Ill-posed retrieval of aerosol extinction coefficient profiles from Raman lidar data by regularization

Abstract

In the analysis of Raman lidar measurements of aerosol extinction, it is necessary to calculate the derivative of the logarithm of the ratio between the atmospheric number density and the range-corrected lidar-received power. The statistical fluctuations of the Raman signal can produce large fluctuations in the derivative and thus in the aerosol extinction profile. To overcome this difficult situation we discuss three methods: Tikhonov regularization, variational, and the sliding best-fit (SBF). Three methods are performed on the profiles taken from the European Aerosol Research Lidar Network lidar database simulated at the Raman shifted wavelengths of 387 and 607 nm associated with the emitted signals at 355 and 532 nm. Our results show that the SBF method does not deliver good results for low fluctuation in the profile. However, Tikhonov regularization and the variational method yield very good aerosol extinction coefficient profiles for our examples. With regard to, e.g., the 532 nm wavelength, the L2 errors of the aerosol extinction coefficient profile by using the SBF, Tikhonov, and variational methods with respect to synthetic noisy data are 0.0015(0.0024), 0.00049(0.00086), and 0.00048(0.00082), respectively. Moreover, the L2 errors by using the Tikhonov and variational methods with respect to a more realistic noisy profile are 0.0014(0.0016) and 0.0012(0.0016), respectively. In both cases the L2 error given in parentheses concerns the second example.

On retrieval of lidar extinction profiles using Two-Stream and Raman techniques

“…The α TS (h) profiles were derived directly from Eq. (4) without any noise-treatment, as the extinction coefficient retrieval is methematically an ill-posed problem and even slight noise filtering can sevearly influence the inversion result (Pornsawad, 2008). Smoothing was applied only to already calculated α TS (h) by a running mean of 300 m.…”

“…This results in significantly noise polluted signals obtained from the Raman channels. The Raman signals are usually strongly averaged in time and range for further analyses, which can severely influence the results of the Raman extinction coefficient retrieval (Pornsawad, 2008).…”

Springtime Arctic aerosol: Smoke versus haze, a case study for March 2008

“…For this study the lidar data was evaluated with a resolution of 10 min and 60 m. As the extraction of the extinction coefficient from lidar data is an ill-posed problem (Pornsawad et al, 2008), any smoothing of the lidar profiles would strongly affect the solution. Hence, no smoothing was applied to the Raman channels.…”

An Adaptive Base Point Algorithm for the Retrieval of Aerosol Microphysical Properties

“…In this paper, we will focus solely on the retrieval of the volume distribution and refractive index, and the properties derived from it, like the effective radius or the volume concentration; of course, there exist several other problems on the chain from lidar signal data to microphysical properties, like obtaining the extinction and backscatter profiles from the preprocessed signals (see [11,12]), the recognition of homogenous aerosol layers in these profiles, see [6], or the computational complexity of the whole problem (see [13]). The EARLINET measurements started in May 2000 and are still ongoing; up to now, the EARLINET database represents the largest database for the aerosol distribution on a continental scale.…”