Prediction of Typhoon-Induced Flood Flows at Ungauged Catchments Using Simple Regression and Generalized Estimating Equation Approaches
Abstract
:1. Introduction
2. Case Study Data and Preliminary Data Analysis
2.1. Geum River Region
- -
- Area is size of the catchment, which affects flood volumes;
- -
- ALTBAR is the mean altitude of catchment above sea level;
- -
- DPS is the mean of the catchment slope, which affects surface runoff response times;
- -
- DD is the Drainage Density, a measure of the total length of all the rivers in a catchment area divided by the total area of the catchment, which affects how efficiently a catchment is drained;
- -
- FF is the Form Factor, the ratio of the catchment area to the squared value of the total catchment drainage length. It varies from zero (in a highly elongated area) to 1 (in a perfectly circular area), affecting runoff response times. DD and FF are calculated based on equations provided by National Water Resources Management Information System (WAMIS) in Korea;
- -
- Curve Number (CN) is an empirical parameter for predicting direct runoff, developed by the US Soil Conservation System, and affects the volume of runoff during a storm [20];
- -
- FARL is Flood Attenuation Factor by Reservoir and Lakes, estimated based on the reservoir data and the catchment terrain database in WAMIS, affecting flood attenuation [21];
- -
- SAAR is Standard Annual Average Rainfall in the period 1981 to 2010, which represents effects of long-term catchment wetness.
2.2. Typhoons in the Geum River Region
3. Method
3.1. PDM Rainfall Runoff Model
3.2. Calibration
3.3. Statistical Regression
3.3.1. Conventional Regression
3.3.2. Generalized Estimating Equations (GEEs)
3.4. Validation
4. Results
4.1. Calibration of the PDM Model
4.2. Statistical Regression
5. Conclusions
- -
- The application of a calibrated PDM model to modelling flood event flows in Geum River catchments shows, overall, an acceptable model performance. This supports the use of the PDM model or comparable rainfall-runoff models for simulating extreme flood events in Korea.
- -
- Using conventional regression equations to regionalize model parameters to ungauged catchments showed mixed success, for example when treating the C4 catchment as ungauged, there were good results for two flood events (typhoons Nari and Dianmu) and underestimated peaks for two events (typhoons Rusa and Kompasu).
- -
- The GEE model extends the conventional regression by including the inter-event variability in PDM model parameters as well as the inter-catchment variability. However only the model parameter b was found to be related to event properties; and validation results showed only slight improvement on the simpler regression approach. While for practical applications we would therefore recommend the simpler regression approach, refinements to the GEE approach may be explored, in particular its potential advantage for estimating an error model and confidence limits on predictions.
Author Contributions
Acknowledgments
Conflicts of Interest
Appendix A. GEE for Regionalization of Rainfall Runoff Model
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Catchments | Area (km2) | ALTBAR (m) | FF () | DD () | SAAR (mm) | FARL () | CN () | DPS (°) | PG () | |
---|---|---|---|---|---|---|---|---|---|---|
Bukil | C1 | 907.1 | 151 | 0.3 | 2.1 | 1222 | 0.92 | 67.4 | 9.7 | 4 |
Boksu | C2 | 162.5 | 229 | 0.1 | 4 | 1274 | 1 | 70.8 | 15.2 | 2 |
Cheoncheon | C3 | 291.2 | 555 | 0.3 | 3.3 | 1093 | 0.96 | 65.4 | 14.6 | 1 |
Cheongju | C4 | 166.3 | 159 | 0.2 | 2.4 | 1192 | 0.98 | 71.7 | 9.7 | 2 |
Cheongseong | C5 | 491 | 270 | 0.1 | 3.1 | 1198 | 0.95 | 65.6 | 12.9 | 2 |
Donghyang | C6 | 165.4 | 647 | 0.2 | 1.7 | 1231 | 0.96 | 60 | 16.2 | 3 |
Gideagyo | C7 | 353.1 | 284 | 0.3 | 3.1 | 1181 | 0.97 | 65.4 | 12.9 | 1 |
Guryong | C8 | 208.2 | 173 | 0.1 | 3 | 1258 | 0.99 | 72.3 | 12.3 | 2 |
Gasangyo | C9 | 183.9 | 141 | 0.3 | 1.7 | 1199 | 0.95 | 68.8 | 6.3 | 2 |
Habgang | C10 | 1853 | 136 | 0.2 | 2.4 | 1225 | 0.95 | 69.1 | 8.4 | 6 |
Indong | C11 | 58.7 | 217 | 0.1 | 3.4 | 1244 | 1 | 64.6 | 14.7 | 2 |
Juengpyung | C12 | 124.1 | 150 | 0.4 | 2.4 | 1206 | 0.96 | 69.3 | 8.6 | 2 |
Mihogyo | C13 | 1596 | 137 | 0.3 | 2.4 | 1192 | 0.98 | 63 | 9.7 | 2 |
Muju | C14 | 390.2 | 615 | 0.1 | 1.5 | 1154 | 0.99 | 59 | 18.9 | 4 |
Nonsan | C15 | 467.7 | 148 | 0.2 | 2.3 | 1318 | 0.91 | 62.5 | 11.4 | 4 |
Ochang | C16 | 564 | 154 | 0.2 | 1.9 | 1221 | 0.91 | 66 | 9.8 | 2 |
Simcheon | C17 | 664.3 | 372 | 0.2 | 2.2 | 968 | 0.98 | 61 | 14.7 | 2 |
Seokdong | C18 | 162.4 | 78 | 0.2 | 2.7 | 1271 | 0.96 | 66.2 | 8.1 | 3 |
Sangyegyo | C19 | 464.9 | 272 | 0.2 | 3.1 | 1195 | 0.96 | 65.6 | 12.9 | 2 |
Songcheon | C20 | 623.4 | 385 | 0.2 | 2.2 | 969 | 0.97 | 60.6 | 14.8 | 2 |
Seokhwa | C21 | 1594.1 | 143 | 0.3 | 2.3 | 1223 | 0.94 | 68.6 | 9.7 | 5 |
Tanbugyo | C22 | 81.7 | 363 | 0.2 | 2.5 | 1090 | 0.93 | 54.2 | 17 | 1 |
Woogon | C23 | 131.8 | 45 | 0.3 | 2.8 | 1235 | 0.98 | 68.9 | 5 | 1 |
Yuseong | C24 | 251.1 | 189 | 0.1 | 3.5 | 1315 | 0.99 | 62.8 | 12.1 | 2 |
Typhoon | Period |
---|---|
Rusa | 23 August 2002~6 September 2002 |
Maemi | 6 September 2003~19 September 2003 |
Nari | 13 September 2007~22 September 2007 |
Dianmu | 8 August 2010~17 August 2010 |
Kompasu | 29 August 2010~8 September 2010 |
Bolaven | 20 August 2012~3 September 2012 |
Typhoon | Rusa | Maemi | Nari | Dianmu | Kompasu | Bolaven |
---|---|---|---|---|---|---|
TR (Total Rainfall, (mm)) | 129 | 72 | 92 | 90 | 41 | 107 |
TD (Total Discharge, (mm)) | 114 | 70 | 79 | 46 | 16 | 66 |
MRI (Maximum Rainfall Intensity, (mm/h)) | 14 | 10 | 10 | 42 | 28 | 21 |
PF (Peak Flood, (mm/h)) | 6 | 3 | 5 | 4 | 3 | 5 |
RD (Rainfall Duration, (h)) | 17 | 9 | 11 | 7 | 2 | 15 |
LT (Lag Time, (h)) | 4 | 3 | 6 | 4 | 1 | 3 |
PE (Potential Evapotranspiration, (mm)) | 21 | 12 | 5 | 3 | 3 | 15 |
RR (Runoff Ratio to rainfall, ()) | 0.88 | 0.98 | 0.85 | 0.52 | 0.38 | 0.62 |
P5 (mm/5 days) | 31 | 43 | 91 | 153 | 44 | 10 |
MPs | Description | Range (Units) |
---|---|---|
Cmax | Maximum storage capacity of the catchment | 1~500 (mm) |
b | Degree of spatial variability of storage capacity in the catchment | 0~2 () |
rtq | Residence time of the quick flow reservoir | 0~15 (h) |
rts | Residence time of the slow flow reservoir | 50~500 (h) |
f | Fraction of effective rainfall that enters the quick flow reservoir and 1-f of effective rainfall that enters the slow flow reservoir | 0~1 () |
Typhoon | Cmax (mm) | b () | rtq (h) | rts (h) | f () | NSE |
---|---|---|---|---|---|---|
Rusa | 367.6 | 0.25 | 9.9 | 51.0 | 0.77 | 0.96 |
Maemi | 211.4 | 0.47 | 14.2 | 69.9 | 0.96 | 0.86 |
Nari | 201.0 | 0.32 | 7.8 | 273.1 | 0.99 | 0.97 |
Dianmu | 497.8 | 0.10 | 8.2 | 427.3 | 0.84 | 0.90 |
Kompasu | 453.0 | 0.05 | 3.5 | 276.0 | 0.81 | 0.90 |
Bolaven | 206.5 | 0.22 | 7.2 | 59.3 | 0.87 | 0.95 |
Averaged | 322.9 | 0.23 | 8.5 | 192.8 | 0.87 | 0.80 |
Catchment | Rusa | Maemi | Nari | Dianmu | Kompasu | Bolaven | No. > 0.5 NSE | No. Events | % |
---|---|---|---|---|---|---|---|---|---|
C1 | 0.87 | 0.79 | 0.79 | 0.48 | 0.77 | 0.83 | 5 | 6 | 83 |
C2 | 0.92 | - | - | 0.53 | 0.76 | 0.72 | 3 | 4 | 75 |
C3 | - | - | 0.76 | 0.89 | 0.90 | 0.96 | 4 | 4 | 100 |
C4 | 0.96 | 0.86 | 0.97 | 0.90 | 0.90 | 0.95 | 6 | 6 | 100 |
C5 | - | 0.24 | 0.27 | −0.43 | −0.44 | 0.87 | 1 | 5 | 20 |
C6 | - | - | 0.75 | 0.69 | 0.8 | 0.89 | 4 | 4 | 100 |
C7 | - | - | 0.8 | 0.55 | 0.55 | 0.83 | 4 | 4 | 100 |
C8 | 0.73 | 0.42 | 0.74 | 0.35 | 0.28 | −0.02 | 2 | 6 | 33 |
C9 | - | - | - | 0.73 | 0.74 | 0.86 | 3 | 3 | 100 |
C10 | - | - | 0.26 | 0.04 | 0.66 | 0.7 | 1 | 3 | 33 |
C11 | 0.85 | 0.79 | 0.96 | 0.4 | 0.62 | 0.67 | 5 | 6 | 83 |
C12 | 0.83 | 0.83 | - | 0.67 | 0.55 | 0.84 | 5 | 5 | 100 |
C13 | - | - | - | 0.12 | −13.5 | 0.5 | 1 | 3 | 33 |
C14 | - | - | 0.43 | 0.68 | 0.34 | 0.3 | 1 | 4 | 25 |
C15 | 0.56 | −0.64 | 0.28 | −0.92 | 0.28 | 0.71 | 2 | 6 | 33 |
C16 | 0.76 | 0.25 | 0.64 | 0.68 | −0.32 | - | 3 | 5 | 60 |
C17 | - | - | 0.49 | 0.77 | 0.24 | 0.79 | 2 | 4 | 50 |
C18 | - | - | −1.5 | −0.56 | 0.49 | 0.39 | 0 | 4 | 0 |
C19 | - | - | 0.57 | −0.14 | −0.60 | 0.71 | 2 | 4 | 50 |
C20 | - | 0.82 | 0.73 | 0.83 | 0.47 | 0.47 | 3 | 4 | 75 |
C21 | 0.79 | 0.72 | 0.43 | 0.67 | −1.12 | 0.68 | 3 | 6 | 50 |
C22 | - | - | 0.9 | −0.37 | −0.14 | 0.03 | 1 | 4 | 25 |
C23 | 0.12 | −0.32 | 0.34 | −0.23 | 0.44 | 0.47 | 0 | 6 | 0 |
C24 | 0.72 | - | 0.82 | 0.52 | 0.73 | 0.87 | 5 | 5 | 100 |
Max | 0.92 | 0.86 | 0.97 | 0.89 | 0.9 | 0.96 | Missing values in observed data | ||
Min | 0.12 | −0.64 | −1.5 | −0.92 | −13.5 | −0.02 | |||
No. > 0.5 NSE | 10 | 6 | 12 | 13 | 12 | 17 | |||
No. Cat. | 11 | 11 | 20 | 24 | 24 | 23 | |||
% | 91 | 55 | 60 | 54 | 50 | 74 |
Model Parameter | Regression Equation | R2 | p-Value |
---|---|---|---|
Cmax | 248.3 − 0.04 Area | 0.10 | 0.16 |
b | 2.35 − 0.0238 CN | 0.10 | 0.17 |
rtq | 32.05 + 0.003 Area − 0.01 ALTBAR − 0.3 CN | 0.52 | 0.00 |
rts | −728.56 − 0.06 Area − 77.16 DD + 1211.31 FARL | 0.55 | 0.00 |
f | −0.6 − 0.0002 Area − 0.12 DD + 1.84 FARL | 0.79 | 0.00 |
Model Parameter | Cmax | b | rtq | rts | f |
---|---|---|---|---|---|
Value | 242 | 0.64 | 9.86 | 264 | 0.88 |
Model Parameter | GEE | R2 |
---|---|---|
Cmax | 232.33 − 0.03 Area | 0.01 |
b | 1.29 − 0.004 TR | 0.11 |
rtq | 22.75 + 0.003 Area − 0.007 ALTBAR − 0.15 CN | 0.24 |
rts | 678.12 − 0.09 Area − 50.46DD − 0.26 SAAR | 0.13 |
f | 1.70 − 0.0002 Area − 0.06 DD − 0.0006 SAAR | 0.08 |
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Lee, H.; McIntyre, N.; Kim, J.; Kim, S.; Lee, H. Prediction of Typhoon-Induced Flood Flows at Ungauged Catchments Using Simple Regression and Generalized Estimating Equation Approaches. Water 2018, 10, 647. https://doi.org/10.3390/w10050647
Lee H, McIntyre N, Kim J, Kim S, Lee H. Prediction of Typhoon-Induced Flood Flows at Ungauged Catchments Using Simple Regression and Generalized Estimating Equation Approaches. Water. 2018; 10(5):647. https://doi.org/10.3390/w10050647
Chicago/Turabian StyleLee, Hyosang, Neil McIntyre, Joungyoun Kim, Sunggu Kim, and Hojin Lee. 2018. "Prediction of Typhoon-Induced Flood Flows at Ungauged Catchments Using Simple Regression and Generalized Estimating Equation Approaches" Water 10, no. 5: 647. https://doi.org/10.3390/w10050647
APA StyleLee, H., McIntyre, N., Kim, J., Kim, S., & Lee, H. (2018). Prediction of Typhoon-Induced Flood Flows at Ungauged Catchments Using Simple Regression and Generalized Estimating Equation Approaches. Water, 10(5), 647. https://doi.org/10.3390/w10050647