Winter Season Winter Season Forecasting Using the Forecasting Using the Winter Disruptiveness Winter Disruptiveness IndexIndex

Methodology and results of the Methodology and results of the 2002/2003 Winter season 2002/2003 Winter season forecast.forecast.

Dan Swank

Meteo 497: Long Range Forecasting

The Winter Disruptiveness Index The Winter Disruptiveness Index (WDI)(WDI)

A quantitative measure of winter A quantitative measure of winter season severity.season severity.

Defined over the time period Defined over the time period November through MarchNovember through March

Designed to be applicable everywhereDesigned to be applicable everywhere A numeric scale: Higher values denote A numeric scale: Higher values denote

cold and snowy winter seasonscold and snowy winter seasons Negative values for mild wintersNegative values for mild winters Values are the sum of seven Values are the sum of seven

componentscomponents

WDI Value scaleWDI Value scale

WDI ValueWDI Value DescriptionDescription Example SeasonExample SeasonIn State CollegeIn State College

> 22> 22 ExtremeExtreme Never Never occurredoccurred

14 to 2214 to 22 SevereSevere 1995-19961995-1996

6 to 146 to 14 HarshHarsh 2002-20032002-2003

0 to 60 to 6 Near NormalNear Normal 1996-19971996-1997

-8 to 0-8 to 0 MildMild 1998-19991998-1999

< -8< -8 Extreme Extreme MildMild

2001-20022001-2002

1.1. Average NDJFM TemperatureAverage NDJFM Temperature

2.2. Total NDJFM SnowfallTotal NDJFM Snowfall

3.3. NDJFM # days with >= 1” NDJFM # days with >= 1” snowcoversnowcover

4.4. Abnormally cold daysAbnormally cold days

5.5. Abnormal daily snowfallAbnormal daily snowfall

6.6. Abnormal daily rainfallAbnormal daily rainfall

7.7. Ice stormsIce storms

The 7 WDI Components:The 7 WDI Components: What can be forecasted with What can be forecasted with WDI?WDI?

How can we forecast How can we forecast the next winters WDI?the next winters WDI?

1.1. Use Analog forecasting. Currently two Use Analog forecasting. Currently two experimental methods.experimental methods.

2.2. Compare global 500 mb height Compare global 500 mb height anomalies during summer/autumn anomalies during summer/autumn months for years when the WDI is months for years when the WDI is between a certain range (i.e. > 12)between a certain range (i.e. > 12)

3.3. Correlate average monthly values of Correlate average monthly values of oceanic-atmospheric indices, before oceanic-atmospheric indices, before November, to that seasons WDI value.November, to that seasons WDI value.

Averaged 500 Mb Height Averaged 500 Mb Height anomalies:anomalies:

Analog forecasting methodAnalog forecasting method This method can gives a general idea of the This method can gives a general idea of the

likely outcome of the coming winter, but does likely outcome of the coming winter, but does not give an exact value for the WDInot give an exact value for the WDI

Take the average height anomaly over 3 Take the average height anomaly over 3 months, such as August, September, and months, such as August, September, and October. Average them over all years where October. Average them over all years where the WDI is within a given rangethe WDI is within a given range

Maps shown on the next slide are composites Maps shown on the next slide are composites of 4 years where the WDI was between a set of 4 years where the WDI was between a set range.range.

These maps would be different if WDI value at These maps would be different if WDI value at another location are usedanother location are used

Interestingly, teleconnection nodes tend to Interestingly, teleconnection nodes tend to show u in the averaged 500 mb analysesshow u in the averaged 500 mb analyses

WDI

>12

6 to 12

0 - 6 <-4

2002 August to October (ASO) 500 mb height anomalies

500 mb analog method500 mb analog method

Often anomaly comparisons may be Often anomaly comparisons may be inconclusive. Unless patterns similar to the inconclusive. Unless patterns similar to the extreme cases are present, go near normal.extreme cases are present, go near normal.

The 2002/03 pattern best matched the The 2002/03 pattern best matched the harsh (6 to 12) regime. Although vaguely.harsh (6 to 12) regime. Although vaguely.

This method can also be applied with any of This method can also be applied with any of the 7 WDI components, to forecast likely the 7 WDI components, to forecast likely temperature and precip trends.temperature and precip trends.

Other month ranges (besides ASO) can be Other month ranges (besides ASO) can be used, however months closer to November used, however months closer to November will probably be more reliable.will probably be more reliable.

Oceanic Atmospheric Oceanic Atmospheric Indices: Analog forecasting Indices: Analog forecasting

methodmethod Correlate the WDI to averaged monthly Correlate the WDI to averaged monthly

values of Ocean/Atmospheric indices such values of Ocean/Atmospheric indices such as the NAO, SOI, and PNA using various as the NAO, SOI, and PNA using various lag/span computations.lag/span computations.

For example: Each years average April For example: Each years average April through August NAO correlated with the through August NAO correlated with the value of WDI for the following winter, value of WDI for the following winter, starting in November.starting in November.

Much more complicated then the 500 mb Much more complicated then the 500 mb method, but gives an exact forecast value method, but gives an exact forecast value for the WDI.for the WDI.

Used to make the 2002/03 forecastUsed to make the 2002/03 forecast

Oceanic Atmospheric Oceanic Atmospheric Indices methodIndices method Must use a computer program to Must use a computer program to

calculate the millions of correlation calculate the millions of correlation possibilities.possibilities.

Output from the program can be Output from the program can be accessed via a web form: accessed via a web form: http://pasc.met.psu.edu/PA_Climatolo gisthttp://pasc.met.psu.edu/PA_Climatolo gist/WDI/correlform.html/WDI/correlform.html

Use the best 4 predictors that can be Use the best 4 predictors that can be found. The values of indices must be found. The values of indices must be taken over months before the winter taken over months before the winter occurs, in order to be useful for occurs, in order to be useful for forecasting.forecasting.

Correlation coefficientsCorrelation coefficients

The WDI correlation calculations were The WDI correlation calculations were done with the Pearson Correlation done with the Pearson Correlation Coefficient (R).Coefficient (R).

1 for a perfect correlation, 0 for no 1 for a perfect correlation, 0 for no relationship what-so-ever.relationship what-so-ever.

> 0.6 indicate a good relationship exists > 0.6 indicate a good relationship exists between the two datasetsbetween the two datasets

0.2 to 0.6 represents a weak relationship.0.2 to 0.6 represents a weak relationship. The best WDI correlations fall between The best WDI correlations fall between

0.4 and 0.60.4 and 0.6

1: Find the best predictors - 1: Find the best predictors - ExampleExample EPO : WDI correlations in State CollegeEPO : WDI correlations in State College

MONTH SPAN STARTING MONTH  

pNOV pDEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT

1 -0.061 0.039 -0.368 -0.204 -0.153 -0.283 -0.329 -0.197 -0.050     -0.073

2 -0.016 -0.192 -0.371 -0.229 -0.264 -0.366 -0.305 -0.153       -0.145

3 -0.190 -0.256 -0.368 -0.310 -0.331 -0.351 -0.253         -0.241

4 -0.249 -0.305 -0.418 -0.356 -0.325 -0.305           -0.227

5 -0.295 -0.356 -0.445 -0.346 -0.298             -0.216

6 -0.339 -0.392 -0.426 -0.324               -0.179

7 -0.371 -0.381 -0.401                 -0.208

8 -0.363 -0.360                   -0.227

9 -0.344                     -0.234

10                       -0.256

EPO is undefined in August and Sept.

For the 2002/03 winter forecast, For the 2002/03 winter forecast, the following predictors were the following predictors were used:used:

Index Period Averaged

Correl. (R)

2002 Value

PNA FEB to SEPT 0.45 -0.66

EPO APR and MAY -0.41 0.6

AO APR to AUG -0.37 0.36

SOI NOVEMBER -0.27 1.21

Next stepsNext steps

2.2. Make a table of values, listing the Make a table of values, listing the WDI, PNA, EPO, AO, and SOI values WDI, PNA, EPO, AO, and SOI values for each year where data is available.for each year where data is available.

3.3. Obtain the index values for the Obtain the index values for the current year.current year.

4.4. Make a list of analog years where the Make a list of analog years where the current index values match previous current index values match previous yearsyears

5.5. Also keep track of how many indices Also keep track of how many indices each analog year matchedeach analog year matched

6.6. Take a weighted average of the Take a weighted average of the analog years WDI values.analog years WDI values.

Analog YearsAnalog Years

Year1Year1..

WDIWDI PNAPNA EPOEPO AOAO SOISOI

CurrenCurrentt

?? --0.660.66

0.60.6 0.360.36 1.211.21

19891989 1.01.0 --0.570.57

0.70.7 0.480.48 2.72.7

20012001 -5.6-5.6 -0.6-0.6 1.11.1 0.370.37 1.81.8

19911991 -0.1-0.1 --0.030.03

1.051.05 0.30.3 1.01.0

19771977 12.212.2 --0.030.03

0.450.45 -0.14-0.14 -1.1-1.1

Single match WDI1953/1954 1.312

1954/1955 -1.0352

1955/1956 1.7793

1957/1958 4.1072

1964/1965 4.277

1970/1971 5.2982

1977/1978 12.1662

1979/1980 -3.027

1984/1985 1.0942

1985/1986 2.2423

1986/1987 2.1446

1988/1989 -2.6423

1996/1997 1.1418

1997/1998 0.4408

1998/1999 -1.9049

2000/2001 1.9351

Double match WDI1989/1990 0.9665

2001/2002 -5.6898

1991/1992 -0.101

Listing of analog years, which matched one (single) index two (double) atmospheric/oceanic indices

Taking the weighted average of each analog winter’s WDI (the double match years are double weighted), gives the value of roughly:

WDI = -0.5

Rounded to the nearest 0.5

2002-03 Analog years

Oceanic/Atmospheric Oceanic/Atmospheric index method index method summarysummary More specific and calculation intensive More specific and calculation intensive

then the 500 mb methodthen the 500 mb method Correlation values may be too low to be Correlation values may be too low to be

dependabledependable Predicted a normal to slightly mild winter Predicted a normal to slightly mild winter

for 2002-03for 2002-03 The two methods should be compared to The two methods should be compared to

see if they agreesee if they agree Other methods not involving the WDI Other methods not involving the WDI

should be incorporated into the final should be incorporated into the final forecast.forecast.

The 2002/03 winter forecastThe 2002/03 winter forecast WDI forecasted to be from 0 to 2, WDI forecasted to be from 0 to 2,

after considering other techniquesafter considering other techniques When the WDI is in this range, the When the WDI is in this range, the

typical conditions usually occur, typical conditions usually occur, typical of an average winter season in typical of an average winter season in this areathis area

1)1) -0.8 to +0.7 degree departure from -0.8 to +0.7 degree departure from average NDJFM temperature.average NDJFM temperature.

2)2) 34-43 inches of snowfall34-43 inches of snowfall3)3) 32 to 44 days with 1” snowcover32 to 44 days with 1” snowcover4)4) 1 major (12”+) snowstorm, or 2 1 major (12”+) snowstorm, or 2

moderate snowfallsmoderate snowfalls5)5) 1 storm with minor ice accumulation1 storm with minor ice accumulation

STC VerificationSTC Verification WDI: 8.0WDI: 8.0 Components, statistics and averages:Components, statistics and averages:Tmean: +1.37 Tmean: +1.37 (30.7 ˚F, AVG = 32.8˚ )(30.7 ˚F, AVG = 32.8˚ )Smean: +2.39 Smean: +2.39 (75.1”, AVG = 41”)(75.1”, AVG = 41”)SCmean: +1.61 SCmean: +1.61 (60 days SC>1”, AVG 36 days)(60 days SC>1”, AVG 36 days)Tdaily: +0.20 Tdaily: +0.20 (16 DCDs, AVG of 15)(16 DCDs, AVG of 15)Sdaily: +2.5Sdaily: +2.5Rdaily: 0Rdaily: 0 Idaily: 0Idaily: 0

• Winter as much colder and snowier then expected. Winter as much colder and snowier then expected. Total snowfall was nearly twice the average. Total snowfall was nearly twice the average.

• However, the predication did not indicate a mild However, the predication did not indicate a mild winter, which is what most people are adjusted to winter, which is what most people are adjusted to because of the past few yearsbecause of the past few years

Insight & explanationsInsight & explanations Analog forecasts are subject to error because Analog forecasts are subject to error because

of the relatively short period of record of of the relatively short period of record of existing weather dataexisting weather data

The WDI definition was changed since the The WDI definition was changed since the forecast was made, values were amplifiedforecast was made, values were amplified

Weak correlation valuesWeak correlation values Perhaps a component-wise analog method Perhaps a component-wise analog method

would be more accurate, this would also give would be more accurate, this would also give more insight into the temperature and more insight into the temperature and precipitation breakdownsprecipitation breakdowns

Weather patterns can change drastically over Weather patterns can change drastically over the period of 5 monthsthe period of 5 months

A few more methods should be developed A few more methods should be developed which use the WDI to make a seasonal which use the WDI to make a seasonal forecast. 2 methods may not be enoughforecast. 2 methods may not be enough