Probabilistic Hydrometeorological

Forecasts

Hydromet 00-3Thursday, 11 May 2000

Bill Drzal

NOAA/NWS Pittsburgh, PA

OVERVIEW

• Probabilistic Hydrometeorological System

• PQPF Methodology

• Interactive PQPF Software

• Probabilistic Reasoning

• PQPF Case Study

• Probabilistic River Stage Forecast

• River Forecast Interface

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)

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

FORECASTFORECASTMETHODOLOGYMETHODOLOGY

LOCALLOCALCLIMATICCLIMATIC

DATADATA

FORECAST FORECAST VERIFICATIONVERIFICATION

THE PQPF SYSTEM

WFOWFO

RFCRFC

GUIDANCEGUIDANCE

PQPF METHODOLOGY

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

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

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

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

A PQPF is Never Right or Wrong

It Just Needs to be

Well Calibrated!

INTERACTIVE SOFTWARE FOR PROBABILISTIC

QUANTITATIVE PRECIPITATION FORECASTING

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

PROBABILISTIC REASONING

SCHEME FOR JUDGMENTAL PROCESSING OF

INFORMATION INTO PQPF

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

MAKING A PQPF

DEVELOPMENDEVELOPMENTT

REVIEWREVIEW

ADJUSTMENADJUSTMENTT

INTEGRATIONINTEGRATION

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.

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.

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.

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

PQPF CASE STUDYWell Organized Frontal System

May18-19,1999

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

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

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

THE INTEGRATION PHASE Case Study May 18-19, 1999

• Integrate “Working PQPF”, local influences & LCG

• Uncertainty small…tend toward “Working PQPF”

24hour POP24hour POP

X50X50

X50X50

X25X25

X25X25

X75X75

X75X75

T50

T50

Z1Z1

Z1Z1

Z2Z2

Z3Z3

Z4Z4

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.

WFOWFOMosaicMosaic

Stage 3Stage 3PrecipPrecip(actual)(actual)

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 21 31

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

ACTUAL 0.31 0 7 93 0

PoP = 100%

Probabilistic River Stage Forecast

(PRSF)

PRSF Methodology

• Interfaces with NWSRFS– Ensemble Streamflow Prediction (ESP) - OH– Bayesian Forecast System (BFS) - UVA

• Output – Exceedance Function– Quantifies total uncertainty about river stage

for a certain day

Integration of PRSF System with NWSRFS

Gridded PQPF

RFC WFO

Preprocessing to getDeterministic QPF

PrecipitationForecast Processor

PFP

River Forecast Viewer

OperationalForecast SystemNWSRFS - OFS

EnsembleStreamflow Prediction

NWSRFS - ESP

Bayesian Forecasting System

BFS

River Forecast Interface

RFI

River Forecast ViewerRFV

WFO Web Site

End-User

Bayesian Forecast SystemFrom NWSRFS: Input for forecast point

PrecipitationUncertaintyProcessor(PUP)

HydrologicUncertaintyProcessor(HUP)

Integrator(INT)

InteractiveReview andAdjustment

(IRA)

Parameter estimatesFrom off-line

simulation

Guidance PRSF

Model PRSF

RIVER FORECAST INTERFACE

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

SUMMARY

• Provided overview of Probabilistic Hydrometeorological Forecasting System

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

• Demonstrated concepts with May18-19, 1999 Case Study

PQPF Lab Exercise

Objective:Prepare a probabilistic QPF of spatially averaged precipitation over fourriver basis to determine how well calibrated the forecasts aft for the class as a whole.

Instructions:Review the Hurricane Floyd case using any available data through 12zon 16 Sep 1999. Prepare probabilistic QPFs of spatially averaged precipitation for the 24 hour period ending on 17 Sep 1999 for eachof the four basins on your lab sheet. For X75, X50, and X25 enter thevalue to the nearest tenth of an inch. For Z(1,2,3,4) enter the percentage of the total rainfall that occurred in each time period.

PQPF LAB EXERCISE

BASIN X75 X50 X25 Z1 Z2 Z3 Z416/12Z-18Z 16/18Z-7/00Z 17/00Z-06Z 17/06Z-12Z

PASSAIC

RARITAN

SCHUYLKILL

SOUTHEAST PA/LWR DELAWARE

7.84

7.34

6.69

8.09

7.76

7.84

6.84

8.23

7.67

7.25

7.43

6.93

7.56

7.67

4.37

3.76

4.44

5.28

8.31

6.66

5.60

6.03

X50 Verification

River X50 Z1 Z2 Z3 Z4

PASSAIC 7.59 34 58 8 0

RARITAN 7.36 46 51 1 2

SCHUYLKILL 5.47 47 50 3 0

SE PA/DELAWARE 5.80 53 45 1 1