In this paper a statistical study of cirrus geometrical and optical properties based on 4 years of continuous ground-based lidar measurements with the Barcelona (Spain) Micro Pulse Lidar (MPL) is analysed. First, a review of the literature on the two-way transmittance method is presented. This method is a well-known lidar inversion method used to retrieve the optical properties of an aerosol–cloud layer between two molecular (i.e. aerosol and cloud-free) regions below and above, without the need to make any a priori assumptions about their optical and/or microphysical properties. Second, a simple mathematical expression of the two-way transmittance method is proposed for both ground-based and spaceborne lidar systems. This approach of the method allows the retrieval of the cloud optical depth, the cloud column lidar ratio and the vertical profile of the cloud backscatter coefficient. The method is illustrated for a cirrus cloud using measurements from the ground-based MPL and from the spaceborne Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP). Third, the database is then filtered with a cirrus identification criterion based on (and compared to) the literature using only lidar and radiosonde data. During the period from November 2018 to September 2022, 367 high-altitude cirrus clouds were identified at 00:00 and 12:00 UTC, of which 203 were successfully inverted with the two-way transmittance method. The statistical results of these 203 high-altitude cirrus clouds show that the cloud thickness is 1.8

The radiative effect of high-altitude cirrus clouds plays a fundamental role in the global radiation budget

Cirrus clouds are mainly composed of ice crystals and can form through different atmospheric mechanisms, giving rise to cirrus clouds with different physical, geometrical and optical properties. In the mid-latitude regions, the most common atmospheric mechanisms for cirrus cloud formation are the deep convective outflow

Ice cloud microphysics and their relationship with optical and radiative properties are complex. Cirrus clouds can be characterized by some key parameters such as the mid-cloud altitude and temperature, cloud extinction coefficient, cloud optical depth, lidar ratio (LR) or linear cloud depolarization ratio (LCDR). While the LR and LCDR are related to the microphysical properties of the ice crystals contained in cirrus clouds, such as their shape and/or orientation, the mid-cloud altitude and temperature as well as the cloud extinction coefficient play an important role in determining the cloud radiative properties. Up to the present date, there has been no exact theoretical solution for scattering and absorption by non-spherical ice particles

Lidar systems are the only remote sensing instruments capable of retrieving simultaneously vertical profiles of extinction and temperature. However, only a few lidar systems are equipped with the technique for temperature detection (in general, the integration lidar technique or the rotational Raman technique; see

The objective of this paper is to show a statistical analysis of cirrus cloud properties based on 4 years of continuous ground-based lidar measurements obtained from NASA (MPLNET;

Five years (2018 to 2022) of continuous lidar measurements performed with the MPL in Barcelona, north-eastern Spain, are used in this paper. Co-located radiosoundings launched by the Meteorological Service of Catalonia (Meteocat) at 00:00 and 12:00 UTC are used as well. For the application of the two-way transmittance method for a high-altitude cirrus scene measured from a spaceborne lidar system, data from the CALIPSO satellite have also been used.

The NASA Micro Pulse Lidar network is a federated network of Micro Pulse Lidar systems designed to measure aerosol and cloud vertical structure and boundary layer heights

The lidar system used in this study is a Polarized Micro Pulse Lidar (P-MPL) system that is integrated into the NASA Micro Pulse Lidar network. The Barcelona MPL is located on the roof of the CommSensLab (

The MPL system consists of a compact, eye-safe lidar designed for full-time unattended operation

Data are centrally processed at NASA GSFC with the MPLNET version 3 (V3, released in 2021) algorithm and level-1.5 (L15, near-real-time, quality-assured) data

The CALIPSO satellite provides new insight into the role that clouds and atmospheric aerosols play in regulating Earth's weather, climate and air quality through the analysis of their vertical structure and properties

CALIOP is an elastic-backscatter lidar that orbits Earth at a height of 705 km and measures attenuated aerosol backscatter profiles at 532 and 1064 nm, including parallel and perpendicular polarized components at 532 nm, with highly variable horizontal and vertical resolutions for different atmospheric layers (i.e. aerosol, cloud and surface returns)

Radiosondes are launched twice every day (at 00:00 and 12:00 UTC) by Meteocat at a distance of less than 1 km from the MPL site. The radiosondes provide measurements of pressure, altitude, temperature, relative humidity, wind speed and direction. Only altitude, pressure and temperature profiles have been used in the present work.

In order to get reliable products of the optical properties of clouds and aerosols, different techniques are currently employed to invert elastic lidar signals. The solution of the inverse problem is not straightforward because there are two unknown parameters in the lidar equation: the backscatter and extinction coefficients. Therefore, over the years, this problem has been approached from several perspectives, such as

In particular, the two-way transmittance method compares the lidar signals just below and above the cloud, assuming that the lidar signals correctly represent the scattering medium and that the zones below and above the cloud are aerosol-free, cloud-free or molecular

In spite of all these disadvantages, it is common to find this method combined with other ones, in order to make a first estimation of the cloud optical depth due to its low computational cost. This first estimation of the cloud optical depth is usually used as a constraint in other methods. For example, the CALIPSO algorithm applies the transmittance method in certain situations. When a molecular region is found immediately above and below the cirrus cloud, the Hybrid Extinction Retrieval Algorithm (HERA) implemented with CALIPSO data uses the two-way transmittance method to obtain the cloud optical depth directly from the ratio of the mean attenuated scattering ratios, without multiple scattering correction

This method is based on the application of the lidar equation and the consideration of two reference points. For the calculation of the cloud optical depth, these points are placed above and below the cloud and the signal is normalized with the standard atmosphere, assuming molecular conditions in at least one of these regions. In this way, the power attenuation because of the cloud can be computed. There are many approaches of this method applied to certain aerosol and cloud layers. The first works using this technique date back to the 1960s–1970s, in which the authors calculated the transmittance of a smoke plume layer using lidar data

In this study, the two-way transmittance method has been applied to a case study, specifically a high-altitude cirrus cloud measured with the MPL and CALIOP at the same time, 11 February 2019 at 02:03:50 UTC, in Barcelona. CALIPSO is at a distance of 78 km from the Barcelona station at that moment, and to illustrate this cirrus case study, the CALIPSO signal that has been analysed has a spatial average of 5 km.

Following the notation of

We first calculate the attenuated molecular backscatter coefficient, which is defined as

The ratio between the normalized range square-corrected signal coefficient in

where COD is the cloud optical depth defined as COD

In order to follow with the same notation, we continue working with the NRB coefficient. With the attenuated total backscatter coefficient

Similarly to Sect.

The multiple scattering effect cannot be neglected for spaceborne lidar signals because of the distance between the satellite and the cirrus clouds. For this reason,

Once the mathematical developments for the application of the two-way transmittance method for ground-based lidars (see Sect.

Application of the two-way transmittance method for

Figure

Returning to the mathematical development, after COD calculation, we can estimate the lidar ratio of the whole cloud

The particle backscatter is solved from Eq. (

Afterwards, the new extinction coefficient profile,

In order to study the optical characteristics of the cirrus clouds, we calculate the LCDR, which is defined as the ratio of the perpendicular and parallel lidar signals in the cloud

The vertical profile of the linear cloud depolarization ratio can be calculated by means of the following expression

MDR is the molecular depolarization ratio and

According to

Characterization of the cirrus cloud on 11 February 2019 at 02:03 UTC measured in Barcelona.

Figure

After the calculation of the cirrus cloud optical retrievals, their associated errors have been estimated, where the COD, LR and LCDR errors have been calculated for each cirrus cloud scene with the classical error propagation equations

Even though there is no widely criterion accepted for the identification of cirrus clouds, the most common definition of cirrus clouds is that they must be composed mainly of ice crystals. This is because their geometrical and optical properties vary with latitude, as illustrated by the different cirrus identification criteria in Table

Summary of the criteria for cirrus cloud identification reported in the literature, where

Table

In this study, cirrus clouds are considered the highest clouds in a vertical profile. In order to ensure that Rayleigh regions both above and below the cirrus cloud are analysed, if there is another cirrus cloud lower, less than 1 km away, the two cirrus clouds are merged and treated as one cirrus cloud layer. In all the cases, it has also been ensured that the lidar signal is not extinguished behind the cloud. After the classification of cirrus scenes, the two-way transmittance method has been applied to our database composed of 367 cirrus clouds. Of these 367 cases, the two-way transmittance method has only been correctly applied to 203 cases denoted as “successful” cirrus. Of the 164 cases of cirrus clouds for which the two-way transmittance method failed, denoted as “failed” cirrus, in 29 %, the Rayleigh zone above and below the cirrus cloud could not be guaranteed (

After having carried out the identification of 367 high-altitude cirrus clouds, measured in Barcelona, through MPLNET products and radiosonde data from November 2018 to September 2022 (only at 00:00 and 12:00 UTC, when radiosondes are available), the two-way transmittance method has been applied successfully to 203 of them, i.e. to 55 % of all the cases. Note that 39 % of the 203 high-altitude cirrus cases have another cloud below the cirrus cloud. The elimination of some cases has been carried out on the basis of no possibility of guaranteeing a cloud- or aerosol-free zone both above and below the cirrus cloud (

Histogram of the number of

The cirrus occurrences in Barcelona, together with the monthly distribution of cirrus scenes classified as sub-visible (SVC; COD

The cloud detection has been performed with the MPLNET CLD product. When in a 1 min vertical profile there was a valid cloud base and cloud top value, it was counted as a cloud case. So, we have strong confidence in MPLNET products and their procedures for both distinguishing between aerosol and cloud and processing the lidar signal to obtain their respective products. The two-way transmittance method has been applied successfully to 203 cirrus clouds, i.e. to 55 % of all cirrus cloud cases. In Fig.

Figure

The probability distribution of cloud base and top heights and the mid-cloud temperature of cirrus clouds are shown in Fig.

Probability distribution of the

Ground-based elastic lidars are very sensitive to the solar background noise. For that reason the nighttime and daytime contributions have been separated. Despite that, the efficiency of the two-way transmittance method does not seem to be affected considerably, since the success rates of this method for cirrus clouds during daytime (62 %) and nighttime (51 %) are similar. In Fig.

Average and standard deviation values of geometrical properties of cirrus clouds at nighttime (00:00 UTC) and daytime (12:00 UTC) from 2018 to 2022 in Barcelona, where CH is mid-cloud height,

In order to better analyse the geometrical properties of the 203 high-altitude cirrus cases measured in Barcelona from the years 2018 to 2022, mean values and standard deviations have been calculated and are shown in Table

Table

It can also be observed that the cloud base and top heights together with the cloud thickness are higher at nighttime than in the daytime. Consequently, mid-cloud temperature is lower at nighttime than in the daytime. These differences are negligible due to their values being lower than their standard deviation, a similar result to that obtained in

These results fit well with the literature, in which diverse studies such as

With respect to the thickness of cirrus clouds,

Continuing with the analysis of the physical and geometrical properties of cirrus clouds, there are studies such as

Probability distributions of the optical properties cloud optical depth, lidar ratio and linear cloud depolarization ratio, calculated using the two-way transmittance method (see Sect.

Probability distribution of

In Fig.

After having shown the probability distributions and the mean and standard deviation values of the cirrus cloud optical retrievals, the basic statistical values of their associated errors are presented in Table

Minimum, mean, median, standard deviation and maximum values of the COD, LR and LCDR errors for cirrus cases from 2018 to 2022 in Barcelona.

Table

Average and standard deviation values of cirrus cloud characteristics with ground-based lidar observations reported in the literature. The optical properties have been calculated at 532 nm, where

Table

A complementary analysis is carried out in this section, classifying the cirrus according to the criteria of

Average and standard deviation of optical properties of cirrus clouds classified with

In Table

In this section the possible correlations between the different cirrus products obtained with the two-way transmittance method, radiosonde and MPLNET data are discussed. First, the linear correlations between the temperature and height of the cirrus base and the effective column lidar ratio with the logarithm of cloud optical depth are analysed, as shown in Fig.

Logarithmic dependence of the cloud optical depth with the

On the one hand, Fig.

On the other hand, the effective column lidar ratio increases with increasing cloud optical depth, a fact that has been observed in other studies

Likewise, the linear cloud depolarization ratio has a slightly positive tendency with the cloud optical depth, which is negligible because of its low

To conclude this section, Fig.

Dependence of the linear cloud depolarization ratio with the effective column lidar ratio and the cloud optical depth for cirrus cases from 2018 to 2022 in Barcelona. The rectangles indicate the areas where the LCDR is lower than 0.3 and for effective column lidar ratio values out of the known range for cirrus clouds.

In Fig.

In this study, the cirrus geometrical and optical properties of 4 years of continuous ground-base lidar measurements with the Barcelona MPL were analysed, applying the two-way transmittance method. First, a review of the literature on the two-way transmittance method which provides cirrus cloud retrievals like the cloud optical depth, the columnar cloud lidar ratio or the vertical profile of the particle backscatter coefficient was presented. The different approaches that have been developed during the year and the main advantages and disadvantages of this method were also explained. For example, one of the major advantages of this new approach of the method was that it is only necessary to assume a Rayleigh zone both above and below the cirrus cloud, without making any a priori optical and/or microphysical hypotheses about the cirrus cloud. Second, a simple mathematical development of the two-way transmittance method for ground-based and spaceborne lidar systems was proposed and was first illustrated for a cirrus cloud in Barcelona, using measurements from the MPL and CALIOP lidars. The results of the two-way transmittance method fitted really well, obtaining a difference in COD for the same cirrus cloud of 0.02. Third, a criterion set for cirrus cloud identification was established that consists of

The MPLNET products are publicly available on the MPLNET website (

CGD prepared the automatic algorithm for the identification of cirrus clouds and the application of the two-way transmittance method for MPL and radiosonde data. CGD prepared the figures of the paper. MS, AC, CMP, ARG SL, JRL and EJW reviewed different parts of the results. DCFdSO took care of the maintenance of the MPL. CGD and MS prepared the paper, with contributions from all the co-authors.

At least one of the (co-)authors is a member of the editorial board of

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The authors acknowledge the support of the ACTRIS European Research Infrastructure Consortium (ERIC).

This research has been partly funded by the Spanish Agencia Estatal de Investigación (grant no. PID2019-103886RB-I00) and the European Commission through the Horizon 2020 Programme (project ACTRIS IMP, grant agreement no. 871115; ATMO-ACCESS, grant agreement no. 101008004; GRASP-ACE, grant agreement no. 778349) and through the Horizon Europe Programme (project REALISTIC, grant agreement no. 101086690).

This paper was edited by Alexander Kokhanovsky and reviewed by three anonymous referees.