# Spatio-Temporal Distribution of Deep Convection Observed along the Trans-Mexican Volcanic Belt
## 4 Results and Discussion
### Relation to Terrain Height  
Another feature connected to the observed DCC frequency in the study area is the terrain height. As previously mentioned, the TMVB holds a complex topography that seems to favor the development of deep convection. In this sense, the correlation value between terrain height and DCC frequency over the entire domain is 0.32. This correlation value takes into account all the grid points in inland Mexico. By dividing the domain into sub-regions (see Figure 1b), the correlation values change to 0.54, 0.57 and \(-\)0.19 for the Transition, Nearctic and Neotropical sub-regions, respectively. The relatively high correlation value in the Nearctic sub-region is associated with the comparably low terrain height variations and the subsequent low DCC frequency. A similar case is the Transition sub-region, where high terrain height variations relate to the high DCC frequency.  
In order to analyze in more detail how the variations in terrain features relate to observed DCC frequencies, cross-sections at constant latitudes (20.5\({}^{\circ}\)N, 19.5\({}^{\circ}\)N, and 19.0\({}^{\circ}\)N) of the total number of observed DCC events and the total number of observed DCC events limited to the corresponding wet phase (June to September) are shown in Figure 7.  
For the cross-section at the constant latitude of 20.5 degrees north (northern part of the domain), the observed DCC frequency shows the Gulf of Mexico as the most active region. The western part also shows relatively high frequencies. As expected, this cross-section shows a relatively stable behavior since the transect includes the dry highlands of the domain and fewer terrain height differences. The correlation coefficients for this section are \(-\)0.67 for the full period and \(-\)0.45 for the wet phase. In the second cross-section, at the constant latitude of 19.5 degrees north, which is just over the TMVB, the influence of the Pacific Ocean is evident in the western part of the domain, with peaks of frequency just over the windward side. The altitude differences mark, in this plot, the higher frequencies of the observed DCC. The correlation values for this transect are 0.63 for the full period and 0.53 for the wet phase. Finally, in Figure 7c at the constant latitude of 19.0 degrees north, including the southern portion of the TMVB and highest elevations, the correlation values increase to 0.77 for the full period and 0.76 for the wet phase. The increase in the frequency of the DCC observed in the eastern part of the domain indicate the significant role that the fluxes from the Gulf of Mexico and mountainous areas play in the generation of deep convective clouds. The relatively high correlation coefficient between observed  
Figure 6: Monthly domain-average of deep convective cloud frequency, accumulated precipitation and tropical cyclone activity. The red line represents the domain-averaged total number of observed DCC based on MODIS data with a horizontal resolution of 0.1 degrees; the blue line represents the domain-averaged monthly mean precipitation amounts based on CHIRPS data with a spatial resolution of 0.05 degrees, and the grey bars represent the number of tropical cyclones that affected the study region. All parameters are shown for the period 2008–2017.  
deep convective clouds and terrain height is a strong indicator of the considerable role of complex topographic features in the forced convection processes within the TMVB region. For spatial distribution maps of seasonal correlation values between MODIS-based frequencies of DCC and CHIRPS accumulated precipitation, we refer to the Figure S1 of the Supplementary Material.