DEVELOPMENT OF A DISCHARGE PREDICTION METHOD BASED ON TOPOLOGICAL CASE-BASED MODELING AND A DISTRIBUTED HYDROLOGICAL MODEL Yamatake CorporationKazuya HARAYAMA Toshiaki OKA DPRI, Kyoto UniversityToshiharu KOJIRI Kenji TANAKA Toshio HAMAGUCHI

2 Contents Background Development of new method Application Conclusion

3 Background Methods for Predicting Discharge TCBM （ Topological Case-Based Modeling ） Application example : Sewage inflow prediction Air conditioners control in buildings (1) Runoff Model +Difficulty in determining accurate parameters +Long time required for model construction (2) Black Box Model Rainfall

4 Overview of TCBM Input Prediction output Model x y ^ Able to predict the discharge 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM Output System （ Unknown mechanism ） ？ xy Discharge Use only input-output relationship Input Example … Rainfall Hours w/o rainfall Temperature Day of the week … Measurement data Rainfall Discharge TCBM : Topological Case-Based Modeling Modeling Modeling data Rainfall Discharge Inputs with a strong connection to the output are selected by using stepwise method.

5 Development objective In predicting discharge for an unprecedented heavy rainfall, the prediction error becomes large. ? New discharge prediction method was named Hydro-TCBM. Creating a new case base by a simulation Distributed hydrological model : Hydro-BEAM Measurement data Rainfall Discharge How to solve TCBM’s main issue 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM

6 Overview of Hydro-BEAM 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM Hydro-BEAM : Hydrological River Basin Environmental Assessment Model 1 kilometer unit meshes Flow direction of water

7 Development of new method

8 Development of a new discharge prediction method: Hydro-TCBM Topological Case-Based Modeling TCBM Distributed Hydrological Model Hydro-BEAM Advantages: Data provided in real-time Operation by PC Advantages: Prediction for unprecedented rainfall Case base 2 Simulation results Case base 1 Historical data Weather forecast Prediction discharge Measurement data Rainfall Discharge 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM

9 Application

10 Discharge estimation in Tama River basin 3.Hydro-TCBM Flow measurement point Tama River, Ishihara (Chofu-shi, Tokyo) PeriodApr 1, 2001 to Mar. 31, 2005 Interval1 hour Rainfall dataRadar rainfall data 1.TCBM 2.Hydro-BEAM Tama river basin Notes Area of the basin 1,240[km 2 ] 50 th largest basin area in Japan Length of river138[km] 23 rd longest river in Japan Annual average discharge 20.40[m 3 /sec] Annual mean rainfall 1,532[mm] 1,800[mm] : Average in Japan Urban Mountain Land use There are 109 large rivers in Japan.

11 Selection of explaining variables by stepwise method 3.Hydro-TCBM 1.TCBM 2.Hydro-BEAM Accumulated Time Series Rainfall for Each Mesh 1hour 3hours 6hours 24hours 32hours 60hours 92hours 480hours 720hours 1440hours 2160hours 1hour-1hour behind 1hour-2hours behind 1hour-3hours behind 3hours-1hour behind 3hours-2hours behind 3hours-3hours behind 6hours-1hour behind 6hours-2hours behind 6hours-3hours behind 163 meshes x 20 rainfall data = 3260 kinds of time series rainfall data Five explaining variables are selected by the stepwise method

12 Comparison of the difference in estimation accuracy by TCBM 3.Hydro-TCBM 1.TCBM 2.Hydro-BEAM 3 years’ data 3 years’ data without heavy rainfall data Expect low estimation accuracy in heavy rain Expect high estimation accuracy Case Base with sufficient cases Case Base lacking cases Several heavy rainfall cases

13 Discharge estimation by TCBM 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM Discharge estimation using 3 years’ case base Discharge estimation using 3 years’ case base without heavy rainfall data Root mean square error [%] Maximum error [m 3 /sec] TCBM with sufficient cases TCBM w/o heavy rainfall data3.11,049 Errors in discharge estimation low estimation accuracy

14 Flow direction 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM 1km x 1km rectangle

15 Calculation case and condition caseExplanation Maximum rainfall per hour [mm] 3 years ’ rainfall [mm] case0repetition445,008 case11.5 times rainfall667,512 case22.0 times rainfall8810,016 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM Simulation Accuracy validation

16 Discharge simulation by Hydro-BEAM case0 (repetition) Accuracy Verification case1(1.5 times rainfall) Simulation case2(2.0 times rainfall) Simulation Addition to case-base of Hydro-TCBM 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM

17 Discharge estimation by Hydro-TCBM 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM Root mean square error [%] Maximum error [m 3 /sec] TCBM w/o heavy rainfall data3.11,049 Hydro-TCBM Errors in discharge estimation Discharge estimation using Hydro-TCBM Discharge estimation using TCBM without heavy rainfall data low estimation accuracy

18 Conclusion TCBM has been used to improve accuracy in many fields. So it was applied to discharge estimation. Issue : Estimation accuracy decreased in an unprecedented heavy rainfall Solution : Adopt Hydro-BEAM to enhance the case base Development of Hydro-TCBM enabled us to raise the estimation accuracy close to that of TCBM without increasing measurement data.

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21 4) Input space quantization is based on output error limit. A discharge prediction based on TCBM (Modeling) 1) Output error limit OUTPUT INPUT 2) Output space quantization 3) Accumulate past cases Completion of the prediction model 5) Average value calculated by using past cases each quantum Discharge || Rainfall

22 A discharge prediction based on TCBM (Prediction) 6) Scales up neighborhood, and searches for similar cases OUTPUT INPUT Discharge || Rainfall

23 Rainfall number

24 Equation of Hydro-BEAM 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM Ground surface, A layer : Kinematic wave method B,C,D layer : Linear storage method Ex.) B layerEx.) A layer

25 Discharge prediction model by TCBM (facet in 3D) 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM Two typical explaining variables selected by stepwise method

26 Overview of Hydro-TCBM 1.TCBM 2.Hydro-BEAM 3.Hydro-TCBM

27 Forecasting rainfall of 48 hours accumulated time series When the prediction discharge of 1 hour ahead... This variable = “ Measurement value of 47 hours accumulated rainfall ” + “ Forecasting rainfall of 1 hour ahead ”.