The first step in order to develop a mathematical model for accurately predicting flood is to identify the parameter that affects the flood predictive model. In this case, the PWRI-DH model has twenty-nine main parameters that need to be clarified in order to understand its influences in the general problem. In this section, the results of this study are presented in detail.
3.1.1 Influence of parameter in the PWRI-DH model
In order to clarify the influence of each of the twenty-nine parameters on the results of the PWRI – DH model, the authors have studied how sensitive the model is to each of these parameters. In this sensitive analysis, each parameter is varied from 0.5 to 1.5 times of the value given as the baseline parameter in the model (see Table 3.1 to 3.4 for baseline parameters). The simulation is performed, keeping the remaining parameters fixed (baseline value) while varying the parameter of interest. In all the cases, cell size is 100 meters length, and the same rain episode at upper Aikawa River (20 to 21st of July, 2009) is used. It is important to emphasize that with this sensitivity analysis we seek to know if a specific parameter has significant impact or not on the result of the model, that is why we carry out the study by varying each parameter within a particular range, that does not necessarily mean that those are the values that parameter can take, but it tells us how sensitive the model is to a specific parameter. In addition to the above, there are two
59 parameters (HIFD and RGWD) that are of zero magnitudes, and they do not take another different value; therefore, they are not included in the analysis.
Table 3.1. Baseline parameter used in the surface tank
Parameter
group Final
infiltration capacity - Io
(cm/s)
Maximum storage height – hf2
(m)
Rapid, intermediate flow – hf1 (m)
The height where ground
infiltration occurs – hf0
(m)
Surface roughness coefficient – N
(m1/3s-1)
Rapid, intermediate
flow regulation coefficient - α
Initial storage height - ha (m) Symbols
use in IFAS SKF HFMXD HFMND HFOD SNF FALFX HIFD
Base line (PD)
1 0.0005 0.1 0.01 0.005 0.7 0.8 0
2 0.00002 0.05 0.01 0.005 2 0.6 0
3 0.00001 0.05 0.01 0.005 2 0.5 0
4 0.000001 0.001 0.0005 0.0001 0.1 0.9 0
5 0.00001 0.05 0.01 0.005 2 0.5 0
Table 3.2. Baseline parameter used in the subsurface tank
Parameter group
Vertical saturated hydraulic conductivity
– Csz (cm/s)
Horizontal saturated hydraulic conductivity
– Csx (cm/s)
Maximum water height – h2max (m)
Soil moisture at saturation -
θs
Soil moisture
at the wilting point - θw
Soil total porosity
- b
Water height h2
-(m)
Vertical hydraulic conductivity at the wilting point - Cz
(cm/s)
Simbols
use in IFAS SKD SKX HMXSD STS STW SBD
HISDO-SS SKOD
Base line (PD) 1 0.0004 0.2 0.6 0.6 0.4 12 0.3 0.000001
2 0.0005 0.2 0.6 0.6 0.4 12 0.3 0.000001
3 0.0006 0.2 0.6 0.6 0.4 12 0.3 0.000001
4 0.0007 0.2 0.6 0.6 0.4 12 0.3 0.000001
Table 3.3. Baseline parameter used in the aquifer tank
Parameter group
Runoff coefficient of unconfined aquifer – Au – (1/mm/day)^1/2
Runoff coefficient of confined aquifer
– Ag – (1/day)
The height where the unconfined aquifer runs off –
h3max (m)
Initial water height – h3 (m)
Symbols use in IFAS
AUD AGD HCGD HIGD
Base line (PD) 1 0.1 0.003 2.0 2.0
2 0.11 0.003 2.0 2.0
3 0.12 0.003 2.0 2.0
4 0.13 0.003 2.0 2.0
Table 3.4. Baseline parameter used in the river tank
Parameter group
Constant of the resume law - C1
Constant of the resume law – C2
Manning roughness coefficient
- n
The initial water table of the river channel
Infiltratio n of aquifer
tank
Coefficie nt of cross shape /
C4
Coefficient of cross shape / C5
Flood channel width / low/chan nel width
– C3
Flood channel slope – C6
River course length calibration coefficient
- L Simbols
use in IFAS
RBW RBS RNS RRID RGWD
R
H W RHS
R
B H
RBET RLCOF
Base line (PD) 1 7 0.5 0.035 0.2 0 9999 1 0.5 0.05 1.4
2 7 0.5 0.035 0.2 0 9999 1 0.5 0.05 1.4
3 7 0.5 0.035 0.2 0 9999 1 0.5 0.05 1.4
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
60 Figure 3.1 shows the hydrogram variation with the “height where rapid, intermediate flow occurs (HFMND)” parameter. As seen, as we increase this parameter, the predicted discharge will decrease. This can be understood by analyzing the problem as a simple tank or vessel: the greater difference between water level height and water exit orifice, the higher is the pressure at the outlet and more significant is the discharge. If we increase the elevation where this exit occurs, then a decrease of the height difference occurs;
therefore, the discharge is decreased. As a result, the water flow will decrease, which turns in delays in the input. Because reducing the parameter of the storage capacity corresponds to the case when the precipitation falls rapidly, it will be converted in more than flow. As shown in the figure, this parameter plays a fundamental role in the PWRI-DH model because the variation of the parameter results in a considerable change in the discharge.
Figure 3.2 shows the hydrogram variation with the “rapid, intermediate flow regulation coefficient (FALFX)” parameter. This parameter has an opposite behavior to that of the parameter HFMND. This behavior occurs because the contribution of this parameter is related to the relationship with other heights of the tank, as it is explained in the previous section.
Figure 3.3 shows the hydrogram variation with the “surface roughness coefficient (SNF)”
parameter. As shown, when the baseline parameter increases, the discharge decreases, and vice versa. The explanation of this phenomenon is found in the fact that this parameter affects the pass of the flow to the aquifer tank. As shown in the figure, this parameter also affects the discharge significantly and thus must be considered as a critical parameter in the calibration of the PWRI-DH model.
Figure 3.4 shows how the hydrogram variation with the “height where ground infiltration occurs (HFOD)” parameter. It is demonstrated that this parameter is responsible for the behavior in the increment period and the recession period. As shown in the figure, this parameter has a considerable influence on the prediction of flood discharge using the PWRI-DH model; thus, it is also a key parameter in the calibration of the model.
The other two parameters of the surface tank: SKF and HFMXD, does not influence the model results as it is shown in Table 3.5, where the pick discharge value is compared.
Similar behavior is observed in Table 3.6, 3.7, and 3.8, where the resulting pick discharge value is compared varying each of the parameters of the unsaturated, the aquifer, and the
61 river tank, respectively. It is clear that the influence of those parameters on the resulting discharge is minimal, so we don’t need to consider them during the calibration of the model. Despite the fact that considering those parameters will deliver more precise results, it has still been a time-consuming task with minimal impact; thus, it is recommended to only focus on the four parameters presented in Figure 3.1 to 3.4 since they together allow to calibrate the model easier.
In case of the parameters HCGD and HIGD, shown in Table 3.7, there is seen a considerable variation on the resulting peak discharge; however these results are not correct since these two parameters depend on each other, so if we vary one without considering the second, the model will deliver a wrong result as it is observed in the table.
Figure 3.1. Variation of discharge with the parameter heigh where a rapid, intermediate flow occurs (HFMND)
0 5 10 15 20
Discharge(m3 /s)
0.5HFMND 0.75HFMND HFMND 1.25HFMND 1.5HFMND Measured
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
62 Figure 3.2. Variation of discharge with the parameter rapid, intermediate flow
regulation coefficient (FALFX)
Figure 3.3. Variation of discharge with the parameter surface roughness coefficient (SNF)
0 5 10 15 20
Discharge(m3 /s)
0.5FALFX 0.75FALFX FALFX 1.25FALFX 1.5FALFX Measured
0 5 10 15 20
Discharge(m3/s)
0.5SNF 0.75SNF SNF 1.25SNF 1.5SNF Measured
63 Figure 3.4. Variation of discharge with the parameter height where ground infiltration
occurs (HFOD)
Table 3.5. Variation of discharge with parameters of the surface tank Variation of the
baseline parameter
SKF HFMXD
0.5P 7.447 8.4459
0.75P 7.9782 8.5088
P 8.2499 8.2499
1.25P 8.406 7.9765
1.5P 8.4619 7.7342
Table 3.6. Variation of discharge with parameters of the Subsurface/unsaturated tank
Variation of the baseline parameter
SKD SKX HMXSD STS STW HISDO_SS SKOF
0.5P 8.2499 8.2499 8.2499 8.2499 8.0263 8.2499 8.2499 0.75P 8.2499 8.2499 8.2499 8.2499 8.1602 8.2499 8.2499 P 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 1.25P 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 1.5P 8.2499 8.2499 8.2499 8.2499 8.2499 8.3456 8.2499
Table 3.7. Variation of discharge with parameters of the aquifer tank 0
5 10 15 20
Discharge(m3 /s)
0.5HFOD 0.75HFOD HFOD 1.25HFOD 1.5HFOD Measured
Variation of the
baseline parameter AUD HCGD HIGD
0.5P 8.2287 177.7 7.5105
0.75P 8.2376 129.36 7.8688
P 8.2499 8.2499 8.2499
1.25P 8.2653 8.2215 129.54
1.5P 8.2837 8.2215 178.06
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
64 Table 3.8. Variation of discharge with parameters of the river tank
Variation of the baseline
parameter RBW RBS RNS RRID RHW RHS RBH RBET RLCOF
0.5P 8.696 8.3081 8.8723 8.2499 8.2499 8.2499 8.2499 8.2499 8.6449 0.75P 8.4507 8.2809 8.5409 8.2499 8.2499 8.2499 8.2499 8.2499 8.4574 P 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 8.2499 1.25P 8.0787 8.2153 7.9869 8.2499 8.2499 8.2499 8.2499 8.2499 8.0314 1.5P 7.9293 8.1776 7.7536 8.2499 8.2499 8.2499 8.2499 8.2499 7.8086
Based on the analysis of the influence on the discharge of each of the twenty-nine (29) parameters associated with the PWRI- DH model, the author has concluded that the effectiveness of the model does not depend on the influence of each of the total number of parameters, rather to a small number of parameters. Thus, the number of parameters to be calibrated for modeling a specific river flood with enough precision is four (4). In the following section, a methodology for the calibration of the PWRI-DH model is presented.
This methodology is based on the conclusion obtained from the sensitivity analysis.