Spatio-Temporal Dynamics of Climatological Variables in the Aid of Decision Making for Irrigated Agriculture

The knowledge of the spatial-temporal dynamics of evapotranspiration is of great importance for the accomplishment of agroclimatic zoning and, therefore, for the design of irrigation systems and management of water use in irrigated perimeters. In this context, this study aimed to generate, with the aid of geotechnologies, information that can support irrigation systems planning and design, based on the temporal distribution of daily climatological normals and on evapotranspiration mapping for the irrigated perimeter of Gorutuba/MG. Climatic data were obtained from the meteorological station of the National Institute of Meteorology (INMET) of the municipality of Janaúba/MG in the period from 1985 to 2014. It was verified the non-tendentiousness and the temporal dependence of the climate data using variogram analysis and the temporal dependence index, respectively. For the interpolation, it was used ordinary kriging. The evapotranspiration mapping was conducted from 180 monthly images, from 2000 to 2014, of the MODIS sensor MOD16A product. The results generated for the irrigated perimeter provided relevant information for decision making of the irrigated agriculture management.


Introduction
The expansion of irrigated areas is often limited by the water availability, what makes it important to search for ways to increase the agricultural production by careful evaluations of the existing irrigated areas.This strategy enables to meet future demands of food and to soften the competition of different sectors for water, besides to reduce the irrigation impacts to the environment (Hamdy, Ragab, & Scarascia-Mugnozza, 2003;Gheysari et al., 2017).
The science of irrigation systems assessment underwent a great development during the past 30 years, from a classic focus on irrigation efficiency (Bos & Nugteren, 1974;Jensen, 1977) to performance indicators (Bos, Murray-Rust, Merrey, Johnson, & Snellen, 1993;Clemmens & Bos, 1990) and more recently to the quantification of the water use and productivity (Molden, 1998;Burt, 1997).The accounting framework of water and productivity developed by Molden (1998) can be used to evaluate the amount of water used and to determine the efficiency and the productivity of water use at several scales.The public domain data obtained by satellite and the scientific development makes the remote sensing an attractive option for irrigation systems management (Bastiaanssen & Bos, 1999;Bos, Burton, & Molden., 2004;Akbari, Toomanian, Droogers, Bastiaanssen, & Gieske, 2007;Rozenstein, Haymann, Kaplan, & Tanny, 2018).This spatial information is increasingly important for large irrigated areas, such as the Gorutuba irrigated perimeter.
The uses of evapotranspiration estimation algorithms are applied in digital images of any orbital sensor that performs radiance measurements in the visible, near-infrared and thermal, such as Terra/MODIS (Ruhoff et al At first, the data exploratory analysis was performed by the descriptive statistics, by means of position measures and dispersion.Then, the geostatistical analysis was performed with the aim to quantify the time dependence degree between the random variables (Equation 1).
where, ( ) is the semivariogram for a vector t in days; Z(x) and Z(x + t) are the pairs of the variables analyzed in the study, separated by a time interval (days) and N(t) is the number of measured pairs.After proving climate variables' time dependence and having the models' parameters adjusted, the interpolation was performed by the method of ordinary kriging, aiming to represent the temporal distribution of the studied climatological normals.

Evapotranspiration Mapping
The mapping of the reference evapotranspiration was performed using the information from the MODIS sensor.
For this determination 15 years of MODIS products were used, totalizing 180 images.The reference evapotranspiration was estimated with the aim of being applied in irrigation systems design planning projects for the DIG.For this, the product MOD16 derived from TERRA platform (officially called EOS AM) belonging to NASA (Liu, 2015) was The data were acquired directly from an FTP portal provided by NTSG (Numerical Terradynamic Simulation Group).
The images were cropped and processed using the MRtools and QGIS 2.8.3 softwares.Some steps of the maps processing should be highlighted to obtain the reference evapotranspiration data in mm month -1 : the images had to be converted to the Geotiff format, referenced and projected, and subsequently multiplied by 0.1 to convert the values to mm month -1 .
After performing the procedures above and obtained the monthly maps of reference evapotranspiration over the 15 years, it was necessary to apply to the images a logical operation.This was performed in the whole time series, with the aim of selecting the highest reference evapotranspiration values, pixel by pixel per month, as Equation 2.
ETp jan max = max (ETp jan2000 , ETp jan2001 , … ETp jan2015 ) By these logics applied in all months of the year, the images of ETp max per month were generated, with the maximum values of each pixel of the DIG's area, during the 15 years of study.

Results and Discussion
The climate data of DR and U presented positive and the other variables presented negative skewness, which is confirmed by the average lower than the median.DR and Insol presented leptokurtic distribution, in other words, with kurtosis higher than zero, and the other climatic data presented platykurtic distribution, which indicates a tendency to have higher data dispersion close to the average.For descriptive analysis, the GS+ software (Robertson, 2009) adopts zero as pattern for mesokurtic distribution.According to the classification proposed by Warrick and Nielsen (1980), all the weather variables had a low variation coefficient (CV), except DR which was classified as high (Table 1).This high variation in DR data was also observed in other studies (Sartori, Silva, Ramos, & Zimback, 2010;Gomes, Souza, Santos, & Paiva, 2011) and can be explained by the lack of rainfall in dry months throughout the series.