Predictive model for phosphorus in large shallow Lake Peipsi: Approach based on covariance structures

Abstract

Long-term datasets of nutrient levels provide a unique opportunity to study the changes that occur in lake ecosystems subjected to multiple man-induced and natural pressures. Unfortunately, the relevant dataset of thousands of records for Lake Peipsi (Estonia/Russia) is rather fragmentary and therefore difficult to analyse. Focusing on the total phosphorus concentration (TP), which is believed to be the main reason for degradation of the shallow lowland lake, we tailored, using SAS/STAT software, a special mixed regression model having 61 linear parameters and a repeated measures approach with spatial covariance structure. The model describes the dependence of TP in the surface water on year number (1985–2010), on the day of year and on geographical coordinates. Based on Akaike's criterion, the present model is superior to the analogous model, where the prediction errors (residuals) are supposed to be independent. Another advantage of the present model is that it distinguishes two groups of factors related to the variation in TP residuals. Factors of the first group affect TP synchronously within the larger areas, while this synchrony is weakening down to about 75 km or even more as has been shown by the SAS VARIOGRAM procedure. Factors in the other group can be associated with sampling instability and random errors in laboratory analyses. The influence of both factor groups on TP is approximately equal, with the related variance components on a log₂-scale being 0.12 and 0.15.

Keywords:

• total phosphorus concentration
• mixed regression model with spatial covariance structure
• eutrophication

Acknowledgements

Funding for this research was provided by the target-financed projects SF0170006s08 and SF0180026s09 of the Estonian Ministry of Education and Research, by the Estonian Science Foundation grant 7643 and by the Estonian Centre of Excellence in Genomics. We are indebted to Dr. Märt Möls for useful suggestions and comments on the theoretical aspects of statistical methods used in this article. Additionally, we gratefully acknowledge Dr. Renee Miller (UK) for language editing.