Indexes of climate variability monitoring

Measurements of precipitation and temperature are the most abundant, both temporally and spatially. For this reason, these data have been used individually or together to characterize the climate of a region or territory. Moreover, the correlation, usually negative, between temperature and precipitation has been verified by many authors. That is, dry periods are generally warm and warm periods are usually dry. Also, annual variability of the registers or series of mean precipitation and temperature can be detected through their standardized anomaly indexes (IAE-its abbreviation in Spanish) defined (^{Elagib & Elhag, 2011}) as:

And

where PA is the annual precipitation in millimeters, PMA its mean value, and DEP its unbiased standard deviation, estimated with equation (3). TM is the mean value of annual temperature in °C, TMA its average value, and DET its unbiased standard deviation evaluated with equation (4).

In the above expressions, n is the number of years of the register or processed series.

Drought detection index

Pedj, in 1975 in the USSR, proposed an index for detecting annual droughts, which are defined by the difference between the IAE of the mean temperature minus that of precipitation (^{Elagib & Elhag, 2011}); that is:

The ISP is the Pedj Drought Index, whose annual value classifies atmospheric weather as humid or drought, according to table 1. ^{Elagib and Elhag (2011)} verified equation (5) empirically, finding that the ISP correlates negatively with precipitation anomaly and varies directly with mean temperature anomaly, but most importantly, it captures both directions or tendencies. This index has been used by several authors for territorial characterization around the world, for example, ^{Gruza, Rankova, Razuvaev and Bulygina (1999)}; ^{Qian and Zhu (2001)}, and ^{Potop and Soukup (2009)}.

Reconnaissance Drought Index

The Reconnaissance Drought Index (RDI) is perhaps the simplest index that has been proposed recently (^{Tsakiris & Vangelis, 2005}; ^{Tsakiris, Tigkas, Vangelis, & Pangalou, 2007}; ^{Campos-Aranda, 2014}). It is calculated initially as the quotient (a _i ) of monthly accumulated precipitation over the respective potential evapotranspiration (ETP), in the k months considered as the duration of drought for each i year of the processed register. When k = 12 in the lapse from January to December, the RDI is an annual index; that is,

Since the magnitudes of a _i can be represented probabilistically by the Log-Normal distribution. The standardized RDI values are then obtained easily with the equation:

in which:

In equation (7), y- is the arithmetic mean and σy is the standard deviation of the yi values. The positive RDI_ST values indicate wet years and negative values are annual droughts, with the following severity: light, up to -1.00; moderate, fluctuating from -1.00 to -1.50; severe, varying from -1.50 to -2.00; and finally, extreme, less than -2.00.

To estimate annual potential evapotranspiration ( ETPi ) in millimeters, from equation (6), the Hargreaves-Samani method can be used. This method is based exclusively on annual mean temperature (TM _i ) expressed in degrees Fahrenheit and on annual mean daily incident solar radiation ( Rsil ) expressed in millimeters depth of evaporated water ( l ). Its formula (^{Hargreaves & Samani, 1982}; ^{Campos-Aranda, 2005}) is:

Average incident solar radiation (Rs _i ) was obtained from the annual map for Mexico presented by ^{Almanza and López (1975}), whose value for the city of Zacatecas is 495 cal/cm²/d. To transform Rs _i to depth of evaporated water per day, the following formula is used:

in which Hvi is the latent evaporation heat, or the energy in calories necessary to evaporate 1 g or 1 cm³ of water, and is estimated with the following expression, with the mean annual temperature (TM _i ) in ºC:

Annual climate registers used

^{Campos-Aranda (2015)} studied the annual precipitation of the state of Zacatecas, Mexico, and observed that 16 rain gauging stations could be selected with a maximum common period of 63 years, the period from 1950 to 2012. These data were expanded to 2014 based on the information provided by the Local Zacatecas Office of the National Water Commission (Conagua). Following a procedure identical to that described for precipitation in the cited references, the 16 yearly registers of mean temperature during the common 65 year period (1950-2014) were integrated. The general characteristics of these 16 climatological stations are presented in table 2 by geographic regions and in progressive order of MAP. Figure 1 shows their location in the state of Zacatecas.

Figure 1 Geographic location of the 16 processed climatological stations in the state of Zacatecas, Mexico.  

Calculation of the series of the Pedj drought index

By applying equations (1) through (5) to the 16 annual registers of precipitation and mean temperature to be processed, we obtain the Pedj drought index (ISP) series, whose extreme values are cited in table 2. Table 3 presents the annual data and results for each of the climatological stations considered representative of the three geographical regions defined. These stations were Leobardo Reynoso, Zacatecas and Nochistlán. The first and the last have homogeneous registers, according to the results of table 4 of the following section, while Zacatecas, the state capital, only has persistence.

Figure 2 shows the annual ISP chronological series of the Cañitas de Felipe Pescador climatological station in bars and its curve of order 5 mobile averages. This station was not homogeneous, according to the basic tests. It has persistence and an ascending linear trend with a slope statistically different from zero, according to the Student t test (^{Campos-Aranda, 2015}) since t = 2.462 and tc = 1.998. Figure 3 presents the annual ISP chronological series of the Nochistlán station, which was homogeneous.

Figure 2 Chronological series of the Pedj drought index (ISP) in bars, curve of order 5 mobile averages and trend line at the Cañitas de Felipe Pescador climatological station, Zacatecas, Mexico. 

Figure 3 Chronological series of the Pedj drought index (ISP) in bars, curve of order 5 mobile averages and trend line at the Nochistlán climatological station, Zacatecas, Mexico. 

Verification of homogeneity

Each annual ISP chronological series was analyzed for statistical quality, searching for deterministic components with three general tests (the Helmert, Sequence and Von Neumann tests) and six specific tests: two persistence tests (Anderson and Sneyers), two trend tests (Kendall and Spearman), one variability test (Bartlett) and one mean change test (Cramer). Most of these tests can be consulted in ^{WMO (1971)}, ^{Machiwal and Jha (2008}, ²⁰¹²) and ^{Campos-Aranda (2015}). Table 4 concentrates the results of these tests. It can be seen that only four registers are perfectly homogeneous, three show a downward trend, one an upward trend, and the rest exhibit persistence, which is a statistical characteristic of most chronological series of annual rainfall and temperature. Table 4 reveals that persistence is associated with the coefficient of first-order serial correlation (r ₁), when the latter is greater than 0.200.

Contrast with RDI_ST

Because the Pedj index is one of the first drought-characterizing algorithms to use mean precipitation and temperature, we believed it convenient to contrast it with a more recent, simpler one that uses potential evapotranspiration as well as precipitation, the RDI_ST. This contrast was based on percentages of each type of drought defined by the two indexes and on the total number of these events (NTS), which have been concentrated in table 9.

Based on the results of the 16 processed climate series of the state of Zacatecas, we observe that both indexes exhibit fluctuating results. The ISP results vary notably in extreme droughts and those of RDI_ST vary in the severe. Regarding the NTS, which should be 32 or 33, the RDI_ST index, in general, underestimates the value while the ISP is closer. Both indexes overestimate the magnitude in the Tlaltenango station. Table 10 presents the annual results of both indexes for contrast in the climatological station Cañitas de Felipe Pescador, one of the most discordant of the stations, according to what is observed or deduced from table 9. In table 10 we observed that both indexes detect 22 common years with drought, of the 29 total (table 9) and, of these, the 10 following years coincide in the type of drought identified: 1954, 1956, 1969, 1972, 1975, 1980, 1995, 1997, 1999 and 2010.