Analysis of the Occurrence of Wet and Drought Periods Using Standardized Precipitation Index in Mato Grosso do Sul State, Brazil

INTRODUCTION

The climate of a region is determined by the long-term average, frequency and extremes of several meteorological variables, most notably temperature and precipitation. In a largely tropical country such as Brazil, rainfall is a precious natural resource and it is quite variable. Thus any fluctuations or trends in its geographical distribution and quantity could have significant implications for socioeconomic sectors, such as, agricultural productivity, food security, water quality, water resource management, land use, human health, as well as ecological impacts, such as, biodiversity (Giddings et al., 2005).

The State of Mato Grosso do Sul (MS), Brazil, covers an area of approximately 350,000 km² of which 13,000 km² are exploited in agriculture, being the crops of higher expression soybeans, corn, cotton, cane sugar and irrigated rice (CONAB., 2014). Agriculture has as main water source the rainfall patterns, which at times has compromised agricultural production due to its variability, sometimes with long drought periods, sometimes with extreme events that exceed the soil water retention capacity, triggering floods (Correa et al., 2014). Besides the influence on agriculture, drought periods affect the water level of water sources and reservoirs of hydroelectric plants, bringing problems to the urban water supply and electricity generation (Rodrigues et al., 2013; Oliveira-Junior et al., 2014).

The Standardized Precipitation Index (SPI) was developed by McKee et al. (1993) to categorize observed rainfall as a standardized departure with respect to a rainfall probability distribution function. It indicates how precipitation for any given duration (1, 2 months, etc.) at a particular observing site compares with the long-term precipitation record at the same site of the same duration (Edwards and McKee, 1997). According to Keyantash and Dracup (2002), the index compares very favorably against several other "drought" indices and has been adopted by the US National Drought Mitigation Center for operational use to replace the traditional Palmer Drought Severity Index (PDSI).

Bordi et al. (2001) demonstrated that SPI can be used as a tool in the historical reconstruction of drought events in locations in Italy. Lloyd-Hughes and Saunders (2002) developed a high spatial resolution, multi-temporal climatology for the incidence of 20th century European drought using SPI. When the SPI analysis was extended to the Northern Hemisphere some interesting spatially remote teleconnections linking the Tropical Pacific with the European area were shown (Bordi and Sutera, 2001). Seiler et al. (2002) used SPI to study the recurrent floods affecting the southern Córdoba Province in Argentina, as a tool for monitoring flood risk in that region. Giddings et al. (2005) verificated that SPI zones of the whole country presented a fresh and useful perspective on the behavior of rainfall in México.

Due to the severe drought impacts in economic and social activities and try to quantify and describe its impact, various methodologies were created among which are: Drought indices that are based on rainfall data, air temperature and capacity water available (Gois et al., 2013). However, it is important to note that in recent years several drought indices have been evaluated in an attempt to characterize the drought; in which they can provide different answers regarding the impact and severity of drought for the same region, owing to the different demands on the input data (Oliveira-Junior et al., 2012). In Brazil, the use of SPI is not yet widespread. Some studies with this technique have been developed with Brazilian States as Amazonas (Li et al., 2008), Espírito Santo (Blain et al., 2010), Paraíba (Macedo et al., 2010), São Paulo (Blain, 2012) and Tocantins (Gois et al., 2013). Thus, in order to generate information relevant to the MS (Brazil), the aim was analyze the occurrence of wet and drought periods through the SPI in this Brazilian State.

MATERIAL AND METHODS

Characterization and location of the study area: The State of Mato Grosso do Sul is located in Brazil’s Midwest region. Has a total area of 357,145,320 km², composed of 79 municipalities. The State has several features edaphoclimatic distributed between three biomes with peculiar climatic attributes: Savanna, Atlantic Forest and Pantanal. Altitudes range from 24 to 1,000 m, in the center of the South American continent (Fig. 1).

In the state there are three major topographical units: (1) Pantanal, in the west portion, with a singular drainage network, spread over an immense plain of modest altitudes between 80-200 m, (2) In the center, shows the Divisor Plateau or Serra de Maracajú, elongated in the NE-SW direction, separating the waters of the Paraguay and Paraná river basins, with altitudes ranging from 300 m (Serra de Bodoquena) to over 650 m (Plateau of Amambaí) and (3) In the eastern portion, is located the Upper Paraná shaft, drained by major rivers of arenitic-basalt plateau, with altitudes ranging between 200 and 250 m along the trough (Zavattini, 2009).

Savanna (or Cerrado) is the second largest biome in South America (SA) and covers 22% of the Brazilian territory. It is at this biome that is the source of three major watersheds of AS (Amazônica/Tocantins, São Francisco and Prata), which results in high aquifer potential and great biodiversity. By virtue of its latitudinal position, the region is characterized by the transition between the warm low latitudes climates and mesothermal toughened type climates, of mid-latitudes (Nimer, 1989).

Atlantic Forest is an environmental complex that includes mountain ranges, valleys and plateaus. It was already one of the richest and varied rainwater forest sets of AS but is currently recognized as the most uncharacterized Brazilian biome.

Pantanal covers 25% of the State of Mato Grosso do Sul, being a biome almost exclusive to Brazil. It is characterized by long-term flooding (due to low permeability soil) that occur each year on the plain and cause changes in the environment, wildlife and local populations’ daily life. Pantanal climate is "AW" with rainfall totals ranging between 1,000 and 2,000 mm and 2 distinct seasons: a dry (May to September) and a rainy (October to April), this latter accounting for more than 80% of the total annual rainfall (Mesquita et al., 2013).

Historical series of monthly rainfall: Rainfall data of 29 stations (sites) of Mato Grosso do Sul (MS) were obtained of the National Water Agency Database (http://www.ana.gov.br/) (ANA., 2014), collected from 1983-2013. At each site and year, the rainfall daily data were added up to obtain the monthly rainfall (mm month^–1), of each month of the year. Thus, were formed 348 time series (12 months×29 sites), that it were used to calculate the SPI in annual scale.

The treatment and the organization of rainfall data of 29 localities in the State were performed. The historical series with failures were eliminated and filled by the climatologically normal from each of the 11 regions of the State. The fit was found Normal distribution of 348 time series of monthly rainfall using the Kolmogorov-Smirnov test, that addition to not depend on the number of classes data grouping, offers more computational advantages. This test promotes on the discrepancy between the distributions:

where, F_n (x) denotes the theoretical distribution and F₀ (x) the adjusted distribution. This test is used to test the null hypothesis versus the alternative hypothesis H1: F ≠ F₀ (Everitt and Dunn, 1991).

Fig. 1:	Localization of mato grosso do Sul State, Brazil, in South America, with their respective biomes (Pantanal, Savanna and Atlantic Forest) and the hypsometry (m)

According to McKee et al. (1993) the historical series is fit to a distribution of gamma probability which is transformed into a normal distribution, where the SPI index for each location and desired period has zero value for its average and unit variance. Gamma distribution is defined by the probability density function (Eq. 1):

(1)

(2)

The parameters and the gamma probability density function were fit to the frequency distribution of the 29 stations rainfall totals. We calculated the shape and scale parameters of the gamma probability density function estimated for each of the stations at the annual scale.

According to Oliveira-Junior et al. (2012) the maximum-likelihood method (MMV) is the most suitable for the parameter estimates for α and β (Eq. 3 and 4):

(3)

(4)

where, A is defined by Eq. 5:

(5)

where, = Arithmetic average rainfall (mm), Ln = neperian logarithm, N = number of observations.

The parameters α and β were calculated to find the cumulative probability of a rainfall event observed for the annual scale which the cumulative probability (Eq. 6 and 7):

(6)

Replacing the value of in Eq. 6 reduces the Eq. 7:

(7)

Which is defined as the incomplete gamma function considering that the incomplete gamma function does not allow null values. The distribution gamma is undefined for rainfall values equal to zero, the cumulative probability can be determined in two parts Eq. 8:

(8)

where, P₀ is the probability of null values (zeros) and G(x) is the theoretical cumulative distribution, where the parameters are estimated on rainy days. The cumulative probability distribution F(x) is transformed into a normal distribution for the random variable Z with zero mean and variance one, where the variable Z corresponds to the value of SPI. Further details of the empirical cumulative probabilities lies on Oliveira-Junior et al. (2012).

From the calculations in SPI values at the annual scale for the sites in the study area were classified as shown in Table 1.

Table 1:	Classification of the wet and drought periods of SPI, according to McKEE et al. (1993)

It were compared with the drought and wet periods with climate variability mode El Niño-Southern Oscillation.(El Niño and La Niña) based on the classification adopted by Weather Forecast and Climate Studies Center-CPTEC, according to link: http://enos.cptec.inpe.br/-(CPTEC., 2015) When the Oceanic Nino Index (ION) is greater than+0.5°C for at least five consecutive months is considered an El Niño and when the ION is less than -0,5°C for at least five consecutive months is considered a La Nina (CPTEC., 2015).