Journal of Quantitative Spectroscopy and Radiative Transfer
Retrieval of ozone profile from ground-based measurements with polarization: A synthetic study
Introduction
Ozone is one of the major greenhouse gases in the Earth's atmosphere [1], [2]. It has been proposed that ozone, especially the lower stratospheric component, can affect the earth's climate significantly [3], [4], [5], [6]. Near the surface, ozone can be produced in high concentrations as a result of industrial activities [7], [8]. With continuous global industrial growth, the near surface ozone has at least doubled during the last century [9], [10], [11]. Therefore, there is an urgent need to quantify ozone variability in the lower stratosphere and the troposphere below the bulk of the ozone layer.
The low concentration of tropospheric ozone beneath the larger concentration of the stratospheric ozone makes it difficult to measure by top of the atmosphere (TOA) based remote sensing techniques. Ground-based measurement therefore becomes a reasonable alternative to TOA ozone profile retrievals. The Umkehr technique is a classical method to derive the ozone vertical distribution from a ground-based instrument. It utilizes the intensity at two wavelengths in the Huggins bands, which is a spectral region with a wide dynamic range of ozone absorption [12]. The Short Umkehr method, which is a modification of the Standard Umkehr method, requires zenith sky measurements of three wavelength pairs instead of one and costs about one third of the observing time [13], [14], [15]. However, both methods provide satisfactory ozone abundance only for the stratosphere. Another simple retrieval scheme was performed by Jiang et al. [16] to retrieve the stratospheric and tropospheric column ozone simultaneously. They utilized a least squares method, fitting the downwelling UV radiance at the bottom of the atmosphere (BOA) calculated with a radiative transfer model. In this paper, we retrieve the ozone number density profile at 9 layers (10 levels, see Table 1) from simulated ground-based measurements between 300 and 345 nm. A retrieval method based on optimal estimation theory is applied to solve this inverse problem rigorously. Our observation geometry is similar to that of the Umkehr method. In the standard setup, we use 226 channels to cover the entire spectral region with a 0.2 nm resolution. By doing that, we try to incorporate the information from both strong and weak absorptions in the Huggins bands. Therefore, this retrieval algorithm can be viewed as an extension of the Umkehr method.
Because of the complicated theoretical formulation and engineering issues, polarization is usually ignored in radiative modeling and measurement. However, if we are able to measure the Stokes parameters Q, U and V with accuracy comparable to that of the intensity, the information contained in the observations will increase and the retrieval will be improved. Scattering by air molecules and aerosols polarizes the diffuse radiation [17]. This effect is much stronger in the troposphere than in the stratosphere and the polarized signature will especially constrain the retrieval of tropospheric ozone. The fact that polarization measurements aid the inverse calculation has also been discussed by Hasekamp and Landgraf [18] and Jiang et al. [19]. However, complete ozone profile retrieval has not been done in either work. In this paper, we perform a retrieval of the ozone number density profile, employing forward models both with and without polarization calculations. The results are compared to demonstrate the benefits of using the vector retrieval, i.e. the retrieval with polarization. The use of polarization provides a further extension of the Umkehr technique.
In Section 2, we briefly discuss the radiative transfer theory and introduce a numerical model which calculates the four Stokes parameters of the downwelling radiation at the BOA. In Section 3, we describe the retrieval scheme and compare the retrievals with and without polarization. Simple sensitivity studies are also presented in this section. In Section 4, we use information theory to test the quality of the inversion and calculate the increase in information content from incorporating the polarization. Conclusions and discussions are presented in Section 5.
Section snippets
Theory of radiative transfer
The equation of radiative transfer can be written as [20]in the absence of thermal emission. I is the diffuse (excluding the direct solar beam) radiance vector, which consists of Stokes parameters [20] I, Q, U and V as its components. τ, u and ϕ denote the optical thickness (measured downward from the upper boundary), the cosine of the polar angle (defined to be positive in the upper hemisphere) and the azimuthal angle (measured counterclockwise, looking down, from
Retrieval theory and Levenberg–Marquardt iteration
The forward model is described bywhere x is the state vector (number density profile of ozone in this case), F refers to the forward model and y is the theoretical radiance corresponding to the state x. For instance, the formulation described in Section 2 is a forward model. A retrieval method is applied in order to solve the inverse problem, i.e. retrieve x from y [1], [32]. Much work has been devoted to the development of theories that detail the translation of remote sensing radiance
Results from information theory analysis
Deriving the atmospheric state from remote sensing measurements is an ill-posed problem, and as such, there are many different approaches to find a solution. Given a spectrum, it is prudent to ask how much information can be derived about the atmospheric state and if this is dependent upon prior knowledge. A formal description of the utility of a measurement can be gained by borrowing concepts from the fields of information theory and source coding and decoding. Rodgers suggests that the
Conclusion and discussion
We perform a retrieval of ozone number density profile from synthetic observations using the L–M iteration method based on optimal estimation theory. Our results show the capability of retrieving the ozone profile with this inverse algorithm, even in the presence of unknown random noise. By comparing the vector and scalar models, i.e. retrieval methods with and without polarization, we conclude that the vector model will significantly enhance the retrieval of ozone concentration, especially in
Acknowledgements
We appreciate the helpful comments from J. Margolis, M. Newchurch, K. Chance, X. Liu, F. Mills, J. Herman, L. Li, X. Jiang, Y. Jiang, S. Herman, C. Kolb and two anonymous reviewers. This research is supported in part by NASA Grant NAG1-02081 and JPL Grant P421407 to California Institute of Technology.
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