Statistical Weather Forecasting: Stratification, Compositing, and Regression - Prof. Eugen, Study notes of Data Analysis & Statistical Methods

Download Statistical Weather Forecasting: Stratification, Compositing, and Regression - Prof. Eugen and more Study notes Data Analysis & Statistical Methods in PDF only on Docsity! 32 Classical Statistical Forecasting Basically, statistical weather forecasting is linear regression: given a predictand (e.g., surface temperature in DCA), choose predictors available in time to perform a forecast. For example, forecast tomorrow’s Tmin given today’s observations. 1) Stratification and compositing: In order to make the coefficients kb more reliable, stratify the data into homogeneous bins, rather than mixing inhomogeneous data. Examples: stratify data according to season, and compute separate regression equations for each season separately. Stratify data for long-range forecasting into El Niño, La Niña, and non-ENSO years. In order to increase the size of the dependent sample, composite several similar dependent data. Example: divide the country into “homogeneous” regions and assume that the same regression equation applies to all the stations within a regions. Or, since La Niña response is approximately equal and opposite to El Niño, composite El Niño events with “minus La Niña” 2) Prediction of a yes-no event. Simple approach: 1 if yes 0 if no y ! " = # $ % & and use regression. 33 Regression estimation of event probabilities (REEP) 0 1ˆi iy b b x= + REEP: Determine a least-squares fit to the observations and interpret the result as a forecast of probabilities!! Problems with this approach: 1) we don’t know whether these are fair probabilities. 2) We can get P(y)<0 or P(y)>1. If we change variables for the linear regression fit: 0 1 1 ˆ 1 exp( ) i i y b b x = + + , we solve 2) but not 1). (see chapter 7 of Wilks for a discussion on verification of probabilistic forecasts). x Dependent sample measurement (y=0 or y=1) P(y) 1.0 0 REEP regression line P(y) 1.0 0 x