State-Space Modeling Allows the Separation of Small- and Large-Scale Variability Components of a Field Solute Leaching Experiment.

Understanding the leaching of surface-applied solutes and pesticides under different land use conditions is critical to our knowledge on water flow and solute transport in soils and efforts to model these flow processes. One problem inherent in the measurement of solute leaching in field experiments is the considerable high natural spatial variability of flow-controlling soil properties. Thus, analyzing treatment effects based on the mean and the variance of observations can become obsolete if there is a huge inherent variance in the set of measurements, and if no spatial range of influence can be derived from the observations. To overcome this limitation, the spatial covariance and cross-variance between measurements was used in the present study. We demonstrate that applying an additive state-space model can help to differentiate between scale-specific variance components within the solute leaching behaviour along an experimental transect. Applying a novel experimental scheme, where the treatments were arranged in a scale-dependent manner, bromide leaching under two contrasting land use systems (cropland vs. grassland) was compared. After surface application of tracer solution (KBr), the experimental field was irrigated using different time delays as well as two different irrigation amounts and two different intensities. At the end, the Br-concentration in the soil profile was determined from soil sampling. Upon spatial statistical data analysis, an additive state-space model was applied to separate the long- and short-wave components of water infiltration and bromide leaching behaviour. Subsequently, the large-scale process was described in an autoregressive state-space model.The experimental approach and the separation of small- and large-scale variability components support studying soil ecosystem processes that vary at different scales even in the presence of underlying large-scale trends that are currently considered obstacles in field research. Our result has implications not only for agricultural management experiments but also for large-scale hydrological and transport studies in landscapes and watersheds.