OVERLAP CORRECTION FUNCTION FOR AN AIRBORNE BASED LIDAR

The present research envisages the estimation of the overlap correction function for an airborne nadir-mounted lidar using multi-angle measurements. We have scanned a series of offnadir angles and after data processing we have been able to determine the instrument’s overlap function down to 95m from the lidar. This function can be used for the correction of lidar profiles and hence reduce the near-range uncertainty of lidar measurements. To our knowledge, the estimation of the overlap function using multi-angle method for a nadir pointing lidar is a première.


INTRODUCTION
The Met Office is one of the main users of the FAAM BAe-146 research aircraft, alongside scientists working in universities funded by the Natural Environment Research Council [1], and is responsible for maintaining the on-board elastic backscatter lidar.Moreover, as a response to the eruption of Eyjafjallajökull in 2010, the Met Office has set up a second aircraft, the Met Office Civil Contingencies Aircraft (MOCCA), a Cessna 421 which is aimed at giving a rapid response in case of natural hazards (especially volcanic ash) [2].A Leosphere ALS450 UV Lidar (with depolarization capability) is set up onboard both aircrafts [3].Besides Lidar, several instruments perform in-situ measurements to characterize the microphysical and optical properties of the aerosol particles and clouds, atmospheric turbulence and gas chemistry [1][2].The current research evaluates the overlap function of the lidar on-board the FAAM aircraft, using multi-angle measurements, which is based on the method developed by Adam et al. [4] for ground-based lidars.

METHODOLOGY
For ground-based Lidar, the multi-angle methods are based on measurements taken by scanning several elevation angles; the main assumption being that the atmosphere is horizontally homogeneous.This assumption is most probably fulfilled for airborne based lidars, provided a suitable altitude is selected, as we expect more homogeneity above the boundary layer (very close to a molecular atmosphere).The main steps of the method are the following.For each height, the logarithm of range corrected signals (RCS) (expressed as a function of height) is plotted versus 1/cos(), where  the off-nadir pointing angle.The slope of the linear regression provides the optical depth.Once we retrieve the optical depth (0,h) and the intercept A*(h) from the linear regression, a synthetic signal for RCS is calculated as in [4]: where j is the angle index.The individual overlap function is then computed as the ratio of the measured RCS and synthetic RCS as a function of height h.
The final steps are the conversion of individual overlap function (eq.2) in terms of range and then compute the average overlap function [4].
The method was first tested over synthetic data.Sensitivity studies were employed to find out a comfortable set of bank angles capable of yielding to a good estimate of the overlap function.The main constraint is given by the capability of the aircraft to provide specific measurements at high bank angles.The Lidar is installed with a fixed pointing angle with respect to the aircraft and thus, we need to roll the aircraft in a turn in order to change the bank angle.As the aircraft spins around 360 degrees with a special bank angle we have an orbit.The steepest orbit available with the

RESULTS
According to the lidar specifications, the full overlap should be around 300m.Time-altitude RCS profiles for the total signal (as a combination of parallel and perpendicular signals) is shown in Fig. 4 a).PBL height was ~1 km at Camborne and ~1.3 km at Exeter (as seen in ceilometers).While at Camborne it was cloud free atmosphere, at Exeter there were clouds in the PBL.As seen in Fig. 4b, there is an increase in the RCS below 1.5km which may be due to the presence of a cloud in the PBL.However, the region below 1.5km altitude will not affect the overlap retrieval (which is of interest in the first few hundred meters from the aircraft which is situated more than 2000m above the PBL).For each bank angle, the mean (total) RCS is calculated [Fig.The flight took place about ~100 km north of Camborne site (Fig. 1).In the paper by Adam [4], for zenith pointing angles Lidar, there are few criteria involved such that we use the correct altitude interval to perform the linear regression ("optimal heights interval") without introducing systematic errors.Those criteria should be adapted for nadir pointing Lidar as the signals look different as compared with zenith pointing lidars.As described in [4], the use of data from incomplete overlap introduces systematic distortions in the retrieval the intercept (and further in the overlap).In the first step we did not restrict the region over the incomplete overlap and thus, all the measurements were taken into consideration.The optical depth and the intercept retrieved in this case are shown in Fig. 5 (down to 1500 m altitude).Also shown, the molecular optical depth, which is calculated using the pressure and temperature profile as given by the radiosonde launched at 12:00 at Camborne.As seen, the optical depth obtained over the incomplete overlap is negative (from the cruise altitude down to ~4500m).In order to avoid the use of data from incomplete overlap, we have chosen to the following option.We extrapolated the optical depth and the intercept from 4400m towards the Lidar using a linear fit over the region 4200m-4400m.The extrapolation is shown as blue line in Fig. 5.Further we have dismissed the first 95m from the Lidar.Now we proceed to compute the synthetic RCS [eq.( 1)] and the individual overlap functions [eq.( 2)].The overlap function, calculated as the average of the individual functions, is shown in Fig. 6.The complete overlap is shown to be around 400m (it is ~0.98 at 300m, the range of the nominal full overlap according to specifications).The overlap function looks very good in the far field up to 5000m.Note that the errors were computed using the error propagation with input error the error on the mean for signals at each bank angle.Note that if we consider from the beginning that signals from the first 300m should not be considered, we arrive to the situation in which it is not possible to estimate the overlap function very close to the lidar.The highest the bank angles the closest to the lidar the overlap function can be retrieved.For more details please see [4], where the smallest the elevation angles the closest to the lidar the overlap function goes.Thus, technically, for 60 bank angle, 300m range corresponds to 150m on altitude.The linear regression is performed if there are at least three points available (corresponding to three different bank angles).Thus, for the highest bank angles (40, 50 and 60) the corresponding heights for a range of 300m are 229.81m,192.84m and 150m.Therefore the linear regression can be first performed at 229.81m away from the lidar.
As seen in Fig. 5 a) the optical depth is slightly larger than the molecular optical depth and thus, the comparison of the measured RCS with synthetic molecular RCS is not appropriate.
A thorough presentation of the method and a complete picture of various steps will be shown during ILRC.

CONCLUSIONS
We have demonstrated an innovative method to determine the overlap function for an airborne Lidar.The main constraint in retrieving the overlap function very close to the Lidar is the availability of the measurements taken at high bank angles, which is possible up to an aircraftdependent limit (60 degrees for the BAe-146).
For the system on-board the FAAM aircraft, in the present study we estimate full overlap to be reached at ~400 m.This has to be compared with a nominal overlap of 300m; note that at this range we estimate the overlap function to be equal to 0.98 The overlap function was retrieved down to ~95m from the Lidar.