ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-11-9631-2011 Using boundary layer equilibrium to reduce uncertainties in transport models and CO<sub>2</sub> flux inversions Williams I. N. 1 Riley W. J. 2 Torn M. S. 2 Berry J. A. 3 Biraud S. C. 2 Department of Geophysical Sciences, University of Chicago, Chicago, IL, USA Lawrence Berkeley National Laboratory, Earth Sciences Division, Berkeley, CA, USA Carnegie Institution of Washington, Stanford, CA, USA 16 09 2011 11 18 9631 9641 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/11/9631/2011/acp-11-9631-2011.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/11/9631/2011/acp-11-9631-2011.pdf

This paper reexamines evidence for systematic errors in atmospheric transport models, in terms of the diagnostics used to infer vertical mixing rates from models and observations. Different diagnostics support different conclusions about transport model errors that could imply either stronger or weaker northern terrestrial carbon sinks. Conventional mixing diagnostics are compared to analyzed vertical mixing rates using data from the US Southern Great Plains Atmospheric Radiation Measurement Climate Research Facility, the CarbonTracker data assimilation system based on Transport Model version 5 (TM5), and atmospheric reanalyses. The results demonstrate that diagnostics based on boundary layer depth and vertical concentration gradients do not always indicate the vertical mixing strength. Vertical mixing rates are anti-correlated with boundary layer depth at some sites, diminishing in summer when the boundary layer is deepest. Boundary layer equilibrium concepts predict an inverse proportionality between CO<sub>2</sub> vertical gradients and vertical mixing strength, such that previously reported discrepancies between observations and models most likely reflect overestimated as opposed to underestimated vertical mixing. However, errors in seasonal concentration gradients can also result from errors in modeled surface fluxes. This study proposes using the timescale for approach to boundary layer equilibrium to diagnose vertical mixing independently of seasonal surface fluxes, with applications to observations and model simulations of CO<sub>2</sub> or other conserved boundary layer tracers with surface sources and sinks. Results indicate that frequently cited discrepancies between observations and inverse estimates do not provide sufficient proof of systematic errors in atmospheric transport models. Some previously hypothesized transport model biases, if found and corrected, could cause inverse estimates to further diverge from carbon inventory estimates of terrestrial sinks.

 References 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 CO<sub>2</sub> fluxes, 1988-2003, Global Biogeochem. Cy., 20, GB1002, doi:10.1029/2004GB002439, 2006. Bakwin, P S., Tans, P P., Zhao, C L., Ussler, W., and Quesnell, E.: Measurements of carbon-dioxide on a very tall tower, Tellus B – Chem. Phys. Meteorol., 47, 535–549, 1995. Bakwin, P S., Davis, K J., Yi, C., Wofsy, S C., Munger, J W., Haszpra, L., and Barcza, Z.: Regional carbon dioxide fluxes from mixing ratio data, Tellus B – Chem. Phys. Meteorol., 56, 301–311, 2004. Betts, A K.: FIFE Atmospheric boundary-layer budget methods, J. Geophys. Res.-Atmos., 97, 18523–18531, 1992. Betts, A K., Helliker, B R., and Berry, J A.: Coupling between CO<sub>2</sub>, water vapor, temperature, and radon and their fluxes in an idealized equilibrium boundary layer over land, J. Geophys. Res.-Atmos., 109, D18103, doi:10.1029/2003JD004420, 2004. Chatfield, C.: The Analysis of Time Series, Chapman & Hall, New York, USA, p 50, 2004. Chen, B Z., Chen, J M., Liu, J., Chan, D., Higuchi, K., and Shashkov, A.: A Vertical Diffusion Scheme to estimate the atmospheric rectifier effect, J. Geophys. Res.-Atmos., 109, D04306, doi:10.1029/2003JD003925, 2004. Chou, W W., Wofsy, S C., Harriss, R C., Lin, J C., Gerbig, C., and Sachse, G W.: Net fluxes of CO<sub>2</sub> in Amazonia derived from aircraft observations, J. Geophys. Res.-Atmos., 107(D22), 4614, doi:10.1029/2001JD001295, 2002. Conway, T J., Tans, P P., Waterman, L S., and Thoning, K W.: Evidence for interannual variability of the carbon-cycle from the National Oceanic and Atmospheric Administration Climate Monitoring and Diagnostics Laboratory Global Air-Sampling Network, J. Geophys. Res.-Atmos., 99, 22831–22855, 1994. Cooley, H S., Riley, W J., Torn, M S., and He, Y.: Impact of agricultural practice on regional climate in a coupled land surface mesoscale model, J. Geophys. Res.-Atmos., 110, D03113, doi:10.1029/2004jd005160, 2005. Dargaville, R J., Doney, S C., and Fung, I Y.: Inter-annual variability in the interhemispheric atmospheric CO<sub>2</sub> gradient: contributions from transport and the seasonal rectifier, Tellus B – Chem. Phys. Meteorol., 55, 711–722, 2003. Denman, K., Brasseur, G., Chidthaisong, A., Ciais, P., Cox, P., Dickinson, R., Hauglustaine, D., Heinze, C., Holland, E., Jacob, D., Lohmann, U., Ramachandran, S., da~Silva~Dias, P., S.C., W., and Zhang, X.: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, in: Climate Change 2007: The Physical Science Basis, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K., Tignor, M., and Miller, H., Cambridge University Press, Cambridge, UK and New York, NY, USA, 2007. Denning, A S., Fung, I Y., and Randall, D.: Latitudinal gradient of atmospheric CO<sub>2</sub> due to seasonal exchange with land biota, Nature, 376, 240–243, 1995. Denning, A S., Holzer, M., Gurney, K R., Heimann, M., Law, R M., Rayner, P J., Fung, I Y., Fan, S M., Taguchi, S., Friedlingstein, P., Balkanski, Y., Taylor, J., Maiss, M., and Levin, I.: Three-dimensional transport and concentration of SF6 - A model intercomparison study (TransCom 2), Tellus Series B – Chem. Phys. Meteorol., 51, 266–297, 1999. Denning, A S., Zhang, N., Yi, C X., Branson, M., Davis, K., Kleist, J., and Bakwin, P.: Evaluation of modeled atmospheric boundary layer depth at the WLEF tower, Agr. For. Meteorol., 148, 206–215, 2008. Erickson, D J., Mills, R T., Gregg, J., Blasing, T J., Hoffman, F M., Andres, R J., Devries, M., Zhu, Z., and Kawa, S R.: An estimate of monthly global emissions of anthropogenic CO<sub>2</sub>: Impact on the seasonal cycle of atmospheric CO<sub>2</sub>, J. Geophys. Res.-Biogeosci., 113, G01023, doi:10.1029/2007jg000435, 2008. Fischer, M L., Billesbach, D P., Berry, J A., Riley, W J., and Torn, M S.: Spatiotemporal variations in growing season exchanges of CO<sub>2</sub>, H<sub>2</sub>O, and sensible heat in agricultural fields of the Southern Great Plains, Earth Interact., 11, 1–21, 2007. Friedlingstein, P., Cox, P., Betts, R., Bopp, L., Von~Bloh, W., Brovkin, V., Cadule, P., Doney, S., Eby, M., Fung, I., Bala, G., John, J., Jones, C., Joos, F., Kato, T., Kawamiya, M., Knorr, W., Lindsay, K., Matthews, H D., Raddatz, T., Rayner, P., Reick, C., Roeckner, E., Schnitzler, K G., Schnur, R., Strassmann, K., Weaver, A J., Yoshikawa, C., and Zeng, N.: Climate-carbon cycle feedback analysis: Results from the (CMIP)-M-4 model intercomparison, J. Climate, 19, 3337–3353, 2006. Fung, I., Prentice, K., Matthews, E., Lerner, J., and Russell, G.: 3-dimensional tracer model study of atmospheric CO<sub>2</sub> – Response to seasonal exchanges with the terrestrial biosphere, J. Geophys. Res.-Ocean. Atmos., 88, 1281–1294, 1983. Gloor, M., Dlugokencky, E., Brenninkmeijer, C., Horowitz, L., Hurst, D F., Dutton, G., Crevoisier, C., Machida, T., and Tans, P.: Three-dimensional SF$_6$ data and tropospheric transport simulations: Signals, modeling accuracy, and implications for inverse modeling, J. Geophys. Res.-Atmos., 112, D15112, doi:10.1029/2006JD007973, 2007. Gurney, K R., Chen, Y H., Maki, T., Kawa, S R., Andrews, A., and Zhu, Z X.: Sensitivity of atmospheric CO<sub>2</sub> inversions to seasonal and interannual variations in fossil fuel emissions, J. Geophys. Res.-Atmos., 110, D10308, doi:10.1029/2004JD005373, 2005. Helliker, B R., Berry, J A., Betts, A K., Bakwin, P S., Davis, K J., Denning, A S., Ehleringer, J R., Miller, J B., Butler, M P., and Ricciuto, D M.: Estimates of net CO<sub>2</sub> flux by application of equilibrium boundary layer concepts to CO<sub>2</sub> and water vapor measurements from a tall tower, J. Geophys. Res.-Atmos., 109, D20106, doi:10.1029/2004JD004532, 2004. Jones, R H.: Estimating the variance of time averages, J. Appl. Meteorol., 14, 159–163, 1975. Krol, M., Houweling, S., Bregman, B., van~den Broek, M., Segers, A., van Velthoven, P., Peters, W., Dentener, F., and Bergamaschi, P.: The two-way nested global chemistry-transport zoom model TM5: algorithm and applications, Atmos. Chem. Phys., 5, 417–432, doi:10.5194/acp-5-417-2005, 2005. Lawrence, M G. and Salzmann, M.: On interpreting studies of tracer transport by deep cumulus convection and its effects on atmospheric chemistry, Atmos. Chem. Phys., 8, 6037–6050, doi:10.5194/acp-8-6037-2008, 2008. Levy, P E., Grelle, A., Lindroth, A., Molder, M., Jarvis, P G., Kruijt, B., and Moncrieff, J B.: Regional-scale CO<sub>2</sub> fluxes over central Sweden by a boundary layer budget method, Agr. For. Meteorol., 98-9, 169–180, 1999. Lloyd, J., Francey, R J., Mollicone, D., Raupach, M R., Sogachev, A., Arneth, A., Byers, J N., Kelliher, F M., Rebmann, C., Valentini, R., Wong, S C., Bauer, G., and Schulze, E D.: Vertical profiles, boundary layer budgets, and regional flux estimates for CO<sub>2</sub> and its C-13/C-12 ratio and for water vapor above a forest/bog mosaic in central Siberia, Global Biogeochem. Cy., 15, 267–284, 2001. Patra, P K., Takigawa, M., Dutton, G S., Uhse, K., Ishijima, K., Lintner, B R., Miyazaki, K., and Elkins, J W.: Transport mechanisms for synoptic, seasonal and interannual SF6 variations and "age" of air in troposphere, Atmos. Chem. Phys., 9, 1209–1225, doi:10.5194/acp-9-1209-2009, 2009. Peters, W., Jacobson, A R., Sweeney, C., Andrews, A E., Conway, T J., Masarie, K., Miller, J B., Bruhwiler, L. M P., Petron, G., Hirsch, A I., Worthy, D. E J., van~der Werf, G R., Randerson, J T., Wennberg, P O., Krol, M C., and Tans, P P.: An atmospheric perspective on North American carbon dioxide exchange: CarbonTracker, Proc. Natl. Acad. Sci. USA, 104, 18925–18930, 2007. Raupach, M R.: Vegetation-atmosphere interaction in homogeneous and heterogeneous terrain - some implications of mixed-layer dynamics, Vegetatio, 91, 105–120, 1991. Raupach, M R., Denmead, O T., and Dunin, F X.: Challenges in linking atmospheric CO<sub>2</sub> concentrations to fluxes at local and regional scales, Austr. J. Bot., 40, 697–716, 1992. Riley, W J., Biraud, S C., Torn, M S., Fischer, M L., Billesbach, D P., and Berry, J A.: Regional CO<sub>2</sub> and latent heat surface fluxes in the Southern Great Plains: Measurements, modeling, and scaling, J. Geophys. Res.-Biogeosci., 114, G04009, doi:10.1029/2009JG001003, 2009. Saltzman, B. and Irsch, F E.: Note on the theory of topographically forced planetary waves in atmosphere, Mon. Weather Rev., 100, 441–444, 1972. 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., and Denning, A S.: Weak northern and strong tropical land carbon uptake from vertical profiles of atmospheric CO<sub>2</sub>, Science, 316, 1732–1735, 2007. Styles, J M., Lloyd, J., Zolotoukhine, D., Lawton, K A., Tchebakova, N., Francey, R J., Arneth, A., Salamakho, D., Kolle, O., and Schulze, E D.: Estimates of regional surface carbon dioxide exchange and carbon and oxygen isotope discrimination during photosynthesis from concentration profiles in the atmospheric boundary layer, Tellus B – Chem. Phys. Meteorol., 54, 768–783, 2002. Yang, Z., Washenfelder, R A., Keppel-Aleks, G., Krakauer, N Y., Randerson, J T., Tans, P P., Sweeney, C., and Wennberg, P O.: New constraints on Northern Hemisphere growing season net flux, Geophys. Res. Lett., 34, L12807, doi:10.1029/2007GL029742, 2007. Yi, C., Davis, K J., Bakwin, P S., Denning, A S., Zhang, N., Desai, A., Lin, J C., and Gerbig, C.: Observed covariance between ecosystem carbon exchange and atmospheric boundary layer dynamics at a site in northern Wisconsin, J. Geophys. Res.-Atmos., 109, D08302, doi:10.1029/2003JD004164, 2004. Yi, C X., Davis, K J., Berger, B W., and Bakwin, P S.: Long-term observations of the dynamics of the continental planetary boundary layer, J. Atmos. Sci., 58, 1288–1299, 2001.