INTRODUCTION

Dry bean, like other crops that commercialize, presents a high vulnerability to the selling price, because of the constant changes in the agricultural market. Provided the problems dry bean production presents in Cuba (climatic variability, pest and disease incidence and water irrigation usage, among others), some tool, supporting the decision making to achieve the lower economic and environmental costs should be available. The use of this kind of tool, such as crops simulation model, is justified when the objective is the resources optimization, among them water irrigation, with the purpose of reaching the largest profits. The relationship between water consumption and yield or total biomass production, can be calculated empirically with the object of obtaining the production functions of water consumption (Martín de Santa Olalla et al., 2005; Toumi et al., 2016), through which yield or total biomass can be related with some measurement of crop water consumption. The problem associated with crop production functions is that these have been utilized independently of specific locality and other limitations (Doorenbos & Kassam, 1979).

An alternative to the empirical production functions is the use of crop simulation models for irrigation management (Steduto et al., 2009; Amiri et al., 2014).Crop simulation models are useful tools to estimate crop yield, taking into account several combinations of crop input, environmental factors and management practices (Masanganise et al., 2012).

AquaCrop can be found among the existent models (Raes et al., 2009; Steduto et al., 2009). It is a model of crop general application, which has been utilized in several parts of the world (Stricevic et al., 2014; Reza et al., 2015; Trombetta et al., 2016), under different environmental conditions; how- ever, in the international literature few investigations with dry bean crop are reported. The aim of this investigation is to evaluate AquaCrop model simulation of canopy cover, dry biomass and soil water balance in dry bean crop cultivated with furrow irrigation method.

Dry bean, like other crops that commercialize, presents a high vulnerability to the selling price, because of the constant changes in the agricultural market. Provided the problems dry bean production presents in Cuba (climatic variability, pest and disease incidence and water irrigation usage, among others), some tool, supporting the decision making to achieve the lower economic and environmental costs should be available. The use of this kind of tool, such as crops simulation model, is justified when the objective is the resources optimization, among them water irrigation, with the purpose of reaching the largest profits. The relationship between water consumption and yield or total biomass production, can be calculated empirically with the object of obtaining the production functions of water consumption (Martín de Santa Olalla et al., 2005; Toumi et al., 2016), through which yield or total biomass can be related with some measurement of crop water consumption. The problem associated with crop production functions is that these have been utilized independently of specific locality and other limitations (Doorenbos & Kassam, 1979).

An alternative to the empirical production functions is the use of crop simulation models for irrigation management (Steduto et al., 2009; Amiri et al., 2014).Crop simulation mod- els are useful tools to estimate crop yield, taking into account several combinations of crop input, environmental factors and management practices (Masanganise et al., 2012).

AquaCrop can be found among the existent models (Raes et al., 2009; Steduto et al., 2009). It is a model of crop general application, which has been utilized in several parts of the world (Stricevic et al., 2014; Reza et al., 2015; Trombetta et al., 2016), under different environmental conditions; however, in the international literature few investigations with dry bean crop are reported. The aim of this investigation is to evaluate AquaCrop model simulation of canopy cover, dry biomass and soil water balance in dry bean crop cultivated with furrow irrigation method.

METHODS

The research was carried out from December, 2013 to March, 2014. The area of research belongs to the UBPC Grito de Yara, which is located at latitude 20o 25’ north and at longitude 76o 53’ west with an altitude of 6 m.s.n.m. The investigation area was a plot, with nine furrows with 0.8 m width and 100 m length. The plot was divided into 3 subplots with 33 m of length and the central furrow of each subplot was utilized for measurement. The inflow rate was 2 L s^-1. Inflow rate delivery was ensured by means of PVC spigots calibrated for 50 mm of diameter. A total of 7 irrigation events were applied. Variety Delicia 360 was sown on December 20th, 2013, with 0, 5 m of plant spacing and 0,8 m of row spacing. Measurements were recorded on 10 day time steps. Evaluated variables were: canopy cover (CF), by means of upright photograph technic and image processing (Steduto et al., 2009); dry biomass (BSA), by means of gravimetric method; and soil water content (CHS) by means of gravimetric method.

According to Raes et al. (2009), AquaCrop model consists of several equations that with climatic date, plant density, genetic characteristics, soil type, fertilization level and irrigation deficit level, simulate crop growth and yield. This model requires the following meteorological information daily, 10-daily or monthly data: minimum and maximum air temperature (Tmin,Tmax), reference evapotranspiration (ETo), rainfall (Pp). AquaCrop considers medium atmospheric CO2 concentration for the year 2000 measured at Mauna Loa Observatory, in Hawaii of 369, 47 parts per million by volume, as the reference. The values of this concentration can be substituted by present emissions (Raes et al., 2009). The climatic data for this investigation were measured at Agrometeorological Station of Veguitas which is located at a distance of 3 km from the study area. Reference evapotranspiration was estimated using the “ETo Calculador ver.3.2” software and then it was exported to AquaCrop model. Biomass and grain productions depend on crop parameters, such as stomata conductance, canopy senescence, water productivity and haverst index.

AquaCrop model estimates crop water requirement by means of soil water balance with equation 1:

where: q is the dependent variable (mm); I is the depth to irrigate (starting point of calculation); j is the updated moisture content at the time of next irrigation; D is the drainage by deep percolation (mm); R+P are irrigation plus precipitation (mm); ES is soil evaporation (mm) and Tr is the transpiration of the crop (mm; .+. are irrigation plus precipitation (mm); ES is soil evaporation (mm), Tr is the transpiration of the crop (mm).

AquaCrop daily provides the moisture content in the soil in its different layers in which the profile is divided at intervals of 0,10 m to the depth of the soil that is described as input parameter to the model. The comparison between observed and simulated moisture was performed using the total content of moisture accumulated to depth of 0, 30 m.

The AquaCrop model simulates the growth of green canopy assuming two cases:

: exponential type growth which is calculated with the equation 2;

: exponential senescence which is calculated with the equation 3:

where: CC is the green canopy cover over time (t) passed (measured in days); CCo is the initial coverage of the green canopy (t=0); CCx is the maximum coverage of the green canopy; CGC is the growth rate of the green canopy per unit of time. The AquaCrop model adjusts green canopy growth with respect to density of population (plants·ha^-1).

Soil characteristics according to the second genetic clas- sification of soils of Cuba, estimated in the Soil Laboratory of Granma Province were:

Type: alluvial.

Texture: clay loam.

Bulk density: 1, 42 g·cm^-3.

Field capacity: 0, 37 cm³·cm³.

Permanent wilting point: 17, 00 cm^3·cm³.

Hydraulic Conductivity: 4, 00 mm·h^-1.

Electrical conductivity of the irrigation water: 0, 30 ds·m^-1.

For the dry bean crop, AquaCrop model does not have previously loaded data. In this investigations soybean crop data were utilized, as soybean crop characteristic of production, management and genetic are very similar to the dry bean crop. Adjusted parameters are presented in Table 1.

For none limiting conditions of hydric stress and fertilizers, only the following local parameters, presented in table 2, are necessary (Raes, 2009).

Evaluation of model performance was carried out by means of the following statistical indicators: coefficient of determination (R²); efficiency coefficient (EF); root mean square error (RMSE); normalized root mean square error (NRMSE); index of agreement (d).

Coefficient of determination is the resultant of correlate linearly simulated and observed values. It ranges from 0 to 1, with values close to 1 indicating a good agreement, and typically values greater than 0.5 are considered acceptable simulations (Moriasi et al., 2007) and values greater than 0.8 are considered good simulations.

where: R² is the coefficient of determination (%); squared sum because of the regression;** the total squared sum.

The Nash-Sutcliffe model efficiency coefficient (EF) determines the relative magnitude of the residual variance compared to the variance of the observations. This parameter is dimensionless and can reach values that vary from –∞ to +1 with better model efficiency when they are close to +1.

where: EF is model efficiency; the observed values; the simulated values; the mean of observed values.

The root mean square error or (RMSE) is one of the most widely used statistical indicators and measures the average magnitude of the difference between predictions and observations. It ranges from 0 to positive infinity, with the former indicating good and the latter poor model performance. A big advantage of the RMSE is that it summarizes the mean difference in the units of P and O. It does however not differentiate between over and underestimation.

where: N is the observations number.

Normalized Root Mean Square Error (NRMSE) is a statistic parameter for model evaluation. A simulation can be considered excellent if NRMSE is smaller than 10%, good if between 10 and 20%, fair if between 20 and 30% and poor if larger than 30%.

Index of agreement (d) is a measurement of the relative error in model estimations. It is a dimensionless number that ranges between 0 and 1, with 0 indicating no agreement and 1 indicating a perfect agreement between the predicted and observed data, typically values greater than 0,65 are considered as high (Krause et al., 2005).

RESULTS AND DISCUSSION

In the calculation process of AquaCrop model, devel- opment of the canopy cover is the first parameter that is calculated. In Figure 1, observed and simulated canopy cover progression is presented. The model underestimates the cano- py cover during the 30 days after sowing. Between 30 and 50 days after sowing the model overestimates canopy cover; this is the period of maximum crop vegetative growth.

In the senescent period after 60 days model overestimates canopy cover, reaching finally a value equal to zero, this variety has as a characteristic that leaf falling occurs almost totally in few days, what can explain the difference with the model; however, the tendency that describes the model curve is similar to reality. The same tendency is showed by (Steduto et al., 2009 and Araya et al., 2010) in the parameterization of maize and barley, respectively.

These authors found that during the growth and senescence periods, model shows de highest differences with respect to the observed data where, moreover, highest standard deviations are presented. Correct simulation of canopy cover is essential for AquaCrop representation; because affects the transpiration rate and therefore biomass accumulation (Farahani et al., 2009).

AquaCrop model overestimates the biomass accumulation between 25 and 40 days approximately as can be seen in Figure 2, which is coincident with the overestimation of canopy cover (Figure 1), this supposes a major biomass accumulation. After 50 days observed biomass production was very low, however, model seems to assume a linear growth until 60 days, this is because the model cannot explain the complexity of the environmental processes (Guendouz et al., 2014; Amiri, 2016) (mainly temperature and wind speed variations) and physiological that occur in the plant and their impacts on biomass production. AquaCrop utilizes in the dry biomass accumulation, a linear model highly con- trasted (Steduto et al., 2009), where dry biomass is related with crop transpiration through water productivity variable (WP). Intending to normalize this variable it is included in this connection reference evapotranspiration (ET00).

In Figure 3 it is observed that the evolution of the soil water content simulated by AquaCrop was similar both in trends and in absolute values to the ones obtained for gravimetric. The model tends to overestimate the evolution of the soil water content in all the realized observations. Between 18 and 61 days it was not necessary to irrigate due to the rains happened in the period.

In general it is considered that the simulation of the development phases was satisfactory; since the statistical indicators for the CF are good (Table 3). There was obtained a high R. (0,95), the NRMSE is inside the limits of ±20 %. EF and d values are high according to Krause et al. (2005); Moriasi et al. (2007).

The statistical indicator obtained in the BSA simulation during the crop period showed good adjustments between the observed and simulated dates with a high coefficient of determination (R.=95), low errors in the BSA (RMSE=0,45 t h^-1), the NRMSE was acceptable (10-20 %) and the EF and d values of 0,94 and 0,98 were very high respectively.

The value of the R. obtained between the simulated soil water content and the field observations was 0,81, which is considered acceptable because it is superior to 0,5 (Moriasi et al., 2007). The statistical of the accumulated soil water content to 0, 30 m indicate that the obtained errors are lower than 7,3 mm. As for the aggregation of the model, this is considered acceptable, with EF and d values of 0, 63 and 0, 92, respectively. These differences of errors are due to the heterogeneity of the soil in the calculation of the water balance to different depths (Delgoda et al., 2016; Montoya et al., 2016).

CONCLUSIONS

• The evolution of the variables canopy cover, dry biomass and soil water content simulated by AquaCrop were similar in tendencies and in absolute values to the observed ones.

• Taking the statistical indicators: R², RMSE, NRMSE, EF and d as criteria, it was possible to prove that the model can adequately reproduce the variables observed.

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