CHR Workshop, 18-19 April 2004, Bregenz, Austria Fuzzy logic approach for reducing uncertainty in flood forecasting Shreedhar Maskey Raymond Venneker Stefan Uhlenbrook UNESCO-IHE Institute for Water Education Delft, The Netherlands
Objectives To present an overview of uncertainty related issues in flood forecasting. To show the impact of rainfall data uncertainty using disaggregation methodology. To introduce a methodology that combines multiple models using fuzzy logic for flood forecasting. The methodology aims to reduce model error/uncertainty.
Modeling for flood forecasting Types of model Physically-based distributed Lumped/semidistributed conceptual Data driven Role of future rainfall in future floods Integration of weather forecasts into flood forecasting system Flow Precipitation Observed Now Now?? Forecast?? Time Time
Uncertainty in flood forecasting Uncertainty comes from Input data Model parameters Model structure Calibration data Initial state of the system Limited knowledge of the system p X1 p Xn μ ~ X 1 μ X ~ n Flow Precipitation ~ X, X 1 1 Observed X n, X ~ n Now Forecasting Model Now Forecast p Y μ Y ~ Time Time Y, Y ~
Uncertainty caused by rainfall data Uncertainty in rainfall comes from Imprecise quantity Low frequency data Spatial regionalization Rainfall data uncertainty propagation using temporal disaggregation Monte Carlo based approach Fuzzy extension principle based approach P i P i /n p i,1 p i,j p i,n j=1 j j=n T Q = f ([ p,1,..., p1, n]... [ pm, 1,..., p 1 mn ])
Rainfall disaggregation and uncertainty propagation 1. Generate randomly W i based on their PDF for all i =1,..., m. 1. Determine UB and LB of W i for given α-cut based on their MF for all i =1,..., m. 2. Generate coefficients b i,j (for i =1,..., m; j =1,...,n) 2. Start GA with parameters W 1,...,W m for precipitation and (b 1,1,...,b 1,k ),...,(b m,1,...,b m,k ) for d isaggregation coefficients 3. Generate disaggregated signals w i,j = W i b i,j 3. Generate initial parameter sets (initial population) 4. Run model using the signals obtained in step 3: Q =f (w i,j ) Repeat for α-cuts 4. Adjust b i,j and generate disaggregated signals calling an extenal program 5. Evaluate fitness of initial parameter sets using the forecasting model and given fitness function Enough samples reached? No 6. Perform selection, crossover and mutation and evaluate fitness of the new parameter set New generation Yes 5. Generate distribution of the output (Q). Based on Monte Carlo method Repeat for ma x and min Termination No criteria met? Yes 7. Output Q from the best fit individual parameter set Based on Fuzzy EP 8. Generate MF for the output (Q)
Rainfall disaggregation and uncertainty propagation Klodzko valley (Poland) Basin area = 1744 km 2 9 sub-basins Model HEC-HMC Forecast for Bardo on River Nysa Klodzka
Rainfall disaggregation and uncertainty propagation Flood of July 1997 Max discharge reached 1700 m 3 /s (50 m 3 /s 3 days before). Precipitation (mm) 0.0 10.0 20.0 30.0 Time (hours) 0 24 48 72 96 120 144 168 2000 Discharge (m3/s) 1500 1000 500 Simulated Observed 0 0 24 48 72 96 120 144 168 Time (hours)
Impact of rainfall uncertainty (Monte Carlo approach) Normalised frequency 1.0 0.5 0.0 (a) Forecast 1 Normalised frequency 1.0 0.5 0.0 (b) Forecast 2 600 650 700 750 800 800 850 900 950 1000 Discharge (m 3 /s) Discharge (m 3 /s) Normalised frequency 1.0 0.5 0.0 (c) Forecast 3 With temporal disaggregation Without temporal disaggregation 1150 1200 1250 1300 1350 Discharge (m 3 /s)
Impact of rainfall uncertainty (Fuzzy EP approach) (a) Forecast 1 (b) Forecast 2 1.0 1.0 Membership 0.5 Membership 0.5 0.0 600 650 700 750 800 0.0 800 850 900 950 1000 Discharge (m 3 /s) Discharge (m 3 /s) (c) Forecast 3 1.0 With temporal disaggregation Membership 0.5 Without temporal disaggregation 0.0 1150 1200 1250 1300 1350 Discharge (m 3 /s)
Model calibration Plays a vital role in model accuracy (more for conceptual models) Problems: Calibrated parameter sets may vary for different flood events. Not a single parameter set satisfies all flood events. Calibration data also possess uncertainty. 5000 4000 Runoff [Cumec] 3000 2000 1000 Observed Computed 0 23-Jun-93 08-Jul-93 23-Jul-93 07-Aug-93 22-Aug-93 06-Sep-93 21-Sep-93 Time [days]
Fuzzy logic for reducing error/uncertainty The basic fuzzy principle: Everything is a matter of degree. Combination of Model 1 & 2 Membership 1 0 Fuzzy Dawn Night Day Intensity of light (brightness) Model 1 Model 2 Runoff Time
0 Fuzzy logic for reducing error/uncertainty Methodology Classify flood events into various classes. Calibrate a model independently for each flood class. Use fuzzy logic to combine the models. Membership M1 M2 M3 M4 Model (M) 1 If FC1 then M1 If FC3 then M3 If FC2 then M2 If FC4 then M4 Membership 1 0 FC1 FC2 FC3 FC4 Flow Class (FC)
Fuzzy logic for reducing error/uncertainty Methodology (contd.) Flow classes can be defined based on antecedent conditions and forecasted rainfall. Requires consistent and robust calibration procedure. Automatic calibration with manual intervention can be used. Define initial parameter values and their upper/lower limits Use automatic calibration to find optimum parameter values (one or more algorithms and/or objective functions) Manually adjust the calibrated values using expert knowledge Re-adjust values of parameters that are dependent on calibrated parameters Evaluate the adjested parameter values using the model If some parameters have most appropriate values exclude them for next calibration Re-adjust parameter limits if appropriate Is the performance satisfactory? Yes No Automatic calibration with manual intervention Calibrated parameter set
Conclusions The methodology uses specific models depending on the respective hydrological situation. The methodology has potential to enhance forecasting capacity/precision of models using the fuzzy logic approach. The methodology provides opportunity to forecast a range of plausible values.