Atmospheric Measurement Techniques Discussions www.atmos-meas-tech-discuss.net 1867-8610 3 1 2010 10.5194/amtd-3-697-2010 http://www.atmos-meas-tech-discuss.net/3/697/2010/ http://www.atmos-meas-tech-discuss.net/3/697/2010/amtd-3-697-2010.html http://www.atmos-meas-tech-discuss.net/3/697/2010/amtd-3-697-2010.pdf 697 784 2010-02-17 Differential optical absorption spectroscopy (DOAS) and air mass factor concept for a multiply scattering vertically inhomogeneous medium: theoretical consideration V. V. Rozanov rozanov@iup.physik.uni-bremen.de A. V. Rozanov Institute of Environmental Physics (IUP), University of Bremen, Bremen, Germany The Differential Optical Absorption Spectroscopy (DOAS) technique is widely used to retrieve amounts of atmospheric species from measurements of the direct solar light transmitted through the Earth's atmosphere as well as of the solar light scattered in the atmosphere or reflected from the Earth's surface. For the transmitted direct solar light the theoretical basis of the DOAS technique represented by the Beer-Lambert law is well studied. In contrast, scarcely investigated is the theoretical basis and validity range of the DOAS method for those cases where the contribution of the multiple scattering processes is not negligible. Our study is intended to fill this gap by means of a theoretical investigation of the applicability of the DOAS technique for the retrieval of amounts of atmospheric species from observations of the scattered solar light with a non-negligible contribution of the multiple scattering. <br><br> Starting from the expansion of the intensity logarithm in the functional Taylor series we formulate the general form of the DOAS equation. The thereby introduced variational derivative of the intensity logarithm with respect to the variation of the gaseous absorption coefficient, which is often referred to as the weighting function, is demonstrated to be closely related to the air mass factor. Employing some approximations we show that the general DOAS equation can be rewritten in the form of the weighting function (WFDOAS), the modified (MDOAS), and the standard DOAS equations. For each of these forms a specific equation for the air mass factor follows which, in general, is not suitable for other forms of the DOAS equation. Furthermore, the validity range of the standard DOAS equation is quantitatively investigated using a suggested criterion of a weak absorption. <br><br> The results presented in this study are intended to provide a basis for a better understanding of the applicability range of different forms of the DOAS equation as well as of the relationship between the air mass factor and the weighting function. To facilitate the understanding of the paper content for unexperienced reader we start our discussion considering in details the standard DOAS technique applied to the observations of the direct solar light transmitted through the Earth's atmosphere. Bovensmann, H., Burrows, J P., Buchwitz, M., Frerick, J., Noël, S., Rozanov, V V., Chance, K V., and Goede, A. P H.: SCIAMACHY: Mission objectives and measurement modes, J Atm Sci., 56, 127–149, 1999. Brewer, A W., McElroy, C T., and Kerr, J B.: Nitrogen dioxide concentrations in the atmosphere, Nature, 246, 129–133, 1973. Bruns, M., Buehler, S A., Burrows, J P., Heue, K.-P., Platt, U., Pundt, I., Richter, A., Rozanov, A., Wagner, T., and Wang, P.: Retrieval of Profile Information from Airborne Multi Axis UV/visible Skylight Absorption Measurements, Appl. Opt., 43, 4415–4426, 2004. Bruns, M., Buehler, S. A., Burrows, J. P., Richter, A., Rozanov, A., Wang, P., Heue, K. P., Platt, U., Pundt, I., and Wagner, T.: NO₂ Profile retrieval using airborne multi axis UV-visible skylight absorption measurements over central Europe, Atmos. Chem. Phys., 6, 3049–3058, 2006. Buchwitz, M., Rozanov, V V., and Burrows, J P.: A near-infrared optimized DOAS method for the fast global retrieval of atmospheric CH₄, CO, CO₂, H₂O, and N₂O total column amounts from SCIAMACHY Envisat-1 nadir radiances, J. Geophys. Res., D105, 15231–15245, 2000. Burrows, J P., Weber, M., Buchwitz, M., Rozanov, V., enmayer, A. L.-W., Richter, A., DeBeek, R., Hoogen, R., Bramstedt, K., Eichmann, K.-U., Eisinger, M., and Perner, D.: The Global Ozone Monitoring Experiment (GOME): Mission concept and first scientific results, J. Atmos. Sci., 56, 151–175, 1999. Coldewey-Egbers, M., Weber, M., Lamsal, L. N., de Beek, R., Buchwitz, M., and Burrows, J. P.: Total ozone retrieval from GOME UV spectral data using the weighting function DOAS approach, Atmos. Chem. Phys., 5, 1015–1025, 2005. Diebel, D., Burrows, J., Beek, R D., Munro, R., Kerridge, B., Frank, H., Platt, U., and Marquard, L.: Tracegas study. Detailed analysis of the retrieval algorithms selected for the level 1–2 processing of GOME data, Progress report 2, ESA Contract 10728/94/NL/CN, 1994. Fish, D., Jones, R., and Strong, E.: Midlatitude observations of the diurnal variation of stratospheric BrO, J. Geophys. Res., 100, 18863–18871, 1995. Frankenberg, C., Platt, U., and Wagner, T.: Iterative maximum a posteriori (IMAP)-DOAS for retrieval of strongly absorbing trace gases: Model studies for CH₄ and CO₂ retrieval from near infrared spectra of SCIAMACHY onboard ENVISAT, Atmos. Chem. Phys., 5, 9–22, 2005. Harrison, A.: Midsummer stratospheric NO₂ at latitude 45&deg; S, Can. J. Phys., 57, 1110, doi:10.1139/p79-155, 1979. Hazewinkel, M. (ed.): Encyclopaedia of Mathematics, Springer-Verlag Berlin Heidelberg New York, 2002. Hönninger, G., von Friedeburg, C., and Platt, U.: Multi axis differential optical absorption spectroscopy (MAX-DOAS), Atmos. Chem. Phys., 4, 231–254, 2004. Hoogen, R., Rozanov, V V., and Burrows, J P.: Ozone profiles from GOME satellite data: Algorithm description and first validation, J. Geophys. Res., 104, 8263–8280, \doi10.1029/1998JD100093, 1999. Klenk, K F., Bhartia, P K., Kaveeshwar, V G., McPeters, R D., Smith, P M., and Fleig, A J.: Total Ozone Determination from the Backscattered Ultraviolet (BUV), J. Appl. Meteorol., 21, 1672–1684, 1982. Marquard, L., Wagner, T., and Platt, U.: Improved air mass factor concepts for scattered radiation differential optical absorption spectroscopy of atmospheric species, J. Geophys. Res., 105, 1315–1327, 2000. McKenzie, R., Johnston, P., McElroy, C., Kerr, J., and Solomon, S.: Altitude distributions of stratospheric components from ground-based measurements at twilight, J. Geophys. Res., 96, 15499–15511, 1991. McKenzie, R L. and Johnston, P V.: Seasonal variations in stratospheric NO₂ at 45&deg; S, Geophys. Res. Lett., 9, 1255–1258, 1982. Noxon, J., Whipple, E., and Hyde, R.: Stratospheric NO₂ 1. Observational Method and Behavior at Mid-Latitude, J. Geophys. Res., 84, 5047–5065, 1979. Palmer, P., Jacob, D., Chance, K., Martin, R., Spurr, R. J. D., Kurosu, T., Bey, I., Ytantosca, R., Fiore, A., and Li, Q.: Air mass factor formulation for spectroscopic measurements from satellites: Application to formaldehyde retrievals from the Global Ozone Monitoring Experiment, J. Geophys. Res., 106, 14539–14550, 2001. Perliski, L. and Solomon, S.: On the evaluation of air mass factors for atmospheric near-ultraviolet and visible absorption spectroscopy, J. Geophys. Res., 98, 10363–10374, 1993. Platt, U.: Air Monitoring by Spectroscopic Techniques, chap. Differential optical absorption spectroscopy (DOAS), John Wiley, New York, 1994. Platt, U. and Perner, D.: Direct measurements of atmospheric CH₂O, HNO₂, O₃, NO₂, and SO₂ by differential optical absorption in the near UV, J. Geophys. Res., 85, 7453–7458, 1980. Platt, U. and Stutz, J.: Differential optical absorption spectroscopy. Principles and Applications., Springer-Verlag Berlin Heidelberg, 2008. Postylyakov, O., Belikov, I., Elansky, N., and Elokhov, A.: Observations of the ozone and nitrogen dioxide profiles in the TROICA-4 experiment, Adv. Space Res., 37, 2231–2237, 2006. Pu\ck\=ite, J., Kühl, S., Deutschmann, T., Platt, U., and Wagner, T.: Extending differential optical absorption spectroscopy for limb measurements in the UV, Atmos. Meas. Tech. Discuss., 2, 2919–2982, 2009. Richter, A.: Absorptionsspectroscopishce Messungen stratosphärischer Spurengase über Bremen, 53&deg; N, Ph.D. thesis, Fachbereich Physik der Universität Bremen, 1997. Richter, A., Eisinger, M., Enmayer, A. L.-W., and Burrows, J P.: DOAS zenith sky observations: 2. Seasonal variation of BrO over Bremen (53&deg; N) 1994–1995, J. Atmos. Chem., 32, 83–99, 1999. Roscoe, H. K., Johnston, P. V., Van Roozendael, M., et~al.: Slant column measurements of 0₃ and NO₂ during the NDSC intercomparison of zenith-sky UV-visible spectrometers in June 1996, J. Atmos. Chem., 32, 281–314, 1999. Rozanov, A.: SCIATRAN 2.X: Radiative transfer model and retrieval software package, online available at: prefixhttp://www.iup.physik.uni-bremen.de/sciatran, 2008. Rozanov, A., Bovensmann, H., Bracher, A., Hrechanyy, S., Rozanov, V., Sinnhuber, M., Stroh, F., and Burrows, J.: NO₂ and BrO vertical profile retrieval from SCIAMACHY limb measurements: Sensitivity studies, Adv. Space Res., 36, 846–854, \doi10.1016/j.asr.2005.03.013, 2005a. Rozanov, A., Rozanov, V., Buchwitz, M., Kokhanovsky, A., and Burrows, J P.: SCIATRAN 2.0 - A new radiative transfer model for geophysical applications in the 175–2400 nm spectral region, Adv. Space Res., 36, 1015–1019, 2005b. Rozanov, V V.: Light Scattering Reviews, vol 1, chap. Adjoint radiative transfer equation and inverse problems, Berlin: Springer, 339–392, 2006. Rozanov, V V. and Kokhanovsky, A A.: Light Scattering Reviews, vol 3, chap. Impact of single- and multi-layered cloudiness on ozone vertical column retrievals using nadir observations of backscattered solar radiation, 133–189, Berlin: Springer, 2008. Rozanov, V V. and Rozanov, A V.: Relationship between different approaches to derive weighting functions related to atmospheric remote sensing problems, J. Quant. Spectrosc. Ra., 105, 217–242, 2007. Rozanov, V V., Kurosu, T., and Burrows, J.: Retrieval of atmospheric constituents in the UV-Visible: A new quasi-analytical approach for the calculation of weighting functions, J. Quant. Spectrosc. Ra., 60, 277–299, 1998. Rozanov, V V., Rozanov, A V., and Kokhanovsky, A A.: Derivatives of the radiation field and their application to the solution of inverse problems, in: Light Scattering Reviews, edited by Kokhanovsky, A A., vol 2, Berlin: Springer, 205–265, 2007. Sarkissian, A., Roscoe, H K., and Fish, D J.: Ozone measurements by zenith-sky spectrometers: an evaluation of errors in air-mass factors calculated by radiative transfer models, J. Quant. Spectrosc. Ra., 54, 471–480, 1995. Slusser, J., Hammond, K., Kylling, A., Stamnes, K., Perliski, L., Dahlback, A., Anderson, D., and DeMajistre, R.: Comparison of air mass computations, J. Geophys. Res., 101, 9315–9321, 1996. Solomon, S., Schmeltekopf, A L., and Sanders, R W.: On the interpretation of zenith sky absorption measurements, J. Geophys. Res., 92, 9315–9321, 1987. Stammes, P. and Koelemeijer, R. B A.: Error analysis of the GOME ozone column retrieval method, in: Proc. European Symposium on Atmospheric Measurements from Space, ESTEC, Noordwijk, The Netherlands, 201–207, 1999. Thomas, G E. and Stamnes, K.: Radiative transfer in the atmosphere and ocean, Cambridge University Press, 1999. Volterra, V.: Theory of functionals and of integral and integro-differential equations, Dover, New York, 1959. Wagner, T., Burrows, J. P., Deutschmann, T., Dix, B., von Friedeburg, C., Frieß, U., Hendrick, F., Heue, K.-P., Irie, H., Iwabuchi, H., Kanaya, Y., Keller, J., McLinden, C. A., Oetjen, H., Palazzi, E., Petritoli, A., Platt, U., Postylyakov, O., Pukite, J., Richter, A., van Roozendael, M., Rozanov, A., Rozanov, V., Sinreich, R., Sanghavi, S., and Wittrock, F.: Comparison of box-air-mass-factors and radiances for Multiple-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) geometries calculated from different UV/visible radiative transfer models, Atmos. Chem. Phys., 7, 1809–1833, 2007. Weber, M., Lamsal, L. N., Coldewey-Egbers, M., Bramstedt, K., and Burrows, J. P.: Pole-to-pole validation of GOME WFDOAS total ozone with groundbased data, Atmos. Chem. Phys., 5, 1341–1355, 2005. Widom, H.: Lectures on integral equations, Amer. Book Comp., 1969. Zabreiko, P P., Koshelev, A I., Krasnoselskii, M A., Mikhlin, S G., Rakovshchik, L S., Stet'senko, V Y., Shaposhnikova, T O., and Anderssen, R S., eds.: Integral equations – a reference text, chap 2, Noordhoff, translated from Russian, 1958.