Distributed Water Modelling Using GIS

DISTRIBUTED HYDROLOGIC MODELING USING GIS
Second Edition


Water Science and Technology Library
VOLUME 48

Editor-in-Chief
V. P. Singh, Louisiana State University, Baton Rouge, U.S.A.
Editorial Advisory Board
M. Anderson, Bristol, U.K.
L. Bengtsson, Lund, Sweden
J. F. Cruise, Huntsville, U.S.A.
U. C. Kothyari, Roorkee, India
S.E. Serrano, Philadelphia, U.S.A.
D. Stephenson, Johannesburg, South Africa
W.G. Strupczewski, Warsaw, Poland

The titles published in this series are listed at the end of this volume.


DISTRIBUTED HYDROLOGIC
MODELING USING GIS
Second Edition

by

BAXTER E. VIEUX
School of Civil Engineering and Environmental Science,
University of Oklahoma,

Norman, U.S.A.

KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW


CD-ROM available only in print edition
eBook ISBN:
1-4020-2460-6
Print ISBN:
1-4020-2459-2

©2005 Springer Science + Business Media, Inc.
Print ©2004 Kluwer Academic Publishers
Dordrecht
All rights reserved
No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,
mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
Visit Springer's eBookstore at:
and the Springer Global Website Online at:





Dedication

This book is dedicated to my
wife, Jean and to our children,

William, Ellen, Laura, Anne,
and Kimberly, and to my
parents.


This page intentionally left blank


Contents

Dedication

v

Preface

xi

Foreword

xv

Acknowledgments
1 DISTRIBUTED HYDROLOGIC MODELING
1.1 INTRODUCTION
1.2 WHY DISTRIBUTED HYDROLOGIC MODELING?
1.3 DISTRIBUTED MODEL REPRESENTATION
1.4 MATHEMATICAL ANALOGY
1.5 GIS DATA STRUCTURES AND SOURCES
1.6 SURFACE GENERATION

1.7 SPATIAL RESOLUTION AND INFORMATION CONTENT
1.8 RUNOFF PROCESSES
1.9 HYDRAULIC ROUGHNESS
1.10 DRAINAGE NETWORKS AND RESOLUTION
1.11 SPATIALLY VARIABLE PRECIPITATION
1.12 DISTRIBUTED HYDROLOGIC MODEL FORMULATION
1.13 DISTRIBUTED MODEL CALIBRATION
1.14 CASE STUDIES
1.15 HYDROLOGIC ANALYSIS AND PREDICTION
1.16 SUMMARY
1.17 REFERENCES

xvii
1
1
2
5
8
9
10
10
11
14
15
15
16
16
17
18
18

19


viii

Distributed Hydrologic Modeling Using GIS

2 DATA SOURCES AND STRUCTURE
1.1 INTRODUCTION
1.2 DIMENSIONALITY
1.3 MAP SCALE AND SPATIAL DETAIL
1.4 DATUM AND SCALE
1.5 GEOREFERENCED COORDINATE SYSTEMS
1.6 MAP PROJECTIONS
1.7 DATA REPRESENTATION
1.8 WATERSHED DELINEATION
1.9 SOIL CLASSIFICATION
1.10 LAND USE/COVER CLASSIFICATION
1.11 SUMMARY
1.12 REFERENCES

21
21
23
23
24
26
26
31
37

42
43
45
46

3 SURFACE GENERATION
1.1 INTRODUCTION
1.2 SURFACE GENERATORS
1.3 SURFACE GENERATION APPLICATION
1.4 SUMMARY
1.5 REFERENCES

47
48
49
66
70
71

4 SPATIAL VARIABILITY
1.1 INTRODUCTION
1.2 INFORMATION CONTENT
1.3 FRACTAL INTERPRETATION
1.4 RESOLUTION EFFECTS ON DEMS
1.5 SUMMARY
1.6 REFERENCES

73
74
78

80
82
88
89

5 INFILTRATION MODELING
1.1 INTRODUCTION
1.2 INFILTRATION PROCESS
1.3 APPROACHES TO INFILTRATION MODELING
1.4 GREEN-AMPT THEORY
1.5 ESTIMATION OF GREEN-AMPT PARAMETERS
1.6 ATTRIBUTE ERROR
1.7 SUMMARY
1.8 REFERENCES

91
92
93
93
101
103
108
111
111

6 HYDRAULIC ROUGHNESS
1.1 INTRODUCTION
1.2 HYDRAULICS OF SURFACE RUNOFF
1.3 APPLICATION TO THE ILLINOIS RIVER BASIN

115
116
117
123


Distributed Hydrologic Modeling Using GIS
1.4
1.5

SUMMARY
REFERENCES

ix
127
127

7 DIGITAL TERRAIN
1.1 INTRODUCTION
1.2 DRAINAGE NETWORK
1.3 DEFINITION OF CHANNEL NETWORKS
1.4 RESOLUTION DEPENDENT EFFECTS
1.5 CONSTRAINING DRAINAGE DIRECTION
1.6 SUMMARY
1.7 REFERENCES

129
129
130
135

138
141
145
146

8 PRECIPITATION MEASUREMENT
1.1 INTRODUCTION
1.2 RAIN GAUGE ESTIMATION OF RAINFALL
1.3 RADAR ESTIMATION OF PRECIPITATION
1.4 WSR-88D RADAR CHARACTERISTICS
1.5 INPUT FOR HYDROLOGIC MODELING
1.6 SUMMARY
1.7 REFERENCES

149
149
151
155
167
172
174
175

9 FINITE ELEMENT MODELING
1.1 INTRODUCTION
1.2 MATHEMATICAL FORMULATION
1.3 SUMMARY
1.4 REFERENCES

177

177
182
194
195

10 DISTRIBUTED MODEL CALIBRATION
1.1 INTRODUCTION
1.2 CALIBRATION APPROACH
1.3 DISTRIBUTED MODEL CALIBRATION
1.4 AUTOMATIC CALIBRATION
1.5 SUMMARY
1.6 REFERENCES

197
197
199
201
208
214
214

11 DISTRIBUTED HYDROLOGIC MODELING
1.1 INTRODUCTION
1.2 CASE STUDIES
1.3 SUMMARY
1.4 REFERENCES

217
218
218

236
237

12 HYDROLOGIC ANALYSIS AND PREDICTION
1.1 INTRODUCTION

239
239


Distributed Hydrologic Modeling Using GIS

x
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9

VFLO™ EDITIONS
VFLO™ FEATURES AND MODULES
MODEL FEATURE SUMMARY
VFLO™ REAL-TIME
DATA REQUIREMENTS
RELATIONSHIP TO OTHER MODELS
SUMMARY
REFERENCES

241
242
245
256
258
259
260
260

Glossary

263

Index

287


Preface

Distributed modeling is becoming a more commonplace approach to
hydrology. During ten years serving with the USDA Soil Conservation
Service (SCS), now known as the Natural Resources Conservation Service
(NRCS), I became interested in how millions of dollars in construction
contract monies were spent based on simplistic hydrologic models. As a
project engineer in western Kansas, I was responsible for building flood
control dams (authorized under Public Law 566) in the Wet Walnut River
watershed. This watershed is within the Arkansas-Red River basin, as is the
Illinois River basin referred to extensively in this book. After building nearly

18 of these structures, I became Assistant State Engineer in Michigan and,
for a short time, State Engineer for NRCS. Again, we based our entire design
and construction program on simplified relationships variously referred to as
the SCS method. I recall announcing that I was going to pursue a doctoral
degree and develop a new hydrologic model. One of my agency’s chief
engineers remarked, “Oh no, not another model!” Since then, I hope that I
have not built just another model but have significantly advanced the state of
hydrologic modeling.
This book sets out principles for modeling hydrologic processes
distributed in space and time using the geographic information system (GIS),
a spatial data management tool. Any hydrologic model is an abstract
representation of a component of a natural process. The science and
engineering aspects of hydrology have been long clouded by gross
simplifications. Representation by lumping of parameters at the river basin
scale such that a single value of slope or hydraulic roughness controls the
basin response may have served well when computer resources were limited
and spatial datasets of soils, topography, landuse, and precipitation did not


xii

Distributed Hydrologic Modeling Using GIS

exist. Shrugging off these assumptions in favor of more representative
modeling will undoubtedly advance the science of hydrology.
To advance from lumped to distributed representations requires reexamination of how we model for both engineering purposes and for
scientific understanding. We could reasonably ask what laws govern the
complexities of all the paths that water travels, from precipitation falling
over a river basin to the flow in the river. We have no reason to believe that
each unit of water mass is not guided by Newtonian mechanics, making

conservation laws of momentum, mass, and energy applicable. It is my
conviction that hydrologists charged with making predictions will opt for
distributed representations if it can be shown that distributed models give
better results. No real advance will be made if we continue to force lumped
models based on empirical relationships to represent the complexity of
distributed runoff. Once we embark on fully distributed representations of
hydrologic processes, we have no other choice than to use conservation laws
(termed “physics-based”) as governing equations.
What was inconceivable a decade ago is now commonplace in terms of
computational power and spatial data management systems that support
detailed mathematical modeling of complex hydrologic processes.
Technology has enabled the transformation of hydrologic modeling from
lumped to distributed representations with the advent of new sensor systems
such as radar and satellite, high performance computing, and orders-ofmagnitude increases in storage. Global digital datasets of elevation at thirty
meters (or smaller) or soil moisture estimates from satellite and data
assimilation offer tantalizing detail that could be of use in making better
predictions or estimates of the extremes of weather, drought, and flooding.
When confronted with the daunting task of modeling a natural process in
uncontrolled non-laboratory conditions, the academic ranks are usually illequipped because neat disciplinary boundaries divide and subdivide the
domain. In reality, water does not care whether it is flowing through the
meteorologist’s domain or that of the soil scientist’s. Thus, any realistic
treatment of hydrology necessarily taps the ingenuity and scientific
understanding of a wide number of disciplines. Distributed hydrologic
modeling requires disciplinary input from meteorology and electrical
engineering in order to derive meaningful precipitation input from radar
remote sensing of the atmosphere. Infiltration is controlled by soil properties
and profile depth, which is the domain of the soil scientist, who most often is
employed by an agricultural agency responsible for mapping soils.
Managing spatial information using GIS requires aspects of geographic
projections to map and overlay parameters and inputs needed in the model.

Indeed, most land use/cover maps were not compiled for hydrologic
purposes. An understanding of the origin and techniques used to map the


Distributed Hydrologic Modeling Using GIS

xiii

land use/cover is required in order to transform such datasets into useable
hydrologic parameters. Computationally, numerical methods are used to
solve the governing conservation equations. Finite difference and finite
element methods applied to hydrology require data management tools such
as GIS. If a GIS is used to supply parameters and input to these
computational algorithms, then the interface between data structures of the
spatial data and those in the numerical algorithm must be understood.
Filling in the gaps between academic disciplines is necessary for a
credible attempt at hydrologic modeling. Thus, the physical geographer who
is involved in modeling river basin response to heavy rainfall for purposes of
studying how floods impact society would likely benefit from seeing in this
book how geographical analysis and datasets may be transformed from
thematic maps into model input. A meteorologist who wishes to gain a
clearer understanding of how terrestrial features transform rainfall into
runoff from hillslope to river basin scale will gain a better appreciation for
aspects of spatial and temporal scale, precision, and data format and their
importance in using radar inputs to river basin models. Soil scientists who
wish to map soils according to hydrologic performance rather than solely as
aids to agricultural production would also likely benefit, especially from the
chapters dealing with infiltration, model calibration, and the case studies.
Several options exist for writing about GIS and hydrology. One choice
would be to weight the book heavily in favor of GIS commands and

techniques for specific software packages. Such books quickly become
outdated as the software evolves or falls into disfavor with the user
community. A more balanced choice is to focus on distributed hydrology
with principles on how to implement a model of hydrologic processes using
GIS. As the subject emerged during the writing of this book, it became clear
that there were issues with GIS data formats, spatial interpolation, and
resolution effects on information content and drainage network that could
not be omitted. Included here are fewer examples of specific GIS commands
or software operation. However, the focus is to illustrate how to represent
adequately the spatially distributed data for hydrologic modeling along with
the many pitfalls inherent in such an undertaking. Many of the details of how
to accomplish the operations specific to various GIS software packages are
left to other books.
This book is not intended to be a survey of existing models or a GIS
software manual, but rather a coherent treatment by a single author setting
forth guiding principles on how to parameterize a distributed hydrologic
model using GIS. Worldwide geospatial data has become readily available in
GIS format. A modeling approach that can utilize this data for hydrology
offers many possibilities. I expect those interested in smaller or larger scales
or other hydrologic components will be able to apply many of the principles


xiv

Distributed Hydrologic Modeling Using GIS

presented herein. For this reason, I beg your indulgence for my narrow
approach. It is my hope that this monograph benefits those hydrologists
interested in distributed approaches to hydrologic modeling.
Since the First Edition, software development and applications have

created a richer set of examples, and a deeper understanding of how to
perform distributed hydrologic analysis and prediction. This Second Edition
is oriented towards a recent commercially available distributed model called
Vflo™. The basic edition of this model is included on the enclosed CDROM.
Baxter E. Vieux, Ph.D., P.E.
Presidential Professor
School of Civil Engineering and Environmental Science
University of Oklahoma
Norman, Oklahoma, USA


Foreword

‘Distributed Hydrologic Modeling Using GIS’ celebrates the beginning
of a new era in hydrologic modeling. The debate surrounding the choice of
either lumped or distributed parameter models in hydrology has been a long
one. The increased availability of sufficiently detailed spatial data and faster,
more powerful computers has leveled the playing field between these two
basic approaches. The distributed parameter approach allows the hydrologist
to develop models that make full use of such new datasets as radar rainfall
and high-resolution digital elevation models (DEMs). The combination of
this approach with Geographic Information Systems (GIS) software, has
allowed for reduced computation times, increased data handling and analysis
capability, and improved results and data display. 21st century hydrologists
must be familiar with the distributed parameter approach as the spatial and
temporal resolution of digital hydrologic data continues to improve.
Additionally, a thorough understanding is required of how this data is
handled, analyzed, and displayed at each step of hydrologic model
development.
It is in this manner that this book is unique. First, it addresses all of the

latest technology in the area of hydrologic modeling, including Doppler
radar, DEMs, GIS, and distributed hydrologic modeling. Second, it is written
with the intention of arming the modeler with the knowledge required to
apply these new technologies properly. In a clear and concise manner, it
combines topics from different scientific disciplines into a unified approach
aiming to guide the reader through the requirements, strengths, and pitfalls
of distributed modeling. Chapters include excellent discussion of theory,
data analysis, and application, along with several cross references for further
review and useful conclusions.


xvi

Foreword

This book tackles some of the most pressing concerns of distributed
hydrologic modeling such as: What are the hydrologic consequences of
different interpolation methods? How does one choose the data resolution
necessary to capture the spatial variability of your study area while
maintaining feasibility and minimizing computation time? What is the effect
of DEM grid resampling on the hydrologic response of the model? When is a
parameter variation significant? What are the key aspects of the distributed
model calibration process?
In ‘Distributed Hydrologic Modeling Using GIS’, Dr. Vieux has distilled
years of academic and professional experience in radar rainfall applications,
GIS, numerical methods and hydrologic modeling into one single,
comprehensive text. The reader will not only gain an appreciation for the
changes brought about by recent technological advances in the hydrologic
modeling arena, but will fully understand how to successfully apply these
changes toward better hydrologic model generation. ‘Distributed Hydrologic

Modeling Using GIS’ not only sets guiding principles to distributed
hydrologic modeling, but also asks the reader to respond to new
developments and calls for additional research in specific areas. All of the
above make this a unique, invaluable book for the student, professor, or
hydrologist seeking to acquire a thorough understanding of this area of
hydrology.
Philip B. Bedient
Herman Brown Professor of Engineering
Department of Civil and Environmental Engineering
Rice University
Houston, Texas, USA


Acknowledgments

I wish to thank my colleagues who contributed greatly to the writing of
the First and Second Editions of this book. I am indebted to Professor
Emeritus, Jacques W. Delleur, School of Civil Engineering, Purdue
University, for his review; and to Philip B. Bedient, and his students, in the
School of Civil and Environmental Engineering, Rice University, for their
continued and helpful suggestions and insights, which improved this book
substantially. I wish to thank my own students who have lent their time and
energies to distributed hydrologic modeling using GIS.
Over the course of many years, I have enjoyed collaborations with
colleagues that have encouraged the development and application of
distributed modeling. In particular, I am indebted to Bernard Cappelaere,
Thierry Lebel, and others with l’Institut de Recherche pour le
Développement (IRD), France. To my colleagues at the Disaster Prevention
Research Institute, Kyoto Japan; Yasuto Tachikawa, Eichi Nakakita and
others, I am indebted. During the writing of the First Edition, I enjoyed

fruitful discussions and support from the NOAA-National Severe Storms
Laboratory (NSSL), and the Cooperative Institute for Mesoscale
Meteorological Studies (CIMMS). I wish to thank, Kenneth Howard and
Jonathan J. Gourley with NSSL, and Professor Peter Lamb, School of
Meteorology, Director of CIMMS, University of Oklahoma, who have
helped promote the application of radar for hydrologic applications. Special
thanks go to Ryan Hoes, Eddie Koehler of Vieux & Associates, Inc.; and
especially to Jean E. Vieux, CEO/President, for her confidence, assistance,
and support. The editing assistance of Carolyn Ahern and Daphne Summers
improved the text immensely.


This page intentionally left blank


Chapter 1
DISTRIBUTED HYDROLOGIC MODELING

1.1

Introduction

An ongoing debate within the hydrology community, both practitioners
and researchers, is how to construct a model that best represents the Earth’s
hydrologic processes. Distributed models are becoming commonplace in a
variety of applications. Through revision of existing models along with new
model development, hydrology is striving to keep pace with the explosive
growth of online geospatial data sources, remote sensing, and radar
technology for measurement of precipitation. When geospatial data is used
in hydrologic modeling, previously unfamiliar issues may arise.

It is not surprising that Geographic Information Systems (GIS) have
become an integral part of hydrologic studies considering the spatial
character of parameters and precipitation controlling hydrologic processes.
The primary motivation for this book is to bring together the key ingredients
necessary to use GIS to model hydrologic processes, i.e., the spatial and
temporal distribution of the inputs and parameters controlling surface runoff.
GIS maps describing topography, land use and cover, soils, rainfall, and
meteorological variables become model parameters or inputs in the
simulation of hydrologic processes.
Difficulties in managing and efficiently using spatial information have
prompted hydrologists either to abandon it in favor of lumped models or to
develop more sophisticated technology for managing geospatial data
(Desconnets et al., 1996). As soon as we embark on the simulation of
hydrologic processes using GIS, the issues that are the subject of this book
must be addressed.


2
1.2

Chapter 1
Why Distributed Hydrologic Modeling?

Historical practice has been to use lumped representations because of
computational limitations or because sufficient data was not available to
populate a distributed model database. How one represents the process in the
mathematical analogy and implements it in the hydrologic model determines
the degree to which we classify a model as lumped or distributed. Several
distinctions on the degree of lumping can be made in order to better
characterize a mathematical model, the parameters/input, and the model

implementation.
Whether representation of hydrologically homogeneous areas can be
justified depends on how uniform the spatially variable parameters are. For
example, the City of Cherokee, Oklahoma suffers repeated flooding when
storms having return intervals of approximately 2-year frequency occur on
Cottonwood Creek (Figure 1-1). A lumped subbasin approach using HECHMS (HEC, 2000) is represented schematically in Figure 1-2. ‘Junction-2’ is
located where the creek crosses Highway 64 on the northwestern outskirts of
the city limits. Each subbasin must be assigned a set of parameters
controlling the hydrologic response to rainfall input.

Figure 1-1. Contour map of the City of Cherokee in northwestern Oklahoma and Cottonwood
Creek draining through town.


1. DISTRIBUTED HYDROLOGIC MODELING

3

Though contour lines are the traditional way of mapping topography,
distributed hydrologic modeling requires a digital elevation model. The
Cottonwood basin represented using a 60-m resolution digital elevation
model is seen in Figure 1-3. Considerable variation in the topographic relief
is evident in the upper portions of the watershed where relatively flat terrain
breaks into steep areas; from there the terrain becomes flatter in the lower
portions of the watershed near the town. A distributed approach to modeling
this watershed would consist of a grid representation of topography,
precipitation, soils, and land use/cover that accounts for the variability of all
these parameters. Lumping even at the subbasin level would not be able to
account for the change in slope and drainage network affecting the
hydrologic response of the basin.

Figure 1-2. HEC-HMS subbasin definitions for the 125 km2 Cottonwood Creek.


422

Chapter 1

Figure 1-3. Hillshade digital elevation model and road network of the Cottonwood Creek
watershed and the City of Cherokee (upper right).

Practitioners are beginning to profit from research and development of
distributed hydrology (ASCE, 1999). As distributed hydrologic models
become more widely used in practice, the need for scientific principles
relating to spatial variability, temporal and spatial resolution, information
content, and calibration become more apparent.
Whether a model is lumped or distributed depends on whether the
domain is subdivided. It is clear that this distinction is relative to the domain.
If the watershed domain is to be distributed, the model must subdivide the
watershed into smaller computational elements. This process often gives rise
to lumped subbasin models that attempt to represent spatially variable
parameters/conditions as a series of subbasins with average characteristics.
In this manner, almost any lumped model can be turned into a semidistributed model. Most often, such lumping results in an empirically-based
model, because conservation equations break down at the scale of the
subbasin. Subbasin lumping is an outgrowth of the concept of hydrologically
homogeneous subareas. This concept arises from overlaying areas of soil,
land use/cover, and slope attributes producing subbasins of homogeneous
parameters. Subbasins then could logically be lumped at this level.
Drawbacks associated with subbasin lumping include:
1. The resulting model may not be physics-based

235

1. DISTRIBUTED HYDROLOGIC MODELING

2. Deriving parameters at the scale of subbasins is difficult because
streamflow is not available at each outlet
3. Model performance may be affected by the number of subbasins
4. Parameter variability is not properly represented by lumping at the
subbasin scale
Subbasin lumping can cause unexpected parameter interaction and degraded
model performance as the number of subbasins are changed.
1.3

Distributed Model Representation

It is useful to consider how physics-based distributed (PBD) models fit
within the larger context of hydrologic modeling. Figure 1-4 shows a
schematic for classifying a deterministic model of a river basin.
Deterministic
River Basin Model

PhysicsBased

Runoff
Generation

Distributed
Parameter

Conceptual

Runoff
Routing

Runoff
Generation

Runoff
Routing

Lumped
Parameter

Distributed
Parameter

Lumped
Parameter

Figure 1-4. Model classification according to distributed versus lumped treatment of
parameters.


624

Chapter 1

Deterministic is distinguished from stochastic in that a deterministic river

basin model estimates the response to an input using either a conceptual
mathematical representation or a physics-based equation. Conceptual
representations usually rely on some type of linear reservoir theory to delay
and attenuate the routing of runoff generated. Runoff generation and routing
are not closely linked and therefore do not interact. Physics-based models
use equations of conservation of mass, momentum, and energy to represent
both runoff generation and routing in a linked manner. Following the lefthand branch in the tree, the distinction between runoff generation and runoff
routing is somewhat artificial, because they are intimately linked in most
distributed model implementations. However, by making a distinction we
can introduce the idea of lumped versus distributed parameterization for both
overland flow and channel flow. A further distinction is whether overland
flow or subsurface flow is modeled with lumped or distributed parameters.
Routing flow through the channels using lumped or distributed parameters
distinguishes whether uniform or spatially variable parameters are applied in
a given stream segment.
Hybrids between the branches in Figure 1-4 exist. For example, the
model TOPMODEL (Beven and Kirkby, 1979) simulates flow through the
range of hillslope parameters found in a watershed. The spatial arrangement
is not taken into account, only the statistical distribution of index values, in
order to develop a basin response function. It is a semi-distributed model
since the statistics of the spatially variable parameters are operated on
without regard to location. TOPMODEL falls somewhere between
conceptual and distributed, though with some physical basis.
Changing time steps of the model input amounts to lumping, can
influence the PBD models significantly depending on the size of the basin.
Unit-hydrograph approaches are based on rainfall accumulations and to a
lesser degree on intensity. Temporal lumping occurs with aggregation over
time of such phenomena as stream flow or rainfall accumulations at 5minute, hourly, daily, 10-day, monthly, or annual time series. Hydrologic
models driven by intensities rather than accumulations can be more sensitive
to temporal resolution. Scale is an issue where a small watershed may be

sensitive to rainfall time series at 5-minute intervals, whereas a large river
basin may be sensitive to only hourly or longer time steps.
The spatial resolution used to represent spatially variable parameters is
another form of lumping. Changing spatial resolution of datasets requires
some scheme to aggregate parameter values at one resolution to another.
Resampling is essentially a lumping process, which in the limit, results in a
single value for the spatial domain. Resampling a parameter map involves
taking the value at the center of the larger cell, averaging, or other operation.