# A New Pabs Model for Quantitatively Diagnosing Phosphorus Nutritional Status in Corn Plants
## 4 Results
### Diagnosis and Verification  
Figures 8 and 9 illustrate the effectiveness of the vegetation index models and the derived PNI. The vegetation index models for phosphorus concentration (Figure 8a) and aboveground biomass (Figure 8b) were constructed using the optimal vegetation indices identified through the sensitivity analysis. Both models exhibited high coefficients of determination (R\({}^{2}\)), confirming the reliability and robustness of the selected vegetation indices as strong predictors of phosphorus concentration and aboveground biomass. Figure 9 demonstrates the correlation between the estimated PNI, derived indirectly from plant phosphorus concentration and aboveground biomass, and the measured PNI. The estimated PNI values exhibited a strong linear relationship with the measured PNI, achieving  
Figure 5: Comparison of predicted plant phosphorus concentration: (**a**) LIBSVM proxy model training set; (**b**) testing set. Figure 6: Comparison of predicted aboveground biomass: (**a**) LIBSVM proxy model training set; (**b**) testing set. an R\({}^{2}\) value of 0.706 and an RMSE of 0.082. These results highlight the feasibility and accuracy of using this indirect method for PNI estimation, providing a valuable approach for assessing phosphorus nutritional status in maize. The multispectral inversion model was applied to assess the spatial distribution of phosphorus status indicators in corn fields across Changchun. The spatial distribution  
Figure 8: Phosphorus regression model constructed with the optimal vegetation index (**a**) and biomass regression model (**b**). Figure 7: Evaluation metrics: (**a**) phosphorus concentration; (**b**) aboveground biomass. Figure 9: Relationship between observed and predicted PNI using MNVI-estimated P and GSAVI-estimated biomass. of the corn plant phosphorus concentration (Figure 10a) reveals minimal variation, with values predominantly between 1.2 and 1.5 g/kg. Similarly, the spatial distribution of aboveground biomass (Figure 10b) shows limited variation, with biomass values mostly ranging from 11 to 12.5 t/ha. The inversion model also provided an indirect estimate of the PNI for corn plants in the region (Figure 10c). The results indicate a generally uniform phosphorus nutrition status, with PNI values predominantly between 0.92 and 1.02, suggesting adequate phosphorus levels. Higher PNI values (1.02-1.12) were observed in some areas of northeastern Yushu. The phosphorus demand distribution, derived from the Pabs model (Figure 10d), confirms that phosphorus deficiency is uncommon, with most regions showing sufficient phosphorus levels, consistent with field survey results. The phosphorus demand was largely concentrated within the 0 to 8 kg/ha range. Areas identified as phosphorus-deficient were primarily located in northeastern Yushu, aligning with local phosphorus nutrition diagnoses. This deficiency is likely due to excessive phosphorus fertilization practices employed by farmers to ensure crop yields. To assess the diagnostic accuracy of the remote sensing model for phosphorus nutrition, corn yield data were collected from 20 sampling points across corn-growing regions around Changchun. Some studies have shown a strong relationship between phosphorus fertilizer and maize yield. [48]. Accordingly, it is assumed that when the grain yield at a sampling point is lower than the local target yield, the phosphorus nutrition is considered deficient, while a yield meeting or exceeding the target indicates sufficient phosphorus nutrition. Sampling points where the PNI exceeds the target value (PNITarget) and the plant is not phosphorus-deficient, as well as those where PNI is below PNITarget and the plant exhibits phosphorus deficiency, are classified as correct diagnosis points (Figure 11). The correct diagnosis points, located in the first and third quadrants, account for 75% of all sampling points. This demonstrates that the model effectively identifies the phosphorus nutritional status of corn, confirming its strong applicability for phosphorus management.