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Data assimilation of stratospheric constituents: a review

W. A. Lahoz, Q. Errera, R. Swinbank, D. Fonteyn

2007
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Atmospheric Chemistry and Physics Discussions
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The data assimilation of stratospheric constituents is reviewed. The data assimilation method is introduced, with particular consideration to its application to stratospheric constituent measurements. Differences from meteorological data assimilation are outlined. Historically, two approaches have been used to carry out constituent assimi-5 lation. One approach has carried constituent assimilation out as part of a numerical weather prediction system; the other has carried it out in a standalone
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... out in a standalone chemical model, often with a more sophisticated representation of chemical processes. Whereas the aim of the numerical weather prediction approach has been to improve weather forecasts, the aims of the chemical model approach have included providing chemical 10 forecasts and analyses of chemical constituents. A range of constituent assimilation systems developed in these two areas is presented and strengths and weaknesses discussed. The use of stratospheric constituent data assimilation to evaluate models, observations and analyses, and to provide analyses of constituents, monitor ozone, and make ozone forecasts is discussed. Finally, the current state of affairs is assessed, 15 future directions are discussed, and potential key drivers identified. Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU European Centre for Medium -range Weather Forecasts, ECMWF, Dethof, 2003) has become routine. A notable feature of the application of the data assimilation methodology to stratospheric constituents has been the strong interaction between the NWP and research communities, for example, in the EU-funded ASSET project . 25 Whereas the aim of the NWP approach has been to improve weather forecasts, the aims of the chemical model approach are broader, and include providing chemical forecasts and analyses of chemical constituents. In this review paper we will focus on these two approaches and compare their strengths and weaknesses. Illustrative 9563 ACPD Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU examples of each approach will be provided. Table 1 provides a summary of stratospheric chemistry satellite observations for the period 1978 to the present, that have been assimilated by NWP-based or chemical model data assimilation systems. References describing the satellites/instruments are provided. 5 The increasing maturity of data assimilation applied to stratospheric constituents, and increasing use of the methodology by the scientific community, means that a review of the field is timely. This review complements and builds on the recent review by Rood (2005) by focusing on two approaches to assimilate stratospheric constituents, NWP models and chemical models, providing examples and comparing and contrast-10 ing the two approaches. It also takes into account recent developments concerning in particular the use of data assimilation to evaluate the quality of observations and models associated with ozone and water vapour. This review summarizes in one publication and puts in context these later results. In the remaining sections of this review we discuss the elements of data assimila-15 tion, with particular consideration to constituent data assimilation (Sect. 2). We then discuss NWP-based approaches to data assimilation (Sect. 3) and chemical model approaches to data assimilation (Sect. 4). We then discuss the evaluation of models, observations and analyses (Sect. 5), and provide examples of applications of stratospheric constituent data assimilation (Sect. 6). Finally, we assess the current state of 20 affairs, discuss future directions and identify potential key drivers (Sect. 7). An Appendix lists acronyms used in this paper. 2 Elements of data assimilation 2.1 Introduction Information on a system from observations based on geophysical measurements (the 25 observed system) is discrete in both space and time, so that there are "information 9564 ACPD Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU gaps". However, many applications require fully-specified geophysical fields. Thus, information needs to be mapped from measurement space (or observational space) to a state space (or model space), such as a (discretized) numerical model representation of the stratosphere. Although the models available for this mapping vary in their complexity, a reasonable choice is a model that embodies the physical laws that govern the 5 observed system. Often, the model itself is said to embody the prior or background information on the observed system; however, the prior information can also represent a prior or background estimate of the observed system. The data assimilation (DA) problem aims to fill the "information gaps" in an optimal way; it can be stated, in non-mathematical terms, as: Find the best representation of the state of an evolving 10 system given measurements made and prior information on the system, taking account of errors in the measurements and the prior information. The observation operator transforms from the model space to the measurement space. It involves a mapping from geophysical inputs in model space (e.g. temperatures, constituent amounts) to simulate an instrument measurement in measurement 15 space (e.g. radiances), taking into account the physics of the measurement and the characteristics of the instrument. The DA problem involves a minimization of the misfit between the model and the observations, and between the model and prior information to produce a solution referred to as the analysis. The model operator, or the forward model, maps the analysis forward in time to give a background state for a subsequent 20 assimilation cycle. In general the number of measurements p is different (and usually smaller than) the dimension n of the state space, making the DA problem ill-posed. Typically, prior or background information is used to correct the ill-posed nature of the DA problem. Although Bayesian estimation (Rodgers, 2000) defines a systematic and rigorous 25 approach to data assimilation, its full-scale implementation in constituent data assimilation is impossible, chiefly due to the size of the problem. However, the Bayesian approach is still useful in that it provides general guidelines for developing a DA system and evaluating its results. Nevertheless, in any practical application it is necessary 9565 ACPD Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU to make drastic simplifying assumptions to the DA algorithm. Two main lines have been followed: (i) statistical linear estimation, and (ii) ensemble assimilation (Talagrand, 2003a) . Most standard DA algorithms, such as optimal interpolation, the Kalman filter and smoother, and variational methods, are built on statistical linear estimation. Bouttier 5 and Courtier (1999) provide details of these algorithms. Ensemble assimilation is a form of Monte-Carlo approximation which attempts to estimate probability distribution functions (PDFs) from the spread of the ensemble. In present applications (e.g. the Ensemble Kalman filter, Evensen, 2003), the size of the analysed ensembles typically lies between a few tens to a few hundreds of model 10 states. There are differences between NWP and stratospheric constituent data assimilation that affect the way the assimilation is set up in the latter. These are: -Stratospheric constituent data assimilation is less mature than NWP data assim- ilation. An example of this concerns parametrizations of ozone chemistry due to 15 Cariolle and Déqué (1986). They have been used to assimilate ozone in the last 5 years or so, but it is only very recently that the performance of these schemes, and their associated errors, has been assessed in the data assimilation context (Geer et al., 2007) . -NWP is primarily an initial value problem. Stratospheric constituent data as-20 similation is commonly posed as an initial value problem, but sources and sinks may need to be considered. -Improvements in NWP can be achieved by more accurate specification of dynamical variables such as temperature, winds and humidity. For stratospheric constituents, a better forecast can be achieved both by a better description of 25 dynamical variables (and hence transport of the constituent), and by a better description of sources and sinks (if applicable). 9566 ACPD 7, 9561-9633, 2007 Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion EGU -The time-scales relevant for NWP are order of days. For stratospheric chemistry, there is a very wide range of time-scales, from decades (e.g. for carbon dioxide) to seconds for very short-lived species. -Chemical equation systems are stiff, i.e., they include reactions with rates varying by several orders of magnitude. This requires the use of sophisticated 5 ACPD 7, 9561-9633, 2007 Abstract ACPD 7, 9561-9633, 2007 Abstract 20 also indicate improved forecast skill for 4D-Var compared to an equivalent 3D-Var configuration (Rawlins et al., 2007). Thus, some of the benefit of 4D-Var can be obtained using the 3D-FGAT approach. 4D-Var has two new features compared to 3D-Var. First, it includes a model operator, M, that carries out the evolution forward in time. The first derivative, or differential, of 25 M, M, is the tangent linear model (if M is linear, represented by M, its derivative is M). The transpose of the tangent linear model operator, M T , integrates the adjoint variables backward in time. Bouttier and Courtier (1999) discuss the conditions for the validity of the tangent linear hypothesis, required to define the tangent linear model. Second, 9571 ACPD 7, 9561-9633, 2007 Abstract 25 Treatment of errors. Many DA systems use the so-called NMC method (Parrish and Derber, 1992) to estimate the background error covariance matrix B; this is based on the premise that forecast errors are similar to the differences between pairs of forecasts that verify at the same time. Polavarapu et al. (2005a) implement a variation 9573 ACPD Abstract 7, 9561-9633, 2007 Abstract ACPD 7, 9561-9633, 2007 Abstract 9578 ACPD 7, 9561-9633, 2007 Abstract ACPD 7, 9561-9633, 2007 Abstract 25 vations, the model and the analyses, and the test of several assumptions built into data assimilation algorithms, e.g., Gaussian errors; unbiased observations and mod-9592 ACPD Abstract ACPD 7, 9561-9633, 2007 Abstract 7, 9561-9633, 2007 Abstract 7, 9561-9633, 2007 Abstract 7, 9561-9633, 2007 Abstract ACPD 7, 9561-9633, 2007 Abstract 5

doi:10.5194/acpd-7-9561-2007
fatcat:2eeiv5syanewtgk4pmuvarcwmi