Evaluation of Artificial Neural Network and Geostatistical Methods in Estimating the Spatial Distribution of Irrigated and Dry Wheat Yield (Case Study: Khorasan Razavi)

Introduction
Access to agricultural information and statistics, is a prerequisite for many agricultural activities. Crop performance is measured and reported as a point data. While this parameter is a random and dynamic variable and due to the spatial variability of crop yields, it is obviously necessary to estimate of yield. Wheat is the oldest cultivated crops in different parts of the world, which is used to produce grain for bread, animal feed and industrial use. Prediction of wheat performance needs data in terms of location, amount and distribution in a given geographical area. Selected of predicting correct method of is essential and important in crop management. In recent years with the growth of science and computer technology and software development models have been used in the management. The model is effective and accurate method in overcoming the limitations and errors of point measurements. The main condition for the success of the model is to select the appropriate method based on factors. In this study, two methods were used for modeling: geostatistical method and artificial neural networks (ANN). Methods of geostatistical, due to the spatial correlation of data and artificial neural networks due to the use of input and output patterns are important as a powerful tool in forecasting.

Methodology
The study area is Razavi Khorasan Province that located in north-east country and at latitudes between 33O and 30' to 37O and 41' north and longitude 56O 19' to 61O and 18' east. This province area is 127 thousand kilometers with 65300 hectares agricultural land. Approximately 36500 hectares of agricultural land under cultivation is irrigated and dry wheat. In this study, we used wheat yield data from 17 cities with at least 26 years of statistics. Choice reason of these cities was according to the statistical period, the appropriate spatial distribution and no need to reconstruct the data.
Wheat from terms of acreage and production rate is the most important agricultural products of the country from the economic point of view. The purpose of this study was to select the most appropriate method in estimating the spatial distribution of irrigated and dry wheat yield in Razavi Khorasan region. For this purpose geostatistics methods of ordinary kriging, simple kriging and universal kriging and ANN approach were applied. In this regard latitude and longitude information of 17 cities were used as input both methods (Geostatistic and artificial neural networks) and annual yield measurements as output. In section of neural network, learning rule of levenberge marqoate, momentum and conjugate gradient with back propagation algorithm and activation function of tangent and sigmoid for hidden layer and output layer were used. Finally, selection of the appropriate method was based on Wilmot index.

Results and Discussion
Results showed that among the methods of geostatistics, simple kriging with circular model with NRMSE=0.120 and ordinary kriging with exponential model with NRMSE=0.348 was suitable to forecast wheat yield. In addition, results showed that the ANN approach with three layers consisting of two neurons in input layer, four neurons in the middle layer and one neuron in output layer had required accuracy in between various structures implemented for predicting wheat yield. Comparison of ANN and geostatistical showed that ANN capability is more than kriging method. The ANN results showed that artificial neural network model, as an independent estimate, can predict wheat yield variables in all 17 cities. Also, comparison of the results of both methods with Willmot index showed the accurately of ANN in prediction of dry wheat yield (81%) and irrigated wheat yield (65%). While in geostatistical method, Wilmot index for predicting dry wheat yield and irrigated wheat yield was 53% and 50%, respectively. In general it can be concluded that the ANN approach with combining latitude and longitude can forecast irrigated and dry wheat yield with sufficient accuracy.

Conclusion
In this study, the statistical methods and artificial neural network were used to estimate the spatial distribution of irrigated and dry wheat yield. In both methods latitude and longitude information were used as input data. The results of this study showed the effects of latitude and longitude as independent variables in estimating the wheat yield of a regional. Also, it was found that the ANN is superior to kriging method and this method corroborate the nonlinear relationship between latitude and longitude value to wheat yield.