Tropospheric ozone information from satellite-based polarization measurements

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D17, 4326, doi:10.1029/2001jd001346, 2002 Tropospheric ozone information from satellite-based polarization measurements Otto P. Hasekamp and Jochen Landgraf Space Research Organization Netherlands, Utrecht, Netherlands Received 28 September 2001; revised 4 February 2002; accepted 4 February 2002; published 10 September 2002. [1] Many current and planned future satellite missions aim at the retrieval of tropospheric ozone from reflectance spectra. However, it is difficult to distinguish between stratospheric and tropospheric ozone on the basis of reflectance spectra only. In this paper we show that satellite-based polarization measurements of backscattered light contain valuable additional information on the tropospheric ozone profile. In contrast to the reflectance the polarization properties of backscattered light show higher sensitivity to ozone in the troposphere than to ozone in the stratosphere. This is because the polarization is most affected by ozone at that altitude where most scattering takes place, which is in the troposphere for wavelengths greater than 300 nm. Retrievals performed on synthetic Global Ozone Monitoring Experiment 2 data show that the vertical resolution of the tropospheric ozone profile is significantly improved if polarization measurements are used in addition to the reflectance spectrum. Problems that are currently encountered in tropospheric ozone retrieval from reflectance spectra may be solved by using additional polarization measurements. INDEX TERMS: 0365 Atmospheric Composition and Structure: Troposphere composition and chemistry; 0394 Atmospheric Composition and Structure: Instruments and techniques; 3260 Mathematical Geophysics: Inverse theory; KEYWORDS: tropospheric ozone, polarization, remote sensing, radiative transfer modeling, inversion methods Citation: Hasekamp, O. P., and J. Landgraf, Tropospheric ozone information from satellite based polarization measurements, J. Geophys. Res., 107(D17), 4326, doi:10.1029/2001jd001346, 2002. 1. Introduction [2] Tropospheric ozone plays an important role in atmospheric chemistry, as it is involved in all primary initiation of oxidation chains in the atmosphere. The production of ozone in the troposphere depends on the presence of hydrocarbons, NO x, and light and is hence a tracer of tropospheric pollution. Ozone is also transported down from the ozone layer via stratospheric-tropospheric exchange. The relative importance of these two sources for tropospheric ozone continues to be a controversial subject. Measurements at several ground-based stations have indicated an increase in tropospheric ozone over the past decades, which may be an indication of increasing anthropogenic pollution. Global measurements of the tropospheric ozone distribution are needed to quantify these changes. [3] The Global Ozone Monitoring Experiment (GOME), launched in 1995 on the European Space Agency s second European Remote Sensing satellite (ERS-2), is the first satellite instrument with the potential to measure tropospheric ozone [Chance et al., 1997]. GOME is a grating spectrometer that measures the backscattered radiance in the wavelength range 240 790 nm with a spectral resolution of 0.2 nm. The range between 240 and 340 nm contains height-resolved information about ozone. Algorithms for ozone profile Copyright 2002 by the American Geophysical Union. 0148-0227/02/2001JD001346$09.00 retrieval from GOME are described by Munro et al. [1998], Hoogen et al. [1999], and Hasekamp and Landgraf [2001]. Similar ozone profile retrievals will be performed on the nadir reflectance spectra that will be measured by the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY), launched on Envisat-1 in 2002 (with an additional limb-viewing mode) and the Ozone Monitoring Instrument (OMI), to be launched on EOS-AURA in 2003. [4] Although tropospheric ozone information is clearly present in the GOME-type reflectance measurements, the vertical resolution in the troposphere and low stratosphere is limited [Hoogen et al., 1999; Hasekamp and Landgraf, 2001; Spurr, 2001], and a strong correlation exists between the errors on tropospheric ozone and the errors on stratospheric ozone. The reason for this is that the backscattered radiation from the troposphere travels back to the satellite through the stratosphere, where 90% of the atmospheric ozone is located, and is thus strongly affected by extinction through absorption by stratospheric ozone. Hence this radiation is more sensitive to stratospheric ozone than to tropospheric ozone. [5] Another problem is the uncertainty in the spectroscopic ozone data for wavelengths >315 nm. Owing to this yet to be solved spectroscopic problem, Hasekamp and Landgraf [2001] restrict their spectral range for ozone profile retrieval to wavelengths less than 315 nm, which limits the tropospheric ozone information for larger solar zenith angles. ACH 3-1

ACH 3-2 HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION [6] Various authors have shown that measurements of the polarization of light scattered back from the Earth s atmosphere contain valuable information on aerosol properties [Hansen and Travis, 1974; Mishchenko and Travis, 1997; Herman et al., 1997; Stam et al., 1999; McLinden et al., 1999; Chowdhary et al., 2001]. The possibility of using polarization measurements to obtain additional ozone profile information has not been considered yet. The spaceborne instrument GOME-2, to be launched on METOP-1 in 2005, will be the first instrument to provide adequate polarization measurements in the spectral range where ozone absorption takes place. The main reason why polarization is measured in this spectral range is to correct the measured radiances for the polarization sensitivity of the instrument. The aim of this paper is to show that these polarization measurements contain valuable information on the tropospheric ozone profile. In section 2 the linearized vector radiative transfer model used in this study is shortly summarized. In section 3, radiative transfer calculations are used to demonstrate the sensitivity of polarization measurements to tropospheric ozone, and finally, in section 4, retrievals performed on synthetic GOME-2 data show the impact of using polarization measurements on the retrieved profile. 2. Radiative Transfer Model 2.1. Stokes Parameters [7] The radiance and polarization of light at a certain wavelength can be described by an intensity vector I, which has the Stokes parameters I, Q, U, and V as its components [Chandrasekhar, 1960; Hansen and Travis, 1974]: I ¼ ½I; Q; U; VŠ T ; ð1þ where T indicates the transposed vector. The intensity vector is defined with respect to a certain reference plane. In this paper we use the local meridian plane as a reference plane. [8] The Polarization Measuring Devices (PMD) of GOME-2 will only measure the intensities parallel and perpendicular to the grooves of the spectrometer grating because this is sufficient to correct the radiance measurements for polarization sensitivity. From the PMD measurements the relative Stokes parameter q can be determined, which is defined as q ¼ Q I : So the first available satellite-based polarization measurements in relatively narrow wavelength bands in the Hartley and Huggins ozone absorption bands will be measurements of q. Therefore we restrict the study of this paper to the relative Stokes parameter q (equation (2)). 2.2. Model Description [9] For the retrieval of an atmospheric state vector x from a measurement vector y a forward model F is needed that describes how y depends on x: y ¼ Fx ð Þþe with measurement error e. Any component y i, F i, and e i of the measurement vector, forward model vector, and error vector, respectively, corresponds to a single measurement, which in this paper is a reflectance or relative Stokes ð2þ ð3þ parameter q measurement at a certain wavelength. The elements of the state vector x in this paper are the ozone densities averaged over 2-km-thick layers of the model atmosphere in the range 0 46 km. In ozone profile retrieval from real measurements, nonozone parameters also have to be included in the state vector [Munro et al., 1998; Hoogen et al., 1999; Hasekamp and Landgraf, 2001] to account for the effect on the measurement of, e.g., surface reflection, aerosol scattering, and wavelength calibration errors. In this case, measurements should also be added to y outside the spectral range where absorption takes place in order to avoid a correlation between the ozone profile and the nonozone parameters. [10] To retrieve the ozone profile x from measurement y we linearize the nonlinear forward model F by a Taylor expansion around a certain ozone profile x o Fx ð Þ ¼ Fx ð o Þþ @F ð @x x oþðx x o ÞþOðx x o Þ 2 : ð4þ Substitution of equation (4) in equation (3) allows us to solve equation (3) iteratively. Since, in this study, F corresponds to reflectance measurements and measurements of the relative Stokes parameter q, F and (@F)/(@x) follow from the Stokes parameters I and Q and their derivatives (@I)/(@x) and (@Q)/(@x), which we calculate with a plane parallel linearized vector radiative transfer model [Hasekamp and Landgraf, 2002]. This model is an extension to polarization of the scalar model described by [Landgraf et al., 2001]. [11] The intensity vector I for a given state of the atmosphere is found by solving the radiative transfer equation in its forward formulation, which is given in operator form by ^L I¼ S; where the transport operator L is an integro-differential operator [Carter et al., 1978], and S is the radiation source, which is in the UV and visible part of the spectrum determined by the unpolarized sunlight that illuminates the top of the Earth s atmosphere: S ¼ m o d z z top d ð o ÞF o : ð6þ Here, d denotes the Dirac delta function, z is altitude, and = (m, j), where m is the cosine of the solar zenith angle and j is the azimuthal angle. Furthermore, z top is the height of the model atmosphere, =( m o, j o ) describes the geometry of the incoming solar beam (we define m o > 0), and F o is given by ð5þ F o ¼ ½F o ; 0; 0; 0Š T ; ð7þ where F o is the extraterrestrial flux. [12] For the solution of the radiative transfer equation (5) we treat multiple scattering using a Gauss-Seidel iteration scheme. A special Fourier expansion is used to handle the azimuthal dependence of the intensity vector and scattering matrix [Hovenier and van der Mee, 1983; de Haan et al., 1987]. [13] The derivatives of the Stokes parameters with respect to the ozone profile are calculated using the forward-adjoint radiative perturbation theory, which was introduced in scalar radiative transfer by Marchuk [1964].

HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION ACH 3-3 Besides the solution of the forward radiative transfer problem (equation (5)) this approach additionally requires the solutions of the four adjoint radiative transfer equations ^L y I y ¼ R i ; with i =1,...,4. In equation (8) I y is the adjoint intensity vector field, and the adjoint operator ^L y is defined by requiring that [see, e.g., Marchuk, 1964; Box et al., 1988] hi 2 ; ^LI 1 i¼h^l y I 2 ; I 1 i for arbitrary vector functions I 1 and I 2. In equation (9) the inner product of I 1 and I 2 is defined by Z hi 1 ; I 2 i¼ Z dz di T 1 I 2; ð8þ ð9þ ð10þ with integration over full solid angle and altitude range of the model atmosphere. The expression for the adjoint operator for vector radiative transfer is given by Carter et al. [1978]. [14] The four adjoint sources R i are given by the response vector functions of the Stokes parameters at the top of the atmosphere in the viewing direction v of the satellite R i ¼ d z z top d ð v Þe i ; ð11þ where e i is the unity vector in the direction of the ith component I i of the intensity vector. The solution of the adjoint radiative transfer problems (equation (8)) can be found with the same solution technique as is used for the solution of the forward radiative transfer problem (equation (5)) [Marshuk, 1964; Box et al., 1988; Hasekamp and Landgraf, 2002]. [15] From the solutions of equations (5) and (8) the derivative of the ith Stokes parameter I i (z top, v ) with respect to the ozone density x k in layer k of the model atmosphere can be calculated @I i z top ; v @x k ¼ sk Z zk 1 z k Z dz 4p di yt ðr i ; z; ÞIðz; Þ; ð12þ where s k denotes the ozone absorption cross section in layer k, and z k and z k 1 denote the height levels of the lower and upper boundary of model layer k. Thus for the needed derivatives of the reflectance as well as of the relative Stokes parameter q with respect to the ozone density in any layer of the model atmosphere we only have to solve three radiative transfer problems: first, the forward problem (equation (5)), second, the adjoint problem (equation (8)) for adjoint source R 1, and third, the adjoint problem for adjoint source R 2. [16] In summary, the forward adjoint perturbation theory in combination with the Gauss-Seidel iteration technique for solving the radiative transfer equation (5) and (8) efficiently combines high computational speed with convincing accuracy and is therefore well suited for use in operational retrieval problems. More details about the model and a validation of the model with a benchmark doubling-adding model [de Haan et al., 1987] are given by Hasekamp and Landgraf [2002]. 3. Sensitivity Analysis 3.1. Reflectance Spectra and Ozone Absorption [17] Ozone profile retrieval from reflectance spectra in the Hartley and Huggins ozone absorption bands is based on the fact that at shorter wavelengths, where the absorption is strong, the photons do not penetrate far into the atmosphere, while the weaker absorption at longer wavelengths allows the photons to travel through the full height of the atmosphere. This causes different sensitivities of the reflectance at different wavelengths with respect to the ozone profile. [18] A good way to visualize the sensitivity of the reflectance to the ozone profile is by means of the derivatives (also called weighting functions) of the reflectance at different wavelengths with respect to the ozone density in different altitude layers. The derivatives are shown in Figure 1 for different solar zenith angles. The shape of the derivative of the reflectance explains the difficulty of retrieving tropospheric ozone from reflectance measurements: at all wavelengths and solar zenith angles the reflectance is more sensitive to changes in stratospheric ozone than to changes in tropospheric ozone. The reason for this is that the part of the radiation that is backscattered in the troposphere is affected by extinction through absorption in the stratospheric ozone layer. This may have the effect that a small bias in the retrieved stratospheric ozone densities will be compensated in the retrieval by large bias in the tropospheric ozone profile. Furthermore, the resolution of the retrieved profile in the troposphere and low stratosphere is low because it is difficult to distinguish between the effect of stratospheric and tropospheric ozone on the reflectance. [19] Another problem that is encountered in ozone profile retrieval from reflectance spectra is the uncertainty in the ozone absorption cross sections for wavelengths greater than 315 nm. In this spectral range differences between the three available cross-section sets [Bass and Paur, 1985; Voigt et al, 1999; Burrows et al., 1999] are found in the range 5 20% [Hasekamp and Landgraf, 2001]. These spectroscopic uncertainties cause severe problems in ozone profile retrieval if wavelengths greater than 315 nm are used. Furthermore, if these wavelengths are used, the temperature profile has to be known to high accuracy [Spurr, 2001], as the absorption structures in the Huggins band strongly depend on temperature. On the other hand, although most of the ozone profile information is present in the spectral range 290 315 nm, the longer wavelengths contain some additional information about the lower atmosphere, so a restriction of the spectral range to wavelengths <315 nm further reduces the vertical resolution of the retrieved profile in the troposphere [Hasekamp and Landgraf, 2001; Spurr, 2001]. 3.2. Polarization and Ozone Absorption [20] Figure 2 shows the relative Stokes parameter q for a Rayleigh-scattering atmosphere in the spectral region 290 336 nm at four different values of the solar zenith angle. Apart from an increase of (the absolute value of) q with increasing solar zenith angle, which follows from the fact

ACH 3-4 HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION Figure 1. Derivatives of the reflectance r with respect to the ozone profile x for four values of the solar zenith angle and a viewing zenith angle of 10. For the calculation a Rayleigh-scattering atmosphere and an ozone profile from a sonde, extrapolated with a climatology profile, are used. Furthermore, a Lambertian surface albedo of 0.1 is used. that Rayleigh scattering shows maximum polarization at a scattering angle of 90 [Hansen and Travis, 1974], the four spectra of q show a similar behavior: an approximately constant value at shorter wavelengths and a decrease for wavelengths greater than 300 nm. This spectral behavior of q is strongly linked with the fraction of photons that is multiply scattered. At the shorter wavelengths the value of the ozone absorption cross section is so large that the light does not penetrate far into the atmosphere and the chance that photons are scattered more than once is very small; that is, the main part of the light is single scattered high in the atmosphere. For single-scattered light, q is only determined by the scattering angle and the scattering matrix. So the state of the atmosphere has no influence on the value of q of single Rayleigh-scattered light, which explains the nearly constant value of q for wavelengths less than 300 nm. Around 300 nm the ozone absorption becomes weaker and the photons are more likely to penetrate through the ozone layer into the lower atmosphere where the chance of multiple scattering increases, which causes a decrease in

HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION ACH 3-5 Figure 2. Relative Stokes parameter q as a function of wavelength. Same scenarios as in Figure 1. the absolute value of q [Aben et al., 1999; Oikarinen, 2001]. [21] From the discussion above it follows that ozone has an influence on q at those wavelengths where light is multiple scattered: an increase in ozone absorption will decrease the amount of multiple scattering and therefore will increase the (absolute value of ) q. The derivatives of q with respect to the ozone profile are shown in Figure 3. In contrast to the derivatives of the reflectance (see Figure 1) the derivatives of q show a clear, pronounced peak in the troposphere for wavelengths greater than 300 nm. This shape can be explained by the fact that q is most sensitive to ozone at that altitude where most of the measured light is multiple scattered. This is because at this altitude an increase in ozone would have the largest impact on the fraction of photons that is multiple scattered. At wavelengths greater than 300 nm the ozone absorption becomes weaker so most of the light can penetrate through the whole atmosphere, and most of the light that is measured by the satellite is scattered back from the troposphere, where the scattering coefficient is largest. In contradiction to the reflectance the value of the relative Stokes parameter q of light scattered back from the troposphere is not affected by extinction through absorption in the ozone layer on its way back to the satellite. The reason herefore is that this extinction has the same effect on the Stokes parameters I and Q, so in the calculation of q equation (2) the extinction term cancels. On the basis of these properties of the derivative (@q)/(@x) it seems reasonable that the coupling in the retrieval between stratospheric and tropospheric ozone becomes less if measurements of q are added to the measurement vector y in equation (3). [22] In Figure 3 it can be seen that the point in the spectrum where the sensitivity to tropospheric ozone is highest shifts to longer wavelengths when the solar zenith angle increases. For solar zenith angles of 30 and 50, a strongly peaked, high sensitivity to tropospheric ozone is found at 307 nm. The sensitivity is still peaked in the troposphere but is much smaller, at 315 nm. For solar zenith angles of 70 and 75, the derivative shows a much more pronounced sensitivity to tropospheric ozone at 315 nm than at 307 nm because the optical path at 307 nm is too large to let most of the radiation penetrate into the troposphere. [23] At wavelengths less than 300 nm, most of the light that is measured by the satellite is scattered back from high in the atmosphere. Here the sensitivity to ozone is small because the main part of the light is single scattered in this spectral region and the value of q of single-scattered light is insensitive to ozone. The small peak in the derivatives near 50 km is due to the small fraction of multiple scattering that takes place here. This peak becomes somewhat larger for higher solar zenith angles because for these angles the optical path of the photons becomes longer and the chance of multiple scattering in this spectral region increases. However, for all cases the sensitivity of q to ozone above 30 km is very small. Thus an efficient retrieval of ozone profiles requires only polarization measurements in the spectral range 307 315 nm. [24] In summary, the relative Stokes parameter q shows low sensitivity to stratospheric ozone and high sensitivity to tropospheric ozone. This means that measurements of q are, from a conceptional point of view, well suited to tropospheric ozone retrieval. 4. Retrieval Simulations [25] In this section we compare ozone profile retrievals from synthetic reflectance spectra only with retrievals which use synthetic reflectance spectra in combination with synthetic measurements of q. This will illustrate the additional tropospheric ozone information that is contained in the polarization measurements. 4.1. Retrieval Method [26] In the retrieval procedure we solve the ill-posed problem of ozone profile retrieval using the Phillips-Tikhonov regularization technique [Phillips, 1962; Tikhonov, 1963] including minimization of the first derivative norm of the profile in addition to the least squares condition, namely, x ¼ min x k S 1 2 y ðfx ð Þ yþ k 2 þg 2 k Hx k 2 ; ð13þ where S y is the error covariance matrix of y, H is the discrete representation of the first derivative, and g is a regularization parameter balancing the minimization of the least squares condition and the minimization of the first derivative norm. The rationale behind the minimization of the first derivative norm as a side constraint is that the measurement y is insensitive to fine scale structures of the ozone profile. These vertical structures do not influence the residual norm but strongly influence the first derivative norm. The regularization parameter g should be chosen such that the retrieved profile contains all vertical structures that influence the measurement while the structures to which the measurement is insensitive should be filtered out. Such a value of the

ACH 3-6 HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION Figure 3. Derivatives of the relative Stokes parameter q with respect to the ozone profile x. Same scenarios as in Figure 1. regularization parameter is found from the L curve [Hansen and O Leary, 1993]. The L curve is a parametric plot of khxk(g) versus k(f(x) y)k(g), which has an L-shaped corner. The corner of the L curve corresponds to the optimum value of the regularization parameter because at this point a decrease of g would not improve the residual norm but would lead to a strong increase of the first derivative norm, while on the other hand, an increase in g would make the residual norm larger. The inversion method is discussed in detail by Hasekamp and Landgraf [2001] in the context of ozone profile retrieval from GOME data. Other atmospheric applications of Phillips-Tikhonov regularization in combination with the L curve have been reported by, e.g., Schimpf and Schreier [1997] and Liu et al. [1999]. [27] The retrieved profile is a smoothed version of the true profile because it does not contain the fine scale vertical structures to which the measurement is insensitive. The relation between the retrieved profile x and the true profile x true is x ¼ Ax true þ e; ð14þ where A is the averaging kernel [Rodgers, 1990]. The dimension of A is N N, where N denotes the number of

HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION ACH 3-7 Table 1. Three Types of Measurements That Are Used for the Simulations a Measurement Type Reflectance, nm Polarization, nm p-bands y 1 290 336 y 2 290 336 311.0 335.0 q 1 q 4 y 3 290 315.5 311.0 315.5 q 1 a Here p-bands denote the bands of the q measurements that are included in the measurement vector, with q 1 = 311.0 315.5 nm, q 2 = 316.2 320.4 nm, q 3 = 321.1 325.5 nm, and q 4 = 330.1 335.0 nm. The synthetic measurements include Gaussian noise in the range 0.25 1.0% for the reflectance and 0.5 1.0% for the polarization. layers in the model atmosphere. In equation (14), e is the error in the profile that is caused by errors in the measurement. The part of e that is determined by measurement noise is called the retrieval noise [Rodgers, 1990]. [28] The rows of the averaging kernel indicate what scale features in the ozone profile can actually be resolved. If the averaging kernel is the identity matrix, the best possible resolution of the ozone profile is obtained; that is, the ozone density in each altitude layer can be uniquely determined. So a possible measure for goodness of resolution is based on the size or spread of the off-diagonal elements of the averaging kernel [Menke, 1984]. In this study we indicate the goodness of resolution by the Backus-Gilbert spread function [Backus and Gilbert, 1967, 1968]. The spread of Figure 4. Averaging kernels corresponding to a retrieval on a reflectance spectrum in the range 290 336 nm (i.e., measurement y 1 ). Same scenarios as in Figure 1.

ACH 3-8 HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION Figure 5. Averaging kernels corresponding to a retrieval on a reflectance spectrum in the range 290 336 nm and additionally four measurements of the relative Stokes parameter q (i.e., measurement y 2 ). Same scenarios as in Figure 1. the averaging kernel corresponding to the ozone density in layer i of the discretized model atmosphere is given by ðiþ ¼ XN j¼1 ½i jš 2 2; A ij d ij ð15þ where d denotes the Kronecker delta. The term [i j] 2 in equation (15) heavily weights values of A far from the main diagonal. If the averaging kernel is the identity matrix, (i) =0. 4.2. Retrieval Scenarios for GOME-2 [29] The GOME-2 instrument will be the first satellite instrument to provide measurements of the relative Stokes parameter q in relatively small wavelength bands in the Hartley and Huggins ozone absorption region. These bands will probably be 311.0 315.5 nm, 316.2 320.4 nm, 321.1 325.5 nm, and 330.1 335.0 nm [Callies et al., 2000]. The reflectance will be measured at a spectral resolution of 0.25 nm. It is important to note that in the retrieval procedure we use the logarithm of the reflectance instead of the reflectance because this makes the forward model more linear. [30] In this study we will consider retrievals on three types of measurement vectors y (see equation (3)) simulated for GOME-2. The first type, y 1, consists only of the reflectance in the spectral range 290 336 nm. The ozone profile retrievals on this type of measurement are also

HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION ACH 3-9 Figure 6. The spread of the averaging kernels corresponding to a retrieval on only a reflectance spectrum in the spectral range 290 336 nm, (y 1 ) (solid line) and a retrieval on a reflectance spectrum, in the same spectral range, in combination with four Polarization Measuring Device (PMD) measurements, (y 2 ) (dotted line). Same scenarios as in Figure 1. representative for retrievals from GOME, OMI, and the nadir mode of SCIAMACHY. The second type of measurement vector, y 2, consists of the same reflectance measurements as the first type and additionally, measurements of q in the four bands mentioned above. The retrieval on this second measurement type will illustrate the maximum increase in tropospheric ozone information that can be obtained from the GOME-2 measurements of q. [31] Obviously, the measurement vector contains two quantities (q and log(r)) which have a completely different order of magnitude and functional behavior. In equation (13) the multiplication with S y (1/2) ensures an appropriate weighting of the two different types of measurement. [32] We also consider a third type of measurement, y 3, which consists of a reduced spectral range 290 315.5 nm for the reflectance measurements and additionally only one measurement of q in the band 311.0 315.5 nm. This third measurement type is chosen because the derivatives in Figure 3 suggests that measurements of q between 307 and 315 nm contain most tropospheric ozone information and also because the spectroscopic uncertainties for wavelengths greater than 315 nm cause severe problems in

ACH 3-10 HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION Figure 7. (left) Retrieval noise s x corresponding to a retrieval on a reflectance spectrum in the range 290 336 nm (y 1 ). (right) Retrieval noise corresponding to a retrieval on a reflectance spectrum in the range 290 336 nm and additionally four measurements of the relative Stokes parameter q (i.e., measurement y 2 ). ozone profile retrieval (see section 3.1). The three types of measurement vectors are summarized in Table 1. [33] Figure 4 shows averaging kernels of retrievals on the reflectance spectra only (y 1 ). The rows of these averaging kernels are very broad in the troposphere which indicates poor vertical resolution. This low resolution is also reported by Hoogen et al. [1999]. Thus it is difficult to distinguish between tropospheric and stratospheric ozone on the basis of reflectance spectra only. [34] The averaging kernels of the retrievals that additionally use all four measurements of q (i.e., y 2 ), shown in Figure 5, show for all solar zenith angles a much more pronounced peak in the troposphere than the averaging kernels of Figure 4, corresponding to y 1. Thus, owing to measurements of the relative Stokes parameter q, the tropospheric part of the retrieved profile is much more clearly distinguished from the stratospheric part than is done on the basis of a reflectance spectrum alone. [35] In order to make a quantitative comparison of the goodness of resolution between the retrievals with and without measurements of q, we show in Figure 6 the spread (Figure 8) of the averaging kernels corresponding to y 1 and y 2, respectively. From Figure 6 it follows that the inclusion of the four measurements of q leads to a significant reduction of the spread by a factor 1.6 2.1 in the troposphere. Figure 7 shows the retrieval noise of the profiles retrieved from y 1 and y 2. From Figure 7 one can see that the profile retrieved from y 2 has a retrieval noise that is approximately a factor of 1.2 1.5 lower in the troposphere than the retrieval noise of the profile retrieved from y 1. Thus, apart from the improvement in resolution, an improvement in retrieval noise is also obtained in the troposphere due to the four measurements of q. [36] In Figure 8 the spread of the averaging kernels corresponding to retrievals on y 3 (a reflectance spectrum in the reduced spectral range 290 315.5 nm and additionally just one measurement of q) is compared with the spread of the averaging kernels corresponding to y 1 (reflectance only) and y 2 (reflectance and four measurements of q), respectively. From Figure 8 it can be seen that the improvement in resolution of profiles retrieved from y 2 in comparison with retrievals from y 1, is for the largest part already obtained in the retrievals from y 3. Thus only one measurement of q in y 3 contains more information than the 200 reflectance measurements in y 1 in the spectral range 315.5 336 nm. Comparison of the spreads in Figure 8 corresponding to y 2 and y 3, respectively, only shows a small difference for solar zenith angles greater than 70. Evidently, if only one measurement of q is used, the wavelengths greater than

HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION ACH 3-11 Figure 8. Difference between the spread corresponding to a retrieval on a reflectance spectrum in the reduced spectral range 290 315.5 nm in conjunction with one PMD measurement and the spread of the averaging kernels shown in Figures 4 and 5. Solid line represents (y 3 ) (y 1 ) and dotted line represents (y 3 ) (y 2 ). 315 nm can be excluded without a large loss in vertical resolution of the retrieved ozone profile. [37] However, an important difference between the retrieval performed on a reflectance spectrum in conjunction with all four measurements of q (i.e., y 2 ) and the retrieval on a reflectance spectrum in the reduced spectral range in conjunction with only one measurement of q (i.e., y 3 )is the reduction in retrieval noise by approximately a factor of 2 in the troposphere. The retrieval noise corresponding to measurement y 3 is shown in Figure 9. Although the reduction in retrieval noise is important, the current uncertainties in the ozone absorption cross sections mentioned in section 3.1 would lead to a larger bias in the profile if the wavelengths greater than 315 nm are used [Hasekamp and Landgraf, 2001]. 5. Conclusions and Discussion [38] In this paper we have shown that spaceborne measurements of the state of polarization contain very valuable

ACH 3-12 HASEKAMP AND LANDGRAF: TROPOSPHERIC OZONE INFORMATION this paper, it is desirable that future ozone monitoring satellite instruments will perform polarization measurements optimized for tropospheric ozone retrieval. [41] Acknowledgments. A. Maurellis and I. Aben are acknowledged for comments on an earlier version of this paper. Figure 9. Retrieval noise s x corresponding to a retrieval on a reflectance spectrum in the reduced spectral range 290 315.5 nm and additionally one measurement of the relative Stokes parameter q in the PMD band 311.0 315.5 (i.e., measurement y 3 ). information on tropospheric ozone and thus provide a new concept for tropospheric ozone retrieval from nadir satellite observations. The relative Stokes parameter q is a polarization quantity that is most sensitive to ozone at that altitude where most scattering takes place, which is in the troposphere for wavelengths greater than 300 nm. Furthermore, the relative Stokes parameter q of light scattered back in the troposphere is not affected by extinction in the ozone layer. Retrievals performed on synthetic GOME-2 data have shown that the vertical resolution of the ozone profile is significantly improved in the troposphere if polarization measurements are used in addition to the reflectance spectrum. Thus the inclusion of a polarization measurement means that the tropospheric part of the ozone profile can be much better distinguished from the stratospheric part than can be done on the basis of a reflectance spectrum only. Another advantage of the inclusion of a polarization measurement is that the spectral range with large uncertainties in the ozone absorption cross sections (greater than 315 nm) can be excluded without a significant loss in vertical resolution of the retrieved ozone profile. [39] It is important to note that in addition to tropospheric ozone, aerosols also affect the observed polarization, though obviously with a different spectral signature. Thus when the concept presented in this paper is applied to real data, polarization measurements are also needed in the spectral range where ozone absorption is negligible in order to separate the effect of tropospheric ozone from the effect of aerosols on the polarization. [40] The results of this paper are based on simulations of the relative Stokes parameter q because this quantity will be measured by GOME-2. For viewing angles that scan away from nadir, the relative Stokes parameter u = U/I also has a value 6¼ 0 and is influenced by tropospheric ozone in a similar way as q. Therefore additional measurements of u may well improve the retrieved tropospheric ozone values. In order to make maximum use of the concept presented in References Aben, I., F. Helderman, D. M. Stam, and P. 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