Experimental assessment of a Micro-Pulse Lidar system in comparison with reference lidar measurements for aerosol optical properties retrieval

Simultaneous observations of a polarized Micro-Pulse Lidar (P-MPL) system and two reference 10 European Aerosol Research Lidar Network lidars, running at the Leipzig site (Germany, 51.4oN 12.4oE, 125 m a.s.l.), were performed during a comprehensive two-month field intercomparison campaign in summer 2019. An experimental assessment regarding both the overlap (OVP) correction of the P-MPL signal profiles and the volume linear depolarization ratio (VLDR) analysis, together with its impact in the retrieval of the aerosol optical properties, is achieved, describing also the experimental procedure used. The 15 optimal lidar-specific OVP function is experimentally determined, highlighting that the one delivered by the P-MPL manufacturer cannot be long used. Among the OVP functions examined, the averaged one between those obtained from the comparison of the P-MPL observations with those of the other two reference lidars seems to be the best proxy at both nearand far-field ranges. In addition, the impact of the OVP function in the accuracy of the retrieved profiles of the total particle backscatter coefficient (PBC) 20 and the particle linear depolarization ratio (PLDR) is examined. The VLDR profile is obtained and compared to that derived from the reference lidar, showing it needs to be corrected by a small offset value within a good accuracy. Once P-MPL measurements are optimally (OVP, VLDR) corrected, both the PBC and PLDR profiles can be accurately derived, being in good agreement with reference aerosol retrievals. In overall, as a systematic requirement for lidar systems, an adequate OVP function determination and VLDR 25 testing analysis is needed to be performed in a regular basis to correct the P-MPL measurements in order to derive suitable aerosol products. A dust event as observed at Leipzig in June 2019 is used for illustration.

summer 2019. An experimental assessment regarding both the overlap (OVP) correction of the P-MPL signal profiles and the volume linear depolarization ratio (VLDR) analysis, together with its impact in the retrieval of the aerosol optical properties, is achieved, describing also the experimental procedure used. The 15 optimal lidar-specific OVP function is experimentally determined, highlighting that the one delivered by the P-MPL manufacturer cannot be long used. Among the OVP functions examined, the averaged one between those obtained from the comparison of the P-MPL observations with those of the other two reference lidars seems to be the best proxy at both near-and far-field ranges. In addition, the impact of the OVP function in the accuracy of the retrieved profiles of the total particle backscatter coefficient (PBC) 20 and the particle linear depolarization ratio (PLDR) is examined. The VLDR profile is obtained and compared to that derived from the reference lidar, showing it needs to be corrected by a small offset value within a good accuracy. Once P-MPL measurements are optimally (OVP, VLDR) corrected, both the PBC and PLDR profiles can be accurately derived, being in good agreement with reference aerosol retrievals. In overall, as a systematic requirement for lidar systems, an adequate OVP function determination and VLDR 25 testing analysis is needed to be performed in a regular basis to correct the P-MPL measurements in order to derive suitable aerosol products. A dust event as observed at Leipzig in June 2019 is used for illustration.

Introduction
Active remote sensing is an excellent tool for vertical monitoring of the atmosphere. In particular, aerosol lidar systems have demonstrated to be a suitable instrumentation for aerosol and cloud profiling in both the 30 troposphere and stratosphere (e.g., Amiridis et al., 2015;Baars et al., 2019). Tropospheric aerosols are usually confined up to 7-8 km height under aerosol intrusion conditions (e.g., Mattis et al., 2008;Pappalardo et al., 2013); otherwise, they are mostly concentrated in the ABL (around less than 1.5 km height). Indeed, lidar systems are widely used due to their high vertical spatial and temporal resolution.
The use of the lidar observations with polarization capabilities is increasing as the lidar depolarization 45 measurements allow a better aerosol speciation (dust, marine aerosol, anthropogenic pollution, volcanic ash, biomass burning, pollen, …) as well as the separation of the optical properties (backscatter, extinction) of particle components within complex aerosol mixtures with vertical resolution (i.e., Ansmann et al., 2011;Burton et al., 2014;Yu et al., 2015;Córdoba-Jabonero et al., 2018;Bohlmann et al., 2019). Therefore, new and promising methods based on the particle depolarization ratio were developed and used to derive aerosol 50 profiles in terms of particle mass concentration, separately for the coarse and fine modes (i.e., Mamouri and Ansmann, 2017), in addition to estimate both the cloud-condesation nucleii (CCN) and ice-nucleating particle (INP) concentrations (i.e., Mamouri and Ansmann, 2016).
The atmospheric lidar scanning provides an accurate characterization at all ranges; however, lidar systems present an incomplete response in the near-range observational field due to the partial intersection of the 55 field-of-view between the transmitter and the receiver for both the biaxial and coaxial lidar configurations.
Therefore, lidar signal profiles must be corrected by this near-field loss of signal, that is, the overlap (OVP) correction (Wandinger and Ansmann, 2002). The full-OVP height depends on the lidar system (e.g., . During the last two decades, Micro-Pulse Lidar (MPL) systems (Campbell et al., 2002;Welton et al., 2002; 60 manufacturer: Sigma Space Corp., currently Droplet Measurement Technologies) were deployed at different latitudes and many of them in the frame of MPLNET; since few years a polarized MPL version (P-MPL) is the standard lidar system in this network. Both MPL and P-MPL observations have been widely performed for continuous monitoring of aerosols and clouds. In particular, MPL/P-MPL measurements were used for: Atmospheric Boundary Layer (ABL) height retrievals (Lewis et al., 2013;Toledo et al., 65 2014Toledo et al., 65 , 2017, detection and characterization of both cirrus clouds Lewis et al., 2016;Córdoba-Jabonero et al., 2017;Lolli et al., 2017;Campbell et al., 2021) and Polar Stratospheric Clouds (PSC) (Campbell et al., 2008;Córdoba-Jabonero et al., 2013), depolarization-based characterization of the optical properties of different aerosol mixtures (Sicard et al., 2016;Córdoba-Jabonero et al., 2016, aerosol mass concentration estimation either in sinergy with airborne measurements (Córdoba-Jabonero et 70 al., 2016) or in comparison with forecast model simulations (Córdoba-Jabonero et al., 2019), determination of the precipitation intensity (Lolli et al., 2018;Lolli et al., 2020) and the cloud thermodynamic phase (Lewis et al., 2020) and assessment of the radiative effect of aerosols and cirrus clouds Lolli et al., 2017;Córdoba-Jabonero et al., 2020Campbell et al., 2021;Sicard et al., 2021), among others. Those works have demonstrated a good MPL performance in aerosol/cloud research. The P-75 MPL is an elastic coaxial single-wavelength (532 nm) system and, differing from older MPL versions 3 (Campbell et al., 2002;Welton et al., 2002), incorporates depolarization capabilities (Flynn et al., 2007).
As a value-added improvement, it can operate in routine continuous (24/7) mode. However, the P-MPL system needs to be well characterized in terms of the backscattered lidar signal detected by both depolarization channels of the instrument (Flynn et al., 2007;Welton et al., 2018) in order to retrieve 80 plausible aerosol optical properties. In particular, due to the very narrow telescope field of view, the lidar system is reaching the full-OVP height at relatively high altitudes (typically at 4-6 km height; Campbell et al., 2002), being particularly relevant for tropospheric aerosol research. For this reason, an accurate overlap correction, among other features, is needed for MPL systems.
MPLNET have stablished methods for overlap calibration, as those described in Berkoff et al. (2003). They 85 are based on either performing measurements under atmospheric stable and homogeneous conditions with the MPL pointing in horizontal, or making use of a secondary wide field-of-view receiver (WFR) telescope.
However, both of them could not be yet applied on site to the MPL system examined in this study. Hence, an alternative experimental procedure for the OVP function determination is introduced in this work, which is based on the cross-comparison of the backscattered signal recorded by the uncorrected lidar system (our 90 MPL) with respect to that collected by a reference (overlap-corrected) lidar. A similar methodology has been also used for the overlap correction of other lidars and ceilometers (i.e., Guerrero-Rascado et al., 2010;Sicard et al., 2020;and references therein). In this framework, an experimental campaign was planned at the EARLINET Leipzig site (Germany), and, in particular, devoted to simultaneously compare the observations of a P-MPL system with reference well-calibrated lidar measurements in order to determine 95 the required P-MPL performance.
The aim of this work is threefold: 1) to achieve an OVP correction of a P-MPL system, i.e., to estimate the experimental OVP function for correcting the P-MPL measurements; 2) to evaluate the volume linear depolarization ratio (VLDR), which is a lidar-derived parameter independent of OVP correction; and 3) to determine the P-MPL correction-induced effects on the retrieval of optical properties, both the height-100 resolved particle backscatter coefficient (PBC) and particle linear depolarization ratio (PLDR). Section 2 introduces the methodology for that purpose: an overview of the field intercomparison campaign performed, a brief description of both the P-MPL and reference lidar systems used, and the experimental approaches applied for the data analysis, regarding the experimental estimation of the OVP function of the P-MPL system (error processing is described in Annex A), the evaluation of the VLDR, and the retrieval 105 of the particle optical properties. Results are presented in Section 3. A dust case as observed during the field campaign is used for that purpose. Main conclusions are presented in Section 4.

Field campaign overview
During a field campaign carried out at the EARLINET station of Leipzig,Germany (51.35ºN 12.43ºE,125 110 m a.s.l.), managed by the Leibniz Institute for Tropospheric Research (TROPOS), for 6 weeks in June-July 2019, the performance of a P-MPL system was experimentally examined, with a special emphasis on the OVP correction and VLDR evaluation. The lidar system used was the MPL44245 unit (formerly Sigma Space Corp., currently Droplet Measurement Technologies) routinely operating at the MPLNET/El 4 Arenosillo station (https://mplnet.gsfc.nasa.gov/data all&s=El_Arenosillo), sited at Huelva, Spain 115 (ARN/Huelva, 37.1ºN 6.7ºW, 40 m a.s.l.), which is managed by the Spanish Institute for Aerospace Technology (INTA). Both stations are also AERONET (AErosol RObotic NETwork, aeronet.gsfc.nasa.gov) sites, accomplishing the requisite for co-location of both networks for the elastic retrieval of the aerosol optical properties. For the campaign, this P-MPL was temporarily deployed outside MPLNET at Leipzig to be compared against two EARLINET lidars routinely operative in this station, as 120 Polly (POrtabLe Lidar sYstem; Althausen et al, 2009;Engelmann et al., 2016) and MARTHA (Multiwavelength Tropospheric Raman lidar for Temperature, Humidity, and Aerosol profiling ;Jiménez et al., 2018) systems. They were used as reference because these lidars are well characterized with respect to EARLINET quality assurance standards (e.g., Böckmann et al., 2004;Pappalardo et al., 2004;Freudenthaler et al., 2008;Pappalardo et al.,2014;Belegante et al., 2016; Table 1.  The laser light is alternatively transmitted linearly and circularly polarized to the atmosphere by switching between two retardation modes of a ferroelectric liquid crystal (FLC) rotator. The corresponding backscattered light to those two polarized states by passing through a beam splitter to the single APD is 145 recorded in dependence of the polarizing or depolarizing atmospheric particles leading to the suppression or not, respectively, of the orthogonally-detected signal w.r.t. the transmitted one into the single APD.
Those two polarized signals are semi-simultaneously detected by alternatively switching in the basis of 50%/50% the FLC polarization mode within every integrating minute. Note that the P-MPL pulse frequency is 2500 Hz, and the polarization state is switched every 250 pulses, but just 249 pulses are collected since 150 one of the pulses is discarded during the FLC switching time ( 100 s). That is, those two signals are alternatively detected by the same APD, being recorded in two polarized channels, i.e., the 532-nm crosssignal ( ) and the 532-nm co-signal ( ) (see a more detailed description in Flynn et al., 2007).
Therefore, since no potentially existing efficiency or alignment differences are between those two signalchannels (as used a single APD), no corrections for these effects are required, as it is typically needed for 155 ordinary two-channel polarization lidars. Particular regular calibrations and signal processing were applied, which are the same as those described by Campbell et al. (2002) and Welton et al. (2002), and also by Flynn et al. (2007), whose data processing techniques remain also applicable for P-MPL systems, as indicated by Welton et al. (2018). Therefore, the measured lidar signal in those two polarized-channels is used to derive both the P-MPL total range-corrected signal (RCS), , and the volume linear depolarization ratio 160 (VLDR), , by adapting the methodology as described in Flynn et al. (2007), that is, = .
( 2) This data processing has been succesfully applicable in particular studies (e.g., Sicard et al., 2016;Córdoba-Jabonero et al., 2018;Lewis et al., 2020), independently of that stablished in MPLNET. Among the required 165 routine instrumental P-MPL corrections (Campbell et al., 2002;Welton et al., 2002), the OVP is a concerning issue, since the typical full-OVP height is reached at rather high altitudes (usually at 4-5 km height), affecting thus the aerosol profiles at ranges in the overall boundary layer and part of the troposphere. Hence, an important issue to be achieved is the particular overlap correction function for this particular P-MPL system. After sale, the P-MPL system is delivered with an original OVP function as 170 provided by the manufacturer company (formerly Sigma Space Corp., currently Droplet Measurement Technologies), which, however, must be re-evaluated with time. Indeed, one of the goals of this work is to show the experimental procedure, similar to other usually applied (i.e., Guerrero-Rascado et al., 2010;Sicard et al., 2020), to obtain a new OVP function for the P-MPL lidar as compared to the original one (see later Sect. 2.3.1) together to examine its effects in the retrieval of the optical properties. The EARLINET Polly (POrtabLe Lidar sYstem) lidars are sophisticated, automated Raman-polarization lidar systems for scientific purpose, but with the advantage of an easy-to-use and well-characterized 6 instrument with same design, same automated operation, and same centralized data processing delivering near-real-time data products. Polly systems have been developed and constructed at TROPOS with 180 international partners since 2002 (Engelmann et al., 2016). All Polly lidar systems are designed for automatic and unattended operation in 24/7 mode. Meanwhile 12 Polly lidar systems are distributed around the globe (e.g., Baars et al., 2016). The Polly lidar system used as a reference in this comparison analysis, is the first one of the Polly family (Engelmann et al., 2016), which was substantially upgraded in 2016 (v. Polly_1v2). It emits linearly polarized light at 532 nm with 5 receiver channels: the elastically backscattered 185 light at 532 nm, the cross-polarized light at 532 nm, the co-polarized light at 532 nm, the rotational-Raman The second EARLINET lidar, which is used as a reference in this work, is the dual receiver field-of-view  Table 1.

Experimental estimation of the overlap (OVP) function
The overlap (OVP) function, , is used to correct the P-MPL (no OVP-corrected) RCS profiles, ( ), as obtained from Eq. 1, at near-field altitudes, that is, where ( ) represents the overlap-corrected P-MPL RCS profiles.
In this work, the experimental procedure to obtain is based on the comparison of the ( ) to either the Polly RCS profiles, ( ), or the MARTHA ones, ( ), which are both used as reference 7 under relatively clean and mostly clear conditions. The Polly and MARTHA lidars present the advantage 215 in contrast to P-MPL system that the OVP function can be experimentally determined using their Raman channels (Wandinger and Ansmann, 2002). The P-MPL overlap function is thus calculated in terms of the ratio between the P-MPL and Polly/MARTHA RCS profiles, i.e., where ( ) denotes the reference RCS profiles as obtained from either Polly, ( ), or MARTHA, 220 ( ), measurements. Both sets of RCS profiles are normalized at a given height (higher than the OVP altitude range under aerosol-free conditions), , and then ( ) can be derived using Eq. 3. In particular, the full-OVP is conservatively obtained at the normalization height = 9.5 km a.g.l., being Once the OVP-corrected RCS is obtained from Eq. 3, the particle backscatter coefficient (PBC), (km -1 sr -1 ) can be derived applying the Klett-Fernald (KF) algorithm (Fernald, 1984;Klett, 1985) by constraining the lidar ratio (LR, extinction-to-backscatter ratio) with the AERONET Aerosol Optical Depth (AOD) (elastic KF solution) (Marenco et al., 1997); hence, an effective LR, , is also obtained after 235 convergence.
The particle linear depolarization ratio (PLDR), , can be determined as follows, where is the backscattering ratio ( = , being the molecular backscattering coefficient), is the volume linear depolarization ratio (VLDR), and is the molecular depolarization ratio. For P-240 MPL systems, = 0.0037 that is almost independent on atmospheric temperature (relative uncertainty < 0.1%), as their FWHM is less than 0.2 nm (Behrendt and Nakamura, 2002). The PLDR is a lidar parameter widely used for defining the aerosol type (Burton et al., 2012;Gross et al., 2013), and for discriminating the particle size mode in some aerosol mixtures (Mamouri and Ansmann, 2017;Córdoba-Jabonero et al., 2018), among others. The determination of PBC is mainly depending on the OVP correction, as will be 245 discussed in Sect. 3.3, and hence, the PLDR is also affected by OVP as well. Therefore, a good knowledge of the OVP function for the specific P-MPL system is also needed to obtain high-quality PBC and PLDR profiles.
The volume linear depolarization ratio (VLDR), , can be determined in relation with the P-MPL depolarization ratio, (Mishchenko and Hovenier, 1995;Gimmestad, 2008 i.e., the Eq. 2 is obtained, where is defined as the ratio between and (the two polarized RCS as described in Sect. 2.2.1). Since the OVP function is equally applied to both those signals, the VLDR is unaffected by the OVP correction; however, it actually affects, together with the PBC, the PLDR estimation 255 (see Eq. 5). Therefore, the VLDR for the P-MPL system was also experimentally evaluated in comparison with that derived from Polly lidar measurements, for instance, similarly to the approach shown by Córdoba-  differences are also found, mostly in the near-field range up to around 3 km height. However, by using ( ) instead of one of two others for P-MPL RCS correction, its relative error is just 14  5% in average from 0.3 up to 10 km height (see Fig. 2-bottom). Taking into account these errors, ( ) can be the OVP function used for correcting the P-MPL RCS profiles at near-field heights, following the expression in Eq.

300
3, as it seems to be the best proxy for OVP correction of the P-MPL RCS profiles.

310
The previous uncorrected and OVP-corrected P-MPL RCS profiles by using both and are shown in Figure 3. Slightly differences are observed for the P-MPL RCS profiles as compared to those Polly and MARTHA ones by using , despite it was calculated from averaging and , which were obtained from measurements on different days (only almost one month between them). Large differences are clearly found when is applied, mostly between 1.5 and 3 km height, evidencing 315 that the OVP function as provided by the manufacturer is not applicable after some time for aerosol research, being necessary an regular OVP determination, as performed and described in this work. Once

Volume linear depolarization ratio (VLDR)
Before analysing the OVP impact in the retrieval of the aerosol optical properties, the VLDR is also examined. As estated before, despite the VLDR is unaffected by the OVP correction, it actually affects, together with the PBC, , the PLDR, , estimation (see Sect. 2.4).
The P-MPL VLDR is calculated using Eq. 6 and compared with that derived from Polly measurements as 330 reference, since TROPOS follows all quality assurance efforts regarding polarization lidar calibration tests in the Polly systems as recommended by EARLINET (Freundenthaler et al., 2008. A dust outbreak case observed at Leipzig site for the night on 29-30 June 2019 is examined for that purpose. Figure 4 shows the VLDR as obtained from both the and profiles as averaged from 18 to 23 UT on 29 June and from 00 to 05 UT on 30 June (for clarity, only averaged profiles are shown). The dust signature is clearly 335 marked, showing a dust layer clearly confined between 3 and 6 km height, with a higher variability for the second interval due to the decay of dusty conditions at the end of that period, as reflected by a larger error uncertainty in time averaging. In overall, despite values seems to be higher than those , peaking between 0.11 and 0.14 in the dust layer, they are within the error range. Hence, the VLDR was averaged within several aerosol-free height-intervals, below and above that defined dust layer, to analyse potential 340 changes and offsets. Those mean values (and their standard deviation, SD) are shown in Table 2.

345
The aerosol-free background is marked by a grey dashed line.  Looking at the results, presents larger errors than those for , as associated to a lower signal-tonoise ratio as height increases for the Polly measurements (no smoothing applied). This is reflected by the higher relative error (%SD) found for the Polly VLDR (23%) w.r.t. to that for the P-MPL ( MPL systems. Therefore, the P-MPL VLDR must be also corrected by that offset using the expression: where is the corrected P-MPL VLDR profile, and is that VLDR as obtained from Eq. 2. Regarding the dust layer extended between 3.5 and 5.0 km height, as expected, a similar value to that obtained for the Polly VLDR ( = 0.11  0.02) is estimated for the corrected P-MPL VLDR, i.e., 365 = 0.12  0.02, as averaged within that dust layer. The corresponding PLDR to those are around 0.3 (as shown in Sect. 3.3), which are typical PLDR values for dust (Burton et al., 2012;Gross et al., 2013).

Particle backscatter coefficient (PBC) and particle linear depolarization ratio (PLDR)
The effect of the OVP correction on the P-MPL RCS is also analysed regarding the retrieval of the KFderived profiles, as obtained by applying both and to the RCS. A dust event as observed 370 at Leipzig on the night from 29 to 30 June 2019 (the same dust case as previously exposed in Sect. 3.2) is selected for that purpose. In addition, both PLDR, (see Eq. 5), and VLDR, (see Eqs. 6 and 7, ∆ offset corrected) are estimated. The OVP-induced effect is illustrated, in particular, using the vertical hourlyaveraged profiling observed on 29 June 2019 at 20-21 UT, corresponding to a well-separated two-layer dust case (dust optical depth of 0.061). Figures 5 and 6 show the vertical profiles of and (and ), 375 respectively, depending on the applied, as retrieved from the P-MPL measurements together to those derived from Polly ones for the selected case.
Both P-MPL and Polly datasets show a dust layer clearly confined between around 3.5 and 5.0 km height.
For comparison, in addition to the AOD-constrained KF solution for the PBC (reference height at 6.0 km, and reference backscatter coefficient of 10 -7 Mm -1 sr -1 ) using = 43 sr (that obtained from Polly elastic 380 13 measurements) (see Figs. 5a), is also retrieved by using the Raman-derived LR ( = 60 sr) for that dust layer as obtained from the night-time Polly Raman measurements (data not shown) (see Figs. 5b). Regarding the dust layer, relatively small differences are found between Polly and P-MPL profiles (see to Polly (red) and MARTHA (blue) data and both the (black) and (cyan) by using the KF solution with (a) the elastic AOD-constrained LR ( = 43 sr), and (b) the Raman-retrieved LR ( = 60 sr) for 400 the dust layer. Corresponding Polly-retrieved profiles are also included (green lines).
Nevertheless, the KF retrieval is mostly affected at near-field ranges (up to 3 km height) (see Fig. 5), as expected, since the OVP correction is rather relevant at those ranges. Negative values are predominantly found for the scenarios when the RCS is OVP-corrected by and , being more pronounced 405 when the is applied, since the LR to be applied in this height-interval must be closer to the elastic of 43 sr. The best fitting seems to be achieved by using and . Among those, however, results show that profiles are in a better agreement by using as compared to those Polly-derived at ranges from around 1 km down (see Fig. 5).

415
By examining the PLDR profiles, the dust signature is also clearly marked between around 3.5 and 5.0 km height, i.e., typical values for dust of around 0.3 are found (see Table 3), indicating a predominance of coarse particles. No differences are found between Polly and P-MPL PLDR profiles for that layer (see Fig.   6), with mean values of 0.330.01 (Polly) and 0.32-0.340.02 (P-MPL, depending on the applied and the LR used) (see Table 3).

4 Conclusions
A comprehensive two-month field intercomparison campaign has been performed in summer 2019 to characterize the performance of a polarized Micro-Pulse Lidar (P-MPL) system, and to check the quality of the retrieved aerosol products. Atmospheric observations of the P-MPL system have been examined against those from two reference EARLINET lidars (Polly and MARTHA), which are operative at Leipzig 425 site (Germany, 51.4ºN 12.4ºE, 125 m a.s.l.) as managed by TROPOS. In particular, an experimental assessment in terms of the overlap (OVP) correction and its impact in the retrieval of the aerosol optical properties has been achieved. Furthermore, the volume linear depolarization ratio (VLDR) has also been cross-checked and corrections applied, allowing an accurate retrieval. The aim of this work has been focused on the determination of the lidar-specific true OVP function and on investigating the accuracy of 430 both the retrieved particle backscatter coefficient (PBC) and particle linear depolarization ratio (PLDR) profiles.
It has been highlighted that the OVP function as delivered by the P-MPL manufacturer cannot be long used.
The reasons are manifold, but an suitable estimation of the OVP function should be recommended for the MPL system. The experimental procedure to determine the OVP function for the P-MPL system has been 435 described in the basis of the comparison to reference lidars. The optimal OVP function for correcting the P-MPL measurements has been obtained, together with its uncertainties, under clean observational conditions from simultaneous P-MPL and Polly/MARTHA observations, and compared with the original one as provided by the manufacturer. In addition, depending on the OVP function applied, the OVP correction-induced effects in the retrieval of both the PBC and PLDR for the P-MPL system have been 440 analysed for two KF solutions by using either the elastic (AOD-constrained) or the Raman-provided lidar ratios in comparison with those PBC and PLDR retrievals as obtained from simultaneous Polly observations. A dust case as observed at Leipzig is analyzed for that purpose. Additionally, despite the VLDR is OVP-unaffected, it has been also examined in comparison with the Polly VLDR regarding its effect in the PLDR determination. A suitable VLDR profile has been obtained, being only needed to be 445 corrected by a small offset value, which has been also estimated. Once P-MPL measurements were optimally OVP-corrected and the VLDR adjusted, both the PBC and PLDR profiles have been accurately derived by using the KF solution.
In overall, as a systematic requirement for lidar systems, an adequate OVP function determination and VLDR testing analysis is needed to be performed in a regular basis in order to correct the P-MPL 450 measurements and, hence, to derive suitable aerosol products (backscatter, depolarization, extinction). The procedure described in this study can be useful to be applied to similar P-MPL systems that cannot regularly where ∆ and ∆ are, respectively, the errors related to and .
∆ can be estimated as composed of two error contributions: one associated to instrumental corrections (energy fluctuations, instrumental calibrations, solar background, …), , as described in Welton and Campbell (2002),

475
In this work, the averaged function between and is also calculated, i.e., where ∆ ( denotes either Polly or MARTHA) is the error as obtained from Eq. A.2.

480
Data availability. All data generated and analysed for this study are available from the authors upon reasonable request.
Author Contributions. CC-J and AA designed the study and wrote the original draft paper. CC-J, AA, CJ and HB provided data. CC-J and CJ performed data analysis with contributions from AA, HB, M-AL-C and RE. All authors reviewed and edited the final version of the manuscript. All the authors agreed to the 485 final version of the paper.
Competing interests. The authors declare that they have no conflict of interest.