Articles | Volume 28, issue 1
https://doi.org/10.5194/npg-28-1-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-28-1-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
14 Jan 2021
Research article |
| 14 Jan 2021
| 14 Jan 2021
A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective
Olivier Pannekoucke
CORRESPONDING AUTHOR
INPT-ENM, Toulouse, France
CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, France
CERFACS, Toulouse, France
Richard Ménard
ARQI/Air Quality Research Division, Environment and Climate Change Canada, Dorval, Québec, Canada
Mohammad El Aabaribaoune
CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, France
CERFACS, Toulouse, France
Matthieu Plu
CNRM, Université de Toulouse, Météo-France, CNRS, Toulouse, France
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Cited articles
Berre, L., Pannekoucke, O., Desroziers, G., Stefanescu, S., Chapnik, B., and Raynaud, L.: A variational assimilation ensemble and the spatial filtering of its error covariances: increase of sample size by local spatial averaging, available at: https://www.ecmwf.int/node/8172 (last access: 13 January 2021),
ECMWF Workshop on Flow-dependent aspecyts of data assimilation, Reading, UK, 11–13 June 2007, 151–168, 2007. a
Boisserie, M., Arbogast, P., Descamps, L., Pannekoucke, O., and Raynaud, L.:
Estimating and diagnosing model error variances in the Meteo-France global
NWP model, Q. J. Roy. Meteor. Soc., 140,
846–854, https://doi.org/10.1002/qj.2173,
2013. a
Boyd, J.: Chebyshev and Fourier Spectral Methods, Dover Publications, Mineola, New York, USA, 2001. a
Carrassi, A. and Vannitsem, S.: Accounting for Model Error in Variational Data
Assimilation: A Deterministic Formulation, Mon. Weather Rev., 138,
3369–3386, https://doi.org/10.1175/2010MWR3192.1,
2010. a
Daley, R.: Atmospheric Data Analysis, Cambridge University Press,
New York, USA,
1991. a
Dee, D.: On-line Estimation of Error Covariance Parameters for Atmospheric Data
Assimilation, Mon. Weather Rev., 123, 1128–1145, 1995. a
Derber, J. and Bouttier, F.: A reformulation of the background error covariance in the ECMWF global data assimilation system, Tellus A, 51, 195–221, 1999. a
Dubinkina, S.: Relevance of conservative numerical schemes for an Ensemble
Kalman Filter, Q. J. Roy. Meteor. Soc., 144,
468–477, https://doi.org/10.1002/qj.3219, 2018. a
Emili, E., Gürol, S., and Cariolle, D.: Accounting for model error in air quality forecasts: an application of 4DEnVar to the assimilation of atmospheric composition using QG-Chem 1.0, Geosci. Model Dev., 9, 3933–3959, https://doi.org/10.5194/gmd-9-3933-2016, 2016. a
Evensen, G.: Data Assimilation: The Ensemble Kalman Filter, Springer
Berlin Heidelberg, https://doi.org/10.1007/978-3-642-03711-5, 2009. a
Grudzien, C., Bocquet, M., and Carrassi, A.: On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments, Geosci. Model Dev., 13, 1903–1924, https://doi.org/10.5194/gmd-13-1903-2020, 2020. a
Hatfield, S., Düben, P., Chantry, M., Kondo, K., Miyoshi, T., and Palmer, T.:
Choosing the Optimal Numerical Precision for Data Assimilation in the
Presence of Model Error, J. Adv. Model. Earth Sy., 10,
2177–2191, https://doi.org/10.1029/2018ms001341, 2018. a
Hirt, C.: Heuristic stability theory for finite-difference equations, J.
Comput. Phys., 2, 339–355, https://doi.org/10.1016/0021-9991(68)90041-7,
1968. a
Houtekamer, P. L., Mitchell, H. L., and Deng, X.: Model Error Representation in
an Operational Ensemble Kalman Filter, Mon. Weather Rev., 137,
2126–2143, 2009. a
Lax, P. D. and Richtmyer, R. D.: Survey of the stability of linear finite
difference equations, Commun. Pur. Appl. Math., 9,
267–293, https://doi.org/10.1002/cpa.3160090206,
1956. a
McCalpin, J. D.: A Quantitative Analysis of the Dissipation Inherent in
Semi-Lagrangian Advection, Mon. Weather Rev., 116, 2330–2336, 1988. a
Ménard, R. and Chang, L.-P.: Assimilation of Stratospheric Chemical Tracer
Observations Using a Kalman Filter. Part II: chi-2-Validated Results and
Analysis of Variance and Correlation Dynamics, Mon. Weather Rev., 128,
2672–2686, https://doi.org/10.1175/1520-0493(2000)128<2672:AOSCTO>2.0.CO;2, 2000. a, b
Palmer, T. N., Buizza, R., Doblas-Reyes, F., Jung, T., Leutbecher, M., Shutts,
G., Steinheimer, M., and Weisheimer, A.: Stochastic Parametrization and Model
Uncertainty, Tech Memo 598, ECMWF, Reading, UK, 44 p., 2009. a
Pannekoucke, O. and Fablet, R.: PDE-NetGen 1.0: from symbolic partial differential equation (PDE) representations of physical processes to trainable neural network representations, Geosci. Model Dev., 13, 3373–3382, https://doi.org/10.5194/gmd-13-3373-2020, 2020. a, b
Pannekoucke, O. and Massart, S.: Estimation of the local diffusion tensor and
normalization for heterogeneous correlation modelling using a diffusion
equation., Q. J. Roy. Meteor. Soc., 134, 1425–1438, 2008. a
Pannekoucke, O., Ricci, S., Barthelemy, S., Ménard, R., and Thual, O.:
Parametric Kalman Filter for chemical transport model, Tellus A, 68, 31547,
https://doi.org/10.3402/tellusa.v68.31547, 2016. a, b
Pannekoucke, O., Bocquet, M., and Ménard, R.: Parametric covariance dynamics for the nonlinear diffusive Burgers equation, Nonlin. Processes Geophys., 25, 481–495, https://doi.org/10.5194/npg-25-481-2018, 2018a. a, b, c, d
Pannekoucke, O., Ricci, S., Barthelemy, S., Ménard, R., and Thual, O.:
Parametric Kalman filter for chemical transport models – Corrigendum, Tellus A, 70, 1–2, https://doi.org/10.1080/16000870.2018.1472954, 2018b. a
Resseguier, V., Mémin, E., and Chapron, B.: Geophysical flows under
location uncertainty, Part I Random transport and general models, Geophys. Astro. Fluid, 111, 149–176,
https://doi.org/10.1080/03091929.2017.1310210, 2017.
a
Shutts, G. J.: A kinetic energy backscatter algorithm for use in ensemble
prediction systems, Q. J. Roy. Meteor. Soc.,
131, 3079–3102,
https://doi.org/10.1256/qj.04.106,
2005. a
Vannitsem, S. and Toth, Z.: Short-Term Dynamics of Model Errors, J.
Atmos. Sci., 59, 2594–2604,
https://doi.org/10.1175/1520-0469(2002)059<2594:STDOME>2.0.CO;2,
2002. a
Warming, R. and Hyett, B.: The modified equation approach to the stability and
accuracy analysis of finite-difference methods, J. Comput.
Phys., 14, 159–179, https://doi.org/10.1016/0021-9991(74)90011-4, 1974. a
Weaver, A. and Courtier, P.: Correlation modelling on the sphere using a
generalized diffusion equation (Tech. Memo. ECMWF, num. 306), Q.
J. Roy. Meteor. Soc., 127, 1815–1846, 2001. a
Weaver, A. T. and Mirouze, I.: On the diffusion equation and its application to
isotropic and anisotropic correlation modelling in variational assimilation,
Q. J. Roy. Meteor. Soc., 139, 242–260, 2013. a
Short summary
Numerical weather prediction involves numerically solving the mathematical equations, which describe the geophysical flow, by transforming them so that they can be computed. Through this transformation, it appears that the equations actually solved by the machine are then a modified version of the original equations, introducing an error that contributes to the model error. This work helps to characterize the covariance of the model error that is due to this modification of the equations.
Numerical weather prediction involves numerically solving the mathematical equations, which...
