Spatial variability of available water and micro-sprinkler irrigation in cambisol

Submitted on April 1, 2014 and accepted on August 1, 2016. 1 This work is part of the first author’s dissertation.. 2 Universidade Federal Rural do Semi-Árido, Departamento de Ciências Ambientais e Tecnológicas, Mossoró, Rio Grande do Norte, Brazil. larissa.nic@hotmail.com; lcalfilho@ufersa.edu.br; marcilioagro@yahoo.com.br; junior182@outlook.com; claranivea@hotmail.com; mariuchy_sammara@hotmail.com *Corresponding author: larissa.nic@hotmail.com Spatial variability of available water and micro-sprinkler irrigation in cambisol


INTRODUCTION
Water is the most important natural resource as it is essential in all aspects of life, including food production, and the proper management of water supply can result in large economy of water and energy and great improvements in agricultural production (Coelho et al., 2005).Irrigation provides adequate water for plant growth, so plants can express all their genetic potential.However, irrigation generally results in excessive application of water in some areas of planting and insufficient water in others because of the natural non-uniformity of the cultivated areas (Lemos Filho, 2010).
Therefore, well designed irrigation systems, with good uniformity of water application and proper irrigation management, provide higher yield, reduce water loss (Prado & Colombo 2011;Oliveira et al., 2012) and leaching (Agostinho, 2011), and maximize available water resources (Santos et al., 2013).For this reason, we need the right combination of the several factors which enable the quantification of water to be applied in each irrigation.
According to Cunha et al. (2008), uniformity of application affects crop yields and is vital for the economy of the project in any irrigation system.Frizzone et al. (2007) emphasized that the uniformity of water content in the soil profile and yield of irrigated crops are highly dependent on the uniformity of water application.Merriam & Keller (1978) proposed the following classification for the coefficients of uniformity of water application: Values are 90% or greater, excellent; 80-90%, good; 70-80%, fair; less than 70%, poor.
A number of studies, including Lima et al. (2015) and Araújo et al. (2014) reported that the variability of physical and hydraulic properties of the soil shows correlation or spatial dependence.Because of this, several geostatistical tools are used to study the spatial variability of soil attributes and can potentially lead to management practices that allow a better understanding of the interaction between the soil-plant-atmosphere system (Lemos Filho, 2010).
Thus, analysis of soil variability using geostatistical techniques may indicate management alternatives to reduce the effects of soil variability on crop production, aiming at maximizing yield potential (Vian et al., 2016).That is, the mapping of the spatial variability of physical and hydraulic soil properties allows the differentiated application of water by management areas, favoring yield optimization, increasing input efficiency, maximizing benefits and reducing costs.Thus, this study aims to analyze the spatial variability of available water capacity in the soil and water application via irrigation using geostatistics.

MATERIAL AND METHODS
The experiment was conducted in a commercial mango (Mangifera indica L.) orchard in Cambisol (Embrapa, 2006) (Carmo Filho et al., 1991), dry, with annual potential evapotranspiration higher than the annual rainfall, with average annual rainfall between 380 and 760 mm and an average temperature of 27.4 °C.
Considering the border effect, a 100 m x 64 m rectangular grid was laid out with at least two rows of plants bordering the experiment, totaling 133 plants.Sampling was carried out in alternating rows, as well as plants of each row selected, so that the sample points were spaced 16 m x 10 m, totaling 40 points.
The experimental area has a micro-sprinkler irrigation system.Rotating micro-sprinklers were used with flow rate of 50 L h -1 and operating pressure of 200 kPa, spaced 8 m between rows and 5 m between plants.The water used in the irrigation was raised from the Piranhas River, transported by canals, pressurized in a pumping substation, and reached the plot with 350 kPa of pressure.During the evaluation of the irrigation system, the flow rate of the emitters was measured twice on different dates, with three replications for each test of the irrigation system as described by Bernardo et al. (2011).
Uniformity of irrigation application was determined according to the methodology proposed by Keller & Karmeli (1975) and Christiansen (1942).
For the characterization of physical and hydraulic soil properties of the area in study, both undisturbed (Uhland sampler) and disturbed soil samples were collected at 0.3 m depth (soil profile of 0-0.3 m) at each sampling point, depending on the crop spacing, totaling 40 sampling points and 80 soil samples collected.The soil samples were used for determining: soil density, particle density, texture, water retention curves in soil and water holding capacity according to Donagema (2011).For determination of the characteristic curves, tensions of 10, 33, 100, 500 and 1500 kPa were applied.All (forty) water-soil retention curves were adjusted by the mathematical model proposed by Van Genuchten (1980) with the software developed by Dourado Neto et al. (2001).
Descriptive statistical analysis and exploratory data analysis were performed to visualize the general behavior and identify possible outlier values, without considering the geographical position of the observed data.The fitting of experimental data was obtained using the spherical, exponential and Gaussian mathematical models, and the Rev. Ceres, Viçosa, v. 63, n.6, p. 782-788, nov/dez, 2016 model parameters nugget effect, sill and range were estimated.
To select the best model to fit the semivariogram into the experimental data, the criteria established were the highest coefficient of determination (R 2 ) and the degree of spatial dependence defined by Cambardella et al. (1994).Data were georeferenced in metric coordinates and a matrix system that allows applications with minimal area deformation.
The analysis of descriptive statistics and geostatistics for all variables were performed using the software Statistica Development Environment, GS+ (Gamma Design Software, 2004) and GeoR (Ribeiro Júnior & Diggle, 2001).After the exploratory analyzes, the experimental semivariograms were built and the theoretical semivariograms for the spherical, exponential and Gaussian models were fitted.
Later, all the parameters required for kriging interpolation of the results were selected.The ratios between the nugget effect and sill (C 0 / C 0 + C 1 ) were calculated for each fitted model.This ratio, according Cambardella et al. (1994) measures the degree of spatial dependence of the sampled attribute.
Contour maps were constructed for the attributes that had spatial dependence, using geostatistical Kriging interpolation (Vieira, 2000).

RESULTS AND DISCUSSION
Table 1 shows the Christiansen Uniformity Coefficients (CUC) and the Distribution Uniformity Coefficients (DUC) for the two measurements of water distribution uniformity.The CUC values show that the irrigation system had excellent application uniformity, according to Mantovani (2000) and Pereira (2001).
However, following the classification of Merriam & Keller (1978), DCU was considered good.Still, according to these authors, for micro-sprinkler irrigation, only below 70%, DCU is considered poor or unacceptable.
Table 2 shows the descriptive statistics for flow rate (L h -1 ) measured in February and March 2012.The average flow rate of emitters were 49.62 and 47.77 L h -1 (ranging from 37.20; 37.40; to 82.36; 84.56 L h -1 ) for each measurement, respectively.The coefficients of variation for the two measurements were 16.02 and 15.57%, respectively, which were classified as very good uniformity according to Bralts & Kesner (1983) and confirmed by the CUC and DCU values.
Table 3 shows the results of the geostatistical analysis for flow rate (L h -1 ) of the two measurements.The scale of spatial dependence proposed by Cambardella et al. (1994) was used in the analyses of the semivariograms showing that there is strong spatial dependence in the three models because the nugget effects (C 0 ) were lower than the sill (GD < 25%).Table 3 also shows that the exponential model had the highest spatial dependence.However, the spherical model stood out for both the coefficients of determination (R²) and the degree of spatial dependence.
The maps in Figures 1 and 2 show the flow rate (L h -1 ) by kriging spatialization for the two measurements.The maps indicate that the irrigation system of the experimental area had a spatial distribution of flow rate similar in the measurements made on the different dates, showing temporal stability of the spatial variation in the flow rate.However, there is large spatial variation in the flow rate within the area.This can damage crop development, since some plants may receive excess water and others insufficient water.Another important observation is that there is a concentration of high flow rates in the center of the area.
Table 4 shows the descriptive statistics for data on texture and soil density determined for the 40 sampling points in the soil of the studied area (0-0.3 m deep).
According to the classification criteria proposed by Warrick & Nielsen (1980) for the coefficient of variation (CV), indicating variability around the mean, the CV values found for dispersion were moderate for the variables silt (24.23%) and clay (25.40%), and low for the  Mantovani (2000) and Pereira (2001).**Classification by Merriam and Keller (1978).

Date
Table 2: Descriptive statistics for flow rate (L h -1 ) variables sand (7.95%), bulk density (5.44%), and particle density (1.27%).The properties sand, bulk density and particle density were classified as low variability, not exceeding 10%.The clay content showed a CV much higher than the sand content, corroborating the findings of Nielsen et al., (1973), as well as similar to the results found by Lima et al. (2006).
Table 5 shows the descriptive statistics for volumetric soil moisture at field capacity (θ Fc ), volumetric permanent wilting point (θ PWP ), and soil available water capacity (AWC, mm).Note that the mean AWC (µ) in the area over the period was 74.29 mm (ranging from 42.42 mm to 104.55 mm).There is also symmetry in the distribution of the data, because of the similarity between the values of measures of position (mean and median), with the distribution being close to the normal distribution, showing symmetrical distributions, which can be confirmed by the values of asymmetry near zero.
The coefficient of variation (CV) was 17.78% and according to the classification proposed by Wilding & Drees (1983), this CV for AWC (mm) can be considered of moderate variability.Values of standard deviation and coefficient of variation give idea of the magnitude of variability of the soil properties analyzed, but inform us nothing of the spatial dependence structure of AWC, which is only possible using geostatistical techniques.(Maroco, 2007).The results indicated that data are normal, which contributes positively to the geostatistical analysis to be performed more accurately and with possibility of expressing better results.
The results of the geostatistical analysis for AWC (mm) are presented in Table 7.Using the scale of spatial dependence by Cambardella et al. (1994), it was found that for the semivariograms obtained, the three models (exponential, spherical and Gaussian) showed strong spatial dependence: the nugget effects (C 0 ) were less than Mean (µ), median (η), maximum and minimum value (V max and V min ), standard deviation (σ), variance (σ 2 ), coefficient of variation (CV), skewness (Ass), kurtosis (Cur) and total sample number (n) for the contents of sand, silt and clay (%), bulk density (d s ), and particle density (d p ).

Figure 3 :
Figure 3: Spatial distribution of soil available water capacity (AWC) measured in the study area.Source: Torres (2012).

Table 1 :
Percentage values of Christiansen Uniformity Coefficient (CUC) and Distribution Uniformity Coefficient (DUC) *Classification by

Table 6
describes the results of Kolmogorov-Smirnov and Shapiro-Wilk normality tests for AWC, with the Shapiro-Wilk test being the most recommended because the sample has less than 50 observations

Table 4 :
Descriptive statistics for the variables sand, silt and clay (%), bulk density (d s ) and particle density (d p )

Table 6 :
Kolmogorov-Smirnov and Shapiro-Wilk normality tests for soil available water capacity (AWC), mm