# Numerical Fit Modeling for Temperature Mitigation in
## 2 Numerical Fit Model for Arid Regions
### Method Details  
The numerical model considered the same data as the SCAM6 program. Over 29 days, all the fronts and troughs that passed through the area were found using weather maps [34]. A front or trough passed through the area every few days. There are stationary fronts on 26 June 1997 and 2 July 1997 for a few days. This is seen in the cool temperatures in Figure 3 around days 8 and 16. Stationary fronts are harder to numerically model since conditions are slowly and actively changing. Since the frontal maps are daily, exact times for the passing of fronts are not known. Atmospheric conditions can change rapidly when a cold front passes through, but often conditions change gradually over the space of a few hours as the air mass changes. The time of passing of the front is approximated from the map. From this, modeling timelines were made by grouping together similar weather conditions. Then the groupings are finalized by confirming that the temperature data in each group appears to have the same pattern. The times for the air mass changes can be shifted a few hours if parts of a day fit better with a different grouping. Wind varied from 0 to 38.9 m/s in the full height of the atmosphere, but in the lowest altitudes, the wind was usually below 10 m/s. The full list of data by hour and altitude are provided in [[http://doi.org/10.17632/n5](http://doi.org/10.17632/n5) xkn597h.1]([http://doi.org/10.17632/n5](http://doi.org/10.17632/n5) xkn597h.1). The biggest effect of the wind speed is on logistics because it was assumed that higher wind requires a greater mass of calcite to maintain a constant effect on solar radiation. Therefore, it is assumed that wind has no effect on the radiation rates in the model. Next, for each air mass, cooling rate versus temperature is found. Figure 4 shows a sample for days 0.5 to 3.5. A weak trough passed through the area around day 3.5, but days 3.5 to 6.5 were found to have about the same cooling rates as days 0.5 to 3.5. Figure 3: Actual temperatures and predicted temperatures from fit model. The fit model shows very close modeling of actual temperature changes. Figure 4 shows that the temperature changes can be bouncy while alternating from reading to reading. It is not the goal to model the apparently random bouncy changes over short time intervals. Smoothing would account for many of the unusually high or low temperature changes. The final step in creating the numerical model is to determine the heating rate \(H\). For days 0.5 to 3.5, the heating rate was 0.00215 degrees per watt per square meter solar radiation at the top of atmosphere. The rate was 0.00130 degrees per watt per square meter while the trough passed through day 3.5 to 4.5 and then 0.00160 degrees per watt per square meter from day 4.5 to 6.5. As mentioned previously, the rate was doubled at sunrise and ramped down to these values at later. Cloud cover was present at various times during this model. Traditional weather reporting labels such as \"partly cloudy\" are insufficient to accurately model the effect of clouds on solar radiation. Instead, cloud results from SCAM6 were used. The variable CONCLD sums up the amount of condensation cloud in the air column. It was found that the model fit well to the actual temperatures on cloudy days when the CONCLD value of 1.2 was taken as reducing the solar radiation by half. The resulting modeling equations for days 0.5 to 3.5 were:  
\[T_{1}=T_{0}+\Delta T_{heat}+\Delta T_{cool} \tag{3}\]  
\[\Delta T_{heat}=0.00215\;\mathrm{K}\times I\times F\times(1-0.5/1.2\times CONCLD) \tag{4}\]  
\[\Delta T_{cool}=7.13\;\mathrm{K}-0.0250\;T_{0} \tag{5}\]  
where \(T_{0}\) is the temperature in Kelvin, \(T_{1}\) is the temperature one hour later, \(\Delta T_{heat}\) is the change in temperature due to solar heating, and \(\Delta T_{cool}\) is the change in temperature due to cooling. The time modeled was in 20-min increments because that is the CAM time.