Understanding the aerosol vertical stratification can help in reducing the uncertainties related to aerosol radiative forcings which remain large . For more accurate estimations, it is essential to improve the knowledge of the aerosol characteristics: shape, size, and optical properties. The diversity of combinations of aerosol sources and transport mechanisms leads to the high variability of the distribution of aerosols with different characteristics, which makes their classification a complicated task .

Lidar has become a widely used tool for studying highly resolved information on the spatial and temporal distribution of aerosols. On this, several key campaigns, such as SAMUM–1, SAMUM–2 , and the ASKOS experiment , were performed, and they successfully demonstrate the capabilities of lidar systems. These were not the first to demonstrate aerosol lidars: earlier works include those of , , and . In contrast to traditional setups with in situ or airborne sensors, like optical particle counters (OPCs) or particle sizers , lidars (ground- or satellite-based) can provide information on the temporal variability and on the vertical structure up to the stratosphere. In addition, they provide insights on aerosol size and optical properties.

Cyprus, situated between large deserts, is actively involved in advancing atmospheric science and aerosol research. The region's unique location has made it an invaluable site for diverse studies on dust, among other aerosol types (e.g., detection of Canadian wildfire smoke over Cyprus; ). For example, Mamouri and Nisantzi's work introduced novel methodologies for dust profiling using polarization lidar, analyzing dust outbreaks over Cyprus. explored lofted fire smoke plumes' mineral dust content and compared extinction ratios for desert dust in Cyprus. comprehensively detailed extreme dust storms in the Cyprus region, showcasing EARLINET observations. Additionally, studies by and compared UAV-based OPC observations with lidar, enriching knowledge on Saharan dust over Cyprus. Moreover, the key campaigns CyCARE and A-LIFE had strong contributions by depolarization lidar and aimed to investigate properties of complex aerosol mixtures often observed over the island of Cyprus . These collective efforts highlight Cyprus's significant contributions to the understanding of aerosol properties.

The contribution of lidar to greater science is undoubtedly important as it is a fundamental tool for monitoring anthropogenic and natural aerosols. Sand and dust storms, or volcanic ash transport in the case of volcanic eruptions, can impact human health and everyday life. The WMO's Sand and Dust Storm Warning Advisory and Assessment System (SDS-WAS) benefits from available lidar networks (e.g., EARLINET; ) for the monitoring of vertical profiles of winds and aerosols . Similarly, lidars installed across different locations aim to improve detection and aid forecasting of volcanic ash in the event of future eruptions by providing observations to local Volcanic Ash Advisory Centers (VAACs) .

The addition of a depolarization channel on a lidar system offers the capability to discriminate between different types of atmospheric particles, for example, low-depolarizing urban aerosols and high-depolarizing dust aerosols or liquid and ice clouds. Discriminating between liquid and ice water can provide a better understanding of the aerosol–cloud interactions (e.g., ). Aerosols can change the properties of clouds, therefore affecting indirectly their radiative forcing . Aerosol typing can be quite complex when the observed atmospheric layers consist of multiple aerosol types.

Lidar depolarization measurements represent an excellent method to detect and quantify some specific aerosol types such as dust and volcanic ash . Using this information, several studies aim to describe the properties and temporal evolution of each of the aerosol layers types . They also permit the distinction between ice crystals and water droplets and the discrimination of types of polar stratospheric clouds . The depolarization lidar technique is simple and reliable and is not as limited by daylight background as in the case of acquiring Raman signals.

Spherical particles in the atmosphere have no depolarization for 180° backscattering ; hence, a depolarization signal is an indication of non-sphericity such as in ice crystals or irregularly shaped aerosols. Most lidar systems use linearly polarized lasers (linear depolarization measurements), and such systems are used also in this paper. Some circular polarization lidar systems exist, such as the Enhancement and Validation of ESA products (eVe), which provide useful information for layers with oriented particles and where multiple scattering cannot be neglected .

The volume linear depolarization ratio (VLDR), or simply volume depolarization ratio (VDR), is usually defined as the ratio between the atmospheric cross sections for cross-polarized and co-polarized backscattering and is a measure of the overall properties of the atmospheric volume, comprising a mixture of molecules and particles. This is typically measured by means of a polarizing beamsplitter (PBS) in the receiving system and by taking the ratio of signals in the two channels. In reality, the measurement is more complex than this, and it requires accounting for the gain ratio of the channels and for the cross-talk between them: this is what we refer to here as the determination of the lidar polarization parameters. If this step is not achieved correctly, systematic errors appear with a significant impact.

Addressing instrumental effects on depolarization channels is pivotal, as numerous optical components within lidar systems can introduce substantial systematic errors in atmospheric depolarization values. introduced analytical equations to assess the dependence of lidar signals on polarization parameters and different calibration setups. Both and emphasize that systematic errors can be significant if the lidar system is not well characterized and aligned, underscoring the need for careful consideration of optical components. Well-characterized VDR measurements permit, on the one hand, reconstruction of the total lidar signal by the recombination of the two channels: this is needed for the retrieval of the particle backscattering and extinction coefficients. On the other hand, they permit the computation of the particle linear depolarization ratio (PLDR), or simply particle depolarization ratio (PDR), which abstracts from the influence of air molecules and is hence an intrinsic property of the particles . In a well-characterized lidar system for depolarization, the channel gain ratio and all the elements contributing to an imperfect separation of the depolarization channels in the hardware are well known. The latter includes the polarizing beamsplitter transmittances and reflectances for the co-polar and cross-polar beams, as well as the laser polarization purity and its rotation angle compared to the frame of reference of the receiver . In particular, the laser rotation angle ϕ is not easily known, and an additional experimental apparatus has been used in a few papers in order to quantify it . The additional apparatus consists of a rotatable half-wave plate (HWP) added in front of the receiver optical path, and a calibration sequence has to be performed where atmospheric measurements are acquired by artificially varying the system’s cross-talk through the rotation of the half-wave plate.

At the Cyprus Institute (CYI), we have recently acquired a new compact Cimel CE376 lidar system, which we have operated continuously in Nicosia, Cyprus, since September 2021. This is a low-power and compact two-wavelength lidar system, ideal for campaigns and mobile observations, able to operate in all weather conditions, and able to detect the molecular signal up to 10 km in the daytime and 18 km in the nighttime with a good signal-to-noise (SNR) ratio. We have, however, found an issue in the initial depolarization calibration related to the observed VDR of purely molecular layers, which is too high compared to the expected value computed according to . Whereas a technological solution is planned with Cimel in the near future, this paper is about a method for correcting past data by correlating the lidar measurements to a reference-calibrated lidar system, also located on the island, which for this paper we consider to be our reference system. This will be called the atmospheric characterization approach to the lidar polarization parameters.

In Sect. 2, we present the depolarization lidar equations to be used for the depolarization characterization. Then, in Sect. 3, we describe the systems used in this study, focusing on the technical characteristics and locations. Section 4 presents the lidar depolarization characterization methodology, providing demonstration examples from past observations. Finally, Sect. 5 summarizes and concludes the main findings of the application of the discussed method.

In an ideal depolarization lidar, the range-corrected signal in the co-polar and cross-polar channels, P∥ and P⟂, can be expressed as follows, in the function of the atmospheric-volume cross sections β∥ and β⟂ for non-depolarizing and depolarizing backscattering, respectively: 1P∥(R)=K∥T(R)β∥(R)2P⟂(R)=K⟂T(R)β⟂(R), where R is the range, T(R) is the two-way atmospheric transmittance between ranges 0 and R, and K∥ and K⟂ are the lidar constants for both channels.

The VDR is defined as the ratio δ=β⟂/β∥. Note that cross-polarizing backscatter β⟂ is unphysical and that other definitions of the VDR exist in the literature see. However, the one used here has been commonly used in the legacy lidar literature e.g.,. In the ideal case, the VDR is computed as 3δ=δ∗K∗, where δ∗=P⟂/P∥ is the ratio of the two lidar signals (a sort of uncalibrated depolarization ratio) and K∗=K⟂/K∥ is the gain ratio between the two channels. For an ideal lidar, determining K∗ is all that is needed to calibrate depolarization. Once this is done, the lidar range-corrected total signal, P, can be reconstructed as a signal proportional to β∥+β⟂. Hence, 4P=P∥+P⟂K∗.

P(R) is what will be used in aerosol inversion schemes such as Fernald–Klett or Raman inversion .

For a real depolarization lidar system, the equations need to account for the cross-talk between the two channels through the cross-talk constants, denoted as g and e in this paper, expressing, respectively, how much co-polar signal enters the cross-polar channel and vice versa, leading to the following expressions: 5P∥=K∥Tβ∥+eβ⟂6P⟂=K⟂Tβ⟂+gβ∥.

By dividing Eqs. () and () we derive δ∗, 7δ∗=K∗δ+g1+eδ, which can be resolved as follows: 8δ=δ∗-K∗gK∗-eδ∗, and the total signal can be then calculated by 9P=(1-g)P∥+(1-e)P⟂K∗.

These full equations are going to be applied for the determination of the polarization parameters. In and , the approach is that they know their system well enough, including the various parameters contributing to errors in depolarization calibration, for calibration to only involve determining K∗. In our case, we assume we do not know our system to this point, and we will retrieve these parameters from observations and a reference system (we call this the three-parameter depolarization characterization, since K∗, g, and e are to be retrieved).

The effect of g will usually dominate in low-depolarization layers (e.g., particle-free or spherical-particle layers), so that we can attempt to simplify Eq. () by neglecting e: 10δ=δ∗K∗-g, which can be summarized in a phrase by saying that, in addition to knowing the gain ratio K∗, we must also know the “depolarization of the lidar system”, g (more precisely diattenuation), or alternatively that the depolarization equation involves a multiplicative and an additive parameter. Whereas it may not be the most correct way to neglect e for all lidar systems, this simplified equation has been used in the past for some systems: for example, it was used in Eq. 5 and in Eq. 6. We call the approach using this simplified equation the two-parameter depolarization characterization (given that only K∗ and g can be determined). It must be noted that in high-depolarizing layers, the contribution of e is larger; therefore it should not be neglected (unless e≪1 for a particular system).

The following sections investigate these approaches and will highlight their advantages and drawbacks and compare their outcomes.

In this section, we describe the methodology on how to determine polarization parameters for the Cimel lidar using the PollyXT as our reference system for selected cases during dust events for both periods 1 and 2, as seen in Table . For the atmospheric depolarization characterization, we selected cases with dust layers that were part of the long-distance advection of dust from nearby deserts. Dust over the island is considered to be fairly homogeneous in the free troposphere, and the distance between the PollyXT and Cimel lidar is much smaller than the distance traveled from source regions. Ideally, an intercomparison should be done with both systems side by side to sample the same air mass. If this is not possible, for example, when already-existing data need to be corrected, someone has to select the cases carefully. For this paper, data were already available from the Cyprus Fall Campaign 2021, during which the two stations were separated by ∼ 60 km. Due to this spatial distance between the two lidars and the mountains in the area, the VDR could change because of atmospheric changes, e.g., temperature and relative humidity. In addition, it is recognized that pollution originating from northern African states might impact long-transported dust plumes. Studies, such as , have demonstrated how this pollution can alter the lidar observations, mainly by reducing the depolarization ratio.

Hence, it is important to carefully select the cases for which both lidars measure similar VDR profiles based on the following criteria: (i) dates with dust layers detected above 3 km, exceeding the topographic obstacle of the Troodos mountain range in the center of the island; (ii) molecular signal above the dust layer; (iii) selection of only nighttime profiles, to improve SNR; (iv) cloud-free scenes or high-level clouds only; and (v) general assessment of the meteorology to confirm the origin of air masses as being due to long-range transport. For all the cases used for the determination of polarization parameters, we have performed HYSPLIT back trajectories (Fig. ) to demonstrate that the air masses at arrival heights corresponding to the peak VDR values are produced over long distances and therefore are not affected by local effects. We believe that it is reasonable to neglect local differences for well-selected cases of free tropospheric layers having been transported from the same source region for more than 3000 km, given the short distance (60 km) between the two stations.

The method is based on some important assumptions. Firstly, we assume that the dust layer VDR is identical above 3 km in the profiles measured by the two systems. The second assumption is that there is no time shift between the two measurements. Only depolarization at 532 nm will be considered from the PollyXT, which is the wavelength of the Cimel lidar depolarization measurements that we wish to characterize.

Before comparing the profiles from the two instruments, we apply time integration and smoothing on the CE376 and PollyXT measurements to a common temporal and vertical range resolution (1 h and 82.5 m, respectively). The timestamps provided in this paper align with the starting moments of each 1 h interval. As a last step, we correct for the vertical shift observed in the profiles of the two lidars. This correction aims to remove the altitude difference between the two locations in the case of a sloping layer (more on this correction in Appendix ).

We demonstrate the proposed depolarization characterization approach using profiles from two nights that follow the criteria described before. As the dataset was limited (due to the selection criteria, i.e., dust layer above 3 km), the selected cases are taken from days with uniform dust layers over the island and for which the profiles of the two systems do not seem to be influenced by any local phenomena. The first profile corresponds to 26 November 2021, 22:00 UTC, and it is taken from a 5 d long dust event arriving from the Sahara (confirmed with HYSPLIT back trajectories; Fig. a), resulting in daily average AOD500nm values of 0.14 and 0.08 over Nicosia and Limassol, respectively (AERONET, https://aeronet.gsfc.nasa.gov, last access: December 2023). During this event, one uniform dust layer was observed from 2 to 4 km. The second profile corresponds to 16 February 2022, 21:00 UTC, and it is extracted from a relatively shorter event (2 d long) during which dust was also advected from the Sahara to Cyprus (Fig. b), but this time it was not as uniform in the vertical direction, with some distinct layers seen around 4 km. A cirrus cloud layer was also identified from 6 to 10 km. For the second event, the daily AOD500nm average over Nicosia was 0.20, whilst no data were available from Limassol's sun photometer. The VDR profile time series of the days from which we extracted the timestamps are seen in Fig. . From this figure we see how similar the VDR is at the high-depolarizing layers.

We have presented and demonstrated a method for determining the polarization parameters using observations from a reference instrument at a nearby location. Our approach accounts for the cross-talk between the co-polar and cross-polar channels by employing a set of equations that contain three parameters, K∗, g, and e, using observations from a reference lidar. We examined the ability of this method to characterize VDR observations from a lidar, for which the standard calibration procedures could not fully account for the cross-talk, by utilizing VDR measurements from a reference lidar and a previously calibrated lidar. The aim is to obtain the correct depolarization of dust layers and approach the calculations based on for the molecular layers.

Results are shown for both a simplified version of this method, the two-parameter approach, where the cross-polar interference into the co-polar channel (e) is neglected, and the three-parameter approach, where all parameters are to be retrieved. As a whole, the depolarization characterization approach of this paper corrects the depolarization values of both high- (i.e., dust) and low-depolarizing (i.e., molecular) layers and permits the estimation of the cross-talk parameters. The reliability of the atmospheric depolarization characterization method is supported by observing reduced discrepancies in the VDR when compared to expected VDR values at molecular layers. The relative difference in VDR to the reference observations at dust layers is less than 1 % after the application of the two-parameter approach.

The application of the three-parameter approach was more challenging, mainly due to there being few cases which satisfy the criterion of having two independent aerosol layers above 3 km in one profile. Based on these cases the recalculated parameters K∗ and g did not change more than 5 %. We found from the results of the three-parameter approach that e was compatible with 0 considering its uncertainty and could therefore be neglected, thus justifying the two-parameter approach.

The calculated polarization parameters from different cases (9 and 12 timestamps for the periods 1 and 2, respectively) vary little over the examined periods, allowing us to apply average parameters calculated for the specific system for calculating the VDR over longer periods, as was shown in this study. The application of the average instead of the profile-specific polarization parameters leads to negligible differences at the high- and low-depolarized layers, which is acceptable as it remains within the uncertainty of the method. Nevertheless, the system's degradation could affect the polarization parameters; therefore, it is suggested that these are re-evaluated on a seasonal basis and at every system upgrade. The applied polarization parameters are found to reduce significantly the VDR discrepancies between the tested and the reference lidar in cases where distinct and similar dust layers are observed, thus justifying their retrospective application to be able to use existing valuable data acquired during campaigns.

The EARLINET campaign 2009 (EARLI09) suggests a detailed methodology on the intercomparison approach, requiring all systems to be placed side by side for several days before being deployed at their measuring locations, in order to be able to combine observations from different instruments and techniques . We need to emphasize that this was not possible in our case, as we are attempting a retrospective characterization of Cyprus 2021 Fall Campaign observations. However, these guidelines should be followed whenever possible, and, for the future, we plan an upgrade of the system to have a reliable calibration upfront.

This depolarization characterization method, demonstrated here for the first time, provides a good alternative for systems for which the user does not know the values of g and e a priori; therefore, it can be applied where traditional calibration procedure fails to correct the cross-talk in the depolarization channels. According to , lidar systems which are not well characterized and well aligned can lead to large systematic errors in the depolarization values. Reducing the errors related to the depolarization observations will therefore reduce the total uncertainty of aerosol typing studies (e.g., ) or mass concentration retrievals (e.g., ), for which the particle linear depolarization ratio is a key parameter.

It is noteworthy to highlight that, in the work of , a comprehensive theoretical framework for depolarization calibration was introduced, significantly expanding the scope of influencing quantities and parameters. A different approach for atmospheric calibration would be to apply an intercomparison that takes into account these parameters and includes a more comprehensive error calculation.

Using the presented method, valuable data obtained during the Fall Campaign 2021 in Cyprus can be corrected and used for further research on aerosol characteristics and stratification.