Factors influencing the temporal coherence of five lakes in the English Lake District

1. The lakes in the Windermere catchment are all deep, glacial lakes but they differ in size, shape and general productivity. Here, we examine the extent to which year-to-year variations in the physical, chemical and biological characteristics of these lakes varied synchronously over a 30-40-year period. 2. Coherence was estimated by correlating time-series of the spring, summer, autumn and winter characteristics of five lakes: Esthwaite Water, Blelham Tarn, Grasmere and the North and South Basins of Windermere. Three physical, four chemical and two biological time-series were analysed and related to year-to-year variations in a number of key driving variables. 3. The highest levels of coherence were recorded for the physical and chemical variables where the average coherence was 0.81. The average coherence for the biological variables was 0.11 and there were a number of significant negative relationships. The average coherence between all possible lake pairs was 0.59 and average values ranged from 0.50 to 0.74. A graphical analysis of these results demonstrated that the coherence between individual lake pairs was influenced by the relative size of the basins as well as their trophic status. 4. A series of examples is presented to demonstrate how a small number of driving variables influenced the observed levels of coherence. These range from a simple example where the winter temperature of the lakes was correlated with the climatic index known as the North Atlantic Oscillation, to a more complex example where the summer abundance of zooplankton was correlated with wind-mixing. 5. The implications of these findings are discussed and a conceptual model developed to illustrate the principal factors influencing temporal coherence in lake systems. The model suggests that our ability to detect temporal coherence depends on the relative magnitude of three factors: (a) the amplitude of the year-to-year variations; (b) the spatial heterogeneity of the driving variables and (c) the error terms associated with any particular measurement.