Hydrological modelling i5

Prepared by Dr. Oeurng Chantha

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


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.


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

DISTRIBUTED LUMPED


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.

MIXED STOCHASTIC DETERMINISTIC

DISTRIBUTED LUMPED

Data Treatment

http://foldoc.org/?pseudo-random


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


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.


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.