Objective Weather Forecasting by Statistical Methods

Abstract

The general subject of objective weather forecasting is briefly discussed. Five statistical techniques, scatter diagrams, linear regression, discriminant analysis, principal components, and adaptive logic, are described and examples of their use in meteorology given.• Techniques Development Laboratory, U.S. Weather Bureau. 111 available. It may then have to be estimated from other data. Even though this estimation is made subjectively and calls for skill on the part of the meteorologist, the forecast scheme would usually still be termed objective.Generally speaking, objective forecasting methods fall into two categories. One is called numerical weather prediction in which numerical models of the atmosphere are formulated and systems of hydrodynamic equations are solved by high-speed electronic computers. This method was first tried by Richardson (1922) a few years prior to 1922 but had its practical beginning about 1950 when Charney, Fjortoft, and Von Neumann (1950) successfully integrated the simplified equations of motion. Great progress has been made in numerical prediction since that time and the U.S. Weather Bureau has been issuing forecasts made by this method since 1955. Even so, nearly all of the success and effort has been in the prediction of the large scale features of the atmospheric pressure distribution and, to a lesser extent, the temperature distribution in the free atmosphere. Small-scale features, those only a few tens of miles in extent, and other weather parameters such as surface temperature, cloudiness, and precipitation are usually not specified by the numerical models. These weather variables are still forecast by other means with heavy reliance on the computer products.The other category of objective forecasting is composed of various statistical methods. This is not to say that numerical forecasting and statistics are divorced from each other. It has been through studies of observational data that numerical models were formulated and improved. Most numerical models contain certain constants that are quasi-empirical in nature. Also, the application of statistical techniques permits the use of predictors that are suggested by numerical models and physical reasoning. The statistical relationships are usually much stronger between concurrently measured variables than between time-lagged variables. For instance, the cloud patterns are more closely related to the simultaneous pressure distribution than they are to the pressure distribution 24 hr earlier. Therefore, the statistical technique should rely on the numerical product for its input in many applications.This paper describes five techniques that can be used to develop statistical forecasting systems. It is not meant to be exhaustive and indeed there are so many ways that techniques can be modified and combined to form new techniques that only basic outlines can be given. These five have been selected for their statistical interest and potential use in many fields as well as meteorology. Other discussions of statistical techniques used...

Ensemble Cloud Model Applications to Forecasting Thunderstorms

“…trast. Oilman (1957), Sellers (1957) and Glahn (1965) are proponents o f the correlation matrix, claiming it puts all variables on equal footing, whereas Resio and Hayden (1975) and Molteni etaL (1983) find cross-products to have utility.…”