Study of the Aerosol Influence on Errors in Retrieving the CO 2 Total Column Amount Yu. M. Timofeyev*, Ya.A. Virolainen, A.V. Polyakov Research Institute of Physics, St.-Petersburg State University, * Nansen International Environmental and Remote Sensing Center, St. Petersburg, Russia Statistical Modeling of Tropospheric Aerosol Characteristics Numerical Modeling of OCO Satellite Experiment Introduction The Orbiting Carbon Observatory, OCO, is a NASA Earth System Science Pathfinder (ESSP) mission to measure the distribution of total column carbon dioxide in the earth’s atmosphere from an earth orbiting satellite [Haring et al., 2004, Toon et al., 2005]. OCO will be launched in September of High-resolution spectra of reflected sunlight in the near infrared at the CO 2 band at 1.61  m and 2.06  m and the oxygen A-band at  m are used to retrieve the column average CO 2 dry mole fraction, Xco2. The 1.61  m CO 2 band provides the maximum sensitivity near the surface while O 2 A-band and 2.06  m CO 2 band provide information needed to determine surface pressure, albedo, atmospheric temperature, water vapor, clouds and aerosols. Stages of the study: -a) a numerical analysis of the sensitivity of outgoing radiation spectra to variations of different parameters, -b) an analysis of the influence of uncertainties in assigning the different parameters on the accuracy of retrieving the total column carbon dioxide. In numerical modeling of the OCO satellite experiment, we use the code SCIATRAN [ bremen.de/sciatran/ ] that makes it possible to calculate the outgoing radiation and variation derivatives with respect to different parameters of the system "atmosphere-underground surface": -temperature profile, -pressure profile, -CO 2, O 2, H 2 О profiles, -surface albedo, -optical aerosol characteristics. All these parameters are assumed to be random functions (vectors) with mean and covariance matrices K xx describing the possible natural variations. Recent experimental and modeled data have been used to construct these matrices. Aerosol optical characteristics (ensembles of extinction and scattering coefficients, scattering indicatrices were modeled using OPAC [Hess et al., 1998]. Conclusion Haring R., R. Pollock, B. Sutin, D. Crisp, 2004: The Orbiting Carbon Observatory (OCO) instrument optical design. Current Development in lens design and optical engineering. V. P. Mouroulis, W. Smith, R.Johnson (Eds), Vol.5523, 51-62, SPIE, Denver, 2004 Hess M., P. Koepke, I. Schult, 1998: Optical properties of aerosol and clouds: The software package OPAC. Bull. Americ. Meteor. Soc., 79, 5, 831–844. Lenoble, J. and P. Pruvost, 1983: Inference of the aerosol Angstrom coefficient from SAGE short–wavelength data. J. Climate and Appl. Meteor., 22, 10, 1717–1725. Oboukhov, A.M., 1959: About statistically orthogonal expansions of empirical functions. Izv. RAS, Geophysics, 3, 432–459 (in Russian). Polyakov A.V., A.V. Vasil'ev, and Yu.M. Timofeev, 2001: Parameterization of the Spectral Dependence of the Aerosol Extinction Coefficient in Problems of Atmospheric Occultation Sounding from Space. Izv. RAS, Atm. and Ocean. Phys., 37, 5, 646–657 (Engl. transl.). Timofeyev Yu.M, A.V. Polyakov, H.M. Steele, M.J. Newchurch, 2003: Optimal Eigenanalysis for the Treatment of Aerosols in the Retrieval of Atmospheric Composition from Transmission Measurements. Appl. Optics, 42, 12, 2635–2646. Toon G. & OCO Level-2 Algorithm Team, 2005: OCO Retrieval algorithm overview. 2- nd International Workshop on Greenhouse gas measurements from Space. Pasadena, California, March 24-25, 2005 Virolainen Ya.A., A.V. Polyakov, Yu.M. Timofeyev, 2004: Statistical optical models of tropospheric aerosol. Izv. RAS, Atm. and Oceanic Phys., 40, 2, 216–227 (Engl. transl.). References Statistical Modeling of Tropospheric Aerosol and Analysis of Optical Characteristics in OCO spectral range Table 1. Characteristics of aerosol models (layer thickness h, height of homogeneous atmosphere H, aerosol fractions and spread of surface concentration N 0 ). Modeling of optical characteristics is based on Database OPAC [Hess et al., 1998]. Characteristics studied: the aerosol extinction coefficient (AEC), the aerosol scattering coefficient (ASC), and the asymmetry parameter (AP) g (the mean scattering cosines). Input data: statistical ensembles of optical characteristics for different aerosol types in three spectral ranges which consist of 500 realizations of number concentration (N i ) profiles for different aerosol fractions at 25 tropospheric altitudes (0– 12 km). Calculations: the complete spectral covariance matrix of studied characteristics. Local ensembles of tropospheric aerosol Optical depth (AOD) and its distribution for tropospheric aerosol Fig.1. Spectral dependence of mean optical depths (with RMS variability) different models of tropospheric aerosol. Fig.2. AOD distribution at  m for ensembles of continental (on the left) and maritime (on the right) models. Correlations between optical characteristics Fig.3. Correlation between AEC (at  m) and other aerosol parameters for continental aerosol. Fig.4. Correlation between AEC (at  m) and other aerosol parameters for maritime aerosol. Fig.5. Spectral dependence of CC between AEC at  m and other optical parameters in different measurement channels. (* – CC between natural logarithms of AEC and ASC.) Optimal parameterization of aerosol optical characteristics Optimal parameterization of any parameter (AEC, ASC or AP) [Oboukhov, 1959]: Here are eigenvectors of spectral covariance matrix of an aerosol parameter, are relevant expansion coefficients. Parameterization based on Angstrom relation [Lenoble and Pruvost, 1983]: Here and are some parameters. Table 2. Errors of two parameterizations of aerosol parameters for different ensembles of tropospheric aerosol Fig.6. Relative errors of approximating the aerosol optical characteristics by optimal method and Angstrom relation. Parameterization Errors Radiance Variations due to Uncertainties in Retrieved Parameters Spectral covariance matrices of radiance variations : is a priori matrix of parameter J variability, K is the matrix of parameter weight functions. Table 3. Mean surface albedo A with r.m.s variations  A for different surface types. Continental aerosol model Marine aerosol model Fig.7. Mean radiance (I 0 ) and radiance variations  caused by parameter uncertainties in O 2 and CO 2 absorption bands for two aerosol models at Sun zenith angle 30 . Curves: I 0 - red, AEC - blue, ASC - alice blue, AP - brown, albedo - green, CO 2 - black. Variability of AEC, ASC, CO 2 is assumed to be natural. 1. Global and regional (continental, maritime, free troposphere) statistical models of aerosol optical characteristics have been constructed by numerical modeling. The aerosol extinction (AEC), scattering (ASC) coefficients, and the asymmetry parameter (AP) are the most variable in the continental ensemble. 2. Correlations between different optical aerosol parameters in the channels 0.765, 1.607,  m have been studied. There are significant correlations between AEC and ASC in all channels. Correlation coefficients (CC) between natural logarithms of these parameters is 0.7–1.0 depending on the model, the channel and the parameter. 3. AEC, ASC and AP spectral dependences have been approximated by optimal parameterization and Angstrom relation. Approximation errors averaged over three channels are 0.02–1.5% for optimal and 1.2–9.9% for Angstrom parameterizations. Errors of optimal parameterization do not exceed 0.1% in several channels for the maritime and the free troposphere models. The Angstrom parameterization error for AEC and ASC increases with wavelength and for ASC in the channel  m ranges up to 22% for the continental aerosol. 4. Calculations of outgoing radiance in 0.76 (О 2 ), 1.61 and 2.06  m (СО 2 ) absorption bands have shown that in O 2 band the radiance is most responsive to variations of the surface albedo and aerosol optical characteristics (AEC, ASC). In CO 2 bands maximal radiance variations is also caused by the albedo variations, but CO 2 variations hold the second-third position in the influence on the radiance. 5. Preliminary estimations have shown that total СО 2 retrieval errors depend on the accuracy of a priori information on the aerosol and this problem calls for further accurate studies. Preliminary Analysis of Total СО 2 Retrieval Errors Residual covariance matrix (the error matrix): Here is the matrix of measurement errors, is the measurement error (a noise). Fig.8. Calculated radiances in three channels and measurement errors (the continental model, the Sun zenith angle 30  ). Fig.9. Relative CO 2 retrieval error and a priori variability (continental model, Sun zenith angle 30  ). Estimates of total CO 2 retrieval errors Table 4. Relative CO 2 retrieval errors for different aerosol models and a priori information. Altitude dependence of CO 2 retrieval errors Total СО 2 retrieval errors at given the complete a priori information on the aerosol are smaller by 10 and 20% (for continental and urban aerosols) than those in the case of minimal a priori aerosol information. Mean optical depths at 765 nm are 0.14 and 0.62 for the continental and urban aerosol models, respectively. Acknowledgement The authors are grateful to Dr. Vladimir Rozanov for the help in applying the code SCIATRAN and useful discussions. Variabilities of temperature, H 2 O, CO 2, AEC, ASC profiles; and albedo, and near-surface pressure are considered. Variabilities of AP; variabilities of AEC, ASC, AP and albedo within bands are not considered.