Climatic and Soil Water Balances for the Melon Crop

The correct estimate of the water requirements of a crop, besides favoring its full development, also allows the rational use of water. In this context, this study aimed to evaluate water balance in the soil and estimated through climatic methods for the melon crop. Field water balance was daily determined along a period of 70 days. Climatic water balance was determined based on the reference evapotranspiration estimated by the methods of Penman-Monteith, Thornthwaite and Hargreaves-Samani. It was concluded that climatic methods do not estimate correctly water storage in the soil and, consequently, also the balance. Therefore, they should not substitute the soil water balance method to determine these variables. The water management for the melon crop based on evapotranspiration estimated through climatic methods results in overestimation of the water depth to be applied in the soil, in the initial growth stage, and underestimation in the periods of highest water demand.


Introduction
Irrigation is essential to meet the water requirements of the plants, especially in regions like Northeast Brazil.This region stands out for the great productive potential, particularly with the melon crop (Cucumis melo L.), responsible for 95% of the national production (IBGE, 2016).In regions where the scarcity of water resources prevails in most of the time, special care must be taken with respect to water use and management, since it is a limiting factor in the production of agricultural crops (Libardi et al., 2015).This way, the measurement of the water requirement of a crop should be made, always when possible, based on parameters obtained in situ (Libardi et al., 2015), because they control the availability of water to plants (Hartmann et al., 2012).According to the same authors, changes in the hydraulic soil properties influence the water supply and the consumption by transpiration and, thus, affect the soil water balance.For Timm et al. (2002), water balance performed in the soil is important for rational water management and consequent maximization of yield.However, the soil water balance equation is not always used because of the difficulty of obtaining its components (Ghiberto et al., 2011), since it requires detailed information about the hydraulic soil properties (Ma et al., 2013;Campos et al., 2016).In this context, climatic water balance has been used because its parameters can be easily obtained, since it utilizes data of climatic temporal series.
Nevertheless, since it is a generalized recommendation for completely different situations, the climatic water balance may not represent the actual conditions of water in the soil, and the greatest disadvantage in this type of balance is the high spatial variability of the climatic components (Libardi et al., 2015).The main component for the determination of climatic water balance is the evapotranspiration, which can be estimated through various physical and empirical models, such as Thornthwaite (Th), Penman-Monteith (P-M) (Bruno et al., 2007) and Hargreaves and Samani (H-S) (Arellano & Irmak, 2016), among others.The difference between these models is in the parameters used to determine the evapotranspiration, because the model of P-M uses data of radiation and wind speed, H-S uses temperature and Th uses temperature and photoperiod (Arellano & Irmak, 2016).

It is worth type of cro use of equ generally v
In this pe representin substituted semi-arid r estimated parameters

Materia
The study altitude of classified rainfall is a where, K() is the hydraulic conductivity as a function of soil water content for the depth of 0.3 m;  t (0.2 m) and  t (0.4 m) are the total potentials at the depths of 0.2 and 0.4 m, respectively.Runoff (R) was disregarded, because the area is considered as flat.Volumetric water content () was obtained through readings of tensiometers at the depths of 0.1, 0.2 and 0.3 m.Water storage and storage variation were daily calculated through the trapezoid rule.Crop evapotranspiration (ET) was obtained through direct measurement of all components of the field balance, thus leaving it as unknown.
The climatic water balance for the melon crop was determined based on the methods of Penman-Monteith (P-M), Thornthwaite (T), Hargreaves-Samani (H-S) and Hargreaves-Samani with data adjusted to the local conditions (H-S adj ).The daily means of ETo were calculated through the previously cited methods using data from the conventional weather station of the Federal University of the Semi-Arid Region.
ETc (maximum or potential crop evapotranspiration) was determined through the multiplication of the reference evapotranspiration by the crop coefficient (Kc).The Kc was considered according to the development stage of the melon crop, as 0.5, 0.8, 1.05 and 0.75 for the initial, vegetative, fruiting and maturation stages, respectively.Potential reference evapotranspiration was daily measured through the Class A Pan method.The variation of soil water storage was estimated using data of water conditions in the soil and the climate of the region, according to Equation 3, where, ±∆WS represents the variation of water storage in the soil (mm) relative to the layer of 0-0.30 m; the negative sign indicates water deficit while the positive sign indicates water excess.When ∆WS is negative, drainage is null (D = 0); when it is positive, the excess includes runoff and drainage.
The Penman-Monteith model is classified by the Food and Agriculture Organization (FAO) as a standard equation to estimate ETo (potential evapotranspiration).Therefore, it is advisable to adjust empirical models of evapotranspiration through this standard (Allen et al., 1998).The model is represented by Equation 4, where, ETo is the reference evapotranspiration (mm day -1 ), Rn is the total net radiation of the grass (MJ m -2 d -1 ), G is the heat flow density in the soil (MJ m -2 d -1 ), Tm is the mean daily air temperature (°C), U 2 is mean daily wind speed at height of 2 m (m s -1 ), e s is the vapor saturation pressure (kPa), e a is the partial vapor pressure (kPa), e s -e a is the vapor saturation deficit (kPa), ∆ is the slope of the vapor pressure curve at the point Tm (kPa °C-1 ) and γ is the psychrometric coefficient (kPa °C-1 ).
The partial vapor pressure (e a ) was estimated by substituting the dew point temperature by the minimum daily air temperature minus 2 ºC (Td = Tn -2 ºC), as suggested by Allen et al. (1998) for semi-arid climates, Equation 5, Global solar radiation (R s ) was estimated through the method of Hargreaves and Samani (1982), Equation 6, where, K rs is the empirical adjustment coefficient -the value depends on the distance from the coast, equal to 0.19 for coastal region and 0.16 for continental region, Tx and Tn are maximum and minimum air temperatures (ºC) and Ra is the radiation on top of the atmosphere (MJ m -2 d -1 ).
The model of Thornthwaite (1948) estimates ET 0 using data of mean daily temperature or of a certain period (T) and photoperiod (N) as entry parameters.In the present study, since the mean annual temperature is higher than 26.5 ºC, ET p was calculated by Equation 7, where, ETp is the mean monthly evapotranspiration (mm 30 d -1 ).Since the water balance in the present study was performed daily, ET 0 was estimated using Equation 8(mm day -1 ), described in Sentelhas et al. ( 2010), ( 8) The time of maximum insolation (N) was determined by Equation 9, in which ω s is the angle of solar radiation at sunset, (9) The model of Hargreaves and Samani (1985) estimates ETo using only the values of maximum, minimum and mean air temperatures and radiation on top of the atmosphere, Equation 10, (10) where, α is an empirical parameter, whose original value was 0.0023, and β is an exponential empirical parameter, whose original value was 0.5.
Prior to comparison and calculation of water balance in the soil using field data, the parameters of the H-S equation were calibrated, thus adjusting the empirical model for ETo estimation to the studied site.The parameters of the Hargreaves and Samani (1985) equation were adjusted using Microsoft Excel ® , through the Solver application, following the methodology described and used by Wraith and Or (1998).This technique allows to minimize the sum of square deviation, so that the closer to zero the difference between the values obtained through P-M and H-S, the better the calibration, Equation 11, (11) where, n is the number of observations.The statistical indices suggested by Legates and McCabe Jr (1999): Willmott's index of agreement (d), Nash-Sutcliffe coefficient (E) and root mean squared error (RMSE), were used to evaluate the models,X where, X i is the value obtained at field (independent variable), Y i is the value estimated by the equation based on climatic data, X is the mean value obtained at field and Y is the mean value estimated based on climatic data.
The components were compared by linear regression, analysis of the coefficients applying the Student's t-test at 0.10 probability level, correlation and/or comparisons between sequenced values.Climatic balances used the following data: available water capacity = 26 mm, field capacity = 79 mm, permanent wilting point = 53 mm, latitude  = -05º08', year 2006, initial NDA (number of days in the Julian calendar) = 3, corresponding to January 03, and ∆t = 1 day.

Results and Discussion
Based on field measurements, the evaluated soil volume maintained, in terms of water depth, approximately 15 mm during all the studied period.When the estimate was made using climatic water balances, this condition was not observed, regardless of the method used, with underestimation until the 50 days after planting and overestimation in the remaining period (Figure 2).The evapotranspiration obtained through field method and climatic methods (P-M, Th, H-S and H-S adj ) is presented in Figure 7. Since these methods are based on different principles to estimate the removal of water from the soil, the first one with measurements directly in the soil and the second one with climatic data, it became evident the difference for the variable in all stages of the melon phenological cycle, differing from the result found by Bruno et al. (2007).These authors compared water balances at field and through climatic methods, and observed similarities in evapotranspiration, water storage variation in the soil and drainage.These differences may result from the number of days of the balance, because, unlike Bruno et al. (2007), the balance was daily calculated in this study, and/or from the different edaphoclimatic conditions.

Figu
The climat after plant the estimat field, beca The Nash-Sutcliffe coefficient (E) was also the highest one for the P-M model, indicating that it is the most efficient to estimate melon ET under the semi-arid conditions.For the estimation model to be classified as satisfactory, its value must be at least 0.50 (Moriasi et al., 2007) and, therefore, the results indicate the viability of using the models P-M and Th to estimate ET.
In turn, the errors, represented by the root mean squared error, were all above 1.8 mm day -1 , although they were lower than those calculated by Jacovides and Kontoyiannis (1995) with the Penman-Monteith equation in a study on statistical models utilized in the analyses of equations that estimate ETo.

Conclusions
The climatic methods do not estimate correctly water storage in the soil and, consequently, also the balance; hence, they should not substitute the soil water balance method to determine these variables.
The water management for the melon crop based on evapotranspiration estimated through climatic methods results in overestimation of the water depth to be applied in the soil in the initial growth stage and in underestimation in the periods of highest water demand.

Figure
Figure methods.P

Table 1 .
Significance test for the difference between the coefficients of the regression equations by the estimation methods of the water balance components