Watershed models simulate natural processes like water flow, sediment movement, and nutrient cycling within watersheds. They also quantify the impacts of human activities on these processes. Watershed models come in different forms with varying complexity and computational requirements. They are used to address a wide range of environmental and water resource issues like flooding, erosion, pollution, and more. Watershed models can be classified based on how they acquire and treat data, and whether they take a lumped or distributed approach. The key steps in developing and applying a watershed model include establishing objectives, model design, calibration, validation, application, and accounting for uncertainty.

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Introduction to modelling
1.1. Introduction of watershed models
Watershed models simulate natural processes of the flow of water, sediment, chemicals,
nutrients, and microbial organisms within watersheds, as well as quantify the impact of
human activities on these processes. Simulation of these processes plays a fundamental role in
addressing a range of water resources, environmental, and social problems. The current
generation of watershed models is quite diverse and varies significantly in sophistication and
data and computational requirements. Newly emerging technologies are being increasingly
integrated into watershed models. This chapter introduces some of these technologies as well
as the theme of the book.
A hydrological model is a simplified simulator of the complex hydrological system. The main
problem in modelling the hydrological processes based on their physical governing laws is the
variability in space and time of the parameters that control these processes (Porter and
Mcmahon, 1971). In the first generation hydrological models, this had been dealt with by
assuming homogeneous properties for the hydrological processes over the whole catchment’s
area or for subdivisions of the catchment’s area (More & al, 1993).
Over the last two decades, the need for hydrological models has shifted from generating flow
hydrographs into predicting the effects of the actual landuse practices on water resource or
estimating the distributed surface and subsurface flow. These needs require better description
of the catchment’s topography and the distributed properties of the hydrological process
acting on it.
Various techniques have been used for hydrological modelling systems. Simulation is one of
the techniques where a system is represented as a model and its behaviour is studied. Digital
simulation is needed in watershed research because it is a complex system to be analysed by
exact mathematical techniques. In digital simulation system models are developed by a
number of mathematical expressions that represents the various hydrological processes of the
system and simulation is done by the integration of these processes in order to produce the
expected output.
1.2. Applications of watershed models
Today it is difficult to think of an environmental or a water resources problem whose solution
does not involve application of some kind of a watershed model. Indeed watershed models
have become a main tool in addressing a wide spectrum of environmental and water resources
problems, including water resources planning, development, design, operation, and
management. Flooding; droughts; upland erosion; streambank erosion; coastal erosion;
sedimentation; nonpoint source pollution; water pollution from industrial, domestic,
agricultural, and energy industry sources; migration of microbes; salinity and alkalinity of
soils; deterioration of lakes; acidn precipitation; disappearance of beaches; desertification of
land; degradation of land; decay of rivers; irrigation of agricultural lands; proper management
of water resources; conjunctive use of surface and groundwater; reliable design of hydraulic
structures; and justifying the need for river training works are some of the critical

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environmental problems which are solved using watershed models. These models are also
employed in military operations. For example, the U.S. Department of Defense (DOD)
employs watershed simulation to support military as well as civilian operations, in
environmental management of approximately 200,000 km2 of land on military installations in
the U.S., and flood control and river improvement (Downer and Ogden, 2004). Watershed
models help understand dynamic interactions between climate and land surface hydrology.
For example, vegetation, snow cover, and the permafrost active layer are some of the features
which are quite sensitive to the lower boundary of the atmospheric system. The water and
heat transfer between the land surface and atmosphere significantly influence hydrologic
characteristics and yield, in turn, agricultural productivity is made possible by the use of
watershed models. Water allocation requires integration of watershed models with models of
physical habitat, biological populations, and economic response. Estimating the value of
instream water use allows recreational, ecological, and biological concerns to compete with
traditional consumptive uses, such as agriculture, hydropower, municipality, and industry
(Hickey and Diaz, 1999). Watershed models are utilized to quantify the impacts of watershed
management strategies linking human activities within the watershed to water quantity and
quality of the receiving stream or lake (Mankin et al., 1999; Rudra et al., 1999) for
environmental and water resources protection.
1.3. Inventory of watershed models
In 1991, the Bureau of Reclamation prepared an inventory of 64 watershed hydrology models
classified into 4 categories, and the inventory has been updated over the past several years.
Burton (1993) compiled the Proceedings of the Federal Interagency Workshop on Hydrologic
Modeling Demands for the 1990s, which contains several important watershed hydrology
models. Singh (1995b) edited a book that summarized 26 popular models from around the
globe. The Subcommittee on Hydrology of the Interagency Advisory Committee on Water
Data (1998) published proceedings of the First Federal Interagency Hydrologic Modeling
Conference which contains many popular watershed hydrology models developed by federal
agencies in the United States. Wurbs (1998) listed a number of generalized water resources
simulation models in seven categories and discussed their dissemination. Singh and Frevert
(2002a, b) edited two books that contain 38 models. There are still some popular models
which have not yet been presented under one cover, and that constitutes the rationale for
preparing this book.
1.4. Development of watershed models
The digital revolution started with the advent of computers in the 1960s. The power of
computers has since increased exponentially. The digital revolution also triggered two other
revolutions, namely, numerical simulation and statistical simulation. As a result, advances in
watershed models have occurred at an unprecedented pace since the groundbreaking
development of the Stanford Watershed Model (SWM) by Crawford and Linsley in 1966.
SWM was the first attempt to model virtually the entire hydrologic cycle. During the decades
of the 1970s and the 1980s, a number of mathematical models were developed. Indeed there
has been a proliferation of watershed hydrology models since, with growing emphasis on
physically based models. Examples of such watershed hydrology models are Storm Water
Management Model (SWMM) (Metcalf and Eddy, Inc., 1971), Precipitation-Runoff Modeling
System (PRMS) (Leavesley et al., 1983), National Weather Service (NWS) River Forecast
System (Burnash et al., 1973), Streamflow Synthesis and Reservoir Regulation (SSARR)
(Rockwood, 1982), Systeme Hydrologique Europeen (SHE) (Abbott et al., 1986a, b),
TOPMODEL (Beven and Kirkby, 1979), Institute of Hydrology Distributed Model (IHDM)
(Morris, 1980), and others. All of these models have since been significantly improved.

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SWM, now called Hydrological Simulation Program-Fortran (HSPF), is far more
comprehensive than its original version. SHE has been extended to include sediment transport
and is applicable at the scale of a river basin (Bathurst et al., 1995). TOPMODEL has been
extended to contain increased catchment information, more physically based processes, and
improved parameter estimation. Development of new models or improvement of the
previously developed models continues today. Today, many federal agencies in the United
States have their own models or some variants of models developed elsewhere. Singh and
Frevert (2002c) traced the evolution of watershed models before and during the computer era.
1.5. Classifications of Hydrological Model
Hydrological models can be classified in different ways. The first classification is based on
data acquisition; therefore, it can be categorized into two types of models: lumped models and
distributed models (Vijay P, 1995).
 Lumped model: generally expressed by ordinary differential equations taking no
account of spatial variability of processes, input, boundary conditions and system
(watershed) geometric characteristics. In most lumped models, some processes are
described by differential equations based on simplified hydraulic laws, and other
processes are expressed by empirical algebraic equations. Examples of lumped models
are HEC-1 (Hydrologic Engineering Center, 1981), HYMO (Williams and Hann,
1972), RORB (Laurenson and Mein, 1983), SSARR (US. Army Engineer, 1972), tank
model (Sugawara et al, 1984).
 Distributed model: taking an explicit account of spatial variability of processes, input,
boundary conditions, and/or system (watershed) characteristics. Obviously, a lack of
data prevents such a general formulation of distributed models. In a majority cases the
system (watershed) characteristic are lumped and even some of the boundary
conditions are lumped, but some of the process are directly linked to the output are
distributed. Examples of distributed models are SHE (Abbott, et al.; 1986a, 1986b),
IHM (Morris, 1980, SWMM (Metcalf and Eddy, Inc., et al., 1971) NWSRFS
(Hydrological Research Laboratory, 1972).
Figure 1-1-Classification of models based on data acquisition
According to the data treatment, the models can be also classified as following (Singh, 1988):
 Deterministic: all input, parameters, and processes in a model are free of random
variation and known with certainty.
Data Acquisition
DISTRIBUTEDLUMPED

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 Stochastic: probabilistic refers to the model governed by probability. The behaviour
of a probabilistic system cannot be predicted exactly but the probability of certain
behaviours is known. Such systems may be simulated using pseudo-random numbers.

 Mixed: defined as the model combined of deterministic and stochastic.
Figure 1-2-Classification based on data treatment
If all of the components of a model are deterministic, the watershed model is deterministic but
if all the components of the model are stochastic, the model is quasi-stochastic. There is also
the combination of deterministic and stochastic components and it is called stochastic-
deterministic or mixed model. A vast majority of the models are deterministic, and virtually
no model is fully stochastic. In some cases, only some parts of the model are described by the
laws of probability, and other pares are fully deterministic. It is then fair to characterize them
as quasi-deterministic or quasi-stochastic.
The concerned model classification is also classified into two categories (Daniela, 2004) as
followings:
 Conceptual model: refers to the models using generally semi-empirical equations
which have a physical basis. Their models parameters could not be estimated from
field data alone but they have to be calibrated (Refsgaard and Storm (1996)). Different
kinds of conceptual models have been used through the world such as Sacramento
Model in USA, the tank model used in Japan, the HBV model used in Scandinavian
countries or TOPMODEL (Beven and Kirkby (1979)) developed in England.
 Physically based model: defined as a model which uses physical laws and equations
to describe the hydrological processes. In the same context of the physical laws
describing hydrological processes and in order to simplify resolution of too complex
physical equations. We can work with simpler hypothesis and then we can speak of
semi-physical hydrological models.
The classifications of models have been differently categorized from various authors.
However, regarding to the above classifications, data acquisition and data treatment are the
better way of classification because those are the ways to work with the data which can be
easy to put into categories.
MIXEDSTOCHASTIC DETERMINISTIC
DISTRIBUTEDLUMPED
Data Treatment

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1.6. Purposes of a Modelling Protocol
 Establish the purpose of the model
 Develop a conceptual model of the systems
 Select the governing equation and a computer code
 Design the model
 Calibrate the designed model (most models)
 Determine the effects of uncertainty on model results
 Verify designed and calibrated Model
 Predict results based on calibrated model
 Determine the effect of uncertainty on model predictions
 Present modelling design and results
 Post audit and redesign model as necessary
1.7. Model calibration
Calibration means adjustment of the model parameters between the observed and simulated
responses and the result is different as small as possible. This can be done manually (trial and
error method) or automatically by searching an optimal value of a given criterion (often called
objective function), which described the fit between observed and simulated data. The value
of a model's predictions is only as good as the model's ability to be effectively calibrated.
1.8. Model parameters
Many hydrologic models are based on conceptual representations of the physical processes
which govern the flow of water through and over the soil. Therefore, there are several
parameters such as physical parameters representing physically measurable properties of the
watershed and process parameters representing watershed properties which are not directly
measurable.
1.9. Model validation
Validation is the process of assessing the performance of a calibrated model over a set of
event period that are distinct from the event period used to calibrate the model. Validation of
the overall set of models tests the effects of compounding errors.
In order to test the ability of the model to predict future behaviours, validation requires
comparing the model predictions with information other than that used in estimating the
model. This step is typically an iterative process linked to model calibration. It involves
checking the model results against observed data and adjusting parameters until model results
fall within an acceptable range of error. If the only way that a model will replicate observed

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data is through the use of unusual parameters and procedures or localized "quick-fixes", then
it is unlikely that the model can reliably forecast future conditions.
1.10.Model Application
Although the model may replicate base year conditions, the application of the model to future
year conditions and policy options requires checking the reasonableness of projections, so
there is a link between application and validation as well. The sensitivity of the models in
response to system or policy changes is often the main issue in model application.
1.11.Model uncertainty
Uncertainty in modelling can happen from errors in model structure and in parameter
estimation. There is not only one single parameter which leads to an optimum but several sets
of parameters lead to equivalent performances. Due to these reasons, the uncertainty
associated with the estimated model parameters became a very important issue in order to
assess the accuracy of a given parameter set. For operational purposes, the uncertainty became
very important to assess the accuracy of model-simulated outputs. The calibration of the
hydrological modelling became often associated with the uncertainty.
According to Refsgard and Storm (1996), four main sources of uncertainty have been
considered as following:
 Random or systematic errors in data input (i.e. precipitation, temperature)
 Random or systematic errors in the recorded data (water level records, rain curves,
discharge data, groundwater levels, soil moisture levels)
 Errors due to non-optimal parameters values
 Errors due to non-optimal structure
To solve the problem of uncertainty associated with model parameters and model outputs,
different statistical have been used. The most well known methods are Monte Carlo method
and the Bayesian method such as GLUE (Generalized likelihood uncertainty Estimation) and
MCMC (Monte-Carlo Markow Chains).
1.12. Uses of models
Models serve three main purposes (Barton, 1997) as following:
Firstly, they give us a framework to assemble our process understanding and to explore the
implied system behaviours that come from that understanding. We can examine the model
results, and consider whether they concur with our overall system analysis or not. If not, we
have a structured framework to analyse whether it is our model or our overall understanding,
or both, that is in error.

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The second main use of a model is as a mechanism for testing data, to check for
inconsistencies and errors, and to fill in missing information. It also gives us a method to
explore the implications of our measurements. In fact, this may be the most useful function of
models, because they help structure scientific enquiry that can elucidate further details behind
observations. These first two uses of models fall into the categories of scientific and
engineering discussed by Passioura (1996). If we intend using models as scientific tools, we
need to ensure that we actually use them to test hypotheses, and not just play computer games
that reinforce our understanding and the conjectures built into the models. The engineer will
take a model to solve some day to day problem within well defined boundary conditions for
which the responses are well understood, and the model essentially provides a decision
support system for them and their client. It gives a semblance of authority and a legally
defendable recommendation.
The third use of models, and probably the most widely publicised and ‘‘commercial’’ use, is
to explore scenario options. These may be options for management of a system or exploring
possible outcomes under a range of different input conditions, perhaps depending on future
climate, political or economic scenarios. However, unless these scenarios are well constrained
within known data boundaries, it is my contention that these activities should be confined
largely to stimulate discussion, should always be tempered by some healthy scepticism, and
retain due regard for our understanding of the whole system being considered.
Major References:
- Oeurng Chantha (2006). Comparative studies of models and application of Model Maker for
conceptual hydrological model development. Gembloux Agricultural University, Master thesis.
- Vijay P. Singh (2006, edited). Watershed Models. Taylor & Francis Group 6000 Broken Sound
Parkway NW, Suite 300.