Climate Downscaling Techniques Marina Timofeyeva UCAR/NWS/NOAA.

Climate DownscalingClimate Downscaling

TechniquesTechniques

Marina TimofeyevaMarina TimofeyevaUCAR/NWS/NOAAUCAR/NWS/NOAA

TALK OUTLINETALK OUTLINE

What is DownscalingWhat is Downscaling

NWS NCEP CPC climate outlooks and NWS NCEP CPC climate outlooks and regional climateregional climate

Downscaling methodsDownscaling methods

Application of CPC methods in Developing Application of CPC methods in Developing Local Climate Products Local Climate Products

Messages to take homeMessages to take home

DOWNSCALINGDOWNSCALING

DOWNSCALING is DOWNSCALING is the transformation the transformation from a LARGE from a LARGE SCALE feature to a SCALE feature to a SMALL SCALE one SMALL SCALE one (not necessarily of (not necessarily of the same kind).the same kind).DOWNSCALING DOWNSCALING implies implies increasesincreases resolutionresolution of of output.output.

NWS NCEP CPC weather & climate outlooksNWS NCEP CPC weather & climate outlooks

NWS NCEP CPC climate outlooksNWS NCEP CPC climate outlooksThis is a map of 344 climate divisions currently in use over the U.S. Note the changing size as one goes from east to west, as well as from one state to another.

CPC uses 102 mega or forecast divisions in their forecasts. The divisions in the West closely correspond to NCDC climate divisions.

NWS NCEP CPC climate outlooksNWS NCEP CPC climate outlooks

National precipitation map based on high-resolution PRISM data National precipitation map based on high-resolution PRISM data (left) and on Climate Divisions (right). Note the large gradients and (left) and on Climate Divisions (right). Note the large gradients and fine-scale variability in the Western U.S. that is not reproduced in the fine-scale variability in the Western U.S. that is not reproduced in the right map. right map.

NWS NCEP CPC climate outlooksNWS NCEP CPC climate outlooks

Precipitation Climatology 1971 - 2000Precipitation Climatology 1971 - 2000

Slide courtesy of Klaus Wolter, CDCSlide courtesy of Klaus Wolter, CDC

Official CDs for Colorado (left) Official CDs for Colorado (left) and Experimental CDs (right) and Experimental CDs (right) based on multivariate statistical based on multivariate statistical analysis of climate data that analysis of climate data that also include SNOTEL data. also include SNOTEL data. Such new CDs are being Such new CDs are being derived for the entire U.S.A.derived for the entire U.S.A.

NWS NCEP CPC climate outlooks and NWS NCEP CPC climate outlooks and Regional ClimateRegional Climate

Slide courtesy of Klaus Wolter, CDCSlide courtesy of Klaus Wolter, CDC


# of

sta

tions

tha

t #

of s

tatio

ns t

hat

did

not

reje

ct t

he t

est

Hdi

d no

t re

ject

the

tes

t H

00

If climate at station is the same as at climate division, then mean and variance If climate at station is the same as at climate division, then mean and variance at station and climate divisions should be the same. THEY ARE NOT!at station and climate divisions should be the same. THEY ARE NOT!

0

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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

NUMBER OF STATIONS (OUT OF 9) THAT HAVE NUMBER OF STATIONS (OUT OF 9) THAT HAVE SQUARED CORRELATION WITH CD >=0.8SQUARED CORRELATION WITH CD >=0.8


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DYNAMICAL DOWNSCALINGDYNAMICAL DOWNSCALING

0 20 40 60 80 100 120

010

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ETA and AVN are examples on ETA and AVN are examples on meteorological meteorological scalescale Climate applicationsClimate applications::

Regional Spectral Model (RSM) and Seasonal Regional Spectral Model (RSM) and Seasonal Forecast Model (SFM) Forecast Model (SFM) Nested in T62 and T40 NCEP coupled AOGCM Nested in T62 and T40 NCEP coupled AOGCM using 50, 30 and 20 km resolution grids using 50, 30 and 20 km resolution grids tested for 1997 winter El Ninotested for 1997 winter El Nino results: results:

• RSM shows improvement in temperature RSM shows improvement in temperature forecast in comparison with AOGCMforecast in comparison with AOGCM• “ “50-km RSM is 50-km RSM is unableunable to forecast anomalies to forecast anomalies over high mountains” over high mountains” • 20-km RSM provides “realistic distribution of 20-km RSM provides “realistic distribution of precipitation”, but precipitation”, but overestimateoverestimate its maxima its maxima


STATISTICAL DOWNSCALINGSTATISTICAL DOWNSCALINGWEATHER GENERATORSWEATHER GENERATORS

Climate observations

Statistics

Climate predictions

Global Circulation

Pattern predicted

Statistics

Class

Calibration

Prediction

Frequency analysis

Global Circulation

Patternobserved

STATISTICAL DOWNSCALINGSTATISTICAL DOWNSCALINGCORRELATION MODELSCORRELATION MODELS

Climate Observations

GCM fields

Statistics Statistics

Statistical relationship

Modeled climateStatistics

Prediction

Calibration

EXAMPLE: PARTNERSHIP PROJECTEXAMPLE: PARTNERSHIP PROJECT

Western Region HQ (Andrea Bair)Western Region HQ (Andrea Bair)

NWS OCWWS CSD (Marina Timofeyeva)NWS OCWWS CSD (Marina Timofeyeva)

NWS NCEP CPC (David Unger)NWS NCEP CPC (David Unger)

APPLICATION OF CPC METHODS IN APPLICATION OF CPC METHODS IN DEVELOPING LOCAL CLIMATE DEVELOPING LOCAL CLIMATE

PRODUCTSPRODUCTS

Utilized CPC Methods of DownscalingUtilized CPC Methods of Downscaling

Use of composites in the Use of composites in the forecast of local climate forecast of local climate using climate variability using climate variability modes modes

Translation of probability Translation of probability of exeedance (POE) of exeedance (POE) outlooks from climate outlooks from climate divisions to local station divisions to local station temperature forecaststemperature forecasts

Temperature Outlook Precipitation Outlook Degree Day Outlook

Temperature Outlook Precipitation Outlook Degree Day Outlook

Utilized CPC Methods of DownscalingUtilized CPC Methods of Downscaling

Utilized CPC Methods of Downscaling - Utilized CPC Methods of Downscaling - POEPOE

PO

F (

%)

PO

F (

%)

Forecasted Temperature (Forecasted Temperature (°F)°F)

Translation of forecast division POE to Translation of forecast division POE to station forecast was developed in station forecast was developed in CPC by Barnston, Unger, and He. CPC by Barnston, Unger, and He. The POE outlooks became available The POE outlooks became available in December 1994, and the in December 1994, and the translations to station temperature in translations to station temperature in 2000.2000.

Observed T

http://www.cpc.ncep.noaa.gov/pacdir/NFORdir/citydir/cpcctytd.dat


-85 -80 -75 -70 -65

- Stats[1:14, 5]

35

40

45

Sta

ts[1

:14

, 4

]

AL

AK

AZAR

CA

CO

CT

DE

FL

GAHI

ID

IL IN

IA

KS

KY

LA

ME

MD

MA

MI

MN

MS

MO

MT

NE

NV

NH

NJ

NM

NY

NC

ND

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VT

VA

WA

WV

WI

WY

Boston

New York City

Rochester

CharlotteGreensboro

Raleigh

Cincinnati

Cleveland

ColumbusDayton PhiladelphiaPittsburgh

Norfolk

Providence

http://www.cpc.ncep.noaa.gov/pacdir/NFORdir/citydir/cpcctytd.dat


Step 1: Defining stations where the station outlooks are usedStep 1: Defining stations where the station outlooks are used


y = 1.2658x - 9.5544R2 = 0.9104

y = 1.1707x - 5.1282R2 = 0.9335

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50

15 20 25 30 35 40 45 50

CD Temperature

Sta

tion

Tem

pera

ture

1458

130

Linear (1458)

Linear (130)

In most cases there is a strong relationship between temperature In most cases there is a strong relationship between temperature at station (y axis) and climate division (x axis). at station (y axis) and climate division (x axis).

Step 2: Developing regression equations for those stationsStep 2: Developing regression equations for those stations

1960 1970 1980 1990 2000SLCtsDiff[1, season, ]

45

67

89

SLC

tsD

iff[3

, se

ason

, ]

season= 9

Utilized CPC Methods of Downscaling - Utilized CPC Methods of Downscaling - POEPOEStep 2: Developing regression equations for those stationsStep 2: Developing regression equations for those stationsRegression coefficients are adjusted for the trendRegression coefficients are adjusted for the trend

years

Dif

fere

nce

Dif

fere

nce

Tst

atio

n –

Tcd

T

stat

ion

– T

cd ((

ºF)

ºF)

D iff D iff D iffyear year year

1

1

0 5 10 0 5

1

0 5 10 0 51 10( . * ) .*

( . * ) .*


Step 3: Test of regression equations stability - Cross validation Step 3: Test of regression equations stability - Cross validation

Calibration data set Verification Year

1971 1971

1972 1972

1973 1973

1974 1974

1975 1975

… …

1997 1997

1998 1998

1999 1999

2000 2000

Cross validation allows expansion of the test sample Cross validation allows expansion of the test sample and protects against over fittingand protects against over fitting

Calibration data set Verification Year

1971 1971

1972 1972

1973 1973

1974 1974

1975 1975

… …

1997 1997

1998 1998

1999 1999

2000 2000


Step 3: Test of regression equations stability - Cross validation Step 3: Test of regression equations stability - Cross validation

Methods for Climate Forecast VerificationMethods for Climate Forecast VerificationRanked Probability ScoreRanked Probability Score and Continuous Ranked Probability ScoreContinuous Ranked Probability Score

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-48%

-45%

-40%

-30%

-20%

-10%

Pf=

Po+

0%

Pf=

Po-

0%

10%

20%

30%

40%

45%

48%

Error in Probability Estimate

RP

S

The Rank Probability Score (RPS), graphically represents the performance of the probability forecast (Wilks, 1995).

RPS F Otile tiletile

tile

% %%

%2

1

13

0

20

40

60

80

100

84 84 85 85 86 86 86 86 87 87 88 88 88

Temp_forecast (F)

PO

E (

%)

Tobs

CRPSSCRPS

CRPSfo recast

c a to y

1lim log

RPS is not sensitive for forecast spread.

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30 40 50 60 70 80 90 100 110

Temp, mean =70

PO

E (

%)

std=15 std=5

Tobs

CRPS T T F Otile tile tile tiletile

tile

% % % %%

%

1 1

2

1

13

Continuous Rank Probability Score (CRPS) takes into account spread of the forecasted distribution.

CRPS Skill Score (CRPSS) is the final measure of the forecast performance.

Progress Report - CRPSSProgress Report - CRPSSWarm Seasons

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Fresno Las Vegas Los Angeles Phoenix Portland

Sacramento Salt Lake City San Francisco Seattle

Cold Seasons

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5

Fresno Las Vegas Los Angeles Phoenix Portland

Sacramento Salt Lake City San Diego San Francisco Seattle

CRPSSCRPS

CRPSfo recast

c a to y

1lim log

Reliability DiagramsReliability Diagrams

Reliability Diagrams exhibit the correspondence between the observed and forecasted percentiles. Reliability Diagrams allow verification of each POE for each station. The analysis is done for a forecast and compared with climatology.

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Forecast Probability

Ob

serv

ed

Re

lati

ve

Fre

qu

en

cy

Under-forecastingUnder-forecasting

Over-forecastingOver-forecasting

Methods for Climate Forecast VerificationMethods for Climate Forecast Verification

Progress Report – Reliability DiagramsProgress Report – Reliability Diagrams

Warm Seasons

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Fre LAS LAX

PHX PDX AVERAGE

Cold Seasons

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Ob

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Perfect upper low er

Fre LAS LAX

PHX PDX Average

Bias AnalysisBias Analysis

MSE F Oyear yearyear

year

1

8

2

1

8

The bias is computed for CPC forecasts and for climatology using the equation shown on the right for climate divisions and stations for each forecast month and each lead season. The bias shows range and sign of deviations between forecasts and observations. Mean Square Error (MSE) is other common accuracy measure of climate forecast leading to skill score (SS) estimates.

Methods for Climate Forecast VerificationMethods for Climate Forecast Verification

B IAS F Oyear yearyear

year

1

8

SSM SE

M SEF

CLIMO

1

0

0.01

0.02

0.03

-40 -20 0 20 40Forecast-Observation

PD

F

Expected PDF of difference between forecasts and observation is normal distribution with mean that is not significantly different from 0.


When this method fails…When this method fails…

y = 1.2658x - 9.5544R2 = 0.9104

y = -0.0711x + 29.528R2 = 0.0009

y = 1.1707x - 5.1282R2 = 0.9335

15

20

25

30

35

40

45

50

15 20 25 30 35 40 45 50

CD Temperature

Sta

tion

Tem

pera

ture

1458

130

9181

Linear (1458)

Linear (9181)

Linear (130)



0.5

0.6

0.7

0.8

0.9

1.0

0.5 0.6 0.7 0.8 0.9 1

0.5

0.7

0.8

0.9

R – Measure of Confidence in Downscaling

ρ

Sta

tio

n F

ore

cast

Sp

read

Sta

tio

n F

ore

cast

Sp

read



Mean = 0.30St. Dev.= 0.38Median = 0.19Mode = 0.01Skewness = 3.11Kurtosis = 14.67

Mean = 60.7St.Dev.= 13.6Median = 59.5Mode = 52.0Skewness = 0.225Kurt = -0.526

Temperature is a Temperature is a normally distributed normally distributed variable, therefore the variable, therefore the downscaling method downscaling method based on regression based on regression can provide good can provide good estimatesestimates

Precipitation (right chart) is too Precipitation (right chart) is too skewed for normal distribution. skewed for normal distribution. The regression would require The regression would require a transformation of this a transformation of this variable. Compositing can be variable. Compositing can be used for Precipitation forecasts used for Precipitation forecasts because it does not employ because it does not employ regression analysis.regression analysis.

Levels of sophistication in use of composites:Levels of sophistication in use of composites:

1.1. Composite meansComposite means

2.2. Raw Composite distributionRaw Composite distribution

3.3. Smooth resampled Composite Distribution - boot Smooth resampled Composite Distribution - boot strapping techniquesstrapping techniques

4.4. All of the above with trend and some other mode of All of the above with trend and some other mode of climate variability taken into account using new climate variability taken into account using new approach developed by Higgins, Unger and Kimapproach developed by Higgins, Unger and Kim

Utilized CPC Methods of Downscaling – Utilized CPC Methods of Downscaling – COMPOSITESCOMPOSITES

Nino 3.4 SST (Nino 3.4 SST (°C)°C)

No

rth

Dak

ota

, D

JF T

emp

N

ort

h D

ako

ta,

DJF

Tem

p

(( °C

)°C

)

198319921987

1973

19581995

1966

1988

1998

Utilized CPC Methods of Downscaling – Utilized CPC Methods of Downscaling – COMPOSITESCOMPOSITES

Utilized CPC Methods of Downscaling – Utilized CPC Methods of Downscaling – COMPOSITES – level 1COMPOSITES – level 1



B N A

Jan 1 3 5

Feb 1 4 4

Mar 5 3 1

JFM 0 7 2

FORECASTFORECAST:: Given El Nino, Denver Tmean has a shift in Tmean toward above normal for Jan, below normal for Mar, and near normal for JFM

Nino3.4

Term

Warm Neutral Cold

Above 2/9=0.22 9/32=0.28 2/9=0.22

Near 7/9=0.78 12/32=0.38 4/9=0.45

Below 0/9=0 11/32=0.34 3/9=0.33

JFM compositesJFM composites

For each Nino 3.4. event we compute probability of For each Nino 3.4. event we compute probability of the climate variable to be in Below/Near/Above the climate variable to be in Below/Near/Above normal category.normal category.


FORECAST USING CURRENT CPC Nino 3.4:FORECAST USING CURRENT CPC Nino 3.4:

CPC CURRENT ENSO FORECASTCPC CURRENT ENSO FORECAST::http://www.cpc.ncep.noaa.gov/products/precip/CWlink/ENSO/total.html

NINO 3.4 INITIAL TIME 3 2003PROJECTION FRACTION BELOW NORMAL ABOVEAMJ 1 0.039 0.372 0.589MJJ 2 0.066 0.446 0.488JJA 3 0.126 0.494 0.380…JFM JFM 99 0.3430.343 0.4340.434 0.2430.243FMA 10 0.318 0.438 0.244

Nino3.4

Term

Warm Neutral Cold

Above 2/9=0.22 9/32=0.28 2/9=0.22

Near 7/9=0.78 12/32=0.38 4/9=0.45

Below 0/9=0 11/32=0.34 3/9=0.33

P P P P P P Pca tegorysta tion

above even tsta tion

aboveN ino

near even tsta tion

nearN ino

below even tsta tion

belowN ino /

./

./

.* * *3 4 3 4 3 4

Example – ElNino with 8.5 month lead (forecast for JFM 2004):Example – ElNino with 8.5 month lead (forecast for JFM 2004):

P

P

P

abovesta tion

nearsta tion

belowsta tion

0 22 0 243 0 28 0 434 0 22 0 343 0 2523

0 78 0 243 0 38 0 434 0 45 0 343 0 5375

0 0 243 0 34 0 434 0 33 0 343 0 2302

. * . . * . . * . .

. * . . * . . * . .

* . . * . . * . .


http://www.cpc.ncep.noaa.gov/products/precip/CWlink/ENSO/total.html


El Nino Years

January February March

1958

1966

1969

1973

1983

1987

1992

1995

1998

X

X

XX

X

X

X

X

X

X

X

X

To obtain a smooth To obtain a smooth distribution we can use distribution we can use resampling, which allows resampling, which allows 9933 = 729 different = 729 different combinations of the combinations of the months in each season. months in each season.

To better represent To better represent extremes in the extremes in the distribution we sample distribution we sample with replacement using with replacement using boot strapping technique.boot strapping technique.


DJF

Nor

th D

akot

a T

emp

DJF

Nor

th D

akot

a T

emp

(( °C

) °C

)

The trend should not be removed arbitrarily. Hinge, for example, explains climate The trend should not be removed arbitrarily. Hinge, for example, explains climate changes during the last decades. 11-year Moving Average (MA) explains decadal changes during the last decades. 11-year Moving Average (MA) explains decadal variations in climate.variations in climate.

Research Products Versus Operational ProductsResearch Products Versus Operational Products

Method Research Output Operational Products

POE Regression equation coefficients

Method performance evaluation based on hind cast applications (1995-2003)

Seasonal forecasts issued monthly for 13 seasonal leads using equations and CPC CD forecasts

Verification issued monthly for forecast made in preceding month

Composites All composite statistics: mean, variance, each category probabilities with and without trend, and POE.

Method performance evaluation based on hind cast applications (1982 – 2003)

Seasonal forecasts issued monthly for 16 seasonal leads using station statistics and CPC Nino 3.4. forecasts

Verification issued monthly for forecast made in preceding month

WR NEW LOCAL CLIMATE PRODUCTSWR NEW LOCAL CLIMATE PRODUCTSWhere do we go…Where do we go…

EXPECTED OPERATIONAL FUNCTIONS: REGIONAL EXPECTED OPERATIONAL FUNCTIONS: REGIONAL CSPMCSPM

1. POE downscaling1. POE downscaling 1.1. Developing the translation equations for 87 sites (completed) 1.1. Developing the translation equations for 87 sites (completed) 1.2. Tests of the equations (2003-2004) 1.2. Tests of the equations (2003-2004) 1.3. Monthly coordination of local product release (starting 2005) 1.3. Monthly coordination of local product release (starting 2005) 1.4. Annual update of the equations (starting 2005)1.4. Annual update of the equations (starting 2005)

2. Composites2. Composites 2.1. Coordination of Composites products existing or released in 2.1. Coordination of Composites products existing or released in the local offices the local offices 2.2. Developing Composites for 87 sites (2003-2004) 2.2. Developing Composites for 87 sites (2003-2004) 2.3. Hind cast test of the composites (2003-2004) 2.3. Hind cast test of the composites (2003-2004) 2.4. Monthly coordination of local product release (starting 2005) 2.4. Monthly coordination of local product release (starting 2005) 2.5. Annual update of the composites (starting 2005)2.5. Annual update of the composites (starting 2005)

WR NEW LOCAL CLIMATE PRODUCTSWR NEW LOCAL CLIMATE PRODUCTSWhere do we go…Where do we go…

EXPECTED OPERATIONAL FUNCTIONS: WFO CSFP EXPECTED OPERATIONAL FUNCTIONS: WFO CSFP

1. POE downscaling: 1. POE downscaling: 1.1. Selection of sites within WFO CWA for downscaling (completed)1.1. Selection of sites within WFO CWA for downscaling (completed) 1.2. Delivering on monthly basis seasonal outlooks for selected 1.2. Delivering on monthly basis seasonal outlooks for selected

sites within WFO CWA (starting in FY05) sites within WFO CWA (starting in FY05) 1.3. Verification of the previous month forecasts (starting in FY05)1.3. Verification of the previous month forecasts (starting in FY05)

2. Composites: 2. Composites: 2.1. Keeping self updated on climate variability mode status 2.1. Keeping self updated on climate variability mode status

(starting in October 2003) (starting in October 2003) 2.2. Developing composites local studies (optional) 2.2. Developing composites local studies (optional) 2.3. Release of monthly and seasonal outlooks for selected 2.3. Release of monthly and seasonal outlooks for selected

sites within each WFO CWA (starting in 2005) sites within each WFO CWA (starting in 2005) 2.4. Verification of the Composites forecasts (starting in 2005) 2.4. Verification of the Composites forecasts (starting in 2005)

3. Public outreach on these new products3. Public outreach on these new products

MESSAGES TO TAKE HOMEMESSAGES TO TAKE HOME

THERE ARE NO THERE ARE NO NWS CONSISTENTNWS CONSISTENT LOCALLOCAL CLIMATE CLIMATE

PRODUCTSPRODUCTS AVAILABLE AVAILABLE NOWNOW

DOWSCALING CAN BE USED AS A TOOL FOR LOCAL DOWSCALING CAN BE USED AS A TOOL FOR LOCAL

CLIMATE PRODUCTS CLIMATE PRODUCTS

THE LOCAL CLIMATE PRODUCT SHOULD BE CONSISTENT THE LOCAL CLIMATE PRODUCT SHOULD BE CONSISTENT

WITH THE NATIONAL WEATHER SERVICE PRODUCTS WITH THE NATIONAL WEATHER SERVICE PRODUCTS

(CPC)(CPC)

CPC METHODS COULD BE USED IN DEVELOPING SUCH CPC METHODS COULD BE USED IN DEVELOPING SUCH

LOCAL CLIMATE PRODUCTSLOCAL CLIMATE PRODUCTS

IN DEVELOPING OF DOWNSCALING AT LEAST THREE NWS IN DEVELOPING OF DOWNSCALING AT LEAST THREE NWS

ENTITIES SHOULD BE INVOLVED: REGIONAL OFFICE, ENTITIES SHOULD BE INVOLVED: REGIONAL OFFICE,

CSD, AND CPCCSD, AND CPC

Climate Downscaling Techniques Marina Timofeyeva UCAR/NWS/NOAA.

Documents

climate divisions

ncdc climate

test h0if climate

forecast divisions

right map

cdcofficial cds

experimental cds

large scale feature