An Integrated Uncertainty and Ensemble Data Assimilation Approach

An Integrated Uncertainty and Ensemble Data Assimilation Approach for Improved Operational Streamflow Predictions Kevin (Minxue) He NOAA/NWS Office of Hydrologic Development (OHD) Riverside Technology, Inc. Acknowledgements: Haksu Lee (OHD), Yuqiong Liu (NASA GSFC) Andy Wood and Stacie Bender (CBRFC), Terri Hogue and Steven Margulis (UCLA) NOAA/NWS/NCEP/EMC, Camp Springs, MD – September 16, 2011

• Introduction Outline § Hydrologic forecasting in US § Hydrologic Ensemble Forecast System § Focus of this presentation • Methodology § Integrated un. Certainty and Ensemble data Assimilation (ICEA) § Study area and experimental design § Verification metrics • Results § Simulation results and parameter uncertainty § Prediction results • Conclusions and ongoing work 2/24

Hydrologic Forecasting in US • Focus: streamflow • Two components: § Forecast model ØNon-snow basins: rainfall-runoff model (SAC-SMA) ØSnow-covered basins: snow model (SNOW 17) + SAC-SMA § Forcing: numerical weather prediction models (NCEP) • Products I. Deterministic (4, 925 sites, short-term) II. Ensemble (climatology forcing, seasonal) 3

Hydrologic Ensemble Forecast System (HEFS) Atmospheric Ensemble Pre-Processor Data Assimilator Hydrology and Water Resources Models GFS/GEFS, CFS/CFSv 2, NAEFS, SREF Ensemble Verification System (EVS) SNOW 17 SAC-SMA Hydrologic Ensemble Post-Processor Hydrology and Water Resources Ensemble Product Generator Forecasters Ensemble Forecast Products Users Verification Products To be operational at RFCs by 2013 4

Data Assimilator Prototypes of the HEFS • Deterministic techniques (Variational method (VAR)) § 1 D-VAR, for routing model § 2 D-VAR, for lumped SAC-SMA model § 4 D-VAR, for distributed SAC-SMA model (4 km resolution) • Ensemble techniques (for SNOW 17 & SAC-SMA) § Ensemble Kalman Filter (En. KF) § Ensemble Kalman Smoother (En. KS) Focus § Integrated un. Certainty and Ensemble data Assimilation (ICEA) • Hybrid deterministic and ensemble technique § Maximum Likelihood Ensemble Filter (MLEF) for SAC-SMA 5

• Introduction Outline § Hydrologic forecasting in US § Hydrologic Ensemble Forecast System § Focus of this presentation • Methodology § Integrated un. Certainty and Ensemble data Assimilation (ICEA) § Study area, modeling procedure, and scenarios § Verification metrics • Results § Simulation results and parameter uncertainty § Prediction results • Conclusions and ongoing work 6/24

ICEA • Model in a systematic view • ICEA: Uncertainty Analysis + Ensemble DA (ISURF+En. KF) Part 1: Uncertainty analysis (He, 2010; He et al. , 2011 a, b) Integrated Sensitivity and Unce. Rtainty analysis Framework (ISURF): v Sensitivity analysis: screening tool v Uncertainty analysis: Markov Chain Monte Carlo technique Parameter uncertainty info. & the optimal parameter set 7

ICEA • ICEA: Uncertainty Analysis + Ensemble DA (ISURF+En. KF) Part 2: En. KF (He, 2010; He et al. , 2011 c) I. Basis: Bayes theorem II. En. KF approximates the Bayesian updating scheme using a Monte Carlo approach: III. En. KF---Two-step procedure: Step 1: forecasting Step 2: updating 8

Study Area North Fork America River Watershed Characteristics Area: 886 km 2 Ppt: 1514 mm Q: 837 mm SNOw TELemetry (SNOTEL) network: ~ 800 sites, Natural Resources Conservation Service (NRCS), daily snow observations (e. g. , snow water equivalent (SWE)) 9

Experimental Design • Areal SWE for upper sub-basin Non-negative least-squares algorithm: • Study period: Training (water year 1979 -1984); Prediction (1991 -1996) • Modeling procedure (obs. MAT/P other than FMAT/P used) Steps to implement ICEA: Step 1: ISURF SNOW 17/SAC-SMA, upper Para. Unc. (training period) Step 2: En. KF SNOW 17 model, upper assimilate areal SWE (prediction period) Step 3: Lower, RFC para. flow + upper flow UH routing outlet flow 10

• Scenarios Experimental Design S 1: RFC parameters S 2: ISURF optimal parameters (S 1 & S 2: deterministic) S 3: Stand-alone En. KF S 4: ICEA (S 3 & S 4: ensemble) • Similarities between S 3 and S 4 (sensitivity tests conducted in He, 2010) § Precipitation uncertainty: § Temperature uncertainty: § Measurement uncertainty: § Ensemble size: 100 § Assimilation frequency: every week § No uncertainty assumed in initial condition (start date Oct. 1, no snowpack) • Difference between S 3 and S 4 § Parameter uncertainty ranges S 3: entire feasible para. range; S 4: ISURF-derived optimal para. range 11

Verification Metrics • Deterministic metrics Correlation (R), Percent Bias, RMSE, Nash-Sutcliffe Efficiency (NSE) (for S 3 & S 4, ensemble mean is used when calculating above metrics) • Ensemble metrics v Normalized RMSE Ratio (NRR) Measure of ensemble dispersion Value = 1 (perfect) > 1 (little spread) < 1 (much spread) v 95 th Percentile Uncertainty Ratio (UR 95) (Anderson, 2002) Aggregated variability of prediction relative to observation Range 0100%, perfect value 0 (Hossain and Anagnostou, 2005) 12

• Introduction Outline § Hydrologic forecasting in US § Hydrologic Ensemble Forecast System § Focus of this presentation • Methodology § Integrated un. Certainty and Ensemble data Assimilation (ICEA) § Study area, modeling procedure, and scenarios § Verification metrics • Results § Simulation results and parameter uncertainty § Prediction results • Conclusions and ongoing work 13/24

Simulation Results • Annual statistics of simulated and observed streamflow during the training period 1979 -1984 (S 1 & S 2) ü ISURF-derived optimal parameters outperform RFC parameters ü ISURF-derived parameter uncertainty information trustable 14

Parameter Uncertainty • ISURF identifies four sensitive parameters, their marginal distributions (in bars) and correlation structure (in dots): Normal Uniform Normal 15

Prediction Results • Overall performance (entire prediction period) Bias RMSE ü RFC prediction can be improved via advanced calibration (e. g. , ISURF) ü DA has added value R NSE RFC/advanced calibration methods ü ICEA outperforms En. KF 16

Prediction Results • Performance on high flow (>95 th percentile) ISURF RFC 1: 1 line En. KF Ens. Mean & Range ICEA Ens. Mean & Range RFC ISURF En. KF ICEA R 0. 80 0. 85 0. 83 0. 87 Bias (%) -19. 58 -13. 70 -14. 91 -10. 02 RMSE (m 3/s) 65. 37 56. 47 58. 33 49. 59 NSE 0. 50 0. 62 0. 60 0. 71 ü Scatter Plot: ICEA mean (best), RFC (worst); DA methods provide ensemble info. ü Statistics: ICEA (best) ~ RFC (worst); ISURF & En. KF comparable 17

Prediction Results • En. KF vs. ICEA: ensemble statistics (annual) NRR: measure of ensemble dispersion (perfect value: 1; too little spread when >1) ü comparable, but not enough spread UR 95: variability relative to observations (perfect value: 0) ü Overall, ICEA has less variability; but not in 1993, 1995, and 1996 Ppt. Flow 18

Prediction Results • En. KF vs. ICEA: finer resolution (daily) I. Selection of the wettest year, 1995, for demonstration II. En. KF and ICEA flow predictions in this year Precipitation high flows; spread is narrow Obs. /RFC streamflow & En. KF Ens. April 18 Obs. /RFC streamflow & ICEA Ens. ü RFC misses peak/recession ü Both ens. capture peak flow & ü En. KF ens. wide in early melting June 8 period, but underestimate later melting parameter samples III. Observed SWE during WY 1995 Melting Accumulation April 18 June 8 215 19

Prediction Results • En. KF vs. ICEA: performance at various lead times Bias RMSE R NSE UR 95 NRR ü Deterministic metrics (a-d): overall, ICEA outperforms En. KF in all lead days ü ICEA ensemble: less variability (e) all lead days; comparable dispersion (f) 20

• Introduction Outline § Hydrologic forecasting in US § Hydrologic Ensemble Forecast System § Focus of this presentation • Methodology § Integrated un. Certainty and Ensemble data Assimilation (ICEA) § Study area, modeling procedure, and scenarios § Verification metrics • Results § Simulation results and parameter uncertainty § Prediction results • Conclusions and ongoing work 21/24

Conclusions • Simulation: ISURF optimal para. outperform RFC para. • Parameter uncertainty: 4 sensitive para. ; 3 normal, 1 uniform • Prediction: § DA methods (En. KF/ICEA) provide improved flow predictions (vs. RFC/ISURF) and ensemble predictions § ICEA ensemble mean prediction best in overall performance & high flow prediction in 4 scenarios; better in all lead days vs. En. KF mean prediction § ICEA ensemble predictions generally have less variability & comparable dispersion vs. Enk. F ones, both on annual basis and at various lead days § ICEA and En. KF ensembles capture high flows, but too narrow Take Home Message ICEA has the potential to supplement the current operational method in 1) providing improved single-valued (ens. mean) forecasts ; 2) meaningful ensemble forecasts. 22

Ongoing and Future Work • Enhance the experimental prototype (ICEA) by: § Investigating ensemble initialization (uncertainty in I. C. ) § Verifying ensembles via other metrics (reliability, resolution) § Considering model structural uncertainty (He et al. , 2011 a) § Evaluating it against the operational snow updating system used at CBRFC across multiple watersheds • Evaluate the enhanced prototype in real-time forecasting: § To digest forecasted ensemble forcing (e. g. processed GFS/PQPF) with educated perturbations of I. C. predictions with wider spread 23

Thank you Questions? Contact: Kevin. He@noaa. gov References Ø He, M. (2010): Data assimilation in watershed models for improved hydrologic forecasting, Ph. D. Dissertation, Civil and Environmental Engineering, University of California, Los Angeles, 173 pp. Ø He, M. , Hogue, T. S. , Franz, K. J. , Margulis, S. A. , and Vrugt, J. A. (2011 a): Corruption of parameter behavior and regionalization by model and forcing data errors: A Bayesian example using the SNOW 17 model, Water Resour. Res. , 47, 10. 1029/2010 WR 009753. Ø He, M. , Hogue, T. S. , Franz, K. J. , Margulis, S. A. , and Vrugt, J. A. (2011 b): Characterizing parameter sensitivity and uncertainty for a snow model across hydroclimatic regimes, Adv. Water Resour. , 34, 114 -127. Ø He, M. , Hogue, T. S. , Margulis, S. A, and Franz, K. J. (2011 c): An integrated uncertainty and ensemblebased data assimilation approach for improved operational streamflow predictions, Hydrol. Earth Syst. Sci. Discuss. , 8, 7709 -7755, 10. 5194/hessd-8 -7709 -2011. 24

Extra Slides

ISURF: a step-wise framework (He, 2010; He et al. , 2011 b) Step 1: Generalized sensitivity analysis (GSA) (Spear and Hornberger, 1980) screening tool sensitive parameters Step 2: Differential Evolution Adaptive Metropolis (DREAM) parameter uncertainty (Jasper et al. , 2008)

ISURF: Methodology GSA: 1) Identify feasible parameter ranges 2) Monte Carlo sampling: Latin Hypercube Sampling (sample size 3) Behavioral /non-behavioral classification Nash-Sutcliffe efficiency (NSE)=0. 3 4) Bin division and CDF calculation - bins - CDF of NSE for each bin 5) (Garbrecht, 2006) Kolmogorov-Smirnov test KS value (Kottegoda and Rosso, 1997) KS )

ISURF: Methodology DREAM: Candidate point Modify proposal Metropolis acceptance Prob. (Jasper et al. , 2008; He et al. , 2011 a, b)

SNOW 17 Model Key notes 1. Ppt forcing SCF×Ppt=Ppt forcing Tair>PXTEMP: rain Tair<PXTEMP: snow 2. Non-rain melt M = N×(Tair-MBASE) MFMAX Dec. 21 Jun. 21 MFMIN 3. Rain-on-snow melt M ~ UADJ×(Tair-32) Ppt: precipitation Tair: air temperature

SAC-SMA Model Precipitation (or SNOW 17 output) ET 1+ET 2 Pervious ET 1 Impervious Additional Impervious PCTIM ADIMP Tension Water Free Water UZTWM Upper zone Direct runoff Surface runoff UZK UZFWM ET 3 RIVA Interflow Percolation Channel inflow ZPERC REXP 1 -PFREE Lower zone ET 2 Tension Water LZTWM PFREE Free Water Primary Supplemental LZFPM LZFSM Routing LZSK Supplemental base flow RSERV Runoff LZPK Primary base flow SIDE Legend Storage Runoff components Parameters Groundwater aquifer