Description and Preliminary Evaluation of the Expanded UW

Short Range Ensemble Forecast System

Maj. Tony Eckel, USAF

University of Washington Atmospheric Sciences Department

Advisor: Prof. Cliff Mass

March 2002

Overview

• UW SREF Methodology

• Generating New Initial Conditions

• Case Study• Error Statistics• Individual SREF Members• Ensemble-Based Probability

• Summary

- Construct the initial state of the atmosphere with multiple, equally likely analyses, or initial conditions (ICs)

Ensemble Forecasting Theory

0

1

2

3

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7

8

1 3 5 7 9 11 13 15 17 19

Fre

quen

cy

Initial State0 5 10 15 20

0.2

0.4

.5

7.6946e-023

dnorm ( ),,x 10 1

200 x

- From our point of view, truth is random sample from the pdf

0 5 10 15 20

0.2

0.4

.5

0.000514093

dnorm ( ),,x 10 3

200 x

0 5 10 15 20

0.2

0.4

.5

7.4336e-007

dnorm ( ),,x 10 2

200 x

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1 3 5 7 9 11 13 15 17 19

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1 3 5 7 9 11 13 15 17 19

24hr Forecast State 48hr Forecast State

- Let all ICs evolve to build PDF at future time (i.e., a forecast pdf)

- Error growth spreads out PDF as forecast lead time increases

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1 3 5 7 9 11 13 15 17 190

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1 3 5 7 9 11 13 15 17 190

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Difficult to consistently construct the “correct” analysis/forecast pdf.Errors in mean and spread result from:

1) Model error

2) Choice of ICs

3) Under sampling due to limits of computer processing

Result: EF products don’t always perform the way they should. (especially a problem for SREF)

Limitations of EFF

requ

ency

Initial State0 5 10 15 20

0.2

0.4

.5

0.000514093

dnorm ( ),,x 10 3

200 x

0 5 10 15 20

0.2

0.4

.5

7.4336e-007

dnorm ( ),,x 10 2

200 x24hr Forecast State 48hr Forecast State0 5 10 15 20

0.2

0.4

.5

7.6946e-023

dnorm ( ),,x 10 1

200 x

analysis pdf

ensemble

pdf

phasespace

T

48hr forecast state (core)

48hr true state

Analysis pdf :

Forecast pdf :

7 “independent” atmospheric analyses, the centroid, plus 7 “mirrored” ICs15 divergent, “equally likely” solutions using the same primitive equation model, MM5

Forecast pdf

48hr forecast state (perturbation)

ngp

uk

eta

cmc

gsp

avn

Analysis pdfcwb

Cngp

eta

cmc

avn

gsp

cwb

uk

UW SREF Methodology Overview

A point in phase space completely describes an instantaneous state of the atmosphere.For a model, a point is the vector of values for all parameters (pres, temp, etc.) at all grid points at one time.

cmcg*

Filling in the Holes of the IC Cloud

STEP 1: Calculate best guess for truth (the centroid) by averaging all analyses.

STEP 2: Find error vector in model phase space between one analysis and the centroid by differencing all state variables over all grid points.

STEP 3: Make a new IC by mirroring that error about the centroid.

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Sea

Lev

el P

ress

ure

(mb)

~1000 km

1006

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1000

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994

cent

170°W 165°W 160°W 155°W 150°W 145°W 140°W 135°W

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tcwbgasp

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cmcg

ICs: Analyses, Centroid, and Mirrors

Strengths• Good representation of analysis error

• Perturbations to synoptic scale disturbances• Magnitude of perturbation(s) set by spread among analyses

• Bigger spread Bigger perturbations• Dynamically conditioned ICs• Computationally affordable

Weaknesses• Limited by number and quality of available analyses

• May miss key features of analysis error• Analyses must be independent (i.e., dissimilar biases)• Calibration difficult; no stability since analyses may change techniques

CASE STUDY: Thanksgiving Day Non-Wind Event

eta-MM5 Initialized: 00z, 21 Nov 2001 (Tuesday evening)

39h, valid 22 Nov 15z 42h, valid 22 Nov 18z

(Thursday 7AM) (Thursday 10AM)

Note: This study used only 13 ensemble members since missing gasp grids.

ZCZC SEANPWSEAWWUS45 KSEA 212348 URGENT - WEATHER MESSAGENATIONAL WEATHER SERVICE SEATTLE WA344 PM PST WED NOV 21 2001 AN INTENSE LOW PRESSURE SYSTEM WILL MOVE ALONG THE NORTH WASHINGTON COAST EARLY MORNING THANKSGIVING DAY...AND MOVE INLAND OVER THE NORTH INTERIOR OF WESTERN WASHINGTON BY MIDDAY. STRONG SOUTH WINDS WILL DEVELOP ALONG THE COAST AFTER MIDNIGHT. AS THIS SYSTEM MOVES INLAND THANKSGIVING MORNING IT HAS THE POTENTIAL TO CAUSE HIGH WINDS ACROSS THE INTERIOR OF WESTERN WASHINGTON AFTER ABOUT 8 AM.  

...HIGH WIND WATCH FOR THURSDAY MORNING THROUGH THURSDAY EVENINGREMAINS IN EFFECT...

Root Mean Square Error (RMSE) by Model VerificationR

MS

E o

f M

SL

P (

mb

)

36kmOuter

Domain

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nav

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eta*

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ps

ng

ps*

ukm

ou

kmo

*tc

wb

tcw

b*

cen

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12h

24h36h48h

12kmInner

Domain

cmcg

cmcg

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nav

n*

eta

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ng

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ukm

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*tc

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00h cmcg 21 Nov 00z 00h cmcg* 21 Nov 00z

00h cent 21 Nov 00z

Initialization

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cmcg

*

36h cmcg 22 Nov 12z 36h cmcg* 22 Nov 12z

36h cent 22 Nov 12z

36 Hour Forecast

00h cent 22 Nov 12z

“Verification”

42h (18z, 22 Nov) mslp and sfc wind.

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ngps*

cmcg*

tcwb*

ukmo*

eta*

“Verification”

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cmcg

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Ensemble-Based Probability of Wind Speed

Prob. of (sustained) Winds > 21 kt

39h, 22 Nov 15z 42h, 22 Nov 18z 39h, 22 Nov 21z

(Thursday 7AM) (Thursday 1PM) (Thursday 10AM)

10%30%50%10%

90%

Summary

• Set of 15 ICs for UW SREF are not optimal, but may be good enough to represent important features of analysis error

• The centroid may be the best bet deterministic model run, in the big picture

• Need further evaluation• How often does the ensemble fail to capture the truth?• How reliable are the probabilities?• Does the ensemble dispersion represent forecast uncertainty?