Predicting Soil Phosphorus Fertilizer Rate Using Hierarchical Segmented Regression Models

Predicting soil phosphorus (P) needs and P fertilizer requirements is important for plant nutrition and reducing environmental risk. The P requirement (PR) can be calculated from three components: the current status of soil P (P0), soil P buffer coefficient (PBC), and the soil P critical level (PCL). The PBC and PCL can be predicted from soil clay content using linear-plateau models. The PR, PBC, and PCL form a hierarchical model because PR depends on PBC and PCL, which, in turn, depend on soil clay content. The objective of this study is to estimate the parameters in this hierarchical model to ensure reasonable performance and behavior of PR in a large range of soil clay contents. Results showed that the linear-plateau model described the change of PBC with soil clay content in the range of 39 to 760 g kg. This model also described the change of PCL with soil clay content in the range of 80 to 760 g kg for six crops, including cotton, cowpea, maize, peanut, soybean, and wheat. The obtained PR showed irregular behavior of PR within soil clay content range from 288 to 357 g kg when PBC and PCL were independently predicted from soil clay. When the join points in the linear-plateau models of PBC and PCL were set to be equal, the irregular change of PR with soil clay content disappeared. The hierarchically modeled system predicts a decrease in PR with increasing current status of soil P and a curve-plateau trend with soil clay content.