Biogeosciences www.biogeosciences.net 1726-4170 1726-4189 6 6 2009 10.5194/bg-6-1089-2009 http://www.biogeosciences.net/6/1089/2009/ http://www.biogeosciences.net/6/1089/2009/bg-6-1089-2009.html http://www.biogeosciences.net/6/1089/2009/bg-6-1089-2009.pdf 1089 1102 2009-06-19 Structure of the transport uncertainty in mesoscale inversions of CO₂ sources and sinks using ensemble model simulations T. Lauvaux thomas.lauvaux@lsce.ipsl.fr O. Pannekoucke C. Sarrat F. Chevallier P. Ciais J. Noilhan P. J. Rayner Laboratoire des Sciences du Climat et de l'Environnement/IPSL,CEA-CNRS-UVSQ, Gif-sur-Yvette, France Centre Nationale des recherches Météorologiques, Toulouse, France We study the characteristics of a statistical ensemble of mesoscale simulations in order to estimate the model error in the simulation of CO₂ concentrations. The ensemble consists of ten members and the reference simulation using the operationnal short range forecast PEARP, perturbed using the Singular Vector technique. We then used this ensemble of simulations as the initial and boundary conditions for the meso scale model (Méso-NH) simulations, which uses CO₂ fluxes from the ISBA-A-gs land surface model. The final ensemble represents the model dependence to the boundary conditions, conserving the physical properties of the dynamical schemes, but excluding the intrinsic error of the model. <br></br> First, the variance of our ensemble is estimated over the domain, with associated spatial and temporal correlations. Second, we extract the signal from noisy horizontal correlations, due to the limited size ensemble, using diffusion equation modelling. The computational cost of such ensemble limits the number of members (simulations) especially when running online the carbon flux and the atmospheric models. In the theory, 50 to 100 members would be required to explore the overall sensitivity of the ensemble. The present diffusion model allows us to extract a significant part of the noisy error, and makes this study feasable with a limited number of simulations. Finally, we compute the diagonal and non-diagonal terms of the observation error covariance matrix and introduced it into our CO₂ flux matrix inversion for 18 days of the 2005 intensive campaign CERES over the South West of France. Variances are based on model-data mismatch to ensure we treat model bias as well as ensemble dispersion, whereas spatial and temporal covariances are estimated with our method. <br></br> The horizontal structure of the ensemble variance manifests the discontinuities of the mesoscale structures during the day, but remains locally driven during the night. On the vertical, surface layer variance shows large correlations with the upper levels in the boundary layer (> 0.6), dropping to 0.4 with the lower levels of the free troposphere. Large temporal correlations were found during the afternoon (> 0.5 for several hours), reduced during the night. The diffusion equation model extracted relevant error covariance signals horizontally, with reduced correlations over mountain areas and during the night over the continent. The posterior error reduction on the inverted CO₂ fluxes accounting for the model error correlations illustrates the predominance of the temporal over the spatial correlations when using tower-based CO₂ concentration observations. Annan, J D., Lunt, D J., Hargreaves, J C., and Valdes, P J.: Parameter estimation in an atmospheric GCM using the Ensemble Kalman Filter, Nonlinear Proc. Geoph., 12(3), 363–371, 2005. Baker, D F., Law, R M., Gurney, K R., Rayner, P., Peylin, P., Denning, A S., Bousquet, P., Bruhwiler, L., Chen, Y.-H., Ciais, P., Fung, I Y., Heimann, M., John, J., Maki, T., Maksyutov, S., Masarie, K., Prather, M., Pak, B., Taguchi, S., and Zhu, Z.: TransCom 3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO2 fluxes, 1988–2003, Global Biogeochem. Cy., 20, GB1002, doi:10.1029/2004GB002 439, 2007. P J. Berre, L., Pannekoucke, O., Desroziers, G., Stefanescu, S E., Chapnik, B., and Raynaud, L.: A variational assimilation ensemble and the spatial filtering of its error covariances: increase of sample size by local spatial averaging. Proceedings of the ECMWF Workshop on Flow-dependent aspects of data assimilation, 11–13~June 2007, Reading, UK, 151–168, 2007. Bousquet, P., Ciais, P., Miller, J B., Dlugokencky, E J., Hauglustaine, D A., Prigent, C., Van der Werf, G R., Peylin, P., Brunke, E.-G., Carouge, C., Langenfelds, R L., LathiÃre, J., Papa, F., Ramonet, M., Schmidt, M., Steele, L P., Tyler, S C., and White, J.: Contribution of anthropogenic and natural sources to atmospheric methane variability, Nature, 443, 439–443, doi:10.1038/nature05132, 2006. Calvet, J C., Noilhan, J., Roujean, J L., Bessemoulin, P., Cabelguenne, M., Olioso, A., and Wigneron, J P.: An interactive vegetation svat model tested against data from six contrasting sites, Agr. Forest Meteorol., 92, 73–95, 1998. Carvalho, A C., Menut, L., Vautard, R., and Nicolau, J.: Air Quality Ensemble Forecast Coupling ARPEGE and CHIMERE over Western Europe, Air Pollution Modeling and its Application XIX, NATO Science for Peace and Security Series, ISBN:978-1-4020-8452-2, 736~pp. 2008. Chevallier, F., Viovy, N., Reichstein, M., and Ciais, P.: On the assignment of prior errors in Bayesian inversions of \chemCO_2 surface fluxes, Geophys. Res. Lett., 33, L13 802, doi:10.1029/2006GL026496, 2006. Courtier, P., Freydier, C., Geleyn, J F., Rabier, F., and Rochas, M.: The Arpege project at Météo-France, Proc. ECMWF Workshop on Numerical Methods in Atmospheric Modelling, 9–13~Sept 1991, 2, 193–231, 1991. Corbin, K D. and Denning, A S.: Using continuous data to estimate clear-sky errors in inversions of satellite CO2 measurements, Geophys. Res. Lett., 33, L12810, doi:10.1029/2006GL025910, 2006. Corbin, K D., Denning, A S., Lu, L., Wang, J W., and Baker, I T.: Possible representation errors in inversions of satellite CO₂ retrievals, J. Geophys. Res., 113, D02301, doi:10.1029/2007JD008716, 2008. Crisp, D., Atlas, R M., Breon, F M., Brown, L R., Burrows, J P., Ciais, P., Connor, B J., Doney, S C., Fung, I Y., Jacob, D J., Miller, C E., O'Brien, D., Pawson, S., Randerson, J T., Rayner, P J., Salawitch, R J., Sander, S P., Sen, B., Stephens, G L., Tans, P P., Toon, G C., Wennberg, P O., Wofsy, S C., Yung, Y L., Kuang, Z., Chudasama, B., Sprague, G., Weiss, B., Pollock, R., Kenyon, D., and Schroll, S.: The Orbiting Carbon Observatory (OCO) mission, Adv. Space Res., 34, 700–709, 2004. Daley, R.: Atmospheric data analysis, edited by: Houghton, J. T., Rycroft, M. J., and Dessler, A. J., Cambridge Univ. Press, New York, USA, 472~pp., 1991. Dolman, A J., Noilhan, J., Durand, P., Sarrat, C., Brut, A., Piguet, B., Butet, A., Jarosz, N., Brunet, Y., Loustau, D., Lamaud, E., Tolk, L., Miglietta, R. R F., Gioli, B., Magliulo, V., Esposito, M., Gerbig, C., Körner, S., Galdemard, P., Ramonet, M., Ciais, P., Neininger, B., Hutjes, R. W A., Macatangay, J. A. E R., Schrems, O., Pérez-Landa, G., Sanz, M J., Scholz, Y., Facon, G., Ceschia, E., and Beziat, P.: CERES, the CarboEurope Regional Experiment Strategy in Les Landes, South West France, May–June 2005, Bull. Am. Meteorol. Soc., 87(10), 1367–1379, doi:10.1175/BAMS–87–10–1367, 2006. Enting, I G.: Inverse Problems in Atmospheric Constituent Transport, edited by: Houghton, J. T., Rycroft, M. J., and Dessler, A. J., Cambridge University Press, Cambridge, UK, 412~pp., 2002. Filippi, D., Ramonet, M., Ciais, P., Picard, D., Roulley, J.-C L., Schmidt, M., and Nedelec, P.: Greenhouse airborne measurements over Europe, Geophysical Research Abstracts, 5, 14226~pp., 2003. Fisher, M. and Courtier, P.: Estimating the covariance matrices of analysis and forecast error in variational data assimilation, Technical Memo 220, ECMWF, Reading, UK, 1995. Fischer, A. M., Schraner, M., Rozanov, E., Kenzelmann, P., Schnadt Poberaj, C., Brunner, D., Lustenberger, A., Luo, B. P., Bodeker, G. E., Egorova, T., Schmutz, W., Peter, T., and Brönnimann, S.: Interannual-to-decadal variability of the stratosphere during the 20th century: ensemble simulations with a chemistry-climate model, Atmos. Chem. Phys. Discuss., 8, 14371–14418, 2008. Geels, C., Gloor, M., Ciais, P., Bousquet, P., Peylin, P., Vermeulen, A. T., Dargaville, R., Aalto, T., Brandt, J., Christensen, J. H., Frohn, L. M., Haszpra, L., Karstens, U., Rödenbeck, C., Ramonet, M., Carboni, G., and Santaguida, R.: Comparing atmospheric transport models for future regional inversions over Europe - Part 1: mapping the atmospheric CO₂ signals, Atmos. Chem. Phys., 7, 3461–3479, 2007. Gerbig, C., Lin, J C., Wofsy, S C., Daube, B C., Andrews, A E., Stephens, B B., Bakwin, P S., and Grainger, C A.: Toward constraining regional-scale fluxes of \chemCO_2 with atmospheric observations over a continent: 1 Observed spatial variability from airborne platforms, J. Geophys. Res., 108(D24), 4756, doi:10.1029/2002JD003018, 2003. Gerbig, C., Körner, S., and Lin, J. C.: Vertical mixing in atmospheric tracer transport models: error characterization and propagation, Atmos. Chem. Phys., 8, 591–602, 2008. Gloor, M., Fan, S M., Pacala, S., and Sarmiento, J.: Optimal sampling of the atmosphere for purpose of inverse modeling: A model study, Global Biogeochem Cy., 14, 407–428, 2000. Gurney, K R., Law, R M., Denning, A S., Rayner, P J., Baker, D., Bousquet, P., Bruhwiler, L., Chen, Y.-H., Ciais, P., Fan, S., Fung, I Y., Gloor, M., Heimann, M., Higuchi, K., John, J., Maki, T., Maksyutov, S., Masarie, K., Peylin, P., Prather, M., Pak, B C., Randerson, J., Sarmiento, J., Taguchi, S., Takahashi, T., and Yuen, C.-W.: Towards robust regional estimates of CO₂ sources and sinks using atmospheric transport models, Nature, 415, 626–630, 2002. Hamazaki, T., Kaneko, Y., and Kuze, A.: Carbon dioxide monitoring from the gosat satellite, Geo-Imagery Bridging Continents, Proceedings of Commission VII, XXth ISPRS Congress, 12-23 July 2004, Istanbul, Turkey, 225~pp., 2004. Kaminski, T., Rayner, P J., Heimann, M., and Enting, I G.: On Aggregation Errors in Atmospheric Transport Inversions, J. Geophys. Res., 106, 4703–4715, 2001. Kaminski, T. and Rayner, P J.: Assimilation and network design, in: Observing the continental scale Greenhouse Gas Balance of Europe, edited by: H. Dolman, A. Freibauer, and R. Valentini, Ecological Studies, Springer-Verlag, New York, chapter 3, pages 33–52, 2008. Krinner, G., Viovy, N., de~Noblet-Ducoudré, N., Ogee, J., Polcher, J., Friedlingstein, P., Ciais, P., Sitch, S., and Prentice, I C.: A dynamic global vegetation model for studies of the coupled atmosphere-biosphere system, Global Biogeochem. Cy., 19, GB1015, doi:10.1029/2003GB002 199, 2005. Lafore, J., Stein, J., Bougeault, P., Ducrocq, V., Duron, J., Fischer, C., Hereil, P., Mascart, P., Masson, V., Pinty, J P., Redelsperger, J., Richard, E., and de~Arellano, J V.: The Meso-NH atmospheric simulation system, Part I: adiabatic formulation and control simulations, Ann. Geophys., 16, 90–109, 1998. Lauvaux, T., Uliasz, M., Sarrat, C., Chevallier, F., Bousquet, P., Lac, C., Davis, K. J., Ciais, P., Denning, A. S., and Rayner, P. J.: Mesoscale inversion: first results from the CERES campaign with synthetic data, Atmos. Chem. Phys., 8, 3459–3471, 2008. Law, R M., Rayner, P J., Steele, L P., and Enting, I G.: Data and modelling requirements for CO₂ inversions using high frequency data, 55B, 2, 512–521, doi:10.1034/j.1600-0560.2003.0029.x, 2003. Law, R. M., Peters, W., Rodenbeck, C., Aulagnier, C., Baker, I., Bergmann, D J., Bousquet, P., Brandt, J., Bruhwiler, L., Cameron-Smith, P J., Christensen, J H., Delage, F., Denning, A S., Fan, S., Geels, C., Houweling, S., Imasu, R., Karstens, U., and Kawa, S R.: TransCom model simulations of hourly atmospheric CO₂: Experimental overview and diurnal cycle results for~2002, Global Biochem. Cy., 22, GB3009, doi:10.1029/2007GB003050, 2008. Lorenc, A.: The potential of ensemble Kalman filter for NWP - a comparison with 4-D-Var, Q. J. R. Meteorol. Soc., 129, 3183–3203, 2003. Lorenz, E N.: Atmospheric predictability with a large numerical model, Tellus, 34, 505–513, 1982. Pannekoucke, O., Berre, L., and Desroziers, L.: Filtering properties of wavelets for the local background error correlations, Q. J. Roy. Meteor. Soc., 133, 363–379, 2007. Pannekoucke, O., Berre, L., and Desroziers, L.: Background error correlation length-scale estimates and their sampling statistics, Q. J. Roy. Meteor. Soc., 134, 497–508, 2008. Pannekoucke, O. and Massart, S.: Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation, Q. J. R. Meteorol. Soc., 1–13, doi:10.1002/qj.000, 2008. Pérez-Landa, G., Ciais, P., Gangoiti, G., Palau, J. L., Carrara, A., Gioli, B., Miglietta, F., Schumacher, M., Millán, M. M., and Sanz, M. J.: Mesoscale circulations over complex terrain in the Valencia coastal region, Spain – Part 2: Modeling CO₂ transport using idealized surface fluxes, Atmos. Chem. Phys., 7, 1851–1868, 2007. Petron, G., Granier, C., Khattatov, B., Lamarque, J F., Yudin, V., Muller, J F., and Gille, J.: Inverse modeling of carbon monoxide surface emissions using Climate Monitoring and Diagnostics Laboratory network observations, J. Geophys. Res., 107, 4761, doi:10.1029/2001JD001305, 2002. Raupach, M R., Marland, G., Ciais, P., Le~Quere, C., Canadell, J G., Klepper, G., and Field, C B.: Global and regional drivers of accelerating CO2 emissions, PNAS, 104, 10 288–10 293, prefixhttp://www.pnas.org/cgi/content/abstract/104/24/10288, 2007. Rayner, P J. and O'Brien, D M.: The utility of remotely sensed CO₂ concentration data in surface source inversions, Geophys. Res. Let., 28, 175–178, 2001. Rayner, P J., Scholze, M., Knorr, W., Kaminski, T., Giering, R., and Widmann, H.: Two decades of terrestrial Carbon fluxes from a Carbon Cycle Data Assimilation System (CCDAS), Glob. Biogeochem. Cy., 19, GB2026, doi:10.1029/2004GB002254, 2005. Rayner, P J., Law, R M., Allison, C E., Francey, R J., Trudinger, C M., and Pickett-Heaps, C.: Interannual variability of the global carbon cycle (1992–2005) inferred by inversion of atmospheric CO2 and 13CO2 measurements, Glob. Biogeochem. Cy., 22, GB3008, doi:10.1029/2007GB003068, 2008. Rodgers, C D.: Inverse methods for atmospheric sounding: Theory and practice, World Scientific Publishing Co. Pte. Ltd. 2000. Sarrat, C., Noilhan, J., Lacarrère, P., Donier, S., Dolman, H., Gerbig, C., Ciais, P., and Butet, A.: Atmospheric \chemCO_2 modeling at the regional scale: Application to the CarboEurope Regional Experiment, J. Geophys. Res., 112, D12105, doi:10.1029/2006JD008107, 2007. Sarrat, C., Noilhan, J., Dolman, A. J., Gerbig, C., Ahmadov, R., Tolk, L. F., Meesters, A. G. C. A., Hutjes, R. W. A., Ter Maat, H. W., Pérez-Landa, G., and Donier, S.: Atmospheric CO₂ modeling at the regional scale: an intercomparison of 5 meso-scale atmospheric models, Biogeosciences Discuss., 4, 1923–1952, 2007. Sarrat, C., Noilhan, J., Lacarrère, P., Dolman, A. J., Gerbig, C., Elbers, J. A., Vellinga, O. S., Gioli, B., Miglietta, F., Neininger, B., Lauvaux, T., Ciais, P., Ramonet, M., Ceschia, E., and Bonnefond, J. M.: Mesoscale modeling of the CO2 interactions between the surface and the atmosphere applied to the April~2007 CERES field experiment, Biogeosciences Discuss., 6, 515–544, 2009. Stephens, B B., Wofsy, S C., Keeling, R F., Tans, P., and Potosnak, M J.: The \chemCO_2 Budget and Rectification Airborne Study: Strategies for measuring rectifiers and regional fluxes, Inverse Methods in Global Biogeochemical Cycles, Geophysical Monograph, 114, AGU, 2000. Stephens, B B., Gurney, K R., Tans, P P., Sweeney, C., Peters, W., Bruhwiler, L., Ciais, P., Ramonet, M., Bousquet, P., Nakazawa, T., Aoki, S., Machida, T., Inoue, G., Vinnichenko, N., Lloyd, J., Jordan, A., Heimann, M., Shibistova, O., Langenfelds, R L., Steele, L P., Francey, R J., Denning, A S.: Weak northern and strong tropical land carbon uptake from vertical profiles of atmospheric CO2, Science, 316, 1732–1735, 2007. Takahashi, T., Feely, R. A., Weiss, R. F., Wanninkhof, R. H., Chipman, D. W., Southerland, S. C., and Takahashi, T. T.: Global air-sea flux of CO₂: An estimate based on measurements of sea-air $p$CO₂-difference, P. Natl. Acad. Sci. USA, 94, 8292–8299, 1997. Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, ISBN 0-89871-572-5, 342~pp., 2005. Talagrand, O., Vautard, R., and Strauss, B.: Evaluation of probabilistic prediction systems, Proceedings of the ECMWF Workshop on Predictability, 20–22 October 1997, ECMWF, Shinfield Park Reading, UK. 157-166, 1997. Uliasz, M.: Lagrangian particle modeling in mesoscale applications, in: Environmental Modelling II, edited by: Zanetti, P., Comput. Mech. Publ., 71–102, 1994. Weaver, A. and Courtier, P.: Correlation modelling on the sphere using a generalized diffusion equation, Q. J. Roy. Meteor. Soc., 127, 1815–1846, 2001.