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Abstract. This paper presents the results of the ensemble Riemannian data assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that, with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in the Lorenz-96 (QG) model. 

Surface freshening through precipitation can act to stably stratify the upper ocean, forming a rain layer (RL). RLs inhibit subsurface vertical mixing, isolating deeper ocean layers from the atmosphere. This process has been studied using observations and idealized simulations. The present ocean modeling study builds upon this body of work by incorporating spatially resolved and realistic atmospheric forcing. Fine‐scale observations of the upper ocean collected during the Dynamics of the Madden‐Julian Oscillation field campaign are used to verify the General Ocean Turbulence Model (GOTM). Spatiotemporal characteristics of equatorial Indian Ocean RLs are then investigated by forcing a 2D array of GOTM columns with realistic and well‐resolved output from an existing regional atmospheric simulation. RL influence on the ocean‐atmosphere system is evaluated through analysis of RL‐induced modification to surface fluxes and sea surface temperature (SST). This analysis demonstrates that RLs cool the ocean surface on time scales longer than the associated precipitation event. A second simulation with identical atmospheric forcing to that in the first, but with rainfall set to zero, is performed to investigate the role of rain temperature and salinity stratification in maintaining cold SST anomalies within RLs. Approximately one third, or 0.1°C, of the SST reduction within RLs can be attributed to rain effects, while the remainder is attributed to changes in atmospheric temperature and humidity. The prolonged RL‐induced SST anomalies enhance SST gradients that have been shown to favor the initiation of atmospheric convection. These findings encourage continued research of RL feedbacks to the atmosphere.