Additive State-Space Model for Decomposing Variation At Different Scales: Opportunities for Experiments In Variable Landscapes.

Inherent soil variability is often considered an obstacle in field or landscape scale experiments because of the difficulty of separating treatment effects from underlying soil heterogeneity. Experimental designs and statistical methods can be chosen to overcome problems of existing approaches based on randomized plots. The objective of this study is to examine non-random cyclic treatment designs using scale-dependent analysis of treatment effects and underlying spatial processes. In a field-scale solute transport experiment, rainfall characteristics as factors controlling leaching depth of a bromide tracer were laid out periodically at different spatial scales. In a fertilizer response experiment, nitrogen fertilizer was applied with a spatially sinusoidal pattern in a field soil that was known for considerable spatial heterogeneity. In both studies, the cyclic variation at the small scale caused by treatments was described by an additive state-space model. This special type of state-space model approach estimates the small-scale cyclic variation component that exists on top of a large scale underlying process. The latter can be caused by inherent underlying soil variation or even another treatment effect induced at a large scale. Both studies were conducted in Kentucky, i.e., the tracer experiment in Lexington, and the nitrogen response study in a farmer’s field in Princeton. The small-scale variation in the tracer experiment is associated with the time lag between tracer application and subsequent precipitation. The large scale variation of leaching is spatially coherent with rainfall amount and intensity, spatially distributed and applied at large scales. Small scale variation of wheat yield in the nitrogen response study is caused by the spatial fertilizer distribution. Large scale variation is spatially associated with landscape topography and soil textural variation. As shown for these field studies, using additive state-space analysis, treatment effects can efficiently be studied especially in variable soils and landscapes.