multiple linear-regression model (one model for all stations and all days) based on the seven climatic variables in Figure 8a explains about 55 percent (53 percent without the square-root transformation) of the daily variance of the DTR. Although the explained variance is substantial, it is apparent that other factors may also need to be considered in order to explain the variations of the DTR (e.g., better representations of the atmospheric stability, external forcing factors, more precise techniques for calculating the mean quantities used in the analysis) and their relationships are not adequately expressed by a linear equation.
On a variable-by-variable basis, the signs of all the partial correlations make qualitative physical sense. It is interesting to note that the partial correlation of ΔTMP with DTR is greater than that of the simple correlation coefficient (Figure 8a), because the correlation between TRAD and ΔTMP mask the importance of ΔTMP in influencing DTR. The decrease of the partial correlation relative to the simple correlation for the variables RH, CIG, and SKY is to be expected, because changes among these variables are all related to each other. The decrease in the partial correlation of SNOW is particularly noteworthy, especially since Cao et al. (1992) attribute the ablation of snow cover in their model to an increase in the DTR. The empirical results in Figure 8a suggest that SNOW is only weakly related to DTR (7.5 percent of the cases, nearly 4,000, had snow cover), especially by comparison with the other variables.
In order to investigate the linearity, or lack thereof, of the relationships implicit in Figure 8a, the data were partitioned by TRAD. Figure 8b provides strong evidence to suggest that the relationships change with the amount of TRAD. In particular, the partial correlation coefficients of RH, WS, and SKY become stronger as TRAD (and thus temperature) increases. This probably has more to do with a reduction of the maximum temperature than an increase of the minimum. During daylight hours high values of the RH, WS, and SKY are indicative of higher albedos, higher potential evapotranspiration, higher atmospheric water-vapor absorption of incoming radiation, and larger-than-normal mechanical mixing. These factors act to reduce the maximum temperature that would otherwise result from high-intensity TRAD, which would be manifested as sensible heat within the surface boundary layer. The non-linearity of RH as TRAD increases is substantially greater than that of WS (Figure 8b). As the TRAD reaching the surface increases, the temperature increases, and comparatively more of the TRAD can be used for evaporation than for raising surface temperature, as would be anticipated by integrating the Clausius-Clapeyron equation to obtain saturation vapor pressure as a function of temperature.
The reduction of the partial correlation of TRAD with the DTR when the sample is partitioned with respect to TRAD (Figure 8b) relates to the balance between long nights and short days. During the late autumn and early winter in the northern half of the United States (areas which include the lowest partition of TRAD), a moderate increase in the TRAD (by inter-seasonal and latitudinal variations) generally results in a higher DTR. Contrarily, in the warm half of the year, TRAD is more than ample, so the relation between TRAD and DTR is near zero. In fact, a further selection for very high values of TRAD (short nights) leads to small negative partial correlations between TRAD and the DTR.
The reduction of the partial correlation of ΔTMP as TRAD increases is related to the decrease in intensity of the day-to-day changes of temperature during the warm season. Rossby waves and extra-tropical cyclones have lower amplitude, speed, and intensity during the warm season.
A change in sign of the partial correlation coefficient of