Evaluation of models to upscale the small scale variability of Cd sorption in a case study

Cadmium sorption, basic soil properties and water retention were jointly analyzed in an acidic sandy podzol under pine forest in the North of Germany. Samples were taken along a 10 m transect at a depth of 0.15 m with a sample-support of 0.15 m. The small-scale Cd sorption variability was upscaled in two steps. Firstly, it was simplified and, secondly, aggregated from the sample to the pedon scale. We evaluated different models to simplify Cd sorption variability at different levels of spatial aggregation. Our evaluation method was the numerical simulation of Cd transport in the topsoil where the variability of Cd sorption is the key input.We described Cd sorption with the Freundlich parameterization and tested three models to simplify its spatial variability. The reference model (model 1) had two and the simplified models only one spatially variable sorption parameter. Model 2 varied the parameter K_f of the Freundlich parameterization and set the exponent constant. Model 3 expressed only the linear variability of sorption. Each sample had a scaling factor that related to a constant sorption reference function. The Freundlich parameter K_f of the third simplification model (model 4), was derived by a local pedotransfer function. Its variability was, therefore, filtered by the available variation of a limited number of basic soil properties.The average sorption was at all aggregation levels not significantly different between the models. However, the corresponding uncertainty was smallest for model 3, intermediate for model 4 and largest for model 2. We evaluated the different sorption variability models with the simulation of Cd transport. The mean Cd concentrations in the topsoil predicted by the different models were statistically not different. However, at all support scales, the uncertainties of the predicted mean Cd concentrations and the RMSE's were smallest when model 3 was used, where the error was about 20% at the sample scale and decreased to below 10% at the pedon scale. Therefore, if measurements of sorption isotherms are available, we recommend to use model 3 to derive the mean sorption behavior with minimal uncertainty.