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This work was supported by the Office of Sponsored Research (OSR) at King Abdullah University of Science and Technology (KAUST) under the Virtual Red Sea Initiative (Grant #REP/1/3268-01-01). The research made use of the KAUST supercomputing facilities.

This work combines two auxiliary techniques, namely the one-step-ahead (OSA) smoothing and the hybrid formulation, to boost the forecasting skills of a storm surge ensemble Kalman filter (EnKF) forecasting system. Bayesian filtering with OSA-smoothing enhances the robustness of the ensemble background statistics by exploiting the data twice: first to constrain the sampling of the forecast ensemble with the future observation, and then to update the resulting ensemble. This is expected to improve the behavior of EnKF-like schemes during the strongly nonlinear surges periods, but requires integrating the ensemble with the forecast model twice, which could be computationally demanding. The hybrid flow-dependent/static formulation of the EnKF background error covariance is then considered to enable the implementation of the filter with a small flow-dependent ensemble size, and thus less model runs. These two methods are combined within an ensemble transform Kalman filter (ETKF). The resulting hybrid ETKF with OSA smoothing is tested, based on twin experiments, using a realistic setting of the Advanced Circulation (ADCIRC) model configured for storm surge forecasting in the Gulf of Mexico and assimilating pseudo-observations of sea surface levels from a network of buoys. The results of our numerical experiments suggest that the proposed filtering system significantly enhances ADCIRC forecasting skills compared to the standard ETKF without increasing the computational cost.

The Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable energy applications, impact assessment, flood forecasting, and more.

The ensemble Kalman filter (EnKF) is widely used for sequential data assimilation. It operates as a succession of forecast and analysis steps. In realistic large-scale applications, EnKFs are implemented with small ensembles and poorly known model error statistics. This limits their representativeness of the background error covariances and, thus, their performance. This work explores the efficiency of the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem to enhance the data assimilation performance of EnKFs. Filtering with OSA smoothing introduces an updated step with future observations, conditioning the ensemble sampling with more information. This should provide an improved background ensemble in the analysis step, which may help to mitigate the suboptimal character of EnKF-based methods. Here, the authors demonstrate the efficiency of a stochastic EnKF with OSA smoothing for state estimation. They then introduce a deterministic-like EnKF-OSA based on the singular evolutive interpolated ensemble Kalman (SEIK) filter. The authors show that the proposed SEIK-OSA outperforms both SEIK, as it efficiently exploits the data twice, and the stochastic EnKF-OSA, as it avoids observational error undersampling. They present extensive assimilation results from numerical experiments conducted with the Lorenz-96 model to demonstrate SEIK-OSA’s capabilities.

Ensemble optimal interpolation (EnOI) is a variant of the ensemble Kalman filter (EnKF) that operates with a static ensemble to drastically reduce its computational cost. The idea is to use a pre-selected ensemble to parameterize the background covariance matrix, which avoids the costly integration of the ensemble members with the dynamical model during the forecast step of the filtering process. To better represent the pronounced time-varying circulation of the Red Sea, we propose a new adaptive EnOI approach in which the ensemble members are adaptively selected at every assimilation cycle from a large dictionary of ocean states describing the Red Sea variability. We implement and test different schemes to select the ensemble members (i) based on the similarity to the forecast state according to some criteria, or (ii) in term of best representation of the forecast in an ensemble subspace using an Orthogonal Matching Pursuit (OMP) algorithm. The relevance of the schemes is first demonstrated with the Lorenz 63 and Lorenz 96 models. Then results of numerical experiments assimilating real remote sensing data into a high resolution MIT general circulation model (MITgcm) of the Red Sea using the Data Assimilation Research Testbed (DART) system are presented and discussed.