A multimodel data assimilation framework for hydrology Antoine Thiboult, François Anctil Université Laval June 27 th 2017
What is Data Assimilation? Use observations to improve simulation 2 of 8
What is Data Assimilation? Use observations to improve simulation How? Kalman Filter Variational method Particle Filter... 2 of 8
Particle Filter In a perfect world Identify most appropriate state variable values Improve initial conditions Better simulation & forecast 3 of 8
Particle Filter In a perfect world Identify most appropriate state variable values Improve initial conditions Better simulation & forecast But life is not perfect... Bias in the forcing Error in the model structure Filter may fail 3 of 8
Error in model structure 4 of 8
Error in model structure Multimodel approach No model is always better than others Cover different conceptualization Compensation of models errors 4 of 8
Error in model structure Multimodel approach No model is always better than others Cover different conceptualization Compensation of models errors 4 of 8
A multimodel data assimilation framework Traditional Particle Filter Multimodel Particle Filter 5 of 8
A multimodel data assimilation framework Traditional Particle Filter One model at a time Multimodel Particle Filter Update all models together 5 of 8
A multimodel data assimilation framework Traditional Particle Filter One model at a time Update model invididually Multimodel Particle Filter Update all models together Make models cooperate during the assimilation 5 of 8
A multimodel data assimilation framework Traditional Particle Filter One model at a time Update model invididually Multimodel Particle Filter Update all models together Make models cooperate during the assimilation Foster compensation of models errors Control multimodel predictive function 5 of 8
A multimodel data assimilation framework Traditional Particle Filter One model at a time Update model invididually Require only one model Multimodel Particle Filter Update all models together Make models cooperate during the assimilation Foster compensation of models errors Control multimodel predictive function Require a large number of models ( 20) 5 of 8
Experimental set-up Comparison between individual and collective model updating 6 of 8
Experimental set-up Comparison between individual and collective model updating Catchments 6 catchments in the Province of Québec Snow accumulation & spring freshet 9-year period 6 of 8
Experimental set-up Comparison between individual and collective model updating Catchments 6 catchments in the Province of Québec Snow accumulation & spring freshet 9-year period Assessment of accuracy and reliability Nash-Sutcliffe Efficiency (NSE) Root mean square error (RMSE) Continuous ranked probability score (CRPS) Normalized root mean square error ratio (NRR) 6 of 8
Preliminary results 1 0.95 0.9 0.85 0.8 NSE 0.75 0.7 0.65 0.6 0.55 0.5 Individual Collective 7 of 8
Preliminary results Accuracy 7 of 8
Preliminary results Accuracy Resolution 7 of 8
Preliminary results Accuracy Resolution Reliability 7 of 8
Conclusion A multimodel data assimilation framework Based on the particle filter Update models jointly in a cooperative mode Possible gain in accuracy and reliability... Work in progress 8 of 8
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50 45 Q [m3/s] 40 35 30 25 1. Force model with perturbed inputs 20 15 10 0 5 10 15 20 25 30 35 40 Time 8 of 8
50 45 Q [m3/s] 40 35 30 25 1. Force model with perturbed inputs 20 15 10 0 5 10 15 20 25 30 35 40 Time 8 of 8
50 45 Q [m3/s] 40 35 30 25 1. Force model with perturbed inputs 2. Compute particle weights based on their likelihood 20 15 10 0 5 10 15 20 25 30 35 40 Time 8 of 8
50 45 Q [m3/s] 40 35 30 25 20 15 1. Force model with perturbed inputs 2. Compute particle weights based on their likelihood 3. Resample 4. Iterate 10 0 5 10 15 20 25 30 35 40 Time 8 of 8
50 1. Force models with perturbed inputs Q [m3/s] 45 40 35 30 25 20 15 10 5 0 0 5 10 15 20 25 30 Time 8 of 8
50 1. Force models with perturbed inputs Q [m3/s] 45 40 35 30 25 20 15 10 5 0 0 5 10 15 20 25 30 Time 8 of 8
50 1. Force models with perturbed inputs Q [m3/s] 45 40 35 30 25 20 15 10 5 0 0 5 10 15 20 25 30 Time 8 of 8
Q [m3/s] 50 45 40 35 30 25 20 1. Force models with perturbed inputs 2. Choose particles to create a predictive PDF that is similar to the PDF of the observation 15 10 5 0 0 5 10 15 20 25 30 Time 8 of 8
Q [m3/s] 50 45 40 35 30 25 20 1. Force models with perturbed inputs 2. Choose particles to create a predictive PDF that is similar to the PDF of the observation 15 10 5 0 0 5 10 15 20 25 30 Time 8 of 8
Q [m3/s] 50 45 40 35 30 25 20 1. Force models with perturbed inputs 2. Choose particles to create a predictive PDF that is similar to the PDF of the observation 15 10 5 0 0 5 10 15 20 25 30 Time 8 of 8
Q [m3/s] 50 45 40 35 30 25 20 15 10 1. Force models with perturbed inputs 2. Choose particles to create a predictive PDF that is similar to the PDF of the observation 3. Compute statistical distance between predictive PDF and PDF of the observation (weights) 5 0 0 5 10 15 20 25 30 Time 8 of 8
Q [m3/s] 140 120 100 80 60 40 20 0 0 10 20 30 40 50 60 70 80 Time 1. Force models with perturbed inputs 2. Choose particles to create a predictive PDF that is similar to the PDF of the observation 3. Compute statistical distance between predictive PDF and PDF of the observation (weights) 4. Resample particles 5. Iterate models 8 of 8
50 Q [m3/s] 40 30 20 10 0 0 5 10 15 20 25 30 Time Foster models error compensation Easier to explore predictive space May respect more model dynamic 8 of 8
50 Q [m3/s] 40 30 20 10 0 0 5 10 15 20 25 30 Time Foster models error compensation Easier to explore predictive space May respect more model dynamic 8 of 8
50 Q [m3/s] 40 30 20 10 0 0 5 10 15 20 25 30 Time Foster models error compensation Easier to explore predictive space May respect more model dynamic 8 of 8