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976 VOLUME 20 JOURNAL OF APPLIED'METEOROLOGY were much greater than for the early afternoon re- sults, which were closest to aircraft observations. This small sample of verification statistics tends to support the need for local afternoon soundings near developing clouds in sp3;ce and time for best model simulations; Note that 13 of the 26 soundings had errors in Cloud-top height within 500 m of that observed. Observed cloud-top heights ranged from 5.3 to 13.7 km; whereas, model-predicted cloud- top heights ranged from 3.3 to 13.6 km for this set of 3 km cloud radius cases. The average observed cloud-top height was 8.65 km in this sample; how- ever, the average cloud-top height predicted by the model varied as a function of input cloud radius. This comparison between model and aircraft observations is not intended to rigorously verify the model, but simply to indicate that the model is able to diagnose basic cloud properties such as base height and cloud-top height which can be used to broadly classify the potential for convective development from a local rawinsonde. Hence, the model is viewed as a more comprehensive Showalter (1953) or Totals Totals Index4 of convective develop- ment to examine the natural variability of thermody- namics related to convective cloud development on the High Plains. Previous studies by Hirsch (1971) showed that the GPCM-diagnosed cloud tops and radar echo tops had a correlation coefficient of 0.82 (sample of 40 cases). Similar studies by Simpson and Wiggert (1971), whose model was similar to GPCM, showed that their model also had reasonably good correlations. e. Predicted convective intensity versus observed cloud types Model analyses of conditions on days having satellite observations of clear, cumulus, cumulus congestus and cumulonimbus 'at the three primary HIPLEX sites (MLS, GLD, BGS) were compared. These subjective visual classifications of satellite photos showed that many of the model-diagnosed lapse rates, moisture and cloud properties varied in a manner consistent with the increasing in- tensity of the four cloud types. Table 4 presents a set of these cases where convective cloud sample statistics of cloud-top areas were derived from digital satellite observations (Reynolds et al., 1978) from 1976 and 1977 HIPLEX field seasons. The digital imagery were analyzed using a man-computer interactive video display system (ADVISAR)5 which permitted the manual selection of appropriate clouds 4 Miller, R. C., 1972: Notes on analysis of severe storm fore- casting procedures of the Air Force Global Weather Central. Tech. Rep 200 (Rev.). Air Weather Service (MAC), U.S. Air Force. 5 All Digital Video Imaging System for Atmospheric Research at Colorado State University. '"I and elimination of contamination problems of cirrus and nonconvective clouds. These cases were se- lected and analyzed independently from the subjec- tive photographic interpretation of the four cloud types. In this sample of 49 days, multiple regres- sion analyses were performed to determine linear relationships between model-analyzed thermody- namic variables and cloud properties, and the total number of convective clouds (towering cumulus and cumulonimbus) observed in satellite imagery each day having cloud-top areas between 10 and 100 km2, 100 and 200 km2 and 1000 and 10 000 km2. These three top areas were independently, objec- tively determined on the ADVISAR system with- out regard to the visual classifications previously determined. The cloud areas and model variables had relatively low individual correlation coef- ficients with maximum values approaching 0.3 to '0.4. However, multiple regression analyses showed that useful relationships may be derived to classify the type of day, using several independent thermo- dynamic variables. In the multiple regression analysis, the number of clouds was the dependent variable and the 10 "best" model thermodynamic variables (selected from 84 possible variables) were the independent variables. These analyses were performed using the Statistical Package for the Social Sciences (SPSS) multiple linear regression programs (Nie et at., 1975). The multiple linear regression models were able to reduce the standard deviation of the number of clouds occurring in each category by a factor of 2-5 and had high multiple correlation coefficients ranging from 0.78 to 0.97, thereby explaining much of the vanance in the cloud sample from thermodynamic variables. These en- couraging results will be discussed in depth in a future paper; however, they are presented here to show that there is a strong statistical relation- ship between observed convective cloud proper- ties and modeled thermodynamic variables. This relationship also parallels the physical relation-' ships between moisture and stability developed by forecasters of convective development (Byers and Braham, 1949; Showalter, 1953). Student's t~tests were performed to test sample means and determine significant differences be- tween samples for different types of clouds. For example, small cumulus and cumulus congestus days were characterized by drier PBL air, with higher and colder cloud-base heights than cumulo- nimbus days. Differences in sample means of cloud- base heights and temperatures for the three cloud types were significant at better than the 5% level in many samples (Table 4). The effects ofthese thermo- dynamic controls on the potential for convective cloud growth diagnosed by the model was reflected by significant (P value = 0.001 to 0.050) differences in variables such as cloud-top heights and depths, I il I