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Winter Season Forecasting Using the Winter Disruptiveness Index Methodology and results of the 2002/2003 Winter season forecast. Dan Swank Meteo 497: Long Range Forecasting

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The Winter Disruptiveness Index (WDI) A quantitative measure of winter season severity. A quantitative measure of winter season severity. Defined over the time period November through March Defined over the time period November through March Designed to be applicable everywhere Designed to be applicable everywhere A numeric scale: Higher values denote cold and snowy winter seasons A numeric scale: Higher values denote cold and snowy winter seasons Negative values for mild winters Negative values for mild winters Values are the sum of seven components Values are the sum of seven components

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WDI Value scale WDI Value Description Example Season In State College > 22 Extreme Never occurred 14 to 22 Severe to 14 Harsh to 6 Near Normal to 0 Mild < -8 Extreme Mild

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1. Average NDJFM Temperature 2. Total NDJFM Snowfall 3. NDJFM # days with >= 1 snowcover 4. Abnormally cold days 5. Abnormal daily snowfall 6. Abnormal daily rainfall 7. Ice storms The 7 WDI Components: What can be forecasted with WDI?

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How can we forecast the next winters WDI? Use Analog forecasting. Currently two experimental methods. Use Analog forecasting. Currently two experimental methods. 1. Compare global 500 mb height anomalies during summer/autumn months for years when the WDI is between a certain range (i.e. > 12) 2. Correlate average monthly values of oceanic-atmospheric indices, before November, to that seasons WDI value.

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Averaged 500 Mb Height anomalies: Analog forecasting method This method can gives a general idea of the likely outcome of the coming winter, but does not give an exact value for the WDI This method can gives a general idea of the likely outcome of the coming winter, but does not give an exact value for the WDI Take the average height anomaly over 3 months, such as August, September, and October. Average them over all years where the WDI is within a given range Take the average height anomaly over 3 months, such as August, September, and October. Average them over all years where the WDI is within a given range Maps shown on the next slide are composites of 4 years where the WDI was between a set range. Maps shown on the next slide are composites of 4 years where the WDI was between a set range. These maps would be different if WDI value at another location are used These maps would be different if WDI value at another location are used Interestingly, teleconnection nodes tend to show u in the averaged 500 mb analyses Interestingly, teleconnection nodes tend to show u in the averaged 500 mb analyses

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WDI >12 6 to <-4

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2002 August to October (ASO) 500 mb height anomalies

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500 mb analog method Often anomaly comparisons may be inconclusive. Unless patterns similar to the extreme cases are present, go near normal. Often anomaly comparisons may be inconclusive. Unless patterns similar to the extreme cases are present, go near normal. The 2002/03 pattern best matched the harsh (6 to 12) regime. Although vaguely. The 2002/03 pattern best matched the harsh (6 to 12) regime. Although vaguely. This method can also be applied with any of the 7 WDI components, to forecast likely temperature and precip trends. This method can also be applied with any of the 7 WDI components, to forecast likely temperature and precip trends. Other month ranges (besides ASO) can be used, however months closer to November will probably be more reliable. Other month ranges (besides ASO) can be used, however months closer to November will probably be more reliable.

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Oceanic Atmospheric Indices: Analog forecasting method Correlate the WDI to averaged monthly values of Ocean/Atmospheric indices such as the NAO, SOI, and PNA using various lag/span computations. Correlate the WDI to averaged monthly values of Ocean/Atmospheric indices such as the NAO, SOI, and PNA using various lag/span computations. For example: Each years average April through August NAO correlated with the value of WDI for the following winter, starting in November. For example: Each years average April through August NAO correlated with the value of WDI for the following winter, starting in November. Much more complicated then the 500 mb method, but gives an exact forecast value for the WDI. Much more complicated then the 500 mb method, but gives an exact forecast value for the WDI. Used to make the 2002/03 forecast Used to make the 2002/03 forecast

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Oceanic Atmospheric Indices method Must use a computer program to calculate the millions of correlation possibilities. Must use a computer program to calculate the millions of correlation possibilities. Output from the program can be accessed via a web form: gist/WDI/correlform.html Output from the program can be accessed via a web form: gist/WDI/correlform.html gist/WDI/correlform.html gist/WDI/correlform.html Use the best 4 predictors that can be found. The values of indices must be taken over months before the winter occurs, in order to be useful for forecasting. Use the best 4 predictors that can be found. The values of indices must be taken over months before the winter occurs, in order to be useful for forecasting.

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Correlation coefficients The WDI correlation calculations were done with the Pearson Correlation Coefficient (R). The WDI correlation calculations were done with the Pearson Correlation Coefficient (R). 1 for a perfect correlation, 0 for no relationship what-so-ever. 1 for a perfect correlation, 0 for no relationship what-so-ever. > 0.6 indicate a good relationship exists between the two datasets > 0.6 indicate a good relationship exists between 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 0.4 and 0.6 The best WDI correlations fall between 0.4 and 0.6

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1: Find the best predictors - Example EPO : WDI correlations in State College MONTH SPANSTARTING MONTH pNOVpDECJANFEBMARAPRMAYJUNEJULYAUGSEPTOCT EPO is undefined in August and Sept.

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For the 2002/03 winter forecast, the following predictors were used: IndexPeriod Averaged Correl. (R) 2002 Value PNAFEB to SEPT EPOAPR and MAY AOAPR to AUG SOINOVEMBER

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Next steps 2. Make a table of values, listing the WDI, PNA, EPO, AO, and SOI values for each year where data is available. 3. Obtain the index values for the current year. 4. Make a list of analog years where the current index values match previous years 5. Also keep track of how many indices each analog year matched 6. Take a weighted average of the analog years WDI values.

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Analog Years Year1.WDIPNAEPOAOSOI Current?

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Single matchWDI 1953/ / / / / / / / / / / / / / / / Double matchWDI 1989/ / / Listing of analog years, which matched one (single) index two (double) atmospheric/oceanic indices Taking the weighted average of each analog winters WDI (the double match years are double weighted), gives the value of roughly: WDI = -0.5 Rounded to the nearest Analog years

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Oceanic/Atmospheric index method summary More specific and calculation intensive then the 500 mb method More specific and calculation intensive then the 500 mb method Correlation values may be too low to be dependable Correlation values may be too low to be dependable Predicted a normal to slightly mild winter for Predicted a normal to slightly mild winter for The two methods should be compared to see if they agree The two methods should be compared to see if they agree Other methods not involving the WDI should be incorporated into the final forecast. Other methods not involving the WDI should be incorporated into the final forecast.

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The 2002/03 winter forecast WDI forecasted to be from 0 to 2, after considering other techniques WDI forecasted to be from 0 to 2, after considering other techniques When the WDI is in this range, the typical conditions usually occur, typical of an average winter season in this area When the WDI is in this range, the typical conditions usually occur, typical of an average winter season in this area 1) -0.8 to +0.7 degree departure from average NDJFM temperature. 2) inches of snowfall 3) 32 to 44 days with 1 snowcover 4) 1 major (12+) snowstorm, or 2 moderate snowfalls 5) 1 storm with minor ice accumulation

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STC Verification WDI: 8.0 WDI: 8.0 Components, statistics and averages: Components, statistics and averages: Tmean: (30.7 ˚F, AVG = 32.8˚ ) Smean: (75.1, AVG = 41) SCmean: (60 days SC>1, AVG 36 days) Tdaily: (16 DCDs, AVG of 15) Sdaily: +2.5 Rdaily: 0Idaily: 0 Winter as much colder and snowier then expected. Total snowfall was nearly twice the average. Winter as much colder and snowier then expected. Total snowfall was nearly twice the average. However, the predication did not indicate a mild winter, which is what most people are adjusted to because of the past few years However, the predication did not indicate a mild winter, which is what most people are adjusted to because of the past few years

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Insight & explanations Analog forecasts are subject to error because of the relatively short period of record of existing weather data Analog forecasts are subject to error because of the relatively short period of record of existing weather data The WDI definition was changed since the forecast was made, values were amplified The WDI definition was changed since the forecast was made, values were amplified Weak correlation values Weak correlation values Perhaps a component-wise analog method would be more accurate, this would also give more insight into the temperature and precipitation breakdowns Perhaps a component-wise analog method would be more accurate, this would also give more insight into the temperature and precipitation breakdowns Weather patterns can change drastically over the period of 5 months Weather patterns can change drastically over the period of 5 months A few more methods should be developed which use the WDI to make a seasonal forecast. 2 methods may not be enough A few more methods should be developed which use the WDI to make a seasonal forecast. 2 methods may not be enough

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