Introduction

Mexico is one of the main producing countries of pecan [Carya illinoinensis (Wangehn.) K. Koch] in the world, coming to establish more than 44 000 hectares (^{Martinez and Nuñez, 2007}) and its production is in arid and semi-arid areas the country, water is the main factor of agricultural management that allows to reach a photosynthetic efficiency for higher output (Godoy-Ávila and López-Montoya, 2000) as the water consumption of the walnut is high compared to the other crops (Andales et al., 2006; Wang et al., 2007).

The crop irrigation requirements, temporally and spatially vary depending on the weather, management, growth phase and the variety sown, so the calculation must be done locally (^{Ojeda et al., 2006}). Incorporating the concept of grade-growth days to describe the parameters associated with irrigation scheduling is a feasible alternative that allow more control over the efficient use of water (^{Barboza et al., 2007}).

Because this crop requires large amounts of water for production, increasingly jeopardize its permanence, its water requirement varies widely ranges from 1 170 to 1 310 mm per year for adults trees, so it is considered a cultivation of high demand. According to reports made to the area of Arizona USA and Hermosillo Mexico, it was found that the annual estimated water requirement for pecan ranges from 1 234 mm in Bonita, Arizona and 2091 mm near Hermosillo, Sonora; This dramatic increase in the use of water in low-lying areas is due to the combined effects of high demand evapotranspiration (ET) and long cycles (^{Brown, 2010}).

In Mexico, around 840 million cubic meters of water are used every year to irrigate 60 000 hectares (^{Godoy and Huitron, 1998}). ^{Miyamoto (1983)} and ^{Worthington et al. (1992)} found that 500 orchards, 95% were irrigated with groundwater applied by flooding with 50% efficiency, this causes a farm level high volumes of water, in the walnut exceed 40% water requirements used.

Trees in orchards mismanaged irrigation show low production (0.8 t ha^-1) and quality (glued husk, walnut germination and lack of fruit filling), which is associated with water stress caused by improper programming irrigation, mainly for almond filling (Stein et al., 1989; ^{Herrera, 1990}; ^{Sparks, 1995c}).

In addition to this, the very climate variability of each ever increasing impact of climate change by region, is causing changes in the phenological cycle of the crop and, consequently their water requirements (^{Sifuentes et al., 2014}). Faced with this situation they have been using models for integrated irrigation scheduling based on thermal time in grains and vegetables in Sinaloa that have allowed coupling the water demands of crops regarding this variation and facing periods of low water availability (^{Sifuentes et al., 2014}). In this work, an integrated model concept was adapted, based on the thermal time pecan cultivation in the Laguna Region of Coahuila, for programming precise irrigation, self-adjusting to temperature variability and applicable to any transplant date or sprouting, soil, irrigation and management.

Materials and methods

The study was conducted in a plantation located in the ejido Hormiguero, Matamoros de la Laguna, Coahuila, located at 25° 41' 15" north latitude and 103° 19' 52" west longitude. The climate is semi-arid with a height above sea level of 1150 meters (Medina, 1998). The annual average temperature is 18-22 °C, presenting the highest in the months of May to August, and reaching values above 35 °C during the day and 18-20 °C overnight. The soil is deep, predominantly Franco clay loam, bulk density 1.23 g cm^-3, 1.31% organic matter and soil moisture of0.1542 cm³ cm^-3. A study section of 0.168 hectares with trees of 22 years old, Western variety distributed real-frame of 14 x 14 m, which resulted in the removal of trees alternately whose original distribution was 7 x 14 m was used; sprouting date was March 20, 2014.

As a source of climate information in real-time, an automated agroclimatic station was used in the Experimental Field La Laguna (CELALA) installed 10 km of the plot, which permanently monitored at intervals of 15 min the variables: air temperature, relative humidity, solar radiation, precipitation, wind speed and direction, besides estimating reference evapotranspiration (ET) with the Penman-Monteith simplified by ^{Allen et al. (2006)}.

The basic model for irrigation scheduling, based on thermal time model was generated by ^{Ojeda et al., (2006)}, whose components are presented in Table 1.

Table 1 Basic model of comprehensive irrigation scheduling for annual crops in Sinaloa (^{Ojeda et al. (2004)}. 

Where: Kco is the coefficient for the first crop phenological stage which depends essentially on the soil evaporation, Kmax is the maximum value of Kc during development, XKmáx corresponds to an auxiliary variable defined by GDA when the crop has its maximum crop coefficient, αl is a regression parameter obtained by fitting experimental data, erfc is the complementary function of x an auxiliary variable error calculated with the following expression:

Where: GDA are accumulated degree days from planting or emergence to a particular time or α and GDA are required to maturity. Pro and PRMAX represent the planting depth and maximum root depth respectively, the value α2 model is adjusted empirically worth about 2/3 of GDA value where the crop reaches maximum rooting depth. The values of the parameters α3 and α4 for abatement factor f are calibrated considering the sensitivity to water stress and crop management practices for irrigation system.

For parameterization of the model in pecan, phenology was monitored from sprouting according to the methodology proposed by Godoy et al., (2000), the day degrees (GD) or thermal time associated with each stage being calculated as follows (^{Ojeda et al., 2006}).

GD= Ta-Tc-min, si Ta<Tc-max

GD= Tc-max-Tc-min, si Ta≥ Tc-max

GD= 0, si Ta ≤ Tc-min

Where: Ta is room temperature, Tc-min is the minimum critical temperature of the crop (15 °C); Tc-max is the maximum critical temperature of the crop (40 °C) (Santamaría et al., 1969).

Kmax was taken from Stein and Worthington (1996), while the depth of root was performed by direct sampling in agronomic wells of 0.50 mx 1.5 mx 2 m, where Pro and PRMAX model was determined, as shown in Figure 1.

Figure 1 Agrological well to determine root depth and the associated comprehensive model parameters. 

Once the parameters of the comprehensive model were defined, a Visual Basic macro was developed in an Excel spreadsheet program for calibration to be in a position to model water requirements. The criterion for application of the last irrigation was defined considering the accumulated of degree days (GDA) and phenological stage besides the soil moisture content at the end of physiological maturity to avoid water stress. In order to validate the model, the phenology observed was compared with the modeled, as well as the modeled variation in moisture in the soil versus the variation measured gravimetrically and with a fixed mark sensor 10 HS Decagon Device which collected data in a Datalogger EM50, discharged through a laptop (Figure 2).

Figure 2 Soil moisture sensor 10HS Decagon Device installed on experimental lot for comprehensive model calibration. 

Also net irrigation sheets (Ln) and gross (Lb) and implementation efficiency of each irrigation (Ea) were measured. The first one through the accumulation of crop evapotranspiration, estimated with the macro-Excel and, the second one by capacity of applied films. Ea was calculated: Ea= Ln/Lb.At the end of the agricultural cycle yield and nut quality was assessed, harvesting every tree of the section studied.

Results and discussion

In Table 2 the phenological stages observed in the test group, expressed in terms of heat accumulation or thermal time (GDA) and the length thereof in calendar days (DDS) are presented. The physiological maturity is reached at 2 356.03 GDA and harvesting at 2 463.94 at the end of October to 231 days after sprouting (DDB).

Table 2 Phenology observed from sprouting (20 March 2014) in the Western variety in the Ejido Anthill, Matamoros, Coahuila. 

The Table 3 shows the parameters of comprehensive irrigation scheduling model, experimentally obtained integrated into the Excel macro.

Table 3 Models with calibrated parameters for comprehensive irrigation, scheduling in growing adult Walnut Pecan in the Laguna Region. 

High level values with high similarity levels were found between the content of modeling humidity using the calibrated model and the content measured gravimetrically and with the humidity sensor 10HS, behavior similar to that found by ^{Sifuentes et al. (2014)} in grains and vegetables in northern Sinaloa, Mexico, which can be seen in Figure 3. The second discrepancy value (73 DDB) operatively due to the irrigation application in that period was delayed.

Figure 3 Comparison of the volumetric soil moisture observed and modeled on the plot studied. 

The calibrated model generated daily and accumulated water requirements (evapotranspiration) of Figure 4, as a function of thermal time or degree days, a total requirement was found of 741 mm, under the minimal requirements reported by ^{Brown (2010)}, which was higher to 1 100 mm for the Costa de Hermosillo, Mexico and Arizona. This difference was due to the following factors: the reduction of evapotranspiration by water stress presented in the Delay Watering mentioned in Figure 3, for the climatic conditions of the area and cycle time mainly as mentioned by the same author.

B= brotación; FM= floración masculina; FF= floración femenina; PP= Pos polinización; CIF= crecimiento inicial del fruto; CRR= crecimiento rápido; CFN= crecimiento final de la nuez; ILLA= inicio llenado de almendra; LLA= llenado de almendra; LLF= llenado final; M= madurez; C= cosecha.

Figure 4 Irrigation requirements by pecan for Laguna Region of Coahuila, Mexico, estimated by comprehensive programming and thermal time concept. 

The model also allowed estimating the crop phenology on different dates sprouting; a scenario likely to be increasingly common, considering the current climate variability (^{Sifuentes et al., 2014}). For a range of dates in which there might be a beginning of sprouting from February 28 to March 31, estimating a difference higher than 20 calendar days at most of the phenological stages, as presented in Table 4. In practice, this difference contributes to the fall in discrepancies in the agronomic management of the orchard and consequently in production losses.

Table 4 Variation of the duration on phenological stages in calendar days, for different dates of pecan budding in the Laguna Region. 

FM= floración masculina; FF= floración femenina; PP= pos polinización; CIF= crecimiento inicial del fruto; CRR= crecimiento rápido; CFN= crecimiento final de la nuez; ILLA= inicio llenado de almendra; LLA= llenado de almendra; LLF= llenado final; M= madurez; C= cosecha.

The Table 5 presents a summary of applied irrigation assistance and the stage in which they were applied in the study plot. A total of 8 irrigations were applied, including the initial watering sprouting (not considered the risks of pre-sprouting). Watering intervals ranging between 12 and 47 days and a net maximum sheet of 82.18 mm, with active trees and a cumulative net sheet of 748.58 mm. The average application efficiency of irrigation ranged from 50-70% and the yield was within the regional average of 2-3 t ha^-1, indicating that the conditions under which the study was conducted were those of conventional the management area.

Table 5 Timing of irrigation applied in the study plot, located in Hormiguero, Matamoros, Coahuila, Mexico. 

Conclusions

There is an integrated model for irrigation scheduling, calibrated for growing pecan in the Laguna Region of Coahuila, Mexico, with acceptable accuracy indicators, such as variation in moisture content of the soil, phenology, application efficiency of irrigation and performance. The irrigation requirement lower than other areas is due to its management, weather conditions and crop phenology, which increases as the crop development conditions are more favorable. The model demonstrates that there can be significant variation in crop phenology by varying the date of sprouting, which may affect the crop management and yield. This technology is recommended to temper climate variability and manage water availability scenarios; for this, it will be necessary to implement validation and transfer programs on a large scale.