Mapping the phosphorus sorption capacity of Danish soils in four depths with quantile regression forests and uncertainty propagation

Managing soil phosphorus is essential for agricultural production and environmental protection. This requires information on the phosphorus sorption capacity (PSC) of the soil. In this study, we map the PSC for Danish soils in four depths. Measuring PSC directly is expensive and time-consuming, and we therefore used a pedotransfer function based on oxalate-extractable aluminum (Al-o) and iron (Fe-o). We mapped Alo, Feo, and their uncertainties using Quantile Regression Forests (QRF). We then calculated the uncertainties for PSC with a quasiMonte Carlo complete combinatorial convolution (CCC) of the prediction quantiles for Alo and Feo. The main factors for predicting Al-o were the parent material, topography and precipitation. In many areas, podzolization also affected the vertical distribution of Al-o. The main factors for Fe-o were the soil texture, organic matter and wetland areas. The average predicted PSC was 36 +/- 9 mmol kg(-1) (+/- 1 SD) in topsoil, but it was generally highest at 25-50 cm depth with a mean value of 37 +/- 9 mmol kg(-1). The weighted root mean squared error of the mapped properties was 14 mmol kg(-1) for Al-o, 32 mmol kg(-1) for Fe-o and 19 mmol kg(-1) for PSC. The prediction accuracies were moderate at best, but the prediction quantiles were generally reliable. The mapped uncertainties were largest in wetland areas, while they were smallest in young loamy moraine deposits.