References

ACP

Atmospheric Chemistry and Physics

ACP

Atmos. Chem. Phys.

1680-7324

Copernicus Publications

Göttingen, Germany

10.5194/acp-7-3749-2007

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

Elbern

¹ Strunk

¹ Schmidt

¹ ³ Talagrand

Rhenish Institute for Environmental Research at the University of Cologne, Köln, Germany

Laboratoire de Meteorologie Dynamique, Paris, France

now at: Max-Planck-Institute for Meteorology, Hamburg, Germany

19 07 2007

7 14 3749 3769

2007

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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. 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 NOx 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 NOx observations.

References 1

Anthes, R A., Hsie, E.-Y., and Kuo, Y.-H.: Description of the Penn State/NCAR Mesoscale Model Version 4 (MM4), Tech. Note NCAR/TN/282+STR, National Center of Atmospheric Research, Boulder, Colorado, 1987.

Bocquet, M.: Reconstruction of an atmospheric tracer source using the principle of maximum entropy. I: Theory, Q J Roy Meteor Soc., 131, 2191–2208, 2005a.

Bocquet, M.: Reconstruction of an atmospheric tracer source using the principle of maximum entropy. II: Applications, Q J Roy Meteor Soc., 131, 2209–2223, 2005b.

Bott, A.: A positive definit advection scheme obtained by nonlinear renormalization of the advective fluxes, Mon Wea Rev., 117, 1006–1015, 1989.

Bousquet, P., Ciais, P., Peylin, P., Ramonet, M., and Monfray, P.: Inverse modeling of annual CO2 sources and sinks, 1. Method and control inversion, J Geophys Res., 104, 26 161–26 178, 1999a.

Bousquet, P., Ciais, P., Peylin, P., Ramonet, M., and Monfray, P.: Inverse modeling of annual CO2 sources and sinks, 2. Sensitivity study, J Geophys Res., 104, 26 179–26 193, 1999b.

Briggs, G A.: Lectures on air pollutants and environmental impact analysis, chap. Plume rise predictions, Am Meteorol Soc., Boston, 59–111, 1975.

Chai, T F., Carmichael, G R., Sandu, A., Tang, Y H., and Daescu, D N.: Chemical data assimilation of Transport and Chemical Evolution over the Pacific (TRACE-P) aircraft measurements, J Geophys Res., 111, D02301, https://doi.org/10.1029?2005JD005883, 2006.

Chang, J S., Brost, R A., Isaksen, I S A., Madronich, S., Middleton, P., Stockwell, W R., and Walcek, C J.: A three-dimensional Eulerian acid deposition model: physical concepts and formulation, J Geophys Res., 92, 618–700, 1987.

Chao, W C. and Chang, L P.: Development of a four-dimensional variational analysis system using the adjoint method at GLA Part I: Dynamics, Mon Wea Rev., 120, 1661–1673, 1992.

Courtier, P.: Dual formulation of four-dimensional variational assimilation, Q J Roy Meteor Soc., 123, 2449–2461, 1997.

Courtier, P., Thépaut, J N., and Hollingsworth, A.: A strategy for operational implementation of 4D-Var, using an incremental approach, Q J Roy Meteor Soc., 120, 1367–1387, 1994.

Daley, R.: Atmospheric Data Analysis, Cambridge~Univ Press, 1991.

Elbern, H. and Schmidt, H.: A four–dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling, J Geophys Res., 104, 18 583–18 598, 1999.

Elbern, H. and Schmidt, H.: Ozone Episode Analysis by Four-Dimensional Variational Chemistry Data Assimilation, J Geophys Res., 106(D4), 3569–3590, 2001.

Elbern, H. and Schmidt, H.: Chemical 4D variational data assimilation and its numerical implications for case study analyses, in: IMA volumes in Mathematics and its Applications, Atmospheric Modeling, edited by: Chock, D P. and Carmichael, G R., 130, 165–184, 2002.

Elbern, H., Schmidt, H., and Ebel, A.: Variational data assimilation for tropospheric chemistry modeling, J Geophys Res., 102, 15 967–15 985, 1997.

Elbern, H., Schmidt, H., Talagrand, O., and Ebel, A.: 4D-variational data assimilation with an adjoint air quality model for emission analysis, Environ Model. Software, 15, 539–548, 2000.

Elbern, H., Baier, F., Bittner, M., Bochorishvili, R., Bovensmann, H., Hoffmann, L., Joppich, W., Meyer, J., Riese, M., Schwinger, J., Stiller, G., and von Clarmann, T.: SACADA, a new chemical data assimilation system for earth observation, in: Results of the German atmospheric research programme AFO2000, final publication, 210–216, GSF, 2005.

Elbern, H. and A. Strunk, Chemical Data Assimilation for Air Quality Forecasting, Proceedings of the ECMWF seminar on Earth observation, 285–296, http://www.ecmwf.int/publications/library/do/references/show?id=86890, 2006.

Engelen, R., Andersson, E., Chevallier, F., Hollingsworth, A., Matricardi, M., McNally, A P., Thépaut, J N., and Watts, P D.: Estimating atmospheric CO2 from advanced infrared satellite radiances within an operational 4D-Var data assimilation system: Methodology and first results, J Geophys Res., 109, D19309, https://doi.org/10.1029/2004JD004777, 2004.

Enting, I G. and Newsam, G N.: Inverse problems in atmospheric constituent studies: II. Sources in the free atmosphere, Inverse~Problems, 6, 349–362, 1990.

Enting, I G., Trudinger, C M., and Francey, R J.: A synthesis inversion of the concentration and d13C of atmospheric CO2, Tellus, 47B, 35–52, 1995.

Errera, Q. and Fonteyn, D.: Four-dimensional variational chemical assimilation of CRISTA stratospheric measurements, J Geophys Res., 106, 12 253–12 265, 2001.

Eskes, H J., Piters, A J M., Levelt, P F., Allart, M A F., and Kelder, H M.: Variational assimilation of total-column ozone satellite data in a 2D lat-lon tracer-transport model, J Atmos Sci., 56, 3560–3572, 1999.

Fan, S M., Gloor, M., Mahlman, J., Pacala, S., Sarmiento, J., Takahashi, T., and Tans, P.: A large terrestrial carbon sink in North America implied by atmospheric data and oceanic carbon dioxide data and models, Science, 282, 442–446, 1998.

Faure, C. and Papegay, Y.: Odyssée Version 1.7 Users Guide, Technical Report 0224, Institut National de Recherche en Informatique et en Automatique, manual adjoint compiler, 1998.

Fedorov, V.: Kriging and other estimators of spatial field characteristics (with special reference to environmental studies), Atmos Environ., 23, 174–184, 1998.

Fisher, M. and Lary, D.: Lagrangian four-dimensional variational data assimilation of chemical species, Q J Roy Meteor Soc., 121, 1681–1704, 1995.

Giering, R. and Kaminski, T.: Recipes for Adjoint Code Construction, ACM~Trans Mathematical~Software, 24, 437–474, adjoint code, 1998.

Gloor, M., Fan, S M., Pacala, S., Sarmiento, J., and Ramonet, M.: A model-based evaluation of inversions of atmospheric transport, using annual mean mixing ratios, as a tool to monitor fluxes of nonreactive trace substances like CO2 on a continental scale, J Geophys Res., 104, 14 245–14 260, 1999.

Grell, G A., Dudhia, J., and Stauffer, D R.: A description of the fifth generation Penn State/NCAR mesoscale model (MM5); NCAR TN-398+IA, Tech. rep., National Center for Atmospheric Research, Boulder, Colorado, 1993.

Gurney, K R.: Towards robust regional estimates of CO2 sources and sinks using atmospheric transport models, Nature, 415, 626–630, 2002.

Hanea, R G., Velders, G J M., and Heemink, A.: Data assimilation of ground-level ozone in Europe with a Kalman filter and chemistry transport, J Geophys Res., 109, D10302, https://doi.org/10.1029/2003JD004283, 2004.

Hanna, S R., Chang, J C., and Fernau, M E.: Monte Carlo estimates of uncertainties in predictions by a photochemical grid model (UAM-IV) due to uncertainties in input variables, Atmos Environ., 32, 3619–3628, 1998.

Hanna, S R., Lu, Z G., Frey, H C., Wheeler, N., Vukovich, J., Arunachalam, S., Fernau, M., and Hansen, D A.: Uncertainties in predicted ozone concentrations due to input uncertainties for the UAM-V photochemical grid model applied to the July1995 OTAG domain, Atmos Environ., 35, 891–903, 2001.

Hass, H., Jakobs, H J., and Memmesheimer, M.: Analysis of a regional model (EURAD) near surface gas concentration predictions using observations from networks, Met Atmos Phys., 57, 173–200, 1995.

Hesstvedt, E., Hov, Ø., and Isaksen, I S A.: Quasi-steady state approximation in air pollution modeling: Comparison of two numerical schemes for oxidant prediction, Int J Chem Kinet., 10, 971–994, 1978.

Hölzemann, J., Elbern, H., and Ebel, A.: PSAS and 4D-var data assimilation for chemical state analysis by urban and rural observation sites, Phys Chem Earth, 26, 807–812, 2001.

Hourdin, F. and Talagrand, O.: Eulerian backtracking of atmospheric tracers. I: Adjoint derivation and parametrization of subgrid-scale transport, Q. J. Roy. Meteor. Soc., 132, 567-583, https://doi.org/10.1256/qj.03.198.A., 2006.

Hourdin, F., O. Talagrand and A. Idelkadi, 2006, Eulerian backtracking of atmospheric tracers. II: Numerical aspects, Q. J. Roy. Meteor. Soc., 132, 585-603, https://doi.org/10.1256/qj.03.198.B., 2006.

Houweling, S., Kaminski, T., Dentener, F., Lelieveld, J., and Heimann, M.: Inverse modeling of methane sources and sinks using the adjoint of a global transport model, J Geophys Res., 104, 26 137–26 160, 1999.

Ide, K., Courtier, P., Ghil, M., and Lorenc, A C.: Unified notation for data assimilation: operational, sequential and variational, J Meteorol Soc Japan, 75, 181–189, 1997.

Issartel, J P.: Rebuilding sources of linear tracers after atmospheric concentration measurements, Atmos. Chem. Phys., 3, 2111–2125, 2003.

Jakobs, H J., Feldmann, H., Hass, H., and Memmesheimer, M.: The Use of Nested Models for Air Pollution Studies: An Application of the EURAD Model to a SANA Episode, J Appl Meteorol., 34, 1301–1319, 1995.

Kaminski, T., Heimann, M., and Giering, R.: A coarse grid three-dimensional global inverse model of the atmospheric transport: 1. Adjoint model and Jacobian matrix, J Geophys Res., 104, 18 535–18 553, 1999a.

Kaminski, T., Heimann, M., and Giering, R.: A coarse grid three-dimensional global inverse model of the atmospheric transport: 2. Inversion of the transport of CO2 in the 1980s, J Geophys Res., 104, 18 555–18 581, 1999b.

Kaminski, T., Knorr, W., Rayner, P J., and Heimann, M.: Assimilating atmospheric data into a terrestrial biosphere model: A case study of the seasonal cycle, Global~Biogeochem Cy., 16, 1066, https://doi.org/10.1029/2001GB001463, 2002.

Kinosian, J R.: Ozone-precursor relationships from EKMA diagrams, Environ Sci Technol., 16, 880–883, 1982.

Lahoz, W.A., A. J. Geer, S. Bekki, N. Bormann, S. Ceccherini, H. Elbern, Q. Errera, H. J. Eskes, D. Fonteyn, D. R. Jackson, B. Khattatov, S. Massart, V.-H. Peuch, S. Rharmili, M. Ridolfi, A. Segers, O. Talagrand, H. E. Thornton, A. F. Vik, von Clarmann, T.: The Assimilation of Envisat data (ASSET) project, Atmos. Chem. Phys., 7, 1773–1796, 2007.

Liu, D C. and Nocedal, J.: On the limited memory BFGS method for large scale optimization, Math Programming, 45, 503–528, 1989.

Lorenc, A C.: Analysis methods for numerical weather prediction, Q J Roy Meteor Soc., 112, 1177–1194, 1986.

Lorenc, A C.: Optimal nonlinear objective analysis, Q J Roy Meteor Soc., 114, 205–240, 1988.

Madronich, S.: Photodissociation in the atmosphere. 1. actinic flux and the effects of ground reflections and clouds, J Geophys Res., 92, 9740–9752, 1987.

McRae, G J., Goodin, W R., and Seinfeld, J H.: Numerical solution of the atmospheric diffusion equation for chemically reacting flows, J Comp Phys., 45, 1–42, 1982.

Memmesheimer, M., Hass, H., Tippke, J., and Ebel, A.: Regional Photochemical Measurement and Modeling Studies, vol 2, chap. Modeling of episodic emission data for Europe with the EURAD Emission Model (EEM), pp. 495–499, Air & Waste Management Association, Pittsburgh, USA, 1995.

Ménard, R., Cohn, S E., Chang, L.-P., and Lyster, P M.: Assimilation of Stratospheric Chemical Tracer Observations Using a Kalman Filter, Part I: Formulation, Mon Wea Rev., 128, 2654–2671, 2000.

Mohnen, V.: Data Quality Assessment – an overview for the TRACT 16./17. September 1992 field intensive, Report to the coordinator of TFS-LT1, IFU Garmisch-Partenkirchen, error estimation, data quality, 1999.

Muller, J F. and Stavrakou, T.: Inversion of CO and NOx emissions using the adjoint of the IMAGES model, Atmos. Chem. Phys., 5, 1157–1186, 2005.

Navon, I M.: Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dyn Atmos Oceans, 27, 55–79, 1997.

Newsam, G N. and Enting, I G.: Inverse problems in atmospheric constituent studies: I. Determination of surface sources under a diffusive transport approximation, Inverse~Problems, 4, 1037–1054, 1988.

Nocedal, J.: Updating Quasi-Newton Matrices With Limited Storage, Math Comput., 35, 773–782, 1980.

Quélo, D., Mallet, V., and Sportisse, B.: Inverse Modeling of NOx Emissions at Regional Scale over Northern France. Preliminary Investigation of the Second-Order Sensitivity, J Geophys Res., 110, D24310, https://doi.org/10.1029/2005JD006151, 2005.

Robertson, L. and Langner, J.: Source function estimate by means of variational data assimilation applied to the ETEX-I tracer experiment, Atmos Environ., 32, 4219–4225, 1992.

Rostaing, N., Dalmas, S., and Galligo, A.: Automatic differentiation in Odyssee, Tellus, 1993.

Schmidt, H. and Martin, D.: Adjoint sensitivity of episodic ozone in the Paris area to emissions on the continental scale, J Geophys Res., 108, 8561, https://doi.org/10.1029/2001JD00158, 2003.

Stajner, I., Riish\ojgaard, L P., and Rood, R B.: The GEOS ozone data assimilation system: Specification of error statistics, Q J Roy Meteor Soc., 127, 1069–1094, 2001.

Stockwell, W R., Middleton, P., and Chang, J S.: The second generation regional acid deposition model chemical mechanism for regional air quality modeling, J Geophys Res., 95, 16 343–16 367, 1990.

Struthers, H., Brugge, R., Lahoz, W A., O'Neill, A., and Swinbank, R.: Assimilation of Ozone Profiles and Total Column Measurements into a General Circulation Model, J Geophys Res., 107, 4438, https://doi.org/10.1029/2001JD000957, 2002.

Talagrand, O.: A posteriori evaluation and verification of analysis and assimilation algorithms, in: Proceedings of the Workshop on Diagnosis of Data Assimilation Systems, European Centre for Medium-range Weather Forecasts Reading, England, 2–4 November, 1998.

Talagrand, O.: Objective Validation and Evaluation of Data Assimilation, in: Proceedings of the Seminar on Recent developments in data assimilation for atmosphere and ocean, ECMWF, European Centre for Medium-range Weather Forecasts, 2004.

Talagrand, O. and Courtier, P.: Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory, Q J Roy Meteor Soc., 113, 1311–1328, 1987.

van Loon, M., Builtjes, P J H., and Segers, A J.: Data assimilation of ozone in the atmospheric transport chemistry model LOTOS, Environ Model. Software, 15, 603–609, 2000.

Verlaan, M. and Heemink, A W.: Reduced rank square root filters for large scale data assimilation problems, in: Second International Symposium on Assimilation of Observations in Meteorology and Oceanography, 1995.

Weaver, A. and Courtier, P.: Correlation Modelling on the Sphere Using a Generalized Diffusion Equation, Q J Roy Meteor Soc., 127, 1815–1846, data assimilation covariance matrix, 2001.

Wesely, M L.: Parameterization of surface resistances to gaseous dry deposition in regional-scale numerical models, Atmos Environ., 23, 1293–1304, 1989.

Yanenko, N N.: The method of fractional steps: solution of problems of mathematical physics in several variables, Springer, 1971.