scholarly journals Application of the ensemble Kalman filter FEM for estimation of flow field in shallow water regions

JSIAM Letters ◽  
2018 ◽  
Vol 10 (0) ◽  
pp. 5-8 ◽  
Author(s):  
Takahiko Kurahashi ◽  
Kiyora Saito ◽  
Masato Nogami
Keyword(s):  
Kalman Filter ◽  
Flow Field ◽  
Shallow Water ◽  
Ensemble Kalman Filter

scholarly journals Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

2015 ◽  
Vol 15 (10) ◽  
pp. 5835-5850 ◽  
Author(s):  
D. R. Allen ◽  
K. W. Hoppel ◽  
D. D. Kuhl
Keyword(s):  
Kalman Filter ◽  
Shallow Water ◽  
Ensemble Kalman Filter ◽  
Stratospheric Ozone ◽  
Localization Length ◽  
Polar Vortex ◽  
Meridional Wind ◽  
Water Model ◽  
Shallow Water Model ◽  
Polar Orbiting Satellite

Abstract. The feasibility of extracting wind information from stratospheric ozone observations is tested using ensemble Kalman filter (EnKF) data assimilation (DA) and a global shallow water model that includes advection of an ozone-like tracer. Simulated observations are created from a truth run (TR) that resembles the Northern Hemisphere winter stratosphere with a polar vortex disturbed by planetary-scale wave forcing. Ozone observations mimic sampling of a polar-orbiting satellite, while geopotential height observations are randomly placed in space and time. EnKF experiments are performed assimilating ozone, height, or both, over a 10-day period. The DA is also implemented using two different pairs of flow variables: zonal and meridional wind (EnKF-uv) and stream function and velocity potential (EnKF-ψχ). Each experiment is tuned for optimal localization length, while the ensemble spread is adaptively inflated using the TR. The experiments are evaluated using the maximum wind extraction potential (WEP). Ozone only assimilation improves winds (WEP = 46% for EnKF-uv, and 58% for EnKF-ψχ), but suffers from spurious gravity wave generation. Application of nonlinear normal mode initialization (NMI) greatly reduces the unwanted imbalance and increases the WEP for EnKF-uv (84%) and EnKF-ψχ (81%). Assimilation of only height observations also improved the winds (WEP = 60% for EnKF-uv, and 69% for EnKF-ψχ), with much less imbalance compared to the ozone experiment. The assimilation of both height and ozone performed the best, with WEP increasing to ~87% (~90% with NMI) for both EnKF-uv and EnKF-ψχ, demonstrating that wind extraction from ozone assimilation can be beneficial even in a data-rich environment. Ozone assimilation particularly improves the tropical winds, which are not well constrained by height observations due to lack of geostrophy.

A Method for Assimilating Lagrangian Data into a Shallow-Water-Equation Ocean Model

2006 ◽  
Vol 134 (4) ◽  
pp. 1081-1101 ◽  
Author(s):  
H. Salman ◽  
L. Kuznetsov ◽  
C. K. R. T. Jones ◽  
K. Ide
Keyword(s):  
Kalman Filter ◽  
Shallow Water ◽  
Ensemble Kalman Filter ◽  
Shallow Water Equation ◽  
Water System ◽  
Direct Consequence ◽  
Ocean Model ◽  
Moving Frame ◽  
Time Interval ◽  
Lagrangian Data

Abstract Lagrangian measurements provide a significant portion of the data collected in the ocean. Difficulties arise in their assimilation, however, since Lagrangian data are described in a moving frame of reference that does not correspond to the fixed grid locations used to forecast the prognostic flow variables. A new method is presented for assimilating Lagrangian data into models of the ocean that removes the need for any commonly used approximations. This is accomplished by augmenting the state vector of the prognostic variables with the Lagrangian drifter coordinates at assimilation. It is shown that this method is best formulated using the ensemble Kalman filter, resulting in an algorithm that is essentially transparent for assimilating Lagrangian data. The method is tested using a set of twin experiments on the shallow-water system of equations for an unsteady double-gyre flow configuration. Numerical simulations show that this method is capable of correcting the flow even if the assimilation time interval is of the order of the Lagrangian autocorrelation time scale (TL) of the flow. These results clearly demonstrate the benefits of this method over other techniques that require assimilation times of 20%–50% of TL, a direct consequence of the approximations introduced in assimilating their Lagrangian data. Detailed parametric studies show that this method is particularly effective if the classical ideas of localization developed for the ensemble Kalman filter are extended to the Lagrangian formulation used here. The method that has been developed, therefore, provides an approach that allows one to fully realize the potential of Lagrangian data for assimilation in more realistic ocean models.

scholarly journals Data assimilation of two-dimensional geophysical flows with a Variational Ensemble Kalman Filter

2014 ◽  
Vol 1 (1) ◽  
pp. 403-446 ◽  
Author(s):  
Z. Mussa ◽  
I. Amour ◽  
A. Bibov ◽  
T. Kauranne
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Shallow Water ◽  
Ensemble Kalman Filter ◽  
Geophysical Flows ◽  
Water Model ◽  
Test Case ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Model Bias

Abstract. The Variational Ensemble Kalman Filter (VEnKF), a recent data assimilation method that combines a variational assimilation of the Bayesian estimation problem with an ensemble of forecasts, is demonstrated in two-dimensional geophysical flows using a Quasi-Geostrophic (QG) model and a shallow water model. Using a synthetic experiment, a two layer QG model with model bias is solved on a cylindrical 40 x 20 domain. The performance of VEnKF on the QG model with increasing ensemble size is compared with the classical Extended Kalman Filter (EKF). It is shown that although convergence can be achieved with just 20 ensemble members, increasing the number of members results in a better estimate that approaches the one produced by EKF. In the second test case, a 2-D shallow water model is described using a real dam-break experiment. The VEnKF algorithm was used to assimilate observations obtained from a modified laboratory dam-break experiment with a two-dimensional setup of sensors at the downstream end. The wave meters are placed parallel to the direction of the flow alongside the flume walls to capture both cross flow and stream flow. In both test cases, VEnKF was able to predict genuinely two-dimensional flow patterns when the sensors had a two-dimensional geometry and was stable against model bias in the first test case. In the second test case, the experiments are complemented with an empirical study of the impact of observation interpolation on the stability of the VEnKF filter. In this study, a novel Courant–Friedrichs–Lewy type filter stability condition is observed that relates ensemble variance to the time interpolation distance between observations. The results of the two experiments shows that VEnKF is a good candidate for data assimilation problems and can be implemented in higher dimensional nonlinear models.

scholarly journals Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

2015 ◽  
Vol 15 (3) ◽  
pp. 3955-3994
Author(s):  
D. R. Allen ◽  
K. W. Hoppel ◽  
D. D. Kuhl
Keyword(s):  
Kalman Filter ◽  
Shallow Water ◽  
Ensemble Kalman Filter ◽  
Stratospheric Ozone ◽  
Localization Length ◽  
Polar Vortex ◽  
Meridional Wind ◽  
Water Model ◽  
Shallow Water Model ◽  
Polar Orbiting Satellite

Abstract. The feasibility of extracting wind information from stratospheric ozone observations is tested using ensemble Kalman filter (EnKF) data assimilation (DA) and a global shallow water model that includes advection of an ozone-like tracer. Simulated observations are created from a truth run (TR) that resembles the Northern Hemisphere winter stratosphere with a polar vortex disturbed by planetary-scale wave forcing. Ozone observations mimic sampling of a polar-orbiting satellite, while geopotential height observations are randomly placed in space and time. EnKF experiments are performed assimilating ozone, height, or both over a 10 day period. The DA is also implemented using two different pairs of flow variables: zonal and meridional wind (EnKF-uv) and streamfunction and velocity potential (EnKF-ψ χ). Each experiment is tuned for optimal localization length, while the ensemble spread is adaptively inflated using the TR. The experiments are evaluated using the maximum wind extraction potential (WEP). Ozone-only assimilation improves winds (WEP = 46% for EnKF-uv, and 58% for EnKF-ψ χ), but suffers from spurious gravity wave generation. Application of nonlinear normal mode initialization (NMI) greatly reduces the unwanted imbalance and increases the WEP for EnKF-uv (84%) and EnKF-ψ χ (81%). Assimilation of only height observations also improved the winds (WEP = 59% for EnKF-uv, and 67% for EnKF-ψ χ), with much less imbalance compared to the ozone experiment. The assimilation of both height and ozone performed the best, with WEP increasing to ~ 87% (~ 90% with NMI) for both EnKF-uv and EnKF-ψ χ, demonstrating that wind extraction from ozone assimilation can be beneficial even in a data-rich environment. Ozone assimilation particularly improves the tropical winds, which are not well constrained by height observations due to lack of geostrophy.

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