Ocean Modelling

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Modelling processes [405]
Science of modeling
A scientific model is a representation of a particular phenomenon in the world using something else to
represent it, making it easier to understand. A scientific model could be a diagram or picture, a physical
model like a computer program, or set of complex mathematics that describes a situation. The main types
of scientific model are visual, mathematical, and computer models.
Why do we need model? The reasons include
1. To develop and enhance understanding
2. To quantify descriptions of processes
3. To synthesize and consolidate our knowledge
4. To establish interaction potential
5. To simulate scenarios of past and future developments
Benefits of ocean modelling and types of ocean model
Ocean circulation models are three-dimensional representations of the ocean which are used for studying
ocean circulation, climate change, organism distribution and dispersal, marine chemistry, and the
distribution and transport of substances in the ocean, including sediments and marine pollutants. These
models include factors such as surface air temperature,water temperature and salinity, wind forcing, ocean
eddies, and realistic coastline and seafloor featuresin their calculations. Numerical models caninclude real-
time oceanographic data from ships and satellites to produce forecasts of oceanic conditions, including the
El Niño in the Pacific, and the position of the Gulf Stream in the Atlantic.
There are two main classes of ocean circulation models:
1. Mechanistic models are simplified models used for studying processes. Because the models are
simplified, the output is easier to interpret than output from more complex models. Many different
types of simplified models have been developed, including models for describing planetary waves,
the interaction of the flow with sea-floor features,or the response of the upper ocean to the wind.
These are perhaps the most useful of all models because they provide insight into the physical
mechanisms influencing the ocean.
2. Simulation models are used for calculating realistic circulation of oceanic regions. These models
are often very complex because all important processes are included, and the output may often be
difficult to interpret.
a. Regional
b. Global
c. Deep basin
d. Shallow coastal: is highly variable driven primarily synoptic wind and other rapidly changing
surface forcing.
e. Free surface ocean modeling
There are three basic types of OGCMs:
1. Idealized geometry models: Models with idealized basin geometry have been used extensively in
ocean modeling and have played a major role in the development of new modeling methodologies.
They use a simplified geometry, offering a basin itself, while the distribution of winds and
buoyancy force are generally chosen as simple functions of latitude.

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2. Basin-scale models: To compare OGCM results with observations we need realistic basin
information instead of idealized data. However, if we only pay attention to local observation data,
we don't need to run whole global simulation, and by doing that we can save a lot of computational
resources.
3. Global models: This kind of model is the most computationally costly one. More experiments are
needed as a preliminary step in constructing coupled Earth system models.
Modeling Global Climate
Climate models are numerical representations of various parts of the Earth’s climate system. Scientists use
these types of global climate models: Earth Balance Models (EBMs), Earth Models of Intermediate
Complexity (EMICs), and General Climate Models (GCMs.
A key limitation of Global Climate Models (GCMs) is the fairly coarse horizontal resolution. For the
practical planning of local issues such as water resources or flood defenses,countries require information
on a much more local scale than GCMs are able to provide. Regional models provide one solution to this
problem. Regional Climate Models (RCMs) work by increasing the resolution of the GCM in a small,
limited area of interest. An RCM might cover an area the size of western Europe, or southern Africa –
typically 5000km x 5000km. RCMs can then resolve the local impacts given small scale information about
orography (land height) and land use, giving weather and climate information at resolutions as fine as 50
or 25km.
GCMs try to simulate as much as possible about the climate system: the incoming and outgoing radiation,
the way the air moves, the way clouds form and precipitation falls, the way the ice sheets grow or shrink,
etc. They are frequently coupled to a representation of the ocean. They may take into account how the
vegetation on the Earth’s surface changes. Critically, they try to calculate how all these different parts of
the climate system interact, and how the feedback processes work.
Climate models divide the surface of the Earth into a horizontal grid, the atmosphere into vertical levels,
and time into discrete time steps. Processes that are smaller than the size of one of these cubes, such as
cloud formation, are difficult to model and so need to be parameterized.
Parameterization in a weather or climate model is a method of replacing processes that are too small-scale
or complex to be physically represented in the model by a simplified process.
For instance, the problem with dividing the atmosphere into lots of little cubes is that there are many
processes that are smaller than the cubes. So, for example, individual clouds may well be smaller than a
grid box. They do still play an important role in the climate system, especially collectively, so somehow
the processes that form them and the consequences of them existing must be represented. So, for example,
based on knowledge of the temperature and humidity in a box, we must estimate how much cloud and how
much rain there is in the box. We also need to know how much dust (i.e.‘aerosol’) is in the box, asraindrops
require a very small solid particle in the air to form on. This process is called parameterizing. There are
many parameterization schemes in the model, such as the scheme which calculates how much cloud there
is.
Advantages and disadvantages of global climate models
1. coarse horizontal resolution
2. require large amounts of computer power
and resources
3. It is very low resolution
1. It cannot produce in small scale (regional
climate )
2. It can run in simple personal computer
3. It is not regionally high resolution and
accurate
4. hopeless at predicting future cloud cover.

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Advantages and disadvantages of regional climate models
1. It is high resolution
2. It can simulate regional climate
3. Shows most important variables/system
Thresholds
4. It is regionally high resolution and
accurate
5. Easy to implement
1. Requires high quality observational data
over a number of decades for calibration
and verification
2. Need to be update continuously
3. Difficult to be adapted to new situation
Why scientists run multiple experiments with climate models?
Climate models are important tools that can be used to advance our understanding of current and past
climate. They also provide qualitative and quantitative information about potential future climate
conditions. But in spite of their sophistication, they remain merely models. They represent simulations of
the realworld, constrained by their ability to correctly capture and portray each of the important processes
that affectclimate. Notwithstanding their complexities, the models remain deficient in many aspectsoftheir
portrayal of the climate, which reduces their ability to provide reliable simulations of future climate.
Scope and importance of modelling in oceanography
Ocean general circulation models (OGCMs) have many important applications: dynamical coupling with
the atmosphere, sea ice, and land run-off that in reality jointly determine the oceanic boundary fluxes;
transpire of biogeochemical materials; interpretation of the paleoclimatic record; climate prediction for both
natural variability and anthropogenic chafes; data assimilation and fisheries and other biosphere
management. OGCMs play a critical role in Earth system model. They maintain the thermal balance asthey
transport energy from tropical to the polar latitudes. To analyze the feedbackbetweenoceanand atmosphere
we need ocean model, which can initiate and amplify climate change on many different time scales, for
instance, the interannual variability of El Niño and the potential modification of the major patterns for
oceanic heat transport as a result of increasing greenhouse gases. Oceans are a kind of undersampled nature
fluid system, so by using OGCMs we can fill in those data blank and improve understanding of basic
processes and their interconnectedness, as well as to help interpret sparse observations. Even though,
simpler models can be used to estimate climate response, only OGCM can be used conjunction with
atmospheric general circulation model to estimate global climate change.
Downscaling
Downscaling is a method for obtaining high-resolution climate or climate change information from
relatively coarse-resolution global climate models (GCMs). Typically, GCMs have a resolution of 150-300
km by 150-300 km. Many impacts models require information at scales of 50 km or less, so some method
is needed to estimate the smaller-scale information. The two main approaches to downscaling climate
information are dynamical and statistical. Dynamical downscaling requires running high-resolution climate
models on a regional sub-domain, using observational data or lower-resolution climate model output as a
boundary condition. These models use physical principles to reproduce local climates, but are
computationally intensive. Statistical downscaling is a two-step process consisting of i) the development
of statistical relationships between local climate variables (e.g., surface air temperature and precipitation)
and large-scale predictors (e.g., pressure fields), and ii) the application of such relationships to the output
of global climate model experiments to simulate local climate characteristics in the future.

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Statistical downscaling first derives statistical relationships between observed small-scale (often station
level) variables and larger (GCM) scale variables, using either analogue methods (circulation typing),
regression analysis, or neural network methods.
Advantages of Statistical Downscaling: Statistically downscaled projections are relatively easy to
produce because they do not require heavy computing resources. Due to the computation advantages mass
ensembles of projections can be produced. Projections can also be downscaled to point-specific locations,
however the data must be carefully interpreted at that scale. The results can be compared to observations
for a historical time period.
Disadvantages ofstatistical downscaling: Two major disadvantages exist: 1) local, small-scale dynamics
and climate feedbacks are not simulated, and 2) assumptions of stationarity between the large- and small-
scale dynamics are made to downscale future projections.
How global and regional models are connected
RCMs only cover a limited domain, the values at their boundaries must be specified explicitly. Regional
models add two different types of small-scale information to the GCMs results. First, they add information
on the local conditions at specific locations. This is typically important when large horizontal gradients
occur, for example related to the topography or the coastline. Second, they add information on processes
that are small scale but which are not necessarily tied to a specific location, like for example frontal systems,
small-scale convective precipitation, and other meso-scale phenomena. RCMsare initialized with the initial
conditions and driven along its lateral-atmospheric-boundaries and lower-surface boundaries with time-
variable conditions. RCMs thus downscale global reanalysis or GCM runs to simulate climate variability
with regional refinements.
Common drawbacks of ecosystems model

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1. Insufficient data for the development of models in order to get reliable prognoses
2. Weakness in parameter estimation
3. Not appropriate reflection of the realproperties of ecosystem
What is model scaling
A scale model is a representation or copy of an object that is larger or smaller than the actual size of the
object being represented. The scale is expressed either as ratio e.g. 1:35 or more commonly as a fraction
e.g. 1/35th
and indicates the size of the model compared to the original object that it is replicating.
How Mathematical model work and explain with example
A mathematical model is a description of a system using mathematical concepts and language. The process
of developing a mathematical model is termed mathematical modeling. A mathematical model usually
describes a system by a set of variables and a set of equations that establish relationships between the
variables. Variables may be of many types; real or integer numbers, boolean values or strings, for example.
The variables represent some properties of the system,
1. Is indispensable in many applications
2. Is successful in many further applications
3. Gives precision and direction for problem solution
4. Enables a thorough understanding of the system modeled
5. Allows the efficient use of modern computing capabilities
For example ; population logistic growth model: Logistic population growth occurs when the growth rate
decreases as the population reaches carrying capacity. Carrying capacity is the maximum number of
individuals in a population that the environment can support. ... When the population approaches carrying
capacity, its growth rate will start to slow
,
N: number of population , r=growth rate ,k ==carrying capacity
How does simplification of a system hamper the outcome of the model ?
Numerical modelling
Numerical models are mathematical models that use some sort of numerical time-stepping procedure to
obtain the models behavior over time. The mathematical solution is represented by a generated table
and/or graph.

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R selected and k selected
The two evolutionary "strategies" are termed r-selection, for those species that produce many "cheap"
offspring and live in unstable environments and K-selection for those species that produce few "expensive"
offspring and live in stable environments.
Drivers of ocean circulation model , advantage and disadvantage
Advantage Disadvantage
useful for gaining insight
mathematical formulations of the processes
usually not possible to solve for realistic condition
and problems
Ecological modelling is the construction and analysis of mathematical models of ecological processes,
including both purely biological and combined biophysical models. Models can be analytic or simulation-
based and are used to understand complex ecological processes and predict how real ecosystems might
change.

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Importance / use of Ecological modeling
Ecological models are been used in a variety of applications, such as the development of biodiversity
conservation policies, the planning and management of natural reserve networks,and the impact assessment
of global climate change, resourcesexploitation and expansion of alien speciesdistributions. Policy makers
and governmental organizations need fast, efficient and reliable management tools in order to develop or
update an environmental legislation framework. The predictive power of the modelling approaches makes
them suitable for the investigation of hot spot scientific issues, such as the understanding of ecosystem
functioning, the evaluation of environmental health, and the monitoring of biodiversity. The ecological
models can be used in both deep and shallow coastal systems to describe estuarine hydrodynamics, water
quality, and ecosystem/food webdynamics. Some researchershave alsoused models which integrate socio-
economic and ecological dynamics, in order to describe the environmental effects of future development
scenarios.
An ecosystem model is an abstract,usually mathematical, representation of an ecological system (ranging
in scale from an individual population, to an ecological community, or even an entire biome), which is
studied to better understand the real system. Using data gathered from the field, ecological relationships
such as the relation of sunlight and water availability to photosynthetic rate,or that between predator and
prey populations—are derived, and these are combined to form ecosystem models. These model systems
are then studied in order to make predictions about the dynamics of the real system.
EcosystemModels have applications in a wide variety of disciplines, suchas: naturalresource management,
ecotoxicology and environmental health, agriculture, and wildlife conservation. There are two major types
of ecological models: analytic models and simulation/computational models.
There are two major types of ecological models, which are generally applied to different types of
problems: (1) analytic models and (2) simulation / computational models.
a. Analytic models are typically relatively simple (often linear) systems that can be accurately
described by a set of mathematical equations whose behavior is well-known.
b. Simulation models on the other hand, use numerical techniques to solve problems for which
analytic solutions are impractical or impossible.

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Available ecological models are
1. Biogeochemical and bioenergetics dynamic models: these are based on causality and on mass or
energy conservation principlaes.
2. Static models :
3. Population dynamics model: widely used for keeping track on the development or recovery of a
population and they have been extensively applied in the management of fisheries and national
parks.
4. Structure dynamic model: used to describe the ecosystem adaptations and shift in species
composition.
5. Fuzzy models : used to identify different benthic communities in an area based on their dominant
taxa.
6. Artificial neural networks
7. Individual based model : IBM models are able to derive the properties of a system from the
properties of the components of this system.
8. Spatial models : these models investigate the spatial distribution of the forcing functions and of the
non-biological and biological state variables.
9. Ecotoxicological model: This type of models includes simple to use bio-geochemical models or
population dynamic models which additionally include an effect component. They can be used to
solve management problems and to perform environmental risk assessments for the application of
chemicals (distribution and effect).
10. Stochastic model: They can be a bio-geochemical, a population dynamic, a spatial, or a structural
dynamic model, which will be able to consider randomness of forcing functions or processes.
11. Hybrid model: the hybrid models can be created by the combination of any two of the previously
mentioned model types, resulting in the synthesis of advantages and the elimination of
disadvantages of the existing models.
Disadvantages in the ecological modeling
1. Insufficient data for the development of models in order to get reliable prognoses
2. Weakness in parameter estimation
3. Not appropriate reflection of the real properties of ecosystem.
4. Lack of motivation for change in the environment
5. Changing lifestyles can be extremely difficult
Major processes of marine ecosystem / What are the processes we need to consider to model an
oceanic ecosystem
1: Distribution and dispersal
The distribution patterns of marine organisms are influenced by physical and biological processes in both
ecological time (tens of years) and geologic time (hundreds to millions of years).
2: Migrations of marine organisms
The migrations of plankton and nekton throughout the water column. Diurnal vertical migrations are
common. For example, some types of plankton, fish, and squid remain beneath the photic zone during the
day, moving toward the surface after dusk and returning to the depths before dawn. It is generally argued
that marine organisms migrate in response to light levels.
3: Dynamics of populations and assemblages

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A wide variety of processes influence the dynamics of marine populations of individual species and the
composition of assemblages (e.g., collections of populations of different species that live in the same area.
a. Commensalism
b. Mutualism
c. colonization and succession
d. disturbance
e. Competition
4: primary Productivity and secondary productivity
Primary productivity is the rate at which energy is converted by photosynthetic and chemosynthetic
autotrophs to organic substances.
5: Upwelling
The most productive waters of the world are in regions of upwelling. Upwelling in coastal waters brings
nutrients toward the surface. Phytoplankton reproduce rapidly in these conditions, and grazing zooplankton
also multiply and provide abundant food supplies for nekton.
6: Seasonal cycles of production
Cycles of plankton production vary at different latitudes because seasonalpatterns of light and temperature
vary dramatically with latitude. In the extreme conditions at the poles, plankton populations crash during
the constant darkness of winter and bloom in summer with long hours of light and the retreat of the ice
field. In tropical waters, variation in sunlight and temperature is slight, nutrients are present in low
concentrations, and planktonic assemblages do not undergo large fluctuations in abundance.
Adiagram showing the open oceanplankton ecosystemmodel developed by Michael Fashamand coauthors
in: (1990). "A nitrogen-based model of plankton dynamics in the oceanic mixed layer". Journal of Marine
Research 48:591–639. The diagram shows 7 ecosystem components: P,phytoplankton; Z, zooplankton; B,
bacteria; D, detritus; Nn, nitrate; Nr, ammonium; Nd, dissolved organic nitrogen. The connecting arrows
indicate flows of material between these components driven by processes such as primary production,
grazing and remineralisation. Closed-headed arrowsindicate flows of material that remain within the model
ecosystem; open-headed arrows indicate flows of material out of the modelled domain, for instance below
the ocean's upper mixed layer.

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Typical ecosystem model in respect of drivers , processes ,fluxes and state variables
Advantages and disadvantage of top down and bottom up models
Top down model Bottom up model
1. Empirical or semi-mechanistic
2. Few processes and parameters,modest
data requirements
3. Potentially very accurate when applied
within domain of measurements
4. Probably invalid for extrapolation .e.g. to
past or future conditions with no modern
analogues
5. Example : NPP algorism that estimate net
primary production based on satellite
sensed FPAR or greenness.
1. Mechanistic at large or long scale
a. Can generate hypothesis
b. Explore non obvious phenomena
2. Typically represent many processes
3. Require a lot of data
4. Many parameters that’s lead high
uncertainty
5. Tend to resolve some processes better
than others
6. Example dynamic global vegetation
model
Difference stochastic and deterministic models
Deterministic model Stochastic
• In deterministic models, the output of the
model is fully determined by the parameter
values and the initial conditions.
• Stochastic models possess some inherent
randomness. The same set of parameter values and
initial conditions will lead to an ensemble of different
outputs.
It is basically a formula It is probabilistic model
Source of uncertainty in model outcomes
There are three main sources of uncertainty in projections of climate: that due to future emissions
(scenario uncertainty, green), due to internal climate variability (orange), and due to inter-model
differences (blue).
Wave model, JONSWAP
Wind wave modeling describes the effort to depict the sea state and predict the evolution of the energy of
wind waves using numerical techniques. These simulations consider atmospheric wind forcing, nonlinear
wave interactions, and frictional dissipation, and they output statistics describing wave heights, periods,
and propagation directions for regional seas or global oceans. Such wave hindcasts and wave forecasts are
extremely important for commercial interests on the high seas. For example, the shipping industry requires
guidance for operational planning and tacticalsea keeping purposes. For example ; WAVEWATCH,WAM,
CCHE2D-COAST etc.
The JONSWAP (Joint North Sea Wave Project) spectra is an empirical relationship that defines the
distribution of energy with frequency within the ocean.
Fetch, significant wave height and saturated data
Fetch, area of ocean or lake surface over which the wind blows in an essentially constant direction, thus
generating waves. The term also is used as a synonym for fetch length, which is the horizontal distance
over which wave-generating winds blow.

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The significant wave height is the average height of the highest one-third of all waves measured which is
equivalent to the estimate that would be made by a visual observer at sea.
Biological model
Biological model may refer to: a mathematical representation of an organism, a non-human species that is
extensively studied to understand particular biological phenomena.
Components of biological modelling
In its mathematical formulation, an ecological model has five components
1. Forcing functions or external variables: forcing function of a nature that influence the state of
ecosystem,the biotic and abiotic components and the process rates. For example in the nitrogen
cycle modeling , forcing functions are outflows, inflows, concentration of nitrogen components ,
solar radiation and temperature etc.
2. State variables: the selection of state variables is crucial to the model structure .for instance, in the
eutrophication model, the state variables are the concentrations of nutrients and phytoplankton.
3. Mathematical equations: they are used to represent the biological, chemical and physical
processes. They describe the relationship between the forcing functions and state variables.
4. Parameters:they may be considered constant for specific ecosystem or part of an ecosystem for a
certain time and will have scientific definitions.
5. Universal constant : such as the gas constant and atomic weights are also used in most models.

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Influx of biological modelling
Principal component analysis
Principal component analysis (PCA) is a mathematical procedure that transforms a number of (possibly)
correlated variables into a (smaller) number of uncorrelated variables called principal components.
Principal components analysis is similar to another multivariate procedure called Factor Analysis.

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Box model for nutrient flux analysis
The main pools (boxes) and fluxes (arrows) of nitrogen cycling in terrestrial ecosystems. Arrow thickness
is proportional to the magnitude of net flux. The dashed line indicates interference with N mineralization
due to the effects of tannins. The path from the pool of dead organic nitrogen and dissolved organic N to
plants short-circuits the conventional microbial route wherebyorganic N is converted to mineral N.Adapted
from Chapin (1995)
Spatial model, why we need to explicitly consider the space ?
Spatial modeling is an analytical process conducted in conjunction with a geographical information system
(GIS) in order to describe basic processes and properties for a given set of spatial features. The objective

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of spatial modeling is to be able to study and simulate spatial objects or phenomena that occur in the real
world and facilitate problem solving and planning.
It is important to be able to model the distribution, movement and dispersal of species and individuals across
a varied and variable landscape. It is important to choose an appropriate scale related to the specific area
because the many process affect different organisms. In fact many processes operate at multiple scales.
Model scaling , range of temporal and spatial scaling of ecosystem model
Classify the spatial models in various categories
a. A model may be descriptive or predescriptive
b. A model may be deterministic or stochastic
c. A model may be static or dynamic
d. A model may be deductive or inductive
1: The Vector Model
The data type: Point, line or Area
2: The Raster Model
The following information should always be recorded when assembling, compiling and utilizing raster
data.
1. Grid size (Number of rows and columns)
2. Grid resolution

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3. Georeferencing information e.g. comer co-ordinates, source projection.
The Modeling Process
1. The first step is to define the goals of the model.
2. The second step is to break down the model into elements and to define the properties of each element
and the interactions between the elements. A flowchart is a useful tool for linking the elements.
3. The third step is the implementation and calibration of the model.
4. The fourth step is to validate the model before it can be generally accepted.
System dynamic, steps involved in the modeling process
System Dynamics (SD) is a widely-used graphical notation for representing continuous systems. A System
Dynamics diagram typically contains four main types of element: compartments, flows, variables and
influences. Compartments represent storages of material, and the flows represent movement of the material
into, out of and between compartments. Simile was designed as a “System Dynamics plus objects”
language, so naturally it is straightforward to represent standard System Dynamics models in Simile.
The modeling process is cyclic and closely parallels the scientific method and the software life cycle for
the development of a major software project. The process is cyclic because at any step we might return to
an earlier stage to make revisions and continue the process from that point.
The steps of the modeling process are as follows:
1. Analyze the problem
We must first study the situation sufficiently to identify the problem precisely and understand its
fundamental questions clearly.
2. Formulate a model
In this stage,we design the model, forming an abstraction of the system we are modeling. Some of the tasks
of this step are as follows:
a. Gather data
We collect relevant data to gain information about the system’s behavior.
b. Make simplifying assumptions and document them
In formulating a model, we should attempt to be as simple as reasonably possible.
c. Determine variables and units
We must determine and name the variables. Anindependent variable is the variable on which othersdepend.
In many applications, time is an independent variable. Establish relationships among variables and sub
models
e. Determine equations and functions
While establishing relationships between variables, we determine equations and functions for these
variables. For example, we might decide that two variables are proportional to each other

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3. Solve the model
This stage implements the model. It is important not to jump to this step before thoroughly understanding
the problem and designing the model. Otherwise,we might waste much time, which canbe most frustrating.
4. Verify and interpret the model’s solution
Once we have a solution, we should carefully examine the results to make sure that they make sense
(verification) and that the solution solves the original problem (validation) and is usable.
5. Report on the model
Reporting on a model is important for its utility. Perhaps the scientific report will be written for colleagues
at a laboratory or will be presented at a scientific conference.
a. Analysis of the problem:
b. Model design
The amount of detail with which we explain the model depends on the situation. In a comprehensive
technical report, we can incorporate much more detail than in a conference talk.
c. Model solution
In this section, we describe the techniques for solving the problem and the solution. We should give as
much detail as necessary for the audience to understand the material without becoming mired in technical
minutia.
d. Results and conclusions
Our report should include results, interpretations, implications, recommendations, and conclusions of the
model’s solution. We may also include suggestions for future work.
6. Maintain the model: As the model’s solution is used, it may be necessary or desirable to make
corrections, improvements, or enhancements.
What are error and uncertainty
Error is the difference between the true value of the measured and the measured value. Uncertainty
characterizesthe range of values within which the true value is assertedtolie with some level of confidence.

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Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system
(numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs.
How does sensitivity relate to uncertainty
Although closely related, uncertainty analysis and sensitivity analysis are two different disciplines.
Uncertainty analysis assesses the uncertainty in model outputs that derives from uncertainty in inputs.
Sensitivity analysis assesses the contributions of the inputs to the total uncertainty in analysis outcomes.
Wave and its anatomy
Waves are moving energy traveling along the interface between ocean and atmosphere, often transferring
energy from a storm far out at sea over distances of severalthousand kilometers. Most waves are driven by
the wind and are relatively small. However other waves include those created by gravitational forces (e.g.
tidal waves) and those created by underwater disturbances, such as earthquakes (e.g. tsunamis).
Anatomy of ocean wave
Figure is adopted from the essential of Oceanography by Thurman.
1. Wave crest :a successive of high part of the waves
2. Wave trough : a successive of low part of the waves
3. Wave height:is the vertical distance between a crest and a trough.
4. Wave length:the horizontal distance between any two corresponding points on successive
waveforms such as from crest to crest or from trough to trough.
5. Wave base:wave base is the water depth beneath which there is no wave movement. This depth
has been determined to be half the distance between the crests of waves.
6. Wave steepness:it is the ratio of wave height to wavelength (
𝑤𝑎𝑣𝑒 ℎ𝑒𝑖𝑔ℎ𝑡(𝐻)
𝑤𝑎𝑣𝑒 𝑙𝑒𝑛𝑔𝑡ℎ(𝐿)
),if the wave
steepness exceeds 1/7 the wave breaks (spills forward) because the wave is too steep to support
itself.
7. Still water level: halfway between the crests and the troughs.
Shallow wave, transition wave and deep water wave

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a. Waves in which depth is less than 1/20 of the wave length are called shallow water waves.
b. If the water depth is greater than the wave base (L/2), the waves are called deep water waves.
They have no interference with the ocean bottom.
c. Waves that have some characteristics of shallow water waves and some of deep water waves are
called transitional waves.
Destructive wave and constructive wave
Empirical modeling refers to any kind of modeling based on empirical observations rather than on
mathematically describable relationships of the system modeled. The empirical model could be either
deterministic (e.g., when the parameters in the model calibrated from the data are fixed at their mean
values), or probabilistic.
JONSWAP / Joint North Sea Wave Project
The JONSWAP (Joint North Sea Wave Project) spectra is an empirical relationship that defines the
distribution of energy with frequency within the ocean. The JONSWAP spectrum is effectively a fetch-
limited version of the Pierson-Moskowitz spectrum, exceptthat the wave spectrum is never fully developed
and may continue to develop due to non-linear wave-wave interactions for a very long time.
Limitations on empirical spectra
1. Fetch limitations
2. State of development or decay
3. Seafloor topography
4. Local currents
5. Effect of distant storms (swells)
Factors that affect wave are wave speed, duration and fetch.
1. Wave speed: it is the rate at which a wave travels. 𝑤𝑎𝑣𝑒 𝑠𝑝𝑒𝑒𝑑 =
𝑤𝑎𝑣𝑒 𝑙𝑒𝑛𝑔𝑡ℎ
𝑝𝑒𝑟𝑖 𝑜 𝑑
, if the wind speed
is slow, only small wavesresult. Wave speedis more accuratelyknown ascelerity which is different
from the traditional concept of speed. Celerity is used only in relation to waves where no mass in
motion, just the waveform.
2. Duration: the length of time during which the wind blows in one direction.
3. Fetch: the distance over which the wind blows in one direction. If strong winds blow for a long
period of time but over a short fetch,no large waves form. The greater the wind velocity, the longer

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the fetch, and the greater duration the wind blows, then the more energy is converted to waves and
the bigger the waves.
Wave model
Wind wave modeling describes the effort to depict the sea state and predict the evolution of the energy
of wind waves using numerical techniques. A wave model requires as initial conditions information
describing the state of the sea. The sea state is described as a spectrum. The output of a wind wave
model is a description of the wave spectra, with amplitudes associated with each frequency and
propagation direction. For example, The SWAN model is a numerical third-generation wave model that
provides realistic estimates of wave parameters in open seas, coastal areas, lakes, and estuaries from
given wind-, bottom, and current conditions.
Beaufort scale
The Beaufort scale is an empirical measure that relates wind speed to observed conditions at sea or on
land. Its full name is the Beaufort wind force scale. There are twelve levels.
Beaufort levels Description Beaufort levels Description
0 Calm 7 Near Gale
1 Light air 8 Gale
2 Light breeze 9 Strong Gale
3 Gentle breeze 10 Storm
4 Moderate breeze 11 Violent storm
5 Fresh breeze 12 Hurricane
6 Strong breeze
Spatial heterogeneity
It refers to the uneven distribution of various concentrations of each species within an area. A landscape
with spatial heterogeneity has a mix of concentrations of multiple species of plants or animals (biological),
or of terrain formations (geological), or environmental characteristics (e.g. rainfall, temperature, wind)
filling its area. For example, the distribution of primary production over the world’s oceans (Fig. 2–30).
Moreover, such heterogeneity occurs at all spatial scales.
Why explicitly consider space?
Heterogeneity in
Time: - a stochastic model
Space: - spatial model
Individual traits:- individual-based model
Abiotic spatial heterogeneity affects
ecological processes
Biotic spatial heterogeneity
1. Habitat quality
2. Resources availability
3. Predation risk
4. Dispersal barriers
5. Dispersal probability
1. Territorial behavior in animals
2. Local interaction between individuals
a. Competition for space,nutrients or light in
plants
b. Competition for food, shelter, etc. in animals

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6. Mortality rate
7. Colonization probability
8. Behavior
c. Predation
d. Disease transmission
3. Local dispersal
How can heterogeneity in space arise and when does it matter?
Abiotic spatial heterogeneity
Spatial heterogeneity/structure of habitat or landscape influences relevant ecological processes
Biotic spatial heterogeneity
Individuals create heterogeneity through their interaction, relevant ecological processes act on a certain
spatial scale, self-organized spatial heterogeneity
Classification of spatial models
1. Cause for heterogeneity:abiotic vs. biotic
2. Representation ofspace I:implicit vs. explicit
a. Spatially implicit models: incorporate assumptions about the the spatial structure of biotic interactions,
but do not include geographical space.
b. Spatially explicit models: represent a heterogeneous space that is continuous or discrete.
3. Representation ofspace II:discrete vs. continuous
A. Discrete: Space is divided into cells/patches/sites, neighborhood relations, within patches/cells/sites
homogeneous
B. Continuous: Space is referenced via a Cartesian coordinate system (x, y)
4. Basic unit: abundance-based vs. site-based vs. individual-based
a. abundance-based: basic unit = population (e.g. PDE)
b. site/grid/patch-based: basic unit = cell (e.g. CA)
c. individual-based: basic unit = individual (e.g. distance models)
5. Number ofdimensions:1, 2, 3

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Five ways to specialize in an ecological model
3.1 Wildfires in boreal forests – Cellular Automaton
3.2 Plant competition and self-thinning – Distance models
3.3 Sustainable management of species-rich tropical forests – Individual- and grid-based ‘interaction’
model
3.4 Population dynamics of a territorial bird with social breeding – Individual- and grid-based ‘movement’
model
3.5 Metapopulation models and Meta-X
Cellular automata
A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a
number of discrete time steps according to a set of rules based on the states of neighboring cells. Cellular
automata were studied in the early 1950s as a possible model for biological systems.
Advantages
1. within-site dynamics
2. local interactions
3. simple rules reflect ecological knowledge
4. single species and community dynamics can be modeled
5. computationally efficient
Disadvantages: the regular and equally-sized shape of sites
Metapopulation ( Levins 1969) = ensemble of populations living in isolated habitat remnants (patches)
With a certain risk of local extinction and the chance of becoming recolonized by migrating individuals.

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driver Affected processes
Habitat loss
Fragmentation
Local extinction
Individual exchange or colonization
What spatial and temporal scales are adequate for resolving hydrodynamic processes
The probability density function (pdf) describes the relative probability that observations of a random
variable will fall within a certain range:
Model uncertainties are the maximum possible deviations (with a probability of typically 95%) of the
calculated values of the output variables of the model from the correct values of the output variables of the
real component for the same values of the input variables.
Sources of uncertainty
Measurement and/or process errors are often the only sources of uncertainty modeled when addressing
complex ecological problems. Uncertainty in the output data from a model can propogate (feed through)
from several sources:
1. Incomplete knowledge of the system being modelled
a. Formulations of processes and relationships (the equations and algorithms in the model)
b. Uncertainty as to the ”correct” parameter values
2. Simplified representation of the system being modelled
a. “missing” processes and parameters
b. Single parameter value to represent a random value from the real world
c. Scale mismatch between model, input data and output data
3. Variability or error in the input data
a. variability in time
b. variability in space
c. errors in measurement, interpolation, output from another model providing input to this one etc.
How does model sensitivity related to uncertainty
An uncertainty analysis attempts to describe the entire set of possible outcomes, together with their
associated probabilities of occurrence. A sensitivity analysis attempts to determine the relative change in
model output values given modest changes in model input values.

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Stochastic model Deterministic model
1: most real world processes are stochastic
2: the output is random variable
3: small scale processes seem
1: some processes
2: have one specific outcome for each set of values
of the input variables
3: larger scales
Sensitivity Uncertainty
1: the study of how the uncertainty in the output of
a mathematical model
2: identifying how dependent the output is on a
particular input value
3: be measured by monitoring changes in the
output, e.g. by partial derivatives or linear
regression
1: the maximum possible deviations (with a
probability of typically 95%) of the calculated
values of the output variables
2: uncertainty due to imperfections and
idealizations made in physical model
3: can be assessed by comparing them with other
more refined methods, or with test results and in-
service experiences
Monte Carlo processes and how to assess the sensitivity by the Monte Carlo method?
Monte Carlo (MC) methods are a subset of computational algorithms that use the process of repeated
random sampling to make numerical estimations of unknown parameters. They allow for the modeling of
complex situations where many random variables are involved and assessing the impact of risk.
Monte Carlo simulation provides a number of advantages over deterministic, or “single-point
estimate” analysis:
 Probabilistic Results. Results show not only what could happen, but how likely each outcome is.
 Graphical Results. Because of the data, a Monte Carlo simulation generates,it’s easy to create graphs of
different outcomes and their chances of occurrence. This is important for communicating findings to other
stakeholders.

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 Sensitivity Analysis. With just a few cases, the deterministic analysis makes it difficult to see which
variables impact the outcome the most. In Monte Carlo simulation, it’s easy to see which inputs had the
biggest effect on bottom-line results.
 Scenario Analysis: In deterministic models, it’s very difficult to model different combinations of values for
different inputs to see the effects of truly different scenarios. Using Monte Carlo simulation, analysts can
see exactly which inputs had which values together when certain outcomes occurred. This is invaluable for
pursuing further analysis.
 Correlation of Inputs. In Monte Carlo simulation, it’s possible to model interdependent relationships
between input variables. It’s important for accuracy to represent how, in reality, when some factors go up,
others go up or down accordingly.
The sensitivity is calculated by dividing the percentage change in output by the percentage change in the
input
Difference between stochastic and deterministic models
Deterministic model Stochastic model
The model describes a phenomenon whose
outcome is fixed
Describes the unpredictable variation of the
outcomes of a random experiment
Models parameters are known with certainty Some uncertain parameters
Has known sets of inputs that result in a unique set
of outputs
Random inputs lead to random outputs
Contain no random variables Has one or more random variables
the output of the model is fully determined by the
parameter values and the initial conditions initial
conditions
Questions from videos section
Distinguish a climate model from other types of models
There are a number of models regarding different phenomena such asbusiness model, port model, statistical
model, ecological model etc. Climate models is based on the climate data and climate related events.
Explain the benefits and limitations of regional approaches to climate model projections
Because these RegionalClimate Models (RCMs) cover a smaller area,they can have higher resolution than
GCMs and still run in a reasonable time. Adisadvantage of climate models is that,although computer power
continues to increase rapidly, global models currently do not resolve features smaller than about 50 miles
x 50 miles. This makes it impossible to resolve smaller-scale climate features.
Already answered (page 4)
Articulate the purposes for using global climate models
A global climate model (GCM) is a complex mathematical representation of the major climate system
components (atmosphere, land surface,ocean, and sea ice), and their interactions. Earth's energy balance
between the four components is the key to long-term climate prediction.
1. A global climate model or general circulation model aims to describe climate behavior by
integrating a variety of fluid-dynamical, chemical, or even biological equations that are either
derived directly from physical laws (e.g. Newton's law) or constructed by more empirical means.

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2. Scientists use climate models to understand complex earth systems.
3. These models allow them to test hypotheses and draw conclusions on past and future climate
systems.
4. This can help them determine whether abnormal weather events or storms are a result of changes
in climate or just part of the routine climate variation
Highlight the main components and limitations of a global climate model
a. Atmospheric dynamics and interactions
b. Model grid
1. Hybrid vertical coordinate ( combination of terrain following and atmospheric
pressure) and 19 vertical levels ( lowest at 50m and highest at 5pa)
2. Regular lat lon grid in the horizontal ( arakawa B grid layout)
c. Physical parameterizations ( important processes occur in the atmosphere on small scales those
are resolved by the grid of the dynamical part ( clouds , precipitation ) .
d. Initial and boundary condition of the model
a. Lateralboundary conditions variables
i. Wind , temperature , surface pressure
e. Downscaling
The main climate system components treated in a climate model are:
1. The atmospheric component, which simulates clouds and aerosols, and plays a large role
in transport of heat and water around the globe.
2. The land surface component, which simulates surface characteristics such as vegetation,
snow cover, soil water, rivers, and carbon storing.
3. The ocean component, which simulates current movement and mixing, and
biogeochemistry, since the ocean is the dominant reservoir of heat and carbon in the
climate system.
4. The sea ice component, which modulates solar radiation absorption and air-sea heat and
water exchanges.
Climate models divide the globe into a three-dimensional grid of cells representing specific
geographic locations and elevations. Each of the components (atmosphere, land surface, ocean,
and sea ice) has equations calculated on the global grid for a set of climate variables such as
temperature. In addition to model components computing how they are changing over time, the
different parts exchange fluxes of heat, water, and momentum. They interact with one another as
a coupled system.

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Limitations
It is worth reiterating that climate models are not a perfect representation of the Earth’s climate – and nor
can they be. As the climate is inherently chaotic, it is impossible to simulate with 100% accuracy.
1. One of the main limitations of the climate models is how well they represent clouds.
2. too coarse to capture global rainfall
3. GCMs do not simulate individual storms and local high rainfall events
4. The double ITCZ “is perhapsthe most significant and most persistent bias in current climate models
Uncertainty is any departure from complete deterministic knowledge of the relevant system (Walker,
2003). Three different types of uncertainty are
1. Natural variability: Natural variability (e.g. day-to-day variation, decade-to-decade variation) is
the temporal variation of the atmosphere–ocean system around a mean state due to natural (not
manmade) processes. Variability may be “internal” (due to natural internal processes within the
climate system,e.g. El Niño), or “external” (due to variations in natural forcing outside the climate
system, from e.g. solar activity or volcanoes). Examples of natural processes affecting climate.
2. Scenario uncertainty:Scenario uncertainty arises because we do not know what the future will be
like; and there are no physical laws that can be used to calculate it. Instead we have to assume
different socioeconomic developments. These assumptions are made to span the range of possible
futures, not to predict them.
3. Model uncertainty: Model uncertainty is the incomplete knowledge about the climate system,
quantified with the help of a large number of climate models that simulate the future climate for
the same emission scenario. Climate models describe atmospheric, land-, seabased and other
environmental processes with physical equations and through parameterizations.
Discuss some of the major sources of uncertainty in climate projections
There are three main sources of uncertainty in projections of climate: that due to future emissions
(scenario uncertainty),due to internalclimate variability, and due to inter-modeldifferences.Internal
variability is roughly constant through time, and the other uncertainties grow with time, but at different
rates.Although there is no perfectway to cleanly separate these uncertainties, different methods have given
similar results. The key messages are that resolving inter-model differences could reduce uncertainty
significantly, but there is still a large irreducible uncertainty due to climate variability in the near-term and,
particularly for temperature, future emissions scenarios in the long-term.
Explain why scientists run multiple experiments with climate models// Paraphrase what the
purpose of a climate change scenario is and the need for multiple different scenarios

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A climate scenario is a plausible image of a future climate based on knowledge of the past climate and
assumptions on future change (on increase of greenhouse gas (GHG) concentrations). They are constructed
to estimate the impact of climate change .Climate models are used by scientists to answer many different
questions, including why the Earth’sclimate is changing and how it might change in the future if greenhouse
gas emissions continue.Models can help work out what has caused observed warming in the past, as well
ashow big a role natural factors play compared to human factors. Scientists run many different experiments
to simulate climates of the past, present and future. These model ensembles allow researchers to examine
differences between climate models, as well as better capture the uncertainty in future projections.
Experiments that modellers do as part of the Coupled Model Intercomparison Projects (CMIPs) include:
Why do scientists use scenarios?
 By constructing scenarios based on different assumptions, we can quantify the impact
of uncertainties about climate change. This can be uncertainties about the emissions of GHG, but
also uncertainties about how the climate will react to an increase in GHG.
 Scenarios are plausible and consistent images ofthe future, based on our current knowledge of
the climate system and about potential changes in GHG concentrations.
 Scenarios help us to understand climate change impacts and determine key vulnerabilities.
They can also be used to evaluate adaptation strategies.
These scenario are:
1. Synthetic scenarios: particular climate elements are changed by a realistic arbitrary amount, for
example, adjustment of temperature variable by +1, +2, and +3°C from a reference state,without
the use of climate models.
2. Analogue scenarios: using a temporal analogue (using past climate record) or a spatial analogue to
represent the possible future climate.
3. Climate model based scenarios: use outputs from Global Climate Models (GCM) or Regional
Climate Models (RCM). They usually are constructed by adjusting a baseline climate (typically
based on regional observations of climate over a reference period) by the absolute or proportional
change between the simulated present and future climates.
Describe what equilibrium climate sensitivity is and its currently projected range
The equilibrium climate sensitivity (ECS) is the temperature increase that would result from sustained
doubling of the concentration of carbon dioxide in Earth's atmosphere, after the Earth's energy budget and
the climate system reach equilibrium. The wide range of estimates of climate sensitivity is driven by
uncertainties in climate feedbacks, including how water vapour, clouds, surface reflectivity and other
factors will change as the Earth warms. Climate feedbacks are processes that may amplify (positive
feedbacks) or diminish (negative feedbacks) the effect of warming from increased CO2 concentrations or
other climate forcings – factors that initially drive changes in the climate.
Define what a tipping point is and provide some examples
The IPCC AR5 defines a tipping point as an irreversible change in the climate system. It states that the
precise levels of climate change sufficient to trigger a tipping point remain uncertain, but that the risk
associated with crossing multiple tipping point’s increases with rising temperature. Examples are the
disappearance of Arctic sea ice, the establishment of woody species in tundra, permafrost loss, the collapse
of the monsoon of South Asia.

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Articulate the purposes for using statistical downscaling
Statistical downscaling encompasses the use of various statistics-based techniques to determine
relationships between large-scale climate patterns resolved by global climate models and observed local
climate responses. These relationships are applied to GCM results to transform climate model outputs into
statistically refined products, often considered to be more appropriate for use as input to regional or local
climate impacts studies.
Statistical downscaling (advantages ) Dynamical downscaling (advantages )
1: computationally cheap
2: can be applied to large number of ensemble realizations
3: requires a limited number of input GCM fields at
relatively coarse temporal resolution
4: can downscale GCM simulated variables directly into
impacts relevant parameters
1: transformation factor based on understood numerical
methods
2: full set of internally consistent downscaled variables
3: not (directly ) dependent of availability of observations
4: can encompass non stationary relationship between large
and small scales as well as potential changes in regional
forcing
Statistical downscaling (limitations ) Dynamical downscaling (limitations )
1:assumes stationary of large small scale transformation
factors
2: transformation factors not always based on well
understood physical mechanisms
3: doesn’t capture systematic changes in regional forcing
4: downscaled variables limited in number and not always
internally consistent
5: dependent on the availability and quality of regional
observations
1: computationally expensive. therefore difficult to apply to
a large ensemble of hindcasts
2: requires a large amount of driving GCM data
3: systematic error also exist in RCMs
4: doesn’t produces impact relevant parameters
Describe the main benefits and limitations of statistical downscaling
Benefits limitations
1: it is easy to apply ( 20 GCM)
2: it accounts for different corrections in different time
windows
3: it can typically be performed on one computer
4: can be flexibly crafted for a specific purpose
5: it incorporates historical information
1: requires a long observational record to build statistical
relationship ( 20-50 years )
2: assumes that the relationships will be valid in the future
3: results can be affected by the errors of the global climate
models
Distinguish between some of the various statistical downscaling approaches
1. Weather generators: random generators of realistic looking ‘weather’
sequences/events conditioned in their occurrence/location statistics by the GCM
large-scale. e.g. daily weather generators: Markov chain approaches.
2. Transfer functions: a (set of) predictive relationship(s) between the large-scale
and the target (local-regional) small scale. Such relationships are generally built
up by (lagged/non-lagged multiple regression) analysis of observed large-scale
climate conditions and local-regional scale (near-surface) observations.
3. Weather typing: based on traditional synoptic climatology (including analogs
and phase space partitioning) that relate a given atmosphere/ocean state to a set
of local climate variables (e.g. Lamb weather types).

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Articulate the purposes for using regional climate models
Regional climate models are complementary to global climate models. A typical use of regional climate
models is to add further detail to global climate analyses or simulations, or to study climate processes in
more detail than global models allow. RCMs can then resolve the local impacts given small scale
information about orography (land height) and land use, giving weather and climate information at
resolutions as fine as 50 or 25km.
Describe the main benefits and limitations of using a regional climate model
Discuss how global and regional climate models are connected (or not connected)

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