New Paradigms for Environmental and Agronomic Research and Education.

Assumptions underlying randomized complete block designs and ANOVA are often not satisfied. Rather than arranging them randomly, treatments can be distributed in a periodic pattern. Such a design provides opportunities with regard to the statistical diagnosis of processes. The idea based on Fourier transformation is not new but has been used in irrigation research in the 1980’s. The analysis of cyclic components of data series originates from the re-occurrence of conditions that lead to repetitive data patterns. In Fourier analysis, the cyclic behavior of the series is manifested in a cosine shape autocorrelation function. Repetitive fluctuations of data cause peaks in the autocorrelation function re-occurring at regular intervals. The power spectrum represents one characteristic peak corresponding to the length between recurring peaks in the autocorrelation function. Several processes occurring at different wave lengths or scales resulting in multiple peaks can overly each other and obscure easy identification of signals at different wave lengths. A tracer transport study showed that the leaching depth spatially fluctuated according to the specific scales at which rainfall amount, intensity and tracer application time delay as well as land use were spatially distributed cyclically repetitive. Cross-spectral analysis is used to quantify common scales of variation and to inform whether two variables are positively or inversely related which is expressed in their phase. In another example, a nitrogen fertilizer experiment was designed periodically. Due to inherent soil variability, the fertilizer rate effect on winter wheat yield would not have been identifiable through ANOVA. However, a large scale trend could be identified and removed through an additive state-space model and the residuals clearly indicated a fertilizer effect. Underlying soil variability does not have to be considered as an obstacle in field research anymore but is treated as a scale-specific variance component that can be separated from treatment effects.