Introduction

Climate is a major factor for the activities that take place in the communities ( ^{Charlton and Arnell, 2011}; Murray et al, 2013). Scientific evidence has shown that climate change begins to manifest in various forms, including the intensity of rainfall and increased temperature and the sea level by the melting ofglaciers (^{Dunn et al, 2012}; ^{Koutroulis et al, 2013}). When talking about climate change, temperature and precipitation are the most important components with alterations in behaviour patterns (^{Chaouche et al, 2010}). The impacts of climate change can be reflected in changes in ecosystems by altering the diversity of plants and animals alike (^{Ostendorf et al., 2001}; ^{Gian-Reto et al, 2002}; ^{Haines et al, 2006}; ^{Heubes et al, 2013} ).

In addition, changes in temperature can also cause adverse effects on human health, higher numbers may result in heat waves causing illness and even death in susceptible communities (^{Paulin and Xiaogang, 2005}; ^{Onoz and Bayazit, 2012}). Increasing trends in precipitation may also result in an increase in the frequency of floods negatively impacting water quality (^{Dore, 2005}; ^{Lensing and Wise 2007}; ^{Arnell et al., 2011}; ^{Lal, 2013}).

There have been a large number of investigations related to climate change in developed countries which have experienced with supporting tools for the timely knowledge of certain events. On the other hand, it is important to note that, the developing countries are the ones that seem most affected by climate change globally. The affect has been observed in a broad context that has contributed to social changes (^{Gasper et al, 2011}; ^{Brugger and Crimmins, 2013}). The effects of climate change on water resources in the United States have been studied by several authors. ^{McBean and Motiee (2008)} used 70 year old databases and analysed the trends in precipitation, temperature and flows in the Great Lakes of North America, using regression and statistics by Mann-Kendall. The results showed statistically significant increases in precipitation in the 1930-2000 period.

In Mexico, ^{De La Mora-Orozco et al. (2011)} estimated the effect of climate change in the concentration of dissolved oxygen (DO) in the Lake Chapala. Based on data from 1961-2003, 2031-2014 and projections for 2050-2060 performed using the model of Thomas Muller and variables including altitude, coefficient of reaeration, photosynthesis and respiration. OD results for 1961-2003 were homogeneous, but the model predicts that the OD at the Lake Chapala will be influenced by the temperature gradient and water circulation patterns in Lake Chapala. However, the model does not predict anoxic conditions in the lake for the simulated years. In addition, ^{Martínez-Austria (2007)} mentioned that water resources in Mexico are already under great pressure mainly due to population growth, social and economic development that have generated an increased demand.

Changes in climate can cause a significant negative effect on the quality and quantity ofwater (^{Moghaddasi and Mushtaq, 2011}; ^{Luo et al, 2013}) and surface water bodies such as the dam La Vega are not exempt from the negative impacts that these changes may cause. As mentioned, the study of climate change impacts on water resources is of significant importance. This work focused on determining the annual trends in temperature and precipitation over a period of 5 to determine the impact of climate change on water resources ofthe dam La Vega in Teuchitlán Jalisco, Mexico.

Methodology

Study área

The dam La Vega is located in the municipality of Teuchitlán, in the centre of the State of Jalisco, in the geographical coordinates 20° 33' 50' and 20° 47' 40' north latitude; and 103° 47' 30' to 103° 51' 20' west longitude, at an elevation of1 300 meters. Bordering at the north with the municipalities, Tequila and Amatitán; south, Tala, Ameca and San Martín Hidalgo; east, Tala andAmatitán; and west, and Ahualulco de Mercado andAmeca, built for irrigation and flood control between 1952 and 1956. The total capacity of the vessel is 44 mm³ and the associated reservoir area is 1 950 hectares. It is vital that the dam service grants to agricultural producers in the area, as the main activity in the communities surrounding the reservoir is agriculture, especially the cultivation of sugarcane, maize and wheat (^{De La Mora-Orozco et al, 2013}). The producers of sugarcane of the municipalities Teuchitlán, Ahualulco de mercado and Ameca are the main users; however, the producers of Ameca in the lower part of the dam occupy the largest area of cultivation of about 10 000 hectares, the main users and beneficiaries of the reservoir, Figure 1 shows the runoff of the basin of the dam The Vega.

Figure 1 Runoff area of the basin of the dam La Vega. 

Data analysis

All the parameters were subjected to the following tests: statistical analysis and Mann-Kendall analysis. In the statistical analysis the mean, median, standard deviation and variance were determined, the parameters are listed below:

Arithmetic mean: the measure of central trend better known is the arithmetic mean. The average is obtained by summing all the observations divided by the number of n observations determined as follows:

)1

Median: The median of a finite set of values is the value that divides the set into two equal parts, so that the number of larger than or equal to the median value equals the number less than or equal to this value. The median of the data set is (n+1)/2-th observation, when the observations have been ordered.

Variance: when the values of a set of observations are located near the middle, the dispersion is less than when they are scattered.Accordingly, the dispersion can be measured based on the scattering of the values around their mean.

)2

Standard deviation: is a measurement of the dispersion of data, for obtain the dispersion measurement, the square root ofthe variance is obtained by the following equation:

)3

Coefficient of variation: the standard deviation is useful as a measure of variation in a given dataset. The coefficient of variation is the standard deviation expressed as a percentage of the average. The equation is:

)4

Evaporation calculation in the dam La Vega

Since we have no precise data ofthe tributaries to the dam La Vega to determine the evaporation by mass balance, is was determined using actual temperature data and calculation of solar radiation and relative humidity. Evaporation was determined using the ^{Penman equation (1963)} shown below:

)5

Where: H= solar radiation (cal/cm²); for Ea,^{Penman (1963)} developed an empirical relationship.

Where: Ea=0.47 (0.5 + 0.01 u2) (ea'- (mm/day); u2= wind speed (mi/day); e2= vapour pressure of the water surface (mb); Δ/ γ = is in function of temperature.

Statistical method of Mann-Kendall

The statistical method of Mann Kendall is widely used for the analysis of climatic trends and hydrological time series (^{Chaouche et al, 2010}). Some advantages of using this method is that it is a non-parametric method and therefore requires data normally distributed.Another advantage is that it has low sensitivity to shocks due to inhomogeneous data (^{Trajkovic and Gocic, 2013}). Another advantage is that any undetected data is included giving a common value lower than the lowest measured value in the data series (^{Ay and Kisi, 2014}). According to this method, the null hypothesis H0 assumes no trend and it is tested against the alternative hypothesis Hi, assuming a tendency (^{Ehsanzadeh et al.,2013}).

The procedure for the analysis of Mann Kendall consider time series of a number n of data sites and T_i and T_j as two subgroups where:

i= 1, 2, 3, n-1 and j= i + 1, i + 2, i + 3,..., n each data of T_i is used as a reference point and is compared with all points Tj as:

)6

The Mann-Kendall statistic (S) is given by:

)7

A very high positive value of S is an indication of an increasing trend, and a very low value is indicative of a downward trend. However, it is necessary to calculate the probability associated with S ofn number ofsamples in order to quantify statistically significant trends (^{Hamed, 2008}).

The variance of S and o was calculated with the following equation:

)8

Where=n corresponds to one data, g is the number ofunified groups (a unified group is a group of data with the same value); and t_p is the number of data in the p^th group.

In the sequence (2,3, not detected, 3, not detected, 3), then n= 6, g= 2, t= 2 for the undetected, and t= 3 for the 3 values unified.

The normalized analysis of Zs was calculated as follows:

)9

The statistical analysis Z_s is used as a measure ofsignificance to this trend. In fact, the statistical analysis is used to analyse the null hypothesis Ho; there is no trend in the data. If Zs is higher than Z_a/2, where a represents the chosen significance level (typically 5% at Z₀₀₂₅= 1.96), then the hypothesis is null, this means that the trend is significant, therefore the cause of the tendency does not occurs randomly or occasionally ifthere is a factor that brings it.

Results and discussion

The Table 1 shows the results of statistical analysis of the maximum temperature, minimum temperature, precipitation and evaporation for the series of data obtained from the weather station 14089, located in the area of influence of the dam "La Vega" from 1961 to 2009. We observed that the highest value corresponded to the years 1961-1969 to 31.3 °C and the lowest value of 30.2 °C, corresponding with the average for the decade 2000-2009. The range ofthe standard deviation varied between 3.54-3.93 °C. Ruíz et al. (2012) reported similar values of maximum temperature, mínimum temperature, precipitation and average evaporation for the same weather station. The maximum and minimum value for the average minimum temperature corresponded to the decade of 1980-1989 and 2000-2009, with values of 13.4 °C and 11.7 °C, respectively. The range of the standard deviation corresponded to 4.93-7.89 (Table 1). The average precipitation (mm) for the 5 decades analysed showed that, the highest average observed corresponded to the period of 1961-1969 with a 2.63 mm, while the lowest value corresponded to the decade 1980-1989 to 2.42 mm. The standard deviation is presented in a range of 7.32-7.89.

Table 1 Statistics of the average maximum temperature of 1961 to 2009, data series of the weather station 14089 in Teuchitlán, Jalisco. 

The maximum evaporation was made in the period 1961 1969 to 4.97 mm, and the minimum value observed corresponded to the period 2000-2009 to 4.08 mm. The range of the standard deviation ranged from 4.60-3.85. The Table 1 also shows the average evaporation of the dam La Vega for the years 1961-2009. The highest value was recorded in the period 1980-1989, with a value of 144 mm, while the lowest value was recorded in the years 2000-2009. The standard deviation fluctuated in a range of 6.46-2.64.

The results of the Mann-Kendall statistic (S) and Z_s for the period 1961-1969 are presented in the Table 2 The results showed a positive value S of 24 and Z_s of 2.4, for the case of precipitation in this period, with a correlation coefficient of 0.7015. These values indicated a significant increase in the trend in evaporation of the dam La Vega between 1961 and 1969. This trend is shown graphically in Figure 2. The maximum temperature, minimum temperature, precipitation and evaporation showed no trend at all.

Table 2 Mann-Kendall statistics for the period 1961-1969. 

Figure 2 Trends in evaporation loss in the dam La Vega in the period 1961-1969. 

In the period comprising 1970-1979, we observed a significant upward trend in the maximum temperature, with a value S of 24 and Z_s of 2.06, with a correlation coefficient of 0.4613. While evaporation showed a significant tendency to decrease with a negative S value of -25 and Z _s -2.15. Precipitation and evaporation ofthe reservoir showed no trend, the results are shown in the Table 3.

Table 3 Mann-Kendall statistics for the period 1970-1979. 

The Table 4 shows the trend of the different meteorological variables included in the analysis for the period 1980-1989. Rainfall had a negative significant trend, indicating decreased rainfall in this period. The Mann-Kendall statistic showed a negative value S of -27 and Z_s of -2.33 with a correlation coefficient of 0.5324. The variables ofmaximum temperature, minimum temperature, evaporation, and evaporation of the reservoir showed no trend at all.

Table 4 Mann-Kendall statistics for the period 1980-1989. 

The Table 5 shows the trends ofall the variables analysed for the period 1990-1999. During this period, positive values of S to the maximum temperature and evaporation of the reservoir 25 and 29, respectively with Z_s value of 2.15 for the maximum temperature and 2.50 for the evaporation of the reservoir. With correlation coefficient of0.5447 for the maximum temperature and 0.6404 for the evaporation of the reservoir. The trend was presented as significant upward for maximum temperature and evaporation loss from the reservoir. The Figure 3 shows the trend of the evaporation of the reservoir for this period. The minimum temperature, precipitation and evaporation showed no trend at all.

Table 5 Mann-Kendall statistics for 1990-1999. 

Figure 3 Evaporation loss trend in the dam La Vega in 1990-1999. 

The Table 6 shows the trends of weather variables over the period 2000-2009. There were similarities in trends with the period of1990-1999, where only the maximum temperature and evaporation of the reservoir showed positive value S of 24 and 25, respectively. With correlation coefficient of 0.6684 and 0.5870 at the maximum temperature for the evaporation of the reservoir. Both variables showed significant upward trend. The minimum temperature, precipitation and evaporation showed no trend. The Figure 4 shows the trend ofevaporative loss ofthe dam La Vega for the period 2000-2009.

Table 6 Mann-Kendall statistics for the period 2000-2009. 

Figure 4 Evaporation trend of the dam La Vega in the period 2000-2009. 

It is noteworthy that, even though in some cases the results showed a positive value of S, the trend was not significant, these results are consistent with those found by ^{Nalley et al. (2013)} , using the Mann-Kendall method to analyse the trends in surface temperature in Ontario and Quebec, Canada. Furthermore, ^{Hamed (2008)} mentioned that a high value of S is an indicator of an increasing trend; however, a low value of S represents a downward oftrend. This theory is confirmed in this investigation, since the values S of 24 corresponded to the increase significant trends. In contrast, the variables with a value S of 20 showed no trend at all.

Although the results from the analysis of the trend of evaporation at the dam La Vega in this study showed significant tendency to increase, ^{Badawy (2009)} mentioned that the evaporation is also determined by other variables such as air temperature and humidity as well as wind speed. Badawy applied a prediction model for 2050 and concludes that while evaporation is expected to increase in 2050 due to the increase of temperature, the results showed a negative increase for evaporation. Furthermore, ^{Liu and Yang (2010)} mentioned that precipitation plays a decisive role in evapotranspiration.

Conclusions

The use of the Mann-Kendall method identified trends in data series from 1961-2009 of maximum temperature, minimum temperature, precipitation, evaporation and evaporation of the dam La Vega. The results showed that, the periods between 1961-1989 presented no clear trends in the variables analysed; however, a different behaviour was observed in the period 1990-2009, where the trends of increasing the maximum temperature is determined as significant. According to the results in this research in the analysis of Mann Kendall, the evaporation loss in the dam La Vega was increased in the period 1990-2009 due to the increased maximum temperature. Measurement is recommended in field for the variables such as wind speed, relative humidity and solar radiation for use them as dynamic variables, which will increase the certainty of the trends and forecast models in future researches. Furthermore, the increase in temperature directly affects the evaporation of surface water, thus, increasing evaporation as a response is a expected condition. In general, according to the results, increase s in temperature might adversely affect evaporation at the dam La Vega.