BAYESIAN PROCESSOR OF OUTPUT FOR PROBABILISTIC QUANTITATIVE - - PDF document

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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

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BAYESIAN PROCESSOR OF OUTPUT FOR PROBABILISTIC QUANTITATIVE PRECIPITATION FORECASTING

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

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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  21/2 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

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EXAMPLE: Three Predictors

Quillayute, WA; cool season

W — 24-H PRECIP. AMOUNT, 12–36 h after 0000 UTC

— 850 REL. VORTICITY at 24 h

Sample Sizes
Distribution Functions
Posterior Parameters
Informativeness Score,

Prior: 818 Joint: 470

G is Weibull:

  0.592,   0.880

is Log-logistic: 6.212, 4.863, 0.641

c0 

– 0.275

T  2  2 

2  – 5.0 — 24H TOTAL PRECIP. ending 36 h — 700 VERTICAL VELOCITY at 12 h

X1 X2

X3

is Weibull: is Log-logistic (–):

3 

3  3 

0.539, 4.313, 1 

1 

9.603, 0.910

c1  c2  c3 

0.505 – 0.025 0.241 0.63 0.43 0.48 0.73 0.73 0.77 X1

X2 X3

X1,X3 X1,X2

X1,X2,X3

IS

K  1 K  2 K  3

– 0.4

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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 x1 = 30.2 850 REL. VORTICITY at 24 h x2 = 4.8 700 VERTICAL VELOCITY at 12 h x3 = -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

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10 20 30 40 50 60 70 80 90 100 110 120

Precip. Amount w [mm]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P(W ≤ w | W > 0)

MOS forecast KUIL 12-36h Cond. Precip. Amount Cool

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10 20 30 40 50 60 70 80 90 100 110 120

Precip. Amount w [mm]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P(W ≤ w | W > 0)

MOS forecast KUIL 12-36h Cond. Precip. Amount Cool

NWP Model Actual

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10 20 30 40 50 60 70 80 90 100 110 120

Precip. Amount w [mm]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P(W ≤ w | W > 0)

BPO forecast Cool KUIL 12-36h Cond. Precip. Amount

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10 20 30 40 50 60 70 80 90 100 110 120

Precip. Amount w [mm]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P(W ≤ w | W > 0)

BPO forecast Cool KUIL 12-36h Cond. Precip. Amount

NWP Model Actual

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10 20 30 40 50 60 70 80 90 100 110 120

Precip. Amount w [mm]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P(W ≤ w | W > 0)

KUIL 12-36h Cond. Precip. Amount

MOS forecast BPO forecast Climatic Prior Dist. NWP Model Estimate Actual Precip. Amount

Cool

NWP Model Actual

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10 20 30 40 50 60 70 80 90 100 110 120

Precip. Amount w [mm]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Conditional Density

BPO forecast Cool KUIL 12-36h Cond. Precip. Amount

Prior Posterior

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COMPARATIVE VERIFICATION

–8 –11 –11

∆ 11 13 13 MOS 4 3 2 BPO

Number of predictors

60 – 66 36 – 42 12 – 18

Informativeness IS Calibration CS

.26 .25 .43

MOS

–.06 –.12 –.01

– ∆

.32 .37 .44

BPO

–.06 –.14 –.12

∆

.14 .16 .16

MOS

.08 .02 .04

BPO

Conditional PQPF: 3 quantiles (p = 0.25, 0.5, 0.75) Season: Cool (Oct.–Mar.) Sample size: 98 from 2 years (Oct. 01–Mar. 03) Buffalo, NY (best) 0 ≤ CS ≤ 0.54 (worst) (worst) 0 ≤ IS ≤ 1 (best) Preliminary Results Sample: validation (not used in estimation)

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ATTRIBUTES OF BPO Implied by Experimental Test

1. More parsimonious definitions of predictors:
Calibration
Informativeness
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:

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IMPLICATIONS

1. Beneficial utilization of climatic data
stable calibration
user-specific calibration

BPO MOS Point-specific Month-specific Regional Seasonal

2. Robustness when joint samples are smaller
modeling complexity
computing requirements
3. Extension to ensemble processing less demanding