Standardized Anomaly Model Output Statistics Over Complex Terrain.

Transcription

1 Standardized Anomaly Model Output Statistics Over Complex Terrain

2 Outline statistical ensemble postprocessing introduction to SAMOS new snow amount forecasts in Tyrol sub-seasonal anomaly prediction over the U.S. NOAA/PSD Seminar Talk May 21,

3 Ensemble Postprocessing Numerical Weather Prediction 1 analysis: current state 2 forecast: future state Error Sources observations simplified model world numerical approximation unknown atmospheric processes Ensemble Prediction Systems to quantify the uncertainty number of members restricted typically underdispersive NOAA/PSD Seminar Talk May 21,

4 Ensemble Postprocessing Forecast Error total error = noise + systematic errors noise: unsystematic error systematic errors: correction possible Ensemble Postprocessing correct bias correct uncertainty discrete full distribution probabilities, quantiles, extremes NOAA/PSD Seminar Talk May 21,

5 Ensemble Postprocessing observations (y) IBK T 12 +5d ensemble mean (x) NOAA/PSD Seminar Talk May 21,

6 Ensemble Postprocessing observations (y) IBK T 12 +5d ensemble mean (x) NOAA/PSD Seminar Talk May 21,

7 Ensemble Postprocessing observations (y) IBK T 12 +5d ensemble mean (x) Non-homogeneous Gaussian Regression (NGR, EMOS) y N ( µ, σ ) µ = β 0 + β 1 x log(σ) = γ 0 + γ 1 log(s x ) NOAA/PSD Seminar Talk May 21,

8 Spatial Postprocessing??????????????? density density NGR allows station-wise corrections not suitable for spatial predictions Alternative approach required. NOAA/PSD Seminar Talk May 21,

9 SAMOS What is SAMOS? NOAA/PSD Seminar Talk May 21,

10 SAMOS What is SAMOS? A probabilistic spatio-temporal ensemble postprocessing method using climatological background information to remove site specific characteristics, which allows to estimate one simple regression model for all stations and forecast lead times at once. NOAA/PSD Seminar Talk May 21,

11 SAMOS Reminder: NGR y N ( µ, σ ) µ = β 0 + β 1 x log(σ) = γ 0 + γ 1 log(s x ) NGR SAMOS Transform all quantities (y, x) into standardized anomalies: y, x : standardized anomalies y = y µ y σ y, x = x µ x σ x µ, σ : climatological properties of y, x NOAA/PSD Seminar Talk May 21,

12 SAMOS Gaussian SAMOS y N ( µ, σ ) µ = β 0 + β 1 x log(σ ) = γ 0 + γ 1 log(s x) NGR SAMOS Transform all quantities (y, x) into standardized anomalies: y, x : standardized anomalies y = y µ y σ y, x = x µ x σ x µ, σ : climatological properties of y, x NOAA/PSD Seminar Talk May 21,

13 SAMOS Gaussian SAMOS y N ( µ, σ ) µ = β 0 + β 1 x log(σ ) = γ 0 + γ 1 log(s x) NGR SAMOS Transform all quantities (y, x) into standardized anomalies: y, x : standardized anomalies y = y µ y σ y, x = x µ x σ x µ, σ : climatological properties of y, x NOAA/PSD Seminar Talk May 21,

14 SAMOS Station A (mean = 3.9 C) Station B (mean = 13.4 C) temperature [ C] climatological mean climatological 90% interval Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec temperature [ F] Convert y to y using y = y µy σ y. NOAA/PSD Seminar Talk May 21,

15 SAMOS Station A Station B Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec standardized anomalies [ C] NOAA/PSD Seminar Talk May 21,

16 SAMOS Summary Spatio-Temporal Climatologies Account for... seasonal and diurnal patterns, spatial differences (longitude, latitude, altitude), and possible interactions. Standardized Anomalies location or station independent independent from season and time NOAA/PSD Seminar Talk May 21,

17 SAMOS Summary density density On the Anomaly Scale combine data from all stations and lead times estimate one simple model for the area of interest correct current ensemble forecast µ, σ de-standardize: µ = µ σ y + µ y σ = σ σ y NOAA/PSD Seminar Talk May 21,

18 Hourly Probabilistic Snow Forecasts Over Complex Terrain A Hybrid Ensemble Postprocessing Approach R Stauffer, GJ Mayr, JW Messner, A Zeileis

19 Snow Forecasts Topography, Tyrol and Surrounding 48.0 DE AT CH 1000 IT Problem: lack of reliable fresh snow observations. NOAA/PSD Seminar Talk May 21,

20 Snow Forecasts Idea: Hybrid Approach forecast temperature & precipitation instead SAMOS hourly temperature forecasts daily precipitation forecasts ensemble copula coupling restore spatio-temporal structure convert temperature & precipitation into snow NOAA/PSD Seminar Talk May 21,

21 Snow Forecasts Station Network Height Distr TAWES EHYD Airport TAWES EHYD Observation Data hourly 2 m air temperature: 90 stations, up to 10+ years daily precipitation sums: 110 stations, up to 40+ years NOAA/PSD Seminar Talk May 21,

22 Snow Forecasts Numerical Weather Forecast Data ECMWF hindcast member ensemble 6-hourly output initialized twice a week (0000 UTC, 20 years) ECMWF ensemble member ensemble hourly output initialized 0000 UTC NOAA/PSD Seminar Talk May 21,

23 Snow Forecasts SAMOS Model Assumptions Temperature T N (µ, σ ) µ = β 0 + β 1 x log(σ ) = γ 0 + γ 1 log(x ) x : std. anomalies of the 2m temperature. Precipitation precip p L cens (µ, σ ) µ = β 0 + β 1 x (1 z) + β 2 z log(σ ) = γ 0 + γ 1 log(s x) (1 z) x : std. anomalies of power-transformed total precipitation. z: split-variable (binary) to handle unanimous predictions. NOAA/PSD Seminar Talk May 21,

24 Snow Forecasts (1) Observations: station observations spatio-temporal climatology standardized anomalies (2) Numerical Weather Forecasts: latest 8 ECMWF hindcast runs model climatology standardized anomalies (3) Estimate SAMOS models: training data set (standardized anomalies) estimate SAMOS regression coefficients (4) Prediction: standardized anomalies of latest EPS run compute corrected SAMOS predictions spatial probabilistic forecasts NOAA/PSD Seminar Talk May 21,

25 Snow Forecasts Temperature Forecasts better 2 10 BIAS [ C] % PI [ C] 8 6 CRPSS [%] worse CLIM raw EPS EMOS SAMOS_hom xsamos_het CLIM raw EPS EMOS SAMOS_hom xsamos_het CLIM raw EPS EMOS SAMOS_hom xsamos_het Verification: Dec mid April NOAA/PSD Seminar Talk May 21,

26 Snow Forecasts Temperature Forecasts better 2 10 BIAS [ C] % PI [ C] 8 6 CRPSS [%] worse CLIM SAMOS raw EPS EMOS SAMOS_hom xsamos_het CLIM raw EPS EMOS SAMOS_hom xsamos_het CLIM raw EPS EMOS SAMOS_hom xsamos_het Slightly outperformed by EMOS,... but allows for spatial predictions. Ensemble spread: barely any additional information. NOAA/PSD Seminar Talk May 21,

27 Snow Forecasts 24 h Precipitation Forecasts BIAS [mm] CRPS [mm] BS for 0 mm CLIM SAMOS raw EPS SAMOS_hom SAMOS_het CLIM raw EPS SAMOS_hom SAMOS_het CLIM raw EPS SAMOS_hom SAMOS_het Outperforms raw EPS, less skillful than for temperature. Ensemble variance barely any additional information. NOAA/PSD Seminar Talk May 21,

28 Snow Forecasts How to Get Hourly Snow Predictions? combine temperature/precipitation using ECC temperature: draw 51 member ensemble from corrected hourly N restore rank order structure 24 h precipitation: draw 51 member ensemble from corrected L 0 restore rank order structure hourly precipitation: re-weight raw hourly ensemble forecasts using: tp ω ms = ˆ copula,ms tp EPS,ms NOAA/PSD Seminar Talk May 21,

29 Snow Forecasts 2m temperature [ C] Forecast March 08, UTC Station HOLZGAU (11315) 1.2 precipitation [mm h 1 ] raw ENS observation forecast step [h] NOAA/PSD Seminar Talk May 21,

30 Snow Forecasts 2m temperature [ C] Forecast March 08, UTC Station HOLZGAU (11315) 1.2 precipitation [mm h 1 ] raw ENS observation SAMOS/ECC forecast step [h] NOAA/PSD Seminar Talk May 21,

31 Snow Forecasts Hourly Snow Forecasts dry if: precipitation ms 0.05 mm h PI ms = rain if: precipitation ms > 0.05 mm h snow if: precipitation ms > 0.05 mm h T 2m,ms > 1.2 C T 2m,ms 1.2 C PI: precipitation type indicator {dry, rain, snow} m/s: copula member and forecast step NOAA/PSD Seminar Talk May 21,

32 Snow Forecasts Forecast March 08, UTC Station HOLZGAU (11315) probability [%] precipitation rain snow fresh snow [cm] precipitation [mm] precipitation (88.5%) precipitation (50.0%) precipitation median fresh snow (88.5%) fresh snow (50.0%) fresh snow median forecast step [h] NOAA/PSD Seminar Talk May 21,

33 Snow Forecasts Expectation for March 10, :00 UTC (+48h) expectation 46.8 N 47 N 47.2 N 47.4 N 47.6 N 10.5 E 11 E 11.5 E 12 E 12.5 E 0mm 0.5mm 1mm 1.5mm 2mm 2.5mm 3mm 3.5mm 4mm NOAA/PSD Seminar Talk May 21,

34 Snow Forecasts observed frequency Precipitation (solid+liquid) Brier Score raw EPS: ECC Q: Rain (liquid) raw EPS raw EPS ECC Q ECC Q raw EPS Brier Score raw EPS: ECC Q: Snow (solid) ECC Q Brier Score raw EPS: ECC Q: observed frequency forecasted probability forecasted probability forecasted probability Empirical frequencies: precipitation 15.8 %, rain 9.8 %, snow 7.5 %. NOAA/PSD Seminar Talk May 21,

35 Snow Forecasts Summary ensemble spread: barely any information large spread for postprocessed temperature improvements: more pronounced for temperature combine different data sources use data sets with different temporal resolution reliable hourly probabilistic spatial snow forecasts NOAA/PSD Seminar Talk May 21,

36 Sub-Seasonal Climate Forecast Rodeo Improve Existing Sub-Seasonal Forecasts, Bureau of Reclamation

37 NOAA/PSD Seminar Talk May 21,

38 The Rodeo The Challenge predict anomalies mean temperature and accumulated precipitation week 3-4 and 5-6 Area of Interest (1 x1 grid) N = 514 NOAA/PSD Seminar Talk May 21,

39 The Rodeo The Price USD in total iff. anomaly forecasts are significantly better than: a damped persistence the CFSv2 itself Area of Interest (1 x1 grid) N = 514 NOAA/PSD Seminar Talk May 21,

40 The Rodeo The Truth Climate Prediction Center s gridded data set gridded gauge data set gridded temperature data set climatology: 2-week mean The Forecasts 4 member CFSv2 mean over 8 runs (8 4 = 32 member mean) The Measure ACC = ( f o ) o 2 f 2 NOAA/PSD Seminar Talk May 21,

41 The Rodeo The Idea CPC: provides observation climatology ( µ y, σ y ) CVSv2 reforecasts: provide ensemble climatology ( µ x, σ x ) apply complex homoscedastic AMOS/SAMOS Model Assumption y D ( µ, σ ) Where µ may include: forecasted anomalies (2 m temperature, dewpoint,... ) spatial effects f(long, lat) teleconnection indices (NAO, NA, PNA; CPC) snow cover data (NSIDC) NOAA/PSD Seminar Talk May 21,

42 The Rodeo ECMWF Based Approach temperature (week 3-4) Gaussian AMOS 70 covariates optimization: based on R package bamlss likelihood-based gradient boosting variable selection & parameter estimation NOAA/PSD Seminar Talk May 21,

43 The Rodeo Observed RAW EPS (0.06) Corrected (0.56) m mean temperature anomaly (week 3 4) in degrees Celsius Observed RAW EPS (0.46) Corrected (0.72) m mean temperature anomaly (week 3 4) in degrees Celsius NOAA/PSD Seminar Talk May 21,

44 The Rodeo Leader Board NOAA/PSD Seminar Talk May 21,

45 The Rodeo ACC Sub seasonal Rodeo Mean Temperature Week 3 4 mean: 0.77 mean: 0.38 in sample out of sample NOAA/PSD Seminar Talk May 21,

46 References I Gneiting, T, AE Raftery, AH Westveld, and T Goldman, 2005: Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation. Monthly Weather Review, 133, , doi: /mwr Dabernig, M, GJ Mayr, JW Messner, and A Zeileis, 2017: Spatial Ensemble Post-Processing with Standardized Anomalies. Quarterly Journal of the Royal Meteorological Society, 143, , doi: /qj Stauffer, R, N Umlauf, JW Messner, GJ Mayr, and A Zeileis, 2017: Ensemble Postprocessing of Daily Precipitation Sums over Complex Terrain Using Censored High-Resolution Standardized Anomalies. Monthly Weather Review, 145, , /MWR-D Dabernig, M, GJ Mayr, JW Messner, and A Zeileis, 2017: Simultaneous Ensemble Postprocessing for Multiple Lead Times with Standardized Anomalies. Monthly Weather Review, 145, , /MWR-D NOAA/PSD Seminar Talk May 21,

47 References II Gebetsberger, M, JW Messner, GJ Mayr, and A Zeileis, 2016: Tricks for Improving Non-Homogeneous Regression for Probabilistic Precipitation Forecasts: Perfect Predictions, Heavy Tails, and Link Functions. Working Papers, Faculty of Economics and Statistics, University of Innsbruck. Stauffer R, GJ Mayr, JW Messner, and A Zeileis, 2018: Hourly Probabilistic Snow Forecasts over Complex Terrain: A Hybrid Ensemble Postprocessing Approach. Working papers, Faculty of Economics and Statistics, University of Innsbruck. NOAA/PSD Seminar Talk May 21,

48 Thank you for your attention and special thanks to Tom for the invitation!

49 Appendix

50 SAMOS Climatological Location Climatological Scale µ~ y σ ~ y µ~ x σ ~ x m air temperature, January 1, 0000 UTC (+24h forecast). Unit: Celsius NOAA/PSD Seminar Talk May 21,

51 Snow Forecast: Hourly Calibration (a) Density Hourly 2 Meter Temperature, raw EPS rank (b) Density Hourly 2 Meter Temperature, ECC Q rank (c) Density Hourly Precipitation Sums, raw EPS rank (d) Density Hourly Precipitation Sums, ECC Q rank NOAA/PSD Seminar Talk May 21,

52 Snow Forecast: Hourly Verification (a) Stationwise Mean CRPS Skill Scores for Hourly Copula (raw EPS as Reference) CRPSS [%] for hourly temperature (b) CRPSS [%] for hourly precipitation sums forecast step or lead time (hours) NOAA/PSD Seminar Talk May 21,