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Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF), which relies on linear updates to minimize variance among the ensemble of forecast states. Recent advancements have seen the emergence of deep learning approaches in this domain, primarily within a supervised learning framework. However, the adaptability of such models to untrained scenarios remains a challenge. In this study, we introduce a novel DA strategy that utilizes reinforcement learning (RL) to apply state corrections using full or partial observations of the state variables. Our investigation focuses on demonstrating this approach to the chaotic Lorenz '63 system, where the agent's objective is to minimize the root-mean-squared error between the observations and corresponding forecast states. Consequently, the agent develops a correction strategy, enhancing model forecasts based on available system state observations. Our strategy employs a stochastic action policy, enabling a Monte Carlo-based DA framework that relies on randomly sampling the policy to generate an ensemble of assimilated realizations. Results demonstrate that the developed RL algorithm performs favorably when compared to the EnKF. Additionally, we illustrate the agent's capability to assimilate non-Gaussian data, addressing a significant limitation of the EnKF.

Efficient downscaling of large ensembles of coarse-scale information is crucial in several applications, such as oceanic and atmospheric modeling. The determining form map is a theoretical lifting function from the low-resolution solution trajectories of a dissipative dynamical system to their corresponding fine-scale counterparts. Recently, a physics-informed deep neural network ("CDAnet") was introduced, providing a surrogate of the determining form map for efficient downscaling. CDAnet was demonstrated to efficiently downscale noise-free coarse-scale data in a deterministic setting. Herein, the performance of well-trained CDAnet models is analyzed in a stochastic setting involving (i) observational noise, (ii) model noise, and (iii) a combination of observational and model noises. The analysis is performed employing the Rayleigh-Benard convection paradigm, under three training conditions, namely, training with perfect, noisy, or downscaled data. Furthermore, the effects of noises, Rayleigh number, and spatial and temporal resolutions of the input coarse-scale information on the downscaled fields are examined. The results suggest that the expected l2-error of CDAnet behaves quadratically in terms of the standard deviations of the observational and model noises. The results also suggest that CDAnet responds to uncertainties similar to the theorized and numerically-validated CDA behavior with an additional error overhead due to CDAnet being a surrogate model of the determining form map.

A risk analysis is conducted considering several release sources located around the NEOM shoreline. The sources are selected close to the coast and in neighboring regions of high marine traffic. The evolution of oil spills released by these sources is simulated using the MOHID model, driven by validated, high-resolution met-ocean fields of the Red Sea. For each source, simulations are conducted over a 4-week period, starting from first, tenth and twentieth days of each month, covering five consecutive years. A total of 48 simulations are thus conducted for each source location, adequately reflecting the variability of met-ocean conditions in the region. The risk associated with each source is described in terms of amount of oil beached, and by the elapsed time required for the spilled oil to reach the NEOM coast, extending from the Gulf of Aqaba in the North to Duba in the South. A finer analysis is performed by segmenting the NEOM shoreline, based on important coastal development and installation sites. For each subregion, source and release event considered, a histogram of the amount of volume beached is generated, also classifying individual events in terms of the corresponding arrival times. In addition, for each subregion considered, an inverse analysis is conducted to identify regions of dependence of the cumulative risk, estimated using the collection of all sources and events considered. The transport of oil around the NEOM shorelines is promoted by chaotic circulations and northwest winds in summer, and a dominant cyclonic eddy in winter. Hence, spills originating from release sources located close to the NEOM shorelines are characterized by large monthly variations in arrival times, ranging from less than a week to more than two weeks. Large variations in the volume fraction of beached oil, ranging from less then 50\% to more than 80% are reported., Comment: 15 pages, 8 figures

Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations of the system states are available. These observations can also be corrupted by noise. Downscaling is a process/scheme in which one uses coarse scale observations to reconstruct the high-resolution solution of the system states. Continuous Data Assimilation (CDA) is a recently introduced downscaling algorithm that constructs an increasingly accurate representation of the system states by continuously nudging the large scales using the coarse observations. We introduce a Discrete Data Assimilation (DDA) algorithm as a downscaling algorithm based on CDA with discrete-in-time nudging. We then investigate the performance of the CDA and DDA algorithms for downscaling noisy observations of the Rayleigh-B\'enard convection system in the chaotic regime. In this computational study, a set of noisy observations was generated by perturbing a reference solution with Gaussian noise before downscaling them. The downscaled fields are then assessed using various error- and ensemble-based skill scores. The CDA solution was shown to converge towards the reference solution faster than that of DDA but at the cost of a higher asymptotic error. The numerical results also suggest a quadratic relationship between the $\ell_2$ error and the noise level for both CDA and DDA. Cubic and quadratic dependences of the DDA and CDA expected errors on the spatial resolution of the observations were obtained, respectively.

This study assesses a Continuous Data Assimilation (CDA) dynamical-downscaling algorithm for enhancing the simulation of the Indian summer monsoon (ISM) system. CDA is a mathematically rigorous technique that has been recently introduced to constrain the large-scale features of high-resolution atmospheric models with coarse spatial scale data. It is similar to spectral nudging but does not require any spectral decomposition for scales separation. This is expected to be particularly relevant for ISM, which involves various interactions between large-scale circulations and regional physical processes. Along with a control simulation, several downscaling simulations were conducted with the Weather Research and Forecasting (WRF) model using CDA, spectral (retaining different wavenumbers) and grid nudging for three ISM seasons: normal (2016), excess (2013), and drought (2009). The simulations are nested within the NCEP Final Analysis and the model outputs are evaluated against the observations. Compared to grid and spectral nudging, the simulations using CDA produce enhanced ISM features over the Indian subcontinent including the low-level jet, tropical easterly jet, easterly wind shear, and rainfall distributions for all investigated ISM seasons. The major ISM processes, in particular the monsoon inversion over the Arabian Sea, tropospheric temperature gradients and moist static energy over central India, and zonal wind shear over the monsoon region, are all better simulated with CDA. Spectral nudging outputs are found to be sensitive to the choice of the wavenumber, requiring careful tuning to provide robust simulations of the ISM system. In contrast, control and grid nudging generally fail to well reproduce some of the main ISM features., Comment: Research Article

Public health officials dealing with pandemics like COVID-19 have to evaluate and prepare response plans. This planning phase requires not only looking into the spatiotemporal dynamics and impact of the pandemic using simulation models, but they also need to plan and ensure the availability of resources under different spread scenarios. To this end, we have developed a visual analytics environment that enables public health officials to model, simulate, and explore the spread of COVID-19 by supplying county-level information such as population, demographics, and hospital beds. This environment facilitates users to explore spatiotemporal model simulation data relevant to COVID-19 through a geospatial map with linked statistical views, apply different decision measures at different points in time, and understand their potential impact. Users can drill-down to county-level details such as the number of sicknesses, deaths, needs for hospitalization, and variations in these statistics over time. We demonstrate the usefulness of this environment through a use case study and also provide feedback from domain experts. We also provide details about future extensions and potential applications of this work.

The Ensemble Adjustment Kalman Filter (EAKF) of the Data Assimilation Research Testbed (DART) is implemented to assimilate observations of satellite sea surface temperature, altimeter sea surface height and in situ ocean temperature and salinity profiles into an eddy-resolving 4 km Massachusetts Institute of Technology general circulation model (MITgcm) of the Red Sea. We investigate the impact of three different ensemble generation strategies (1) Iexp, uses ensemble of ocean states to initialize the model on 1st January, 2011 and inflates filter error covariance by 10 percent, (2) IAexp, adds ensemble of atmospheric forcing to Iexp, and (3) IAPexp, adds perturbed model physics to IAexp. The assimilation experiments are run for one year, starting from the same initial ensemble and assimilating data every three days. Results demonstrate that the Iexp mainly improved the model outputs with respect to assimilation free MITgcm run in the first few months, before showing signs of dynamical imbalances in the ocean estimates, particularly in the data-sparse subsurface layers. The IAexp yielded substantial improvements throughout the assimilation period with almost no signs of imbalances, including the subsurface layers. It further well preserved the model mesoscale features resulting in an improved forecasts for eddies, both in terms of intensity and location. Perturbing model physics in IAPexp slightly improved the forecast statistics and also the placement of basin scale eddies. Increasing hydrographic coverage further improved the results of IAPexp compared to IAexp in the subsurface layers. Switching off multiplicative inflation in IAexp and IAPexp leads to further improvements, especially in the subsurface layers., Comment: 23 pages, 13 figures, 2 tables. Under Revision in JGR-Oceans

Continuous data assimilation (CDA) is successfully implemented for the first time for efficient dynamical downscaling of a global atmospheric reanalysis. A comparison of the performance of CDA with the standard grid and spectral nudging techniques for representing long- and short-scale features in the downscaled fields using the Weather Research and Forecast (WRF) model is further presented and analyzed. The WRF model is configured at 25km horizontal resolution and is driven by 250km initial and boundary conditions from NCEP/NCAR reanalysis fields. Downscaling experiments are performed over a one-month period in January, 2016. The similarity metric is used to evaluate the performance of the downscaling methods for large and small scales. Similarity results are compared for the outputs of the WRF model with different downscaling techniques, NCEP reanalysis, and Final Analysis. Both spectral nudging and CDA describe better the small-scale features compared to grid nudging. The choice of the wave number is critical in spectral nudging; increasing the number of retained frequencies generally produced better small-scale features, but only up to a certain threshold after which its solution gradually became closer to grid nudging. CDA maintains the balance of the large- and small-scale features similar to that of the best simulation achieved by the best spectral nudging configuration, without the need of a spectral decomposition. The different downscaled atmospheric variables, including rainfall distribution, with CDA is most consistent with the observations. The Brier skill score values further indicate that the added value of CDA is distributed over the entire model domain. The overall results clearly suggest that CDA provides an efficient new approach for dynamical downscaling by maintaining better balance between the global model and the downscaled fields., Comment: 27 Pages, 13 figures

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback-Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback-Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.