Developing accurate Multivariate Linear Regression (MLR) models for meteorologically influenced response variables with focus on extreme events

Many environmental variables, including beach bacteria concentrations and extreme temperatures, are affected by meteorological conditions. Multivariate Linear Regression (MLR) models prove useful for relating response variables to explanatory variables when modeling average conditions. However, extreme values are often of greater interest; this is true of bacterial concentrations in beach water or freezing temperatures in vineyards. In both instances the effects can be severe to humans or plants. These phenomena are not unrelated as the conditions that lead to extreme temperatures may also be conducive to high bacterial concentration in water. Also, examinations of model results often reveal bias in extreme forecasts. In the vineyard example, the extremes of both low and high temperatures will be underestimated. With beach bacteria, correctly predicted violations of health standards are often overshadowed by a great number of false negative predictions. This work attempts to reduce the tendency to bias extreme predictions to the mean. One technique is to develop response variables that are expressed relative to some reference quantity. For example, it can be shown that in many lowland locations the 850mb temperature is a function of the tropospheric air column thickness. It proves useful to define an 850mb reference temperature based on the regression of these variables. The difference between the surface temperature and the reference temperature becomes the response variable. This approach has the inherent advantage of placing the variable of interest, the overnight low surface temperature, into a seasonal context. Some selected explanatory variables are key parameters in global circulation models, as maintained by the United States National Weather Service. They are readily available and can be shown to be predicted accurately. In addition, to the 1000-500mb thickness and 850mb temperature, other variables include precipitable water, wind, and sky cover. Recommended variables and methods discussed herein help produce accurate forecasts of extreme events.