Reconciling the water balance of large lake systems

Abstract

Water balance models are commonly employed to improve understanding of drivers behind changes in the hydrologic cycle across multiple space and time scales. Generally, these models are physically-based, a feature that can lead to unreconciled biases and uncertainties when a model is not encoded to be faithful to changes in water storage over time. Statistical methods represent one approach to addressing this problem. We find, however, that there are very few historical hydrological modeling studies in which bias correction and uncertainty quantification methods are routinely applied to ensure fidelity to the water balance. Importantly, we know of none (aside from preliminary applications of the model we advance in this study) applied specifically to large lake systems. We fill this gap by developing and applying a Bayesian statistical analysis framework for inferring water balance components specifically in large lake systems. The model behind this framework, which we refer to as the L2SWBM (large lake statistical water balance model), includes a conventional water balance model encoded to iteratively close the water balance over multiple consecutive time periods. Throughout these iterations, the L2SWBM can assimilate multiple preliminary estimates of each water balance component (from either historical model simulations or interpolated in situ monitoring data, for example), and it can accommodate those estimates even if they span different time periods. The L2SWBM can also be executed if data for a particular water balance component are unavailable, a feature that underscores its potential utility in data scarce regions. Here, we demonstrate the utility of our new framework through a customized application to the Laurentian Great Lakes, the largest system of lakes on Earth. Through this application, we find that the L2SWBM is able to infer new water balance component estimates that, to our are knowledge, are the first ever to close the water balance over a multi-decadal historical period for this massive lake system. More specifically, we find that posterior predictive intervals for changes in lake storage are consistent with observed changes in lake storage across this period over simulation time intervals of both 6 and 12 months. In additional to introducing a framework for developing definitive long-term hydrologic records for large lake systems, our study provides important insights into the origins of biases in both legacy and state-of-the-art hydrological models, as well as regional and global hydrological data sets.