Ensemble Kalman filter inference of spatially-varying Manning’s n coefficients in the coastal ocean

Abstract

Ensemble Kalman (EnKF) filtering is an established framework for large scale state estimation problems. EnKFs can also be used for state-parameter estimation, using the so-called "Joint-EnKF" approach. The idea is simply to augment the state vector with the parameters to be estimated and assign invariant dynamics for the time evolution of the parameters. In this contribution, we investigate the efficiency of the Joint-EnKF for estimating spatiallyvarying Manning's n coefficients used to define the bottom roughness in the Shallow Water Equations (SWEs) of a coastal ocean model.Observation System Simulation Experiments (OSSEs) are conducted using the ADvanced CIRCulation (ADCIRC) model, which solves a modified form of the Shallow Water Equations. A deterministic EnKF, the Singular Evolutive Interpolated Kalman (SEIK) filter, is used to estimate a vector of Manning's n coefficients defined at the model nodal points by assimilating synthetic water elevation data. It is found that with reasonable ensemble size (O(10)), the filter's estimate converges to the reference Manning's field. To enhance performance, we have further reduced the dimension of the parameter search space through a Karhunen-Loéve (KL) expansion. We have also iterated on the filter update step to better account for the nonlinearity of the parameter estimation problem. We study the sensitivity of the system to the ensemble size, localization scale, dimension of retained KL modes, and number of iterations. The performance of the proposed framework in term of estimation accuracy suggests that a well-tuned Joint-EnKF provides a promising robust approach to infer spatially varying seabed roughness parameters in the context of coastal ocean modeling.

Bayesian inference of spatially varying Manning’s n coefficients in an idealized coastal ocean model using a generalized Karhunen-Loève expansion and polynomial chaos

“…Even when the model is assumed to be perfect in describing the underlying physical processes, the model solutions are always subject to uncertainties that emerge on account of errors originating from numerous sources [20], e.g., initial conditions, model parameters, forcing fields, and resolution of the implemented numerical methods. To provide robust and reliable forecasts of the ocean states, uncertainty quantification and reduction techniques have, in recent years, played a major role toward enhancing stateof-the-art coastal ocean simulation systems [20,59,28,1,46,62,57].…”

“…Sequential Bayesian inference method, such as the ensemble Kalman filter (EnKF) [4,7,27], has also been intensively utilized for parameter estimation of ocean models (e.g., [2,3,5,11,55,66,70]). The EnKF has been found efficient, with advantages over the MCMC approach in accommodating large state-parameter vectors at reasonable computational cost [46,57,58]. Recently, the EnKF has been successfully used for the inference of a spatially varying Manning's n field in an idealized coastal ocean framework, both in the full and reduced KL space [57].…”

“…The EnKF has been found efficient, with advantages over the MCMC approach in accommodating large state-parameter vectors at reasonable computational cost [46,57,58]. Recently, the EnKF has been successfully used for the inference of a spatially varying Manning's n field in an idealized coastal ocean framework, both in the full and reduced KL space [57]. The main merit in using an EnKF is its ability to accommodate larger member of parameters or KL modes.…”

“…In both MCMC-and EnKF-based inference, presented in [44] and [57], respectively, the underlying Gaussian process is associated with prior covariance models that are often poorly known. This is because a prior covariance model that describes the stochastic parameter field is subjected to the uncertainty in hyper-parameters, e.g., prior variance and length scales.…”

Combining ensemble Kalman filter and multiresolution analysis for efficient assimilation into adaptive mesh models

“…Recently, uncertainty propagation/reduction methods based on Bayesian inference have been widely applied to enhance the predictive capability of the geophysical fluid dynamics and hydrological models in number of studies [39,40,18,38,37]. Within the Bayesian framework, uncertainty in model input is represented using random variables with known probability laws.…”