Experimental calibration assessment of a MPLNET/Micro-Pulse Lidar system in comparison with EARLINET lidar measurements for aerosol optical properties retrieval

Simultaneous observations of a polarized Micro-Pulse Lidar (P-MPL) system, currently operative within MPLNET (NASA Micro-Pulse Lidar Network), with two referenced EARLINET (European Aerosol Research Lidar Network) lidars, running at Leipzig site (Germany, 51.4oN 12.4oE, 125 m a.s.l.), were performed during a comprehensive two-month field campaign in summer 2019. A calibration assessment regarding the overlap (OVP) correction of the P-MPL signal profiles and its 15 impact in the retrieval of the optical properties is achieved, describing also the experimental procedure used. The optimal lidar-specific OVP function for correcting the P-MPL measurements is experimentally determined, highlighting that the OVP function as delivered by the P-MPL manufacturer cannot be 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 referenced lidars seems to be the best proxy at both 20 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) and the particle linear depolarization ratio (PLDR) is examined. First, the volume linear depolarization ratio (VLDR) profile is obtained and compared to the reference lidars, showing it needs to be corrected by a small offset value within a good accuracy. Once P-MPL measurements are optimally OVP-corrected, the PBC profiles (and hence the 25 PLDR ones) can be derived using the Klett-Fernald approach. In addition, an alternative method based on the separation of the total PBC into their aerosol components is presented in order to estimate the total particle extinction coefficient (PEC) profile, and hence the Aerosol Optical Depth, from elastic P-MPL measurements. A dust event as observed at Leipzig in June 2019 is used for illustration. In overall, an adequate OVP function is needed to be determined in a regular basis to calibrate the P-MPL system in 30 order to derive suitable aerosol products.

3 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) in order to retrieve plausible aerosol optical properties.
The P-MPL is an elastic coaxial single-wavelength (532 nm) system and, differing from older MPL 80 versions (Campbell et al., 2002;Welton et al., 2002), incorporates depolarization capabilities (Flynn et al., 2007). It can operate in routine continuous (24/7) mode. From an instrumental point of view, the principal disadvantage 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. Then, a qualified calibration must be performed in these systems. In this framework, an experimental campaign 85 was planned at the EARLINET Leipzig site (Germany, 51.4ºN 12.4ºE, 125 m a.s.l.), and devoted to compare P-MPL observations simultaneously with reference well-calibrated lidar measurements, and hence to determine the required P-MPL calibrations.
The aim of this work is fourfold: 1) to achieve an OVP calibration of the P-MPL system, i.e., to estimate the experimental OVP function for correcting the P-MPL measurements; 2) to evaluate the volume linear 90 depolarization ratio (VLDR), which is a lidar-derived parameter independent of OVP calibration; 3) to determine the P-MPL calibration-induced effects on the retrieval of optical properties, both the heightresolved particle backscatter coefficient (PBC) and particle linear depolarization ratio (PLDR); and 4) to present an alternative method based on the separation of the PBC into their aerosol components (for instance, as applied to a dust event) in order to estimate the vertical profile of the particle extinction 95 coefficient (PEC) (and also the columnar total extinction, i.e., the Aerosol Optical Depth, AOD) from elastic P-MPL measurements. Section 2 introduces the methodology for that purpose, where the field campaign performed, the P-MPL and reference lidar systems used and the data analysis of the experimental approaches applied are particularly described: the experimental procedure for accurately characterizing the OVP function of the P-MPL systems, the correction of the VLDR, and the 100 determination of the optical properties. Results are presented in Section 3, regarding the experimental estimation of the OVP function (error processing is described in Annex A), the evaluation of the VLDR, and the retrieval of the particle optical properties. A dust case as observed during the field campaign is used for that purpose. Main conclusions are presented in Section 4.
2 Methodology 105 2.1 Field campaign A field campaign was performed at the EARLINET station of Leipzig, Germany (51.35ºN 12.43ºE, 125 m a.s.l.), managed by the Leibniz Institute for Tropospheric Research (TROPOS), for 6 weeks in June-July 2019 in order to mainly calibrate a P-MPL system with a special emphasis on the OVP correction.
The lidar system used was the MPL44245 unit (Sigma Space Corp.) routinely operating at the 110 MPLNET/El Arenosillo station at Huelva, Spain (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 campaign, the ARN/Huelva P-MPL was temporarily deployed at Leipzig to be 4 compared against two EARLINET lidars routinely operative in this station. Those are the Polly 115 (POrtabLe Lidar sYstem;Althausen et al, 2009;Engelmann et al., 2016) and the MARTHA (Multiwavelength Tropospheric Raman lidar for Temperature, Humidity, and Aerosol profiling; Jiménez et al., 2018) systems, which were used as reference since 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;Wandinger et al., 2016;Belegante et al., 2016;120 Aranda et al., 2016;Freudenthaler et al., 2016   The laser light is alternatively transmitted linearly and circularly polarized to the atmosphere by switching between two retardation modes of a liquid crystal retarder (LCR). The corresponding backscattered light to those two polarized states by passing through a beam splitter to the single APD is registered in 140 5 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 LRC polarization mode (LCR switching time of 133 µs) within every integrating minute. That is, those two signals are alternatively detected by the same APD, being recorded in two polarized 'channels': the 145 532-nm cross-signal ( ) and the 532-nm co-signal ( ). Therefore, since no potentially existing efficiency or alignment differences are between those two 'channels' (as used a single APD), no corrections for these effects are required, as it is typically needed for ordinary two-channel polarization lidars. The measured lidar signal in those two polarized-channels is used to derive the P-MPL total rangecorrected signal (RCS), , following the methodology as described in Flynn et al. (2007), that is, 150 = + 2 . More details on P-MPL signal correction and data processing can be found in Córdoba-Jabonero et al. (2018). Among the required instrumental P-MPL calibrations (Campbell et al., 2002;Welton et al., 2002), the OVP correction 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. Therefore, after purchase, the P-MPL system is 155 delivered with an original OVP function as provided by the manufacture company (Sigma Space Corp.), which, however, must be re-evaluated with time. Indeed, one of the goals of this work is to show the experimental procedure to obtain a new OVP calibration for the P-MPL lidar as compared to the original one, as will be exposed in Sect. 2.3.1, together to examine their 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 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 165 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 170 backscattered light at 532 nm, the cross-polarized light at 532 nm, the co-polarized light at 532 nm, the The second EARLINET lidar, which is used as a reference in this work, is the dual receiver field-of-view (RFOV) Multiwavelength polarization/Raman lidar for Temperature, Humidity, and Aerosol profiling 180 (MARTHA) (Mattis et al., 2008;Schmidt et al., 2013, Jimenez et al., 2019. MARTHA has a powerful laser, transmitting in total 1 J per pulse at a repetition rate of 30 Hz, with an 80-cm telescope diameter, being thus well designed for tropospheric and stratospheric aerosol observations. This lidar system measures Raman signals at 532 nm ( , which is that used in this work) and 607 nm and the polarization-sensitive 532-nm backscatter signals at two RFOVs so that, besides aerosol profiles, cloud 185 microphysical properties can be retrieved from measured cloud multiple scattering effects. MARTHA can provide the 532-nm particle depolarization ratio as measured with the smaller RFOV, and also the 355-, 532-, and 1064-nm particle backscatter coefficients and the 355-and 532-nm extinction coefficient profiles with their corresponding lidar ratio profiles. For this large telescope (and a selected receiver FOV of 0.5 mrad) the overlap between laser beam and receiver FOV is complete around 2000 m height. The 190 overlap profile of this laboratory lidar is very stable. The main instrumental features of the MARTHA system are shown in Table 1.

Experimental estimation of the overlap (OVP) function for P-MPL systems
The overlap (OVP) function, , is used to correct the P-MPL RCS profiles, ( ), 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 under mostly clean and clear conditions. The Polly and MARTHA lidars present the advantage 200 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, 205 ( ), measurements. Both sets of RCS profiles are normalized at a given height (higher than the OVP altitude range), , and then ( ) can be derived using Eq. 2. In particular, the full-OVP is obtained at the normalization height = 9.5 km a.g.l., being ( ) = 1 at ≥ . Errors associated to the estimation of ( ) using this experimental approach are described in Annex A. Lidar observations performed under relatively clean conditions at the Leipzig station were used for the P-MPL 210 OVP calibration.
2.4 Determination of the aerosol optical properties 2.4.1 Retrieval of the particle backscatter coefficient, and both the volume and particle linear depolarization ratios Once the OVP-corrected RCS is obtained from Eq. 1, the particle backscatter coefficient (PBC), (km -1 215 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); hence, an effective LR, , is also obtained after 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 ( = 0.0037 for P-MPL systems; 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), 225 among others. The determination of PBC is mainly depending on the OVP correction, as will be 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 230 depolarization ratio, (Mishchenko and Hovenier, 1995;Gimmestad, 2008). Following Flynn et al. (2007), can be easily expressed as where is defined as the ratio between and , which are the two polarized RCS as described in Sect. 2.2.1. Since the OVP correction is equally applied to both those signals, the VLDR is unaffected 235 by the OVP calibration. Hence, the VLDR for the P-MPL system was examined in comparison with that derived from Polly lidar measurements. All those variables are height-resolved, but the altitude dependence is omitted for simplicity. A dust case occurring for the night on 29-30 June 2019 at the Leipzig station is selected for that purpose.
2.4.2 Estimation of the particle extinction coefficient from elastic P-MPL measurements 240 The particle extinction coefficient (PEC) is also a height-resolved variable. However, its estimation from elastic lidar observations is a relevant concern due to the indetermination in solving the lidar equation for elastic systems. Usually, a KF solution can be derived by assuming an effective LR, , which is a constant in height value (see Sect. 2.4.1).
An alternative simple method is introduced in order to estimate the PEC profiles, ( ), from elastic P-245 MPL measurements without assuming a constant LR. That approach is based in the combination of the POLIPHON algorithm (Mamouri and Ansmann, 2017) with elastic P-MPL measurements, as described in Córdoba-Jabonero et al. (2018), and was similarly used in Giannakaki et al. (2020), showing the potential of elastic and polarized lidars for vertical extinction retrieval. A dust case study observed at Leipzig in where refers to the Dc, Df, and ND components, being their corresponding pure LR, which are assumed to be 55 sr for Dc and Df, and 25 sr for ND components (Ansmann et al., 2019). The vertical total PEC, ( ), can be calculated as follows the total aerosol extinction in the overall atmospheric column (i.e., the AOD), where ∆ is the lidar vertical resolution, and indicates the discrete n-bin height-level ( = 1, …, N), being the reference 265 height under aerosol-free conditions.   differences are also found, mostly in the near-field range up to around 3 km height. However, by using 300 ( ) 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 calibration function used for correcting the P-MPL RCS profiles at near-field heights, following the expression in Eq. 1, as it seems to be the best proxy for OVP correction of the P-MPL RCS profiles. 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 315 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 that the OVP function as provided by the manufacturer is not applicable after some time for aerosol research, being necessary an regular OVP recalibration, 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 330 examined. Despite the VLDR is unaffected by the OVP calibration, it actually affects, together with the PBC, , the PLDR, , estimation (see Sect. 2.3.2).
The P-MPL VLDR is calculated using Eq. 8 and compared with that derived from Polly measurements as 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, 2016. A dust 335 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 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 340 reflected by a larger error uncertainty in time averaging. In overall, values are higher than those , peaking between 0.11 and 0.14 within the dust layer. Hence, the VLDR was averaged within several aerosol-free height-intervals, below and above that defined dust layer, to analyse potential changes and offsets. Those mean values (and their standard deviation, SD) are shown in Table 2.

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This offset represents a correction to account for any slight mismatch in the transmitter and detector polarization planes and any impurity of the laser polarization state (Sassen, 2005), as also found in Córdoba-Jabonero et al. (2013) by characterizing the VLDR of a relatively older version (MPL-4) of the polarized MPL systems. Therefore, the P-MPL VLDR must be also corrected by that offset using the expression:  (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 KF-  Regarding the dust layer, relatively small differences are found between Polly and P-MPL profiles (see Figs. 5a and 5b), at least within error uncertainties. In order to assess those differences between both 395 datasets, the layer-averaged PBC, (Mm -1 sr -1 ), and the integrated backscatter, (sr -1 ), for this 3.5-5.0km dust layer were calculated to be used as a proxy of the degree of agreement. Derived and values in dependence of for both the KF solutions (using either or ) are shown in Table 3. In general, and are higher for P-MPL w.r.t. Polly retrievals. Concerning the KF solutions for P-MPL profiles, a better agreement is achieved when the of 60 sr is applied (no AOD-constrain), i.e., 400 lower differences for and are found w.r.t. Polly-retrieved values. range of between 0.5 and 3.5 km height (the x-axis is also accordingly scaled). Corresponding Pollyretrieved profiles are also included (green lines).

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Nevertheless, the KF retrieval is mostly affected at near-field ranges (up to 3 km height) (see Figs. 5b and 5d), 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 when the is applied, since the LR to be applied in this height-interval must be 415 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 Figs. 5a and 5c).

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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 large differences are found between Polly and P-MPL PLDR profiles for that layer (see Figs. 6a and 6b), with mean values of 0.29 (Polly) and 0.31-0.34 (P-MPL, 430 depending on the applied and the LR used) (see Table 3).

Particle extinction coefficient (PEC) retrieval for a dust case study
Once is experimentally determined to correct the P-MPL RCS profiles (see Sect. 3.1), the total PBC can be retrieved by using the KF algorithm (a is also estimated against AERONET AOD constraint).
The PLDR was also obtained by using the PBC and the corrected VLDR (see Sect. 3.2). In addition, 435 using the approach as described in Sect. 2.4.2, the vertical total PEC profile, , and that corresponding to by using the KF-derived effective LR ( = 43 and 25 sr are obtained, respectively, for the pure and mixed dust cases) and those by applying Eq. (6) are clearly shown for both dust scenarios.
In general, the KF solution for the total extinction seems to be underestimated, although values as obtained from Eq. 7 differ from the effective total extinction (by using ) in -6.4% and +25.7%, respectively, for the pure ( = 0.103; Fig.7) and mixed ( = 0.264; Fig. 8) dust cases. However, in those 455 particular dust scenarios, the largest discrepancies are mostly found in layers with dust (Dc and Df) detection (see and profiles, i.e., red and green lines, respectively, in Figs. 7-left and 8-left), regarding the difference in the LR applied between the effective value and that assumed typical for dust (55 sr). This is mainly observed for the dust mixed case (Fig. 8), as that LR difference is higher than that for the pure case. Indeed, the total extinction associated to layers with dust predominance is +26.7% and 460 +56.7% of the corresponding effective value found, respectively, for the pure (3.5-5.0 km; see

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Therefore, the crucial point is concerning to the particular vertical aerosol extinction layering that is estimated by using either the effective KF-derived solution or the introduced depolarization-based method as observed in both dust scenarios. Indeed, this is especially relevant for the aerosol impact in atmospheric and climate research (atmospheric composition, radiative effect, cloud nucleation, …).
Moreover, this method can be easily used as an alternative approach for extinction retrieval in other 470 elastic polarized lidar systems.

Conclusions
A comprehensive two-month field 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 products. Atmospheric observations with the P-MPL system, currently operative within MPLNET, have 475 been examined against those from two referenced EARLINET lidars (Polly and MARTHA), which are characterization assessment in terms of the overlap (OVP) correction and its impact in the retrieval of the 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 480 been focused on the determination of the lidar-specific true OVP function and on investigating in detail the accuracy of 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 used.
The reasons are manifold, but an experimental assessment of the OVP calibration should be recommend 485 for the MPL systems. The experimental procedure to determine the OVP function for the P-MPL system has been described in the basis of the comparison to reference lidars. The optimal OVP function for correcting our P-MPL measurements has been experimentally 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 490 function applied, the calibration-induced effects on the retrieval of both the PBC and PLDR for the P-MPL system have been 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.
Additionally, the VLDR has been also examined in comparison with the Polly VLDR regarding its effect 495 in the PLDR determination. A suitable VLDR profile has been usually obtained, being only needed to be corrected by a small offset value, which has been also estimated.
Once P-MPL measurements were optimally OVP-corrected, the PBC, and also the PLDR, profiles have been accurately derived by using the KF solution (an effective LR is obtained in constraint with AERONET AOD). In addition, an alternative method has been introduced to derive the vertical particle 500 extinction coefficient (PEC) profiles from elastic P-MPL measurements in combination with the POLIPHON algorithm by separating the optical properties into those corresponding to each component within aerosol mixtures. A dust event occurred at Leipzig in June 2019 is used for illustration, selecting two different dust scenarios: a well-differentiated dust layer and a mixed dust case. This is especially relevant for elastic lidars, as the P-MPL system among others, due to the indetermination in solving the 505 lidar equation.
In overall, an adequate OVP function is needed to be determined in a regular basis in order to calibrate the P-MPL system and, hence, to derive suitable aerosol products (backscatter, depolarization, extinction). where ( ) are the P-MPL RCS profiles, which are compared against those reference lidar measurements, ( ) ( denotes either Polly or MARTHA) using the experimental approach as described in this work.

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The error associated to the determination of the OVP function, ∆ , is obtained from error propagation calculations of the Eq. A.1. In this sense, it can be expressed as ( -dependence is omitted for simplicity, hereafter) where ∆ and ∆ are, respectively, the errors related to and .

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∆ 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), and another one reflecting the atmospheric variability within the time- where ∆ ( denotes either Polly or MARTHA) is the error as obtained from Eq. A.2.
Data availability. All data generated and analysed for this study are available from the authors upon 535 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, MAL-C and RE. All authors reviewed and edited the final version of the manuscript. All the authors agreed to the final version of the paper.

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Competing interests. The authors declare that they have no conflict of interest.