Probability of induced extreme precipitation events in Central America due to tropical cyclone positions in the surrounding oceans

The preparedness of national and local authorities for extreme hydrometeorological events could alleviate the impacts in many socioeconomical sectors. A statistical tool for the prediction or assessment of extreme precipitation probabilities caused by the presence of Tropical Cyclones (TCs) in the surrounding oceans of Central America is presented. The model is based in fitting precipitation probability distributions associated with the location of the TCs. The probabilities of medium, high, and very high levels of extreme rain and associated with the observed precipitation of the 60, 75, and 90 percentiles, are displayed in a map which can be used (with other tools) to issue alerts by emergency and response authorities. Impacts related to TCs can be classified in direct or indirect. In the case when the TCs are located in the Caribbean/Atlantic basin, there is a critical configuration near the Gulf of Honduras that drives both high probabilities of direct (in the northern countries) and indirect (in the southern countries) extreme precipitation. In the Eastern Tropical Pacific TC locations, probabilities of indirect impacts are usually lower than for the Caribbean/Atlantic. This is related to the usual trajectories in this former basin, that move away from the continent. Both, in Caribbean/Atlantic and Eastern Tropical Pacific’s TCs, the probabilities of indirect effects usually are higher in the Pacific slope of the isthmus than in the Caribbean. Here we present one tool that can be used with others analyses by emergency officials to determine the locations where alerts of extreme weather must be issued to prevent human life’s lost.


Introduction
Previous studies have reported a robust relationship between extreme hydrometeorological disaster reports in Central America and the presence of tropical cyclones (TCs) in certain critical positions of the Caribbean Sea (Retana 2012;Pérez-Briceño et al. 2016; Alfaro and 1 3 (2013). Furthermore, Jong-Suk et al. (2020) used a Fuzzy c-means clustering algorithm on historical data of typhoon's trajectories to predict accumulative induced rain in the southeast coast of China, within a 500 km range from the low-pressure center of the TC. The model showed a 51.2 mm average error through the rain stations involved.
The objective of this work is to present a statistical tool that estimates the extreme rainfall conditions probability, in any local Central American government political division, given a TC position (observed or forecasted) in the CS or in the ETP. This tool can be used with other types of operational forecasts by authorities in the anticipation of extreme precipitation events associated with TCs around Central America. The tool presents an estimation of the probability maps of extremely wet rainfall for each country. Next section describes the data and methodology used in this analysis, Sect. 3 describes the main results and their discussion and finally, Sect. 4 presents the conclusions of this work.

Data and methodology
Historical precipitation data covering Central America were obtained through the Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) data set for the period 1981-2020, consisting of gridded daily precipitation data in mm day −1 for every grid-point 0.05 degrees apart (Funk et al. 2015). Shapefiles of the sub-division of all Central American countries were obtained from the Database of Global Administrative Areas (GADM) (Global 2018) to extract vertices and centroids of Central American municipalities using the QGIS software (QGIS 2022). These data were used to identify all the points of the CHIRPS data set inside each municipality or local government administrative division. Then, an average value of daily precipitation from all grid-points inside the polygon that define each municipality were computed, this will be referred as precipitation data from now on.
In order to classify extreme precipitation events, an empirical distribution is generated for each municipality's historical data, then, this empirical distribution is fitted with a probability density function (PDF) using the DistFit library (Taskesen 2019) from the programming language Python. The routine uses the goodness of fit test and computes the residual sum of squares (RSS) to find the most appropriate PDF from 89 potential theoretical statistical distributions and its parameters (Fig. 1a). Once the fitting is done, Python's Scipy library is used to obtain the corresponding inverse distribution function (IDF) or quantile function as is shown in Fig. 1b (Wilks 2019). To acquire the precipitation thresholds that classify extreme precipitation levels, a quantile is needed to input into the IDF. In this work, three quantiles were used: 0.60, 0.75, and 0.90, corresponding to a medium, high, and very high levels of extreme rain in any given municipality location. This threshold definition is arbitrary for this work and they could be changed according to the local authorities definition. Then, corresponding precipitation thresholds for each of these conditions were calculated.
TCs records from 1981 to 2020 seasons, located at the CS and ETP ocean were obtained from the HURDAT project by the NOAA National Hurricane Center (Landsea and Franklin 2013), and also from the Unisys database from the repositories of the United States National Aeronautic and Space Administration. These data include TC's latitude and longitude coordinates every 3-6 h, which later was converted into a daily average position using UTC time zone.
Over the CS and ETP, individual hexagonal grids were used to divide the surrounding oceans in sectors in order to determine groups of TCs locations. The geometrical configuration of the grid was selected due to its efficiency of covering the area of analysis. When comparing a squared grid against a hexagonal grid, Elsner et al. (2012) found a 7% improvement when a hexagonal grid is used to track tropical cyclone trajectories. In this work, the efficiency of the hexagonal grid is attributed to the increase in density of each hexagon, meaning that the amount of TCs data per area covered shows higher density, contrary to a rectangular grid which covers more area, thus, less density. The former implies a more accurate computing of extreme precipitation probabilities for every hexagon. The abstract representation of the grid is a two dimensional array, one dimension correspond to longitudinal degrees and the other dimension correspond to latitudinal degrees. Each hexagon of the grid is identified by its center, which will be used throughout the document to make an accurate reference of the TCs area of study for the given examples. It should be noted that the structure of the hexagonal grid can be customized in the tool, including both: the size of the hexagon and the amount of hexagons for each dimension.
Precipitation data and TCs data were concatenated via temporal occurrence, that is, any two events occurring in the same time interval were considered in the same day. In this case, the time interval is approximately 18 h. These data will be referred as induced precipitation from now on. Next, the induced precipitation caused by TCs within a hexagon of the Fig. 1 a Burr (type III) distribution with the appropriate parameters fits the historical daily rain data for the Bocas del Toro municipality in Panama, with centroid in 82.25 • W, 9.22 • N. Vertical lines are the confidence intervals. b corresponding IDF of the distribution in a to obtain the thresholds using the quantiles 0.60, 0.75, and 0.90 as medium, high and very high events accordingly, c generalized logistic distribution and its proper parameters fits the induced precipitation in Bocas del Toro due to TCs located inside the hexagon of center 107.00 • W, 17.90 • N and d corresponding CDF of the distribution in c to compute cumulative probabilities using the thresholds of medium, high and very high events as input grid is analyzed, obtaining a frequency distribution which is then fitted with a PDF, using again the DistFit library mentioned previously (Fig. 1c). Only hexagons containing more than seven data points were taken into account to discard hexagons with a low sample-size. The data were smoothed to provide a better fit; also using the Distfit library. Summing up, induced precipitation on every municipality is fitted with a PDF for each hexagon of the grid. Once the PDF and its parameters are established, the associated cumulative distribution function (CDF) is obtained to use the previously computed precipitation thresholds for extreme precipitation levels as input for the CDF (Fig. 1d). The probability of exceeding a threshold c of extreme precipitation, is given by for observed data. If a TC position forecast is used, a conditional probability should be calculated, considering the probability of Eq. 1 and the probability of the TC predicted position (Wilks 2019). Using this procedure, probabilities for the percentiles 60, 75, and 90 defined in this work as the thresholds for medium, high and very high extreme event occurrence were obtained for every municipality due to TCs inside a hexagon within the grid. To represent the corresponding probabilities, all municipalities' centroids for a specific country were plotted in an image using the PyGMT library (Uieda et al. 2021), which implements the software Generic Mapping Tools (GMT) in Python. The representation of municipalities' centroids instead of the municipalities' surface area was chosen because countries in the region have very different municipalities sizes, and some of them would be difficult to display and distinguished. Furthermore, every country has different civil defense institutions managing decisions through distinct processes, and therefore the individual maps allow the characterization of the details at the country level. With the intention to ease readability, each figure has its own scale according to its maximum probability value.
Additionally, data of wind circulation on the ETP, Atlantic Ocean, and Central America were analyzed during the period of study. These data were obtained from the ERA5 reanalysis (Hersbach et al. 2020) database through the Copernicus Climate Change Service (Copernicus 2018), corresponding to the fifth generation of global climate and weather of the European Centre for Medium-Range Weather Forecasts (ECMWF). It consists of the zonal (u) and meridional (v) wind components above 10 m from the surface, with 2 h frequency. Temporal and spatial wind composites were made to characterize wind circulation caused by TCs within a hexagon of the grid and plotted using the library. A flowchart of the procedure previously described is given in Fig. 2.

Atlantic basin
TC average positions in a 24 h lapse and the hexagonal grid for the Atlantic Basin are showed in Fig. 3, covering mostly the Intra Americas Sea, near Central America. Most of the TCs represented in Fig. 3 occurred between May and December, in consistency with the rainy season in most of the Central American isthmus (Enfield and Alfaro 1999) and the TC season of the Atlantic basin (Pérez-Briceño et al. 2016;. Notice a few data points in the ETP, this is the case for TCs formed in the Atlantic Ocean but went through the Central American Isthmus, like Hurricane Joan-CS:Miriam-ETP in 1988 (Lawrence and Gross 1989) or Hurricane Otto in 2016 (Maldonado et al. 2020). Likewise, some data points will be present in the CS during the ETP analysis later on in the document for the same reason.
For this analysis, the tool provides 90 images for each country, corresponding to 3 images form medium, high and very high probabilities of extreme precipitation for each of the 30 hexagons analyzed of the grid in Fig. 3. The set of images shows probabilities of induced precipitation by location of the TCs. High probabilities were observed when TC's location is in latitudes and longitudes near the Gulf of Honduras and the eastern side of the Gulf of Mexico, mainly affecting the Pacific coast of Central America in concordance with Hidalgo et al. (2020) and Hernández-Castro et al. (2021). For example, TCs inside the hexagon with center 88.0 • W and 20.99 • N, observed in the wind response in Fig. 4, produce the probabilities of extreme precipitation occurrence shown in Fig. 5 for Costa Rica. Similar figures for other countries in the region are found in  the Supplementary Information (Figs. S 1 − 5 ). All probabilities of municipalities near the Pacific coast range from 30 to 43% in Costa Rica for very high events (Fig. 5c), supporting the observation that indirect effects in Costa Rica are mainly located in the opposite coast of the location of the TC. In Honduras, Fig. 6, similar probabilities extended further, across the country to the Caribbean coast, as there are direct and indirect effects associated with presence of the low-pressure system. In addition, the North Pacific region of Costa Rica has the highest probabilities of extreme precipitation. This territory could be a highly affected area, although the TCs are located far away. Those results shows the importance of indirect effects and the relevance of a better understanding of this kind of phenomena. Note that probabilities for medium events are higher than high and very high events as expected, and the most affected municipalities kept the top probabilities, but some municipalities' probabilities decreases abruptly because of its thresholds, which can vary greatly from medium to high and very high events. This means that municipalities with common heavy rain events (from 1981 to 2020) will have higher precipitation thresholds, thus, probabilities for very high events are lower. For example municipalities a bit east from the center of Honduras maintained the highest probabilities among all events (Fig. 6), while municipalities on the northern side that were on the top probabilities for medium events (Fig. 6a) did not prevail for very high events (Fig. 6c).
In general terms, the above results follow the same tendency explained by Hidalgo et al. (2020). TCs are low pressure systems, causing oceanic warm and high humidity air flowing to the TC, showing a cyclonic spiral-like form. Because the area of study relies in the North Hemisphere, this flow is anticlockwise. Looking back to Fig. 4, the previous pattern described is observed and most importantly, the overall wind direction over the Pacific slope due to the TCs location, as Peña and Douglas (2002) explained previously. On the Pacific coast, it seems that the angle of incidence of the wind direction with respect to the tangential line of the coast might be an indicative factor of the resulting extreme precipitation probabilities, getting higher probabilities when the angle of incidence is closer to a perpendicular angle.
Based on the previous findings, the location of TCs has a great impact on wind direction and significantly determines indirect effects in precipitation. Humidity transportation by the induced air circulation over the isthmus might be the main cause for high probabilities of extreme precipitation on the Central American Pacific slope, following a similar mechanism explained by Durán-Quesada et al. (2017). Low level westerly winds presented in Fig. 4 are locally known as synoptic westerlies or oestes sinópticos in Spanish (Muñoz et al. 2002), and are associated with the ocurrence of temporales, which are periods of one or several days of continuous stratiform rain (Amador et al. 2006).

Pacific basin
The hexagonal grid implemented on the Eastern Pacific Ocean and TCs' daily average position are plotted in Fig. 7. There is a small density of TCs values near Central America, but it increases rapidly further away from the coast. Positions in the Gulf of Mexico and CS are for those rare cases in which the TC crossed the isthmus from ETP, like Tropical Storm Alma-ETP:Arthur-CS in 2008 (Blake and Pasch 2010) and the recent case of Tropical Storm Amanda-ETP:Cristobal-GM in 2020 (Amador et al. 2021). As for the Atlantic Basin, most of the TCs represented in Fig. 7 occurred also between May and December, in concordance with most of the the isthmus rains and the ETP hurricane season (Enfield and Alfaro 1999;Farfán et al. 2013). A total of 69 images per country were obtained, containing the computed probabilities for 23 hexagons of the grid. Contrary to results on the Atlantic Basin, probabilities due to TCs located on the Pacific Ocean were lower and mainly restricted to four countries in northern Central America: Guatemala, El Salvador, Honduras, and Nicaragua. Figure 8 displays the hexagon with center 89.00 • W, 12.70 • N. This is a case of possible direct effects of TCs, associated with its close proximity to El Salvador. Using the developed tool, probabilities of up to 70% or higher are observed in Honduras, Nicaragua, and El Salvador for very high events and even higher for medium and high events (for example, see probabilities of El Salvador, Honduras, and Nicaragua in Figs. 9, 10 and S9, respectively). For El Salvador, high probabilities of medium and high events (Figs. 9a,b) are dominant all over the country, but very high events peaks at the eastern side (Fig. 9c). In Honduras, medium and high events (Figs. 10a, b) have a similar distribution and probability values, nevertheless, it is clear in Figure 10c that the southwestern part of Honduras could be the most affected area. Based on those results, regions near the Gulf of Fonseca have the highest probabilities of extreme precipitation due to TCs inside the hexagon showed in Fig. 8. Probabilities in Guatemala are around the 40% for very high events and just a small sector in the southwestern side of the country (see Fig. S8c). However, TCs in this location also generates high probabilities of extreme precipitation in Costa Rica and Panama (Figs. S7 and S10).
Due to the anti-cyclonic rotation of the TCs in the Northern Hemisphere, the presence of the low-pressure systems in the ETP basin, produces atmospheric circulations that favor the entrance of humidity from the Pacific Ocean to that coast of Central America and therefore, an important amount of indirect effects are located in that slope as well, associated also with temporales by the induced synoptic westerlies (Muñoz et al. 2002;Amador et al. 2006). Humidity transport from the Pacific plays also an important role in this season as Durán-Quesada et al. (2017) explained.
Indirect effects in Central America are less common for the case of the ETP when they compare with those of the CS, as the trajectories of the TCs in ETP basin usually causes the systems to move offshore from the west coast of the continent, causing less indirect effects. However, impacts associated with TC occurrences in this basin are extremely important for Mexico (Farfán et al. 2013).

Conclusions
Every year, direct and indirect impacts are reported in Central America due to occurrences of TC in the ETP and CS, affecting multiple socioeconomic sectors and associated also with disasters reports and even fatalities on different locations (Amador et al. 2021;Pérez-Briceño et al. 2016).
Direct impacts are associated with TC positions near the isthmus or TC landings. They are more common in the northern countries, from Nicaragua to Belize and Guatemala, and the occurrences of extreme events associated with TC in the CS are higher when compare with those in the ETP.
Indirect effects occur mainly on the Pacific slope of countries in southern Central America, i.e., Costa Rica and Panama, associated with TC positions around the Gulf of Honduras ), but some less frequent positions of TC in the ETP can produce also extreme events associated also with indirect effects. These positions in both oceans surrounding the isthmus, induce low level westerly winds from the ETP to the CS (e.g., Figs. 4 and 8 ), triggering the transport of warm and humid air that interacts with the Central American mountain chain and stratiform rains are observed on the Pacific slope. These events can persist for several days and are locally known as temporales in Spanish.
Previous statements were supported using the tool presented and developed in the programming language Python for this study. All the libraries implemented are available for free and relatively easy to install. In addition, thanks to the flexibility of the algorithm it can be used in any region if the data format required to run the script is satisfied. The computational demands to run the tool are low, but because of the nature of the algorithm, that is, evaluating 89 theoretical distributions to fit the data, running time may extend from 1 3 hours to days depending mainly on the amount of: hexagons of the grid and precipitation stations/spatial sub-division. Although the logic behind this work relies on probability distributions, a well know subject, it is due to the computational processing that this research was accomplished.
The statistical tool developed in this work, estimates the extreme rainfall probability, in any local Central American government political division, given a TC position (observed or forecasted) in the CS or in the ETP. This tool shows extreme precipitation probabilities that are consistent with atmospheric circulation patters during the events and with impact reports from other studies. Among the flexibility that this kind of approach can offer to the local emergency authorities is that gauge station or grid precipitation of daily data can be used, the size of the hexagon in latitude and longitude can be modified and a different time series seasons of TC and rain could be chosen. Notice that when data sets and domains are selected or fixed by users, it is necessary to run the code of the tool just only in one occasion to obtain all the maps for the three probability thresholds of extreme precipitation for all countries and hexagons. This maps could be archive and consulted by emergency authorities when the National Weather Service alert about a TC position (observed or forecasted) near Central America. The tool can be used with others analyses by emergency officials to anticipate the locations where alerts of extreme weather must be issued to prevent human life's lost, because it also demonstrated the importance of preparedness for direct and indirect effects.