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Abstract State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface observations. Directly implementing an ensemble Kalman filter based on the full forecast model is usually expensive. One widely used method in practice projects the information of the observed layer to other layers via linear regression. However, large errors appear when nonlinearity in the highly turbulent flow field becomes dominant. In this paper, we develop a multi-step nonlinear data assimilation method that involves the sequential application of nonlinear assimilation steps across layers. Unlike traditional linear regression approaches, a conditional Gaussian nonlinear system is adopted as the approximate forecast model to characterize the nonlinear dependence between adjacent layers. At each step, samples drawn from the posterior of the current layer are treated as pseudo-observations for the next layer. Each sample is assimilated using analytic formulae for the posterior mean and covariance. The resulting Gaussian posteriors are then aggregated into a Gaussian mixture. Therefore, the method can capture strongly turbulent features, particularly intermittency and extreme events, and more accurately quantify the inherent uncertainty. Applications to the two-layer quasi-geostrophic system with Lagrangian data assimilation demonstrate that the multi-step method outperforms the one-step method, particularly as the tracer number and ensemble size increase. Results also show that the multi-step CGDA is particularly effective for assimilating frequent, high-accuracy observations, which are scenarios where traditional EnKF methods may suffer from catastrophic filter divergence. 

Abstract We present the Arctic atmospheric river (AR) climatology based on twelve sets of labels derived from ERA5 and MERRA-2 reanalyses for 1980–2019. The ARs were identified and tracked in the 3-hourly reanalysis data with a multifactorial approach based on either atmospheric column-integrated water vapor (IWV) or integrated water vapor transport (IVT) exceeding one of the three climate thresholds (75th, 85th, and 95th percentiles). Time series analysis of the AR event counts from the AR labels showed overall upward trends from the mid-1990s to 2019. The 75th IVT- and IWV-based labels, as well as the 85th IWV-based labels, are likely more sensitive to Arctic surface warming, therefore, detected some broadening of AR-affected areas over time, while the rest of the labels did not. Spatial exploratory analysis of these labels revealed that the AR frequency of occurrence maxima shifted poleward from over-land in 1980–1999 to over the Arctic Ocean and its outlying Seas in 2000–2019. Regions across the Atlantic, the Arctic, to the Pacific Oceans trended higher AR occurrence, surface temperature, and column-integrated moisture. Meanwhile, ARs were increasingly responsible for the rising moisture transport into the Arctic. Even though the increase of Arctic AR occurrence was primarily associated with long-term Arctic surface warming and moistening, the effects of changing atmospheric circulation could stand out locally, such as on the Pacific side over the Chukchi Sea. The changing teleconnection patterns strongly modulated AR activities in time and space, with prominent anomalies in the Arctic-Pacific sector during the latest decade. Besides, the extreme events identified by the 95th-percentile labels displayed the most significant changes and were most influenced by the teleconnection patterns. The twelve Arctic AR labels and the detailed graphics in the atlas can help navigate the uncertainty of detecting and quantifying Arctic ARs and their associated effects in current and future studies. 

This repository contains the 12 sets of Arctic atmospheric river labels based on the 3-hourly ERA5 and MERRA-2 data for 1980–2019 and the high-resolution version of figures in Zhang, Tung, & Cleveland (ERCL 2023, https://doi.org/10.1088/2752-5295/acdf0f).