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.

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.

Balanced Ocean-Data Assimilation near the Equator

2002 ◽  
Vol 32 (9) ◽  
pp. 2509-2519 ◽  
Author(s):  
Gerrit Burgers ◽  
Magdalena A. Balmaseda ◽  
Femke C. Vossepoel ◽  
Geert Jan van Oldenborgh ◽  
Peter Jan van Leeuwen
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
General Circulation ◽  
General Circulation Models ◽  
Density Field ◽  
Water Model ◽  
Optimal Interpolation ◽  
Shallow Water Model ◽  
Ocean Data Assimilation ◽  
Zonal Velocity

Abstract The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.

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 dynamic multilayer shallow water model for polydisperse sedimentation

2019 ◽  
Vol 53 (4) ◽  
pp. 1391-1432 ◽  
Author(s):  
Raimund Bürger ◽  
Enrique D. Fernández-Nieto ◽  
Víctor Osores
Keyword(s):  
Shallow Water ◽  
Bottom Topography ◽  
Mining Industry ◽  
Mass Conservation ◽  
Variable Density ◽  
Solid Particles ◽  
Water Model ◽  
Reduced Form ◽  
Momentum Balance ◽  
Shallow Water Model

A multilayer shallow water approach for the approximate description of polydisperse sedimentation in a viscous fluid is presented. The fluid is assumed to carry finely dispersed solid particles that belong to a finite number of species that differ in density and size. These species segregate and form areas of different composition. In addition, the settling of particles influences the motion of the ambient fluid. A distinct feature of the new approach is the particular definition of the average velocity of the mixture. It takes into account the densities of the solid particles and the fluid and allows us to recover the global mass conservation and linear momentum balance laws of the mixture. This definition motivates a modification of the Masliyah–Lockett–Bassoon (MLB) settling velocities of each species. The multilayer shallow water model allows one to determine the spatial distribution of the solid particles, the velocity field, and the evolution of the free surface of the mixture. The final model can be written as a multilayer model with variable density where the unknowns are the average velocities and concentrations in each layer, the transfer terms across each interface, and the total mass. An explicit formula of the transfer terms leads to a reduced form of the system. Finally, an explicit bound of the minimum and maximum eigenvalues of the transport matrix of the system is utilized to design a Harten–Lax–van Leer (HLL)-type path-conservative numerical method. Numerical simulations illustrate the coupled polydisperse sedimentation and flow fields in various scenarios, including sedimentation in a type of basin that is used in practice in mining industry and in a basin whose bottom topography gives rise to recirculations of the fluid and high solids concentrations.

scholarly journals A Consistent Hybrid Variational-Smoothing Data Assimilation Method: Application to a Simple Shallow-Water Model of the Turbulent Midlatitude Ocean

2011 ◽  
Vol 139 (11) ◽  
pp. 3333-3347 ◽  
Author(s):  
Monika Krysta ◽  
Eric Blayo ◽  
Emmanuel Cosme ◽  
Jacques Verron
Keyword(s):  
Data Assimilation ◽  
Shallow Water ◽  
Covariance Matrix ◽  
Hybrid Method ◽  
Water Model ◽  
Shallow Water Model ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
The Matrix

Abstract In the standard four-dimensional variational data assimilation (4D-Var) algorithm the background error covariance matrix remains static over time. It may therefore be unable to correctly take into account the information accumulated by a system into which data are gradually being assimilated. A possible method for remedying this flaw is presented and tested in this paper. A hybrid variational-smoothing algorithm is based on a reduced-rank incremental 4D-Var. Its consistent coupling to a singular evolutive extended Kalman (SEEK) smoother ensures the evolution of the matrix. In the analysis step, a low-dimensional error covariance matrix is updated so as to take into account the increased confidence level in the state vector it describes, once the observations have been introduced into the system. In the forecast step, the basis spanning the corresponding control subspace is propagated via the tangent linear model. The hybrid method is implemented and tested in twin experiments employing a shallow-water model. The background error covariance matrix is initialized using an EOF decomposition of a sample of model states. The quality of the analyses and the information content in the bases spanning control subspaces are also assessed. Several numerical experiments are conducted that differ with regard to the initialization of the matrix. The feasibility of the method is illustrated. Since improvement due to the hybrid method is not universal, configurations that benefit from employing it instead of the standard 4D-Var are described and an explanation of the possible reasons for this is proposed.

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