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. 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

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

Emission rate and chemical state estimation by 4-dimensional variational inversion

This study aims to assess the potential and limits of an advanced inversion method to estimate pollutant precursor sources mainly from observations. Ozone, sulphur dioxide, and partly nitrogen oxides observations are taken to infer source strength estimates. As methodology, the four-dimensional variational data assimilation technique has been generalised and employed to include emission rate optimisation, in addition to chemical state estimates as usual objective of data assimilation. To this end, the optimisation space of the variational assimilation system has been complemented by emission rate correction factors of 19 emitted species at each emitting grid point, involving the University of Cologne mesoscale EURAD model. For validation, predictive skills were assessed for an August 1997 ozone episode, comparing forecast performances of pure initial value optimisation, pure emission rate optimisation, and joint emission rate/initial value optimisation. <br><br> Validation procedures rest on both measurements withheld from data assimilation and prediction skill evaluation of forecasts after the inversion procedures. Results show that excellent improvements can be claimed for sulphur dioxide forecasts, after emission rate optimisation. Significant improvements can be claimed for ozone forecasts after initial value and joint emission rate/initial value optimisation of precursor constituents. The additional benefits applying joint emission rate/initial value optimisation are moderate, and very useful in typical cases, where upwind emission rate optimisation is essential. In consequence of the coarse horizontal model grid resolution of 54 km, applied in this study, comparisons indicate that the inversion improvements can rest on assimilating ozone observations only, as the inclusion of NO<sub>x</sub> observations does not provide additional forecast skill. Emission estimates were found to be largely independent from initial guesses from emission inventories, demonstrating the potential of the 4D-var method to infer emission rate improvements. The study also points to the need for improved horizontal model resolution to more efficient use of NO<sub>x</sub> observations

Tropospheric Chemical State Estimation by Four-Dimensional Variational Data Assimilation on Nested Grids

The University of Cologne chemistry transport model EURAD and its four-dimensional variational data assimilation implementation is applied to a suite of measurement campaigns for analysing optimal chemical state evolution and flux estimates by inversion. In BERLIOZ and VERTIKO, interest is placed on atmospheric boundary layer processes, while for CONTRACE and SPURT upper troposphere and tropopause height levels are focussed. In order to achieve a high analysis skill, some new key features needed to be developed and added to the model setup. The spatial spreading of introduced observational information can now be conducted by means of a generalised background error covariance matrix. It has been made available as a flexible operator, allowing for anisotropic and inhomogeneous correlations. To estimate surface fluxes with high precision, the facility of emission rate optimisation using scaling factors is extended by a tailored error covariance matrix. Additionally, using these covariance matrices, a suitable preconditioning of the optimisation problem is made available. Furthermore, a module of adjoint nesting was developed and implemented, which enables the system to operate from the regional down to the local scale. The data flow from mother to daughter grid permits to accomplish nested simulations with both optimised boundary and initial values and emission rates. This facilitates to analyse constituents with strong spatial gradients, which have not been amenable to inversion yet. Finally, an observation operator is implemented to get to assimilate heterogeneous sources of information like ground-based measurements, airplane measuring data, Lidar and tethered balloon soundings, as well as retrieval products of satellite observations. In general, quality control of the assimilation procedure is obtained by comparison with independent observations. The case study analyses show considerable improvement of the forecast quality both by the joint optimisation of initial values and emission rates and by the increase of the horizontal resolutions by means of nesting. Moreover, simulation results for the two airplane campaigns exhibit outstanding characteristics of the assimilation system also in the middle and upper troposphere region

Ensemble-based chemical data assimilation I: An idealized setting

Data assimilation is the process of integrating observational data and model predictions to obtain an optimal representation of the state of the atmosphere. As more chemical observations in the troposphere are becoming available, chemical data assimilation is expected to play an essential role in air quality forecasting, similar to the role it has in numerical weather prediction. Considerable progress has been made recently in the development of variational tools for chemical data assimilation. In this paper we assess the performance of the ensemble Kalman filter (EnKF). Results in an idealized setting show that EnKF is promising for chemical data assimilation

Efficiency and Sensitivity Analysis of Observation Networks for Atmospheric Inverse Modelling with Emissions

The controllability of advection-diffusion systems, subject to uncertain initial values and emission rates, is estimated, given sparse and error affected observations of prognostic state variables. In predictive geophysical model systems, like atmospheric chemistry simulations, different parameter families influence the temporal evolution of the system.This renders initial-value-only optimisation by traditional data assimilation methods as insufficient. In this paper, a quantitative assessment method on validation of measurement configurations to optimize initial values and emission rates, and how to balance them, is introduced. In this theoretical approach, Kalman filter and smoother and their ensemble based versions are combined with a singular value decomposition, to evaluate the potential improvement associated with specific observational network configurations. Further, with the same singular vector analysis for the efficiency of observations, their sensitivity to model control can be identified by determining the direction and strength of maximum perturbation in a finite-time interval.Comment: 30 pages, 10 figures, 5 table