# Spatio-Temporal Distribution of Deep Convection Observed along the Trans-Mexican Volcanic Belt
## 3 Material and Methods
### Definition of Deep Convective Cloud  
There are several established ways to detect and characterize deep convection from satellite-based passive imagery. In general terms, deep convective clouds have pronounced vertical growth, leading to low observed brightness temperatures and thus to retrievals of low values of cloud top temperature (CTT) and cloud top pressure (CTP). They also have high liquid/ice contents that produce high reflectances in the solar part of the spectrum, which leads to, e.g., retrievals of high cloud optical thicknesses (COTs). Cloud classification schemes based on joint histograms of two or more cloud parameters retrieved from passive observations have been widely used in the satellite research community. For example, in [PERSON] et al. [5], a combination of cloud top properties, optical and micro-physical properties were used to describe MODIS-observed spatial and temporal distributions of cloud regimes on a global scale; among others, those associated with deep convective activity. Threshold values of MODIS-based cloud brightness temperature (BT) and COT have been used for the detection and DCC property description over different locations of the globe by [PERSON] and [PERSON] [38], while [PERSON] et al. [39] used a combination of MODIS-based CTP and COT to describe large-scale characteristics of tropical convective systems. Similar parameters were used by [PERSON] and [PERSON] [40] to estimate the probability of deep convection in Africa. For this study, we used a straightforward cloud type definition of deep convective cloud taken from the well-established International Satellite Cloud Climatology Project (ISCCP) [41; 42]. For many years, in a time period starting in the early 1980s until 2015, ISCCP has been providing a large set of gridded atmospheric products with temporal resolutions ranging from 3 h to monthly means and spatial resolutions ranging from 2.5 degrees up to 10 km in more recent efforts. The cloud climatologies are based on a combination of measurements from geostationary satellites and AVHRR instrumentsmounted on several National Oceanic and Atmospheric Administration (NOAA) polar-orbiting satellites. Specifically, a satellite pixel covers a deep convective cloud when the retrieved CTP is equal or less than 440 hPa and the retrieved COT is equal or greater than 23. Here, we took advantage of the advanced MODIS cloud retrievals, higher pixel resolution and large sampling. The MODIS-based deep convective cloud observations were collected for a grid with resolution 0.1\({}^{\circ}\), which allowed the analysis of deep convection frequencies and their relationship with local characteristics such as the topography. The DCC frequency per grid cell was obtained from average CTP and COT values, which were computed from the collected MODIS cloudy pixels that fell within the grid cell for each daytime satellite overpass. Note that only cloudy pixels with successful CTP and COT retrievals were used (and that the cloud phase was not explicitly taken into account). To count a MODIS-observed DCC event, both CTP and COT average values needed to fulfill the threshold requirements mentioned above. The monthly values of the total number of observed DCCs, or DCC frequencies, were obtained by adding daily DCC counts. A CTP of 440 hPa relates to a height of about 6.5 km. In the study area, parts of the Transition and Nearctic sub-regions consist of high plains (altiplano) with an elevation height of about 2 km. In addition to a horizontal extent of at least about 10 km \(\times\) 10 km, meaning that single clouds at the very beginning of convective development are not considered, the clouds can still have a considerable vertical extent, also at higher elevations. Moreover, the combination with the COT threshold ensured that only clouds with a high liquid/ice content, which depends on thermodynamic variables, were included. In that sense, COT can be considered as additional information on cloud vertical development, noting that the retrieval of COT is largely independent of cloud top height.