FLOOD09697

• County: Statewide
• Community: Nationwide
• Basin: Statewide
• Title: Mathematical Modeling of a Sociological and Hydrologic Decision System
• Date: 6/1/1978
• Prepared By: Institute for Social Science Research on Natural Resources, Utah State Univ.
• Floodplain - Doc Type: Educational/Technical/Reference Information

Time and Space Increments

The.incremenls of time and space need 10 be
carefully selected during model design. Data, such
as temperature and precipitation readings, usually are
available as point measurements in time and space. and
inlegration in both dimensions usually is accomplished
by the method of fmite incremenl.s.

The complexity of a model to represent a hydro-
logic system varies with Ihe magnitude of the time and
space increments utilized. Large increments, how-
ever, cannol be used for phenomena which change
over relatively small i'lcremenls of space and time. In
addition, the time increment can be chosen to coin-
cide wilh Ihe period of cycllc changes in certain hydro-
logic phenomena so thai net changes in these phenom-
ena during a time interval are usually negligible. For
example, storage changes within a hydrologic syslem
from year to year are often insignificant whereas, the
magnilude of Ihese changes from month 10 month
are frequently appreciable and need to be considered.
As one attempts to achieve fmer resolution in time
and space, improved defmition of Ihe hydrologic pro-
cesses is required. Short-term transient effects or ap-
preciable variations in space cannot be neglected, and
Ihe required malhematical model, therefore, becomes
more complex with an accompanying increase in re-
quired computer capacity and capability.

However, as shown on Figure 3.2, it is often
possible to simplify high resolution models by elimin-
ating processes which do not appreciably affect the
output of interest. For example, in modeling Ihe
rural portions of the watershed, bolh a daily time
incremenl. (Figure 3.3) and an hourly time increment
(Figure 3.4) were used. For Ihe daily time increment
model, all of the hydrologic processes are included.
On the olher hand, to estimate peak surface runoff
rates from cloudburst storms, some processes, such as
snowmelt and soil moisture movement, need not be
included bul a high degree of resolution in Ihe time
dimension is necessary. For this reason, the hourly
time increment model (Figure 3.4) represenls fewer
processes than the daily model, but at a high degree
of time resolution. Thus, the application is a prime
consideration in_model formulation.

For Ihe urban hydrology model of the sludy,
a 3D-minute time increment and small space units
(zones) were adopled. Zones were dermed to enable
spatially varying watershed conditions, such as slope
and infiltration rate, to be considered by the model
and marked offas shown by Figure 2.2 along hydro-
logic boundaries matching points of data availability.
The probable issues in reaching flood management de-
cisions were considered in selecting the time and space
increments for the models.

System Processes

The system processes included in the hydrologic
models of this study (for bolh urban and rural drain-
age areas) are discussed in the following paragraphs.

Precipitation

Waler enters the hydrologic syslem as precipita-
tion. Precipitation on a catchment area is estimated
by a spatial integralion techriique, such as Ihe isohye-
lal melhod or the Thiessen v.eighting procedure, from
point data from a gage network. The Thiessen network
was applied in this study (Figure 2.7), and Ihe inpul
hydrographs for individual storm events were deter-
mined by a compuler program. Since rain causes Ihe
major flood events in the Salt Lake Valley, the
snow accumulation and melt processes are not in-
cluded in the model.

Surface Water Inflows

Streamflow is precipitation which streams and
rivers collect from a drainage area. If only a portion
of the drainage area is included within the boundary
of the area being modeled, streamflow inpuls to the
modeled area are either measured or estimaled by cor-
relation.

Interceplion

Rainfall excess is calculated by subtracting inter-
ception on the leaves of trees and other intercepting
objects from the measured precipitation. The rate of
interception is assumed to reduce exponentially with
an increase in interception storage. and can be expressed
as follows:

i ; ie -PIS,
co

. (3.2)

in which
icc capacity rate of inflow into intercep-
tion storage
; rate of precipilation

P ; cumulative precipitation
S, ; volume of interception slorage capacity
expressed as an average depth over the
catchmenl area

The actual interception rate, iea' is defmed by the fol-
lowing expressions:

iea = i, for i ~ ice'

. . (3.3)

and

iea = ice' for i > ice

2S