World Library  


Add to Book Shelf
Flag as Inappropriate
Email this Book

The Effects of the Model Errors Generated by Discretization of On-off'' Processes on Vda : Volume 13, Issue 3 (25/07/2006)

By Zheng, Q.

Click here to view

Book Id: WPLBN0004019768
Format Type: PDF Article :
File Size: Pages 12
Reproduction Date: 2015

Title: The Effects of the Model Errors Generated by Discretization of On-off'' Processes on Vda : Volume 13, Issue 3 (25/07/2006)  
Author: Zheng, Q.
Volume: Vol. 13, Issue 3
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2006
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

Citation

APA MLA Chicago

Zheng, Q., & Mu, M. (2006). The Effects of the Model Errors Generated by Discretization of On-off'' Processes on Vda : Volume 13, Issue 3 (25/07/2006). Retrieved from http://hawaiilibrary.net/


Description
Description: LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China. Through an idealized model of a partial differential equation with discontinuous on-off'' switches in the forcing term, we investigate the effect of the model error generated by the traditional discretization of discontinuous physical on-off'' processes on the variational data assimilation (VDA) in detail. Meanwhile, the validity of the adjoint approach in the VDA with on-off'' switches is also examined. The theoretical analyses illustrate that in the analytic case, the gradient of the associated cost function (CF) with respect to an initial condition (IC) exists provided that the IC does not trigger the threshold condition. But in the discrete case, if the on switches (or off switches) in the forward model are straightforwardly assigned the nearest time level after the threshold condition is (or is not) exceeded as the usual treatment, the discrete CF gradients (even the one-sided gradient of CF) with respect to some ICs do not exist due to the model error, which is the difference between the analytic and numerical solutions to the governing equation. Besides, the solution of the corresponding tangent linear model (TLM) obtained by the conventional approach would not be a good first-order linear approximation to the nonlinear perturbation solution of the governing equation. Consequently, the validity of the adjoint approach in VDA with parameterized physical processes could not be guaranteed. Identical twin numerical experiments are conducted to illustrate the influences of these problems on VDA when using adjoint method. The results show that the VDA outcome is quite sensitive to the first guess of the IC, and the minimization processes in the optimization algorithm often fail to converge and poor optimization retrievals would be generated as well. Furthermore, the intermediate interpolation treatment at the switch times of the forward model, which reduces greatly the model error brought by the traditional discretization of on-off'' processes, is employed in this study to demonstrate that when the on-off'' switches in governing equations are properly numerically treated, the validity of the adjoint approach in VDA with discontinuous physical on-off'' processes can still be guaranteed.

Summary
The effects of the model errors generated by discretization of on-off'' processes on VDA

Excerpt
Bao, J. W. and Warner, T. T.: Treatment of on/off switches in the adjoint method: FDDA experiments with a simple model, Tellus, 45A, 525–538, 1993.; Bao, J. W. and Kuo, Y.-H.: On-off switches in the adjoint method, Step functions, Mon. Wea. Rev., 123, 1589–1594, 1995.; Bergur, M. S.: Nonlinear and functional analysis, Academic Press, New York, 1977.; Courtier, P. and Talagrand, O.: Variational assimilation of meteorological observations with adjoint vorticity equation: Part II. Numerical results, Quart. J. Roy. Meteor. Soc., 113, 1329–1368, 1987.; Deimling, K.: Nonlinear and functional analysis, Springer-Verlag, 1985.; Fillion, L. and Mahfouf, J.-F.: Coupling of moist-convective and stratiform precipitation processes for variational data assimilation, Mon. Wea. Rev., 128, 109–124, 2000.; Fillion, L. and Belair, S.: Tangent Linear Aspects of the Kain-Fritsch Moist Convective Parameterization Scheme, Mon. Wea. Rev., 132, 2477–2494, 2004.; Marecal, V. and Mahfouf, J.-F.: Variational retrieval of temperature and humidity profiles from TRMM precipitation data, Mon. Wea. Rev., 128, 3853–3866, 2000.; Kuo, Y. H., Zou, X., and Guo, Y. R.: Variational assimilation of precipitable water using nonhydrostatic mesoscale adjoint model. Part I: Moisture retrievals and sensitivity experiments, Mon. Wea. Rev., 124, 122–147, 1996.; LeDimet, F. X. and Talagrand, O.: Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects, Tellus, 38A, 97–110, 1986.; Mu, M. and Wang, J. F.: An adjoint method for variational data assimilation with physical on-off processes, J. Atmos. Sci., 60, 2010–2018, 2003.; Mu, M. and Zheng, Q.: Zigzag Oscillations in Variational Data assimilation with Physical On-Off Processes, Mon Wea. Rev., 133, 2711–2720, 2005.; Verlinde, J. and Cotton, W. R.: Fitting microphysical observations of non-steady convective clouds to a numerical model: An application of the adjoint technique of data assimilation to a kinematic model, Mon. Wea. Rev., 121, 2776–2793, 1993.; Vuki\'cevi\'c, T. and Bao, J. W.: The effect of linearization errors on 4DVAR data assimilation, Mon. Wea. Rev., 126, 1695–1706, 1998.; Xu, Q.: Generalized Adjoint for Physical Processes with Parameterized Discontinuities. Part I: Basic Issues and Heuristic Examples, J. Atmos. Sci., 53, 1123–1142, 1996.; Xu, Q.: Generalized Adjoint for Physical Processes with Parameterized Discontinuities. Part IV: Problems in Time Discretization, J. Atmos. Sci., 54, 2722–2728, 1997.; Xu, Q., Gao, J., and Gu, W.: Generalized adjoint for physical processes with parameterized discontinuities. Part V: Coarse-grain adjoint and problems in gradient check, J. Atmos. Sci., 55(11), 2130–2135, 1998.; Xu, Q. and Gao, J.: Generalized Adjoint for Physical Processes with Parameterized Discontinuities. Part VI: Minimization Problems in Multidimensional Space, J. Atmos. Sci., 56, 994–1002, 1999.; Zou, X.: Tangent linear and adjoint of on-off processes and their feasibility for use in 4-dimensional variational data assimilation, Tellus, 49A, 3–31, 1997.; Zou, X., Navon, I. M., and Sela, J. G.: Variational data assimilation with moist threshold processes using the NMC spectral model, Tellus, 45A, 370–387, 1993.; Zupanski, D.: The effect of discontinuities in the Betts-Miller cumulus convection scheme on four-dimensional data assimilation, Tellus, 45A, 511–524, 1993.; Zou, X. and Mesinger, F.: Four-dimensional variational assimilation of precipitation data, Mon. Wea. Rev., 123, 1112–1127, 1995.

 

Click To View

Additional Books


  • Hyperbolicity in Temperature and Flow Fi... (by )
  • Finding Recurrence Networks' Threshold A... (by )
  • Image-model Coupling: a Simple Informati... (by )
  • Hysteresis-controlled Instability Waves ... (by )
  • Stochastic Resonance in a Nonlinear Mode... (by )
  • Predictability of a Low-order Interactiv... (by )
  • Using Sparse Regularization for Multires... (by )
  • Image-model Coupling: Application to an ... (by )
  • Impulse Exchange at the Surface of the O... (by )
  • Size Distribution and Structure of Barch... (by )
  • On the Predominance of Oblique Disturban... (by )
  • Hamiltonian Formulation for the Descript... (by )
Scroll Left
Scroll Right

 



Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.