Estimation of winter respiration rates and prediction of oxygen regime in a lake using Bayesian inference

Abstract

In this paper, we estimate the winter respiration (oxygen depletion per unit area of hypolimnetic surface) in a hyper-eutrophic shallow lake (Tuusulanjärvi) in the northern hemisphere (Finland, northern Europe, latitude 60 ∘26′, longitude 25 ∘03′) under ice-cover periods in the years 1970–2003. We present a dynamic nonlinear model that can be used for predicting of the oxygen regime in following years and to dimensioning of needed artificial oxygenation efficiency that will prevent fish kills in the lake. We use Bayesian estimation of respiration using Markov chain Monte Carlo (MCMC) method (Adaptive Metropolis–Hastings algorithm). This allows for analysis and predictions that take into account all the uncertainties in the model and the data, pool information from different sources (laboratory experiments and lake data), and to quantify the uncertainties using a full statistical approach. The mean estimated respiration in the study period was 301 ± 105 mg m −2 d −1, which is on the upper limit of winter respiration of eutrophic Canadian lakes on the same latitude. The reference rate of the respiration k (d −1) at 4 ∘C indicated cyclic behavior of about 9-year amplitude and had a statistically significant negative trend through out the study period. The temperature coefficient and respiration rate of the model prove to be highly correlated and unidentifiable with the given data. The future winters can be predicted using the posterior information coming from the past observations. As new observations arrive, they are added to the analysis. Methods are shown to be applicable to the dimensioning of artificial oxygenation devices and to the anticipation of the need for oxygenation during the winter.