# Quantifying Nutrient Content in the Leaves of Cowpea Using Remote Sensing
## 3 Results and Discussion
### Model Validation  
From the work data, two-thirds of the samples were selected for model calibration, while the final third was set aside for the validation phase. The validation process for the models was conducted using the following statistical metrics: coefficient of determination (R\({}^{2}\)), Root Mean Square Error (RMSE) and the Residual Prediction Deviation (RPD). The parameters used for analysing model fit for the variable phosphorus using a single band presented an R\({}^{2}\) of 0.62, RPD of 1.61 and RMSE of 0.54 g.kg\({}^{-1}\), classifying them as moderate for R\({}^{2}\) and RMSE and satisfactory for RPD (Figure 8a). The phosphorus estimate tends to underestimate the values of this nutrient. The parameters used for analysing the model fit for the variable potassium using a single band presented an R\({}^{2}\) of 0.60, RPD of 1.21 and RMSE of 5.37 g.kg\({}^{-1}\), classifying them as moderate for R\({}^{2}\) and insufficient for RPD and RMSE (Figure 8b). The potassium estimate tends to underestimate all values of this nutrient. Figure 8: Relationships between the measured and estimated P (**a**), K (**b**) and Ca (**c**) content, using the single-band model. The parameters used for analysing model fit for the variable calcium using a single band presented an R\({}^{2}\) of 0.65, RPD of 1.66 and RMSE of 5.21 g.kg\({}^{-1}\), classifying them as moderate for R\({}^{2}\), satisfactory for RPD and insufficient for RMSE (Figure 8c). The calcium estimate tends to underestimate all predicted values. Despite the model underestimating the concentrations, it presents the same trend; that is, underestimating the lower and higher values of calcium. According to [PERSON] [77], the models used for predicting phosphorus and calcium are highly accurate; however, the RMSE of the model for estimating calcium is insufficient, electing the model for estimating phosphorus as the most reliable among the single-band models. Model performance using band ratios for estimating phosphorus presented an R\({}^{2}\) of 0.60, RPD of 1.52 and RMSE of 0.65 g.kg\({}^{-1}\), classified as moderate for R\({}^{2}\) and satisfactory for RPD and RMSE (Figure 9a). Model performance using band ratios to estimate potassium presented an R\({}^{2}\) of 0.68, RPD of 1.67 and RMSE of 5.02 g.kg\({}^{-1}\), classified as moderate for R\({}^{2}\) and satisfactory for RPD and RMSE (Figure 9b). Model performance using band ratios for estimating calcium presented an R\({}^{2}\) of 0.67, RPD of 1.63 and RMSE of 5.42 g.kg\({}^{-1}\), classified as moderate for R\({}^{2}\) and satisfactory for RPD and RMSE (Figure 9c). Model performance using band ratios for estimating zinc presented an R\({}^{2}\) of 0.57, RPD of 1.50 and RMSE of 30.63 g.kg\({}^{-1}\), classified as moderate for R\({}^{2}\) and satisfactory for RPD and RMSE (Figure 9d). Using band ratios allowed for the obtainment of predictive models for each of the nutrients studied; however, the best-fitted model was the one used to estimate phosphorus. Nutrient estimates tend to overestimate lower values and underestimate higher values. Figure 9: Relationships between the measured and estimated P (**a**), K (**b**), Ca (**c**) and Zn (**d**) content, using the band-ratio model. RMSE values for zinc prediction are excessively high compared to other nutrients. [PERSON] [78] confirms that micronutrient predictions are generally not as good as those reported for macronutrients. Using samples from all phenological stages as a set, the model using band ratios also proved to be efficient only in predicting phosphorus content using selected bands, with an R\({}^{2}\) of 0.60, RPD of 1.62 and RMSE of 0.65 g.kg\({}^{-1}\). The parameters used for analysing the model performance for the variable calcium using PLSR in phenological stage V4 presented an R\({}^{2}\) of 0.78, RPD of 1.10 and RMSE of 3.10 g.kg\({}^{-1}\), classifying them as moderate for R\({}^{2}\) and insufficient for RPD and RMSE (Figure 10a). The calcium estimate tends to overestimate all values for this nutrient.