Lake Superior water level fluctuation and climatic factors: A dynamic linear model analysis

We use Dynamic Linear Models (DLM) to analyze the time series of annual average Lake Superior water levels from 1860 to 2007, as well as annual averages of climate drivers including precipitation (1900-2007), evaporation and net precipitation (1951-2007). Our results indicate strong evidence favoring the presence of a systematic trend over a random walk for Lake Superior water levels, and this trend has been negative in recent decades. We then show decisive evidence, in terms of improved predictive performance, favoring a model in which the trend component is replaced with regression components consisting of climatic drivers as predictor variables. Because these models use lagged values of precipitation or net precipitation as predictors, the models can be used to forecast water levels, with the associated uncertainty, several years into the future. We use several of the best fit models and compare one (2008) and two step-ahead (2009) forecasts. The 2008 forecasts compare very well with the observed 2008 water level; the two step-ahead 2009 forecasts are offered as testable hypotheses. The Bayesian context in which these models are developed provides a rigorous framework for data assimilation and regular model updating.