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Abstract:

Optimal estimation retrieval is a nonlinear regression scheme to determine the conditions statistically most-likely to produce a given measurement, weighted against any a priori knowledge. The technique is applied to three problems within the field of lidar data analysis. A retrieval of the aerosol backscatter and either the extinction or lidar ratio from two-channel Raman lidar data is developed using the lidar equations as a forward model. It produces profiles consistent with existing techniques at a resolution of 10-1000 m and uncertainty of 5-20%, dependent on the quality of data. It is effective even when applied to noisy, daytime data but performs poorly in the presence of cloud. Two of the most significant sources of uncertainty in that retrieval are the nonlinearity of the detectors and the instrument's calibration (known as the dead time and overlap function). Attempts to retrieve a nonlinear correction from a pair of lidar profiles, one attenuated by a neutral density filter, are not successful as uncertainties in the forward model eliminate any information content in the measurements. The technique of Whiteman et al. [1992] is found to be the most accurate. More successful is a retrieval of the overlap function of a Raman channel using a forward model combining an idealised extinction profile and an adaptation of the equations presented in Halldórsson and Langerholc [1978]. After refinement, the retrieval is shown to be at least as accurate, and often superior to, existing methods of calibration from routine measurements, presenting uncertainties of 5-15%. These techniques are then applied to observations of ash over southern England from the Eyjafjallajökull eruption of April 2010. Lidar ratios of 50-60 sr were observed when the plume first appeared, which reduced to 20-30 sr after several days within the planetary boundary layer, indicating an alteration of the particles over time.

Abstract:

The overlap function of a Raman channel for a lidar system is retrieved by nonlinear regression using an analytic description of the optical system and a simple model for the extinction profile, constrained by aerosol optical thickness. Considering simulated data, the scheme is successful even where the aerosol profile deviates significantly from the simple model assumed. Applicationto real dataisfound to reduce by a factor of 1.4-2.0 the root-mean-square difference between the attenuated backscatter coefficient as measured by the calibrated instrument and a commercial instrument. © 2012 Optical Society of America.

Abstract:

The overlap function of a Raman channel for a lidar system is retrieved by non-linear regression using an analytic description of the optical system and a simple model for the extinction profile, constrained by aerosol optical thickness. Considering simulated data, the scheme is successful even where the aerosol profile deviates significantly from the simple model assumed. Application to real data is found to reduce by a factor of 1.4 – 2.0 the root-mean-square difference between the attenuated backscatter coefficient as measured by the calibrated instrument and a commercial instrument.

Abstract:

Lidars are ideally placed to investigate the effects of aerosol and cloud on the climate system due to their unprecedented vertical and temporal resolution. Dozens of techniques have been developed in recent decades to retrieve the extinction and backscatter of atmospheric particulates in a variety of conditions. These methods, though often very successful, are fairly ad hoc in their construction, utilising a wide variety of approximations and assumptions that makes comparing the resulting data products with independent measurements difficult and their implementation in climate modelling virtually impossible. As with its application to satellite retrievals, the methods of non-linear regression can improve this situation by providing a mathematical framework in which the various approximations, estimates of experimental error, and any additional knowledge of the atmosphere can be clearly defined and included in a mathematically ‘optimal’ retrieval method, providing rigorously derived error estimates. In addition to making it easier for scientists outside of the lidar field to understand and utilise lidar data, it also simplifies the process of moving beyond extinction and backscatter coefficients and retrieving microphysical properties of aerosols and cloud particles. Such methods have been applied to a prototype Raman lidar system. A technique to estimate the lidar’s overlap function using an analytic model of the optical system and a simple extinction profile has been developed. This is used to calibrate the system such that a retrieval of the profile extinction and backscatter coefficients can be performed using the elastic and nitrogen Raman backscatter signals.