Recent Developments In Evolutionary Data Assimilation And Model Uncertainty Estimation For Hydrologic Forecasting Hamid Moradkhani

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1 Feb 6-8, 208 Recen Developmens In Evoluionary Daa Assimilaion And Model Uncerainy Esimaion For Hydrologic Forecasing Hamid Moradkhani Cener for Complex Hydrosysems Research Deparmen of Civil, Consrucion and Environmenal Engineering

2 Uncerainies in Hydrologic Modeling ) Meeorological forcing Earh s chaoic amosphere makes forecasing unreliable a exended lead imes 2) Iniial condiion (saes) Land surface hydrological condiions are highly variable spaially (e.g., snow and soil moisure) Snow Soil Moisure 3) Hydrologic model Hydrologic models are simplificaions o land surface processes?

3 Click Quanifying o edi Maser Uncerainy ile syle Requires he formulaion of a probabilisic model p(y) = f (p(x), p(u),q)+ p(w) pu p py px Snow Soil Moisure Probabilisic Forecas

4 Sequenial Daa Assimilaion he Generic Framework P(o) P(X) Sae (Prognosic Variable) X () Updaing Uncerain Observaions O() Sreamflow SWE SCA Daa Assimilaion Forcing daa I() Temperaure Precipiaion P(I) Hydrologic Model Parameers θ Forecasing Uncerain Model Oupu y() Sreamflow Snowfall Soil Rainfall moisure Mel SWE SWE SCA SCA Pack hea defici Pack hea defici P(y) P(θ)

5 Daa Assimilaion: Paricle Filer p(x y : ) + x x Poserior x x + Observaion y p(y x ) Likelihood p(x y : ) Poserior p(x y : ) Prior ) ( ) ( ) ( ) ( Y y p Y x p x y p Y x p x dx Y x p x x p Y x p ) ( ) ( ) ( ) ( ) ( ) ( x dx Y x p x y p Y y p

6 Enhancemen of DA by Evoluionary Paricle Filer Paricle Filers (PFs) have received increasing aenion from differen disciplines as an effecive ool o improve model predicions in nonlinear and non-gaussian dynamical sysems. Despie he success of he PF, one concern has been he paricle degeneracy. To alleviae his problem, Sampling-Imporance Resampling (SIR) is used o force paricles o areas of high likelihood by muliplying high weighed paricles while discarding low weighed paricles. This, however, may cause anoher problem: sample impoverishmen or loss of diversiy in paricles.

7 How o Enhance Paricle Filer DA? Markov Chain Mone Carlo (MCMC) wih Paricle Filer (Moradkhani e al., 202) Inelligen search and opimizaion mehods caegorized as Meaheurisic Algorihms (MAs) have also been used o miigae he degeneracy problem. Geneic Algorihm (GA), (Higuchi, 997; Kwok e al., 2005; Park e al., 2009) Evoluion Sraegy (ES), (Uosaki e al., 2003; Uosaki e al., 2004) Paricle Swarm Opimizaion (PSO), (Wang e al., 2006; Li e al., 203) An Colony Opimizaion (ACO), (Xu e al., 2009; Park e al., 200; Zhu e al., 200) Immune Geneic Algorihm (IGA), (Han e al., 20) Inverse Weed Opimizaion, (Ahmadi e al., 202)

8 Earlier Version of GA- Paricle Filer and limiaions An Illusraion of GA-PF algorihm: (Yin e al., 205) Limiaion of using a single evoluionary algorihm wih he PF: This approach reduces he weighs of large-weigh paricles and may lead o subopimal performance. I is possible ha he shuffled paricles afer he GA operaion move ouside he poserior disribuion and lead o a degraded performance!

9 A new approach (GA-MCMC) We modified he GA approach suiable for hydrogeoscience applicaions. In paricular, we use a MCMC move inside he GA o guide he PF performance. This procedure is inroduced as a GA-MCMC process.

10 Evoluionary Paricle Filer wih MCMC The proposed approach akes our earlier developed PF-MCMC algorihm (Moradkhani e al., 202) as a benchmark o furher improve he assimilaion resuls. The presened hybrid PF approach, he so-called Evoluionary Paricle Filer wih MCMC (EPFM), joins he srenghs of GA-MCMC and PF-MCMC algorihms. MCMC is used wice: a) before resampling sep in order o accep or rejec he new generaed sae variable which leads o an opimal prior disribuion, and b) afer resampling sep during parameer updaing sep.

11 A Synheic Case The Sacrameno Soil Moisure Accouning Model (SAC-SMA) was used o simulae he sreamflow in boh a synheic and hree real daa assimilaion experimens.

12 Three real case sudies

13 Why Evoluionary Paricle Filer? Prior Densiy Poserior Densiy day = 50 day = 43 day = 76

14 Performance Assessmen- real case sudies

15 Forecasing skill The comparison of he PF-MCMC and EPFM skills in one-day ahead sreamflow forecas for he synheic (a and b) and a real case sudy (c and d), Chehalis River Basin in WA, during he flood season. The comparison of he PF-MCMC and EPFM skills in five-day ahead sreamflow forecas for he synheic (a and b) and a real case sudy (c and d), Chehalis River Basin in WA, during he flood season.

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17 Waer Resources Research

18 Schemaic of he Sae-Dependen Model Uncerainy Esimaion (SDMU) Mehod The sysem saes are parially observed Minimal prior knowledge of he model error processes is available, excep ha he errors display sae dependence. I includes an approach for esimaing he uncerainy in hidden model saes, wih he end goal of improving predicions of observed variables. A raining period of model simulaions and observaions is used o develop he PDF of addiive errors in observed variables condiioned on model saes and inpus.

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20 Scaled Probabiliy Densiy Funcion of difference in prediced y and rue y Sae Dependen Model Uncerainy Esimaion Gaussian Perurbaion

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