# Numerical Fit Modeling for Temperature Mitigation in
## 3 Results
### Mitigation  
Considering that fit factors were only necessary when the air masses changed, it can be argued that the numerical model is capturing changes in heating and cooling rates. A mitigation using plumes of calcite would not significantly change the air mass locally over the city. Therefore, the same air mass heating and cooling rates can be used for mitigation cases.  
During a long mitigation, ground temperatures may significantly cool. This method of modeling does not account for changes in ground temperatures.  
[PERSON] [6] showed that interaction with water clouds significantly affected the SCAM6 modeling results in humid regions but not arid regions. To accurately check the model against results for humid regions, this interaction needed to be included. Rather than adjusting the numerical fit model to be much more complex, the solar radiation input to the numerical fit model was taken as the SCAM6 downwelling solar radiation.  
Figure 5 shows the numerically predicted temperatures. [PERSON] [6] produced similar results using SCAM6. The days with greater cooling in one model also have greater cooling in the other. An exception is that from days 16 to 18, the SCAM6 model shows no cooling, but there is a small cooling found with the numerical fit on days 17 and 18 but a warming on day 16. The average temperature change was a decrease of 2.12 K, but for the SCAM6 model, the drop was 0.98 K for aircraft dispersal. When comparing the CAM and numerical fit results for mitigation, the \(p\)-value is less than 0.001.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Time (Days)** & **\(H\) (K m\({}^{2}\)/Watt)** & **\(C_{rate}\) (K/K)** & **\(C_{base}\) (K)** \\ \hline
0.0–0.5 & 0.00215 & \(-\)0.0409 & 11.22 \\
0.5–3.5 & 0.00215 & \(-\)0.0250 & 7.13 \\
3.5–4.5 & 0.0013 & \(-\)0.026  
A few reasons are discussed for the difference between the SCAM6 and fit models. The most significant reason may be that CAM considers horizontal advection, but the fit model does not. Advection would reduce cooling because warm air blowing into an area defeats some of the benefit. Therefore, it is reasonable to assume that the SCAM6 results would show fewer benefits. The effects of advection will be accounted for later. Since both methods show similar patterns, the numerical model can be said to be an approximation of the results from the single-column model when there is no significant water cloud interaction and if advection is accounted for. Another reason for differences is that the two models had different assumptions about whether cooling from mitigation would build up through changes in the ground temperatures.  
Next, an arid region was modeled with the numerical method considering that the full effect of the mitigation would be achieved. The optical depth of calcite was chosen to reduce the solar radiation by half. No interactions of the calcite with water clouds is anticipated because it is an arid location. Therefore, the heating at ground should be reduced by half due to the plume. Figure 6 shows the results of the mitigation.  
The mitigation shows a dramatic drop in temperatures. The average temperatures are 6.37 K below the actual temperatures. The daytime highs are reduced by much higher amounts than the nighttime lows. In Figure 6, it is common to see a drop of 10 K during the daytime. The differences at night are usually less than 5 K. This suggests that the mitigation is well suited to reducing extreme temperatures.  
Figure 5: Temperatures (K) in the actual and mitigated cases at the 992 hPa level using numerically fitted temperatures for humid conditions. Most days show cooling, but the amount of cooling varies with atmospheric conditions.