Development of synthetic unit hydrographs using the time-area method and geographic information systems

Material Information

Development of synthetic unit hydrographs using the time-area method and geographic information systems
Medde, Karen Sue
Publication Date:
Physical Description:
137 leaves : illustrations ; 29 cm

Thesis/Dissertation Information

Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Civil Engineering, CU Denver
Degree Disciplines:
Civil engineering


Subjects / Keywords:
Hydrologic models ( lcsh )
Hydrological forecasting -- Mathematical models -- Colorado -- Cherry Creek Watershed (El Paso County-Denver County) ( lcsh )
Hydrography -- Graphic methods ( lcsh )
Geographic information systems ( lcsh )
Geographic information systems ( fast )
Hydrography -- Graphic methods ( fast )
Hydrologic models ( fast )
Hydrological forecasting -- Mathematical models ( fast )
Colorado -- Cherry Creek Watershed (El Paso County-Denver County) ( fast )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Includes bibliographical references.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Karen Sue Medde.

Record Information

Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
26794077 ( OCLC )
LD1190.E53 1992m .M42 ( lcc )

Full Text
Karen Sue Medde
B.S.C.E., University of Colorado at Denver, 1991
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering

This thesis for the Master of Science
degree by
Karen Sue Medde
has been approved for the
Department of
Civil Engineering
Date?//ky /

Medde, Karen Sue (M.S., Civil Engineering)
Development of Synthetic Unit Hydrographs Using the Time-
Area Method and Geographic Information Systems
Thesis directed by Associate Professor Lynn E. Johnson
The time-area method for developing synthetic unit
hydrographs is one of many methods used to approximate
runoff amounts. An advantage of the time-area method is
the inclusion of actual basin parameters in the
hydrograph development. However, defining the time area
curves is a tedious, time consuming process when done
manually. Geographic Information System (GIS) technology
provides a convenient computerized method to manipulate
and process the spatial data reguired to develop the
time-area curves. This thesis describes the general
theory of the time-area method, details a procedure which
uses GIS and digital elevation information to determine
the time area relationship for any basin, and uses
historic runoff data to calculate the effect of basin
storage on the time-area relationship.
The form and content of this abstract are approved. I
recommend its publication.
iynn E. Johns

Tables............................................. vill
Figures ............................................. x
I. INTRODUCTION ........................................ 1
Literature Review ................................. 1
History of Hydrologic Modeling ............... 1
Unit Hydrograph Development .................. 5
Synthetic Unit Hydrograph Development ... 7
Geographic Information Systems (GIS) ... 7
GIS in Watershed Modeling.................... 10
Thesis Scope and Presentation .................... 12
UNIT HYDROGRAPH THEORY ........................... 16
Unit Hydrograph Theory ........................... 17
Assumptions.................................. 17
Methods for deriving a unit hydrograph . 20
Synthetic Unit Hydrographs ....................... 25
(1) Snyder's Method.......................... 26
(2) Soil Conservation Service (SCS) Method 28
(3) Time-Area Method ........................ 29
Background.............................. 29

Storage Routing ........................ 40
MANUAL CALCULATIONS .............................. 43
Time-Area Procedure Applied to a Hypothetical
Basin........................................ 43
Time-area results for the Cherry Creek Basin
Using Manual Calculations ................... 51
GIS Terminology.............................. 61
V. IDRISI............................................ 64
Module Descriptions .............................. 65
Peripheral modules .......................... 65
General Analysis ............................ 66
GIS Modules.................................. 66
Data Entry Modules........................... 68
Display Modules ............................. 68
Idrisi Limitations ............................... 69
VI. TIME-AREA METHOD USING GIS ........................ 70
Elevation Data Reguired .......................... 70
Stream Data Required.............................. 76
Coefficients Required for Calculations ........... 79
Watershed Boundary Determinations ................ 82
Travel Time Determinations ....................... 85

Stream path velocities ...................... 87
Overland Flow Velocities .................... 88
Travel time calculations .................... 88
Time-Area Procedure for the Hypothetical basin . 91
GIS Time-area results for the Cherry Creek
RESEARCH DIRECTIONS .............................. 110
Verification Procedures .......................... 110
Direction of Research Using the GIS Time-Area
IX. CONCLUSIONS.......................................119
SELECTED BIBLIOGRAPHY ................................ 121
CALCULATIONS ................................ 126

2.1 Main Channel Travel Times....................... 37
3.1 Main Channel Travel Times for the Hypothetical
Basin........................................ 44
3.2 Storage Routing Coefficient Determinations for
the Hypothetical Basin ........................... 45
3.3 Storage Routing for the Hypothetical Basin ... 46
3.4 Unit Graph Ordinates for the Hypothetical Basin 47
3.5 Time-Area Values Calculated for the Cherry
Creek Basin using the Manual Method .......... 52
3.6 Storage Routing Coefficient Determination for
the Cherry Creek Basin ........................... 52
3.7 Storage Routing for the Cherry Creek Basin ... 53
3.8 3-hour Unit Hydrograph Calculations for the
Cherry Creek Basin above Franktown, Colorado . 55
6.1 Land Use Factors k coefficient............. 81
7.1 Time-Area Values Determined Based on Figure 7.4
(Hypothetical Basin) ............................. 93
7.2 Storage Routing Calculations for Example
Hypothetical Basin Using the GIS Time-Area
Method....................................... 94
7.3 Unit Hydrograph Calculations for the
Hypothetical Example Basin Using the GIS
Procedures................................... 95

7.4 Time-Area Values Determined from the Time-Area Image
for the Cherry Creek basin above Franktown, ColorefldJti
7.5 Storage Routing Calculations for the Cherry
Creek basin above Franktown, Colorado .............. 102
7.6 3-Hour Unit Hydrograph Calculations for the Cherry
Creek basin above Franktown, Colorado Using the GIS
Time-Area Procedures ............................ 104
8.1 Travel Time Comparison Based on Varying Channel
8.2 Results Based on Varying the Storage
Coefficient "R"...................................116

1.1 Hydrologic Cycle .................................. 2
1.2 Black Box Systems Concept ......................... 6
1.3 Basic Geographic Information System ............... 8
2.1 SCS Dimensionless Unit Hydrograph................. 29
2.2 Time-Area Procedure .............................. 33
3.1 Hypothetical Basin with Streams .................. 48
3.2 Hypothetical Basin Channel Profile ............... 48
3.3 Time-Area Values for the Hypothetical Basin . . 49
3.4 Historic Runoff Hydrograph for the Hypothetical
Basin............................................. 49
3.5 Routed and Unrouted Time-Area Graphs ............. 50
3.6 1-hour Unit Hydrograph for the Hypothetical
Basin............................................. 50
3.8 l-to-500,000 Scale Map of the Cherry Creek
Basin above Franktown............................. 57
3.9 Time-Area Illustration for the Cherry Creek
Basin above Franktown............................. 57
3.10 Historic Runoff Hydrograph for May 5-7, 1992
Cherry Creek Basin above Franktown ............... 58
3.11 Routed and Unrouted Time-Area Curves for Cherry
Creek Basin above Franktown ...................... 58
3.12 3-hour Unit Hydrograph for Cherry Creek Basin
above Franktown................................... 59

3.13 1-hour Unit Hydrograph for Cherry Creek Basin
above Franktown.................................. 59
4.1 Vector Data Representation ....................... 61
4.2 Raster Data Representation ....................... 61
5.1 Idrisi Version 3.2 Modules ....................... 64
6.1 Time-Area Procedure using Idrisi ................. 71
6.2 Orthographic Illustration of the USGS 1-to-
250,000 scale Elevation Data Set (15 minute
region) .......................................... 75
6.3 Orthographic Illustration of the NGDC TOPO30
Data Set (15 minute region)....................... 75
6.4 DLG Stream Network (Raster and Vector Image)
for a 15-minute Area in Northeastern Colorado . 78
6.5 Land Cover Example................................ 82
6.6 Comparison of Manual and Idrisi Generated
Watershed Areas .................................. 85
7.1 Raster Contour Image for the Hypothetical Basin 96
7.2 DEM Image for the Hypothetical Basin.............. 96
7.3 Stream Paths and Watershed Boundaries for the
Hypothetical Basin ............................... 97
7.4 Basin Velocities for the Hypothetical Basin . 97
7.5 Time-Area Image for the Hypothetical Basin ... 98
7.6 Routed and Unrouted Time-Area curves for the
Hypothetical Basin ............................... 98
7.7 1-Hour Unit Hydrograph for the Hypothetical
Basin............................................. 99
DEM image for the Cherry Creek Basin Area . .

Major Streams in the Cherry Creek Basin (Raster
Image) ..........................................
Velocities Image for each cell in the Cherry
Creek Basin .....................................
Time-Area image for the Cherry Creek Basin . .
Routed and Unrouted Time-Area Graphs for the
Cherry Creek Basin ..............................
3-Hour Unit Hydrograph for the Cherry Creek
Basin ...........................................
1-Hour Unit Hydrograph for the Cherry Creek
Basin ...........................................
Comparison of the Time-Area Curves for the
Hypothetical basin using the Manual and GIS
Methods .........................................
Comparison of the One-Hour Unit Hydrographs
Calculated for the Hypothetical Basin using the
Manual and GIS Methods ..........................
Comparison of the Time-Area Curves for Cherry
Creek Basin Using the Manual and GIS Methods
Comparison of the One-hour Unit Hydrographs
Calculated Using the Manual and GIS Methods .
Comparison of the Three-Hour Unit Hydrographs
for the Cherry Creek Basin with an SCS and for
varying R values ................................

Hydrology is concerned with the movement of water
through the hydrosphere or the hydrologic cycle:
rainfall, the interaction of rainfall with the earth's
surface, and evaporation or evapotranspiration. Figure
1.1 is a general depiction of this cycle as it was
presented by Chow (1964). The ability to determine the
surface runoff aspect of the hydrologic cycle based on
some rainfall event is the subject of this thesis, and of
a considerable amount of hydrologic literature.
Following is a review of the pertinent literature as well
as a presentation of basic information on Geologic
Information System (GIS) technology.
Literature Review
History of Hydrologic Modeling
Hydrologic forecasting has a long tradition of
applications and research. Chow, Maidment and Mays
(1988) discuss the interest in the circulation of water
by the poet Homer (about 1000 B.C.) and by many of the
other early philosophers. During the eighteenth century,
experimentation related to hydrology increased and led to
the development of new principles and equations such as
those of Bernoulli and Chezy.
During the nineteenth century, improved
instrumentation facilitated considerable advancements in

Hydrologic Cycle

the science of hydrology. Dalton (1802) established
principles for evaporation and the Hagen-Poiseuille
eguation (1839) established the theory for capillary
flow. The need to size channels and predict flood peaks
was traced by Dooge (1973) as far back as 1851. (Dooge
credits Mulvaney with the Rational Method as early as
1851.) McCuen (1989) credits the publication of the
Rational Method to Emil Kuichling in 1889. Also during
the nineteenth century, Manning (1891) proposed his open
channel flow equation and Darcy (1856) developed his law
for flow through porous mediums.
Many of these early attempts to determine runoff
amounts were based on calculations involving critical
basin parameters. Meyer's formula (prepared in 1879) for
computing the cross-sectional area of a drainage way as
presented by McCuen is:
Ac=CmA0-5 (1.1)
where: Ac is in square feet
Cm reflects the slope of the drainage area and
the rainfall intensity
A is the drainage area in square feet.
Meyer's equation illustrates the importance placed on the
basin slope, rainfall intensity, and drainage area for
the calculation of peak runoff. Other early work was
done by Burkli-Ziegler (approximately in 1880) to
determine unit peak runoff, and by Talbot (approximately

in 1887) to compute waterway cross-sections.
Many of the runoff modeling methods currently in use
have not changed considerably from the original models.
Current methods, however, attempt to improve the
precision of the formulas by providing criteria for
selection of the coefficients (Chow, 1962), and by the
addition of empirical coefficients.
The computer has made the analysis of hydrologic
systems a much easier task, and the ability to simulate
and model complex systems is now a reality for most
hydrologists. This has undoubtedly contributed to the
wide range of information still being generated in the
field of hydrology. (A listing of recent (1988-1992)
articles that make a reference to hydrology includes 1235
separate articles.)
An examination of current articles relating to
runoff modeling (articles published since 1988) reveals a
number of trends. One major trend is the interest in
parameter estimation. Articles on the topic of
determining the parameters associated with runoff
modeling are often based on a particular region and the
accumulation of basin-specific information (Kuczera,
1990, Boyd, 1989, and Burakov, 1989). This illustrates
the limitation of "generic" runoff models. Other trends
found in the current general hydrology literature
include: the need to improve existing methods such as the

Rational Method (Lyngfelt, 1991); use of the kinematic
flow equations (Blandford and Meadows, 1990; Sander,
Hogarth, and Rose, 1990); general runoff simulation and
modeling (Fedora and Beschta, 1989; Wang, Guo, and Huang,
1991); and the calibration and comparison of models
(Calver, 1988; Franchini and Pacciani, 1991).
Unit Hvdroaraph Development
Sherman (1932) introduced the methodology for unit
hydrograph theory. His introduction appeared in an
article printed in the Engineering News Record on April
7, 1932. This was the first of a large number of
published articles (or sections included in text books)
concerning unit hydrograph theory, use, and development.
Sherman's theory for transforming effective rainfall to
runoff remains one of the most common transformation
functions in use today.
The use of a unit hydrograph as the transformation
between rainfall and runoff is based on viewing the
watershed as a lumped linear system. When using the
"black box" description, as illustrated in Figure 1.2,
the unit hydrograph is the operator. For basins
containing a stream flow gauge and precipitation data,
the unit hydrograph can be derived using deconvolution or
matrix calculations.
The unit hydrograph determined using these methods
is well documented in the literature. Most hydrology

Effective Basin Runoff
Rainfall Unit
Figure 1.2
Black Box Systems Concept
textbooks devote considerable space to the procedures
required to determine a unit hydrograph based on actual
event dataMcCuen (1989); Chow, Maidment, and Mays
(1988); Hoggan (1989); and Shaw (1983) are just a few of
the textbooks that provide detailed illustrations for
development of a unit hydrograph for a specific basin.
Numerous articles that deal with the use, accuracy,
and development of unit hydrographs continue to be
published. Typically, the primary focus of these
articles is improvement of the parameters or the
calculation methods, or both. For example, various
recent articles in the Journal of Hydrology. Water
Resources Research and Advances in Water Resources have
focused on improvement of basic unit hydrograph
techniques. Other articles discuss the effects of
parameters such as uncertainty (Hromadka, 1989), shape
parameters (Clutha, 1990) and hillside effects (van der
Tak, 1990) on the unit hydrograph. Alternate methods for
the development of unit hydrographs were the subject of
articles by Turner (1989), Dooge (1989) and Jakeman

(1990). These articles continue to support the unit
hydrograph as a tool for runoff modeling.
Synthetic Unit Hvdroqraph Development
Seldom are both the stream gauge and the
precipitation data available at the study location. For
this reason, a variety of synthetic methods have been
derived for development of unit hydrographs. As with
other hydrograph development, synthetic hydrograph
development is we11-documented in the textbooks. Each
hydrologic textbook listed in the previous section
contains information on the development of synthetic unit
hydrographs using one or more of the standard methods
(Snyder's, Soil Conservation Service-Dimensionless, and
Time-Area Methods). The current literature focusses on
parameter estimation and calculation procedures, as well
as the use of GIS as it relates to determining the
required parameters.
Geographic Information Systems (GIS)
Depending entirely on which publication one reads, a
slightly different definition for GIS can be found. In
pre-computer times, a GIS might have consisted of a
filing cabinet filled with maps. However, GIS today is
generally defined as a computerized system which allows
for the capture, storage and manipulation of geographic
or spatially-referenced data (See Figure 1.3). Star and


' '

Basic Geographic Information System
Estes (1990) provide an excellent introductory
description of a GIS. Their book traces the earliest GIS
development to the mid-eighteenth century, when the first
accurate base maps were produced. Parent and Church
(1988) credit the industrial revolution with the early
evolution of GIS. Parent and Church (from Streich, 1986)
specifically credit Herman Hollerith (1860-1929), who
adopted a punch-card technique for the processing of the
United States Census data in 1890, with being the father
of automated geoprocessing. Colby (1936) gave direction
to geographic based research by laying out a research
challenge: to develop a quantitative approach to map-
based problems. These early geographers set the stage
for the present day automated GIS processes.

In the early 1960's, digital geographic information
systems were being developed despite the hindrance of
limited computer power. Green (1964) details the
development of the Public Health Service system, STORET,
a system for storing spatial information about water
quality. Also during this period, the United States
Forest Service developed MIADS to analyze hydrology in
relation to recreation possibilities. The Canadian
Geographic Information System (CGIS), the first modern
GIS, was in use by 1964 (Tomlinson, 1982). Due primarily
to the advancements of microcomputer technology, GIS is
now recognized as a powerful tool for the management of
spatial data and is used by many local, state and federal
While a complete review of the wide range of GIS-
related articles published in the past few years is
beyond the scope of this thesis, it can be said that one
of many trends in the GIS literature focuses on the
improvement of data capture techniques. Several articles
that appeared in 1991 discuss the need for improved
capture techniques. An article in Surveying and Land
Information Systems (Holmes, 1991) provides a complete
discussion of the needs and problems associated with
current scanning techniques. Further, articles on the
topic of automated data capture and integration of
remotely-sensed data are found in Photoarammetric

Engineering & Remote Sensing, and Cartography and
Geographic Information Systems.
Conferences and symposia with GIS as the featured
topic are common, and the subjects covered at these
conferences are quite varied. The proceedings from GIS
conferences are an excellent source of up-to-date
research on the advancements in GIS technology. In
addition, a number of short courses are being developed
based on the GIS technology. One such course is outlined
in Digital Geologic and Geographic Information Systems,
edited by Van Driel and Davis (1989). The book provides
an illustration of the development and use of GIS as it
relates to geology. Clearly, the application of GIS
technology is being explored in a variety of fields that
deal extensively with spatial data.
GIS in Watershed Modeling
GIS is being used more effectively as a tool for
watershed modeling. Johnson (1989) discusses extensive
use of GIS as a hydrologic modeling tool, and his work
provides some of the most thorough information regarding
the combination of watershed modeling and GIS. Many
other watershed modelers are using GIS to determine the
parameters required for various external models such as
the Soil Conservation Service (SCS) curve numbers.
Stuebe (1990), for example, combined a GIS program
(GRASS) with a watershed model (Watershed) to calculate

runoff using the SCS methods. Berry and Sailor (1987)
focussed on the use of GIS for storm runoff prediction,
also based on the SCS techniques. Sircar, et. al. (1991)
published an article concerning the use of GIS to
directly develop time area curves. That work provides
extensive references for hydrologic applications of GIS.
Sasowsky and Gardener (1991) present a detailed
examination of the use of a GIS to determine the
topographic and soil parameters for the SPUR runoff
The availability and potential use of spatial data
for runoff modeling is well documented in a Journal of
Geophysical Research article by Wyss and Williams (1990).
This article does not directly discuss GIS, but
illustrates the potential of combining spatial radar data
with a runoff model. According to this article "Time-
integrated comparisons of rain gauge amounts and radar
measurements over the gauge suggest that accuracies of
50% can be achieved in the measurement of rainfall with
radar at a point." In addition to this article, Weather
Radar and Flood Forecasting (Collinge and Kirby, eds.,
1987) provides a detailed examination of radar used for
flood forecasting in real-time operational situations in
the United Kingdom. Additionally, this book provides
extensive references on the general subject of flood
predictions using rainfall radar data. Finally, a

current study at the University of Colorado at Boulder,
(Ulysses Sherman, 1992) is investigating the error found
between gauge data and properly calibrated radar.
Sherman concludes that the benefits to using radar to
establish the spatial variability of rainfall increases
as the number of available rainfall gauges decreases.
These books and articles indicate the ability to use
existing radar technology to supplement the ground
rainfall gauge network and provide the basis for using
GIS technology to incorporate spatial variability in
watershed modeling.
The above information is a general review of the
current state of hydrology and GIS. The following
paragraphs and chapters will expand on the concept that
the time-area method is an accurate (although labor
intensive) method to determine the unit hydrograph for
specific basins. This thesis provides a link between the
existing, accepted time-area procedure and the evolving
GIS technology which effectively eliminates some of the
tedious, time-consuming aspects of the time area
Thesis Scope and Presentation
The United States National Weather Service (NWS) is
in the process of modernizing its forecast operations.
As part of the modernization, expanded hydrologic
functions will be included in computer workstations and

database systems. To effectively utilize these expanded
capabilities, additional unit hydrographs are required
for various headwater basins around the United States.
The project on which this thesis is based entailed
working with the Denver Weather Service Forecast Office
(Denver WSFO) to develop synthetic unit hydrographs for
headwater basins located in Colorado.
The following paragraphs provide a summary of each
chapter in the thesis, including content and scope.
Chapter II presents a basic review of the goals and
methods used in hydrologic modeling, including a general
discussion of two common synthetic unit hydrograph
techniques in use, and a more detailed discussion of the
theory and procedures of the time-area method. The
chapter does not extensively examine alternate
techniques, but provides some comparison with the method
for the subject research.
Chapter III is a detailed look at the application of
the time-area method to actual project data. The time-
area procedures are illustrated first on a hypothetical
basin, and then specifically applied to the Cherry Creek,
Colorado basin. This chapter also explains the manual
(rather than computerized) calculations of time-area
method, and provides the basis for comparison to Chapter
VI, which repeats the calculations using GIS.
Chapter IV is a basic description of a Geographic

Information System and is not intended to be all-
inclusive. This chapter provides information on the
technology available to GIS users and also provides a
limited section on the specific GIS terminology used in
the thesis.
Chapter V provides a description of the GIS software
IDRISI, including the modules (subprograms) used for the
subject research and limitations of the particular
software when used for rainfall-runoff modeling. This
chapter also provides information on the availability of
the software and expected upgrades to the software.
Chapter VI is the primary focus of the thesis
research. This section describes the procedures
developed using GIS Idrisi software and applied first to
a hypothetical basin and then to the Cherry Creek basin
above Franktown, Colorado. The chapter details the steps
required to obtain the time-area relationships and is
later compared with the manual procedures described in
Chapter III.
Chapter VII explains in detail the limited
verification procedures used, recommends improvements,
and also compares the various methods used to determine
the time-area relationships for the Cherry Creek basin.
Chapter VIII provides conclusions drawn from the
work performed to date and briefly discusses the
direction the writer feels this research should take,

application of the research to spatially-varied rainfall
and the use of rainfall radar images.

The primary purpose of hydrologic modeling is to
depict and simplify the complexity of the real world.
Using a simplified-system concept, the focus can be
placed on the relationship between input and output, thus
eliminating the need to fully understand and model all of
the specific details involved in a complex hydrologic
Increased understanding of the hydrologic process
benefits many people the hydrologist and the public at
large. The hydrologist learns and uses hydrologic
knowledge to reduce the risk of injury, death, and
property damage caused directly or indirectly by
flooding. This may result in prohibition of building on
floodplains or in specifying what, where, and how
structures should be built to limit damages caused by
flooding. The knowledge may be used to improve
forecasting of potential storms and floods. However the
knowledge is applied, the quest to better model and
understand the hydrologic system has been a goal for
hydrologists over the past two centuries.
The amount of surface runoff and the time at which

this surface runoff will reach a peak are both important
elements in predicting the damages caused by flooding. A
discharge hydrograph relates the volume of the surface
runoff to the times of runoff. For any known storm
hyetograph, however, a transfer function is required to
determine the runoff from the storm event. One such
transfer function is a unit hydrograph.
Two of the currently-used synthetic unit hydrograph
procedures (Soil Conservation Service Dimensionless
and Snyder's) employ a non-conceptual black box approach.
The "box" contains no basin-specific information. By
contrast, the time-area method allows a more conceptual
approach to the development of synthetic unit hydrographs
and includes a variety of basin specific parameters such
as topography, land cover, basin shape, and stream
locations. All three synthetic unit hydrogaph procedures
will be detailed in this chapter.
Unit Hvdrograph Theory
Once the amount of rainfall and any associated
evaporation and infiltration losses have been determined
(the loss determination procedures are not addressed in
this thesis), the surface runoff caused by the excess
rainfall must be calculated. Unit hydrograph theory,
which was introduced by Sherman in 1932, has become a
widely-used method for estimating the direct surface

runoff. The unit-graph, as proposed by Sherman, is
defined as the runoff resulting from a unit of excess
rainfall; occurring uniformly over a basin; at a constant
rate; for an effective duration. Sherman used the word
"unit to denote a unit of time, and also defined the
unit hydrograph as being applicable to surface runoff
The unit hydrograph is the unit pulse response
function of a linear hydrologic system (Chow, Maidment,
and Mays, 1988). In their textbook, Chow, Maidment and
Mays present a complete description of the hydrologic
process as a linear system. The text also provides the
details of the response of linear systems. For example,
the solution for the linear transfer function follows two
basic principles:
principle of proportionality: if a solution to
the function is multiplied by a constant the
result is also a solution; and
principle of additivity or superposition: if
two solutions are added the result is also a
The response (or the runoff value, Q) for all values of
time is the convolution integral as shown by equation
(2.1). (The theory and procedures associated with the
convolution process will be fully described in the
following paragraphs.):

Q{t) =ftI(z) u(t-r) J 0
The unit hydrograph is based on a linear system and
can be used as the transfer function to estimate the
runoff occurring from any amount of excess rainfall. The
basic assumptions associated with a unit hydrograph model
the excess rainfall is uniformly distributed
over the entire drainage basin
the duration or time step for the unit
hydrograph is the same as the duration of the
rainfall hyetograph
the excess rainfall is of constant duration
over the specified time interval
the hydrograph reflects the unchanging
characteristics of the drainage basin it is
the signature for the basin
the principles of superposition and
proportionality apply
In a natural basin setting, it is not possible to fully
satisfy all assumptions. However, the unit hydrograph
model is acceptable for practical use (Heerdegen, 1974).
The unit hydrograph was derived for use on large
basins, making it an appropriate choice for headwater
basins. However, the unit hydrograph model has been
found to be valid for use on basins as small as one acre

(Chow, Maidment, and Mays, 1988). Using a unit
hydrograph for modeling runoff based on snow or ice melt
is not considered to be valid. Also, basins containing a
considerable amount of storage (ie. basins with several
reservoirs) are thought to violate the conditions for use
of the unit hydrograph. Based on the above information,
application of the unit hydrograph can net only an
approximation of the actual system; its use, therefore,
should be carefully considered on a case-by-case basis.
Methods for Deriving a Unit Hvdroaraph
In the past, before the availability of computers,
deriving a unit hydrograph from a complex storm was
especially difficult. Today, with the use of computers,
the process of determining a unit hydrograph based on
known storm and runoff data can be accomplished by a
variety of methods. Convolution is the theory of linear
superpositioning and is the basis for these methods. The
convolution integral was presented as equation (2.1) and
is conceptually the process of combining the storm
information with the unit hydrograph to determine the
direct surface runoff hydrograph. Deconvolution is the
process of determining the unit hydrograph (or the
transfer function) from the runoff hydrograph using the
rainfall information for the storm event. Both of these
processes are described in a variety of textbooks,
including Hydrologic Analysis and Design (McCuen, 1989)

and Applied Hydrology (Chow, Maidment, and Mays, 1988).
In general, the convolution process, for a discrete
time interval, is based on solving a set of simultaneous
equations of the form:
On=T^PUn-m* 1 (22)
where M is the upper limit for the summation and is
the number of input pulses (rainfall)
n is the time interval for each pulse
m = 1, and n < M
Using the unit hydrograph allows the transformation
from any amount of excess rainfall (evenly distributed
over the entire basin) to the runoff from the basin.
The deconvolution process provides the means to
determine the unit hydrograph from the input (excess
rainfall) and the output (basin runoff). The
deconvolution process is also the solution of the
convolution equations, except that the unit hydrograph
ordinates are unknown. A variety of methods exist for
the determination of the unit hydrograph ordinates but
the principal method is a series of approximations.
Collins (1939), details the method of "successive
approximation." Using the method of successive
approximations involves the assumption of a unit
hydrograph, application of the excess rainfall, and
comparison of the resulting runoff hydrograph to the

actual runoff hydrograph. These procedures are
systematically repeated until the "approximated" runoff
hydrograph (based on the assumed unit hydrograph) matches
the actual runoff hydrograph within the acceptable
The unit hydrograph resulting from the deconvolution
process may include erratic values. The erratic values
may be due to the nonlinearity of the actual system
(versus the linear assumptions for the calculations), or
to other problems associated with the data collection
process. Adjusting the curve to provide a "smooth fit"
of the data may be necessary to produce a reasonable
approximation of the unit hydrograph for the watershed.
The deconvolution process may also be accomplished
using the time-area method, as was done by the U.S. Army
Corps of Engineers for the June, 1965 flood in Colorado.
Using the time-area method and the process of
deconvolution, a one-hour unit hydrograph was developed
using a portion of the basin area determined by the storm
pattern. The ability to apply the spatial variation of
the storm pattern to a time-area representation of the
watershed basin provides evidence and incentive for full
development and use of the procedures presented in this
The unit hydrograph may also be determined through
the use of linear regression techniques. The linear

regression procedure produces the least-squares error
between the actual flow value and the flow value
determined based on the unit hydrograph ordinates. This
method is illustrated by the following equations where
equation (2.3) is an example of the linear matrix
solution, equation (2.4) is the general equation for the
actual runoff Q, and equation (2.5) is the runoff Q'
calculated from the assumed unit hydrograph ordinates:
in the following
for the unit
The unit hydrograph solution obtained by matrix
calculations does not ensure that the ordinates
determined for the unit hydrograph will be non-negative.
Newton and Vinyard (1967) provide alternate computer
methods for determining the unit hydrograph using the
least-squares techniques. Linear regression techniques
(Chow, Maidment, and Mays, 1988) are also used to
determine the least squares solution. However, the
P1 0 0 Vi Qi
X =
0 P2 0 U2 02
\P\ \U\ = |0|
\P\ \U\ = \Q'\
The solution that minimizes the error
equation is the "best" representation
101 |0'|

matrix transformations required by the linear regression
method make the solution difficult to determine.
Using linear programming techniques, it is also
possible to obtain a unit hydrograph that minimizes the
absolute value of the error between the actual flow value
and the flow value determined by the unit hydrograph.
Linear programming may be applied to any problem stated
as a linear objective function which is to be optimized
based on some constraints. For example, the objective
function would be:
MIN YZ--1 I Qn ~ On
where Q is the actual runoff value
Q' is the runoff value determined from the unit
Constraints would be included to assure the solution does
not contain negative values and to assure that the sum of
Q' plus the deviations equals the actual runoff value Q.
Linear programming packages are available worldwide
(Loucks, Stedinger, and Haith, 1981) and provide a method
for comparing all possible solutions that satisfy the
constraints. Using linear programming techniques assures
that all unit hydrograph ordinates obtained will be non-
negative and minimizes the absolute error between the
actual runoff, Q, and the calculated runoff, Q'. (The
accuracy of the unit hydrographs determined using the

deconvolution techniques, complex runoff hydrographs, and
storm hyetographs will vary depending upon loss
assumptions. Errors based on loss assumptions are beyond
the scope of this thesis, but are described in the
literature Newton and Vinyard, 1967; Unver and Mays,
Synthetic Unit Hydrographs
Various methods exist for determining unit
hydrographs on basins with limited or non-existent data
for rainfall, runoff or both. Often, as stated earlier,
ungauged basins or basins with limited gauging require
synthetic unit hydrographs for runoff modeling. Three
basic types of synthetic unit hydrograph techniques are
in use:
(1) unit hydrographs that relate peak flow rates,
base time, time to peak, and lag time to watershed
characteristics, such as Snyder's technique
(2) unit hydrographs that relate the ratio of peak
discharge and discharge to the ratio of time to time
to peak, such as the SCS (Soil Conservation Service)
(3) unit hydrographs based on the instantaneous unit
hydrograph, such as Clark's method or the time-area
The first two methods, Snyder's and the SCS, are
known as "bureaucratic" or administrative" unit

hydrograph techniques. Neither procedure includes basin
specific-information, but is based on studies at a
specific location (or locations) and the coefficients
extrapolated for use at other areas. The third
procedure, the time-area method, includes basin-specific
information such as topography, ground cover, and stream
networks. Including these basin-specific parameters
potentially makes the time-area method more accurate as a
procedure to determine a synthetic unit hydrograph.
General information on the three methods is presented in
the following paragraphs with additional detail included
for the time-area method.
(1) Snvder's Method
Snyder's technique is applicable to large basins.
Because Snyder's technique was developed using specific
basin data and expanded to be more universal by the U.S.
Army Corp of Engineers, McCuen (1989), recommends
calibration of the coefficients prior to use on a
specific basin. Snyder's method is based on two basic
parametersstandard lag time and a storage coefficient.
The original equation for the lag time was determined for
watersheds in the Appalachian mountain regions (Hoggan,
1989), which is the reason for recommending calibration
prior to use on other basins. The equation used to
estimate the lag time is:

tp~Ct (L*Lca) 0-3 (2.8)
where tp = lag time in hours
ct = coefficient representing basin slopes and storage
L = length of the main channel from the basin outlet to the divide in miles
Lca = length of the main channel to a point opposite the centroid of the basin area in miles
Using the lag time based on the above equation, the peak
discharge for rainfall excess (of standard duration) can
then be calculated using the following equation:
0P- 640CC^ (2.9) UP
where Qp = = peak discharge in cubic feet per second (cfs)
Cp = = runoff and storage coefficient
A = basin area in square miles (sq. mi.)
The standard duration of rainfall excess is defined as:
where At At- tp (2.10) 5.5 is the duration of rainfall excess in hours.
To calculate the lag time and the unit hydrograph for

other durations, the following equation can be used to
determine the adjusted lag time.
tpz = tp + 0.25 (Atr At) (2.11)
where tpr is the adjusted lag time in hours
Atr is the new unit hydrograph duration in
Both of the coefficients for storage and runoff (Ct and
Cp) should be calibrated to the specific basin. Snyder's
parameters can be determined based on regional parameters
(parameters for similar basins within a similar region to
the basin being modeled).
(2) Soil Conservation Service (SCS) Method
The SCS method for determining unit hydrographs is
based on the analysis of a large number of small rural
watersheds covering a variety of geographic
characteristics. An average dimensionless unit
hydrograph for all basins included in the study was
computed and is shown in Figure 2.1. If the time to peak
and the peak discharge for a particular basin are known,
then the dimensionless unit hydrograph can be used to
estimate the unit hydrograph for the basin. The peak
runoff can be estimated as:
where C = 483.4 (English system, 2.08 S.I.)
A = drainage area in square miles (km2 S.I.)

SCS Dimensionsless Unit Hydrograph
The time to rise, T can be determined as:
where tp = rainfall duration
t = is the basin lag time and can be estimated
as 0.6 times the time of concentration, Tc
Application of the SCS method is straightforward and
discussed widely in the hydrologic literature.
(3) Time-Area Method
Background. The time-area method is based on the
instantaneous unit hydrograph (IUH) and is what would
occur, conceptually, if one unit of excess precipitation
were spread evenly over an entire basin and allowed to

begin running off simultaneously. The rate of runoff is
calculated using the convolution integral:
r is the time of the unit pulse
t-r is the time lag since the previous unit
U(t-T) is the unit hydrograph ordinate
I(r) is the excess precipitation ordinate
This instantaneous unit hydrograph is then converted,
using a standard technique such as the S-graph method,
into a unit hydrograph of a specific duration.
The time-area method presented in the following
paragraphs and chapters does not directly calculate the
instantaneous unit hydrograph. The S-graph
(dimensionless time-area relationship) is calculated
based on the areas associated with each discrete time
increment and this time-area curve is then converted to a
unit hydrograph of some specific duration using the
standard S-graph technique.
The principles associated with the S-graph are based
on superposition. Theoretically the S-graph is the
result of a continuous excess rainfall amount, at some
constant rate, for an indefinite period of time (Chow,
where Q(t) is the runoff at time t

Maidment, and Mays, 1988). It is the unit step response
of a linear basin. The derived curve then can be offset
by the desired unit hydrograph duration (At'), and the
difference between the original and offset S-graphs
determined. Dividing the difference values determined by
the time duration (At') gives the ordinates for the unit
hydrograph for the duration (At').
A time-area diagram represents the relationship
between the times required for various areas within the
basin to contribute their flow volume to the outlet. The
relationship between the times and the areas are defined
by dividing the basin into discrete areas with distinct
travel times from each area to the outlet. Multiplying
the area associated with each distinct time increment by
the unit of excess precipitation provides a volume of
runoff during a discrete time increment, as shown in
equation (2.15).
AxX Pz(t) = Vz(t) (2.15)
where Aj is the incremental area
Pj is the excess precipitation over the area
for the discrete time interval (t)
Each of these volumes is representative of the flow
passing the outlet during a specific time interval.
Using a routing process to represent the basin storage
effects allows the transformation of the time-area curve

into a representative unit hydrograph for the basin (See
Figure 2.2).
Two aspects of the time-area hydrograph procedure
make it potentially more accurate for use with headwater
basins. First, the travel times are based directly on
the basin being modeled. Basin slopes, land use/land
cover, and stream locations are directly considered in
the travel time calculations. Secondly, the basin
storage effects can be included directly from historic
runoff data. Headwater basins typically outlet at an
existing stream gauge, providing the historic runoff
hydrograph recessions required for the calculation of the
storage coefficients.
Shortcomings of the time-area method include:
the assumption of a lumped, linear system to
represent the actual, complex, nonlinear
hydrologic system
the amount of time required to determine the
time-area relationship
the errors included with manual area
determinations of channel resistance
The tediousness, time, and the difficulty of accurately
determining the areas involved in these procedures can be
reduced by using the GIS procedures. However, the basic

Time-Area Procedure

assumption included in the time-area procedure of
linearity and the need to determine the roughness
coefficients associated with channel velocities cannot be
improved by the GIS techniques presented in this thesis.
Procedure. Chapter III provides a detailed
illustration of the manually-calculated time-area
procedures as they were applied to a hypothetical basin
and to the Cherry Creek basin above Franktown, Colorado.
The basic principles to be described in this chapter are
also applicable to the procedures developed using GIS.
Determining the travel time for a basin requires a
topographical map with a scale appropriate to the
specific basin. Typically, a l-to-500,000 scale map
provides enough detail for these procedures when used to
determine a unit hydrograph for a headwater basin. The
initial step, then, after acquiring an appropriate map,
is the definition of the watershed boundaries.
The area to be included within a specific watershed
is defined as that area that sheds or drains water to a
particular outlet. Defining the watershed boundaries can
be accomplished by locating the ridge or high areas that
are the limits for runoff occurring in the area. Using a
planimeter or other measurement procedure, the basin area
can be determined. However, when working with headwater
basins (where a stream gauge is located at the outlet),
the area within the basin can be determined from

published information. For example, the USGS and the
State of Colorado annually publish a water resource book
which includes basin areas and a variety of other
Once the watershed boundaries have been identified,
the longest drainage path for the basin must be
determined. Including additional channels in the
calculations increases the accuracy. However, the more
channels included in the travel time calculations, the
more complex and time-consuming the calculations become.
Plotting the channel profile will aid in the travel time
calculations and is the method used on the example
basins. Working from the channel profile, the average
slope for various reaches along the channel can be
determined and used for velocity calculations. In
addition, the basic channel description can be noted and
used to determine the channel resistance coefficient.
For the subject research, the channel resistance
coefficient is defined as: 1.49R2/3/n, where R is the
hydraulic radius for the channel and n is the Manning's
roughness coefficient.
The determination of the channel resistance
coefficient is a difficult task primarily due to the lack
of detailed channel cross-section information. However,
the values included in Table 2.1 were used throughout
this research study. Table 2.1 was developed based on

the following information/assumptions:
bankfull (flood stage) conditions exist in the
the slopes along the channels are relatively
steep and therefore the information in Robert
D. Jarrett's article "Hydraulics Research in
Mountain Rivers" is applicable
information included in Roughness
Characteristics of Natural Channels. a
Geological Survey Water-Supply paper for
roughness coefficients in natural channels is
Table 2.1 provides the basic information needed to select
a roughness coefficient for steep channels flowing under
flood (bankfull) conditions when the basic channel
conditions are known. However, when more detailed
information is available for the study area, it should be
used in place of the information provided in Table 2.1.
In addition to the information presented in the
table, Appendix C includes a series of graphs that
compare the channel roughness coefficient to Manning's n
for several different channel cross sections. Where the
channel shape and approximated roughness conditions are
known, these curves can be used to determine a channel
roughness coefficient value. Calculating the velocity
for the channel travel times is dependent on the accuracy

Channel Resistance Coefficients
Channel Description 1.49R2/3/n
Wide straight channels with relatively smooth boundary materials and little vegetation in either the main or adjacent over flow channels 93.1 82.8
Wide meandering main channel with relatively smooth boundary materials and grass in the overflow channels 74.5 62.1
Sandy gravel main channel with some cobbles and boulders. Trees and brush in the overflow channels 59.6 53.2
Highly irregular mountain channel of cobbles and boulders with trees and brush in the overflow channel 53.2 49.7
of the channel cross section and roughness information
used. A more accurate result is obtained with more
accurate channel information.
The velocity for each channel reach is determined
using the Manning equation and the appropriate value from
the table, as shown below:
T/ - jpO.61
where: CmRi/ni is from Table 2.1 and is based on channel
geometry, roughness and English units
conversion factor
S is the average slope for the reach

The overland flow velocities would typically be included
in velocity calculations. However, due primarily to the
size of the watersheds being considered the overland flow
velocities were not included in the manual calculations.
This allowed the travel-time calculations to be based
entirely on the total average channel velocities as
calculated above. However, the procedures developed
using the GIS for calculations include the travel times
associated with overland flow. These procedures are
detailed in Chapter VI.
Once the velocities for each reach have been
determined, calculating travel time is simply based on
the two formulas below. Travel time for each individual
reach along the channel is calculated using
Tt. = ^ (2.17)
ci y
where Tti =
D. =
V; =
The travel times
the travel time for the section of
the reach in the same time units as
the velocity (feet or miles per time)
equal to the length of the individual
reach in units which correspond to
the velocity units
is the velocity value as calculated
previously for the reach
for the entire channel or the time of
concentration for the basin can then be determined by

summing the individual channel travel times for each
rt=£ T (2.18)
The above calculations determine the travel time or
the time of concentration associated with the longest
channel within the basin. To fully determine the time-
area curves, these calculations are repeated for various
other channels within the basin, or by estimating the
travel times for the entire basin using the elevation
contours. Examples of these calculations for a simple
hypothetical basin, along with the calculations for the
Cherry Creek basin, are included in Chapter III.
Once the travel times for various points within the
basin have been determined, the next step is to plot a
series of equal travel time lines (isochrones). Using
the existing topographical information and plotting
accumulated travel times from the basin outlet to the
extreme points within the basin provides the information
necessary to plot the isochrones. Once the areas of
equal travel times have been determined, the area
associated with each time increment is calculated to
provide the time-area relationship. The plotted time-
area relationship resembles an S-curve (or hydrograph, if
incremental areas are plotted) and is referred to as a
"translation" hydrograph in some texts (Hoggan, 1989).
This curve represents the runoff with no account for the

time delay associated with the storage characteristics of
the basin. Using linear reservoir routing techniques,
the effects of storage and resistance can be accounted
for in the basin.
Storage Routing. Linear reservoir outflow and
storage are related by the equation:
Si=ROi (2.19)
where Si = storage at the end of period i
0i = outflow during period i
R = the storage coefficient
and the simplified form of the continuity equation:
J-0=-^ (2.20)
where I is the average inflow
6 is the average outflow
A is the change in storage
A is the change in time
The storage coefficient, R, can be obtained from historic
hydrographs of observed events. The storage coefficient,
R, represents the slope of the storage outflow curve for
a linear reservoir. If the basin is assumed to behave as
a linear reservoir, this coefficient may be estimated by
dividing the average of the direct-runoff discharge at
the inflection point on the recession curve by the slope
of the curve at the inflection point. In effect R is
dependent on the time interval, At, and is the value that

best reproduces the historic recession curve.
Superior results are obtained when a variety of
historic runoff hydrographs are used to determine R, and
an average of the results is used for the actual routing
coefficient. Regression equations for R have been
developed for some regions (Hoggan, 1989) by the Soil
Conservation Service.
Using the storage coefficient R, the routing
coefficients C1 and C2 can be determined as follows:
Having determined the routing coefficients, the routing
is performed based on the following linear reservoir
routing equation:
<^=0.5(1 -C2)
the original area at time step i
the original area at time step i+1
the routed area at time step i
the routed area at time step i+1
C, C2 = the routing coefficients determined
Converting the dimensionsless area versus time
values (based on the assumption of uniform distribution
of rainfall over the basin) results in a dimensionless S-
graph for the basin. This S-graph includes all of the

characteristics of the basin of study, and can be used to
generate a unit hydrograph for any duration based on the
characteristics of an S-graph. Lagging this S-graph by
the desired time duration, and determining the difference
between the S-graph ordinates, completes the unit
hydrograph calculations. (See Appendix A for a step-by-
step summary of the manual time-area procedure.)

Time-Area Procedure Applied to a Hypothetical Basin
This chapter uses a simple hypothetical basin to
illustrate the manual calculation procedures described in
Chapter II, and also presents the data calculated for the
Cherry Creek basin using the time-area method.
Figure 2.2 (included in Chapter II) is an
illustration of the general steps associated with
applying these procedures to a hypothetical basin.
Figure 3.1 (the figures are all included at the end of
this section) is a more detailed illustration of the
hypothetical basin and the major stream path used for the
calculations. From Figure 3.1 the drainage area was
determined to be 83 square miles and the length of the
longest stream path was determined to be 18 miles. The
channel profile was plotted from the topographic map data
and is included as Figure 3.2. From the profile, the
channel was divided into three separate reaches (as shown
on the profile) and the channel roughness coefficients
were determined for each reach using Table 2.1.
Applying the channel profile information, the
velocity was determined for each even contour elevation
along the channel (see Table 3.1). This table also

Main Channel Travel Times
for the Hypothetical Basin
5100 0.00 - 0.00 0.00
5200 0.10 0.020 53.0 5.12 0.02
5400 1.80 0.021 53.0 5.25 0.36
5600 0.65 0.058 53.0 5.25 0.48
5800 0.65 0.058 53.0 5.25 0.61
60000 0.65 0.058 53.0 5.25 0.73
6200 1.10 0.034 53.0 6.69 0.89
6400 1.50 0.025 56.5 6.10 1.14
6600 1.60 0.024 56.5 5.98 1.41
6800 1.90 0.020 56.5 5.46 1.76
7000 1.80 0.021 56.5 5.59 2.08
7200 1.80 0.021 56.5 5.59 2.40
7400 0.90 0.042 56.5 7.91 2.51
7600 0.90 0.042 51.0 7.20 2.64
7800 0.90 0.042 51.0 7.20 2.76
8000 0.70 0.054 51.0 8.16 2.85
8200 0.25 0.152 51.0 13.69 2.76
8400 0.25 0.152 51.0 13.69 2.78
8600 0.20 0.189 51.0 15.27 2.79
8800 0.15 0.253 51.0 17.66 2.80
9000 0.10 0.379 51.0 - 2.80
9200 0.10 0.379 51.0 - 2.80
includes the accumulated travel time associated with each
even contour to the outlet location. Using additional

flow paths and the travel time values calculated for the
main channel, the basin travel times were plotted (see
Figure 3.3) along with the isochrone lines for each time
increment. Figure 3.4 is an example of a historic
hydrograph for this location. Table 3.2 is the storage
coefficient determination based on the recession for the
historic hydrograph event. Using various approximations,
it was determined that a value of R = 0.76 provided the
best representation for the historic event.
Storage Routing Coefficient Determinations
for the Hypothetical Basin
1825 1824
1400 1387
1050 1064
Using R = 0.76, the routing coefficients were determined
to be: C1 = 0.12 and C2 = 0.76
Table 3.3 illustrates the dimensionless routed time-area
values obtained. Figure 3.5 is a graph illustrating the
routed and unrouted dimensionless (S-graph) areas for the
hypothetical basin. Table 3.4 presents the S-graph and
one hour duration unit hydrograph calculations for this
information. Figure 3.6 is an illustration of a 1-hour

unit hydrograph for the hypothetical basin.
Storage Routing
for the Hypothetical Basin
0 0.00 0.00 0.00
1 0.25 0.00 0.03 0.00 0.03
2 0.59 0.03 0.07 0.02 0.12
3 1.00 0.07 0.12 0.09 0.28
4 1.00 0.12 0.12 0.22 0.46
5 1.00 0.12 0.12 0.35 0.59
6 1.00 0.12 0.12 0.45 0.69
7 1.00 0.12 0.12 0.52 0.76
8 1.00 0.12 0.12 0.58 0.82
9 1.00 0.12 0.12 0.62 0.86
10 1.00 0.12 0.12 0.66 0.90
11 1.00 0.12 0.12 0.68 0.92
12 1.00 0.12 0.12 0.70 0.94
13 1.00 0.12 0.12 0.71 0.95
14 1.00 0.12 0.12 0.73 0.97
15 1.00 0.12 0.12 0.73 0.97
16 1.00 0.12 0.12 0.74 0.98
17 1.00 0.12 0.12 0.74 0.98
18 1.00 0.12 0.12 0.75 0.99
19 1.00 0.12 0.12 0.75 0.99
20 1.00 0.12 0.12 0.75 0.99
21 1.00 0.12 0.12 0.75 0.99
22 1.00 0.12 0.12 0.76 1.00

Unit Graph Ordinates
0 0.00 0 0
1 0.03 1606 0 1606
2 0.12 6620 1606 5013
3 0.28 15251 6620 8630
4 0.46 24445 15251 9194
5 0.59 31433 24445 6988
6 0.69 36744 31433 5310
7 0.76 40781 36744 4036
8 0.82 43848 40781 3067
9 0.86 46180 43848 2331
10 0.90 47951 46180 1771
11 0.92 49298 47951 1346
12 0.94 50321 49298 1023
13 0.95 51099 50321 777
14 0.96 51420 51099 320
15 0.97 52140 51420 719
16 0.98 52481 52140 341
17 0.98 52740 52481 259
18 0.99 52938 52740 197
19 0.99 53088 52938 149
20 0.99 53201 53088 113
21 0.99 53288 53201 86
22 1.00 53354 53288 65
23 1.00 53354 53354 0

a h
P> Q
01 g
S' w
n w

1 1 -\p \ \ I- 1
Rocky canyon stream bad mostly boulders and cobbles -
\ over flow channels
\ contain heavy vegetaitlon
/ 1 -

\o Mountain valley .
silty clay channel
V? bed with some boulders
\- and cobbles
- \ wide over flow channels containing -
numerous trees and .
* 0> \ thick brush
0 Z \ .
o 9 \
S 2 \
- Z \ Rocky canyon
r* \ Irregular stream bed \ of cobblee and -
^ boulders restricted over flow channels V/ -
- -

i l_ is
Hypothetical Basin with Streams

Time-Area Values for the Hypothetical Basin
Historic Runoff Hydrograph for the Hypothetical Basin


Routed and Unrouted Time-Area Graphs
for the Hypothetical Basin
1-hour Unit Hydrograph for the Hypothetical Basin

Time-area results for the Cherry Creek Basin Using Manual
Without repeating all of the individual steps
associated with the calculations the following Figures
and Tables are the results obtained from manually
calculating data for the Cherry Creek basin above
Franktown, Colorado.
TABLE 3.5 Velocity and travel time calculations
TABLE 3.6 Storage routing coefficient determinations. The storage routing coefficient was determined through a trial and error procedure to best represent the historic runoff curve. Intermediate values are not shown in this table.
TABLE 3.7 storage routing calculations
TABLE 3.8 3-hour unit hydrograph calculations
FIGURE 3.7 Reproduction of the 1 to 500,000 scale map used for the calculations
FIGURE 3.8 Time area (isochrone) illustration
FIGURE 3.9 Historic hydrograph used for determining the storage coefficient
FIGURE 3.10 Routed and unrouted time-area curves
FIGURE 3.11 3-hour unit hydrograph
FIGURE 3.12 1-hour unit hydrograph

Time-Area Values Calculated for the
Cherry Creek Basin Using the Manual Method
1 5.0 5.0 0.030
2 15.0 20.0 0.118
3 26.0 46.0 0.272
4 31.0 77.0 0.456
5 30.0 107.0 0.633
6 29.0 136.0 0.805
7 25.0 161.0 0.953
7.7 8.0 169.0 1.000
Storage Routing Coefficient Determination
for the Cherry Creek Basin
Historic Runoff from Hydrograph Recession Calculated Runoff Using R = .84
3120 3121
2550 2618
2110 2139
1720 1770
1350 1443

Storage Routing for the Cherry Creek Basin
0 0.00 0.00
1 0.03 0.00 0.01 0.00 0.01
2 0.12 0.01 0.02 0.01 0.04
3 0.27 0.02 0.04 0.03 0.09
4 0.46 0.04 0.05 0.08 0.17
5 0.63 0.05 0.06 0.14 0.25
6 0.80 0.06 0.08 0.21 0.35
7 0.95 0.08 0.08 0.30 0.45
8 1.00 0.08 0.08 0.38 0.54
9 1.00 0.08 0.08 0.45 0.61
10 1.00 0.08 0.08 0.52 0.68
11 1.00 0.08 0.08 0.57 0.73
12 1.00 0.08 0.08 0.61 0.77
13 1.00 0.08 0.08 0.65 0.81
14 1.00 0.08 0.08 0.68 0.84
15 1.00 0.08 0.08 0.70 0.86
16 1.00 0.08 0.08 0.73 0.89
17 1.00 0.08 0.08 0.74 0.90
18 1.00 0.08 0.08 0.76 0.92
19 1.00 0.08 0.08 0.77 0.93
20 1.00 0.08 0.08 0.78 0.94
21 1.00 0.08 0.08 0.79 0.95
22 1.00 0.08 0.08 0.80 0.96
23 1.00 0.08 0.08 0.81 0.97
24 1.00 0.08 0.08 0.81 0.97
25 1.00 0.08 0.08 0.82 0.98

26 1.00 0.08 0.08 0.82 0.98
27 1.00 0.08 0.08 0.82 0.98
28 1.00 0.08 0.08 0.83 0.99
29 1.00 0.08 0.08 0.83 0.99
30 1.00 0.08 0.08 0.83 0.99
31 1.00 0.08 0.08 0.83 0.99
32 1.00 0.08 0.08 0.83 0.99
33 1.00 0.08 0.08 0.83 0.99
34 1.00 0.08 0.08 0.84 1.00
TABLE 3.7 (Continued)
Storage Routing for the Cherry Creek Basin

3-hour Unit Hydrograph Calculations
for the Cherry Creek Basin above Franktown, Colorado
0 0.00 0 0 0
1 0.01 430 430
2 0.04 1497 1497
3 0.09 3374 0 3374 3374
4 0.17 6001 430 5571
5 0.25 9222 1497 7725
6 0.35 12858 3374 9484 9484
7 0.45 16480 6001 10479
8 0.54 19659 9222 10437
9 0.61 22331 12858 9473 9473
10 0.68 24574 16480 8095
11 0.73 26459 19659 6800
12 0.77 28042 22331 5712 5712
13 0.81 29372 24574 4798
14 0.84 30489 26459 4030
15 0.86 31427 28042 3385 3385
16 0.89 32216 29372 2844
17 0.90 32878 30489 2389
18 0.92 33434 31427 2006 2006
19 0.93 33901 32216 1685
20 0.94 34294 32878 1416
21 0.95 34623 33434 1189 1189
22 0.96 34900 33901 999
23 0.97 35133 34294 839

24 0.97 35328 34623 705 705
25 0.98 35492 34900 592
26 0.98 35630 35133 497
27 0.98 35746 35328 418 418
28 0.99 35843 35492 351
29 0.99 35925 35630 295
30 0.99 35993 35746 248 248
31 0.99 36051 35843 208
32 0.99 36100 35925 175
33 0.99 36140 35993 147 147
34 1.00 36174 36051 123
35 1.00 36354 36100 254
36 1.00 36354 36140 214 214
37 1.00 36354 36174 179
38 1.00 36354 36354 0
TABLE 3.8 (Continued)
3-Hour Unit Hydrograph Calculations
for the Cherry Creek Basin above Franktown, Colorado

l-to-500,000 Scale Map of the Cherry Creek Basin
above Franktown
Time-Area Illustration for the Cherry Creek Basin
above Franktown

0 10 20 30 40 SO 60 70 SO
otvit9 1200 vn a*ay i i*to
Historic Runoff Hydrograph for May 5-7, 1992
Cherry Creek Basin above Franktown
Routed and Unrouted Time-Area Curves for
Cherry Creek Basin above Franktown

3-hour Unit Hydrograph for
Cherry Creek Basin above Franktown
1-hour Unit Hydrograph for
Cherry Creek Basin above Franktown

Geographic information systems (GIS) provide a
powerful tool for the manipulation of spatial data. Due
primarily to recent advances in technology, GIS is usable
on many microcomputers. This chapter defines pertinent
GIS terminology and provides basic background on GIS
applicable to watershed modeling.
GIS, as mentioned in the literature review, can be
defined in a variety of ways. Basically it is a
combination of hardware and software which provides the
means for manipulating, storing, analyzing and displaying
spatially-referenced data. A typical GIS system links a
database and a graphics driver with tools for analyzing
and manipulating the stored information.
There are two types of digital graphic data
associated with a GIS. The first is vector-based. A
vector system uses lines, points and polygons, and areas
are determined by the bounds of a polygon. The second
type of digital data representation is raster-based. A
raster system represents an area as a grouping of cells.
Each cell within the area represents a parameter of
interest. A raster structure can be thought of as an
array over space. Figures 4.1 and 4.2 illustrate the
general principles associated with these two data types.

a a a a a a a a a
a a a a a a a a a
a a a a a a a a a
a a a l'' \ 3 a a
a a a a / l > a a
a a a a a -a- a a a
-a- -3.. a a a a a a a
a a a a a a a a

Vector Data
Raster Data
Most GIS systems allow some form of conversion
between these data types. However, certain conversions
may be extremely complex, and must be made carefully to
avoid inaccurate results. Star and Estes (1990) provide
a detailed description of the data types, conversions and
storage of spatial data.
GIS Terminology
Following is a list of basic GIS terminology,
boolean image: An image containing only ones or
zeros. Also called a binary or
logical image.
cell: The basic block for the array
structure. A cell represents some
actual ground area.
cell identifier: A unique value associated with a

DEM: single cell in a raster image. For example, an elevation value in a DEM image is a cell identifier. Digital Elevation Model. An array of elevation values.
DLG: Digital Line Graph. A vector product of the United States Geographic Survey (USGS) containing stream locations and various other geographic features.
image: A representation of a map or geographic region.
map algebra: The ability to combine, through standard arithmetic operations, entire map images. Using map algebra it is possible to add maps, to add a single value to a map, or to perform a number of operations which affect the entire image.
pixel: The same as a cell. The representation of the smallest unit which can be uniquely represented.
raster image: A group of cells or a matrix of cells which represents a map or other geographic region.
target cell: A single cell or a group of cells

which is used during a map algebra
vector image: A collection of lines, polygons
and/or points that are associated
based on some form of attributes.

Idrisi is a raster-based GIS created at Clark
University. It is a relatively inexpensive GIS which
operates on an IBM microcomputer system. Idrisi version
3.2 was used to develop the procedures described in
Chapters VI and VII. Idrisi is composed of a group of
modules (subprograms) which can be used to manipulate,
store and display spatial data. Figure 5.1 illustrates
the major modules included with Idrisi. Each individual
module contains a series of executable commands that can
be used to manipulate the stored data.
IDRISI : A Grid-Based Geographic Analysis Systen Version 3.2
Systen Operation nodules
Data Entry nodules
Data Storage and Hanagenent
Display nodules
General Analysis
GIS nodules
Spatial Statistics
Inage Processing
Peripheral Hodules
Vector / DIMS
Exit Henu Systen
Idrisi Version 3.2 Modules

Idrisi supports vector images through conversion
routines and digitizing. The file structure used for
storing image data in Idrisi is a single column of
identifiers. Each identifier represents the map
descriptor being modeled. (For example, in a DEM file
all of the identifiers represent the elevation associated
with the cell location.) Using the document file
associated with each Idrisi image, the image can be
reconstructed by one of the various Idrisi display
commands. Data to be used with Idrisi must be in the
appropriate format prior to use.
The Idrisi users manual identifies the file types it
will support and appropriate formats. The manual also
provides detailed documentation for all of the modules
and commands available in the program. The following
information is therefore provided only as general
background to clarify the time-area procedures developed
using Idrisi.
Module Descriptions
Peripheral Modules
Idrisi provides a group of commands for importing
data from various sources. These commands can be used to
import the DEM data and also provide the necessary
structure for importing DLG data. When using the DEM
data from TOP030, however, no conversion is required.
Only the creation of a document file is necessary for the

image to be displayed.
General Analysis
Idrisi includes a group of commands which can be
used to perform a variety of map algebra processes.
These commands make it possible to overlay images by
addition, subtraction, division, multiplication, or
cover. Scaler operations are also available in the
General Analysis module. Scaler operations allow the
arithmetic operations to be performed on a single image
using a single scaler value. In addition to the overlay
and scaler commands, the reclass and assign commands
allow the flexibility to change, correct and vary the
identifiers associated with an image.
GIS Modules
Idrisi provides operations for directly working with
the spatial data. The commands included in the GIS
modules make it possible to determine the area associated
with specific identifiers; perform slope, aspect and
watershed determinations; and sum values from some target
to every location within the image using the shortest
path. These latter commands are extremely powerful and
are the basis for the calculations performed in this
research. Following is a brief description of the GIS
module operating principles.
SURFACE: The surface command determines both slope
and aspect associated with a DEM image.

IDRISI uses a procedure known as the
"rook's case" to determine the slope
associated with each cell in the image.
This procedure determines the slope from
each cell by examining the cells directly
above, below, to the left, and to the
right of the cell in question. The aspect
is then determined based on these
calculations as the direction of the
maximum slope. Idrisi considers cells of
zero slope to be able to flow in any
direction, and assigns them an identifier
of one.
The cost command computes an image where
the individual cell identifiers are the
distance measured as the "least effort" to
move from the cell to an outlet specified
as a target. The costs are calculated in
a radial direction from the target cell to
all cells included in the image. The cost
command requires a friction image (which
for the time-area procedure is the travel
times associated with each cell), and a
target image. The movements are
calculated for a possible eight directions
and the cost assigned to the cell is based

on the lowest possible cost. Diagonal
movements are calculated as 1.4 times the
cell value.
AREA: The area command measures the area
associated with integer identifiers of an
image. The output from this command can
be an image (where the identifier is the
area associated with the cell from the
original image), a summary table, or an
attributes file which can be used in other
WATRSHED: This command determines the watershed
limits associated with one or more surface
target cells by examining the aspect
image. Flat areas are assumed to be able
to flow in any direction. A more detailed
explanation of this process is included in
Chapter VI.
Data Entry Modules
The commands included in the data entry module
provide the ability to digitize vector representations of
lines, points and polygons. This module also provides
the means to convert vector data to a raster image, and
to update or change an existing image.
Display Modules
The various commands in the display module provide

the support for graphics display both at a monitor and at
a printer/plotter. The Color-a command and a screen
capture program were used to present all Idrisi images
included in this thesis.
Idrisi Limitations
It is essential that all modules within Idrisi be
accessed through command line processing because of the
large number of images that must be processed. However,
the majority of modules do not currently have this
ability. The next version of Idrisi, which is currently
being disseminated, provides command line processing to
most of the modules/commands. This will allow the full
automation of the procedures outlined in Chapter VI.
Once the procedures are automated, the processing of the
information to determine the time-area relationship will
be a simple function which can be run as batch file.

The time area procedure using GIS is the same basic
procedure outlined in Chapter II. The primary difference
is not in the procedure itself, but in the method of
manipulating the data (i.e., manual versus computer).
Figure 6.1 is a flow-chart identifying the major steps
reguired to determine the time-area relationship using
Elevation Data Required
The data required to establish the time-area
relationship is the same as that required when the
procedure is performed manually. The difference is in
the required format of the data. To use the GIS for
processing, all of the elevation data must be in a
digital format.
The initial information required to develop a unit
hydrograph is the digital elevation data for the study
area. This data can be obtained from a variety of
sources. However, the time-saving benefit of using a GIS
is dependent on importing the data from an existing
The United States Geologic Survey (USGS) has Digital
Elevation Models (DEMs) available in a variety of scales.
The basic format for this data is thoroughly detailed in
the USGS publication Geological Survey Circular 895-B.

Time-Area Procedure Using Idrisi

The USGS publication describes both the format and
structure of the data. The data is obtainable on a nine-
track magnetic tape (and in some cases on CD-ROM). The
elevation data is provided in a series of profiles that
together form the array of elevation values that make up
the DEM. The number of profiles is dependent on the map
scale in use.
Each profile contains header information. The
header provides the profile location, number of elevation
points for the individual profile, and other accuracy
information that may be available. Currently, two DEM
data sets are available:
(1) DEMs that correspond to the 7.5 x 7.5 data
(2) DEMs that correspond to the 1 to 250,000 scale
data files.
The two sets vary from one another in the sampling
interval, the geographic reference system used, the areas
covered, and in their accuracy. For example, most areas
of the United States are covered by the 1 to 250,000
scale data, to which set (2) is applicable. Only
selected quadrangles are covered by the 7.5 minute data
files. The accuracy associated with either data set is,
of course, dependent upon the accuracy of the source
The data set files are stored in ASCII (American

Standard Code for Information Interchange) format for
ease of information exchange. However, a primary
drawback to using the data directly from the USGS is that
the elevation data must be extracted from the header
information in the files. This step requires additional
processing of the data before importing it into Idrisi.
Due to the size of the files, the additional processing
is no small task. Another drawback of USGS DEM data for
the hydrologic modelling done in the subject research is
the high level of data resolution provided by USGS data
sets. Using the 1 to 250,000 scale DEMs, an elevation
value exists for each three arc-seconds of ground
distance. This equates to a ground distance of 90 meters
in the north-south axis, and a varying distance of 60-90
meters in the east-west axis (due to the convergence of
the meridians). Figure 6.2 is an orthographic
illustration using the USGS l-to-250,000 DEM data for an
area in northeastern Colorado.
The USGS DEM data is available from the USGS, Earth
Science Information Center, Reston, Virginia.
The National Geophysical Data Center (NGDC) has
created a data access tool to provide medium resolution
topographic data. NGDC software, TOP030, allows easy,
seamless access to a range of elevation values that are
directly usable by most GIS, including Idrisi (Idrisi
requires only the creation of a document file prior to

display or use by other modules). TOP030 provides access
to elevation data at 30 second intervals. (Using this
data provides one elevation value for every 100 values
obtained using the USGS data directly.) Figure 6.3 is an
orthographic image using TOP030 data for the same general
area represented in Figure 6.2 (both of these images
cover the same size area). These two figures illustrate
the difference in data resolution between the two
different data sources.
The TOP030 software was written to operate on an
IBM-compatible microcomputer, and data for the entire
United States may be purchased from NGDC, Boulder,
Colorado on floppy diskettes.
TOP030 software was used in the subject research on
the Cherry Creek basin. The data resolution was
acceptable; however, some preprocessing was required
before watershed boundaries could be determined, due to
local depressions or undrained areas caused by the DEM
resolution. ("The Effect of DEM Resolution on Slope and
Aspect Mapping" by Chang and Tsai (1991), presents a
detailed description of the effect of the DEM resolution
on the calculation of slope and aspect.) The resolution
of the data also limited the use of digital line graphs
for the stream networks.
Considering the ease of using TOP030, it appears to
be the best software available except where a computer



3ta s

^gj^sO n
*t)) oc


system has large storage capabilities. The use of TOPO30
requires obtaining the stream path locations from a
source other than the digital line graphs (DLGs), or
determining a method to select individual streams from
the DLG files. For the work done in the subject research
stream paths were digitized using the Idrisi software.
With most GIS systems, DEM images can also be
created from digitized contour maps (the map can be from
AutoCad or other computer aided drafting programs or be
directly digitized in the GIS). Using this procedure
requires interpolation between the contour lines to
create the required surface image, and is strongly
influenced by the accuracy of the digitized image. Most
interpolation packages are slow, however, and the one
included with IDRISI is no exception. This procedure is
therefore not a recommended option for working with large
watershed areas, but may be appropriate for the study of
a small area. Digitizing contours and interpolating them
to form the DEM was the method used to establish and
verify the procedures for the time-area method in the
subject research.
Stream Data Required
As stated earlier stream data is available in
digital form from the USGS and it can be obtained on
nine-track magnetic tape. Idrisi provides a direct
method for extracting the stream data from a DLG file.

The Idrisi routine contains the identifiers associated
with each of the "optional" format DLG files, allowing
direct access to the data. Figure 6.4 is an example of a
stream image obtained from a DLG file for northeastern
Colorado. This figure illustrates the density of a
stream network in a 15 minute area in both, the original
vector format (white lines) and in raster format (thick-
black lines).
A second method was also used to determine the
stream path locations for the study area: the major
stream paths were directly digitized for the study area.
This was accomplished using Idrisi (it can also be
accomplished using any digitizing method that creates a
vector file able to be incorporated into the GIS).
Digitizing stream paths allows the modeler to select only
those stream paths that most define the basin. However,
this method requires making the kind of judgments that
can easily result in increased errors.
In the subject research, several combinations of
stream paths were used to define the watershed boundaries
and the travel times. Although the research outcomes are
based on a very limited number of actual and hypothetical
basins, they appear to most closely resemble outcomes
obtained by manual calculations when major streams
representing various geographic areas in the basin were
included in the calculations.

DLG Stream Network (Raster and Vector Image)
for a 15-minute Area in Northeastern Colorado

Coefficients Required for Calculations
The coefficients required to perform the velocity
calculations using GIS are no different than those
coefficients required for doing calculations manually.
Storage routing coefficients and their usage was
explained in detail in Chapter II, and will not be
repeated here. The hydraulic radius and channel
roughness can be determined as described in Chapter II,
or can be based on other digital data when such data is
available. For example, actual stream cross-section
data, where available, could be used to calculate the
wetted perimeter and stream area for various cross-
sections along a stream path. The information would then
be averaged and included in calculations of the hydraulic
radius and roughness coefficients. Using a program such
as AutoCad, simple lisp routines could be used to build
tables of values applicable to various locations along
the stream path. It is important to note however, each
piece of information added to the process increases
processing times and complicates the procedures.
Additional data is often not warranted in this type of
hydrologic study. The GIS techniques described in this
chapter include the travel times associated with overland
flow. Determination of the coefficients for overland
flow calculations are detailed later in this chapter.
A complete sensitivity analysis is required to

determine exactly what additional information actually
improves the results. Based on the limited data from the
subject research, no conclusions could be reached about
which data to add to the synthetic unit hydrograph
development procedure. An obstacle to completing a
sensitivity analysis is the number of calculations
required for each different trial. Automating the
procedures allows for preparation of an input file and
running the program in batch mode. This will become
possible with the release of the next version of Idrisi.
Using digital data to determine an overland flow
coefficient is more practical than using digital data to
determine the various hydraulic properties of a stream.
Existing land use data is currently available and allows
for easy extrapolation to a GIS system. The limiting
factor with this approach is the determination of the
coefficient based on land use. SCS curve number
information could be incorporated, or, as was done for
this study, the values presented in McCuen (and presented
in Table 6.1) may be used.
Using a GIS it is simple to assign a value to a
contiguous area to represent a given land condition. For
example, Figure 6.5 represents a basin consisting of
various land covers. Assigning coefficients representing
the coefficient "k" to these areas allows for their
direct usage in velocity calculations. Again, a user

must determine if the added information is truly valuable
to the results. The question that should be asked is, if
the addition of data allows the model to more closely
match the actual system, the additional data should be
included. Determining the answer to this question is the
focus of considerable research.
Land Use Factors k coefficient (McCuen)
Coefficient k Land Use Description
0.25 Forest with heavy ground litter; hay meadow (overland flow)
0.50 Trash fallow or minimum tillage cultivation; contour or strip cropped; woodland (overland flow)
0.70 Short grass pasture (overland flow)
0.90 Cultivated straight row (overland flow)
1.00 Nearly bare and untilled (overland flow); alluvial fans in western mountain regions
1.50 Grassed waterway
2.00 Paved area (sheet flow); small upland gullies

htflUY FOREST aoe
rnnn uve HXH
IP LAND 6ULL1 11*1*3

Land Cover Example
Watershed Boundary Determinations
As described in Chapter II, a watershed is that area
that sheds or drains water to an outlet or design point
during a rainstorm. The watershed boundaries may be
determined manually, or by using the GIS software.
Determining the boundaries of the watershed using the GIS
software Idrisi is accomplished with the WATRSHED module
and the DEM data (see description in Chapter V). The
watershed image created with this module is a boolean
image. It consists of an identifier of one for all areas
within the watershed, and a zero for all areas outside

the watershed basin. Note that although the watershed
procedure in Idrisi requires the creation of an aspect
image only (as opposed to both an aspect image and a
slope image), the aspect is determined based on the
slopes; and the velocity calculations also require the
use of a slope image. Therefore, it is logical to create
both the slope and aspect images during the watershed
definition. The slope and aspect images are created
based on the DEM. The slope image consists of maximum
slope for each cell within the region as the image
identifier. The aspect image is the direction of the
maximum slope in reference to the adjacent cells. These
two images combined can be used to determine the flow
directions from any location in the watershed.
Determining the boundaries of a watershed using most
GIS software is based on flow directions and is affected
by local depressions within the image. These local
depressions are often drained by small streams that are
not discernable in the DEM. This is particularly a
problem when working with the 30 second DEM resolution.
To limit the effects of the problem, two methods
suggested in the Idrisi users manual appeared to provide
acceptable results. The two methods are:
(1) Use a mean filter to smooth the DEM image before
determining the slopes and aspects for the DEM.
(2) Use the stream network as the "target for the

Once the aspect image has been created, running
the watershed module requires only the definition of a
target. The target can be a single outlet point or a
group of cells defining the stream network. In the
subject research using the stream network provided the
most accurate definition of the watershed boundaries.
Figure 6.6 is an overlay of a watershed determined by
using manual techniques on one determined by using the
GIS procedures outlined in this thesis.
Comparing the areas of each watershed indicates a
difference of less than 5 percent.
As with the creation of DEM images, the greatest
time savings associated with using a GIS to develop the
time area curves is accomplished when the computer does
the majority of the work. Allowing the GIS to define the
watershed boundaries also provides a considerable time
savings. Any error in calculation of the boundaries does
have an effect on the definition of the unit hydrograph,
and using published USGS basin areas as the actual area
of a watershed (as compared with the GIS-determined
watershed area) increases the error. However, using the
Cherry Creek basin as an example, the research determined
that a variety of other coefficients used in these
procedures had a greater effect on the outcome. (For
example, the storage routing coefficient

Comparison of Manual and Idrisi Generated Watershed Areas
and the roughness strongly impact the final results
obtained using these methods.)
Travel Time Determinations
Travel time, as explained in Chapter II, is the time
for one drop of water to travel to the basin outlet from
some point within the basin. A wide variety of methods
exist for determining this value. The subject research
compared several methods, all based on combinations of
stream flow and overland flow.
Technically, the more stream paths included the more
accurate the travel times will be. This assumes that
overland flow is valid for approximately 300 yards before

the formation of channel. Using a stream network
consisting exclusively of the major streams provided a
time of concentration eguivalent to the values calculated
using the SCS method. Using the limited actual data
included in this research, the travel times are primarily
affected by the slopes along the main stream paths. The
addition of more channels did not greatly affect the
final outcome.
Determining the velocities for the channels was
based on the procedure outlined in Chapter II. Following
is a more detailed explanation of the procedure using
GIS, as well as more detail on the determination of
overland flow velocities and the principles of map
algebra. Figure 6.1 illustrates the procedure.
The concepts of map algebra are foreign to those who
are unfamiliar with GIS. The main principle is that the
entire area (map) is affected by the arithmetic
operations performed. For example, the boolean watershed
image is comprised of all zeros and ones. It is possible
to use map algebra to multiply, divide, add, subtract or
raise this image to some power using a scaler quantity.
Multiplying, dividing, or using an exponential value
would only affect the area containing the value of one.
On the other hand, adding or subtracting a scaler value
would affect the entire image. Additionally, two images
may be combined using standard arithmetic operators. For

example, the boolean watershed image could be used as
multiplier against the slopes for the entire region. The
results of this operation would be a slope image for just
the areas within the watershed. These procedures were
used extensively for determining the travel times in the
example basins included in this research.
Stream Path Velocities
Determining the stream path velocities was also
based on the methods outlined in Chapter II. Manning's
equation was used with a value chosen from Table 2.1 for
the hydraulic radius and roughness coefficient. Using
Manning's equation, the individual cell velocities are
calculated and become the cell identifiers for the new
V=k/*S0-5 (6.1)
with k' = (1.49/n)*R0-667 chosen from Table 2.1
S = to the slope in feet/foot along the drainage
paths only
Using the slope image created during the watershed
definition requires map algebra to eliminate the slope
values that are not on the stream paths, and to convert
the slopes in decimal format to feet/foot. To accomplish
this, the entire slope image must be multiplied by the
stream path locations. All of the map algebra steps
require a careful understanding of the desired outcomes

to assure that correct units and values are maintained.
For example, when calculating the slopes along the
drainage paths it is possible to multiply by an image
that would adversely affect these values. (When using
the multiplication procedure, one image must always be a
boolean image, values of ones and zeros. This prevents
inadvertently changing the desired output.)
Overland Flow Velocities
After the creation of a new image consisting of the
square root of the slope values along the stream path, a
similar procedure is followed to determine the velocities
associated with overland flow. Using the equation
V-kS0,50 (6.2)
where k = coefficient for land cover from Table 6.1
or an image where k values are the
identifiers for various landuse area
S = the slope image for the entire watershed
the individual cell velocities are determined.
Combining the stream velocity image and the overland
flow velocity image using the "overlay" command in Idrisi
creates a composite image containing a velocity value for
travel through each cell within the watershed.
Travel Time Calculations
Conversion of the velocities to travel times is done
using a constant value for the distance across a cell.

This step does not produce exact results for two reasons.
The first is that the actual flow can travel in an
infinite number of patterns across a cellfor example,
directly horizontally, directly vertically, or at any
number of possible angles, each with a variable distance.
However, using an average value (a value that combines
the horizontal and vertical distances) for the cell
distance provides adequate results. The diagonal travel
is accounted for by the Cost command. When Cost is used
to sum these values, diagonal flow is calculated as 1.4
times the cell identifier, which has the effect of
considering an angular flow direction. Dividing an image
that has this average distance as its cell identifier by
the velocity image creates a new image consisting of
individual flow times for each cell within the watershed.
The next step in establishing the time area
relationship requires the summation of travel times from
each cell in the image to the basin outlet. This step is
performed using the Idrisi module COST. The basic
principle of COST is that it performs a summation using
the shortest path to the target from any cell within the
image. This new image is the time area image. The time
units are based on the velocity and distance units used.
Reassigning a range of time values to a convenient
increment (15 minutes, 30 minutes or 1 hour) based on the
time of concentration completes the images required for