Estimation of the effective rainfall by reverse solution method and using artificial intelligence (Case study: Kermanshah Province)

Introduction
Precipitation is one of the most important climatic phenomena affecting the globe. In each round of rainfall, only a part of the rainfall is used by the plant, and the rest is removed from the reach of the plant through different ways such as runoff and passing through the root zone. For this purpose, the concept of effective rainfall is used to express the part of the precipitation that directly responds to the plant's water needs. Estimating effective rainfall is one of the essential components in water resources management, irrigation planning decisions, and a guiding factor for crop production estimation. To make the best possible use of rainfall for the agricultural sector in rainfed lands, estimating the effective rainfall is vital. Since the only source of water supply for rainfed crops is rainfall and the yield of rainfed crops depends on the amount of water absorbed by the plant, almost all of the effective rainfall is spent on evapotranspiration. Therefore, the purpose of this research is to estimate the amount of effective precipitation through the estimation of the evapotranspiration rate of rainfed crops and also to develop a model of effective precipitation estimation based on an artificial neural network.
 
Materials and Methods
Considering the importance of estimating the effective rainfall and since rainfall is the only source of water supply for rainfed crops and the yield of rainfed crops is dependent on the amount of water absorbed by the plant, almost all of the effective rainfall is spent on evapotranspiration. Therefore, to more accurately estimate the effective rainfall, by having the yield of rainfed crops for a region and using the relationship between evapotranspiration and crop yield, it is possible to obtain the actual evapotranspiration ration and, as a result, the effective rainfall amount. The study area of ​​this research is Kermanshah Province, one of the western Provinces of Iran, where extensive rainfed crops are cultivated every year. The meteorological parameters of 10 meteorological stations in Kermanshah Province were received and calculated a result of the weather condition of Kermanshah Province. Then, the potential evapotranspiration was calculated using meteorological parameters and CROPWAT software. In addition, the amount of cultivated area (ha) and the amount of production (t) of rainfed wheat in Kermanshah Province were extracted from the agricultural statistical yearbooks, and the yield of rainfed wheat for 14 crop years (crop years 2005 to 2019) was calculated. Then, with the crop factor and potential evapotranspiration rate in hand, using the Doorenbos and Kassam equation, the actual rate of evaporation and transpiration during the crop growth period for the aforementioned 14 agricultural years was estimated. Then the correlation between effective precipitation and meteorological parameters (such as maximum temperature, minimum temperature, humidity, wind speed, sunshine hours, growing degree days, and precipitation) was investigated and the most effective parameters were used to develop a model using feedforward neural network (FFNN). 5 networks were developed under different scenarios (with different inputs and outputs of effective precipitation) and the error of the networks was evaluated with the evaluation criteria of root mean square error (RMSE), mean bias error (MBE) and index of agreement (D). Finally, the best network with the least error was introduced to predict effective rainfall.
 
Results and Discussion
The total rainfall during the growing period of the dry wheat crop in crop years varied between 204.59 and 748.79 mm and the yield of the crop varied between 0.3 and 1.63 t ha^-1. The results showed that the highest amount of yield in crop years is not related to the highest amount of rainfall and this result increases the importance of estimating the effective rainfall. The results show that the amount of effective precipitation estimated using Doorenbos and Kassam's equation during the studied period (14 years) and during the growth of the dry wheat crop varied between 119.85 and 279.90 mm. Then, in order to accurately estimate, an effective rainfall estimation model was created in Kermanshah Province with the help of a neural network. In this model, the effect of each of the meteorological parameters on the effective precipitation estimated by the inverse solution method was investigated with the Pearson correlation method, and the most effective parameters were used for modeling in several scenarios. Among all the meteorological parameters such as temperature, humidity, sunshine hours, wind speed, growing degree days (GDD), and precipitation, the precipitation parameter with a correlation of 0.99 was recognized as the most effective parameter in estimating effective precipitation. Meteorological parameters were prioritized based on correlations and used for modeling by a neural network. Then, networks were trained under different scenarios (various inputs individually and together), among which the network with rainfall input had the best performance in estimating effective rainfall. R^2 (Coefficient of Determination) of effective rainfall prediction with the help of this model was estimated to be 0.99 and its RMSE (root mean square error) and MBE (mean bias error) value was 4.61 and -1.4 mm and index of agreement (D) was estimated 0.997.
 
Conclusion
In order to use water optimally in agriculture and drainage projects, it is necessary to know and estimate effective rainfall. Several experimental methods have been presented to estimate effective precipitation. However, considering that these experimental methods were developed for areas with special characteristics and their generalization to all areas is not error-free, in this research effective precipitation was estimated by the inverse solution method, and a suitable model was used. Meteorological information and information from crop yearbooks and CROPWAT software were used to calculate effective precipitation by the inverse solution method. In order to present a model based on artificial intelligence, the correlation of meteorological variables with effective precipitation was investigated. Finally, a model based on a neural network was proposed in Kermanshah Province to estimate effective rainfall. The results of this research showed that neural networks, which are based on mathematical and natural theories, are more successful in predicting effective rainfall based on the amount of rainfall directly.