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I. Hoteit
,
D-T. Pham
,
G. Triantafyllou
, and
G. Korres

Abstract

This paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a low-rank kernel representation of the state’s probability density function. In the resulting low-rank kernel particle Kalman (LRKPK) filter, the standard (weight type) particle filter correction is complemented by a Kalman-type correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filter’s solution is then obtained as the weighted average of several low-rank square root Kalman filters operating in parallel. The Kalman-type correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the low-rank approximation, it allows the implementation of the LRKPK filter with high-dimensional oceanic and atmospheric systems. The new filter is described and its relevance demonstrated through applications with the simple Lorenz model and a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea.

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I. Hoteit
,
B. Cornuelle
,
V. Thierry
, and
D. Stammer

Abstract

The sensitivity of the dynamics of a tropical Pacific Massachusetts Institute of Technology (MIT) general circulation model (MITgcm) to the surface forcing fields and to the horizontal resolution is analyzed. During runs covering the period 1992–2002, two different sets of surface forcing boundary conditions are used, obtained 1) from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis project and 2) from the Estimating the Circulation and Climate of the Ocean (ECCO) assimilation consortium. The “ECCO forcing” is the “NCEP forcing” adjusted by a state estimation procedure using the MITgcm with a 1° × 1° global grid and the adjoint method assimilating a multivariate global ocean dataset. The skill of the model is evaluated against ocean observations available in situ and from satellites. The model domain is limited to the tropical Pacific, with open boundaries located along 26°S, 26°N, and in the Indonesian throughflow. To account for large-scale changes of the ocean circulation, the model is nested in the global time-varying ocean state provided by the ECCO consortium on a 1° grid. Increasing the spatial resolution to 1/3° and using the ECCO forcing fields significantly improves many aspects of the circulation but produces overly strong currents in the western model domain. Increasing the resolution to 1/6° does not yield further improvements of model results. Using the ECCO heat and freshwater fluxes in place of NCEP products leads to improved time-mean model skill (i.e., reduced biases) over most of the model domain, underlining the important role of adjusted heat and freshwater fluxes for improving model representations of the tropical Pacific. Combinations of ECCO and NCEP wind forcing fields can improve certain aspects of the model solutions, but neither ECCO nor NCEP winds show clear overall superiority.

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I. Hoteit
,
D.-T. Pham
,
M. E. Gharamti
, and
X. Luo

Abstract

The stochastic ensemble Kalman filter (EnKF) updates its ensemble members with observations perturbed with noise sampled from the distribution of the observational errors. This was shown to introduce noise into the system and may become pronounced when the ensemble size is smaller than the rank of the observational error covariance, which is often the case in real oceanic and atmospheric data assimilation applications. This work introduces an efficient serial scheme to mitigate the impact of observations’ perturbations sampling in the analysis step of the EnKF, which should provide more accurate ensemble estimates of the analysis error covariance matrices. The new scheme is simple to implement within the serial EnKF algorithm, requiring only the approximation of the EnKF sample forecast error covariance matrix by a matrix with one rank less. The new EnKF scheme is implemented and tested with the Lorenz-96 model. Results from numerical experiments are conducted to compare its performance with the EnKF and two standard deterministic EnKFs. This study shows that the new scheme enhances the behavior of the EnKF and may lead to better performance than the deterministic EnKFs even when implemented with relatively small ensembles.

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M. U. Altaf
,
T. Butler
,
T. Mayo
,
X. Luo
,
C. Dawson
,
A. W. Heemink
, and
I. Hoteit

Abstract

This study evaluates and compares the performances of several variants of the popular ensemble Kalman filter for the assimilation of storm surge data with the advanced circulation (ADCIRC) model. Using meteorological data from Hurricane Ike to force the ADCIRC model on a domain including the Gulf of Mexico coastline, the authors implement and compare the standard stochastic ensemble Kalman filter (EnKF) and three deterministic square root EnKFs: the singular evolutive interpolated Kalman (SEIK) filter, the ensemble transform Kalman filter (ETKF), and the ensemble adjustment Kalman filter (EAKF). Covariance inflation and localization are implemented in all of these filters. The results from twin experiments suggest that the square root ensemble filters could lead to very comparable performances with appropriate tuning of inflation and localization, suggesting that practical implementation details are at least as important as the choice of the square root ensemble filter itself. These filters also perform reasonably well with a relatively small ensemble size, whereas the stochastic EnKF requires larger ensemble sizes to provide similar accuracy for forecasts of storm surge.

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M. U. Altaf
,
T. Butler
,
X. Luo
,
C. Dawson
,
T. Mayo
, and
I. Hoteit

Abstract

This paper presents a robust ensemble filtering methodology for storm surge forecasting based on the singular evolutive interpolated Kalman (SEIK) filter, which has been implemented in the framework of the H filter. By design, an H filter is more robust than the common Kalman filter in the sense that the estimation error in the H filter has, in general, a finite growth rate with respect to the uncertainties in assimilation. The computational hydrodynamical model used in this study is the Advanced Circulation (ADCIRC) model. The authors assimilate data obtained from Hurricanes Katrina and Ike as test cases. The results clearly show that the H -based SEIK filter provides more accurate short-range forecasts of storm surge compared to recently reported data assimilation results resulting from the standard SEIK filter.

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T. Butler
,
M. U. Altaf
,
C. Dawson
,
I. Hoteit
,
X. Luo
, and
T. Mayo

Abstract

Accurate, real-time forecasting of coastal inundation due to hurricanes and tropical storms is a challenging computational problem requiring high-fidelity forward models of currents and water levels driven by hurricane-force winds. Despite best efforts in computational modeling there will always be uncertainty in storm surge forecasts. In recent years, there has been significant instrumentation located along the coastal United States for the purpose of collecting data—specifically wind, water levels, and wave heights—during these extreme events. This type of data, if available in real time, could be used in a data assimilation framework to improve hurricane storm surge forecasts. In this paper a data assimilation methodology for storm surge forecasting based on the use of ensemble Kalman filters and the advanced circulation (ADCIRC) storm surge model is described. The singular evolutive interpolated Kalman (SEIK) filter has been shown to be effective at producing accurate results for ocean models using small ensemble sizes initialized by an empirical orthogonal function analysis. The SEIK filter is applied to the ADCIRC model to improve storm surge forecasting, particularly in capturing maximum water levels (high water marks) and the timing of the surge. Two test cases of data obtained from hindcast studies of Hurricanes Ike and Katrina are presented. It is shown that a modified SEIK filter with an inflation factor improves the accuracy of coarse-resolution forecasts of storm surge resulting from hurricanes. Furthermore, the SEIK filter requires only modest computational resources to obtain more accurate forecasts of storm surge in a constrained time window where forecasters must interact with emergency responders.

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