The natural climatic variability of the Earth has always existed. From this perspective, climate change or global warming is not new since it dates from geological times. Paleoclimatology gives accounts of this process by means of diverse techniques. One technique is the impressions created by the climatic factors in remote times by means of the proxies like diatoms, foraminifers, corals, ice and of some sedimentary rock cores, tree rings [1] and lake, lagoon and wetlands sediments [2]. During the last 5000 years the Earth has had strong oscillations of heating and cooling [1] generated by natural processes; however, at present the most accepted hypothesis about the climatic instability of the Earth is that global warming is due to anthropogenic actions. The objective is to analyze the evidence of climate change in the Comitan valley and point out the methodological errors that are committed. It was studied of 54 and 30 years of the weather stations 07205 Comitan and 07374 La Esperanza, located within the Grijalva-Usumacinta, Mexico hydrological region (HR) in the context of natural or anthropogenic climatic instability.

The region to which the study area (SA) belongs is temperate and is located at an approximate altitude of 1550 mamsl, with average temperatures that vary between 16˚C and 18˚C. Precipitation is from 2000 to 2500 mm/year. The orography is abrupt, and together with the climate allows for the existence of diverse types of forests (conifers, mountain mesophiles and oaks) and induced vegetation [3]. The SA is a flat agricultural valley located between the cities of Comitan (16˚10'43''N and 92˚04'20''W) and La Esperanza (16˚9'15''N and 91˚52'5''W), Chiapas, Mexico. In this valley there are two standard weather stations, La Esperanza (07374) and Comitan (07205), both within the Technified Rainfed Agricultural District 011 (DDT 011, by its Spanish acronym) which has an approximate area of 30,000 hectares (Figure 1). The area of influence of both stations is approximately 12,000 hectares, due to the orography of the SA. Within the limits of DTT 011, anthropogenic alteration has modified the natural vegetation and the forest has been deforested and replaced by agricultural crops [4] by the slow but permanent

urbanization in the last 5 decades in this agricultural valley. Currently in the SA there is a wide variety of secondary vegetation and agricultural crops.

There are not many studies related to climatic change in the Comitan valley. Although the results presented by [5] are the product of global models, a mesoscale study by [6] was found that includes not only the SA but also the 07205 Comitan weather station. Alonso [6] studied the climate change indices in the Rio Grande watershed of Chiapas, specifically the sub-watershed RD30Gl-Río Grande Comitan that has an area of 6212.51 km². The indices were calculated from “...the series of observed data of temperatures (maximum and minimum) and precipitation of a period of more than 50 years in three weather stations of which two had a statistically significant tendency in six indexes related to air temperature; both stations show an increasing trend in summer days (SU25), extreme maximum temperature (TXx), frequency of hot days (Tx90p) and daytime temperature range (DTR). Alonso [6] concludes in the study that “...the minimum and maximum temperatures have a significant upward trend at stations 07205 (Comitan) and 07104 (Las Margaritas), the number of days in a year when the maximum temperature is higher than 25˚C, has had an increase of 2743 and 2816 days/year, the maximum annual value of the maximum daily temperature has increased by 0.047˚C/year and 0.109˚C/year, and an annual average of the difference between maximum temperature and minimum temperature increments of 0.028˚C/year and 0.054˚C/year”. However, the study is weak. The methodology used and its conclusions are hasty and lack scientific rigor for the following reasons: 1) It is not possible to obtain surface atmospheric temperature trends of only three weather stations for such a large area as the sub-watershed RD30Gl-Río Grande Comitan. It is an unacceptable generalization; 2) The climate of the sub-basin is very varied due to its orography, with heights above sea level ranging from 160 m to 2614 m, therefore there are multiple micro-climates in the study area generated by abrupt hills, the presence of large bodies of water such as lakes, rivers, and streams, and there are valleys, canyons and large areas in the process of deforestation; 3) According to [7] a network of dispersed weather stations is insufficient for the study of the maximum and minimum temperature of an area. A very dense network is needed to examine the climatology of precipitation, wind, frost and fog, especially in regions of steep topography [7] such as the sub-watershed RD30Gl-Río Grande Comitan; 4) The influence of a weather station to measure the air temperature in many areas of the sub-watershed RD30Gl-Río Grande Comitan, does not go beyond 10 km which is equivalent to an area of 78.5 km², as in the case of the station 07295 Comitan; 5) According to [8] the horizontal meteorological scale of the [6] should be the mesoscale, however only three weather stations were studied (at least one of them with local meteorological scale scopes) to obtain their conclusions; 6) The methodology of [6] is enunciative but not demonstrative, because it does not indicate the percentage of filled data or its temporality. The method used to homogenize the series is also enunciated and the tests “t” and “F” are only used alone without taking into account one of the most relevant tests: The Standard Normal Homogeneity Test (SNHT); 7) On the other hand, within the methodology described in [6] there is no description of what percentage of data were missing from the studied time series and it does not state or describe the method used to fill in missing data; 8) It tacitly conveys the idea that the maximum and minimum temperatures of the three stations are a homogeneous time series, however at least one of them is not. Weather station 07205 data is heterogeneous, that is, the maximum and minimum temperatures have significant changes due to alterations in the environment where it is located as demonstrated in [9]; 9) The results and conclusions of [6] change if the data of the 07205 Comitan weather station is homogenized; 10) Finally, the aforementioned document states that the minimum and maximum temperatures show a significant upward trend that shows a coincidence with what was predicted for the state of Chiapas as reported by [5]. This is a wrong argument for the meteorological scales: the results presented in [5] are on a synoptic scale and the stations which were analyzed are on a local scale.

In this study, simple linear regression was used to detect climate change trends in the Comitan and La Esperanza weather stations. Simple linear regressions are shown in Figure 2 and Figure 3. Figure 2 of the Comitan weather station shows an increase in temperature, while Figure 3 La Esperanza shows an increase t_max but without significance, nevertheless the t_min decreases. However, the simple linear regression does not represent any statistical analysis, for these reasons Spearman’s rho and Mann Kendall test were used.

Spearman’s rho (SR). The SR test is a simple method with uniform power for

linear and non-linear trends and is commonly used to verify the absence of trends [18] [19]. In this test, the null hypothesis (H₀) is that all the data in the time series are independent and identically distributed, while the alternative hypothesis (H₁) is that increasing or decreasing trends exist [20]. The SR test statistic D and the standardized test statistic Z_SR are expressed as follows [21] [22]:

D = 1 − 6 ∑ i = 1 n ( R i − i ) 2 n ( n 2 − 1 ) (6)

Z S R = D n − 2 1 − D 2 (7)

β = Median [ X j − X i j − 1 ] for all i < j (8)

where R_i is the rank of its observation X_i in the time series and n is the length of the time series. Positive values of Z_SR indicate upward trends, while negative Z_SR indicates downward trends in the time series. When Z S R > t n − 2 , 1 − α ; the null hypothesis is rejected and a significant trend exists in the time series. t n − 2 , 1 − α / 2 is the critical value of t from the t-student table, for 5% significant level [22]. Spearman’s rho correlation values are shown in Table 7 [21].

Table 7 shows a moderate correlation for the Comitan weather station. The rest of the variables have weak and inappropriate correlation as can be seen in Table 8. For that reason, the coefficient Spearman’s rho was not taken into account in this investigation.

The Mann-Kendall test (MKT). [23] considers that the MKT test is the most appropriate method to analyze trends in climatological series. The MKT is a rank nonparametric test that was developed by [24] and [25], and it is superior for detecting linear or non-linear trends. In this test, the null (H₀) and alternative hypotheses (H₁) are equal to the non-existence and existence of a trend in the time series of the observational data, respectively. The related equations for calculating the MKT statistic S and the standardized test statistic Z_MK are as follows [22] [26] (Table 9):

S = ∑ i = 1 n − 1 ∑ j = i + 1 n sgn ( X j − X 1 )

sgn ( X j − X i ) = { + 1     if   ( X j − X i ) > 0 0           if   ( X j − X i ) = 0 − 1     if   ( X j − X i ) < 0 (10)

V a r ( S ) = 1 18 [ n ( n − 1 ) ( 2 n + 5 ) − ∑ p = 1 q t p ( t p − 1 ) ( 2 t p + 5 ) ]

Z M K = { S − 1 V a r ( S )       if   S > 0 0                             if   S = 0 S + 1 V a r ( S )       if   S < 0 (12)

where X_i and X_j are the sequential data values of the time series in the years i and j, n is the length of the time series, t_p is the number of ties for the pth value, and q is the number of tied values. Positive values of Z_MK indicate increasing trends, while negative Z_MK values indicate decreasing trends in the time series. When Z_MK > Z_1−α/2, the null hypothesis is rejected and a significant trend exists in the time series. Z_1−α/2 is the critical value of Z from the standard normal table, for 5% significant level the value of Z_1−α/2 is 1.96 [22].

In Figures 4-7 you can see the trends with the MKT method.

According to Figure 4 and Figure 5 a trend of temperature increase is observed at the Comitan weather station. The MKS trend test revealed an increase in the t_max and t_min. While the t_max no statistically significant, the t_min is statistically significant. According to Figure 6 and Figure 7 a trend of temperature increase and decrease are observed at the La Esperanza weather station. The MKS trend test revealed an increase in the t_max. While the t_max no statistically significant, thet_min is statistically significant. The time series of Comitan y La Esperanza weather stations were significant at the 5% significant level.

The maximum and minimum temperature series, t_max and t_min, were studied for weather stations 07205 Comitan and 07374 La Esperanza located in the DTT 011 Margaritas-Comitan in the HR Grijalva-Usumacinta which have a registry of 54 and 30 years, respectively. Because the series had 2.07% and 19.04% of missing information, they were filled with the WS method. Homogeneity was analyzed with the SNHT method. Due to its heterogeneity, it was homogenized with climatol. The objective was to analyze the evidence of climate change in the Valle of Comitan with three methods: simple linear regression, Spearman’s rho and Mann Kendall test were used. The Mann-Kendal test method confirmed the warming trend at the Comitan weather station for both variables with Z_MK statistic values equal to 1.57 (statistically not significant) and 4.64 (statistically significant). A trend of temperature increase and decrease is observed at the La Esperanza weather station. The MKT trend revealed an increase in the t_max at Z_MK = 1.16, nevertheless, this value is statistically not significant, while the Man Kendal test trend revealed a decrease in the main at Z_MK = −2.27 which is statistically significant. These results indicate that the warming trend in the Comitan weather station is produced by the heat islands, in a city of 150,000 inhabitants. While in the Esperanza weather station (in a field area), the trend is negative (the decrease of temperature), for a significance level α = 0.05.

María Concepción Villagran Alegria, Ricardo Fidel García Sánchez, José Enrique Ruiz Sarmiento and José Eduardo Solórzano Jiménez, student of the Faculty of Engineering of the Autonomous University of Chiapas, who carried out the depuration of the meteorological data, filled in the time series and supported this investigation by carry out the statistical studies. Special thanks to Michael J. Greces for translating this paper.

The authors declare no conflicts of interest regarding the publication of this paper.

Mundo-Molina, M., Godinez-Gutiérrez, E.A., Pérez-Díaz, J.L. and Hernández-Cruz, D. (2021) Detecting Climate Change in Using Extreme Data from Two Surface Weather Stations: Case Study Valle of Comitan and La Esperanza, Chiapas, Mexico. Journal of Water Resource and Protection, 13, 1061-1075. https://doi.org/10.4236/jwarp.2021.1312057