Temporal Distribution of EPEs

Figure 4 shows the inter-annual variations in EPEs. Activity peaks occurred in 1992, 1998, 2003, and 2014, with 1998 being the year when most events (18) were recorded. Although the El Niño Southern Oscillation (ENSO) is a climatic pattern closely related to precipitation in Mexico (^{Bravo Cabrera et al., 2018}; ^{Magaña et al., 2003}; ^{Pavia et al., 2006}), no clear trend in the occurrence of events being favored by a particular phase of ENSO could be observed. Further studies on the influence of different climatic oscillations on the study area and their likely role in generating EPEs are necessary. Detecting changes in precipitation patterns and their extremes is key for identifying the likely impacts of global warming.

Figure 4 Annual variation of extreme precipitation events (EPEs) in the State of Colima over the 1981-2018 period. The lines show the trends of non-CT (continuous line) and CT (dotted line) EPEs over the study period. 

Clear differences were found between EPEs associated (TC, henceforth) and non-associated (non-TC) with tropical cyclones. Non-CT EPEs outnumbered CT EPEs almost throughout the entire study period. This can be explained by the fact that the conditions necessary for generating a local storm occur much more frequently than the formation of a tropical cyclone that affects the State. Moisture advection from the Pacific Ocean and its interaction with the complex local orography have been identified as determining factors for the formation of deep convection events and intense rains in the region (^{León-Cruz et al., 2021}).

A comparative analysis of CT and Non-CT EPEs showed that the frequency of non-TC events increased slightly while that of CT events showed the opposite trend. The increased frequency of extreme rainfall events under climate change scenarios has been widely documented. It is likely that anthropogenic forcing might eventually lead to a global increase in extreme precipitation events, mainly due to the increase in atmospheric water vapor and the associated instability environments (^{Kunkel, 2003}; ^{Oliveira et al., 2017}; ^{Semmler and Jacob, 2004}). The trends observed in our study should be examined using longer time series to fully understand the changes in precipitation patterns and their extremes.

EPEs were more frequent during the humid months of summer and autumn, from June to October, with an activity peak in September (Figure 5). Activity was low between November and May, reaching a minimum in the dry months of March and April. Records of non-CT events started in June, increased gradually in July and peaked in August. Their frequency decreased gradually during September and October and kept a low frequency between November and May. Eastern waves are relevant for the formation of this type of EPEs (Dominguez et al., 2020) and, particularly, for the generation of mesoscale convective systems in Colima State (^{Ríos-García, 2016}). No clear correlation between the monthly distribution of this type of EPEs and the curve of TC influence in the state was evident.

Figure 5 Monthly variation in the frequency of extreme precipitation events in the state of Colima over the 1981-2018 period. The dotted line denotes the influence of CT (as percent days per month) on Colima State. 

Records of TC-EPEs also started in June, but with a lower frequency than non-TCs; they became more frequent in July and then decreased in August. Such decrease might be related to the influence of the mid-summer dry spell (locally known as canícula) in this part of Mexico (^{Magaña et al., 1999}). The frequency of TC EPEs increased significantly towards September, when their peak coincided with the curve of TC influence in Colima State (Figure 5). Thus, a greater influence of TC on the study area increases the probability of generating extreme events. The number of events decreased in October and became null between December and April. This analysis included all the TCs that affected the territory of Colima State and not only those that impacted its mainland portion.

Spatial Distribution of EPEs

Figure 6 shows the spatial distribution of the total number of EPEs, as well as their breakdown by type (CT and non-CT events), and the average associated precipitation. EPEs can be twice as frequent in the northern as in the southern region of the State (Figure 6, top row). The topographic gradient and landforms seem to determine, to a large extent, the distribution of EPEs in the state. High frequencies, higher than 30 EPEs, were also found on the northern part of the municipality of Manzanillo. This area coincides with La Espumilla hill, which again shows the importance of orography in generating these events through terrain-driven deep convection processes.

Figure 6 Total number of EPEs, and number of CT and non-CT EPEs, and their associated average precipitation in the state of Colima over the 1981-2018 period. 

The most intense events, with cumulative rainfall greater than 180 mm, were recorded in the southern part of the state. The average values of associated precipitation decreased towards the north, reaching a minimum on the eastern part of the municipality of Colima where the average EPE had a cumulative rainfall of about 100 mm. While this value is not negligible, it clearly shows the marked differences between EPEs of the central, northern, and southern parts of the state. In summary, while EPEs were more common in the northern municipalities, the most extreme events generally occurred on the southern part of the State.

The highest frequencies of CT events (Figure 6, intermediate row) occurred on the southern part of the State, mainly on the municipalities of Tecomán and Armería, and extending northwards to Coquimatlán, Villa de Álvarez, and Comala. Contrary to what we expected, the municipality of Manzanillo did not show high values. The concentration of a high number of CT EPEs on the central portion of the state may be related to the transport of moisture by flow channeling processes over this zone, which would trigger rain in the area. This should be further examined in detail to establish such behavior with certainty. The largest (greater than 200 mm) average cumulative rains associated to CT EPEs occurred over the entire coastal strip. In other words, although CT EPEs were not frequent on the southern portion of the state (mainly in Manzanillo), they often were quite severe.

Non-CT EPEs were most frequent (Figure 6, bottom row) on the northeast zone, mainly on the municipalities of Cuauhtémoc and Colima. The elevation gradient seems to play a more important role in this type of events than for CT EPEs. Previous studies have documented the presence of deep convective clouds (^{León-Cruz et al., 2019}), which are commonly associated with extreme events, in the northern portion of the state of Colima. The total number of non-CT EPEs ranged from over 18 events on the northeast and decreasing to the south. Average rainfall values were higher over the coastline and lower in the north of the state. These areas showed differences of around 100 mm, revealing the significant spatial variability of these systems.

Characteristics of EPEs

The box plots in Figure 7 show the volume of precipitation associated with EPEs, both in general and by type of EPE, with particular attention to the wet season of the year. The central line of each box represents the median and ‘X’ represents the mean. The bottom of the box denotes the first quartile, and the top is the third quartile. The whiskers denote the extreme values, and the points above them the outliers.

Figure 7 Box plots of the rainfall associated with each type of EPEs for the wet months of the entire study period. 

Box plots help to analyze the characteristics of EPEs based on their associated precipitation. As there was no significant EPE activity during the dry season of the year (November to May), the analysis focuses on the wet season data.

Figure 7 shows that the CT EPEs had cumulative rainfall values ranging from 70 mm to 340 mm and around 170 mm on average. Atypical values exceeded 400 mm of daily rainfall and represent the most extreme cases. The influence of the Tropical Depression and later Tropical Storm "Greg", which hit Colima on September 5-6, 1999, is revealed by a 400.1 mm EPE; the influence of Hurricane "Jova" (Figure 8), which reached category 3 on the Saffir-Simpson Scale and hit the State on October 10-12, 2011, can be seen in a 404.5 mm EPE. Declarations of natural disaster were issued by CENAPRED in both cases². These two extreme events caused the historical maximum cumulative rains in Colima State and are a clear example of the threat that they can pose on the population of this region.

Figure 8 GOES-13 satellite products (^{Knapp and Wilkins, 2018}) for Hurricane Jova and a Mesoscale Convective System. 

Non-CT EPEs had, on average, lower cumulative rainfall values close to 125 mm. The lower (first quartile) and upper (third quartile) limits were around 100 m and 140 mm per event (Figure 7). The highest values were around 220 mm, well below the 340 mm observed with CT events. Some atypical events identified for non-CT EPEs included a 382-mm cumulative rainfall event on October 29, 2015, associated with a Mesoscale Convective System formed by the remnants of Hurricane "Patricia" (Figure 8), and a 382-mm cumulative rainfall event on November 26, 1982, for which no information was available.

EPEs also showed differences related to their month of origin. The cumulative rainfall associated with non-CT EPEs (Figure 7) did not vary significantly with the month of record. Average values ranged between 116 mm (in August) and 133 mm (in October). The lower limits did not vary significantly either and varied around 94 mm per day. The upper limits ranged between 132 mm in June and 156 mm in September. Extreme monthly values never exceed 220 mm and atypical cases mostly occurred in September and October. We inferred that the availability of moisture associated with remnants of tropical cyclones or the passage of tropical waves through the region were the main triggers of activity during this period.

The characteristics of non-CT EPEs evidently make them less severe events. Nevertheless, in the absence of tracking and early warning protocols, these events³ can also pose significant threats to society. Similarly, the threshold set for identifying these events was at least 67 mm per day, which qualifies as a very intense rain according to classifications proposed by other authors (for example, ^{Zúñiga and Magaña, 2018}).

A different picture is observed with CT EPEs (Figure 7). Our results showed that these systems exhibit strong variations in the associated precipitation related to the month of record. The most severe events were recorded in September and October, coinciding with the period when more CT-EPEs occurred. The average rainfall associated with EPEs was 117 mm in June, 149 mm in July, 137 mm in August, 168 mm in September, and up to 188 mm in October. There was an overall increasing trend in EPE severity towards the end of the wet season, when extreme values exceeded 400 mm in October. The lower limits (first quartile) did not vary significantly and ranged between 90 and 120 mm. On the contrary, upper limits varied widely, ranging from 147 mm in June and up to 242 mm in October. Outliers calculated based on the seasonal variation in EPEs intensity were mainly concentrated in September.