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Parameter Sensitivity in Hydrologic
Modeling
Tanya HoogerwerfMarch 7th, 2002
Outline Flood discharge calculation
overview Problem statement and
research objectives Case studies Sensitivity analysis of
hydrologic parameters Conclusions
Flood Discharge Calculation
Soil Type and Land Use
Hydrologic Modeling Parameters
SLOPE
Longest Flow Path (LFP)
AREA
Slope
Longest Flow Path
Area
Soil Type and Land Use (CN)
How Are Parameters Calculated?
Level 1:
From Paper Maps (Traditional Method)
Map Wheel Planimeter
Level 2:
From Scanned Maps
How Are Parameters Calculated?
Level 3:
From Grid-Based Digital Elevation Models (DEMs)
Level 4:
From Triangulated Irregular Networks (TINs)
Lag Calculation
Soil Type and Land Use
SLOPE
Longest Flow Path (LFP)
Lw is Longest Flow Path
CN is Curve Number (derived from Soil and Land Use Data)
s is slope
s
CNL
tw
lag67.31
91000
(min)
7.08.0
SCS Lag Formula (1972)
Flood Discharge Calculation
s
CNL
tw
lag67.31
91000
(min)
7.08.0
SCS Lag Formula (1972)
Q
t
Qpeak
Problem Statement
Differences encountered in lag results between traditional methods and automated methods
Traditional MethodsAutomated Methods
Research Objectives
For traditional and automated processes, determine Sources of error Range of errors Significance of errors
Outline Flood discharge calculation
overview Problem statement and
research objectives Case studies Sensitivity analysis of
hydrologic parameters Conclusions
What Was Used to Test? Set up the four levels of case studies 3 differently sized areas
0.5mi2
8.8mi2
1.6 mi2
Determination of Parameter Sensitivity
% change in slope…% change in lag…% change in Q
Case 1: Measurement From Paper Maps
Case II: On Screen From Raster Maps
Case IIIA: 10m and 30m Digital Elevation Models, Using GIS/CRWR-
PrePro
Case IIIB: 10m and 30m Digital Elevation Models Using WMS
Case IV: Automated Methods Using WMS and a Triangulated Irregular Network Model (TIN)
Longest Flow Path
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
1 2 3
Area
Mile
s
PrePre30
PrePre10
Hand
Digitized
WMS-30
WMS-10
Coefficient of Variation
0
1
2
3
4
5
6
7
8
9
Area Curve Num ber LFP Slope
%C
v
Area 1
Area 2
Area 3
%Cv = /
Case Study Results
Outline Flood discharge calculation
overview Problem statement and
research objectives Case studies Sensitivity analysis of
hydrologic parameters Conclusions
Elasticity As a Measure of Sensitivity
Elasticity is dimensionless
Provides measure of sensitivity <1 is “inelastic” >1 is “elastic”
y
xX*
Y*
input
output
change
change
XdxY
dy
elasticity%
%
*
*
Area 2
95.0
100.0
105.0
110.0
115.0
120.0
2.80 2.90 3.00 3.10 3.20 3.30 3.40
LFP- miles
LAG
Longest Flow Path
Analytical Calculation of Gradients
Q t
As the longest flow path varies by 13.2%, the lag varies by 10.6%
The elasticity is 10.6/13.2 = +0.80…inelastic
13.2%
10.6%
% Change in LAG
Dis
char
ge (
Q)
Numerical Calculation of Gradient
Q t
10.6%
-3.04%
Elasticity =-0.29
Sensitivity Results
% change in parameter…..% change in lag…..% change in Q
-35.0%
-30.0%
-25.0%
-20.0%
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
20.0%
% V
ari
ati
on
fro
m M
ea
n
Param eter Input
Lag Ouput
Q Output- 2 Yr
Elasticity
SLOPE
14.0%
%
Slope
Q
Change
Change
LONGEST FLOW PATH (LFP)
29.0%
%
LFP
Q
Change
Change
CN
01.1%
%
CN
Q
Change
Change
Elasticity
AREA
14.1%80.1
%05.2
%
%
Area
Q
Change
Change
CN
01.1%99.8
%09.9
%
%*
%
%
%
%
lag
Q
CN
lag
CN
Q
Change
Change
Change
Change
Change
Change
Conclusions
Automated methods using grid-based DEMs are less time consuming than traditional methods…USE AUTOMATED METHODS
Slope and longest flow path measurements do not greatly influence discharge
Measurements of area do not vary greatly, spend time/resources obtaining accurate soil and land use data for CN
~Thanks ~
Dr. Maidment
David Stolpa
Dr. Charbeneau
Dr. Barrett
Dr. Nelson
CRWR Group
EWRE Friends
Environmental Modeling Systems, Inc.
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