Selection of annual precipitation records

Based on the Excel file of the climatological information available in the state of San Luis Potosí, provided to the author by the local office of the National Water Commission (CONAGUA), the chronological series of total monthly precipitation that did not have missing years and had extensive records were selected. Given these restrictions, 32 weather stations were identified, with a number of years of records, ranging from 45 to 55 data. Their names and general characteristics are shown in Table 1 and their geographical location in the state is shown in Figure 1.

Figure 1 Geographic location of the 32 weather stations processed, from the state of San Luis Potosí, Mexico. 

For each record and based on their monthly values, the medians of the sample were obtained, with which the few incomplete years (generally less than three) were completed. Annual precipitation (AP) values were then obtained. The median was adopted because it is not affected by the extreme values in the series. The arithmetic mean of the AP values is the mean annual precipitation (MAP), which is the basic parameter for classifying the 32 records to be processed, whose statistical values are shown in Table 1 in order of increasing MAP size.

Statistical tests applied

In a study about the occurrence of annual meteorological droughts, the statistical tests should look for changes in the mean, which return to the non-homogenous AP record. It is also important to identify trends in the series and look for their physical causes. In a study of droughts, the occurrence of persistence or autocorrelation in the record does not make it difficult or inconvenient to process, since that component is an intrinsic part of the chronological series.

In this study of meteorological droughts, seven statistical tests were applied. These included one general test against deterministic un-specified components (Von Neumann test) and six specific tests: two of persistence (Anderson and Sneyers), two of trends (Kendall and Spearman), one of change in the mean (Cramer) and one of variability (Bartlett). These tests can be consulted in WMO (1971), ^{Machiwal and Jha (2008)}, and ^{Campos-Aranda (2015)}.

Climatic spectrum

^{Ponce, Pandey, and Ercan (2000}) classified climates into eight types, based exclusively on the quotient of mean annual precipitation (MAP) and annual global terrestrial precipitation (AGTP). To estimate the latter, they indicated that the amount of moisture stored in the atmosphere is a function of latitude and climate, ranging from 2 to 15 millimeters in polar and arid regions and 45 to 50 mm in humid regions. An average value of 24 mm was adopted for the estimation of the AGTP, also considering that the atmospheric moisture is recycled every 11 days on average, which is why 33 cycles occur per year, and then the AGTP is on the order of the 800 mm. The quotient of MAP and AGTP is designated by CP, and the eight types of climates and their numerical limits are indicated in Figure 2.

^{Ponce et al. (2000}) also established limits for the quotient (CE) between mean annual potential evapotranspiration (ETp) and MAP for the eight groups of climates, and defined these exclusively based on the MAP, as shown in Figure 2. Moreover, they indicated the durations of the wet season (DWS) in months. Based on the MAP value in Table 1, the climatic group of each processed weather station is indicated in the final column.

Figure 2 Groups on the climatic spectrum and their classification limits (^{Ponce et al., 2000}; ^{Pandey & Ramasastri, 2001}; ^{Pandey & Ramasastri, 2002}). 

Basic technique for drought detection

According to ^{Pandey and Ramasastri (2001}, ²⁰⁰²⁾, in a year when precipitation (AP) is less than 75% of the mean annual precipitation (MAP), a drought has occurred. Then, L1 = 0.75·MAP, establishes the upper limit of moderate droughts and the lower one will be L2 = 0.625·MAP. A final limit, L3 = 0.375·MAP, defines the lower threshold of severe droughts and is also the upper limit of extreme droughts. This tries to fulfill the drought conditions occurring with AP < L1 and with their types, which according to ^{Ponce et al. (2000)} establish that moderate droughts have an AP/MAP = 0.75, the severe ones an AP/MAP = 0.50, and the extreme ones an AP/MAP = 0.25.

Indicators of occurrence and severity of droughts

The number of annual droughts (NS) (AP< L1) divided by the size (n) of the AP series and expressed as a percentage, is its probability of occurrence (%O), since it is the quotient between the number of favorable cases to the number of possible cases, that is:

^{Pandey and Ramasastri (2001}, ²⁰⁰²⁾ used the reciprocal (n/NS) and designated that the average return period (ARP) of droughts, in years. The indicator of drought severity is its average intensity (AI), defined (^{Ponce et al., 2000}) as the average relative deficit, that is:

Results of statistical tests

Ten AP records did not result fully homogeneous. In the Reforma and Ciudad del Maíz weather stations, excessive variability was detected with the Bartlett test, given its extreme maximum value. Nine AP records were non-random, according to the Von Neumann test, and with persistence in the respective tests. These were from the stations: Vanegas, Col. Álvaro Obregón, Ciudad del Maíz, Santa Rosa, El Pujal, Micos, Ballesmi, Santa Cruz, and Tancuilín. Lastly, a downward trend was detected only in the Ciudad del Maíz station, with no change in the mean, according to Cramer's test. There was no evidence of change in mean or loss of homogeneity, except for persistence, and therefore the 32 AP records were considered acceptable for the study of annual meteorological droughts.

Occurrence of droughts (number and average intensity per climate)

The following assertions, in general, were formulated based on the median values of the results, shown in Table 2. In the arid climate, the representative percentage of occurrences (%O) was 26.9, with an average intensity (AI) of 0.446. In the semi-arid climate the %O dropped to 22.2 with an AI of 0.379. In the sub-humid climate, both indicators fell, to 18.5 and 0.336, respectively. Lastly, in the humid climate, the %O decreased to 16.4, but the AI slightly increased to 0.344.

Extreme droughts occur only in arid and semi-arid climates. In the arid climate, the %O and its AI for moderate, severe, and extreme droughts were: 41.2 with 0.307, 50.0 with 0.483, and 11.8 with 0.736, respectively. These same indicators in the semi-arid climate were: 58.3 with 0.308, 36.4 with 0.472, and 8.3 with 0.678, respectively. Lastly, in the sub-humid climate the %O and its AI for moderate and severe droughts were: 75.0 with 0.292 and 25.0 with 0.429, respectively. And for the humid climate: 70.0 with 0.310 and 30.0 with 0.405, respectively.

The %O of droughts for each climate were equivalent to the following average return periods: in the arid climate ARP = 3.8 years; in the semi-arid ARP = 4.3 years; in the sub-humid ARP = 5.5 years; and finally in the humid climate ARP = 6.2 years. ^{Pandey and Ramasastri (2001}, ²⁰⁰²⁾ reported that for India, by processing 95 weather stations with records ranging from 65 to 89 years, in the arid climate the ARP ranged from 2 to 3 years, in the semi-arid climate the ARP ranged from 3 to 5 years, and in the sub-humid climate it ranged from 5 to 8 years. Thus, the results for the occurrence of droughts obtained in the state of San Luis Potosí, Mexico, coincide approximately with those obtained in India.

It was observed that the ARP for the humid climate of San Luis Potosí, Mexico fell in the range reported by ^{Pandey and Ramasastri (2001}, ²⁰⁰²⁾ for the sub-humid climate in India. Nevertheless, it should be greater. This anomaly is probably due to the more regular precipitation in humid climates in India, caused by the monsoon.

Evaluation of the severity of droughts with the MAP

In Figure 3, the 32 average intensity (AI) values of the droughts, taken from column 6 of Table 2, were plotted on the vertical axis against their respective MAP on the horizontal axis, in millimeters, obtained from column 10 of Table 1. As can be seen, three points (stations 6, 8, and 13) deviate from the general hyperbolic type of behavior, and therefore they were removed. Those points correspond to the Ojo Caliente, El Peaje, and Nogal Oscuro weather stations.

Figure 3 Evolution of the average intensity (AI) of the droughts with the mean annual precipitation (MAP) in the 32 processed weather stations in the state of San Luis Potosí, México. 

The least-squares fitting of residuals results in the equation shown in Figure 3, whose linear correlation coefficient was 0.8947, with a standard error of the estimate of 0.0696. The hyperbolic curve is considered representative of the MAP range of 300 to 1 400 millimeters, and therefore its ends are represented by a dotted line.

Occurrence of droughts (types per year)

Table 3a indicates the occurrence of each type of drought, per year, during the first half of the analysis period (years 1961 to 1988), in the 32 processed weather stations. Table 3b shows the occurrences of the types of droughts in the second half of the period (years 1989 to 2015). It is notable that there are a total of 160 drought occurrences in the first period, covering 28 years, and 188 in the second half, which covers 27 years. Therefore, it is concluded from this analysis that the occurrence of droughts has increased over recent decades in the state of San Luis Potosí, Mexico. Having processed 32 weather stations, the years with 20 drought occurrences corresponded to years with widespread drought in the state, primarily 1980, 1982 and 2011, and to a lesser extent to the years 1977, 1979, 1996, 2000, and 2006.

Meanwhile, the years with widespread droughts in the arid and semi-arid climates of the Potosino high plains and central zone were: 1974, 1983, 1989, 1999, and 2011. Lastly, the years with widespread droughts in the sub-humid and humid climates, in the Huasteca region, were: 1962, 1963, 1980, 1982, 1997, 2002, and 2006.