On the interaction of observation and prior error correlations in data assimilation
Tóm tắt
The importance of prior error correlations in data assimilation has long been known; however, observation‐error correlations have typically been neglected. Recent progress has been made in estimating and accounting for observation‐error correlations, allowing for the optimal use of denser observations. Given this progress, it is now timely to ask how prior and observation‐error correlations interact and how this affects the value of the observations in the analysis. Addressing this question is essential to understanding the optimal design of future observation networks for high‐resolution numerical weather prediction. This article presents new results, which unify and advance upon previous studies on this topic.
The interaction of the prior and observation‐error correlations is illustrated with a series of two‐variable experiments in which the mapping between the state and observed variables (the observation operator) is allowed to vary. In an optimal system, the reduction in the analysis‐error variance and spread of information is shown to be greatest when the observation and prior errors have complementary statistics: for example, in the case of direct observations, when the correlations between the observation and prior errors have opposite signs. This can be explained in terms of the relative uncertainty of the observations and prior on different spatial scales. The results from these simple two‐variable experiments are used to inform the optimal observation density for observations of a circular domain (with 32 grid points). It is found that dense observations are most beneficial when they provide a more accurate estimate of the state at smaller scales than the prior estimate. In the case of second‐order auto‐regressive correlation functions, this is achieved when the length‐scales of the observation‐error correlations are greater than those of the prior estimate and the observations are direct measurements of the state variables.
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Tài liệu tham khảo
BergerH ForsytheM.2004.‘Satellite wind superobbing’. Met Office Forecasting Research Technical Report 451.http://research.metoffice.gov.uk/research/nwp/publications/papers/technical_reports/2004/FRTR451/FRTR451.pdf.
Bormann N, 2016, Enhancing the impact of IASI observations through an updated observation‐error covariance matrix, Q. J. R. Meteorol. Soc., 1420, 1767, 10.1002/qj.2774
Browne PA, 2014, RMetS Special Interest Group Meeting: High resolution data assimilation, Atmos. Sci. Lett., 150, 354, 10.1002/asl2.512
Daley R, 1996, Atmospheric Data Analysis
Desroziers G, 2005, Diagnosis of observation, background and analysis‐error statistics in observation space, Q. J. R. Meteorol. Soc., 1310, 3385, 10.1256/qj.05.108
Eresmaa R, 2014, ‘Implications of observation‐error correlation on the assimilation of interferometric radiances’
Gray R, 2006, Chapter in ‘Foundations and Trends in Communications and Information Theory 2’, 155
HiltonF CollardA GuidardV RandriamampianinaR SchwaerzM.2009.Assimilation of IASI radiances at European NWP centres. In Proceedings of Workshop on the Assimilation of IASI Data in NWP 6–8 May 2009. ECMWF Reading UK.
Hodyss D, 2017, The Treatment, Estimation, and Issues with Representation Error Modelling, 10.1007/978-3-319-43415-5_8
Janjic T, 2017, On the representation error, Q. J. R. Meteorol. Soc.
Kalnay E, 2003, Atmospheric Modeling, Data Assimilation and Predictability
Lean HW, 2008, Characteristics of high‐resolution versions of the met office unified model for forecasting convection over the united kingdom, Mon. Weather Rev., 1360, 3408, 10.1175/2008MWR2332.1
Miyoshi T, 2013, Estimating and including observation‐error correlations in data assimilation, Inverse Prob. Sci. Eng., 210, 387, 10.1080/17415977.2012.712527
Pahl PJ, 2012, Mathematical Foundations of Computational Engineering: A Handbook
Pozrikidis C, 2014, An Introduction to Grids, Graphs and Networks
Stewart LM, 2008, Correlated observation errors in data assimilation, Int. J. Numer. Methods Fluids, 560, 1521, 10.1002/fld.1636
Sun J, 2014, Use of NWP for nowcasting convective precipitation: Recent progress and challenges, Bull. Am. Meteorol. Soc., 950, 409, 10.1175/BAMS-D-11-00263.1
van Leeuwen PJ, 2015, Representation errors and retrievals in linear and nonlinear data assimilation, Q. J. R. Meteorol. Soc., 141, 612, 10.1002/qj.2464