References

ACP

Atmospheric Chemistry and Physics

ACP

1680-7324

Copernicus GmbH

Göttingen, Germany

10.5194/acp-8-209-2008

Retrieving global aerosol sources from satellites using inverse modeling

Dubovik

¹ ² Lapyonok

³ ⁴ Kaufman

Y. J.

⁵ Chin

⁵ Ginoux

⁶ Kahn

R. A.

⁵ ⁷ Sinyuk

³ ⁴

Laboratoire de Optique Atmosphérique, Université de Lille 1/CNRS, Villeneuve d 'Ascq, France

Substantial part of this study was done while worked at: Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, MD, USA

Laboratory for Terrestrial Physics, NASA Goddard Space Flight Center, Greenbelt, MD, USA

Science Systems and Applications, Inc., Lanham, MD, USA

Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, MD, USA

Geophysical Fluid Dynamics Laboratory, NOAA, Princeton, NJ, USA

Geophysical Jet Propulsion Laboratory, Pasadena, CA, USA

18 01 2008

8 2 209 250

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Understanding aerosol effects on global climate requires knowing the global distribution of tropospheric aerosols. By accounting for aerosol sources, transports, and removal processes, chemical transport models simulate the global aerosol distribution using archived meteorological fields. We develop an algorithm for retrieving global aerosol sources from satellite observations of aerosol distribution by inverting the GOCART aerosol transport model. The inversion is based on a generalized, multi-term least-squares-type fitting, allowing flexible selection and refinement of a priori algorithm constraints. For example, limitations can be placed on retrieved quantity partial derivatives, to constrain global aerosol emission space and time variability in the results. Similarities and differences between commonly used inverse modeling and remote sensing techniques are analyzed. To retain the high space and time resolution of long-period, global observational records, the algorithm is expressed using adjoint operators. Successful global aerosol emission retrievals at 2°×2.5 resolution were obtained by inverting GOCART aerosol transport model output, assuming constant emissions over the diurnal cycle, and neglecting aerosol compositional differences. In addition, fine and coarse mode aerosol emission sources were inverted separately from MODIS fine and coarse mode aerosol optical thickness data, respectively. These assumptions are justified, based on observational coverage and accuracy limitations, producing valuable aerosol source locations and emission strengths. From two weeks of daily MODIS observations during August 2000, the global placement of fine mode aerosol sources agreed with available independent knowledge, even though the inverse method did not use any a priori information about aerosol sources, and was initialized with a "zero aerosol emission" assumption. Retrieving coarse mode aerosol emissions was less successful, mainly because MODIS aerosol data over highly reflecting desert dust sources is lacking. The broader implications of applying our approach are also discussed.

References 1

Anderson, T. L., Wu, Y., Chu, D. A., Schmid, B., Redemann, J., and Dubovik, O.: Testing the MODIS satellite retrieval of aerosol fine-mode fraction, J. Geophys. Res., 110, D18204, doi:10.1029/2005JD005978, 2005.

Balkanski, Y. J., Jacob, D. J., Gardener, G. M., Graustein, W. C., and Turekian, K. K.: Transport and residence times of tropospheric aerosols inferred from a global 3-dimensional simulations of PB-210, J. Geophys. Res., 98 , 20 573–20 586, 1993.

Brasseur, G. P., Orlando, J. J., and Tyndall, G. S.: Atmospheric Chemistry and Global Change, Oxford University Press, 1st ed., 654 pp., 1999.

Boesenberg, J., Matthias, V., Amodeo, A., et al., EARLINET: A European Aerosol Research Lidar Network to Establish an Aerosol Climotology, Report 348, Max Planck Institute for Meteorology, Hamburg, Germany, 2003.

Cacuci, D. G.: Sensitivity theory for non-linear systems. I: Nonlinear functional analysis approach, J. Math. Phys., 22, 2794–2802, 1981.

Chin, M., Rood, R. B., Lin, S. J., Muller, J. F., and Thompson, A. M.: Atmospheric sulfur cycle simulated in the global model GOCART: Model description and global properties, J. Geophys. Res., 105(D20), 24 671–24 687, 2000.

Chin, M., Ginoux, P., Kinne, S., Torres, O., Holben, B. N., Duncan, B. N., Martin, R. V., Logan, J. A., Higurashi, A., and Nakajima, T.: Tropospheric aerosol optical thickness from the GOCART model and comparisons with satellite and Sun photometer measurements, J. Atmos. Sci., 59, 461–483, 2002.

Chin, M., Chu, D. A., Levy, R., Remer, L. A., Kaufman, Y. J., Holben, B. N., Eck, T., and Ginoux, P.: Aerosol distribution in the northern hemisphere during ACE-Asia: Results from global model, satellite observations, and sunphotometer measurements, J. Geophys. Res., 109, D23S90, doi:10.1029/2004JD004829, 2004.

Collins, W. D., Rasch, P. J., Eaton, B. E., Khattatov, B. V., Lamarque, J. F., and Zender, C. S.: Simulating aerosols using a chemical transport model with assimilation of satellite aerosol retrievals: Methodology for INDOEX, J. Geophys. Res., 106, 7313–7336, 2001.

Collins, W. D., Rasch, P. J., Eaton, B. E., Fillmore, D. W., Kiehl, J. T., Beck, C. T., and Zender, C. S.: Simulation of aerosol distributions and radiative forcing for INDOEX: Regional climate impacts, J. Geophys. Res., 107, 8028, doi:10.1029/2000JD000032, 2002.

Courtier, P. and Talagrand, O.: Variational assimilation of meteorological observations with the adjoint of the vorticity equations: Part II. Numerical results, Q. J. Roy. Meteor. Soc., 113, 1311–1328, 1987.

Dee, D. P. and Da Silva, A. M.: Data assimilation in the presence of forecast bias, Q. J. Roy. Meteor. Soc., 124(545), 269–295, Part A, 1998.

Deschamps, P. Y., Breon, F. M., Leroy, M., Podaire, A., Bricaud, A., Buries, J. C., and Seze, G.: The POLDER mission: Instrument characteristics and scientific objectives, IEEE Trans. Geosci. Remote Sens., 32, 598–615, 1994.

Deuzé, J. M., Breon, F. M., Devaux, C., Goloub, P., Herman, M., Lafrance, B., Maignan, F., Marchand, A., Nadal, F., Perry, G., and Tanré, D.: Remote sensing of aerosols over land surfaces from POLDER-ADEOS-1 polarized measurements, J. Geophys. Res., 106, 4913–4926, 2001.

Di Girolamo, L., Bond, T. C., Bramer D., Diner, D.J., Fettinger F., Kahn, R. A., Martonchik, J. V., Ramana, M. V., Ramanathan, V., and Rasch, P. J.: Analysis of Multi-angle Imaging SpectroRadiometer (MISR) aerosol optical depths over greater India during winter 2001–2004, Geophys. Res. Lett., 31, L23115, doi:10.1029/2004GL021273, 2004.

Diner, D. J., Beckert, J. C., Reilly, T. H., Bruegge, C. J., Conel, J. E., Kahn, R. A., Martonchik, J. V., Ackerman, T. P., Davies, R., Gerstl, S. A. W., Gordon, H. R., Muller, J. P., Myneni, R. B., Sellers, P. J., Pinty, B., and Verstraete, M.: Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview IEEE Trans. Geosci. Remote Sens., 36, 1072–1087, 1998.

Dubovik, O. and King, M. D.: A flexible inversion algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements, J. Geophys. Res., 105, 20 673–20 696, 2000.

Dubovik, O., Holben, B. N., Eck, T. F., Smirnov, A., Kaufman, Y. J., King, M. D., Tanré, D., and Slutsker, I.: Variability of absorption and optical properties of key aerosol types observed in worldwide locations, J. Atmos. Sci., 59, 590–608, 2002.

Dubovik, O.: Optimization of Numerical Inversion in Photopolarimetric Remote Sensing, in: Photopolarimetry in Remote Sensing, edited by: Videen, G., Yatskiv, Y., and Mishchenko, M., Kluwer Academic Publishers, Dordrecht, Netherlands, 65–106, 2004.

Edie, W. T., Dryard, D., James, F. E., Roos, M., and Sadoulet, B.: Statistical Methods in Experimental Physics, North-Holland Publishing Company, Amsterdam, 155 pp., 1971.

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. Modell. Software, 15, 539–548, 2000.

Elbern, H. and Schmidt, H.: Ozone episode analysis by four-dimensional variational chemistry data assimilation, J. Geophys. Res., 106, 3569–3590, 2001.

Elbern, H., Strunk, A., Schmidt, H., and Talagrand, O.: Emission rate and chemical state estimation by 4-dimensional variational inversion, Atmos. Chem. Phys., 7, 3749-3769, 2007

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

Gill, P. E., Murray, W., and Wright, M. E.: Practical optimization, Academic Press, London, p 401, 1982.

Ginoux, P., Chin, M., Tegen, I., Prospero, J., Holben, B. N., Dubovik, O., and Lin, S. J.: Sources and distributions of dust aerosols simulated with the GOCART model, J. Geophys. Res., 106, 20 255–20 274, 2001.

Ghan, S., Easter, R., Chapman, E., Abdul-Razzak, H., Zhang, Y., Leung, L., Laulainen, N., Saylor, R., and Zaveri, R.: A physically based estimate of radiative forcing by anthropogenic sulfate aerosol, J. Geophys. Res., 106, 5279–5293, 2001a.

Ghan, S., Laulainen, N., Easter, R., Wagener, R., Nemesure, S., Chapman, E., Zhang, Y., and Leung, R.: Evaluation of aerosol direct forcing in MIRAGE, J. Geophys. Res., 106, 5295–5316, 2001b.

Hakami, A., Henze, D. K., Seinfeld, J. H., Chai, T., Tang, Y., Carmichael, G. R., and Sandu, A.: Adjoint inverse modeling of black carbon during the Asian Pacific Regional Aerosol Characterization Experiment, J. Geophys. Res., 110, D14301, doi:10.1029/2004JD005671, 2005.

Hartley, D. and Prinn, R.: Feasibility of determining surface emissions of trace gases using an inverse method in a 3-dimentional chemical-transport model, J. Geophys. Res., 98, 5183–5197, 1993.

Hsu, N. C., Tsay, S. C., King, M. D., and Herman, J. R.: Aerosol properties over bright-reflecting source regions, IEEE Trans. Geosci. Remote Sens., 42, 557–569, 2004.

Holben, B. N., Eck, T. F., Slutsker, I., Tanré, D., Buis, J. P., Setzer, A., Vermote, E., Reagan, J. A., Kaufman, Y. J., Nakajima, T., Lavenu, F., Jankowiak, I., and Smirnov, A.: AERONET – A federated instrument network and data archive for aerosol characterization, Remote Sens. Environ., 66, 1–16, 1998.

Hourdin, F. and Talagrand, O.: Eulerian backtracking of atmospheric traces: I Adjoint derivation and parametrisation of subgrid-scale transport, Quart. J. Am. Meteorol. Soc., 132, 567–583, 2006.

Houweling, S., Breon, F.-M., Aben, I., Rödenbeck, C., Gloor, M., Heimann, M., and Ciais, P.: Inverse modeling of CO2 sources and sinks using satellite data: a synthetic inter-comparison of measurement techniques and their performance as a function of space and time, Atmos. Chem. Phys., 4, 423–538, 2004.

Jacob, D. J.: Introduction to Atmospheric Chemistry, Princeton University Press, 266 pp., 1999.

Kahn, R. A., Gaitley, B. J., Martonchik, J. V., Diner, D. J., and Crean, K. A.: Multiangle Imaging Spectroradiometer (MISR) global aerosol optical depth validation based on 2 years of coincident Aerosol Robotic Network (AERONET) observations, J. Geophys. Res., 110, D10S04, doi:10.1029/2004JD004706, 2005.

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 threedimensional 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.

Kasibhatla, P. S., Heimann, M., Rayner, P., Mahowald, N., Prinn, R. G., Hartley, D. E.: Inverse Methods in Global Biogeochemical Cycles, American Geophysical Union, 324 pp., 2000.

Kalman, R. E.: A New approach to linear filtering and prediction problems, J. Basic. Eng., 82, 35–40, 1960.

Kaufman, Y. J., Tanré, D., Remer, L. A., et al.: Operational remote sensing of tropospheric aerosol over land from EOS moderate resolution imaging spectroradiometer, J. Geophys. Res., 102, 17 051–17 067, 1997.

Kaufman, Y. J., Tanré, D., and Boucher, O.: A satellite view of aerosols in the climate system, Nature, 419(6903), 215–223, 2002.

King, M. D., Byrne, D. M., Herman, B. M., and Reagan, J. A.: Aerosol size distributions ob-tained by inversion of spectral optical depth measurements, J. Atmos. Sci., 21, 2153–2167, 1978.

King, M. D., Kaufman, Y. J., Tanré, D., and Nakajima, T.: Remote sensing of tropospheric aerosols from space: Past, present, and future, B. Am. Meteorol. Soc., 80, 2229–2259, 1999.

Kinne, S., Lohmann, U., Feichter, J., Schulz, M., Timmreck, C., Ghan, S., Easter, R., Chin, M., Ginoux, P., Takemura, T., Tagen, I., Koch, D., Herzog, M., Penner, J., Pitari, G., Holben, B., Eck, T., Smirnov, A., Dubovik, O., Slutsker, I., Tanré, D., Torres, O., Mishchenko, M., Geogdzhayev, I., Chu, D. A., and Kaufman, Y.: Monthly averages of aerosol properties: A global comparison among models, satellite data and AERONET ground data, J. Geophys. Res., 108, 4634, doi:10.1029/2001JD001253, 2003.

Kinne, S., Schulz, M., Textor, C., et al.: An AeroCom initial assessment – optical properties in aerosol component modules of global models, Atmos. Chem. Phys., 6, 1815–1834, 2006.

Khattatov, B., Lamarque, J.-F., Lyjak, L. V., Menard, R., Levelt, P., Tie, X., Brasseur, G. P., and Gille, J. C.: Assimilation of satellite observations of long-lived chemical species in global chemistry-transport models, J. Geophys. Res., 105, 29 135–29 144, 2000.

Koch, D.: The transport and direct radiative forcing of carbonaceous and sulfate aerosol in the GISS GCM, J. Geophys. Res., 106, 20 311–20 332, 2001.

Koch, D., Jacob, D., Tegen, I., Rind, D., and Chin, M.: Tropospheric sulfur simulation and sulfate direct forcing in the Goddard Institute for Space Studies (GISS) general circulation model, J. Geophys. Res., 104, 23 799–23 822, 1999.

Labonne, M., Breon, F-M., and Chevallier, F.: Injection height of biomass burning aerosols as seen from a spaceborne lidar, Geophys. Res. Lett., 34, L11806, doi:10.1029/2007GL029311, 2007.

Lahoz, W. A., Errera, Q., Swinbank, R., and Fonteyn, D.: Data assimilation of stratospheric constituents: a review, Atmos. Chem. Phys., 7, 5745-5773, 2007

Le Dimet, F. and Talagrand, O.: Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects, Tellus A, 38, 97–110, 1986.

Lin, S.-J. and Rood, R. B.: Multidimensional flux-form semi-Lagrangian transport schemes, Mon. Wea. Rev., 124, 2046–2070, 1996.

Marchuk, G. I.: Method of numerical mathematics, Nauka, Moscow, 1977 (in Russian).

Marchuk, G.: Mathematical Models in Environmental Problems, Elsevier, New York, 1986.

Menut, L., Vautard, R., Beekmann, M., and Honoré, C.: Sensitivity of photochemical pollution using the adjoint of a simplified chemistry-transport model, J. Geophys. Res., 105, 15 379–15 402, 2000.

Menut, L.: Adjoint modeling for atmospheric pollution process sensitivity at regional scale, J. Geophys. Res., 108, 8562, doi:10.1029/2002JD002549, 2003.

Michalak, A. M., Bruhwiler, L., and Tans, P. P.: A geostatistical approach to surface flux estimation of atmospheric trace gases, J. Geophys. Res., 109, D14109, doi:10.1029/2003JD004422, 2004.

Mishchenko, M. I., Cairns, B., Hansen, J. E., Travis, L. D., Burg, R., Kaufman, Y. J., Martins, J. V., and Shettle, E. P.: Monitoring of aerosol forcing of climate from space: analysis of measurement requirements, J. Quant. Spetrosc. Radiat. Transfer, 88, 149–161, 2004.

Mishchenko, M. I., Cairns, B., Kopp, G., Schueler, C. F., Fafaul, B. A., Hansen, J. E., Hooker, R. J., Itchkawich, T., Merimg, H. B., and Travis, L. D.: Accurate monitoring of terrestrial aerosola and total solar irradiance: introducing the Glory, Mission, B. Am. Meteorol. Soc., 88, N5, 677–691, 2007

Nakajima, T., Tonna, G., Rao, R., Boi, P., Kaufman, Y., and Holben, B.: Use of sky bright-ness measurements from ground for remote sensing of particulate polydisper-sions, Appl. Opt., 35, 2672–2686, 1996.

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

Patra, P. K., Maksyutov, S., Sasano, Y., Nakajima, H., Inoue, G., and Nakazawa, T.: An evaluation of CO2 observations with Solar Occultation FTS for Inclined-Orbit Satellite sensor for surface source inversion, J. Geophys. Res., 108, 4759, doi:10.1029/2003JD003661, 2003.

Phillips, B. L.: A technique for numerical solution of certain integral equation of first kind, J. Assoc. Comp. Mach., 9, 84–97, 1962.

Poole, L. R., Winker, D. M., Pelon, J. R., and McCormick, M. P.: CALIPSO: global aerosol and cloud observations from lidar and passive instruments, Proc. SPIE 4881, 419–426, 2003.

Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in FORTRAN. The art of Scientific Computing, Cambridge University Press, 965 pp., 1992.

Rao, C. R.: Linear Statistical Inference and Its Applications, Wiley, New York, 500 pp., 1965.

Reddy, M. S. and Boucher, O.: A study of the global cycle of carbonaceous aerosols in the LMDZT general circulation model, J. Geophys. Res., 109, D14202, doi:10.1029/2003JD004048, 2004

Remer, L. A., Kaufman, Y. J., Tanré, D., Mattoo, S., Chu, D. A., Martins, J. V., Li, R.-R., Ichoku, C., Levy, R. C., Kleidman, R. G., Eck, T. F., Vermote, E., and Holben, B. N.: The MODIS Aerosol Algorithm, Products and Validation, J. Atmos. Sci., 62, 947–973, 2005.

Remer, L. A., Kaufman, Y. J., and Kleidman, R. G.: Comparison of Three Years of Terra and Aqua MODIS Aerosol Optical Thickness Over the Global Oceans, IEEE Geosci. Remote Sens. Lett., 3, 537–540, 2006.

Rodenbeck, C., Houweling, S., Gloor, M., and Heimann, M.: CO2 flux history 1982–2001 inferred from atmospheric data using a global inversion of atmospheric trace transport, Atmos. Chem. Phys., 3, 1919–1964, 2003.

Rodgers, C. D.: Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation, Rev. Geophys. Space Phys., 14, 609–624, 1976.

Roeckner, E., Arpe, K., Bengtsson, L., Christoph, M., Claussen, M., Duemenil, L., Esch, M., Giorgetta, M., Schlese, U., and Schulzweida, U.: The atmospheric general circulation model ECHAM-4: Model description and simulation of present-day climate, Tech. Rep. 218, Max-Planck-Inst. für Meteorol., Hamburg, Germany, 1996.

Sato, M., Hansen, J., Koch, D., Lacis, A., Ruedy, R., Dubovik, O., Holben, B., Chin, M., and Novakov, T.: Global atmospheric black carbon inferred from AERONET, Proc. Nat. Acad. Sci., 100(11), 6319–6324, 2003.

Schmidt, H. and Martin, D.: Adjoint sensitivity of episodic ozone in Paris area to emissions on the continental scale, J. Geophys. Res., 108, 8561, doi:10.1029/2001JD001583, 2003.

Smirnov A., Holben, B. N., Dubovik, O., Frouin, R., Eck, T. F., and Slutsker, I.: Maritime component in aerosol optical models derived from Aerosol Robotic Network data, J. Geophys. Res., 108, 4033, doi:10.1029/2002JD002701, 2003.

Strand, O. N. and Westwater, E. R.: Statistical estimation of the numerical solution of a Fredholm internal equation of the first kind, J. Assoc. Comput. Mach., 15, 104–114, 1968.

Takemura, T., Okamoto, H., Maruyama, Y., Numaguti, A., Hiragushi, A., and Nakajima, T.: Global three dimensional simulation of aerosol optical thickness distribution of various origins, J. Geophys. Res., 105, 17 853–17 873, 2000.

Takemura, T., Nakajima, T., Dubovik, O., Holben, B., and Kinne, S.: Single scattering albedo and radiative forcing of various aerosol species with a global three-dimensional model, J. Climate, 4, 333–352, 2002.

Thacker, W. C.: Fitting models to inadequate data by enforcing spatial and temporal smoothness, J. Geophys. Res., 93, 10 655–10 665, 1988.

Thacker, W. C. and Long, R. B.: Fitting dynamics to data, J. Geophys. Res., 93(C2), 1227–1240, 1988.

Talagrand, O.: A study of the dynamics of four dimensional data assimilation, Tellus, 33, 43–60, 1981a.

Talagrand, O.: On the mathematics of data assimilation, Tellus, 33, 321–339, 1981b.

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

Tarantola, A.: Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam, 614 pp., 1987.

Tanré, D., Herman, M., and Kaufman, Y. J.: Information on aerosol size distribution contained in solar reflected spectral radiances, J. Geophys. Res., 101, 19 043–19 060, 1996.

Tanré, D., Kaufman, Y. J., Herman, M., and Mattoo, S.: Remote sensing of aerosol properties over oceans using the MODIS/EOS spectral radiances, J. Geophys. Res., 102, 16 971–16 988, 1997.

Tegen, I., Hollrig, P., Chin, M., Fung, I., Jacob, D., and Penner, J.: Contribution of different aerosol species to the global aerosol extinction optical thickness: Estimates from model results, J. Geophys. Res., 102, 23 895–23 915, 1997.

Tegen, I., Koch, D., Lacis, A., and Sato, M.: Trends in tropospheric aerosol loads and corresponding impact on direct radiative forcing between 1950 and 1990: A model study, J. Geophys. Res., 105, 26 971–26 989, 2000.

Textor, C., Schulz, M., Guibert, S., et al.: Analysis and quantification of the diversities of aerosol life cycles within AeroCom, Atmos. Chem. Phys., 6, 1777–1813, 2006.

Tikhonov, A. N.: On the solution of incorrectly stated problems and a method of regu-larization, Dokl. Akad. Nauk SSSR, 151, 501–504, 1963.

Twomey, S.: On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature, J. Assoc. Comp. Mach., 10, 97–101, 1963.

Van der Werf, G. R., Randerson, J. T., Collatz, G. J., Giglio, L., Kasibhatla, P. S., Arellano, A. F., Olsen, S. C., and Kasischke, E. S.: Continental-scale partitioning of fire emissions during the 1997 to 2001 El Nino/La Nina period, Science, 303(5654), 73–76, 2004.

Vautard, R., Beekmann, M., and Menut, L.: Applications of adjoint modelling in atmospheric chemistry: Sensitivity and inverse modeling, Environ. Model. Software, 15, 703–709, 2000.

Vukicevic, T. and Hess, P.: Analysis of tropospheric transport in the Pacific Basin using the adjoint technique, J. Geophys. Res., 105, 7213–7230, 2000.

Vukicevic, T., Steyskal, M., and Hecht, M.: Properties of advection algorithms in the context of variational data assimilation, Mon. Wea. Rev., 129(5), 1221–1231, 2001.

Weaver, C., da Silva, A., Chin, M., Ginoux, P., Dubovik, O., Flittner, D., Zia, A., Remer, L., Holben, B. N., and Gregg, W.: Direct Insertion of MODIS Radiances in a Global Aerosol Transport Model, J. Atmos. Sci., 64(3), 808–827, 2007.

Yaremchuk, M. L., D. A. Nechaev, K.R. Thompson, Seasonal variation of the North Atlantic Current, J. Geophys. Res., 106, 6835–6852, doi:101029/2000JC900166, 2001

100

Yaremchuk, M. L. and Maximenko, N. A.: A dynamically consistent analysis of the mesoscale eddy field at western North Pacific Subarctic Front, J. Geophys. Res., 107, 3223, doi:10.1029/2002JC001379, 2002