Sampling Design and Spatial Modeling of Available Phosphorus in a Complex Agricultural Area in Southern Brazil

In this study, we have compared three sampling designs and two modeling methods applied in the spatial prediction of available P in the soil. The study was conducted in a 160 ha where three sampling methods were tested — simple regular grid (RG) with a fixed distance between points, spatial coverage sampling (SCS) containing points over short distances, and simulated annealing sampling considering the marginal distribution of environmental covariates (DIST) — as a basis for prediction of the available phosphorus content in the soil, at a depth of 0–10 cm. Thus, each calibration set contains 160 samples, which were used to calibrate two predictive models: kriging with external drift (KED), considered a mixed model because it encompasses the geostatistical and deterministic approaches; and ordinary kriging (OK). The results were validated with an external and independent set containing 50 points. The best prediction result was found by combining the DIST sampling with the KED model, which has a lower mean absolute error (MAE) = 14.62 mg dm −3 , mean error (ME) = −3.12 mg dm −3 , and root mean squared error (RMSE) = 23.44 mg dm −3 and higher Nash-Sutcliffe efficiency (NSE) = 0.13. Sampling designs that consider environmental covariables contribute to the increase in the quality of the predicted available phosphorus maps. The most accurate map was generated from the DIST sampling combined with KED modeling.