A climatology of icing conditions aloft would be useful for a number of reasons associated with the development of improved forecasts of in-flight icing conditions. First, such a climatology would provide a climatological basis for new forecasting techniques, and, in fact, might be an important component of new objective forecasting methods. Second, such a climatology could be used as a tool for evaluating the overall capabilities of icing forecasts, including current operational forecasts (i.e., the AIRMETs issued by the National Weather Service (NWS) Aviation Weather Center); in particular, over the long run, the forecast climatology should be similar to the observed climatology. For this study, the climatological variable of interest is the relative frequency of observed icing conditions, fI, at a particular location (e.g., Denver) and for a specified period of time (e.g., the month of February). It would be desirable to know the values of fI at locations distributed across the region of interest (e.g., the continental U.S.).
Unfortunately, the only widespread observations of icing conditions aloft are based on pilot reports (PIREPs) in which pilots report the existence of icing and other weather conditions. PIREPs have numerous problems for use as a dataset for developing a climatology. In particular, PIREPs are biased in space, with most reports occurring along common flight paths and in the vicinity of larger cities, where more aircraft are arriving and departing. While it is possible to compute icing frequencies based simply on the PIREP data (denote this frequency by fP), fP is an unreliable indicator of fI, except in the vicinity of large cities, due to the spatial biases in the PIREP data. However, it is possible to use the systematic nature of PIREPs around large cities, along with other information, to develop estimates of fI for locations with smaller populations. For the larger cities, fP can be assumed to be equivalent to fI. For smaller cities, fP is an underestimate of fI.
Earlier work on this topic indicated that (i) fP is related both to population and the number of aircraft departures at an airport (the latter variable is a measure of the "availability" of aircraft to report icing conditions); (ii) fP also is related to various common surface climatological variables, such as the mean temperature and the number of rainy days; and (iii) the number of aircraft departures is strongly related to the city population. The current study uses these facts to develop regression models to predict fI for smaller cities. Specifically, the approach taken in the current study involves (i) development of regression models to predict fI for very large cities, using the values of fP and various surface climatological variables for these cities; and (ii) application of the resulting regression equations to surface climatological data from the smaller cities, to obtain predictions of fI for these cities.
For this study, 131 cities, distributed across the continental United States, were selected. All of the cities have basic surface observation data available for the 1961-1990 period. Among the cities, 48 are large (with a population of at least one million within a radius of 100 km) and 83 are relatively small (with populations ranging from less than 10,000 to just under one million). F. McDonough summarized surface observations into a very large number of climatological variables that were expected to be correlated with the frequency of icing conditions aloft (e.g., frequency of overcast days; frequency of falling snow; frequency of freezing precipitation). Values of fP were computed using PIREPs from 1992-1997, with altitudes less than 10,000 ft, counting all PIREPs within 80 km of each city. Geographic information (e.g., latitude, longitude, nearness to water) also was included in the dataset. The initial study is based on PIREPs and surface observations for the month of February.
McDonough and B. Brown used stepwise regression to guide selection of the surface climatological and geographic variables to include in the regression model for the larger cities. However, the final model was selected using insight from a forecaster who has experience forecasting icing conditions. The final model included latitude (which is strongly related to fP for the larger cities), as well as variables related to temperature, drizzle, snow, and freezing precipitation. The coefficient of determination for the fitted model is 0.92, indicating that the fitted model explains 92% of the variation in fP for the large cities.
Application of the regression model developed for the larger cities to predict fI for the smaller cities (i.e., using the climatological surface observations and latitude values for the smaller cities) indicates that the approach worked appropriately. Figure 1 shows the values of fI predicted by the regression model, for all of the cities (large and small), as a function of fP. This figure indicates that (i) the regression model fits the values of fP quite well for the larger cities (i.e., as expected, fI and fP are approximately equivalent for the larger cities); and (ii) the values of fI for the smaller cities, predicted by the model, generally are larger (frequently much larger) than the values of fP computed for them solely on the basis of PIREPs. Thus, the model is functioning as expected. In fact, the cities with the largest differences between fP and predicted fI are the smallest cities; the few "small" cities for which the predicted value of fI is smaller than fP all have a population just slightly less than one million. Finally, a map depicting the values of fP (= fI) for the larger cities, and predicted fI for the smaller cities, provides a much smoother (and presumably more realistic) representation of the icing threat across the continental United States than is obtained using the values of fP for the smaller cities.
Further work remains to be done to evaluate the capabilities of the regression model. In particular, it is desirable to determine the influence of particular sets of cities on the selected regression model. Due to the distribution of population in the United States, many of the large cities used to develop the regression model are located in the northeast, and few are located in the west. Cross-validation techniques will be used to determine the impact of these geographic factors on the regression models developed. Once a model has finally been accepted, prediction intervals will be estimated for the values of fI for each small city, to represent the uncertainty in the climatology. Finally, the study will be extended to other months and to different categories of icing reports (e.g., reports of more severe icing conditions).
