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Kevin (Minxue) He

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)

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Kevin (Minxue) He

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  1. 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

  2. Outline Introduction Hydrologic forecasting in US Hydrologic Ensemble Forecast System Focus of this presentation Methodology Integrated unCertainty 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

  3. Hydrologic Forecasting in US Focus: streamflow Two components: Forecast model Non-snow basins: rainfall-runoff model (SAC-SMA) Snow-covered basins: snow model (SNOW17) + SAC-SMA Forcing: numerical weather prediction models (NCEP) Products II. Ensemble (climatology forcing, seasonal) I. Deterministic (4,925 sites, short-term) 3

  4. Ensemble Verification System (EVS) Ensemble Forecast Products Verification Products To be operational at RFCs by 2013 Hydrologic Ensemble Forecast System (HEFS) Hydrologic Ensemble Forecast System (HEFS) GFS/GEFS, CFS/CFSv2, NAEFS, SREF Atmospheric Ensemble Pre-Processor Data Assimilator SNOW17 SAC-SMA Hydrology and Water Resources Models Hydrologic Ensemble Post-Processor Hydrology and Water Resources Ensemble Product Generator Forecasters Users

  5. Data Assimilator Prototypes of the HEFS Focus • Deterministic techniques (Variational method (VAR)) • 1D-VAR, for routing model • 2D-VAR, for lumped SAC-SMA model • 4D-VAR, for distributed SAC-SMA model (4 km resolution) • Ensemble techniques (for SNOW17 & SAC-SMA) • Ensemble Kalman Filter (EnKF) • Ensemble Kalman Smoother (EnKS) • Integrated unCertainty and Ensemble data Assimilation (ICEA) • Hybrid deterministic and ensemble technique • Maximum Likelihood Ensemble Filter (MLEF) for SAC-SMA 5

  6. Outline Introduction Hydrologic forecasting in US Hydrologic Ensemble Forecast System Focus of this presentation Methodology Integrated unCertainty 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

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

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

  9. Study Area Characteristics North Fork America River Watershed Area: 886 km2 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

  10. 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 SNOW17/SAC-SMA, upper  Para. Unc. (training period) Step 2: EnKF  SNOW17 model, upper  assimilate areal SWE (prediction period) Step 3: Lower, RFC para.  flow + upper flow UH routing outlet flow 10

  11. Experimental Design • Scenarios S1: RFC parameters S2: ISURF optimal parameters (S1 & S2: deterministic) S3: Stand-alone EnKF S4: ICEA (S3 & S4: ensemble) • Similarities between S3 and S4 (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 S3 and S4 • Parameter uncertainty ranges S3: entire feasible para. range; S4: ISURF-derived optimal para. range 11

  12. Verification Metrics • Deterministic metrics Correlation (R), Percent Bias, RMSE, Nash-Sutcliffe Efficiency (NSE) (for S3 & S4, ensemble mean is used when calculating above metrics) • Ensemble metrics • Normalized RMSE Ratio (NRR) • 95th Percentile Uncertainty Ratio (UR95) Measure of ensemble dispersion Value = 1 (perfect) > 1 (little spread) < 1 (much spread) (Anderson, 2002) Aggregated variability of prediction relative to observation Range 0-100%, perfect value 0 (Hossain and Anagnostou, 2005) 12

  13. Outline Introduction Hydrologic forecasting in US Hydrologic Ensemble Forecast System Focus of this presentation Methodology Integrated unCertainty 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

  14. Simulation Results • Annual statistics of simulated and observed streamflow during the training period 1979-1984 (S1 & S2) • ISURF-derived optimal parameters outperform RFC parameters • ISURF-derived parameter uncertainty information  trustable 14

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

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

  17. Prediction Results ISURF RFC 1:1 line ICEA Ens. Mean & Range EnKF Ens. Mean & Range • Performance on high flow (>95th percentile) • Scatter Plot: ICEA mean (best), RFC (worst); DA methods provide ensemble info. • Statistics: ICEA (best) ~ RFC (worst); ISURF & EnKF comparable 17

  18. Prediction Results Flow Ppt. • EnKF vs. ICEA: ensemble statistics (annual) NRR: measure of ensemble dispersion (perfect value: 1; too little spread when >1) • comparable, but not enough spread UR95: variability relative to observations (perfect value: 0) • Overall, ICEA has less variability; but not in 1993, 1995, and 1996 18

  19. Prediction Results Precipitation III. Observed SWE during WY1995 Obs./RFC streamflow & EnKF Ens. Melting Accumulation April 18 June 8 215 Obs./RFC streamflow & April 18 ICEA Ens. June 8 • EnKF vs. ICEA: finer resolution (daily) I. Selection of the wettest year,1995, for demonstration II. EnKF and ICEA flow predictions in this year • RFC misses peak/recession • Both ens. capture peak flow & high flows; spread is narrow • EnKF ens. wide in early melting period, but underestimate later  melting parameter samples 19

  20. Prediction Results RMSE Bias R NSE NRR UR95 • EnKF vs. ICEA: performance at various lead times • Deterministic metrics (a-d): overall, ICEA outperforms EnKF in all lead days • ICEA ensemble: less variability (e) all lead days; comparable dispersion (f) 20

  21. Outline Introduction Hydrologic forecasting in US Hydrologic Ensemble Forecast System Focus of this presentation Methodology Integrated unCertainty 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

  22. Conclusions Simulation: ISURF optimal para. outperform RFC para. Parameter uncertainty: 4 sensitive para.; 3 normal, 1 uniform Prediction: DA methods (EnKF/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. EnKF mean prediction ICEA ensemble predictions generally have less variability & comparable dispersion vs. EnkF ones, both on annual basis and at various lead days ICEA and EnKF 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

  23. 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., 2011a) 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

  24. Thank youQuestions? Contact: Kevin.He@noaa.gov • References • 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. • He, M., Hogue, T. S., Franz, K. J., Margulis, S. A., and Vrugt, J. A. (2011a): Corruption of parameter behavior and regionalization by model and forcing data errors: A Bayesian example using the SNOW17 model, Water Resour. Res., 47, 10.1029/2010WR009753. • He, M., Hogue, T. S., Franz, K. J., Margulis, S. A., and Vrugt, J. A. (2011b): Characterizing parameter sensitivity and uncertainty for a snow model across hydroclimatic regimes, Adv. Water Resour., 34, 114-127. • He, M., Hogue, T. S., Margulis, S. A, and Franz, K. J. (2011c): An integrated uncertainty and ensemble-based data assimilation approach for improved operational streamflow predictions, Hydrol. Earth Syst. Sci. Discuss., 8, 7709-7755, 10.5194/hessd-8-7709-2011. 24

  25. Extra Slides

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

  27. ISURF: Methodology KS • GSA: • Identify feasible parameter ranges • Monte Carlo sampling: Latin Hypercube Sampling(sample size ) • Behavioral /non-behavioral classification • Nash-Sutcliffe efficiency (NSE)=0.3 (Garbrecht, 2006) • Bin division and CDF calculation • -  bins • - CDF of NSE for each bin • Kolmogorov-Smirnov test • KS value • (Kottegoda and Rosso, 1997)

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

  29. SNOW17 Model MFMAX Dec.21 Jun.21 MFMIN Key notes 1. Ppt forcing SCF×Ppt=Ppt forcing Tair>PXTEMP: rain Tair<PXTEMP: snow 2. Non-rain melt M = N×(Tair-MBASE) 3. Rain-on-snow melt M ~ UADJ×(Tair-32) Ppt: precipitation Tair: air temperature

  30. SAC-SMA Model Precipitation (or SNOW17 output) Direct runoff ET1+ET2 Pervious Impervious Additional Impervious ET3 PCTIM ADIMP Surface runoff ET1 Tension Water Free Water UZK UZTWM UZFWM Interflow Percolation ZPERC REXP Channel inflow 1-PFREE PFREE Free Water Routing LZSK Primary Supplemental Supplemental base flow ET2 Tension Water LZFPM LZFSM LZTWM RSERV Runoff LZPK Primary base flow SIDE Legend Groundwater aquifer Parameters Storage Runoff components RIVA Upper zone Lower zone

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