A Bayesian Consistent Dual Ensemble Kalman Filter for State-Parameter Estimation in Subsurface Hydrology

Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The Joint-EnKF directly updates the augmented state-parameter vector while the Dual-EnKF employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. In this paper, we reverse the order of the forecast-update steps following the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem, based on which we propose a new dual EnKF scheme, the Dual-EnKF$_{\rm OSA}$. Compared to the Dual-EnKF, this introduces a new update step to the state in a fully consistent Bayesian framework, which is shown to enhance the performance of the dual filtering approach without any significant increase in the computational cost. Numerical experiments are conducted with a two-dimensional synthetic groundwater aquifer model to assess the performance and robustness of the proposed Dual-EnKF$_{\rm OSA}$, and to evaluate its results against those of the Joint- and Dual-EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, further providing reliable estimates of their uncertainties. Compared with the standard Joint- and Dual-EnKFs, the proposed scheme is found more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25% more accurate state and parameters estimates

Low-Rank Kalman Filtering in Subsurface Contaminant Transport Models

Understanding the geology and the hydrology of the subsurface is important to model the fluid flow and the behavior of the contaminant. It is essential to have an accurate knowledge of the movement of the contaminants in the porous media in order to track them and later extract them from the aquifer. A two-dimensional flow model is studied and then applied on a linear contaminant transport model in the same porous medium. Because of possible different sources of uncertainties, the deterministic model by itself cannot give exact estimations for the future contaminant state. Incorporating observations in the model can guide it to the true state. This is usually done using the Kalman filter (KF) when the system is linear and the extended Kalman filter (EKF) when the system is nonlinear. To overcome the high computational cost required by the KF, we use the singular evolutive Kalman filter (SEKF) and the singular evolutive extended Kalman filter (SEEKF) approximations of the KF operating with low-rank covariance matrices. The SEKF can be implemented on large dimensional contaminant problems while the usage of the KF is not possible. Experimental results show that with perfect and imperfect models, the low rank filters can provide as much accurate estimates as the full KF but at much less computational cost. Localization can help the filter analysis as long as there are enough neighborhood data to the point being analyzed. Estimating the permeabilities of the aquifer is successfully tackled using both the EKF and the SEEKF

Towards an end-to-end analysis and prediction system for weather, climate, and marine applications in the Red Sea

Author Posting. © American Meteorological Society, 2021. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 102(1), (2021): E99-E122, https://doi.org/10.1175/BAMS-D-19-0005.1.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 development of the Red Sea modeling system is being supported by the Virtual Red Sea Initiative and the Competitive Research Grants (CRG) program from the Office of Sponsored Research at KAUST, Saudi Aramco Company through the Saudi ARAMCO Marine Environmental Center at KAUST, and by funds from KAEC, NEOM, and RSP through Beacon Development Company at KAUST

Estimation of Ocean Biogeochemical Parameters in an Earth System Model Using the Dual One Step Ahead Smoother: A Twin Experiment

Ocean biogeochemical (BGC) models utilise a large number of poorly-constrained global parameters to mimic unresolved processes and reproduce the observed complex spatio-temporal patterns. Large model errors stem primarily from inaccuracies in these parameters whose optimal values can vary both in space and time. This study aims to demonstrate the ability of ensemble data assimilation (DA) methods to provide high-quality and improved BGC parameters within an Earth system model in an idealized perfect twin experiment framework. We use the Norwegian Climate Prediction Model (NorCPM), which combines the Norwegian Earth System Model with the Dual-One-Step ahead smoothing-based Ensemble Kalman Filter (DOSA-EnKF). We aim to estimate five spatially varying BGC parameters by assimilating salinity and temperature profiles and surface BGC (Phytoplankton, Nitrate, Phosphate, Silicate, and Oxygen) observations in a strongly coupled DA framework—i.e., jointly updating ocean and BGC state-parameters during the assimilation. We show how BGC observations can effectively constrain error in the ocean physics and vice versa. The method converges quickly (less than a year) and largely reduces the errors in the BGC parameters. Some parameter error remains, but the resulting state variable error using the estimated parameters for a free ensemble run and for a reanalysis performs nearly as well as with true parameter values. Optimal parameter values can also be recovered by assimilating climatological BGC observations or sparse observational networks. The findings of this study demonstrate the applicability of the DA approach for tuning the system in a real framework

Estimation of Ocean Biogeochemical Parameters in an Earth System Model Using the Dual One Step Ahead Smoother: A Twin Experiment

Ocean biogeochemical (BGC) models utilise a large number of poorly-constrained global parameters to mimic unresolved processes and reproduce the observed complex spatio-temporal patterns. Large model errors stem primarily from inaccuracies in these parameters whose optimal values can vary both in space and time. This study aims to demonstrate the ability of ensemble data assimilation (DA) methods to provide high-quality and improved BGC parameters within an Earth system model in an idealized perfect twin experiment framework. We use the Norwegian Climate Prediction Model (NorCPM), which combines the Norwegian Earth System Model with the Dual-One-Step ahead smoothing-based Ensemble Kalman Filter (DOSA-EnKF). We aim to estimate five spatially varying BGC parameters by assimilating salinity and temperature profiles and surface BGC (Phytoplankton, Nitrate, Phosphate, Silicate, and Oxygen) observations in a strongly coupled DA framework—i.e., jointly updating ocean and BGC state-parameters during the assimilation. We show how BGC observations can effectively constrain error in the ocean physics and vice versa. The method converges quickly (less than a year) and largely reduces the errors in the BGC parameters. Some parameter error remains, but the resulting state variable error using the estimated parameters for a free ensemble run and for a reanalysis performs nearly as well as with true parameter values. Optimal parameter values can also be recovered by assimilating climatological BGC observations or sparse observational networks. The findings of this study demonstrate the applicability of the DA approach for tuning the system in a real framework.publishedVersio

Estimation of Ocean Biogeochemical Parameters in an Earth System Model Using the Dual One Step Ahead Smoother: A Twin Experiment

Ocean biogeochemical (BGC) models utilise a large number of poorly-constrained global parameters to mimic unresolved processes and reproduce the observed complex spatio-temporal patterns. Large model errors stem primarily from inaccuracies in these parameters whose optimal values can vary both in space and time. This study aims to demonstrate the ability of ensemble data assimilation (DA) methods to provide high-quality and improved BGC parameters within an Earth system model in an idealized perfect twin experiment framework. We use the Norwegian Climate Prediction Model (NorCPM), which combines the Norwegian Earth System Model with the Dual-One-Step ahead smoothing-based Ensemble Kalman Filter (DOSA-EnKF). We aim to estimate five spatially varying BGC parameters by assimilating salinity and temperature profiles and surface BGC (Phytoplankton, Nitrate, Phosphate, Silicate, and Oxygen) observations in a strongly coupled DA framework—i.e., jointly updating ocean and BGC state-parameters during the assimilation. We show how BGC observations can effectively constrain error in the ocean physics and vice versa. The method converges quickly (less than a year) and largely reduces the errors in the BGC parameters. Some parameter error remains, but the resulting state variable error using the estimated parameters for a free ensemble run and for a reanalysis performs nearly as well as with true parameter values. Optimal parameter values can also be recovered by assimilating climatological BGC observations or sparse observational networks. The findings of this study demonstrate the applicability of the DA approach for tuning the system in a real framework