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Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics (``climate'') can be produced by employing a feedback loop, whereby the model is trained to predict forward one time step, then the model output is used as input for multiple time steps. In the absence of mitigating techniques, however, this technique can result in artificially rapid error growth. In this article, we systematically examine the technique of adding noise to the ML model input during training to promote stability and improve prediction accuracy. Furthermore, we introduce Linearized Multi-Noise Training (LMNT), a regularization technique that deterministically approximates the effect of many small, independent noise realizations added to the model input during training. Our case study uses reservoir computing, a machine-learning method using recurrent neural networks, to predict the spatiotemporal chaotic Kuramoto-Sivashinsky equation. We find that reservoir computers trained with noise or with LMNT produce climate predictions that appear to be indefinitely stable and have a climate very similar to the true system, while reservoir computers trained without regularization are unstable. Compared with other regularization techniques that yield stability in some cases, we find that both short-term and climate predictions from reservoir computers trained with noise or with LMNT are substantially more accurate. Finally, we show that the deterministic aspect of our LMNT regularization facilitates fast hyperparameter tuning when compared to training with noise. 

This paper describes an implementation of the Combined Hybrid-Parallel Prediction (CHyPP) approach of Wikner et al. (2020) on a low-resolution atmospheric global circulation model (AGCM). This approach combines a physics-based numerical model of a dynamical system (e.g., the atmosphere) with a computationally efficient type of machine learning (ML) called reservoir computing (RC) to construct a hybrid model. This hybrid atmospheric model produces more accurate forecasts of most atmospheric state variables than the host AGCM for the first 7-8 forecast days, and for even longer times for the temperature and humidity near the earth's surface. It also produces more accurate forecasts than a purely ML-based model, or a model that combines linear regression, rather than ML, with the AGCM. The potential of the approach for climate research is demonstrated by a 10-year long hybrid model simulation of the atmospheric general circulation, which shows that the hybrid model can simulate the general circulation with substantially smaller systematic errors and more realistic variability than the host AGCM. 

ABSTRACT Coastal margins are important areas of materials flux that link terrestrial and marine ecosystems. Consequently, climate-mediated changes to coastal terrestrial ecosystems and hydrologic regimes have high potential to influence nearshore ocean chemistry and food web dynamics. Research from tightly coupled, high-flux coastal ecosystems can advance understanding of terrestrial–marine links and climate sensitivities more generally. In the present article, we use the northeast Pacific coastal temperate rainforest as a model system to evaluate such links. We focus on key above- and belowground production and hydrological transport processes that control the land-to-ocean flow of materials and their influence on nearshore marine ecosystems. We evaluate how these connections may be altered by global climate change and we identify knowledge gaps in our understanding of the source, transport, and fate of terrestrial materials along this coastal margin. Finally, we propose five priority research themes in this region that are relevant for understanding coastal ecosystem links more broadly. 

Abstract Polar marine ecosystems are particularly vulnerable to the effects of climate change. Warming temperatures, freshening seawater, and disruption to sea‐ice formation potentially all have cascading effects on food webs. New approaches are needed to better understand spatiotemporal interactions among biogeochemical processes at the base of Southern Ocean food webs. In marine systems, isoscapes (models of the spatial variation in the stable isotopic composition) of carbon and nitrogen have proven useful in identifying spatial variation in a range of biogeochemical processes, such as nutrient utilization by phytoplankton. Isoscapes provide a baseline for interpreting stable isotope compositions of higher trophic level animals in movement, migration, and diet research. Here, we produce carbon and nitrogen isoscapes across the entire Southern Ocean (>40°S) using surface particulate organic matter isotope data, collected over the past 50 years. We use Integrated Nested Laplace Approximation‐based approaches to predict mean annual isoscapes and four seasonal isoscapes using a suite of environmental data as predictor variables. Clear spatial gradients in δ¹³C and δ¹⁵N values were predicted across the Southern Ocean, consistent with previous statistical and mechanistic views of isotopic variability in this region. We identify strong seasonal variability in both carbon and nitrogen isoscapes, with key implications for the use of static or annual average isoscape baselines in animal studies attempting to document seasonal migratory or foraging behaviors.