## 2 Materials and Methods
### Data  
The Institute of Hydrology, Meteorology, and Weather Studies (IDEAM by its Spanish acronym) is a public entity of the Colombian government whose functions include monitoring the country's climatic conditions [46]. To carry out this monitoring, it has around nine thousand climate stations distributed in different areas of the Colombian territory. IDEAM, in its databases (publicly available), has information on the accumulated monthly precipitation levels (PTPM) of all stations between 2010 and 2019. We chose this window period as it was the most balanced available data from IDEAM that included the coffee crop zones. To diminish the basis risk associated with the difference between the data recording and the crop sites, we selected the weather stations near coffee-growing regions. As a result, we obtained data consisting of 163 meteorological stations whose altitude is between 1000 and 1890 m with a median of 1513 m above sea level. The distribution of altitudes is presented below (Figure 2). This graph shows that most stations are close to 1750 m above sea level, and there are fewer stations with an altitude of less than 1400 m.  
In Colombia, there are two seasons for coffee cultivation, dry and wet, and four productive zones in the country: eastern north, central north, central south, and south [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47]. According to the sample data, the mean monthly rainfall in the dry season is 131 PTPM, while in the wet season, the mean is 168 PTPM. In addition, a boxplot shows that the dispersion of the data is similar between the two seasons, and in the case of the dry season, the data are more asymmetric (Figure 3). Figure 1: Methodology applied to derive payout rates for each principal component in precipitation index insurance. Source: authors. Figure 2: Frequency histogram of altitude for the 163 selected stations. Source: authors’ processing. The production of coffee crops comprises four stages: the first two stages II and II) are known as the first-growing and flowering phases. In these stages, there is a slow but consistent demand for water. The following two stages are known as the second-growing and filling stages, where the demand for water rises uniformly [48]. The months in which these stages take place vary according to the location of the productive zones in the country and their weather seasons (Figure 4). As stages I and II are highly water sensitive, throughout these stages, ongoing index insurance programs, such as Cafe Seguro, protect against flooding. Whereas during stages III and IV, which comprise the second-growing and filling phases, insurance programs protect against drought. In these programs, the payouts are tailored to the deficit or excess of precipitation [33]. Multiple factors influence coffee quality. Among the most relevant are the amount and distribution of rain, which allows for homogeneous growing stages and, as a result, higher-quality coffee. It is during the growing stage that coffee needs intense but acceptable rainfall. Temperature is another significant factor. Due to climate change, producers have had to move their crops to different altitudes, usually higher [49]. In most of the coffee-producing regions of Colombia, the preferred method for farmers to irrigate their crops is rain; when rainfall levels are adequate, the coffee is of a better quality than that irrigated artificially. According to a study by [PERSON] [48], \"Artificial watering is challenging and expensive; it also requires expert knowledge of natural rainfall levels, where excessive  
Figure 4: Weather seasons in Colombia per region. Source: Cenicafé, 2016 [47]. Note: eastern: Santander and eastern Cundinamarca; central north: Caldas, Antioquia, Risaralda, northern Tolima, and northern Cundinamarca; central south: Quindio, Tolima, Valle Cauca, and northern Hula; south: Cauca, Narino, and Hula.