Calculation of drought recognition rate (IRS)

IRS calculation is based on the relationship between precipitation (P) and potential evapotranspiration (ETP). The initial value of the index for a certain period of time begins with the first month of hydrological year (k) and during that year, from the following equation (^{Tsakiris and Vangelis, 2005}):

Where: k= represents the initial value of IRS and P_j and ETP_J= is the precipitation and potential evapotranspiration from month j of the hydrological year, respectively.

In this region, P occurs in winter, while summers are usually dry so in several research papers has been noted the beginning of the hydrological year in October (^{Campos Gaytan, 2008}, ^{Barrandas- Argüelles, 2010} and ^{Del Toro-Guerrero, 2014}). The average initial value of IRS agrees with the aridity index proposed by the Food and Agriculture Organization of the United Nations to assess aridity of a given area (^{Tsakiris et al., 2007c}).

Normalized IRS (IRS_n) is calculated using the following equation for each year of the time series (^{Tsakiris et al., 2007b}):

Where: ā_k= symbolizes the arithmetic mean of a_k; a third equation represents standardized IRS (IRS_std), which is calculated from the following expression (^{Tsakiris et al., 2007b}):

Where: y_k= means ln (a_k); ȳ_k= represents the arithmetic mean; and ds_k= is the standard deviation.

In its behavior IRS_std has great similarity to the standardized precipitation index (IEP) (^{Tsakiris and Pangalou, 2009}), so that the interpretation of the results fits to the following table (Table 1).

^{Tikgas (2008)} also found that the corresponding values ranging from 0 to 0.99 can be set as a normal-wet condition, while values ranging from 0 to -0.50 can also be considered within the normal-dry setting.

Data processing and weather stations

IRS estimates can be complex because it involves the evaluation of spatial distribution of indicators or environmental variables (precipitation, temperature and potential evapotranspiration) (^{Tsakiris et al., 2007c}). The Drinc program (drought index calculator), was designed to facilitate ETP calculation through Thornthwaite and IRS method, using ETP and P data from some weather station. This program was developed by the laboratory of reclamation works and water resources management from the National Technical University of Athens (^{Tsakiris et al., 2007c}). The online version of the program can be found at: www.ewra.net/drinc (^{Tigkas, 2008}). The network of weather stations in northwestern Mexico is large, however most of the information contains series of discontinuous time, missing values or not recorded, therefore it becomes difficult to draw the same set of data between two or more stations.

In this study the meteorological data of eight weather stations from CONAGUA (Table 2) were evaluated. These are located within the Guadalupe basin (Figure 1), however most of them have series of discontinuous data and the distance between the stations and the area of interest is greater than its area of influence, which is ~ 5 km radius according to the World Meteorological Organization, when topography is flat (^{WMO, 2011}) (Figure 1). Only stations from El Porvenir and Agua Caliente met the criteria necessary to carry out the research work, which are: to have a series of continuous data (or as complete as possible to avoid errors in estimating missing data) and the climatological influence area corresponds to the area of study. Both have a data set of 22 and over 30 year respectively of partially continuous climatological information. The estimation of missing data was carried out with the method from the US National Weather Service described by ^{Campos-Aranda (1992)}, which considers that the data can be approximate based on information estimated in the surrounding stations (Equation 4).

Where: P= missing data in mm or °C; Pi= precipitation or temperature observed for the month of the missing data in auxiliary stations in mm or °C; and Wi= 1/Di². Where: Di represents the distance between the auxiliary stations and incomplete station in km.

Precipitation and potential evapotranspiration data is appreciated in Figure 2.

Figure 2. Annual values of P and ETP in mm of weather stations from CONAGUA in their respective time series; the bottom line represents the average historical value of P from the weather stations Agua Caliente (278 mm/year) and El Porvenir (342 mm/year). The top represents the average historical value of ETP from weather stations Agua Caliente (890 mm/year) and El Porvenir (830 mm/year). 

Weather analysis and identification of drought periods

IRS values were estimated with the results from weather station data, shown in Figure 3. In the northeastern portion of the Guadalupe Valley, where the station Agua Caliente is, it was observed a persistent drought that lasted 10 years (1999 -2009), during this period only the hydrological year 2005 was classified as moderately moist. Other hydrological years were classified with mild drought (1999, 2000, 2003, 2004, 2008 and 2009), moderate drought (2006), severe drought (2007) and extreme drought (2002). Other periods of drought were observed in hydrological years 1989 and 1990, being classified with severe and moderate drought respectively.

Figure 3. IRS (bars) values and average annual P (solid line with marks), where moist years differentiate from dry years separated by the value of the annual average historical P (line with spaces) and drought periods from Agua Caliente and El Porvenir stations. 

In the central area from Guadalupe Valley, El Porvenir station was observed a drought lasting 4 years (2005-2009). During this period hydrological drought years were classified with mild drought (2008 and 2009), moderate drought (2006) and severe drought (2007). In addition another representative event was observed during the period (1999-2002), only the hydrological year 2001 was slightly damp. 1999 was classified with mild drought, 2000 moderate drought and 2002 severe drought (Figure 3). Severe and extreme drought coincide in the same periods for both seasons (2001-2002 and 2006-2007), and listed as hydrological years with less precipitation in the time series.

Agua Caliente station, by having a greater number of data is more evident to observe over time increased hydrologic years where annual P is smaller than average (Figure 2). Between 1979 and 1995 eight hydrological years showed this condition, while between 1996 and 2013, fourteen hydrological years exhibited a P lower than annual average. This scenario can be an indicator of a change in regional climate. By relating the above with the results shown in Figure 3, can be seen that the years in which it is documented that the P is lower than the annual average coincide with drought periods. Also, in most cases it could be classified to a hydrological year as dry when this condition is present (Figure 2 and 3) and as lower P is during the hydrological year, drought intensity increases (Figure 3).

Other important aspects to assess are drought duration and frequency. It has been seen that even moderate droughts can cause major problems if it persist for several years (^{Tigkas, 2008}). Arid and semiarid regions may be vulnerable to these characteristics because the annual volume rainfall tends to be limited. Drought severity in the Guadalupe Valley region has a direct relationship with the reduced volume of precipitation (Figure 3); however, severe and extreme droughts have been rare (8.5% Agua Caliente and 9% El Porvenir) with respect to the corresponding time series analysis. While frequency and duration have had great importance in the region by analyzing drought.

With an approximate duration of 10 years, the most representative period (1999-2009) and some other events throughout the study. The Regional Hydraulic Program 2003-2006, states that the aquifer was listed with a status of sub exploitation, because the volume of recharge was estimated at 24 million m³/year and an extraction of 22 million m³/year (^{Kurczyn-Robledo, 2007}). In 2009, the National Water Commission reported a deficit of 19 million m³/year, this means that in just three years the aquifer went from being classified as sub exploited to overexploit. In 2013, the same institution estimated a deficit of 12 million m³/year which are extracted from non-renewable aquifer storage, so until today the aquifer is still considered in a status of overexploitation.