Information Theoretic Approaches to Characterize Uncertainty in Computational Models of Coupled Human and Natural Systems: Insights from an Integrated Model Predicting Water Quality in Lake Champlain under Alternate Hydro-Climatic, Land Use, And Nutrient

Traditional approaches to characterize uncertainty in computational models of coupled natural and human systems range from global sensitivity analysis of model parameters to Monte Carlo simulation experiments, decomposition analyses and propagation of errors analysis. In this paper, we propose that information theoretic approaches, such as Shannon’s Entropy, MaxEnt, Kullback Leibler Divergence (KLD), and Fisher’s Index etc., provide powerful complementary approaches to characterize uncertainty. The application of information theoretic approaches to characterize uncertainty may also lead to novel discoveries about understanding the dynamics of complex adaptive systems. We explore these propositions by applying unsupervised machine learning algorithms (Bayesian Network Models and Random Forest Models) to the simulation outputs derived from 180 scenarios of an integrated model that predicts water quality in Missisquoi Bay of Lake Champlain under alternate hydro-climatic, land use and nutrient management regimes for 2000-2050 timeframe. The best fit machine learned models are then analyzed to characterize the uncertainty by measuring node force derived from KLD, normalized symmetric mutual information and relative uncertainty of water quality predictor variables extracted from the integrated model. The network structure provides information about the modularity and connectivity of predictors across coupled human and natural systems. In the case of application in the Lake Champlain, we discover that predictor variables representing evaporation and transpiration connect hydro-climatic processes occurring in terrestrial watersheds with the biogeochemical processes occurring in the freshwater lakes. We also find that the variability in nutrient fluxes, temperature, evaporation, seasonality, snowpack, precipitation, land management, and river and stream discharge induce largest uncertainty in predictions of the algal blooms in Missisquoi bay. Both Bayesian Network Models and Random Forest Models generate similar list of uncertainty inducing predictors in the coupled system, However, we also observe differences in quantitative estimates of uncertainties induced by coupled state variables and their respective importance in predicting water quality.