Abstract
Many coupled human-natural systems have the potential to exhibit a highly nonlinear threshold response to external forcings resulting in fast transitions to undesirable states (such as eutrophication in a lake). Often, there are considerable uncertainties that make identifying the threshold challenging. Thus, rapid learning is critical for guiding management actions to avoid abrupt transitions. Here, we adopt the shallow lake problem as a test case to compare the performance of four common data assimilation schemes to predict an approaching transition. In order to demonstrate the complex interactions between management strategies and the ability of the data assimilation schemes to predict eutrophication, we also analyze our results across two different management strategies governing phosphorus emissions into the shallow lake. The compared data assimilation schemes are: ensemble Kalman filtering (EnKF), particle filtering (PF), pre-calibration (PC), and Markov Chain Monte Carlo (MCMC) estimation. While differing in their core assumptions, each data assimilation scheme is based on Bayes’ theorem and updates prior beliefs about a system based on new information. For large computational investments, EnKF, PF and MCMC show similar skill in capturing the observed phosphorus in the lake (measured as expected root mean squared prediction error). EnKF, followed by PF, displays the highest learning rates at low computational cost, thus providing a more reliable signal of an impending transition. MCMC approaches the true probability of eutrophication only after a strong signal of an impending transition emerges from the observations. Overall, we find that learning rates are greatest near regions of abrupt transitions, posing a challenge to early learning and preemptive management of systems with such abrupt transitions.
Highlights
The Earth system can respond with abrupt and often persistent changes in response to slow and potentially small forcings (e.g., [1])
We explore the ability of each method to identify the true parameters of the lake model and their skill in predicting an impending eutrophication tipping point before the point of no return
ensemble Kalman filtering (EnKF), particle filter (PF), PC, and Markov Chain Monte Carlo (MCMC) methods simulate an ensemble of trajectories, but only their mean values are shown
Summary
The Earth system can respond with abrupt and often persistent changes in response to slow and potentially small forcings (e.g., [1]). Abrupt changes can result from highly nonlinear processes that can trigger transitions between stable states. Information feedbacks play a key role for adapting management strategies to better detect and reflect negative threshold impacts [3, 4, 9]. An important body of research related to learning has emerged that seeks to better understand how to detect a catastrophic transition to an undesirable state with sufficient lead time so that adequate management steps can be taken to avoid it. The value (s) of the forcing(s) at which this transition occurs depends upon the underlying physical processes, and is commonly referred to as the ‘tipping point’ or the ‘critical threshold’
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