Hydrological Modelling in Arid and SemiArid Areas

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Hydrological Modelling in Arid and Semi-Arid Areas

Arid and semi-arid regions are defined as areas where water is at its most scarce. The hydrological

regime in these areas is extreme and highly variable, where flash floods from a single large storm

can exceed the total runoff from a sequence of years. Globally, these areas face the greatest

pressures to deliver and manage freshwater resources. Problems are further exacerbated by

population growth, increasing domestic water use, expansion of agriculture, pollution, and the

threat of climate change. However, there is little guidance on the hydrology of arid areas, and none

on the decision support tools that are needed to underpin flood and water resource management.

As a result, UNESCO initiated the Global Network for Water and Development Information

for Arid Lands (G-WADI), and arranged a workshop of the world’s leading experts to discuss

the hydrological modelling tools required to support water management in these areas. This

book presents chapters from contributors to the workshop. It includes case studies from the

world’s major arid regions, including Africa, the Middle East, the USA, India, and Australia, to

demonstrate model applications. It contains web links to tutorials and state-of-the-art modelling

software. This volume will be valuable for researchers and engineers working on the water

resources of arid and semi-arid regions.

Howard Wheater is Head of Environmental and Water Resource Engineering in the Depart￾ment of Civil and Environmental Engineering at Imperial College London, and co-chair of

G-WADI.

Soroosh Sorooshian is Distinguished Professor of Civil and Environmental Engineering

and Director of the Centre for Hydrometeorology and Remote Sensing at the Henry Samueli

School of Engineering, University of California at Irvine.

K. D. Sharma is Director of the National Institute of Hydrology, India, and a member of the

G-WADI Steering Committee. He is also a Visiting Fellow at the Chinese Academy of Sciences

and the Winand Staring Centre, the Netherlands.

INTERNATIONAL HYDROLOGY SERIES

The International Hydrological Programme (IHP) was established by the United Nations Educational, Scientific and Cultural

Organization (UNESCO) in 1975 as the successor to the International Hydrological Decade. The long-term goal of the IHP is to

advance our understanding of processes occurring in the water cycle and to integrate this knowledge into water resources management.

The IHP is the only UN science and educational programme in the field of water resources, and one of its outputs has been a steady

stream of technical and information documents aimed at water specialists and decision-makers.

The International Hydrology Series has been developed by the IHP in collaboration with Cambridge University Press as a major

collection of research monographs, synthesis volumes and graduate texts on the subject of water. Authoritative and international in

scope, the various books within the series all contribute to the aims of the IHP in improving scientific and technical knowledge of

fresh-water processes, in providing research know-how and in stimulating the responsible management of water resources.

editorial advisory board

Secretary to the Advisory Board

Dr Michael Bonell Division of Water Sciences, UNESCO, 1 rue Miollis, Paris 75732, France

Members of the Advisory Board

Professor B. P. F. Braga Jr Centro Technologica de Hidr ´ aulica, S ´ ao Paulo, Brazil ˜

Professor G. Dagan Faculty of Engineering, Tel Aviv University, Israel

Dr J. Khouri Water Resources Division, Arab Centre for Studies of Arid Zones and Dry Lands, Damascus, Syria

Dr G. Leavesley US Geological Survey, Water Resources Division, Denver Federal Center, Colorado, USA

Dr E. Morris Scott Polar Research Institute, Cambridge, UK

Professor L. Oyebande Department of Geography and Planning, University of Lagos, Nigeria

Professor S. Sorooshian Department of Civil and Environmental Engineering, University of California, Irvine, California, USA

Professor K. Takeuchi Department of Civil and Environmental Engineering, Yamanashi University, Japan

Professor D. E. Walling Department of Geography, University of Exeter, UK

Professor I. White Centre for Resource and Environmental Studies, Australian National University, Canberra, Australia

titles in print in the series

M. Bonell, M. M. Hufschmidt, and J. S. Gladwell Hydrology and Water Management in the Humid Tropics: Hydrological Research

Issues and Strategies for Water Management

Z. W. Kundzewicz New Uncertainty Concepts in Hydrology and Water Resources

R. A. Feddes Space and Time Scale Variability and Interdependencies in Hydrological Processes

G. Dagan and S. Neuman Subsurface Flow and Transport: A Stochastic Approach

J. C. van Dam Impacts of Climate Change and Climate Variability on Hydrological Regimes

J. J. Bogardi and Z. W. Kundzewicz Risk, Reliability, Uncertainty and Robustness of Water Resource Systems

G. Kaser and H. Osmaston Tropical Glaciers

I. A. Shiklomanov and J. C. Rodda World Water Resources at the Beginning of the Twenty-First Century

A. S. Issar Climate Changes during the Holocene and their Impact on Hydrological Systems

M. Bonell and L. A. Bruijnzeel Forests, Water and People in the Humid Tropics: Past, Present and Future Hydrological Research for

Integrated Land and Water Management

F. Ghassemi and I. White Inter-Basin Water Transfer: Case Studies from Australia, United States, Canada, China and India

K. D. W. Nandalal and J. J. Bogardi Dynamic Programming Based Operation of Reservoirs: Applicability and Limits

H. S. Wheater, S. Sorooshian, and K. D. Sharma Hydrological Modelling in Arid and Semi-Arid Areas

Hydrological Modelling in Arid and

Semi-Arid Areas

Howard Wheater

Imperial College of Science, Technology and Medicine, London

Soroosh Sorooshian

University of California, Irvine

K. D. Sharma

National Institute of Hydrology, Roorkee, India

CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press

The Edinburgh Building, Cambridge CB2 8RU, UK

First published in print format

ISBN-13 978-0-521-86918-8

ISBN-13 978-0-511-37710-5

© Cambridge University Press 2008

2007

Information on this title: www.cambridge.org/9780521869188

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relevant collective licensing agreements, no reproduction of any part may take place

without the written permission of Cambridge University Press.

Cambridge University Press has no responsibility for the persistence or accuracy of urls

for external or third-party internet websites referred to in this publication, and does not

guarantee that any content on such websites is, or will remain, accurate or appropriate.

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

eBook (EBL)

hardback

Contents

List of contributors page vi

Preface viii

Acknowledgements ix

1 Modelling hydrological processes in arid and

semi-arid areas: an introduction 1

H. S. Wheater

2 Global precipitation estimation from satellite imagery using

artificial neural networks 21

S. Sorooshian, K.-L., Hsu, B. Imam, and Y. Hong

3 Modelling semi-arid and arid hydrology and water

resources: The southern Africa experience 29

D. A. Hughes

4 Use of the IHACRES rainfall-runoff model in

arid and semi-arid regions 41

B. F. W. Croke and A. J. Jakeman

5 KINEROS2 and the AGWA modelling Framework 49

D. J. Semmens, D. C. Goodrich, C. L. Unkrich,

R. E. Smith, D. A. Woolhiser, and S. N. Miller

6 Ephemeral flow and sediment delivery modelling in the

Indian arid zone 69

K. D. Sharma

7 The modular modelling system (MMS): a toolbox

for water and environmental resources

management 87

G. H. Leavesley, S. L. Markstrom, R. J. Viger,

and L. E. Hay

8 Calibration, uncertainty, and regional analysis of conceptual

rainfall-runoff models 99

H. S. Wheater, T. Wagener, and N. McIntyre

9 Real-time flow forecasting 113

P. C. Young

10 Real-time flood forecasting: Indian experience 139

R. D. Singh

11 Groundwater modelling in hard-rock terrain in

semi-arid areas: experience from India 157

S. Ahmed, J.-C. Marechal, E. Ledoux, ´

and G. de Marsily

Appendix Access to software and data products 191

Index 193

v

Contributors

S. Ahmed

National Geophysical Research Institute,

Indo-French Centre for Groundwater Research,

Hyderabad, India

B. F. W. Croke

Integrated Catchment Assessment and

Management Centre, Centre for Resource and Environmental

Studies, The Australian National University,

Canberra, Australia

G. de Marsily

Universit´e Pierre et Marie Curie – Paris VI,

UMR CNRS Sisyphe,

Paris, France

D. C. Goodrich

USDA Agricultural Research Service,

Southwest Watershed Research Center,

Tucson, Arizona, USA

L. E. Hay

USGS, WRD,

Denver, Colorado, USA

Y. Hong

Department of Civil and Environmental Engineering,

University of California,

Irvine, California, USA

K.-L. Hsu

Department of Civil and Environmental Engineering

University of California, Irvine, California, USA

D. A., Hughes

Institute for Water Research, Rhodes University,

Grahamstown, South Africa

B. Imam

Department of Civil and Environmental Engineering,

University of California, Irvine, California, USA

A. J. Jakeman

Integrated Catchment Assessment and Management Centre,

Centre for Resource and Environmental Studies,

The Australian National University,

Canberra, Australia

G. Leavesley

USGS, WRD,

Denver, Colorado, USA

E. Ledoux

Ecole Nationale Sup´erieure des Mines de Paris,

UMR CNRS Sisyphe, Fontainebleau, France

J.-C. Mar´echal

Bureau de Recherches G´eologiques et Mini`eres,

Montpellier, France

S. L. Markstrom

USGS, WRD,

Denver, Colorado, USA

N. McIntyre

Department of Civil & Environmental Engineering,

Imperial College,

London, UK

S. N. Miller

University of Wyoming,

Department of Natural Resources,

Laramie, Wyoming, USA

D. J. Semmens

USEPA/ORD/NERL,

Landscape Ecology Branch,

Las Vegas, Nevada, USA

vi

LIST OF CONTRIBUTORS vii

K. D. Sharma

National Institute of Hydrology,

Jalvigyan Bhawan,

Roorkee, India

R. D. Singh

National Institute of Hydrology

Jalvigyan Bhawan,

Roorkee, India

R. E. Smith

USDA Agricultural Research Service,

Fort Collins, Colorado, USA

S. Sorooshian

Center for Hydrometeorology and Remote Sensing (CHRS),

Department of Civil and Environmental Engineering,

University of California,

Irvine, California, USA

C. L. Unkrich

USDA Agricultural Research Service,

Southwest Watershed Research Center,

Tucson, Arizona, USA

R. J. Viger

USGS, WRD,

Denver, Colorado, USA

T. Wagener

Civil and Environmental Engineering,

The Pennsylvania State University,

University Park, Pennsylvania, USA

H. S. Wheater

Department of Civil and Environmental Engineering,

Imperial College,

London, UK

D. A. Woolhiser

USDA Agricultural Research Service,

Fort Collins, Colorado, USA

P. Young

Centre for Research on Environmental Systems & Statistics,

CRES/IEBS,

Lancaster University, Lancaster, UK

Preface

This book is the product of an international workshop sup￾ported by UNESCO and co-sponsors under the G-WADI initiative.

G-WADI is UNESCO’s Global Network for Water and Develop￾ment Information for Arid Lands. It has the strategic objective

of strengthening global capacity to manage water resources in

arid and semi-arid areas and seeks to provide a global forum for

the exchange of experience, information, and tools. Its specific

objectives include:

improved understanding of the special characteristics of

hydrological systems and water management needs in arid

areas;

capacity building of individuals and institutions;

broad dissemination of understanding of water in arid zones

to the user community and the public;

sharing data and exchanging experience to support research

and sound water management;

raising awareness of advanced technologies for data provi￾sion, data assimilation, and system analysis;

promoting integrated basin management and the use of

appropriate decision support tools.

Information on G-WADI products and a news-watch service can

be found on the G-WADI web-site (www.g-wadi.org).

Hydrological modelling is playing an increasingly important

role in the management of catchments with respect to floods, water

resources, water quality, and environmental protection. G-WADI

identified a particular gap in the information available to support

hydrological modelling for arid and semi-arid areas and hence

designed an international workshop, bringing together some of

the world’s leading specialists in data products, modelling and

arid-zone hydrology, to provide state-of-the-art material to work￾shop participants from arid regions world-wide, including South

America, the Middle East, North Africa, Southern Africa, Aus￾tralia and, particularly, Asia, where the workshop was hosted.

This book is a product of that workshop, held in Roorkee, India in

March 2005, and the material, comprising state-of-the-art reviews

and case studies, is intended to provide insight and tools to help

practitioners world-wide. The focus of the workshop was on the

modelling of surface water systems, and a specialist workshop on

groundwater modelling is planned for 2007. However, in response

to workshop requests, a chapter on groundwater modelling is

included in this book for completeness.

The structure of the book is as follows:

Chapter 1 provides a review of some of the special hydrological

features of arid areas and an introduction to modelling concepts,

and Chapter 2 introduces new data products, focusing on satellite￾derived estimates of precipitation.

Experience of hydrological modelling in southern Africa is

reported in Chapter 3, and in Australia in Chapter 4, together with

an introduction to the IHACRES software. In Chapter 5 the USDA

KINEROS model – one of the few models specifically designed to

represent arid-zone processes – is presented, in its current GIS for￾mat, with applications from the arid United States. In Chapter 6

ephemeral flow and sediment modelling is discussed, based on

Indian experience. Chapter 7 introduces the USGS Modular Mod￾elling System, which incorporates a varied suite of models and

support systems, with applications to North Africa and China,

and in Chapter 8 tool-boxes for stochastic analysis are discussed,

together with the problem of model regionalization – i.e., the

application of models to ungauged catchments.

In Chapters 9 and 10 the focus is on the problem of forecasting

floods in real time. The current state-of-the art of time-series mod￾els is presented in Chapter 9, with an example from a semi-arid

Australian catchment. In Chapter 10 Indian flooding problems are

reviewed and the Indian flood forecasting experience is reported,

largely based on traditional methods, but rapidly being updated

with more modern modelling methods and communications

technology.

Issues of groundwater modelling are addressed in Chapter 11,

with examples drawn from India, and the book concludes with

a summary of web-site access to data products, modelling tools,

and tutorials.

viii

Acknowledgements

The editors particularly wish to thank the contributors to the book

for their enthusiastic input to both the workshop and the book,

the sponsors of the workshop, without whom none of this activ￾ity would have been possible, and the workshop attendees, who

provided an informed audience and helpful feedback. Financial

support for the contributors, regional representatives and inter￾national organization was provided by UNESCO’s International

Hydrology Programme and the UK Government’s Department for

International Development. We are indebted to the National Insti￾tute of Hydrology, Roorkee, who provided local organization and

superb hospitality, together with their sister institution IIT Roor￾kee. Support for participants from the Asian region to attend the

workshop was provided by UNESCO’s regional offices in Delhi

and Tehran.

ix

1 Modelling hydrological processes in arid and semi-arid

areas: an introduction to the workshop

H. S. Wheater

1.1 INTRODUCTION

In the arid and semi-arid regions of the world, water resources are

limited, and under severe and increasing pressure due to expand￾ing populations, increasing per capita water use and irrigation.

Point and diffuse pollution, increasing volumes of industrial and

domestic waste, and over-abstraction of groundwater provide a

major threat to those scarce resources. Floods are infrequent, but

extremely damaging, and the threat from floods to lives and infras￾tructure is increasing, due to urban development. Ecosystems are

fragile, and under threat from groundwater abstractions and the

management of surface flows. Added to these pressures is the

uncertain threat of climate change. Clearly, effective water man￾agement is essential, and this requires appropriate decision support

systems, including modelling tools.

Modelling methods have been widely used for over 40 years

for a variety of purposes, but almost all modelling tools have

been primarily developed for humid area applications. Arid and

semi-arid areas have particular challenges that have received little

attention. One of the primary aims of this workshop is to bring

together world-wide experience and some of the world’s leading

experts to provide state-of-the-art guidance for modellers of arid

and semi-arid systems.

The development of models has gone hand-in-hand with devel￾opments in computing power. While event-based models origi￾nated in the 1930s and could be used with hand calculation, the

first hydrological models for continuous simulation of rainfall￾runoff processes emerged in the 1960s, when computing power

wassufficient to represent all of the land-phase processes in a sim￾plified, “conceptual” way. Later, in the 1970s and 1980s, increases

in power enabled “physically based” hydrological models to be

developed, solving a coupled set of partial differential equations to

represent overland, in-stream, and subsurface flow and transport

processes, together with evaporation from land and water sur￾faces. And currently, global climate models are able to represent

the global hydrological cycle with simplified physics-based

models. In parallel, recent developments in computer power pro￾vide the ability to use increasingly powerful methods for the analy￾sis of model performance and to specify the uncertainty associated

with hydrological simulations. There have, as a result, been impor￾tant developments in our understanding of modelling strengths

and limitations. The workshop will present a range of modelling

approaches and introduce methods of uncertainty analysis.

The relationship between models and data is fundamental to

the modelling task. Current technology and computing power can

provide powerful pre- and post-processors for hydrological mod￾els through Geographic Information Systems, linking with digital

data sets to provide a user-friendly modelling environment. Some

of these methods will be demonstrated here, and an important issue

for discussion is the extent to which such methods are applicable

to data-sparse environments, and for countries where the under￾lying digital data may be hard to obtain. Global developments in

remote sensing, coupled with modelling and data assimilation, are

providing new sources of information. For example, precipitation

estimates for mid-latitudes are now available in near real-time;

remote sensing of water body elevation is approaching the point

where resolution is useful for real-time hydrological modelling.

Again, the workshop will illustrate new data products and discuss

their applicability (see Chapter 2 by Sorooshian et al.).

This introductory chapter aims to set the scene with a per￾spective on the strengths and weaknesses of alternative modelling

approaches, the special features of arid areas, and the consequent

modelling challenges.

1.2 RAINFALL-RUNOFF MODELLING

The book presupposes a basic understanding of modelling, and

for those requiring more introductory material, the text book by

Beven (2000) provides an excellent introduction, and several

Hydrological Modeling in Arid and Semi-Arid Areas, ed. Howard Wheater, Soroosh Sorooshian, and K. D. Sharma. Published by Cambridge University Press.

C Cambridge University Press 2008.

1

2 H. S. WHEATER

recent advanced texts are also available (e.g., Wagener et al.,

2004; Duan et al., 2003; Singh and Frevert, 2002a,b.). Never￾theless a brief introduction to modelling terminology and issues

is included here, to provide a common framework for subsequent

discussion.

A model is a simplified representation of a real-world system,

and consists of a set of simultaneous equations or a logical set

of operations contained within a computer program. Models have

parameters, which are numerical measures of a property or char￾acteristics that are constant under specified conditions. A lumped

model is one in which the parameters, inputs, and outputs are spa￾tially averaged and take a single value for the entire catchment.

A distributed model is one in which parameters, inputs, and out￾puts vary spatially. A semi-distributed model may adopt a lumped

representation for individual subcatchments. A model is determin￾istic if a set of input values will always produce exactly the same

output values, and stochastic if, because of random components,

a set of input values need not produce the same output values. An

event-based model produces output only for specific time periods,

whereas a continuous model produces continuous output.

The tasks for which rainfall-runoff models are used are diverse,

and the scale of applications ranges from small catchments, of the

order of a few hectares, to that of global models. Typical tasks for

hydrological simulation models include:

modelling existing catchments for which input–output data

exist, e.g., extension of data series for flood design of water

resource evaluation, operational flood forecasting, or water

resource management;

runoff estimation on ungauged basins;

prediction of effects of catchment change, e.g., land use

change, climate change;

coupled hydrology and geochemistry, e.g., nutrients, acid

rain

coupled hydrology and meteorology, e.g., Global Climate

Models

Clearly, the modelling approach adopted will, in general, depend

on the required scale of the problem (space-scale and time-scale),

the type of catchment, and the modelling task. Some of the tasks

pose major challenges, and it is helpful to consider a basic clas￾sification of model types, after Wheater et al. (1993), and their

strengths and weaknesses.

1.2.1 Metric models

At the simplest level, all that is required to reproduce the

catchment-scale relationship between storm rainfall and stream

response to climatic inputs, is a volumetric loss, to account for

processes such as evaporation, soil moisture storage, and ground￾water recharge, and a time-distribution function, to represent the

various dynamic modes of catchment response. This is the basis

of the unit hydrograph method, developed in the 1930s, which, in

its basic form, represents the stream response to individual storm

events by a non-linear loss function and linear transfer function.

The simplicity of the method provides a powerful tool for data

analysis. Once a set of assumptions has been adopted (separating

fast and slow components of the streamflow hydrograph and allo￾cating rainfall losses), rainfall and streamflow data can be readily

analyzed, and a unique model determined.

This analytic capability has been widely used in regional analy￾sis. In the UK, for example, the 1975 Flood Studies Report (NERC,

1975) used data from 138 UK catchments to define regression rela￾tionships between the model parameters, and storm and catchment

characteristics for the rainfall loss and transfer functions. This

lumped, event-based model provides the basic tool for current

UK flood design, and, through the regional regression relation￾ships, a capability to model flow on ungauged catchments (the

regional relationships were updated in the 1999 Flood Estimation

Handbook (Institute of Hydrology, 1999) through the replacement

of manual by digital map-based characteristics).

The unit hydrograph is also widely adopted internationally in

the form of the US Soil Conservation Service model, available

within the US Corps of Engineers HEC1 model. For an applica￾tion to flood protection in Jordan, see Al-Weshah and El-Khoury

(1999). Synthetic unit hydrographs can readily be generated based

on default model parameters, which is particularly helpful in data￾scarce situations. However, relatively little work has been done to

evaluate the associated uncertainty with these estimates.

This data-based approach to hydrological modelling has been

defined as metric modelling (Wheater et al., 1993). The essential

characteristic of metric models is that they are based primarily on

observations and seek to characterise system response from those

data. In principle, such models are limited to the range of observed

data, and effects such as catchment change cannot be directly

represented. In practice, the analytical power of the method has

enabled some effects of change to be quantified; the UK regional

analysis found the degree of urban development to be an important

explanatory variable, and this is used in design to mitigate impacts

of urbanization.

The unit hydrograph is a simple, event, model with limited

performance capability. However methods of time-series analysis

can be used to identify more complex model structures for event

or continuous simulation. These are typically based on parallel

linear stores, and provide a capability to represent both fast- and

slow-flow components of a streamflow hydrograph (see for exam￾ple Chapter 4 by Croke and Jakeman). These provide a powerful

set of tools for use, with updating techniques, in real-time flood

forecasting (see Chapter 9 by Young).

AN INTRODUCTION TO THE WORKSHOP 3

1.2.2 Conceptual models

The most common class of hydrological model in general applica￾tion incorporates prior information in the form of a conceptual rep￾resentation of the processes perceived to be important. The model

form originated in the 1960s, when computing power allowed,

for the first time, integrated representation of the terrestrial phase

of the hydrological cycle, albeit using simplified relationships, to

generate continuous flow sequences. These conceptual models are

characterized by parameters that usually have no direct, physically

measurable identity. The Stanford Watershed Model (Crawford

and Linsley, 1966) is one of the earliest examples, and, with

some 16–24 parameters, one of the more complex. To apply these

models to a particular catchment, the model must be calibrated,

i.e., fitted to an observed data set to obtain an appropriate set of

parameter values, using either a manual or automatic procedure.

Many of the models presented in the workshop (e.g., by Hughes

(Chapter 3), Sharma (Chapter 6), Leavesley et al. (Chapter 7),

and Wheater et al. (Chapter 8)) fall into this category.

The problem arises with this type of model that the information

content of the available data is limited, particularly if a single per￾formance criterion (objective function) is used (see Kleissen et al.

1990) and hence in calibration the problem of non-identifiability

arises, defined by Beven (1993) as “equifinality.” For a given

model, many combinations of parameter values may give sim￾ilar performance (for a given performance criterion), as indeed

may different model structures. This has given rise to two major

limitations. If parameters cannot be uniquely identified, then they

cannot be linked to catchment characteristics, and there is a major

problem in application to ungauged catchments. Similarly, it is dif￾ficult to represent catchment change if the physical significance

of parameters is ambiguous.

Developments in computing power, linked to an improved

understanding of modelling limitations, have led to some impor￾tant theoretical and practical developments for conceptual mod￾elling. Firstly, recognizing the problem of parameter ambiguity,

appropriate methods to analyze and represent this have been devel￾oped. The concept of generalized sensitivity analysis was intro￾duced (Spear and Hornberger, 1980), in which the search for a

unique best fit parameter set for a given data set is abandoned;

parameter sets are classified as either “behavioral” (consistent

with the observed data) or “non-behavioral” according to a defined

performance criterion. An extension of this is the generalized

likelihood uncertainty estimation (GLUE) procedure (Beven and

Binley, 1992; Freer et al., 1996). Using Monte Carlo simulation,

parameter values are sampled from the feasible parameter space

(conditioned on prior information, as available). Based on a perfor￾mance criterion, a “likelihood” measure can be evaluated for each

simulation. Non-behavioral simulations can be rejected (based on

a pre-selected threshold value), and the remainder assigned re￾scaled likelihood values. The outputs from the runs can then be

weighted and ranked to form a cumulative distribution of out￾put time-series, which can be used to represent the modelling

uncertainty. This formal representation of uncertainty is an impor￾tant development in hydrological modelling practice, although it

should be noted that the GLUE procedure lumps together various

forms of uncertainty, including data error, model structural uncer￾tainty and parameter uncertainty. More generally, Monte Carlo

analysis provides a powerful set of methods for evaluating model

structure, parameter identifiability, and uncertainty. For example,

in a recent refinement (Wagener et al., 2003a,b), parameter iden￾tifiability is evaluated using a moving window to step through the

output time-series, thus giving insight into the variability of model

performance with time.

A second development is a recognition that much more infor￾mation is available within an observed flow time-series than is

indicated by a single performance criterion, and that different seg￾ments of the data contain information of particular relevance to

different modes of model performance (Wheater et al., 1986). This

has long been recognised in manual model calibration, but has

only recently been used in automatic methods. A formal method￾ology for multi-criterion optimization has been developed for

rainfall-runoff modelling (e.g., Gupta et al., 1998; Wagener et al.,

2000, 2002). Provision of this additional information reduces the

problem of equifinality (although the extent to which this can be

achieved is an open research issue), and provides new insights into

model performance. For example, if one parameter set is appro￾priate to maximize peak flow performance, and a different set to

maximize low flow performance, this may indicate model struc￾tural error, or in particular that different models apply in different

ranges. Modelling tool-kits for model building and Monte Carlo

analysis are currently available, which include GLUE and other

associated tools for analysis of model structure, parameter iden￾tifiability, and prediction uncertainty (Lees and Wagener, 1999;

Wagener et al., 1999).

An important reason for detailed analysis of model structure and

parameter identifiability is to explore the trade-off between iden￾tifiability and performance to produce an optimum model (or set

of models) for a particular application. Thus for regionalization,

the focus would be on maximizing identifiability (i.e., minimiz￾ing parameter uncertainty), so that parameters can be related to

catchment characteristics.

In several senses, therefore, current approaches to parsimo￾neous conceptual modelling represent an extension of the met￾ric concept (and have thus been termed hybrid metric–conceptual

models). There has been a progressive recognition that the 1960s

first-generation conceptual models, while seeking a comprehen￾sive and integrated representation of the component processes,