On the use of structured time-series to detect and test hypotheses about within-lakes relationships

Abstract

Aquatic scientists using empirical relationships developed from point measurements or averages from different lakes often assume that these relationships also apply to individual lakes over time. However, this assumption is difficult to test because the extent of variation within a single system is generally much smaller and the relationship accordingly less defined than across a number of systems. We present a new method to extract empirical relationships from the internal structure of a time-series within a single lake. When we applied the method to an extreme simulation, we were able to recover accurately the parameters of the relationship in spite of the absence of any apparent relationship between the variables. When applied to empirical data for phosphorus and chlorophyll concentrations collected daily over one field season, the estimated structural relationship was nearly identical to that estimated from cross-sectional data even though the empirical trend appeared much shallower and very weak.