evaporation (mm) Lysimeter
Paper 3
Daily comparison

0
5
10
15
200.0
0.2
0.4
0.6
0.8
1.0
1.2
Precipitation(mm/day)
Ker
Precip (mm) FAO 56 HYDRUS 1D -0.5m
0
5
10
15
200.0
0.2
0.4
0.6
0.8
1.0
1.2
1/1/2002
1/16/2002
1/31/2002
2/15/2002
3/2/2002
3/17/2002
4/1/2002
4/16/2002
5/1/2002
5/16/2002
5/31/2002
6/15/2002
6/30/2002
7/15/2002
7/30/2002
8/14/2002
8/29/2002
9/13/2002
9/28/2002
10/13/2002
10/28/2002
11/12/2002
11/27/2002
12/12/2002
12/27/2002
Ker
Precip (mm) FAO 56 - skin HYDRUS 1D -0.5m
Comparison of Hydrus-1D and FAO-56
Paper 3
Daily
comparison

0
5
10
15
200.0
0.2
0.4
0.6
0.8
1.0
1.2
Precipitation(mm)
Ker
0
5
10
15
200.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
1/1/2002
1/16/2002
1/31/2002
2/15/2002
3/2/2002
3/17/2002
4/1/2002
4/16/2002
5/1/2002
5/16/2002
5/31/2002
6/15/2002
6/30/2002
7/15/2002
7/30/2002
8/14/2002
8/29/2002
9/13/2002
9/28/2002
10/13/2002
10/28/2002
11/12/2002
11/27/2002
12/12/2002
12/27/2002
Evaporation(mm/day)
Comparison of Hydrus-1D and FAO-56
0
5
10
15
200.0
50.0
100.0
150.0
200.0
250.0
300.0
1/1/2002
1/16/2002
1/31/2002
2/15/2002
3/2/2002
3/17/2002
4/1/2002
4/16/2002
5/1/2002
5/16/2002
5/31/2002
6/15/2002
6/30/2002
7/15/2002
7/30/2002
8/14/2002
8/29/2002
9/13/2002
9/28/2002
10/13/2002
10/28/2002
11/12/2002
11/27/2002
12/12/2002
12/27/2002
Cum.Evap.(mm)
Precip (mm) FAO 56 - skin HYDRUS 1D -3m
y = 1.08x - 0.06
R² = 0.88
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
Evaporation(mm)FAO56
Evaporation (mm) HYDRUS 1D
Paper 3
Daily comparison

Conclusions and Recommendations
 Model was able to simulate reasonable values of surface energy
fluxes
 Simulation of ET between the satellite overpass dates without the
thermal band based surface temperature was challenging
 Model was able to simulate reasonable values of surface
temperatures inside surface energy balance
 NARR reanalysis data and METRIC data was able compute surface
energy balance in between the satellite overpass dates
 Difference in simulated and METRIC surface temperature create
some differences in fluxes

 Daily and hourly simulated ET followed the a similar pattern of ET
as compared to METRIC at next satellite overpass date
 Simulated soil surface resistance and canopy resistances using
the soil water balance had expected values under wet and dry
conditions
 Irrigation sub-model was able to simulate irrigation in agricultural
land
 Mismatch in irrigation created differences ET in lower NDVI areas
 Rooting depth is important in low NDVI areas where frequent
irrigation is needed

 FAO-56 model was able to simulate similar soil water balance and
evaporation compared to Hydrus 1D model and Lysimeter data
 Computations of fluxes using two source model generated massive
amount of data
 Convergence process was difficult in extremely low wind speed
and very small solar radiation etc.
 Simulation of ET for every three hours required substantial
computer time and was computationally intensive using DELL multi-
core 64-bit Windows-based work station
 Enhanced FAO-56 model was able capture small precipitation
events when compared to advanced Hydrus 1D model

 Sensitivity analysis of higher blending height is recommended
 Sensitivity analysis with other environmental factors in Jarvis
function is recommended
 Dynamic rooting depth is recommended in irrigated agricultural
land

Time integration of evapotranspiration using a two source surface energy balance model using NARR reanalysis weather data and satellite based METRIC data

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