The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model

2013 ◽  
Vol 76 ◽  
pp. 33-49 ◽  
Author(s):  
F. Fang ◽  
C.C. Pain ◽  
I.M. Navon ◽  
D.G. Cacuci ◽  
X. Chen
Keyword(s):  
Finite Element ◽  
Data Assimilation ◽  
Perturbation Method ◽  
Shallow Water ◽  
Independent Set ◽  
Water Model ◽  
Efficient Computation ◽  
Shallow Water Model

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.

A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries

2000 ◽  
Vol 23 (4) ◽  
pp. 359-372 ◽  
Author(s):  
Mourad Heniche ◽  
Yves Secretan ◽  
Paul Boudreau ◽  
Michel Leclerc
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Dimensional Finite Element

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 Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2832 ◽  
Author(s):  
Shin-Jye Liang ◽  
Chih-Chieh Young ◽  
Chi Dai ◽  
Nan-Jing Wu ◽  
Tai-Wen Hsu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Free Surface ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Shallow Water Model

A two-dimensional non-hydrostatic shallow-water model for weakly dispersive waves is developed using the least-squares finite-element method. The model is based on the depth-averaged, nonlinear and non-hydrostatic shallow-water equations. The non-hydrostatic shallow-water equations are solved with the semi-implicit (predictor-corrector) method and least-squares finite-element method. In the predictor step, hydrostatic pressure at the previous step is used as an initial guess and an intermediate velocity field is calculated. In the corrector step, a Poisson equation for the non-hydrostatic pressure is solved and the final velocity and free-surface elevation is corrected for the new time step. The non-hydrostatic shallow-water model is verified and applied to both wave and flow driven fluid flows, including solitary wave propagation in a channel, progressive sinusoidal waves propagation over a submerged bar, von Karmann vortex street, and ocean circulations of Dongsha Atolls. It is found hydrostatic shallow-water model is efficient and accurate for shallow water flows. Non-hydrostatic shallow-water model requires 1.5 to 3.0 more cpu time than hydrostatic shallow-water model for the same simulation. Model simulations reveal that non-hydrostatic pressure gradients could affect the velocity field and free-surface significantly in case where nonlinearity and dispersion are important during the course of wave propagation.

A discontinuous/continuous low order finite element shallow water model on the sphere

2012 ◽  
Vol 231 (6) ◽  
pp. 2396-2413 ◽  
Author(s):  
Peter D. Düben ◽  
Peter Korn ◽  
Vadym Aizinger
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model ◽  
Low Order
Sign in / Sign up

Export Citation Format

Share Document