BAYESIAN PROCESSOR OF OUTPUT FOR PROBABILISTIC QUANTITATIVE - PDF document

BAYESIAN PROCESSOR OF OUTPUT FOR PROBABILISTIC QUANTITATIVE PRECIPITATION FORECASTING By Coire J. Maranzano and Roman Krzysztofowicz University of Virginia Presented at the 18 th Conference on Probability and Statistics in the Atmospheric Sciences Atlanta, Georgia 29 January  2 February 2006 Acknowledgments: Work supported by the National Science Foundation under Grant No. ATM  0135940. Data provided by the Meteorological Development Laboratory of the National Weather Service.

BAYESIAN PROCESSOR of OUTPUT for PROBABILISTIC QUANTITATIVE PRECIPITATION FORECASTING BPO for PQPF COMPREHENSIVE EVALUATION Estimation Samples Prior: NCDC archive  7 y (Jan. 97  Dec. 03) Joint: MOS archive  4 y (Apr. 97  Mar. 01) Validation Sample Joint: MOS archive  2 1/2 y (Apr. 01  Sept. 03) Benchmark : AVN-MOS Model cycle time : 0000 UTC Periods : 6-h, 12-h, 24-h (beginning at 12 h, 36 h, 60 h) Seasons : cool, warm Stations : 14 regions x 2 stations = 28

EXAMPLE: Three Predictors Quillayute, WA; cool season W — 24-H PRECIP. AMOUNT, 12–36 h after 0000 UTC X 1 — 24H TOTAL PRECIP. ending 36 h X 2 — 850 REL. VORTICITY at 24 h X 3 — 700 VERTICAL VELOCITY at 12 h • Sample Sizes Joint: 470 Prior: 818 • Distribution Functions   0.880   0.592, G is Weibull:  1  1  0.910  1  K 9.603, is Weibull:  2  – 5.0  2  4.863,  2  6.212,  2 is Log-logistic: K  3   3  – 0.4  3 0.539,  3  is Log-logistic (–): 4.313, K • Posterior Parameters c 0  – 0.025 c 1  0.505 c 2  T  0.241 0.641 c 3  – 0.275 • Informativeness Score, IS  X 1 , X 3   X 1 , X 2 , X 3   X 1 , X 2  X 1 X 2 X 3 0.73 0.77 0.73 0.43 0.48 0.63

EXAMPLE: Conditional PQPF Quillayute, WA Cool season 24-h, 12–36 after 0000 UTC 21 February 2002 • BPO: 3 predictors; 15 parameters 24-H TOTAL PRECIP. ending 36 h x 1 = 30.2 850 REL. VORTICITY at 24 h x 2 = 4.8 700 VERTICAL VELOCITY at 12 h x 3 = -0.95 • MOS: 15 predictors; 80 parameters (5 catego.) 12-H TOTAL PRECIP. GB (6.35 mm) ending 24 h 12-H TOTAL PRECIP. GB (25.4 mm) ending 24 h 12-H TOTAL PRECIP. GB (0.254 mm) ending 36 h 24-H TOTAL PRECIP. ending 36 h 12-H TOTAL PRECIP. GB (2.54 mm) ending 24 h 24-H TOTAL PRECIP. GB (12.7 mm) ending 36 h 850 REL. VORTICITY at 12 h LONGITUDE 12-H TOTAL PRECIP. GB (12.7 mm) ending 24 h ELEVATION LATITUDE 24-H CONV. PRECIP. GB (0.254 mm) ending 36 h 850 REL. VORTICITY at 24 h 500 VERTICAL VELOCITY GB (-0.9) at 24 h 500 VERTICAL VELOCITY GB (-0.5) at 12 h

KUIL 12-36h Cond. Precip. Amount Cool MOS forecast 1.0 0.9 0.8 0.7 P(W ≤ w | W > 0) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 60 70 80 90 100 110 120 Precip. Amount w [mm]

KUIL 12-36h Cond. Precip. Amount Cool MOS forecast NWP Model Actual 1.0 0.9 0.8 0.7 P(W ≤ w | W > 0) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 60 70 80 90 100 110 120 Precip. Amount w [mm]

KUIL 12-36h Cond. Precip. Amount Cool BPO forecast 1.0 0.9 0.8 0.7 P(W ≤ w | W > 0) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 60 70 80 90 100 110 120 Precip. Amount w [mm]

KUIL 12-36h Cond. Precip. Amount Cool BPO forecast NWP Model Actual 1.0 0.9 0.8 0.7 P(W ≤ w | W > 0) 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 60 70 80 90 100 110 120 Precip. Amount w [mm]

KUIL 12-36h Cond. Precip. Amount Cool NWP Model Actual 1.0 0.9 0.8 0.7 P(W ≤ w | W > 0) 0.6 0.5 0.4 MOS forecast 0.3 BPO forecast Climatic Prior Dist. 0.2 NWP Model Estimate Actual Precip. Amount 0.1 0.0 0 10 20 30 40 50 60 70 80 90 100 110 120 Precip. Amount w [mm]

KUIL 12-36h Cond. Precip. Amount Cool BPO forecast 1.0 0.9 0.8 0.7 Conditional Density 0.6 Prior Posterior 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 60 70 80 90 100 110 120 Precip. Amount w [mm]

COMPARATIVE VERIFICATION Conditional PQPF: 3 quantiles (p = 0.25, 0.5, 0.75) Season: Cool (Oct.–Mar.) Sample: validation (not used in estimation) Sample size: 98 from 2 years (Oct. 01–Mar. 03) Buffalo, NY Preliminary Results Calibration Informativeness Number of CS IS predictors BPO MOS ∆ BPO MOS – ∆ BPO MOS ∆ 2 13 12 – 18 .04 .16 –.12 .44 .43 –.01 –11 3 13 36 – 42 .02 .16 –.14 .37 .25 –.12 –11 4 11 60 – 66 .08 .14 –.06 .32 .26 –.06 –8 (best) 0 ≤ CS ≤ 0.54 (worst) (worst) 0 ≤ IS ≤ 1 (best)

ATTRIBUTES OF BPO Implied by Experimental Test 1. More parsimonious definitions of predictors: • grid-binary predictors not needed • reduced number of potential predictors 176 36 2. More efficient extraction of predictive information: • reduced number of optimal predictors PoP: (4 – 7) (1 – 4) PQPF (cond.): (5 – 15) (1 – 4) • reduced number of parameters PQPF (cond.): 80 20 3. Better representation of distribution function: discrete (3 – 5 points) continuous 4. Equal or better performance: • Calibration • Informativeness

IMPLICATIONS 1. Beneficial utilization of climatic data • stable calibration • user-specific calibration BPO MOS Point-specific Regional Month-specific Seasonal 2. Robustness when joint samples are smaller 3. Extension to ensemble processing less demanding • modeling complexity • computing requirements