Coefficients of variation for chlorophyll, green algae, diatoms, cryptophytes and blue-greens in rivers as a basis for predictive modelling and aquatic management

Biological systems are variable and there are fundamental limits on the predictability of, e.g. phytoplankton concentrations in rivers and lakes. How does inherent uncertainties in empirical data constrain our approaches to prediction? This paper addresses this question in discussing one of the most fundamental concepts in predictive ecosystem modelling, the uncertainty in the empirical y-variable used to validate model predictions. So, the focus of this paper is not on concentrations but on coefficients of variation (CV: S.D./MV; S.D.: standard deviation, MV: mean value). The CV-values regulate the theoretically highest predictive power of models and the reliability of data used for model validations. We have collected an extensive data-base from the River Danube (at a site close to Regensburg) as a basis for these analyses. The water samples have been analysed using delayed fluorescence (DF), a technique which makes it possible to obtain compatible data on the five algal variables used in this study, green algae, diatoms, cryptophytes and blue-greens (cyanobacteria) as well as total chlorophyll. We have also compared these results on CVs with results from other river sites and lakes. This study shows that: (1) The monthly variations in CV based on data from several years show similar patterns for the five algal variables, but the CVs are generally somewhat higher for all five variables in September and October and lower in April and May. (2) The monthly CVs do not seem to be significantly related to the mean values or the flow velocity. (3) There are no significant differences in monthly CVs among the five variables, although the blue-greens may have the highest CV and cryptophytes and green algae the lowest. (4) The daily, weekly, monthly (based on individual months, e.g. January a given year), monthly (based on data from several years, e.g. January for several years) and yearly CVs increase from 0.3, 0.35, 0.55, 0.80 to 0.95, respectively, for chlorophyll (and similar values also apply to the four other algal variables). This means that it is unlikely that a model for monthly chlorophyll concentrations in rivers would yield r2-values higher than about 0.6. This information is of great importance in science and water management since it means that we can never expect to derive models that could predict monthly chlorophyll concentrations in rivers well. (5) The mean CV for chlorophyll based on all data from the Regensburg site is 0.96, which is close to the median value from 19 rivers sites in the UK. (6) The correlation between the monthly mean values and the monthly peak values were found to be strong, but this is partly spurious.