A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. In the companion paper (Sandu et al., 2012) we derive an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. Here we apply this methodology to quantify the signal and degrees of freedom for signal information metrics of satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical transport model. The assimilation of a subset of data points characterized by the highest information content yields an analysis comparable in quality with the one obtained using the entire data set

Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. In the companion paper [Sandu et al.(2011)] we derived an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. Here we apply this methodology to quantify two information metrics (the signal and degrees of freedom for signal) for satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical transport model. The assimilation of a subset of data points characterized by the highest information content, gives analyses that are comparable in quality with the one obtained using the entire data set

A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. I: Methodology

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different data points is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. This paper focuses on the four dimensional variational (4D-Var) data assimilation framework. Metrics from information theory are used to quantify the contribution of observations to decreasing the uncertainty with which the system state is known. We establish an interesting relationship between different information-theoretic metrics and the variational cost function/gradient under Gaussian linear assumptions. Based on this insight we derive an ensemble-based computational procedure to estimate the information content of various observations in the context of 4D-Var. The approach is illustrated on linear and nonlinear test problems. In the companion paper [Singh et al.(2011)] the methodology is applied to a global chemical data assimilation problem

Forward and Inverse Analysis of Chemical Transport Models

Assessing the discrepancy between modeled and observed distributions of aerosols is a persistent problem on many scales. Tools for analyzing the evolution of aerosol size distributions using the adjoint method are presented in idealized box model calculations. The ability to recover information about aerosol growth rates and initial size distributions is assessed given a range of simulated observations of evolving systems. While such tools alone could facilitate analysis of chamber measurements, improving estimates of aerosol sources on regional and global scales requires explicit consideration of many additional chemical and physical processes that govern secondary formation of atmospheric aerosols from emissions of gas-phase precursors. The adjoint of the global chemical transport model GEOS-Chem is derived, affording detailed analysis of the relationship between gas-phase aerosol precursor emissions (SOx, NOx, and NH3) and the subsequent distributions of sulfate - ammonium - nitrate aerosol. Assimilation of surface measurements of sulfate and nitrate aerosol is shown to provide valuable constraints on emissions of ammonia. Adjoint sensitivities are used to propose strategies for air quality control, suggesting, for example, that reduction of SOx emissions in the summer and NH3 emissions in the winter would most effectively reduce non-attainment of aerosol air quality standards. The ability of this model to estimate global distributions of carbonaceous aerosol is also addressed. Based on new yield data from environmental chamber studies, mechanisms for incorporating the dependence of secondary organic aerosol (SOA) formation on NOx concentrations are developed for use in global models. When NOx levels are appropriately accounted for, it is demonstrated that sources such as isoprene and aromatics, previously neglected as sources of aerosol in global models, significantly contribute to predicted SOA burdens downwind of polluted areas (owing to benzene and toluene) and in the free troposphere (owing to isoprene)

Profiling tropospheric CO_2 using Aura TES and TCCON instruments

Monitoring the global distribution and long-term variations of CO_2 sources and sinks is required for characterizing the global carbon budget. Total column measurements are useful for estimating regional-scale fluxes; however, model transport remains a significant error source, particularly for quantifying local sources and sinks. To improve the capability of estimating regional fluxes, we estimate lower tropospheric CO_2 concentrations from ground-based near-infrared (NIR) measurements with space-based thermal infrared (TIR) measurements. The NIR measurements are obtained from the Total Carbon Column Observing Network (TCCON) of solar measurements, which provide an estimate of the total CO_2 column amount. Estimates of tropospheric CO_2 that are co-located with TCCON are obtained by assimilating Tropospheric Emission Spectrometer (TES) free tropospheric CO_2 estimates into the GEOS-Chem model. We find that quantifying lower tropospheric CO_2 by subtracting free tropospheric CO_2 estimates from total column estimates is a linear problem, because the calculated random uncertainties in total column and lower tropospheric estimates are consistent with actual uncertainties as compared to aircraft data. For the total column estimates, the random uncertainty is about 0.55 ppm with a bias of −5.66 ppm, consistent with previously published results. After accounting for the total column bias, the bias in the lower tropospheric CO_2 estimates is 0.26 ppm with a precision (one standard deviation) of 1.02 ppm. This precision is sufficient for capturing the winter to summer variability of approximately 12 ppm in the lower troposphere; double the variability of the total column. This work shows that a combination of NIR and TIR measurements can profile CO_2 with the precision and accuracy needed to quantify lower tropospheric CO_2 variability

Construction of non-diagonal background error covariance matrices for global chemical data assimilation,

Abstract. Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about 5 their correlations. As models evolve toward finer resolutions, the use of diagonal background covariance matrices is increasingly inaccurate, as they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing non-diagonal background error covariance matrices which account for the spatial correlations of errors. The correlation length scales are specified by the user; a correct choice of correlation lengths is important for a good performance of 10 the data assimilation system. The benefits of using the non-diagonal covariance matrices for variational data assimilation with chemical transport models are illustrated

Construction of non-diagonal background error covariance matrices for global chemical data assimilation,

Abstract. Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about their correlations. As models evolve toward finer resolutions, the use of diagonal background covariance matrices is increasingly inaccurate, as they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing nondiagonal background error covariance matrices which account for the spatial correlations of errors. The correlation length scales are specified by the user; a correct choice of correlation lengths is important for a good performance of the data assimilation system. The benefits of using the nondiagonal covariance matrices for variational data assimilation with chemical transport models are illustrated

Adjoint of the global Eulerian-Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com), with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e−14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated into a variational inversion system designed to optimize surface fluxes of greenhouse gases