Estimation of maize yield based on projection pursuit with particle swarm optimization

Abstract: Scientific and accurate estimation of crop yields is of great significance for strengthening crop production management, guiding and adjusting crop planting structures, formulating social development plans and ensuring national food security. In this paper, the central plain of Hebei Province is taken as the study area, which includes 5 Cities. Remotely sensed vegetation temperature condition index (VTCI) and leaf area index (LAI), which are closely related to soil moisture and maize growth status, are used for estimating maize yields. In view of the fact that most of the previous studies only considered the single growth stage of maize, the main growth stages (seedling-jointing, jointing-booting, booting-milking, milking-mature) are considered in this paper. In addition, the effect of water stress on maize yields at each growth stage is different. Therefore, the projection pursuit method is used to determine the weights of VTCI and LAI at each growth stage of maize. The weights of VTCI and LAI at each growth stage of maize are obtained when the projection direction is optimal, but the optimal projection direction is difficult to determine by traditional methods. To this end, the particle swarm optimization with linearly decreasing weight is chosen to find the optimal projection direction. The weights of VTCI and LAI at each growth stage of maize determined by the projection pursuit method are objective and reasonable and consistent with the growth pattern of maize. Then the weighted VTCI and LAI from 53 Counties (districts) in the study area are calculated from 2010 to 2018 and the yield estimation models are constructed with weighted VTCI and LAI from 2010 to 2015. The results show that except the single parameter model based on VTCI in the overall regression models, the correlation between parameter and maize yields reach significant levels (P<0.05), and most of them reach extremely significant levels (P<0.001). The accuracy of models with the two-parameter is higher than that of models with single parameter. The determination coefficient (R2) of each City in the study area based on the two-parameter model is also the largest compared with other models, and the largest in Langfang City with R2 of 0.472 and the smallest in Baoding City with R2 of 0.187. Except Baoding City, the R2 of two-parameter models are higher than that of the variation coefficient method. In order to further verify the accuracy of the model based on the projection pursuit method, the average relative error (RE) and root mean square error (RMSE) are calculated between estimated yield and actual yield of maize. The average RE of the model based on the projection pursuit method is 7.33%, and the RMSE is 566.43 kg/hm2. Compared with the variation coefficient method, the average RE is reduced by 0.88 percentage points, and the RMSE is reduced by 50.56 kg/hm2. Based on the two-parameter regression model determined by projection pursuit method, the maize yields pixel by pixel in the study area are calculated from 2010 to 2018. The results show that the yield of maize in the western part of the study area is the highest, followed by the north and the south, and the lowest in the east. During the years of the study, maize yield first declined in fluctuation and then increased. In conclusion, it is feasible to apply projection pursuit optimized by particle swarm optimization with linearly decreasing weight to the estimation of maize yield in the study area, which can provide some reference for yield estimation in other areas.