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Statistical Downscaling Approach & its Application in EMC

Statistical Downscaling Approach & its Application in EMC. Bo Cui 1 , Zoltan Toth 2 , Yuejian Zhu 2 1 SAIC at Environmental Modeling Center, NCEP/NWS 2 Environmental Modeling Center, NCEP/NWS Acknowledgements Ken Mitchell, EMC/NCEP Manuel Pondeca, EMC/NCEP.

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Statistical Downscaling Approach & its Application in EMC

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  1. StatisticalDownscaling Approach & its Application in EMC Bo Cui1, Zoltan Toth2, Yuejian Zhu2 1SAIC at Environmental Modeling Center, NCEP/NWS 2Environmental Modeling Center, NCEP/NWS Acknowledgements Ken Mitchell, EMC/NCEP Manuel Pondeca, EMC/NCEP

  2. Downscaling Method with Decaying Averaging Algorithm • True = High Resolution Analysis • operational North American Real-Time Mesoscale Analysis (RTMA) • 5x5 km National Digital Forecast Database (NDFD) grid (e.g. G. DiMego et al.) • 4 variables available: surface pressure, T2m, 10m U and V • other data can also be used • Downscaling Method: apply decaying averaging algorithm Downscaling Vector= (1-w) * prior DV + w * (GDAS – RTMA) • four cycles, individual grid point, DV = Downscaling Vector • GDAS analysis interpolated to RTMA grids • regime (not flow) dependent • choose different weight: 0.5%, 1%, 2%, 5%, 10% • Downscaling Process Downscaled Forecast= Bias-corrected Forecast – Downscaling Vector • subtract DV from bias-corrected forecast valid at analysis time • bias-corrected forecast interpolated to RTMA grids

  3. Downscaling Application & Verification • Experiments • control 1: operational GEFS ensemble after interpolated to RTMA grids • control 2 : NAEFS bias corrected ensemble after interpolated to RTMA grids • 5 downscaled ensembles : 0.5%, 1%, 2%, 5%, 10% weights when calculating DV • Application • off-line experiments starting from 08/11/2006, different decaying weights • baseline for evaluating other sophisticated flow dependent downscaling methods • Verification • Domain averaged bias (absolute values) comparison: before & after downscaling • Accumulated bias are derived from 7 experiments against RTMA with 2% weight Accumulated Bias= (1-w) * prior accumulated bias + w * ( mean forecast – RTMA) • mean forecast from control 1, 2 and 5 downscaled ensemble mean, respectively • Ensemble mean & bias comparison before & after downscaling: 00 hr, 24 hr • Continues Ranked Probability Scores (CRPS) • Ensemble mean RMSE and ensemble spread • Downscaling Vector comparison

  4. 2m Temperature:Accumulated Bias Before/After RTMA Downscaling 1.7 1% 2% 10% 0.2 Black- control 1, operational ensemble mean, bias range 1.1- 1.7 Red - control 2, NAEFS bias corrected ensemble mean, bias range 1-1.6 Blue- downscaled & bias corrected ensemble mean, 1%, bias range 0.5-0.6 Green- downscaled & bias corrected ensemble mean, 2%, bias range 0.3- 0.5 Yellow- downscaled & bias corrected ensemble mean, 10%, bias range 0.2-0.4

  5. 10m U Wind: Accumulated Bias Before/After RTMA Downscaling 0.7 1% 2% 10% 0.2 Black- control 1, operational ensemble mean, bias range 0.7-0.85 Red - control 2, NAEFS bias corrected ensemble mean, bias range 0.6-0.8 Blue- downscaled & bias corrected ensemble mean, 1%, bias range 0.4-0.45 Green- downscaled & bias corrected ensemble mean, 2%, bias range 0.3-0.35 Yellow- downscaled & bias corrected ensemble mean, 10%, bias range 0.2-0.3

  6. 10m V Wind: Accumulated Bias Before/After RTMA Downscaling Black- control 1, operational ensemble mean, bias range 0.6-0.8 Red - control 2, NAEFS bias corrected ensemble mean, bias range 0.55-0.65 Blue- downscaled & bias corrected ensemble mean, 1%, bias range 0.4-0.5 Green- downscaled & bias corrected ensemble mean, 2%, bias range 0.3-0.4 Yellow- downscaled & bias corrected ensemble mean, 10%, bias range 0.2-0.25

  7. 00hr GEFS Ensemble Mean & Bias Before/After Downscaling 10% 2m Temperature 10m U Wind Before Before After After

  8. 24hr Ensemble Mean & Bias Before/After RTMA Downscaling 10% Before Before After • Left top: operational ens. mean and its bias vs. RTMA • Right top: bias corrected ens. mean and its bias • Left bottom: bias corrected & downscaled ( 10% ) ens. mean and its bias vs. RTMA • After Downscaling • More detailed forecast information • Bias reduced, especially high topography areas

  9. 24hr Ensemble Mean & Bias Before/After RTMA Downscaling 10% Before Before After • Left top: operational ens. mean and its bias vs. RTMA • Right top: bias corrected ens. mean and its bias • Left bottom: bias corrected & downscaled ( 10% ) ens. mean and its bias vs. RTMA • After Downscaling • More detailed forecast information • Bias reduced, especially high topography areas

  10. 24hr Downscaled Ensemble Bias Comparison : 2%, 5% & 10% 2% 5% 10% • Bias corrected & downscaled ensemble mean and its bias left vs. RTMA: T2m • more bias are reduced for 10% test • lakes have different bias from surrounding areas. 10% can eliminate most of the cold bias. • Downscaling vectors display the similar bias over lakes. Which system is doing the poor job of analysis over lake?GFS analysis or RTMA?

  11. GDAS Analysis & Downscaling Vector ( 10% )

  12. GDAS Analysis & Downscaling Vector ( 5% )

  13. GDAS Analysis & Downscaling Vector ( 2% )

  14. 2m Temperature: Continuous Ranked Probability Scores (CRPS) Average for 20070212 to 20070305 Before downscaling After downscaling

  15. CRPS: 2m Temperature CRPS: 10m U CRPS: 10m V • Preliminary results: • 2%, 5% & 10% have significant improvements compared with raw & calibrated fcst. till day 7 • 10% is better than 2% and 5% in short range, 2%, 5% and 10% are close for long range • Limitation: • small samples, 22 cases • more samples in short range than long range

  16. 2m Temperature: Ensemble Mean RMSE and Ensemble Spread Average for 20070212 to 20070305

  17. 2m Temperature 10m U 10m V • Preliminary results: • downscaled forecast have reduced RMSE compared with raw & bias-corrected forecast • small ensemble spread changes for different tests • distance between RMSE and ensemble spread has a decreasing tendency with forecast lead time. The ens. mean RMSE and spread curves are becoming close for long lead time

  18. Summary & Future Plan • Summary • systematic (time mean) error: downscaling method with decaying averaging algorithm can effectively reduce systematic forecast errors. The 10% weight has the best performance, ~ 70% of T2m, 10m U and V wind systematic errors are reduced. • more detailed forecast information available in the downscaled forecast. • CRPS show that the downscaled & bias-corrected ensemble forecasts have been improved compared with the raw and bias corrected ensembles. • RMSE: downscaled forecasts have reduced ensemble mean RMSE compared with the raw and bias-corrected forecasts, 10% - 20% of RMS errors reduced. • Future Plan • more weight factor tests choosing 20% and do comparison with 10%. • study on systematic and random error components, respectively. • add downscaled 10-50-90 percentile forecast values for selected variables. • Downscaled method scheduled to be implemented later in 2007.

  19. Background !!!!!

  20. Introduction • Definition of downscaling for this discussion (there are other ways to define): • Relationship between coarse & fine resolution geo-science information • How we create fine resolution info based on coarse resolution fields • In space and/or in time • Related to finite spatial/temporal resolution • Not directly related to any numerical model • Eg, relationship between low and high resolution analyses: How can we predict hires from low-res? • Definition of “forecast bias correction” • Removal of systematic (time mean) error from forecast • On original forecast grid • Related to “drift” of numerical model forecast • Relationship between bias correction & downscaling • They are “orthogonal” • Different problems, different methods can (or should?) be used • Benefit from understanding differences between forecast bias correction & downscaling • Some studies address both forecast bias correction & downscaling with same method • Objectives for downscaling • Systematic (time mean) errors on fine scale • Want to eliminate • From all ensemble members • Variability on fine scales • Want to insert variability so down-scaled info has realistic variance • Will hurt individual forecast • Will help ensemble forecast • Ensemble mean should be unchanged

  21. Statistical Post-Processing Issues • Statistical Downscaling Method • Regression:MOS techniques; Bayesian technique • “PDF” matching:(aka CDF matching) • Matching cumulative probability density functions (frequency of occurrence) • Neural Networks • Analog Methods: Tom Hamill and Jeff Whitaker; Self Organizing Maps (SOMs) • Downscaling Vectors (DV) with decay averaging algorithm • requires an independent hi-res analysis (e.g. RTMA applied to GFS forecast) • derive static DV for past N times: subtract hi-res anal from low-res fcst valid at anal time • averaged DV: apply decreasing weights to past N static DVs (above bullet) • Canonical Correlation Analysis: CCA • e.g. widely used in CPC (Huug Van den Dool) • Redundacy Analysis: a variant of CCA • Singular Value Decomposition: a variant of CCA • Bias Correction vs. Downscaling • Bias Correction : remove lead-time dependent bias on model grid • Working on coarser model grid allows use of more complex methods • Feedback on systematic errors to model development • Downscaling: downscale bias-corrected forecast to finer grid • Further refinement/complexity added • No dependence on lead time, No dependence on model

  22. Downscaling: Some basic preliminariesby Ken Mitchell • Definition: • Any method to represent a global or regional model’s atmospheric, oceanic or land analysis or forecast at substantially finer resolution than the original product • Common Motivation: • Represent the influence of finer scale topography • Main Types of Methods • Dynamical: predictive models, with temporal evolution • imbed finer scale predictive model inside parent global or regional model • often the most expensive approach to develop, execute and maintain • Physical: no temporal predictive element • Kinematic:includes adjustment of large scale wind and pressure field to finer scale topography • Static: usually applied 1-D in vertical, without spatial adjustment of wind and pressure field to finer terrain • Statistical: analog techniques, neural networks, others • The broadest category, usually requires long archive of parent model prediction • Combination: combination of two or more of above • Prediction Range • short-range (1-3 days), medium-range (1-15 days), sub-seasonal (1-6 weeks) or seasonal to annual (1-12 months)

  23. Bias Correction Method & Application • Bias Correction Techniques – array of methods • Estimate/correct bias moment by moment (e.g., D. Unger et al.). • Simple approach, implemented partially • May be less applicable for extreme cases • Bayesian approach (e.g., Roman Krzysztofovicz) • Allows simultaneous adjustment of all modes considered, under development • Moment-based method at NCEP: apply adaptive (Kalman Filter type) algorithm decaying averaging mean error = (1-w) * prior t.m.e + w * (f – a) • For separated cycles, each lead time and individual grid point, t.m.e = time mean error • Test different decaying weights. • 0.25%, 0.5%, 1%, 2%, 5% and • 10%, respectively • Decide to use 2% (~ 50 days) • decaying accumulation bias • estimation 6.6% 3.3% 1.6% Toth, Z., and Y. Zhu, 2001

  24. Bias Before/After Bias Correction ( NCEP NH) 500hPa height 850hPa temperature Before bias correction (1x1) After bias correction (1x1) 2m Temperature Sea level pressure before downscaling (5x5 km) after downscaling (5x5 km) before bc. (1x1) after bc. (1x1)

  25. 24hr Ensemble Mean Forecast & Bias Left: 2%,5% & 10% 2% 5% 10% • Bias corrected & downscaled ensemble mean and its bias left vs. RTMA: 10m U: • more bias are reduced for weight 10% test

  26. 24hr Downscaled Ensemble Mean & Bias Comparison : 2%,5% & 10% 2% 5% 10% • Bias corrected & downscaled ensemble mean and its bias left vs. RTMA: T2m • more bias are reduced for weight 10% test • lakes have different bias from surrounding areas. 10% can eliminate most of the cold bias. Downscaled vectors also display this bias. Which system is doing the poor job of t2m analysis over lake?The GFS analysis or RTMA?

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