Precipitation Products Statistical Techniques Tom Hopson, NCAR

Outline “Quantile-to-Quantile Mapping” (Q2Q) bias correction technique “Quantile Regression” (QR) corrections Multi-model ensemble generation “Schaake Shuffle” for flood prediction applications Preserving spatial covariances Preserving temporal autocovariances

Forecast “calibration” or “post-processing” “bias” obs Forecast PDF Probability Probability Forecast PDF obs “spread” or “dispersion” calibration Flow rate [m3/s] Flow rate [m3/s] Post-processing has corrected: the “on average” bias as well as under-representation of the 2nd moment of the empirical forecast PDF (i.e. corrected its “dispersion” or “spread”) Our approaches: “quantile-to-quantile mapping” and under-utilized “quantile regression” approach probability distribution function “means what it says” daily variation in the ensemble dispersion directly relate to changes in forecast skill => informative ensemble skill-spread relationship

ECMWF 51-member Ensemble Precipitation Forecasts 5 Day Lead-time Forecasts => Lots of variability 2004 Brahmaputra Catchment-averaged Forecasts black line satellite observations colored lines ensemble forecasts -Basic structure of catchment rainfall similar for both forecasts and observations -But large relative over-bias in forecasts Discharge forecasts employ a blend of precipitation forecasts (ECMWF) and near-real-time “observations” (GPCP or CMORPH) Precipitation “observations” used to initialize discharge model conditions (soil-moisture, lagged subcatchment discharges, etc.) before the forecast period. GPCP and CMORPHprecipitation “observations” based on IR and microwave satellite data, but distinctly different approaches. (Note: potential systematic error in GPCP in 2003 data shown here) Adjust ECMWFcatchment-average ensemble forecasts to satisfy similar distribution as the “observations” using the criterion of the uniformity of the verification rank; method similar to that proposed method of Hamill and Colucci, 1997

Specific Necessity of Post-Processing Weather Forecasts for Hydrologic Forecasting Applications Hydrologic forecast model calibration can often implicitly remove biases in input weather variables (i.e. precipitation) However, if you use one product (i.e. satellite rainfall) to calibrate your hydrologic model, but use *more* than one product (i.e. satellite rainfall and numerical weather prediction rainfall) or weather forecasts at different lead-times (with different biases for each lead-time) to generate hydrologic forecasts, then biases *between* each product or forecast lead-time must be removed This is because hydrologic model calibration cannot (implicitly) remove all biases of all input weather products simultaneously Statistical post-processing can improve not only statistical (unconditional) accuracy of forecasts (as measured by reliability diagrams, rank histograms, etc), but also factors more related to “conditional” forecast behavior (as measured by, say, RPS, skill-spread relations,etc.) Last point: inexpensive statistically-derived skill improvements can equate to significant NWP developments (expensive)

Forecast Bias Adjustment done independently for each forecast grid (bias-correct the whole PDF, not just the median) Model Climatology CDF “Observed” Climatology CDF Pmax Pmax Precipitation Pfcst Padj 25th 50th 75th 100th 25th 50th 75th 100th Quantile Quantile In practical terms … ranked forecasts ranked observations Precipitation 1m Precipitation 1m

Bias-corrected Precipitation Forecasts Original Forecast Brahmaputra Corrected Forecasts Corrected Forecast => Now observed precipitation within the “ensemble bundle”

Outline “Quantile-to-Quantile Mapping” (Q2Q) bias correction technique “Quantile Regression” (QR) corrections Multi-model ensemble generation “Schaake Shuffle” for flood prediction applications Preserving spatial covariances Preserving temporal autocovariances

Quantile Regression (QR) Our application Combining rainfall forecasts from 5 centers: CMA, CMC, CPTECH, ECMWF, NCEP conditioned on: Ensemble mean of each center Ranked forecast ensemble

PDFs: raw vs. calibrated Blue is “raw” ensemble Black is calibrated ensemble Red is the observed value Notice: significant change in both “bias” and dispersion of final PDF (also notice PDF asymmetries) obs

Outline “Quantile-to-Quantile Mapping” (Q2Q) bias correction technique “Quantile Regression” (QR) corrections Multi-model ensemble generation “Schaake Shuffle” for flood prediction applications Preserving spatial covariances Preserving temporal autocovariances

A Cautionary Warning about using Probabilistic Precipitation Forecasts in Hydrologic Modeling (Importance of Maintaining Spatial and Temporal Covariances for Hydrologic Forecasting => one option: “Schaake Shuffle”) River catchtment A ensemble1 ensemble2 ensemble3 subC subB QC QB QA QA same For all 3 possible ensembles Scenario for smallest possible QA? No. Scenario for average QA? Scenario for largest possible QA? No.

Early May 2011, floods in southwestern Africa -- examine ens forecasts … NCEP GEFS 5day precip

Outline Overview of stations Regenerating time-series autocorrelation “Schaake Shuffle” Results for select stations Difference histograms Autocorrelation Error histograms Summary

Re-generating Temporal Autocorrelation of Ensembles Sampled from Analog PDF’s using Historical Observational Sequences Slide from Demargne, Brown, Adams, Wood

Re-generating Temporal Autocorrelation of Ensembles Sampled from Analog PDF’s using Historical Observational Sequences (cont) Slide from Demargne, Brown, Adams, Wood

“I have a very strong feeling that science exists to serve human welfare. It’s wonderful to have the opportunity given us by society to do basic research, but in return, we have a very important moral responsibility to apply that research to benefiting humanity.” Dr. Walter Orr Roberts (NCAR founder) “I have a very strong feeling that science exists to serve human welfare. It’s wonderful to have the opportunity given us by society to do basic research, but in return, we have a very important moral responsibility to apply that research to benefiting humanity.” Walter Orr Roberts

Summary