1

PQPF: THEORY AND OPERATIONAL USE

Theresa Rossi

NOAA/NWS Pittsburgh, PA

Presented at Hydromet 00-2

Monday, 28 February 2000

2

OVERVIEW

• Probabilistic Hydrometeorological System

• PQPF Methodology

• Interactive PQPF Software

• Probabilistic Reasoning

• PQPF Case Study

• River Forecast Interface

3

NWS End-to-End Probabilistic Risk Reduction

• Define AWIPS-compatible PQPF/PRSF methodologies, PQPF guidance, and public product formats.

• Approach is grid-based and benefits from HPC, TDL and OH input.

• 1998-2000. With funding, similar Risk Reductions in other Regions after 2001.

• UVA/PBZ/RLX/OHRFC/TDL/HPC/OH/ OM

• Users (County EMA & Barge Industry)

4

PROBABILISTIC HYDROMETEOROLOGICAL

FORECASTING SYSTEM

ProbabilisticProbabilistic QuantitativeQuantitative PrecipitationPrecipitation

Forecasting SystemForecasting SystemPQPFPQPF

WFO

To improve the reliability and lead time of flood warnings.To improve the reliability and lead time of flood warnings.

Probabilistic River StageProbabilistic River Stage Forecasting SystemForecasting System

PRSFPRSF

River FloodRiver FloodWarning SystemWarning System

RFIRFI

USERSUSERS

RFC

WFO

Probabilistic RSFs

Flood Watches & Warnings

5

FORECASTFORECASTMETHODOLOGYMETHODOLOGY

LOCALLOCALCLIMATICCLIMATIC

DATADATA

FORECAST FORECAST VERIFICATIONVERIFICATION

THE PQPF SYSTEM

WFOWFO

RFCRFC

GUIDANCEGUIDANCE

6

PQPF METHODOLOGY

7

PQPFTOTAL AMOUNT

• Precipitation amount accumulated during a period: W

• Probability of Precipitation: PoP=P(W>0)

• Conditional Exceedance Fractiles of Amount:– P(W>X25|W>0)=0.25

– P(W>X50|W>0)=0.50

8

CONDITIONAL EXCEEDANCE FUNCTIONW = 24-hour Basin Average Precipitation Amount

0

0.25

0.5

0.75

1

50% CREDIBLE INTERVAL

ww

(P W>w|W>0)(P W>w|W>0)

X75 - 75% FractileX50 - 50% FractileX25 - 25% Fractile

Conditional Probability

X75 X50 X25

calculated

9

ASSESSMENT OF CONDITIONAL EXCEEDANCE FRACTILES

X50

Judgments of equally likely events

X25

ACTUAL PRECIPITATION W

HYPOTHESIS: X50 <WACTUAL PRECIPITATION W

P(W>X25 |W >0)=.25

P(W>X50 |W>0)=.50

HYPOTHESIS: 0<W

10

PQPFTemporal Disaggregation

• Precipitation amount during subperiod i: Wi

• Expected subamounts: mi=E(Wi|W>0); i=1,2,3,4;12,34

• Expected fractions: zi=E(Wi/W|W>0); i=1,2,3,4;12,34

13%

17%57%

13% z1z2Z3Z4

11

INTERACTIVE SOFTWARE FOR PROBABILISTIC

QUANTITATIVE PRECIPITATION FORECASTING

12

Purpose

• Aids field forecasters in preparing PQPFs.

• Provides crucial input to Probabilistic River Stage Forecast System.

• Prototype Testing– Weather Service Forecast Offices

• Pittsburgh, PA

• Charleston, WV

13

14

15

16

17

18

19

20

21

22

23

PROBABILISTIC REASONING

24

SCHEME FOR JUDGMENTAL PROCESSING OF

INFORMATION INTO PQPF

25

NMC NUMERICAL

MODELS

TDL MODEL OUTPUT STATISTICSNMC MANUAL GUIDANCE

LOCALSUBJECTIVE ANALYSIS

REVIEW-MODEL ASSESSMENT/COMPARISON

-GUIDANCE REVIEW

ISPRECIP

PROBABLE?

STOP

ISSIGNIFICANT

AMOUNTPROBABLE?

FURTHUR ANALYSIS-MODEL OUTPUTS-LOCAL ANALYSIS

WHAT IS PREDICTABILITY OF

PATTERN?

WHAT ISPREDICTABILITY OF

PATTERN

LIMITEDFURTHER ANALYSIS

-FOLLOW CLOSELYLOCAL ADJUSTMENTS

TO GUIDANCE-LARGE UNCERTAINTY

-FOLLOW CLOSELYGUIDANCE WITH MINORLOCAL ADJUSTMENTS

-SMALLER UNCERTAINTY

-MIX GUIDANCE WITH LOCAL

ADJUSTMENTS-LARGER UNCERTAINTY

-FOLLOW GUIDANCECLOSELY

-SMALLERUNCERTAINTY

LOCAL CLIMATOLOGICALGUIDANCE

INTEGRATIONEXPERT KNOWLEDGE OF

LOCAL HYDROMETINFLUENCES

OBSERVATIONS

NO

YES

YES NO

LOW

HIGH

LOW HIGH

WORKING QPF

POSTERIOR QPF

RE

VIE

WD

EV

EL

OPM

EN

TA

DJU

ST

ME

NT

INT

EG

RA

TIO

N

26

MAKING A PQPF

DEVELOPMENDEVELOPMENTT

REVIEWREVIEW

ADJUSTMENADJUSTMENTT

INTEGRATIONINTEGRATION

27

THE REVIEW PHASEExamine Observations and Guidance

• Review Initial Conditions– Diagnose past/current conditions, trends

and how well models initialized.

– Compare Model Outputs• If Agree…confidence is increased.• If Not…uncertainty decreases confidence.

28

THE DEVELOPMENT PHASEJudge Likelihood/Predictability of

Precipitation• Ask three questions:

– Is precipitation probable?– Is a significant amount probable?– What is predictability of pattern?

• No significant amount & predictability:– high…more confidence in guidance.– low…less confidence/further analysis

• Significant amount…further analysis.

29

THE ADJUSTMENT PHASEAdjust Guidance/Ascertain Uncertainty • Nonsignificant Event

– Predictability high…follow guidance/uncertainty smaller.

– Predictability low…may adjust guidance/ uncertainty larger.

• Significant Event– Predictability high…local analysis should corroborate

guidance/uncertainty smaller.

– Predictability low…extensive use of analysis, may significantly adjust guidance/uncertainty larger.

• “Working PQPF”…includes amounts & uncertainties.

30

THE INTEGRATION PHASE“Working PQPF” Integrated with LCG

• Integrate Information From:– “Working PQPF”– Knowledge of local influences– Local Climatic Guidance (LCG)

• Uncertainty small…tend toward “Working PQPF”

• Uncertainty large…tend toward LCG

31

PQPF CASE STUDYWell Organized Frontal System

May18-19,1999

32

THE REVIEW PHASECase Study May 18-19, 1999

• Examine Observations and Guidance– 00Z 5/18/99 ETA Model

• Models initialized well & in agreement

–confidence increased

33

34

35

36

37

38

39

40

41

42

43

44

45

46

THE DEVELOPMENT PHASE Case Study May 18-19, 1999

• Judge Likelihood/Predictability of Precipitation– A significant amount of precipitation probable– Predictability of pattern is high

• Models in agreement on speed & movement of system

• Precipitation of convective nature & spatially variable with localized higher amounts possible

47

THE ADJUSTMENT PHASE Case Study May 18-19, 1999

• Adjust guidance/Ascertain Uncertainty

• Significant Event– Predictability high…local analysis corroborated

guidance/uncertainty smaller

• “Working PQPF”…includes amounts & uncertainties

48

THE INTEGRATION PHASE Case Study May 18-19, 1999

• Integrate “Working PQPF”, local influences & LCG

• Uncertainty small…tend toward “Working PQPF”

49

24hour POP24hour POP

50

X50X50

51

X50X50

52

X25X25

53

X25X25

54

X75X75

55

X75X75

56

T50

57

T50

58

Z1Z1

59

Z1Z1

60

Z2Z2

61

Z3Z3

62

Z4Z4

63

Summary of Case Study May 18-19, 1999Well Organized Frontal System

• Precipitation probable & significant.

• Predictability of pattern high…models in agreement. Analysis corroborate guidance.

• Convective nature, spatially variable, localized higher amounts possible.

• Uncertainty reflected in wide credible interval.

64

WFOWFOMosaicMosaic

Stage 3Stage 3PrecipPrecip(actual)(actual)

65

Summary of Case Study May 18-19, 1999Monongahela River Basin

24-h period ending 1200 UTC 5/19/99

Exceedance Fractiles Expected Fractions(inches) (%)

X75 X50 X25Z1 Z2 Z3 Z4

PQPF .54 1.10 2.00 10 30 50 10

LCG* .34 0.47 0.74 28 20 2131

*LCG estimates are conditioned on a minimum of 0.25 inches.

ACTUAL 0.31 0 7 93 0

PoP = 100%

66

RIVER FORECAST INTERFACE

67

GRAPHICAL RIVER FORECAST INTERFACE

• Input - Probabilistic River Stage Forecasts (PRSF)

• Purpose– Display PRSF– Aid forecaster in deciding flood alarm

(watch/warning)– Communicate flood alarms to users– Aid users in making decisions based on PRSF

68

69

70

71

SUMMARY

• Provided overview of Probabilistic Hydrometeorological Forecasting System

• Focused on PQPF – Methodology– Interactive Software– Probabilistic Reasoning

• Demonstrated concepts with May18-19, 1999 Case Study