Method climatic water balance

According to the equation of the water balance in the soil water content of soil on a particular day, θ_i, is estimated based on the water content of the previous day, θ_i-1, as is shown in the following equation (^{Silva, 2001}).

Where:R_i = irrigation of the particular day; P_i = effective precipitation of the particular day, ETc_i = evapotranspiration of the crop of the particular day; D_i = draining a particular day it is considered “0”, the above expressed in (mm day^-1).

To start with the water balance was required to determine the start of the watering period (sowing date) and lead to field capacity (soil moisture (HA) to 100%) where the values of field capacity (θ_CC) and point permanent wilting (θ_PMP) in (cm³ cm^-3) are consulted depending on soil texture (^{Saxton et al., 1986}) and Pr is the depth of exploration of the roots in cm. This will be the starting point for initiating the BHC, which subsequently accumulates the evapotranspiration water loss (ETc) of the previous day, and the amount is subtracted of effective precipitation (Pe) and irrigation (R). When the accumulated ETc is equal or greater than the critical point (θ_C) (ecuation 2) should be watered down and return the amount of water previously lost due to evapotranspiration. Then the amount of water, net film (Ln) to be irrigated will depend on ecuation 3.

Where: FAM is the maximum collapse fraction; that is, the amount of water leaving the system before applying the next irrigation.

To estimate the ETc (ecuationn 4) of crop, the program uses the specific Kc of each crop which reported ^{Bravo et al. (2006)}. In order to facilitate the coding of the online system, the values were adjusted to a cubic polynomial.(Table 1). Ks is a dimensionless coefficient due to the effect of the residual water stored in the soil, since it is an irrigation zone and it is expected that the plants will not be subjected to water stress, its value is 1.

Table 1 Kc models for various crops.  

With the fraction values of vegetative cycle in X axis and the crop coefficients in Y axis was made a graph for each crop, and the curve was smoothed by taking 10 freehand points to obtain the Kc model. They were fitted to a third-degree polynomial model with least squares method (^{SAS, 1999}). The models obtained for each crop are shown in Table 1.

To obtain the ETo the program consults the climatological database of the agrometeorological station previously selected. The calculation of ETo is done daily of according to Penman-Monteith (^{Allen et al., 2006}). The FAO Penman-Monteith method for estimating ETo is derived from the original Penman-Monteith equation and the aerodynamic and surface resistance equations, obtaining equation 5.

Where: ETo= reference evapotranspiration (mm day^-1), R_n= net radiation at the culture surface (MJ m^-2 day^-1), G= floor heat flow (MJ m^-2 day^-1), T= mean air temperature at 2 m height (°C), u₂= wind speed at 2 m height (m s^-l), e_s = saturation vapor pressure (kPa), e_a = actual vapor pressure (kPa), (e_s - e_a)= vapor pressure deficit (kPa), Δ = slope of the vapor pressure curve (kPa ^oC^-1), γ = psychrometric constant (kPa ^oC^-1).

For the calculation of the effective precipitation (Pe), the precipitation is multiplied by a correction factor according to the climatic conditions (0.75) when this is greater than 5 mm. and if under the Pe= 0 (^{Serna et al., 2011}). To define the time and the gross watering sheet (Lb) in mm. To be applied to the irrigation system, Lr is divided by the application efficiency (Ea), which is the relation between the water applied by the irrigation system and the water stored in the root zone, considering a range of 0.85 to 0.95 for drip irrigation and 0.45 to 0.65 for multi-door irrigation expressed in (%).

To calculate watering time (Tr) expressed in hours, necessary to calculate the hourly rate (TH) refers to that amount of water in the system serving millimeters in one hour (mm h^-1), in the system of drip irrigation with belt, TH is estimated based on the emitter's expenditure in lph, (Qe), the spacing between emitters in m, (Ee), and spacing between irrigation lines in m, (ELr), (ecuation 6). The multigate for irrigation is taken into account spending entrance to the irrigation section lps (QseC) and the surface to be irrigated in ha (S_ha) (ecuation 7).

The irrigation time in hours (Tr) is the relationship between the gross irrigation sheet to be applied between the TH which indicates the number of hours to be irrigated. When watering is carried to θ_C to 100% of HA, and the calculation is restarted until the end of the crop cycle obtained a water balance in the soil over time.

Programming languages: For the development of the system in WEB platform PHP and HTML were used. Together they are: a very powerful programming language that allows you to create dynamic websites. This system allows to obtain in an integral way the irrigation schedule that consists of irrigation date, irrigation sheet and time of application of water to cover the water requirements of the crop. To access the system for irrigation scheduling is necessary to enter the website http://www.zacatecas.inifap.gob.mx/riego, which the login screen and log appears. When entering the system the map of the network of agroclimatic stations is shown, where the user will select the station closest to his property.

And followed by that will be requested input data divided into three sections 1) general and crop data; 2) soil data and irrigation criteria; and 3) data on the irrigation system (Figure 1). To facilitate the use of the program, help texts describing input and output concepts and variables are included. 1) general and crop data: season, plot name, plot coordinates, crop, date of planting or transplant, crop cycle; 2) soil data and irrigation criteria: texture, root depth, irrigation criterion: a) depletion or b) by days; 3) data on the irrigation system: this section will select the type of irrigation system a) multigates; and b) belt. When selecting the type of irrigation to use, the following data must be filled in to calculate the hourly rate: a) multigates: system expenditure, irrigation surface; and b) belt: issuer expenditure, spacing between emitters, spacing between irrigation lines, application efficiency.

Figure 1 Input data.  

The main report of this application is shown in Figure 2 beginning with the dates of planting or transplants and shows three columns with: date of irrigation. Net sheet and irrigation time.

Figure 2 Irrigation report.  

In the Figure 3 shows the water balance in the soil over time graphically from the sowing or transplant to the crop harvest.

Figure 3 Graph of soil moisture balance.  

The runs were performed for growing chili and the result was 557.5 mm (5 575 m³ ha^-1) total irrigation depth throughout the cycle. ^{Serna and Zegbe (2012)} reported average volumes of water applied in three years, growing of pepper 5 010 ± 821 m³ ha^-1. ^{Khah et al. (2007)} determined a total volume of 5 560 m³ ha^-1 as the right to get the most business performance in drip irrigation.

The program and scheduling of irrigation in real time, gives a very accurate approach to the actual behavior of moisture in the soil, which helps in making decisions regarding when and how much watering more accurately. This online system is a useful tool for most irrigation users, who do not perform some measure of the water status of the soil or plants to decide when and how much to irrigate their crops.

Conclusions

This application can be used for didactic purposes by teachers and students, to better understand the theoretical principles involved in their development; as well as by researchers to help establish possible research actions oriented towards the definition of irrigation treatments or towards the improvement of the techniques used. It is recommended for the next version to add control systems and mobile communication devices via radio or MSN messaging to efficiently automate the irrigation system and obtain greater performance and profit from this application.