Modeling wind drift and evaporation losses during sprinkler irrigation in arid areas (case of Touggourt - Algeria)


 In recent years, agriculture development in South-eastern Algeria progressed rapidly which increased the demand for agricultural products. Given that this region is characterized by hard agro-climatic conditions, irrigation seems to be a necessary factor for ensuring optimal development and high agricultural production. Like many irrigation technics widely used, sprinkler irrigation performance was considerably affected by these conditions, mainly evaporation, which causes water losses. This study aims to propose an adequate mathematical model predicting wind drift and evaporation losses under different weather conditions resume by the complex indicator of climatic intensity (ɸ). Results showed that complex indicators of climatic intensity, were significant factors affecting the wind drift and evaporation losses, puissance relationship between wind drift and evaporation losses, and complex indicators of climatic intensity, obtained model are adopted can be useful tools in the determination of the overall losses in terms of environmental conditions (air temperature, relative humidity, and wind speed). Totally 25 measure samples were used for training the model, and 15 measure samples for testing and validation of the model. The developed model for the WDEL modeling shows high good performance with a coefficient of determination (R2) = 0.808, mean squared error (RMSE) = 3.39%, and Mean Absolute Error MAE = 8.41%.

Climatic conditions, in the region of Touggourt, are very hard in particular the period which extends between April and September. Temperature daily average can exceed 40° C, the relative humidity average of air is often less than 40% and the wind speed average oscillates between 2 and 4 m·s -1 ., the most common irrigation method was gravity irrigation (board's lines), but new methods have been introduced in recent years such as sprinklers. requires studying water losses (Gheriani et al.,2020).
On the other hand, Sapunkov's relation involved a parameter called a complex indicator of climatic intensity (ɸ) which was defined by Khabarov (1982) and introduces climatic parameters: WDEL=overall losses as a percentage of volume; (a) And (b) = are coefficients according to geographical areas; ɸ = complex indicator of climatic intensity; evaluated by the following formula: Unfortunately, these methods were not developed under the same geographical conditions as the study region.
Therefore, this study aims to present a model that can estimate the overall WDEL specifically using the ɸ parameter.

Experimental database
The model has been developed using experiences Data from the published study by Gheriani et al. (2020) Merriam and Keller (1978). The test area was equal to 0.52 ha. The distribution of water under the sprinklers was assessed by collecting the amounts of water using the catch containers that were arranged in a grid at 4 to 4.5 of spacing. The catch containers were measured with 100 mm of diameter and 200 mm of height with a total of 273 containers. Furthermore, climatic parameters such as temperature, air humidity, and wind speed at the test area were measured with a conventional meteorological station installed near the field. Finally, the evaporation and wind drift losses were calculated using the following equation (Keller and Bliesner, 1990): where h (m) is the total depth of water in the catch containers, A(m 2 ) the irrigated area around each container and V (m 3 ) the volume of sprinkler discharge.

Statistical analysis
nonlinear regressions were performed, for a correct prediction of WDEL, in terms of climatic intensity complex indicator (ɸ), depending on the model indicated in equation (6). Analyses were performed using the SPSS version. 20 software.

Performance evaluation criteria
Mean absolute error (MAE), mean squared error (RMSE) determined by Maroufpoor et al. (2018), and coefficient of determination (R 2 ) defined by Yasar et al. (2012) were used to see the convergence between the observed and the expected values: Where: O = observed value; P = expected value; n = number of observations

Results and discussions
Measurements of total losses, climatic parameters (air temperature, air humidity, and wind speed), and climatic intensity complex indicator parameter values (ɸ) were presented in Table 2.
The relationship between wind drift, evaporation losses (WDEL), and complex indicator of climatic intensity (ɸ), according to the equation (6) the optimal solution was summarized in Table 3.
The model of relation was written as follows:

Relationship between predicted and observed WDEL values
The present experiment allowed us to record the R 2 between predicted and observed WDEL values with 0.808 ( Fig. 2a-b). This situation was also confirmed by the straight regression lines which express 80.8% of the overall variance. Also, a sample size of (N = 25˂ 50) and data that follows the normal distribution at Sig. a value greater than 50 % (Kim, 2015;Gerald, 2018), Shapiro-Wilk significant values were equal to 0.02 and 0.086 for observed and predicted WDEL respectively. (Table 5).
Therefore, the parametric tests for the observed and the predicted values follow the abnormal distribution at a 95% confidence interval. In this case, the nonparametric test of Mann-Whitney was used in this comparison (Conover, 1999). The last test indicated that Sig Asymp's significance level value of 0.764 was less than 0.05, which means that there was no difference between the observed and predicted values of the WDEL, which confirmed that the model was precise. These results are confirmed by Sapounkov's results, which determine the wind drift and evaporation losses (WDEL) models to different spray devices depends on complex indicator of climatic intensity (ɸ).

Conclusion
Because of the climatic and agrological conditions, the region of Touggourt (arid climate) saw a quick development of sprinkler irrigation technic that exposed enormous losses evaporation and entrainment.
In this study, an adequate mathematical model predicting wind drift and evaporation losses under different weather conditions was resumed by the complex indicator of climatic intensity (ɸ), in sprinkler irrigation, allowing their use by considering them in the correction of watering doses.
The experimentation showed that overall water losses were affected by weather factors i.e., air temperature, wind speed, and air humidity respectively. Formula 13, shows high good performance, with R 2 = 0.808, RMSE = 3.39 % and MAE = 8.41%, were the adopted model that seems to fit the conditions of the study region. We circulate this approach to study on various sprayers in future studies so that we can optimize water resources.
Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.

Declaration on conflict of interest:
No conflict of interest was declared.