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.

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.

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 Vortex erosion in a shallow water model of the polar vortex

2017 ◽  
Vol 78 ◽  
pp. 137-151 ◽  
Author(s):  
Robin Beaumont ◽  
Frank Kwasniok ◽  
John Thuburn
Keyword(s):  
Shallow Water ◽  
Polar Vortex ◽  
Water Model ◽  
Shallow Water Model

scholarly journals Hybrid ensemble 4DVar assimilation of stratospheric ozone using a global shallow water model

2016 ◽  
Author(s):  
Douglas R. Allen ◽  
Karl W. Hoppel ◽  
David D. Kuhl
Keyword(s):  
Shallow Water ◽  
Hybrid System ◽  
Stratospheric Ozone ◽  
Water Model ◽  
Advection Equation ◽  
Length Scale ◽  
Shallow Water Model ◽  
Optimal Length ◽  
Large Ensembles ◽  
Optimal Blending

Abstract. Wind extraction from stratospheric ozone (O3) assimilation is examined using a hybrid ensemble 4DVar shallow water model (SWM) system coupled to the tracer advection equation. Stratospheric radiance observations are simulated using global observations of the SWM fluid height (Z), while O3 observations represent sampling by a typical polar-orbiting satellite. Four ensemble sizes were examined (25, 50, 100, and 1518 members), with the largest ensemble equal to the number of dynamical state variables. The optimal length scale for ensemble localization was found by tuning an ensemble Kalman filter (EnKF). This scale was then used for localizing the ensemble covariances that were blended with conventional covariances in the hybrid 4DVar experiments. Both optimal length scale and optimal blending coefficient increase with ensemble size, with optimal blending coefficients varying from 0.2 to 0.5 for small ensembles to 0.5 to 1.0 for large ensembles. The hybrid system outperforms conventional 4DVar for all ensemble sizes, while for large ensembles the hybrid produces similar results to the offline EnKF. Assimilating O3 in addition to Z benefits the winds in the hybrid system, with the fractional improvement in global vector wind increasing from ~35 % with 25 and 50 members to ~50 % with 1518 members. For the smallest ensembles (25 and 50 members), the hybrid 4DVar assimilation improves the zonal wind analysis over conventional 4DVar in the Northern Hemisphere (winter-like) region and also at the equator, where Z observations alone have difficulty constraining winds due to lack of geostrophy. For larger ensembles (100 and 1518 members), the hybrid system results in both zonal and meridional wind error reductions, relative to 4DVar, across the globe.

scholarly journals Hybrid ensemble 4DVar assimilation of stratospheric ozone using a global shallow water model

2016 ◽  
Vol 16 (13) ◽  
pp. 8193-8204 ◽  
Author(s):  
Douglas R. Allen ◽  
Karl W. Hoppel ◽  
David D. Kuhl
Keyword(s):  
Shallow Water ◽  
Hybrid System ◽  
Stratospheric Ozone ◽  
Water Model ◽  
Advection Equation ◽  
Length Scale ◽  
Shallow Water Model ◽  
Optimal Length ◽  
Large Ensembles ◽  
Optimal Blending

Abstract. Wind extraction from stratospheric ozone (O3) assimilation is examined using a hybrid ensemble 4-D variational assimilation (4DVar) shallow water model (SWM) system coupled to the tracer advection equation. Stratospheric radiance observations are simulated using global observations of the SWM fluid height (Z), while O3 observations represent sampling by a typical polar-orbiting satellite. Four ensemble sizes were examined (25, 50, 100, and 1518 members), with the largest ensemble equal to the number of dynamical state variables. The optimal length scale for ensemble localization was found by tuning an ensemble Kalman filter (EnKF). This scale was then used for localizing the ensemble covariances that were blended with conventional covariances in the hybrid 4DVar experiments. Both optimal length scale and optimal blending coefficient increase with ensemble size, with optimal blending coefficients varying from 0.2–0.5 for small ensembles to 0.5–1.0 for large ensembles. The hybrid system outperforms conventional 4DVar for all ensemble sizes, while for large ensembles the hybrid produces similar results to the offline EnKF. Assimilating O3 in addition to Z benefits the winds in the hybrid system, with the fractional improvement in global vector wind increasing from  ∼  35 % with 25 and 50 members to  ∼  50 % with 1518 members. For the smallest ensembles (25 and 50 members), the hybrid 4DVar assimilation improves the zonal wind analysis over conventional 4DVar in the Northern Hemisphere (winter-like) region and also at the Equator, where Z observations alone have difficulty constraining winds due to lack of geostrophy. For larger ensembles (100 and 1518 members), the hybrid system results in both zonal and meridional wind error reductions, relative to 4DVar, across the globe.

scholarly journals Hybrid 4DVAR with a Local Ensemble Tangent Linear Model: Application to the Shallow-Water Model

2016 ◽  
Vol 145 (1) ◽  
pp. 97-116 ◽  
Author(s):  
Douglas R. Allen ◽  
Craig H. Bishop ◽  
Sergey Frolov ◽  
Karl W. Hoppel ◽  
David D. Kuhl ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Shallow Water ◽  
Linear Model ◽  
Bottom Topography ◽  
Grid Point ◽  
Model Error ◽  
Water Model ◽  
State Variables ◽  
Shallow Water Model

Abstract An ensemble-based tangent linear model (TLM) is described and tested in data assimilation experiments using a global shallow-water model (SWM). A hybrid variational data assimilation system was developed with a 4D variational (4DVAR) solver that could be run either with a conventional TLM or a local ensemble TLM (LETLM) that propagates analysis corrections using only ensemble statistics. An offline ensemble Kalman filter (EnKF) is used to generate and maintain the ensemble. The LETLM uses data within a local influence volume, similar to the local ensemble transform Kalman filter, to linearly propagate the state variables at the central grid point. After tuning the LETLM with offline 6-h forecasts of analysis corrections, cycling experiments were performed that assimilated randomly located SWM height observations, based on a truth run with forced bottom topography. The performance using the LETLM is similar to that of the conventional TLM, suggesting that a well-constructed LETLM could free 4D variational methods from dependence on conventional TLMs. This is a first demonstration of the LETLM application within a context of a hybrid-4DVAR system applied to a complex two-dimensional fluid dynamics problem. Sensitivity tests are included that examine LETLM dependence on several factors including length of cycling window, size of analysis correction, spread of initial ensemble perturbations, ensemble size, and model error. LETLM errors are shown to increase linearly with correction size in the linear regime, while TLM errors increase quadratically. As nonlinearity (or forecast model error) increases, the two schemes asymptote to the same solution.

The instability of vertically curved fronts in a two-layer shallow water model

2020 ◽  
Vol 32 (12) ◽  
pp. 124117
Author(s):  
M. W. Harris ◽  
F. J. Poulin ◽  
K. G. Lamb
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model
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