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.
65 grouping the parameter as a family. In this way, we can keep the number of interaction smaller.
• Once we achieve the best approximation for the first parameter, we must repeat the process for the second, the third, and the fourth, until the estimate is good enough compared with the observed discharge from the flood event, always keeping the parameter value obtained from previous step constant.
• In case there is a lag time comparing the simulated and the observed discharge, we must adjust the hydrograph time or even delete the last step.
• Estimate the accuracy of the model using the Nash-Sutcliffe coefficient, as shown in Equation 3.1
𝑁𝑆 = 1 − ∑ (𝑄𝑂𝑏𝑠−𝑄𝑐𝑎𝑙)2
𝑗 𝑖
∑ (𝑄𝑗𝑖 𝑐𝑎𝑙𝑐−𝑄̅̅̅̅̅̅̅)𝑜𝑏𝑠 2 (3.1)
Where Qobs represents the observed discharge, and Qcal represents the simulated.
• Group the new set of parameters as a family referred to the specific rain event (Group P1 for example)
• Repeat Step 1 to 8 for each of the m rain events until to get the Pm group of parameters.
• Simulate each rain event using each of the Pm group of parameters associated with a specific rain event
• Tabulate the NS coefficient for each rain event and for each group of parameters
• Get the average of the NS coefficient for each group of parameters.
• Choose the group of parameters that the best average of NS coefficient has. The final group of parameters selected must accomplish two essential points: obtain the best average value of NS and be accepted by the m of events. This group of parameters is recommended for calibrating the specific watershed.
A schematic of the methodologic is shown in Figure 3.5.
3.2.1 Study case
The Aikawa River is used as an example.This river is a tributary of the Yodo River, located in the Osaka area. The Upper Aikawa Basin is in a mountainous area, covered with vegetation and a few urban areas. The Upper Aikawa basin has a catchment area of 90.63 km2. From Shuttle Radar Topography Mission data, the elevation varies from 8 to
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
66 520 meters above the mean level of the sea (mMSL), as shown in Figure 3.6. Two points are used in the calibration; the upper point is at Kuwanohara with a latitude of 34 ° 51’
41.5” and a longitude of 135 ° 33’ 36.22’’; the lower position is at Senzai with a latitude of 34° 49’ 22.06” and a longitude of 135° 34’ 48.18’’.
Figure 3.5. Process for the calibration of the PWRI-DH model.
In order to validate the proposed methodology, we choose the five (5) highest events of flood occurred in the Aikawa River in the period of 1969 to 1999 (since 1969-6-25 to 1969-6-27 (event 1), since 1972-7-12 to 1972-7-13 (event 2), since 27 to 1983-9-29 (event 3), and since 1986-7-20 to 1986-7-22 (event 4) and since 26 to 1999-6-28 (event 5)).
Figure 3.6 to 3.10 show the hydrograms of each rain event together with the precipitation.
Using the rain and discharge data showing in those figures, we proceeded to find the parameters that calibrate each event individually, following the above methodology, i.e., we obtain five (5) groups of parameters (P1, P2, P3, P4, and P5). Each parameter group is tested in the other four (4) events to observe the discharge behavior and obtain the NS value. Table 3.9 resumes the results. Note that in some cases a specific group of parameters does not allow us to get results from a rain event (whitespace in the table), this is due to the fact that the model could not run with some combination of parameters;
since some parameters are related to others as it was explained in Section 2.5.3.
P1
P 2
P 3
P m Event 1
Event 2
Event 3
Event m
Parameter Set
Validation ℎ𝑓1, ℎ𝑓0,
𝑁, 𝛼
67 Figure 3.6. Observed data for flood event 1
Figure 3.7. Observed data for flood event 2
-5 5 15 25 35
1969/06/25 10:00 1969/06/26 6:00 1969/06/27 2:00 1969/06/27 22:000 50
100 150 200 250
Precipitation in mm
Period of Time
Discharge in m3/s Precipitation
Discharge
-5 5 15 25
1972/07/12 0:00
1972/07/12 12:00
1972/07/13 0:00
1972/07/13 12:00 0
50 100 150 200 250
Precipitation in mm
Period of Time
Discharge in m3/s
Precipitation Discharge
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
68 Figure 3.8. Observed data for flood event 3
Figure 3.9. Observed data for flood event 4
-5 1983/09/26 10:00 1983/09/27 11:00 1983/09/28 12:00
0 20 40 60 80 100 120
Precipitation in mm
Period of Time Discharge in m3/s Precipitation
Discharge
-5 5 15 25 35 45 55
1986/07/200 1986/07/21 1986/07/22 1986/07/22 50
100 150 200 250 300
Precipitation in mm
Period of Time
Discharge in m3/s
Precipitation Discharge
69 Figure 3.10. Observed data for flood event 5
-5 5 15 25 35
1999/06/27 10:00
1999/06/27 22:00
1999/06/28 10:00
1999/06/28 22:00 0
50 100 150 200 250 300 350 400 450 500
Precipitation in mm
Period of Time
Discharge in m3/s
Precipitation Discharge
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
70 Figure 3.11. The upper Aikawa River basin
Figures 3.12 to 3.16 show the comparison of the discharge observed values and the discharge obtained by simulation of each rain event using each of the groups of parameters. Table 3.9 shows the Nash-Sutcliffe coefficient for each of the flood events, where the values in parenthesis are the lag times in hours (H), and the last column corresponds to the observed peak discharge for each rain event. In this specific case, parameter group P4 is the one that best NS coefficient has, in addition, that it was able to simulate each of the rain events; thus, it is the parameters group recommended for calibrating this river when using the PWRI-DH model.
It is noted that IFAS works by solving a set of mathematical equations that are composed of a series of variables (parameters), many of them geometric. Within these parameters, we can mention the heights of the tanks, for example. It is essential to mention that these parameters must be obtained, either experimentally or through mathematical approximations. In some cases, not all values are available; therefore, they are approximated by trial and error. On the other hand, several of the parameters are related
71 to each other; in fact, some are conditioned to the value of others. It can be the case that a value is assigned to a parameter, and this does not fulfill the relationship that it must have with another parameter producing that the software does not converge, and therefore, we do not obtain a solution to the problem. The last is the case observed in Table 3.9 that appears without data (Event 1 for P2, P3, and P5; Event 3 for P2; Event 4 for P2, P3, and P5) In such case we must change the value given to the parameter until a solution is obtained.
Table 3.9. Nash-Sutclifle coefficient for different flood events.
Events
Nash-Sutclifle coefficient (lag time)
P1 P2 P3 P4 P5 OBS
Data
Event 1 0.95(0 H) -- -- 0.74(0 H) -- 72 Event 2 0.39 (5H) 0.56 (5H) 0.39(5H) 0.26 (5H) 0.46(5H) 39
Event 3 0.77 (4H) -- 0.89 (2H) 0.82(0H) 0.77 (3H) 66
Event 4 0.78 (0 H) -- -- 0.78 (0H) --- 72
Event 5 0.50 (1H) 0.76 (1 H) 0.73 (1 H) 0.87 (1H) 0.90 (2H) 35
Average 0.68 -- -- 0.69 --
Figure 3.12. Comparison of the hydrograms in event 1 using different group parameters.
0 50 100 150 200 250 300
10 14 18 22 2 6 10 14 18 22 2 6
25 26 27
June, 1969
Discharge m3/s
OBS P_1 P_4
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
72 Figure 3.13. Comparison of the hydrograms in event 2 using different groups of
parameters.
Figure 3.14. Comparison of hydrograms in event 3 using different groups of parameters.
0 50 100 150 200 250 300
0 3 6 9 12 15 18 21 0 3 6 9 12
12 13
July,1972
Discharge 3/s
OBS P_1 P_2 P_3 P_4 P_5
0 50 100 150 200 250 300 350 400 450
6 10 14 18 22 2 6 10 14 18 22 2 6
27 28 29
September,1983
Discharge m3/s
OBS P_1 P_3 P_4 P_5
73
Figure 3.15. Comparison of the hydrograms in event 4 using different groups of parameters.
Figure 3.16. Comparison of the hydrograms in event 5 using different groups of parameters.
0 50 100 150 200 250 300 350
10 14 18 22 2 6 10 14 18 22 2 6 10 14 18
20 21 22
July,1986
Discharge m3/s
OBS P_1 P_4
0 50 100 150 200 250 300 350 400 450 500
0 2 4 6 8 10 12 14 16 18 20 22
JUNE 27,1999
Discharge m3/s
OBS P_1 P_2 P_3 P_4 P_5
River Flood Modelling under Limited Data Acquisition using PWRI Hydrologic Model
74
The results shown in each of Figures 3.12 to 3.16 indicate that the assumed four key parameters are adequate to calibrate the PWRI-DH model.