Understanding Aerosol-Cloud Interactions Through Lidar Techniques: A Review

1. Introduction

Aerosol and clouds are two fundamental components of the Earth’s atmosphere, exerting significant influences on climate, weather, and atmospheric chemistry. Aerosol is a suspension of tiny solid or liquid particles in air. Aerosol particles originate from natural sources such as dust storms, volcanic eruptions, and sea spray, as well as anthropogenic activities like industrial emissions and vehicle exhaust. Clouds, on the other hand, consist of water droplets or ice crystals suspended in the atmosphere, forming in response to changes in temperature, humidity, and atmospheric dynamics. It is well known that without aerosol particles, clouds would be a different phenomenon in their morphology and probably a rare occurrence in the atmosphere, since significant supersaturations of atmospheric water vapor are needed to trigger the homogeneous nucleation of the liquid phase. Aerosol particles serve as nuclei for water vapor condensation at relatively low levels of supersaturation, thereby eliminating the need to achieve much higher supersaturation levels for condensation to take place. For this reason, the presence and characteristics of the aerosol particles are closely linked to the micro and macrophysical properties of clouds. Conversely, clouds act as scavengers for atmospheric particles, either by exploiting them as condensation nuclei and by capturing aerosol through collision and coalescence processes. As a result, clouds serve as effective collectors for removing particles from the atmosphere, leading to their vertical redistribution and finally to deposition onto Earth’s surface through precipitation. Moreover, clouds can serve as reactive environments where aerosol particles undergo chemical transformations. Aqueous-phase reactions within cloud droplets can lead to the production or depletion of certain particle species through oxidation, acid-base reactions, and aqueous-phase chemistry, thus influencing atmospheric composition.

It is evident that studying the interaction between aerosol particles and clouds—two closely intertwined atmospheric components—represents a complex and dynamic phenomenon. This formidable challenge has significant implications for the climate system. Aerosol and clouds have direct radiative effects through scattering and absorbing solar and infrared radiation. But by far the most fascinating and complicated part of their interaction is that part by which different types and amounts of aerosol impact the properties of the clouds. Aerosol, due to their capability to serve as cloud condensation nuclei (CCN) or solid ice nucleating particles (INP), affects cloud microphysical properties such as droplet size distribution, cloud albedo, and cloud lifetime. These properties of clouds in turn change their radiative behavior, which play a crucial role in regulating the planet’s temperature and climate variability. Furthermore, through these processes, such as cloud droplet nucleation and cloud phase transition, aerosol particles can influence precipitation processes thus impacting regional rainfall patterns, droughts, extreme weather events and the whole hydrological cycle. These aerosol effects, and their future projections, still have large margins of uncertainty.

A difficulty encountered in the study of Aerosol-Cloud Interaction (ACI) is that the effect of the aerosol on the morphological, microphysical and radiative properties of the clouds and on the precipitation is mediated and conditioned by the dynamic and thermodynamic state of the atmosphere, so that it is a combination of many factors that finally determines the final state and fate of the clouds. Given the complexity and interdipendence of ACI, advanced observational techniques combined with modeling approaches are thus required to disentangle the mixing of factors, unravel underlying mechanisms and quantify the impacts of aerosol on climate and the environment. In recent years, ACI has been the subject of many review articles [1,2,3,4,5,6] and its effects on the climate system has also been extensively surveyed [7,8,9,10,11]. While we refer the interested readers to these works for an in-depth overview of the current understanding of ACI, in this review we will focus our interest on the contributions of lidar techniques to this field. Furthermore, to keep the article within reasonable dimensions, we will seek to select results achieved by the lidar as a stand-alone instrument and will only briefly mention its potential when used in synergy with other instruments. The article is organized as follows: In the next section, to provide the context, we will schematically illustrate the ways in which aerosol influence the main types of clouds. Subsequently we will describe the capabilities and recent developments of lidar technologies that allow to investigate aspects of ACI. Then we will report the some main observational results presented in the recent literature and discuss some case studies. We will then indicate the current challenges and limitations in studying ACI and propose future research directions and technological advancements, with emphasis on potential multi-instrument approach to address remaining gaps.

2. Aerosol-Cloud Interactions

In a nutshell, aerosol can influence clouds in two directions: i. An aerosol increase and consequently a proportional increase in CCN induces an increment in the number of cloud particles which, for the same amount of condensed water, leads to a corresponding decrease in their average dimension, an increase in their surface area density (SAD), cloud optical thickness ($\tau$) and albedo ($\mathcal{A}$). This is the well-known "Twomey effect" [12], observable in the different optical characteristics of continental (i.e. formed in an aerosol-rich atmosphere) compared to marine low level clouds. An increase in cloud albedo for low level clouds ("Cloud brightening") has a net cooling effect on climate [13]. This aerosol effect on mixed-phase and ice clouds is more complex due to the complicated mechanisms of ice nucleation, multiplication and accretion and will be dealt with later on; ii. Smaller cloud particles depress collision and coalescence and consequently delay or cancel the onset of precipitation, resulting in increased cloud extents, thicknesses, and lifetimes [14,15]. This "lifetime" or "Albrecht effect" further enhances planetary cooling. However ACI are inserted into a complex of meteorological factors that call for feedback and adjustments, so the dominant effect of aerosol varies with respect to the type of cloud, its life phase and its environment. The increase in lifetime is a well-documented effect for warm clouds, such as shallow cumulus and stratocumulus, while in mixed-phase clouds and in deep convection this aerosol effect is complicated by the dynamic processes and thermodynamics inside the cloud.

ACI parameters [16,17,18,19], are often used to quantify the aerosol effect: The indirect-effect parameter

$$AC{I}_N=\frac{\partial ln\left(N_c\right)}{\partial ln\left({\alpha }_p\right)}$$

(1)

with the aerosol particle extinction coefficient ${\alpha }_p$, usually measured at the cloud’s base, as a proxy for the aerosol load, describes the increase of the droplet number concentration with increasing aerosol load for constant Liquid Water Path (LWP) (or Liquid Water Content, LWC) conditions. Similar to $AC{I}_N$, the nucleation-efficiency parameter $AC{I}_r$ can be defined as:

$$AC{I}_r=\frac{\partial ln\left(r_c\right)}{\partial ln\left({\alpha }_p\right)}$$

(2)

and quantifies the relative change of the cloud droplet effective radius $r_c$ with a relative change in the aerosol parameter. $AC{I}_r$ equals 3 $AC{I}_N$ for constant LWC according to the $r_c\propto N_c^{-1/3}$ relationship. $AC{I}_r$ and $AC{I}_N$ can vary between zero (no dependence) and 0.33 and 1 respectively.

Below we will detail what is known about aerosol effects in relation to different types of clouds.

2.1. Warm Clouds

Warm clouds are clouds that exist above 0${ }^{\circ }$C and are among the most interesting clouds from a climatic point of view given that, being low altitude clouds and therefore dwelling at temperatures not significantly different from the surface, they reflect visible radiation without particularly influencing the infrared emission, so they are defined one of the "air conditioners" of climate system [20]. This effect is specifically important for marine stratocumulus that drastically change the surface albedo with respect to the ocean below [21]. Their study is simplified by the fact that their microphysics includes exclusively the gaseous and liquid phase. For such kind of clouds it is well established that an increase in aerosol leads to increasing the albedo, suppressing the collision-coalescence process and therefore depressing the rain, increasing the cloud lifetime and coverage.

At the cloud’s base, the number of CCN activated to become cloud droplets $N_c$ depends on the initial availability of CCN and on the updraft velocity. The activation of a particle of dry radius $r_d$ to a CCN depends on whether the supersaturation S exceeds its critical value $S_c$ given by [22] :

$$S_c={\left(\frac{4A^3}{27\kappa r_d^3}\right)}^{\frac{1}{2}}$$

(3)

where A is the Kelvin coefficient, proportional to the surface tension and inversely proportional to temperature and $\kappa$ is the hygroscopicity, a phenomenological parameter depending on the water activity of the solution [23]. The formula describes the fact that large, hygroscopic particles with low surface tension act more effectively as CCN. Aerosol particles take up water hygroscopically before they activate, thereby decreasing water vapour supersaturation, and this is even more the case when they activate and create droplets, so there is a ’saturation’ mechanism with respect to their number density that makes the concentration of cloud droplets non-linearly dependent on the concentration of CCNs. Reutter et al. [24] identify two asymptotic regimes, one CCN-limited at small values of the CCN concentration (few hundreds $c{m}^{-3}$) and one updraft-limited (since the updraft speed in turns controls supersaturation) at high values of CCN concentrations (several thousands $c{m}^{-3}$). Figure 1 shows the dependence of the cloud droplet concentration on the CCN concentration, this latter proportional to the total aerosol concentration reported in figure, and the transition from a CCN-limited regime to an updraft-limited regime. The data were collected in airborne measurement campaigns in 2013 [25].

Since the concentration of cloud droplets $N_c$ is controlled by the CCN concentration , the latter can in turn control the cloud albedo $\mathcal{A}$. To evaluate this effect we write, for a cloud of geometric thickness h, its optical thickness $\tau$ as

$$\tau ={\int }_h{\int }_0^{\infty }{Q}_e\pi r^2{n}_c\left(r\right)drdz$$

(4)

where $n_c\left(r\right)$ is the cloud droplet size distribution, and $Q_e\sim 2$ - in the geometrical optics approximation - is the extinction efficiency. Introducing the effective radius $r_e$ and the Liquid Water Content (LWC) in a unit volume of air as:

$$r_e=\frac{{\int }_0^{\infty }r\pi r^2{n}_c\left(r\right)dr}{{\int }_0^{\infty }\pi r^2{n}_c\left(r\right)dr}$$

(5)

$$LWC=\frac{4\pi }{3}{\rho }_w{\int }_0^{\infty }\pi r^3{n}_c\left(r\right)dr$$

(6)

we can rearrange $\tau$ as:

$$\tau ={\int }_h\frac{3}{2{\rho }_w}\frac{LWC\left(z\right))}{r_e\left(z\right)}dz$$

(7)

We can easily connect the cloud droplet concentration $N_c$ with the LWC through the droplet volume mean radius $r_v$ and if the cloud droplet distribution is such that $r_v\sim r_e$ we write [26]:

$$N_c\left(z\right)=\frac{LWC\left(z\right)}{{\rho }_w\frac{4\pi r_e^3\left(z\right))}{3}}$$

(8)

We can account for the non adiabaticity of the cloud by defining the adiabatic fraction, $f_{ad}$, the ratio of the liquid water content (LWC) in a real cloud to the LWC that would be present if the cloud were strictly adiabatic, and represents the occurrence and amount of cloud mixing with the surrounding subsaturated air. At the clooud base and close to its centre, $f_{ad}$ is close to 1 [27,28]. We can indicate with ${\mathrm{\Gamma }}_{ad}$ the rate of increase of LWC with height in fully adiabatic conditions, a function of temperature and pressure that can be assumed to be relatively constant throughout the cloud depth for shallow clouds [29]. Thus, taking into account the entrainment of substaurated air in the cloud, we can pose for LWC(z) at height z from cloud base:

$$LWC\left(z\right)=f_{ad}{\mathrm{\Gamma }}_{ad}z$$

(9)

so we can write the cloud optical thickness $\tau$ in terms of $N_c$ and of the Liquid Water Path (LWP), the amount of liquid water per unit area in the column of air from the cloud base to its top:

$$\tau =N_c^{\frac{1}{3}}LW{P}^{\frac{5}{6}}A{\left(\frac{32}{f_{ad}{\mathrm{\Gamma }}_{ad}}\right)}^{\frac{1}{6}}$$

(10)

where $A={(243\pi /250{\rho }_w^2)}^{1/3}$. Finally, using Lacis and Hansen [30] and Meador and Weaver [31] we connect optical thickness and albedo $\mathcal{A}$:

$$\mathcal{A}=\frac{\tau }{\tau +\eta }$$

(11)

where $\eta$ depends on the particle scattering phase function asymmetry, and can vary by a few units around 10.

So, eqs. (11) and (10) tells us that increasing aerosol could produce higher cloud optical thickness and albedo ("Cloud brightening"). Here too we note in both eqs. the presence of a ’saturation’ effect which makes the increase in optical thickness and albedo less and less relevant as the concentration of cloud droplets increases.

Opposed to those considerations, it should be noted that a greater number of cloud droplets with smaller size favors more evaporation. When droplets evaporate, the surrounding air cools and this can enhance the instability of the cloud and can increase the rate of entrainment, thus triggering the so-called "evaporation-entrainment feedback" [32] . This effect could sometime overcome the cloud lifetime effect described above, in very polluted conditions [33]. In addition, a higher concentration of smaller droplets slows the sedimentation, which in turn may enhance the entrainment of dry air into the cloud, enhancing the droplet evaporation and reducing the albedo and water content, the so-called "sedimentation-entrainment feedback" [34].

For what concerns precipitation in warm clouds, the collision-coalescence rate that drives rain depends on $\sim r_e^5$[35] so $r_e$ should be greater than a threshold value ∼ 19$\mu$m, the so-called Hocking limit [36] to initiate rain within cloud. Freud and Rosenfeld [37] demonstrated that the relationship between the number of activated cloud droplets near the cloud base $N_c$, and the cloud depth where $r_e$ reaches the threshold value, is nearly linear. Since $N_c$ at cloud base is positively influenced by the abundance of CCN, that means that deeper clouds need more CCN to suppress rain formation.

Complicating the picture is the fact that the presence of the aerosol itself has an effect on cloud deepening and on its overall macrostructure. In fact, there are some theoretical studies [38] and observations [39] that show how an increase in CCN can in fact invigorate the vertical development of clouds, increasing their thickness, LWP and rain rate [40], as we will detail when treating in more detail the effect of aerosol on deep convective clouds. Moreover, in the case of marine stratocumulus, a change of the cloud decks from open cells to closed cells is documented, as the aerosol increases compared to the background [41]. This has an effect on precipitation, since closed-cell clouds are reported be more stable and generally do not produce rain, whereas open cells, more prone to raining, dissipate as rain begins to fall.

To summarize, the warm cloud precipitation response to aerosol is predominantly to delay or suppress it. However, it is a complex and multifaceted process whose magnitude and direction depends on various factors, including aerosol properties, concentration, distribution, cloud regime and dynamics, and meteorological conditions. Figure 2 from Christensen et al. [42] reports a schematic of the micro and macrophysical processes that regulates the warm stratocumulus morphology (upper panel). The interested reader can refer to the exaustive review of Wood [21].

2.2. Mixed Phase Stratiform Clouds

These are low-altitude clouds composed of droplets of supercooled water and ice crystals, occurring at all latitudes and very frequent in the polar areas where they can have lifespans of many days. In mixed-phase clouds, the process of transferring water from the liquid to the solid phase (the Wegener-Bergeron-Findeisen (WBF) process) is likely to be more effective in a population of smaller cloud droplets, leading to larger ice crystals, and probably inducing greater precipitation and a shorter lifetime of the cloud ("Glaciation effect").

Among these types of clouds, the polar ones have attracted particular attention. Contrary to the behavior of their medium and low latitude counterparts, these clouds in polar regions do not have a large surface cooling effect because the sea-ice at the surface is already bright so that the cloud induced change of albedo is not significant. On the contrary, since the clouds also absorb IR radiation efficiently, they re-emit that energy back so that they could even warm the underlying surface. For these long lasting arctic clouds, the ineffectiveness of the process of transferring water from the liquid to the solid phase (the Wegener-Bergeron-Findeisen (WBF) process) and riming mechanism to complete the glaciation of these clouds is explained by the fact that the few ice particles nucleated at the top of the cloud, where the temperature is coldest due to radiative cooling, grow rapidly in its supersaturated environment and sediment out very fast , thus failing to complete the glaciation of the cloud [43]. The frequent presence of moist inversion layers above the cloud, and the process of entrainment at the cloud top help to sustain the cloud. Cloud phase plays a key role in how they affect the polar surface radiation as glaciation can limit the cloud lifetime and render it less optically and thermally opaque, but still producing an overall positive radiative effect on the surface [44]. The lifetime of these clouds depends on the balance between CCN and INP concentrations. Studies have therefore focused on the effect not only of CCN, but also of INP which are necessary to freeze liquid droplets at temperatures that are not low enough for homogeneous nucleation. The percentage of CCN that can act as INP (about one particle in 10${ }^{-3}$ - 10${ }^{-6}$ acts as an INP) is thus a parameter of great importance, given that an increase in CCN at the expense of the INP component would lead to a greater number of small droplets, for which glaciation is less likely, and riming is less efficient, leading to a longer lifespan of the cloud, greater emissivity and less precipitation. On the contrary, increasing the percentage of INP leads to rapid glaciation, an enhancement of the WBP and reduction in the duration of the cloud [45,46]. Aerosol types that can efficiently act as INPs are mineral dust, biological particles (pollen, bacteria, fungal spores and plankton), carbonaceous combustion products, soot, volcanic ash and sea spray. Figure 2 from Christensen et al. [42] reports a schematic of the micro and macrophysical processes that regulate the mixed-phase stratocumulus morphology (lower panel).

2.3. Deep Convective Clouds

Aerosol impacts these clouds by changing how condensation and glaciation develop along the vertical, influencing not only the type and sizes of the condensate, but also the overall cloud’s dynamics though changes in latent heat release within the cloud. At cloud’s base, an increase of CCN has the effect to create more numerous and smaller droplets. In the warm part of the cloud, the additional SAD made available may be more efficient in reducing the supersaturation, so that more water can condense and the additional latent heat release can speed up the updraft. Moreover, smaller droplets may disfavour the onset of coalescence until high altitudes are reached. If the coalescence regime region lay above the freezing level, more liquid water can be transported aloft and made available to freezing. The enhanced latent heating release at those altitudes may further enhance the buoyancy and promote stronger updrafts. Both effects go in the direction of promoting convection strenght. These are two declinations of a "convective invigoration" induced by the increase of aerosol [47,48]. Once ice starts forming, smaller cloud droplets and narrower size distributions enhance the WBF process but depress riming. However, the combined effect of increased CCN and INP generally results in more efficient ice secondary multiplication due to the increased availability of supercooled droplets and initial ice crystals, which enhance interaction processes critical for secondary ice formation. Supercooled water droplets are essential for secondary ice formation processes like rime splintering (Hallett-Mossop process) when supercooled droplets collide with existing ice particles and freeze, causing splintering and the generation of additional ice crystals. Increasing CCN are responsible of greater numbers of supercooled droplets available to collide with ice crystals, potentially enhancing the rime splintering process, while an increase in INP leads to more primary ice crystals forming. This provides more initial ice particles that can interact with supercooled droplets or other ice crystals. Thus, higher concentrations of both CCN and INP increase the number of interactions between supercooled droplets and ice crystals, enhancing processes like rime splintering. Besides that, other secondary ice multiplication mechanisms such as mechanical fracturing of ice during collisions, sublimation, and condensation processes can also be influenced by increased CCN and INP concentrations. More initial ice crystals provide more opportunities for these processes to occur.

The depression of warm rain and consequently higher ice water content may impact the formation of snow, grauper and hail, and enhance cloud electrification [49] and precipitation rates [50]. The formation of snow, graupel, and hail, along with the cold rain resulting from their melting, is influenced by the dynamic and thermodynamic structures of the clouds and the availability of giant cloud condensation nuclei CCN and INP[51]. Smaller and narrower cloud droplet sizes and distribution, supercooled liquid water at greater altitude, enhanced cold rain and larger hail, higher cloud tops and stronger updrafts are effects clearly discernible at the scale of the single cloud. Figure 3 from Fan et al. [52] illustrates how an increase of aerosol in polluted environments is reflected in the increase of cloud top height, cloudiness, and cloud thickness. Convective cores release a significant amount of smaller cloud ice particles, resulting in the extensive spread and prolonged dissipation of anvil clouds, as these smaller ice crystals fall more slowly.

An increase of INP can trigger a faster glaciation of the cloud, frequently resulting in the formation of precipitation via the ice-ice pathway (ice-ice collection and riming) at the expense of the mixed-phase pathway, thus depressing hail production.

Quantifying the impact of aerosols on a regional scale is more ambiguous, given that adjustments to the circulation and to the environment in which the cloud systems develop, are involved. An in-depth review of the interactions between aerosols and deep convective clouds can be found in [6].

2.4. Cirrus Clouds

These high altitude ice clouds can be grouped into two types, according to their different origins and microphysical properties [53]: the first type forms directly as ice (in situ origin cirrus) within updrafts, nucleating both homogeneously and heterogeneously from the gas phase. The second type is composed of thick cirrus remnant of mixed phase clouds, whose liquid droplets glaciated while lifted to a temperature below 235 K (liquid origin cirrus) where ice is formed heterogeneously and, possibly, homogeneously as well. In situ origin cirrus are often thinner and with lower Ice Water Content (IWC), while liquid origin cirrus are mostly thick with higher IWC and more numerous and larger ice crystals [54]. As ice formation can occur either from homogeneous nucleation of supercooled aqueous aerosol and cloud water droplets, or heterogeneously from the small subset of solid aerosol that can act as INP, the impact of aerosol on those clouds depends on which is the dominant mechanism. Which one between the two is prevailing, depends on ambient temperature, relative humidity and INP abundance. For those in-situ formed cirrus clouds whose origin can be dominated by homogeneous nucleation, an increase of INP would become significant if it can shift the prevailing nucleation mechanism towards the heterogeneous one. If so, the glaciation would involve a few INPs resulting in less numerous ice crystals but larger in size [55,56]. For cirrus clouds of liquid origin in cases where heterogeneous nucleation prevails, larger aerosol corresponds to a larger density of smaller droplets, which leads to a greater number of ice particles with smaller dimensions, i.e. with lower sedimentation speeds, leading to a greater persistence of the cloud [57]. However, there are indications that the coupling between the amount of CCN and INP with the concentration and morphology of ice crystals is weaker than with concentration of cloud droplets for the case of warm clouds, and is more dependent on the meteorological and thermodynamic conditions governing the formation and lifetime of cirrus clouds [58].

Table 1 summarizes the response of different cloud types to an increase of CCN or INP.

3. Lidar Techniques for Studying Aerosol-Cloud Interactions

3.1. Lidar Fundamentals

Lidar technology has long been used to improve our understanding of atmospheric composition and dynamics, particularly for cloud and aerosol detection and atmospheric composition. Several configurations, including simple elastic lidar, polarization lidar, multiwavelength lidar, Raman lidar, high-spectral-resolution lidar (HSRL), Differential Absorption Lidar (DIAL) and dual-field-of-view lidar, endows researchers with a comprehensive toolkit for probing atmospheric particulate. In its essence, the lidar emits pulses of laser light and detect, at a time t after the pulse was emitted, the light backscattered from the armosphere at a distance $R=ct/2$. The factor 1/2 takes into account the double travel from the emitter to the illuminated volume at distance R and back to the colocated receiver. The backscattered light is collected with a telescope and detected with suitable sensors. The basic elastic Rayleigh lidar equation connecting the power received from the light backscattered from a distance R, P(R) at wavelength $\lambda$ to the atmospheric optical parameters at R, formulated under the single scattering hypothesis, is:

$$P\left(R,\lambda \right)=P_0\frac{c\tau }{2}O\left(R\right)\eta \frac{A}{R^2}\beta \left(R,\lambda \right)exp\left[-2{\int }_0^R\alpha \left(R,\lambda \right)dr\right]+P_{bkg}$$

(12)

where $P_0$ is the laser pulse power, and $\tau$ is the temporal length of the pulse so that $c\tau /2$ is the geometrical length of the volume illuminated by the laser light at a given time. The term O(R) is a function that represent the overlap of the laser-beam and the receiver-field-of-view, unity in the lidar far range (i.e. usually few hundreds of meters from it) and the solid angle $A/R^2$ is the angle the lidar views of the light scattered from distance R. $\eta$ is the overall system efficiency. The term $P_{bkg}$ represent a constant contribution from the light conditions of the atmosphere and increases with the telescope field of view (FOV). The optical parameters of interest are the volume backscatter coefficient $\beta ={\beta }_m+{\beta }_p$ and the extinction coefficient $\alpha ={\alpha }_m+{\alpha }_p$, where the subscript m and p refers to molecules and particles. While for their molecular part a link between the two quantities is provided by molecular scattering theory, resulting ${\alpha }_m/{\beta }_m=8\pi /3$, the ratio ${\alpha }_p/{\beta }_p$ (a.k.a. lidar ratio, LR) is not known and depends on the particular aerosol. In general we may pose, for a collection of scatterers with particle size distribution (PSD) $n\left(r\right)$ (usually expressed in $c{m}^{-3}\mu m^{-1}$):

$${\beta }_p={\int }_0^{\infty }n\left(r\right)\pi r^2{Q}_{back}\left(r\right)dr$$

(13)

$${\alpha }_p={\int }_0^{\infty }n\left(r\right)\pi r^2{Q}_{ext}\left(r\right)dr$$

(14)

In the case of spherical scatteres, the efficiencies $Q_{back}\left(r\right),Q_{ext}\left(r\right)$ can be computed in terms of Mie Theory [59] and for non-absorbing aerosol their asimptotic value (i.e. for particle dimensions significantly greater than the lidar wavelenght) are, respectively, 1 and 2. There is no general analytical solution for scatterers of arbitrary shape and different approaches have been developed for those conditions [60]. Here we want to underline how the lidar is essentially sensitive to the second moment of the PSD, i.e. to the averaged cross-sectional area of the particles.

The elastic Rayleigh lidar serves as the foundation of lidar-based aerosol detection, interpreting elastically backscattered light to estimate aerosol properties such as concentration and assess altitude distribution and optical thickness. As stated above, in eq. (12) two unknow quantities appear so assumptions on the LR should be made in order to invert the equation [61,62] and different LRs should be carefully choses with respect to different types of aerosols. This LR estimate can lead to large sistematic errors in the retrieval of aerosol extinction coefficients [63,64] and should be done carefully taking into account the expected aerosol type, based on geographical location and meteorological conditions of the measurement site [65].

Polarization diversity lidar enhances the aerosol classification capability by exploiting the polarization state of backscattered light, allowing for discrimination between different aerosol types based on their distinct polarization signatures. In fact, simple spherical particles backscatter the radiation with no change in its polarization state, while aspherical scatteres change the state of the incident polarization. This polarization diversity discrimination enables more accurate characterization of aerosol properties in term of their morphology [66]. The parameter used in lidar practice is the particle depolarization ${\delta }_p$[67,68] , defined as the ratio between the particle backscattering coefficients measured in two reception channels, one which selects the polarization parallel to that of the emitted light, the other the orthogonal one. With obvious choice of symbols ${\delta }_p={\beta }_p^{cross}/{\beta }_p^{par}$. ${\delta }_p$ depends on the size and shape of the particle: it is small for particles with dimension smaller than the lidar wavelenght and, as the particle dimension increases, it grows non-monotonically towards an asymptotic value that depends on the morphology of the particle [69].

Raman lidar can detects the vibrational Raman scattering from various atmospheric molecules, such as nitrogen, oxygen, ozone, water vapour, resulting each one in distinctive shifts in the scattered wavelength. In the case of nitrogen molecules, Raman scattering detection offers the advantage of providing an additional, independent equation for of the atmospheric extinction, allowing for a more accurate determination of extinction coefficient, hence of the LR, without relying on assumptions about aerosol properties [70]. The spectrally resolved detection of the Raman rotational lines of $N_2$ and $O_2$ also allows the determination of the temperature of the atmosphere [71].

A different approach to disentangle the backscatter - extinction relationship is the one provided by the high-spectral-resolution lidar (HSRL) capable of resolving the spectrum of backscattered radiation at very high resolution, identifying and separating aerosol Mie scattering from molecular Cabannes-Brillouin scattering by the different amplitude of their Doppler line broadening, so the aerosol backscatter and extinction coefficient can be retrieved directly [72].

Multiwavelength lidars further extend the capabilities of traditional lidar systems by emitting laser pulses at multiple wavelengths, enabling the characterization of aerosols in terms of the spectral dependence of their scattering. This approach facilitates the differentiation between various aerosol types and provides valuable information about aerosol microphysics, optical properties and aerosol size distribution [73]. For a typical two-wavelength lidar with ${\lambda }_1>{\lambda }_2$, the ratio of the backscattering coefficients ${\beta }_p\left({\lambda }_1\right)/{\beta }_p\left({\lambda }_2\right)$ defines the Color Ratio (CR).

The Differential Absorption Lidar (DIAL) technique utilizes two closely spaced laser wavelengths to probe the atmosphere, with one acting as a reference and the other being absorbed by a target gas, such as water vapour, enabling precise measurements of its concentration and vertical profiles.

Doppler lidars can measure the airmass velocity in the atmosphere by analyzing the frequency shift (Doppler shift) of the backscattered light, Doppler lidar can determine the speed and direction of wind and other airborne particles. This technology is widely used in meteorology for wind profiling, turbulence detection, and studying atmospheric dynamics.

Finally, different reception geometries of the backscattered signal, as different telescopes at different receiving angles, or the use of different FOVs for the same receiving telescope, allow to estimate some properties of the scattering medium, as relevant portions of the phase function of the scatterers and other cloud properties as the extinction coefficient and particle effective radius [65,74].

The diverse capabilities of lidar technology, ranging from simple elastic lidar to more advanced configurations, allows to effectively characterize the aerosol in its dimensional component from about 0.1 $\mu$m up, thin clouds (i.e. with optical thicknesses less than 3) and, in the case of thick clouds, the base of the cloud and, through the analysis of the signal along the depth of penetration into it, some microphysical characteristics of it.

The interested reader may refer to books on lidar application to atmospheric research, as the classical Measures [75] or the more recent Weitkamp et al. [76].

3.2. Aerosol Characterization

3.2.1. Aerosol Classification

Basic lidar parameters for describing the particulate are the backscattering and extinction coefficients, extensive quantities dependent on the amount of particulate present in the investigation volume, its optical depth $\tau$, and the particle linear depolarization ratio ${\delta }_p$, the lidar ratio LR and the color ratio CR as intensive quantities. These parameters are used to classify different aerosol types [77,78]. An example of aerosol classification is shown in Figure 4 from Gro et al. [79], where different types of aerosols are reported with respect to their ${\delta }_p$, LR and CR (in this case ratio of aerosol backscatter coefficient at 532 nm and 1064 nm). In their work, the authors report results from airborne measurement campaigns where a two-wavelength, polarization-diversity HSRL lidar was deployed from an aircraft, and the characterization results were validated by concomitant in situ measurements and Lagrangian analysis of the air masses being measured. From panel (a) one can see that even a simpler single wavelength polarization diversity lidar with the ability to measure LR either with HSRL or Raman approach is already effective in discerning different aerosol types. Basic elastic Rayleigh lidar with polarization diversity still allows aerosol classification if additional information is introduced in the classification algorithm, such as altitude, location or surface type suggesting the expected aerosol, as was done in the aerosol classification in the case of the satellite borne CALIOP lidar [80,81].

Figure 4. Characteristic lidar quantities of various atmospheric aerosol types (a)–(c) with frequency distribution (d)–(f), as well as the total number of measurement points (n) for each aerosol type. Each point in (d)–(f) represents a single lidar observation. (Figure and caption from Figure 5 in Gro et al. [79] licensed under CC BY 3.0 )

Figure 4. Characteristic lidar quantities of various atmospheric aerosol types (a)–(c) with frequency distribution (d)–(f), as well as the total number of measurement points (n) for each aerosol type. Each point in (d)–(f) represents a single lidar observation. (Figure and caption from Figure 5 in Gro et al. [79] licensed under CC BY 3.0 )

3.2.2. Aerosol quantitative specification

Of interest is the estimate of quantities characterizing the aerosol distribution, such as particle mass density, SAD, volume density, particle mean or effective radius. This has been carried out either by means of numerical simulations [82,83,84] or by comparing the lidar measurements with in situ measurements carried out in the same air mass probed by the lidar [85,86,87] to derive heuristic relationships.

A reconstruction of the aerosol PSD is possible starting from multiwavelength Raman/HRSL with polarization diversity lidars that can provide sets of extinction and backscattering coefficients [88]. In 2002 Veselovskii et al. [89] presented an inversion algorithm for the retrieval of particle size distribution parameters, i.e., mean or effective radius, number, surface area, and volume densities, and complex refractive index, from multiwavelength lidar data, and successively Veselovskii et al. [90] used the extinction and backscattering coefficients at 355, 532 and 1064 nm to retrieve the parameters of a PSD expressed as a sum of two lognormals. Such kind of retrievals derive the PSD in size ranges from fractions to few tens of $\mu$m, have been extensively used and have been validated with comparison to other indipendent remote sensing retrievals (i.e. inversions of spectral measurements of sky radiance and atmospheric transmittance from sunphotometers) or colocated in-situ data. [91,92,93,94,95,96]

3.2.3. Aerosol Hygroscopicity

The aerosol hygroscopicity is an important factor determining its ability to act as a CCN. Lidars can detect changes in aerosol optical properties as they absorb water and grow. By monitoring these changes we can deduce hygroscopic scattering enhancement factors of different aerosol types. Ferrare et al. [97] used Water Vapour Raman lidar to simultaneously measure aerosol backscatter and RH and demonstrated how the the increase of backscattering measured by the lidar can be correlated to RH, and Pahlow et al. [98] showed good correlations between a lidar-derived enhancement factor (measured over the range 85% RH to 96% RH) with the same parrameter measured by a nephelometer over the RH range 40% to 85%. More recently, Fernández et al. [99] investigated the hygroscopic characteristics using a multi-wavelength Water Vapour Raman lidar and in-situ aerosol observations. They inferred profiles of RH from Water Vapour Raman lidar data and described changes in aerosol optical properties under varying humidity conditions in terms of extinction enhancement, CR and LR. Specifically, they found that increasing RH leads to aerosols absorbing water vapor, which increases their size and consequently decreases the CR while increasing the LR. They also estimated the RH-related scattering enhancement factor for the backscatter coefficient at 532 nm, which characterizes aerosols from a hygroscopic perspective. A similar study was conducted by Navas-Guzmán et al. [100] using continuous observations of aerosol backscatter coefficient, temperature, and water vapor mixing ratio from a Water Vapour Raman lidar system at the aerological station of MeteoSwiss in Payerne, Switzerland, since 2008.

Lv et al. [101] studied the extinction and backscattering coefficient at 355, 532, and 1064 nm to infer aerosol hygroscopicity according to an aerosol hygroscopic scattering enhancement factor $f\left(RH\right(z\left)\right)$ defined as the ratio between the particle backscatter coefficient when RH varies and that at a fixed RH, and and using colocated lidar for backscatter coefficient profiles, and radiosondes for RH profiles. The homogeneity of the aerosol along the vertical was guaranteed by well-mixed conditions assessed by concomitant measurement of potential temperature and water mixing ratio. Concurrent increases in the aerosol backscattering coefficient and RH were used to derive $f\left(RH\right(z\left)\right)$, then fitted to derive the parameters of the Kasten model [102]. Such derivations and comparison were performed for different types of aerosol and conditions. The lidar $f\left(RH\right(z\left)\right)$ results were then confronted with ground based in-situ data from a humidified nephelometer showing good agreement. The relationship between the nephelometer-derived f(RH), which is based on the particle total scattering and the one derived from a backscatter lidar was extensively addressed by Feingold and Morley [103] which compared lidar data with optical computations from airborne in-situ measurements of aerosol size and composition. Lidar derived enhancement factors may differ from the commonly used f(RH) based on humidified nephelometers at RH greater than 95%, In such high RH conditions, the lidar-derived enhancement factor is greater than the one from the computed extinctions, that a nephelometer would measure. The disagreement is dependent on the PSD and aerosol composition. However, over the range 85% < RH < 95% the two factors were in reasonable agreement. Recently, other aerosol hygroscopic studies based on lidar measurements have been carried out, where backscatter and extinction enhancement factors are derived from lidar measurements and RH profiles are provided from radiosoundings or from water vapour lidar themselves [104,105,106]. The amount of water vapor absorption by aerosols can also be inferred from the use of the DIAL lidar, which simultaneously measures water vapor concentration and aerosol backscatter. In particular, this technique has proven effective in deriving the enhancement factor f(RH(z)) in a well mixed boundary layer, capped by clouds [107]. We should stress the fact that lidars are useful tool for measuring aerosol growth not only because of their remote sensing capability, but also for conditions when RH>85% as those encountered close to cloud bases, since for such elevated RH humidified nephelometers works poorly. It should be noted, however, that the hygroscopicity scattering enhancement factors measured with a nephelometer or a lidar and the growth factor measured with, as istance, a Humidified Tandem Differential Mobility Analyzer (HTDMA) are both characterizing aerosol hygroscopic properties, but they are not identical. They represent different aspects of how aerosol particles interact with water vapor and how these interactions affect their optical properties (scattering) and physical properties (size) [108] .

3.3. Cloud Characterization

3.3.1. Semitransparent Clouds

Semi-transparent clouds sampled by lidars predominantly belong to the cirrus cloud category and it is on them that we will focus. Cirrus clouds [109], characterized by their thin, wispy appearance and high altitudes, often exhibit optical transparency to varying degrees, allowin lidar systems to effectively penetrate entirely into these clouds, making them a primary focus of lidar-based research in atmospheric science. Given the extensive body of literature on cirrus lidar studies, we will not delve into exhaustive details on each aspect. Instead, we summarize lidar key capabilities in detecting and characterizing these clouds through various optical techniques. Readers interested in more comprehensive insights are encouraged to explore the rich literature of research in this field.

Basic backscatter lidars can identify cloud boundaries and unveils internal cloud structures [110,111,112]; scanning polarization diversity lidars gain insights into cloud particle phase [66], shape [113,114], orientation [115,116], and associated aerosols[117], this capability improved by the simultaneous use of more than one wavelength [118,119]; Raman or HSRL can provide calibrated data on ice water content, optical attenuation coefficient and optical depth [120,121,122]. Ice water content can be also retrieved from optical extinction [123,124,125,126] and possibly validated by comparison with colocated in-situ measurements [87,127]. Differential Absorption Lidar (DIAL) analyzes particle backscattering and determines water vapor density/relative humidity within the cirrus cloud environment[128]. Interestingly, information on the effective size of ice crystals in cirrus clouds can also be retrieved measuring the fall speed that can be derived from lidar data [129,130].

3.3.2. Opaque Clouds

In lidar jargon, opaque clouds are those whose optical thickness exceeds 3. Lidars are not capable of probing them entirely; however, a penetration length within them can be defined in which the lidar is still able to produce a signal not totally attenuated for several tens of metres, and information can be obtained. Here we will focus prevalently on warm clouds, for which we can assume the cloud droplets to be spherical. This simplifies the treatment of multiple scattering within the cloud. The angular distribution of the light scattering from cloud droplets is a function of the effective size $r_e$, and the forward scattering increases monotonically with the droplet dimension. Moreover, in such optically dense medium, a significant amount of the backscattered light comes from multiple scattering.

Due to lidar receiving geometry, most of the multi-scattered photons received come from small-angle forward scatterings plus a single backscattering at an angle close to 180°. Bissonnette et al. [131] describes an algorithm that uses multiple field-of-view (FOV) lidar measurements between 1 and 12 mrad, to retrieve the extinction coefficient at the lidar wavelength and the effective particle diameter from which secondary products such as the LWC can be derived. These techniques have been used to characterize the structure of dense low-level water clouds [132].

Schmidt et al. [133] uses two coaxial FOVs to detect the nitrogen Raman signal of light scattered in the forward direction by cloud droplets but backscattered inelastically by nitrogen. As the phase function for Raman scattering by nitrogen molecules is nearly isotropic in the backward direction, the scattering computation effort is significantly relieved as the angular distribution of the received light depends only on the scattering phase function of the droplets. In this way the complication arising from the droplet size dependency of multiply-scattered light is eliminated, and this is an advantage respect to the detection of multiple elastic scattering from droplets.

For cloud droplets, single-scattered light in the backward direction does not change its polarization state, while scattering events at different angles, which overall leads to backward scattering, change the polarization. So the the profile of the polarization is related to the intensity of multiple scattering, in turn depending on particle size and concentration. Research has also explored the correlation between light depolarization induced by multiple scattering, measured across various fields of view (FOVs), and the characteristics of cloud droplet sizes [134,135]. Jimenez et al. [136] uses lidar depolarization rations at two different FOV to retrieve microphysical properties of liquid-water clouds (cloud extinction coefficient, droplet effective radius, liquid-water content, cloud droplet number concentration) in a cloud penetration depth of 100 m above the cloud base.

Donovan et al. [137] proposed a method that uses single FOV observations of depolarization, under the assumption of linear LWC, increase with height (an assumption that correspons to fixing the degree of non-adiabaticity of the cloud development) and constant cloud droplet number density $N_d$ at the cloud base. They used Monte Carlo multiple scattering modelling on a modified gamma function PSD, to create a database for various values of LWC lapse rate, $r_e$, different cloud-base heights and different lidar FOVs. An optimal estimation Bayesian scheme was then used to infer profiles of $r_e$ and LWC as well as mean values of $N_d$ and the LWC lapse rate (from which the cloud subadiabaticity can be retrieved) within the cloud penetration length. Relatively few studies are available that exploit penetration depth in opaque cirrus clouds, due to the lack of knowledge of the phase function for ice crystal scattering [138].

It may seem limiting to only be able to sample the base of the cloud for only a few tens or hundreds of metres. However, the maximum supersaturation (above which no new CCN are activated) lies typically only a few tens of metres above cloud base [139], so this is the region dictating the cloud droplet condensation, up to the level where collision/coalescence processes begin to take place. it is thus a region of utmost importance for cloud microphysical studies.

In case the LWP could be retrieved independently, from radars [140], microwave radiometers [141] or IR [142] and visible spectrometers [143], different approaches become viable. Grosvenor et al. [144] reviewed how passive satellite remote sensing retrieves cloud droplet number concentration ($N_d$) using cloud optical depth, cloud droplet effective radius ($r_e$), and cloud-top temperature. Ground-based active remote sensing, on the other hand, relies on cloud radar reflectivity factor (Z) or lidar extinction (backscatter) coefficient ($\alpha$, $\beta$), along with microwave radiometer-retrieved liquid water path (LWP). To connect these retrievals, a droplet size distribution (DSD) assumption is necessary. For semi-transparent clouds, lidar-based retrievals offer an advantage because the optical parameters they measure depend on the second moment of the DSD, rather than the sixth moment as with radars. This sensitivity to $N_d$ makes lidar retrievals less dependent on the effective shape of the DSD. An empirical parameter k that equals the ratio of the mean volume radius to the mean effective radius Schumann et al. [145] can be defined which implicitly incorporates the dependence on the DSD in the relation between $N_d$, $r_e$ and $LWC$ which, from 14 , 5 and 6 we can write as:

$$N_c=\frac{2{\rho }_w^2}{9\pi k}\frac{{\alpha }^3}{LW{C}^2}$$

(15)

at any given level in the cloud, thus linking $N_c$ to the lidar extinction $\alpha$ Zhang et al. [146]. Brenguier et al. [147] reported k parameter values ranging from 0.7 to 0.9 for stratiform clouds in various atmospheric conditions and cloud systems. In absence of ancillary measurements for LWC, its profile can be guessed from cloud-base temperature and pressure measurements by assuming an educated value for the adiabatic fraction $f_{ad}$ as in eq. (9).

4. Observational Results

4.1. Detection of CCN and INP

Estimating concentrations of cloud condensation nuclei (CCN) is crucial for comprehending aerosol-cloud interactions. However, in situ observations of CCN are scarce, and many passive remote sensing methods can only offer proxies like total aerosol optical depth (AOD) for column-effective CCN assessments. [148].The potential of lidars in the study of aerosol-cloud interactions should be clear, and in this section we will present some findings from observational studies using lidars to characterize the presence of CCN and INP.

A method to extend the CCN spectrum measured at the surface to high altitudes was proposed by Ghan and Collins [149]. The lidar measured value $\beta \left(z\right)$ at altitude z where aerosol is exposed to the RH(z), is recalculated to the value it would have in dry conditions using an independent measurement of the vertical profile of RH and surface measurements made with a humidified nephelometer providing the dependence of the extinction on relative humidity. A light scattering hygroscopic growth factor $f\left(RH\right)$ is defined as the ratio between the extinction coefficient at a various RHs and the extinction coefficient at dry conditions. The same factor is used also to quantify the amount of change in the particle backscattering coefficient due to water uptake: ${\beta }_{dry}\left(z\right)=\beta \left(z\right)/f\left(RH\left(z\right)\right)$. Then, surface measurements of the CCN spectrum CCN($z_0$) are scaled by the ratio of the backscatter (or extinction) profile ${\beta }_{dry}\left(z\right)$ to the backscatter (or extinction) retrieved at or near the surface, ${\beta }_{dry}\left(z_0\right)$. This method assumes that the hygroscopic growth factor $f\left(RH\right)$ measured at the surface is the same as the one $f\left(RH\right(z\left)\right)$ measured at z, and this implies the assumption that the vertical structure of CCN concentration is identical to the vertical structure of dry extinction or backscatter. These assumptions are equivalent to require that both the PSD shape (but not the total aerosol number) and the aerosol composition and particle shape are independent of altitude. In fact, Ghan et al. [150] showed that vertical inhomogeneity in the PSD and presumably in particle shape and composition are the mail sources of error in such CCN retrieval, as near-surface CCN properties could be significantly different from CCN properties near the cloud base.

The ability of aerosols to act as CCN depends more on their size rather than chemical composition or mixing state [151]. This allows to give an assessment on CCN through a determination of the aerosol PSD and an assesment of the number of particles whose dimension is above a certain threshold. It follows that in order to derive CCN concentration one should first use lidar derived optical parameters to retrieve the aerosol PSD. Then an assessment of particle hygroscopicity for different types of aerosol is needed to assess the ability of particles to act as CCN. In should be noted that high RH near clouds can change the aerosol optical properties and complicate the CCN retrieval.

Lv et al. [152] developed a method for profiling CCN concentrations that usees backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm. Three types of aerosols (urban industrial, biomass burning, and dust) are considered, each with a different bimodal PSD. This PSD was inferred by using look-up tables developed based on the aerosol PSD database of the Aerosol Robotic Network (AERONET) database [153]. The best bimodal size distribution parameters were selected by comparing lidar observations and Mie optical computation [59] on the aerosol PSD, varying the PSD parameters through typical ranges for the three types of aerosols, until an agreement between measurement and calculations is reached. This "wet" PSD, measured at ambient RH, is then corrected to its "dry" version by using a hygroscopic scattering enhancement factor obtained from Humidified Tandem Differential Mobility Analyzer (HTDMA) or Raman lidar data. Then the aerosol critical radius ($r_c$) for CCN activation at selected critical supersaturation is computed from the maximum of the $\kappa$-Köhler curve [23]. As, according to $\kappa$-Köhler theory, $r_c$ depends on the hygroscopicity parameter $\kappa$ which changes according to aerosol type, such critical radius ($r_c$) depends on the aerosol type and for the three types of aerosols in the study, it is taken from the literature [154,155,156]. CCN number concentrations are then determined from the integration of the retrieved PSD, from $r_c$ upward.

In 2019, Tan et al. [157] similarly proposed to retrieve CCN concentrations from multi-wavelength Raman lidar measurements, but instead of using AERONET datasets and estimations of hygroscopicity according to aerosol classification, they relied on in-situ measured PSD, mixing states, and chemical compositions data to define the relationship between CCN concentrations and lidar-derived optical properties. Hygroscopic enhancements of backscatter and extinction with relative humidity have been used to create humidograms, to derive both dry backscatter and extinction and hygroscopicity at different wavelengths. These, together with lidar color ratios, extinctions and backscatters data have been used as input to a Random Forest Regression machine learning algorithm that produces the best estimate for the ratio CCN-to-extinctions. Optical data simulated with Mie computations on in-situ-measured PSD and $\kappa$-Köhler curve from in-situ measured chemical compositions are used as the training data. A similar in-situ dataset is used as test data.

Lenhardt et al. [158] explored the connections between aerosol backscatter and extinction coefficients using the airborne High Spectral Resolution Lidar 2 (HSRL-2) in biomass burning aerosol (BBA)-influenced air masses over the southeast Atlantic. They also examined in situ measurements of cloud condensation nuclei (CCN) concentrations that were spatiotemporally collocated. To ensure accuracy and avoid detecting swollen, highly hygroscopic aerosols that could artificially inflate backscatter and extinction values without corresponding increases in CCN concentration, observations taken at relative humidity (RH) greater than 40% were filtered out. Their findings, illustrated in Figure 5, demonstrate robust linear relationships between lidar-derived backscatter and extinction coefficients and CCN concentration.

Figure 5. CCN concentration versus HSRL-2 (a) backscatter and (b) extinction coefficients with blue scatter points representing 355 nm and red scatter points representing 532 nm. This combined data set represents 10 d of observations and 80 total collocated data points (per coefficient), covering all 3 years of ORACLES. Supersaturation for these observations ranges between 0.22 %–0.4 %. The Pearson correlation coefficient is shown, with the Spearman rank correlation coefficient given in parentheses. Error bars are given for a CCN relative uncertainty of 10% and for calculated HSRL-2 uncertainties. Lines of best fit are forced through the origin to represent the practicality of using linear regression equations to quantitatively obtain CCN concentrations using HSRL-2 observables. (Figure and caption from Figure 8 in Lenhardt et al. [158] licensed under CC BY 4.0 )

Figure 5. CCN concentration versus HSRL-2 (a) backscatter and (b) extinction coefficients with blue scatter points representing 355 nm and red scatter points representing 532 nm. This combined data set represents 10 d of observations and 80 total collocated data points (per coefficient), covering all 3 years of ORACLES. Supersaturation for these observations ranges between 0.22 %–0.4 %. The Pearson correlation coefficient is shown, with the Spearman rank correlation coefficient given in parentheses. Error bars are given for a CCN relative uncertainty of 10% and for calculated HSRL-2 uncertainties. Lines of best fit are forced through the origin to represent the practicality of using linear regression equations to quantitatively obtain CCN concentrations using HSRL-2 observables. (Figure and caption from Figure 8 in Lenhardt et al. [158] licensed under CC BY 4.0 )

These studies employ multi-wavelength Raman or HRSL lidars, commonly called 3$\beta$ + 2$\alpha$ lidars, systems of a certain complexity, coupled with in-situ measurement and RH profiling by means of radiosoundings or remote sensing. A simplified approach was suggested by Mamouri and Ansmann [159] who proposed an inversion algorithm for data from a more manageable single-wavelength polarization diversity lidar. This lidar is still able to specify aerosol classes (desert, nondesert continental, and marine). The possible presence of external mixing in the aerosol is handled with the procedure outlined in Tesche et al. [160]. Following a methodology proposed by Shinozuka et al. [161], extensive datasets from AERONET and lidar correlated observations are then used to connect lidar derived extinction to total particle number concentrations (for dry particle dimensions above defined thresholds depending on aerosol class) for the three aerosol classes. An evaluation of the correction for water-uptake [23,162] is performed, this time assuming fixed RH values for the typical conditions of observation. Finally, a simple parametrization is used to connect the particle concentrations to the CCN concentrations, obtained from the formers with scaling factors dependent on supersaturation and aerosol class. Thus, height profiles of CCN concentrations can be retrieved from lidar-derived ambient aerosol extinction. This approach has lent itself to derive global climatologies of CCN from the analysis of the satellite borne lidar CALIOP [163]. A similar approach was also used by Choudhury and Tesche [164]. In their study, they employed normalized volume size distributions and refractive indices based on the CALIPSO aerosol model [80] for six aerosol types identified by the CALIPSO lidar. These size distributions were adjusted until agreement was reached between the extinction coefficient inferred from CALIPSO measurements and that calculated through light-scattering computations. These modified size distribution were then used to compute the aerosol number concentration for particles with dimension above defined thresholds depending on aerosol type. Again, the CCN concentration at a certain set of supersaturations was estimated by multiplying the aerosol number concentration with scaling factors which depend on the aerosol type and on the level of supersaturation.

Lidars have been utilized to retrieve profiles of INP concentrations. This is achieved by integrating particle concentration profiles derived from lidar measurements with parameterizations of INP efficiency specific to different aerosol types and freezing mechanisms (such as immersion, condensation, deposition, or contact freezing). Mamouri and Ansmann [159] apply a regression of lidar derived extinction vs SAD to retrieve the INP concentration from the latter. Indeed, precise knowledge of aerosol type is crucial for using lidar retrievals to estimate INP concentrations. This is because INP concentrations are inferred solely from physical properties such as particle number concentration and/or size distribution (SAD), using parameterizations that have been developed for specific aerosol types. Examples include dust [165,166,167,168], marine aerosols [169], soot [167], and global aerosols [170]. Therefore, studies of INPs have typically focussed on estimating INP concentrations within these specific aerosol classes.

Using a similar methodology, Haarig et al. [171] presented vertical profiles of cloud condensation nuclei (CCN) number concentration, particles with diameter greater than 500 nm, size distribution, mass, and INP concentration. These profiles were derived from measurements of 3$\beta$ + 2$\alpha$ Raman lidar with polarization diversity. They compared these measurements with in situ CCN concentrations and INP-relevant aerosol properties collected by aircraft in the Saharan Air Layer (SAL) over the Barbados region.

Extinction coefficient profiles were separately retrieved for mineral dust, marine, and continental aerosols. Empirical conversion factors [172] were applied to convert these extinction coefficients into particle number concentrations (for particles above a threshold size dependent on aerosol type) and size distributions (SADs). Subsequently, various INP parameterizations [166,170] were tested, using particle number concentration and SAD as inputs.

Comparisons with in situ data of mass concentrations and particle number concentrations, which were used as inputs for the INP parameterizations, demonstrated good agreement.

Similarly, Marinou et al. [173] have retrieved cloud-relevant particle number concentrations (i.e particles whose linear dimension in dry conditions are above 250 nm) and SAD${ }_{dry}$ using lidar measurements froma a $\beta$ + 2$\alpha$ Raman lidar with polarization diversity. INP concentration profiles were estimated using various ice nuclei parameterizations. These lidar-derived results were subsequently compared with direct INP measurements obtained by sampling aerosols along the lidar profile using two UAVs equipped with INP samplers. The collected samples were then analyzed offline using the FRIDGE (FRankfurt Ice nucleation Deposition freezinG Experiment) INP counter [174]. This approach allowed them to evaluate the effectiveness of different INP parameterizations across different temperature ranges and types of particles.

Wieder et al. [175] also provided a direct validation of the INP concentration retrievals. They tested INP retrievals based on data from a $\beta$ + 2$\alpha$ Raman lidar with polarization diversity by comparing them with in situ observations of aerosols and INP taken at a nearby mountain site in the Swiss Alps. The sampled air masses predominantly contained Saharan dust and continental aerosols. Various INP parameterizations were also evaluated in this study.

4.2. Impact of Aerosol on Mixed and Cirrus Clouds

Lidars are very effective in studying the impact of particular types of aerosols on the microphysics of clouds. Choi et al. [176] demonstrated the ability to distinguish supercooled liquid clouds from ice clouds for the satellite-borne lidar CALIOP from the layer-integrated particle depolarization ratio and backscatter coefficient at 532nm, together with the cloud top and bottom temperatures, and demonstrated an inverse correlation between supercooled cloud presence and dust presence. Utilizing its capability to discriminate cloud phases, Tan et al. [177] directly investigated the ice-nucleating potential of dust, polluted dust, and smoke aerosols in mixed-phase clouds. They analyzed vertically-resolved profiles of cloud thermodynamic phase and aerosols from global spaceborne lidar data spanning 5 years. Their findings revealed that the presence of dust aerosols, both in their clean and polluted forms, in various regions globally at temperatures conducive to mixed-phase clouds, reduces the fraction of supercooled clouds compared to total cloud cover in those regions. This reduction was attributed to the ability of dust aerosols to nucleate ice crystals.

The influence of desert dust aerosols on cirrus microphysical properties was investigated using concurrent and co-located datasets from CALIOP, CloudSat, and MODIS over the Taklimakan Desert [178]. The study highlighted the negative "Twomey effect" under arid conditions [56], where cloud albedo decreases due to increased heterogeneous nucleation. This process results in fewer but larger ice crystals with higher fall velocities.

The role of wildfire smokes on cirrus formation was investigated by Mamouri et al. [179] who showed strong evidence that long range transport of aged smoke (organic aerosol particles) originating from wildfires triggered significant ice nucleation causing the formation of extended cirrus layers, upon gravity wave activity close to the tropopause.

The impact of aerosols on cloud thermodynamic phase was also addressed by Zhang et al. [180] over east Asia by combining the 4 years datasets of CloudSat radar and CALIOP lidar measurements. Although temperature differences at cloud top showed to be the most important drivers of the cloud thermodynamic phase, regional differences and seasonal anomalies of glaciated and mixed-phase relative cloud fractions correlated well with variations of dust occurrence frequency. Moreover, the relative frequency of glaciated clouds associated with concomitant presence of mineral dust was higher than the frequency of glaciated clouds associated with presence of polluted dust, smoke, and background aerosols at any given cloud top temperature.

Hofer et al. [181] investigated the efficiency of heterogeneous ice formation across stations located in New Zealand (Lauder), Germany (Leipzig), and southern Chile (Punta Arenas), as influenced by cloud-top temperature. They observed that Lauder and southern Chile, which typically experience low concentrations of free-tropospheric aerosols, exhibit lower ice formation efficiency compared to polluted mid-latitude regions like Germany. This suggests that the reduced ice formation efficiency at Lauder and Punta Arenas is linked to low concentrations of INP. Additionally, episodes of continental aerosol outbreaks, more frequent at Lauder than Punta Arenas, moderately enhance the ice formation efficiency at Lauder relative to Punta Arenas.

The diurnal cycle of the supercooled water cloud fraction was investigated by Wang et al. [182] using 33 months of lidar observations from the Cloud-Aerosol Transport System aboard the International Space Station. This system provides cloud top phase information at various local times within specific grid and isotherm parameters. The study revealed a strong and statistically significant negative correlation between the dust aerosol extinction coefficient near the location and time of liquid/ice cloud footprints, and the fraction of supercooled water clouds. Specifically, higher dust aerosol extinction coefficients corresponded to lower supercooled water cloud fractions in the observed regions.

4.3. Impact of Aerosol on Warm Clouds

Studies investigating the influence of aerosols on warm clouds predominantly employ dual-FOV lidar techniques. Schmidt et al. [183] utilized colocated dual-FOV Raman lidar observations to examine aerosol and cloud optical and microphysical properties beneath and within thin layered liquid water clouds. They complemented these observations with Doppler lidar measurements of updrafts and downdrafts at cloud base to explore the relationship between aerosol concentrations near cloud base and cloud characteristics and dynamics.

The dual-FOV lidar setup enabled the use of two multiple-scattering channels (elastic and nitrogen Raman multiple-backscatter channels) to profile single-scattering extinction coefficient, effective radius, cloud droplet number concentration, and liquid water content [133]. The study included two case studies that tracked the evolution of altocumulus clouds in clean and moderately polluted conditions.

The impact of updrafts, downdrafts, turbulent mixing, and entrainment of dry air on the microphysical properties of layered clouds was investigated using a combination of Doppler lidar and cloud radar. Significant differences in cloud properties were documented during updraft and downdraft episodes, particularly in droplet extinction, number concentration, and effective radius. Updraft episodes showed a notable increase in extinction coefficient and droplet number concentration, accompanied by lower droplet effective radii attributed to new droplet formation. The liquid water content (LWC) profile retrieved during updraft periods closely resembled the adiabatic LWC profile, whereas during downdraft episodes, higher LWC values indicated an absence of dry intrusions.

Conversely, signs of dry entrainment during downdrafts—such as lower effective radii and reduced LWC values observed around the cloud center—were documented in another case study. This scenario occurred when weaker vertical motions facilitated downward mixing of dry air from above the shallow cloud layer.

Various studies highlight the challenges of studying aerosol-cloud interactions (ACI) in turbulent environments, where turbulent motions can influence processes like evaporation, drop collision, and new droplet formation, leading to opposing effects on cloud microphysical parameters [184]. Schmidt et al. [185] conducted a statistical analysis spanning two years, demonstrating a clear aerosol impact on cloud evolution and cloud droplet number concentration in the lower portions of altocumulus layers during updrafts. Their analysis underscored the importance of considering cloud dynamics in assessing ACI parameters, emphasizing the need to incorporate vertical wind information.

Furthermore, a comprehensive review of contemporary field studies on aerosol-cloud interactions in warm clouds (depicted in Figure 6) supported findings that Aitken and accumulation-mode particles are activated at cloud base when rapidly uplifted, irrespective of whether clouds form over oceans or continents. This dynamic contrasts with passive satellite remote sensing, which typically yields lower estimates of $AC{I}_N$ compared to ground-based lidar and airborne observations, potentially due to differences in cloud-top dynamics.

Jimenez et al. [186] conducted cloud measurements in pristine marine conditions at Punta Arenas in southern Chile using a multiwavelength polarization Raman lidar with dual-field-of-view (FOV), coupled with a Doppler lidar for vertical wind component measurements. They performed a detailed study on aerosol-cloud interactions (ACI), resolving updrafts and downdrafts. The study utilized profiles of aerosol-related parameters near cloud base, cloud microphysical properties just above cloud base, and 1-minute resolution vertical wind data. CCN number concentration was derived from lidar-measured aerosol extinction following Mamouri and Ansmann [159]. They observed high $AC{I}_N$ values ranging from 0.8 to 1.0. The study highlighted the impact of aerosol water uptake on ACI, noting that the highest $AC{I}_N$ values were obtained when considering aerosol extinction measurements taken approximately 500 meters below cloud base (indicating dry aerosol conditions) in ACI computations.

Wang et al. [187] utilized a dual-FOV HSRL to simultaneously profile aerosols and liquid water clouds clouds, focusing on assessing the adiabaticity of these low-level clouds. They found in some case that observed profiles of microphysical properties in these clouds are not perfectly adiabatic, contrary to common assumptions in current retrieval methods [35,188,189]. Additionally, the study confirmed that increased aerosol loading leads to higher droplet number concentrations and reduced droplet effective radius, although no discernible increase in liquid water path (LWP) was detected. This suggests that aerosol-induced water reduction through enhanced evaporation may offset increases caused by suppressed rain formation. The lidar observations were validated through concurrent measurements with cloud radar, Raman lidar, and sun photometer instruments.

5. Challenges and Future Directions

Up-to-date Earth System Model simulations that include a realistic description of microphysical properties and processes suggests that the equilibrium climate sensitivity (ECS) has been underestimated so far [190]. There are indications that the main reason for the increase of the current estimation of the ECS depends on the representation of processes involved in the formation of clouds and, specifically, on mixed-phase cloud microphysics and ACI [191,192].

Lidar techniques have significantly advanced our understanding of the complex interactions between aerosols, clouds, and the atmosphere, however, several challenges remain. Technological progress may partially increase the lidar capability demonstrated so far. The increasingly stringent demands of topographic mapping have led to lidar instruments whose vertical resolutions are well below one meter, and high-repetition laser systems allow temporal resolutions below one second. Enhancing the spatial and temporal resolution of lidar observations enables the detection of smaller-scale features within aerosol and cloud layers. High-resolution lidar systems allow for detailed mapping of aerosol and cloud properties with fine spatial granularity. Additionally, advancements in temporal resolution enable the study of rapid atmospheric processes, such as cloud evolution and aerosol transport, which can vary on short timescales. Lidars with a resolution at the submeter scale have been recently employed to sample the depth of the droplet activation layer of stratiform clouds with unprecedented accuracy[193].

Furthermore, we have limited our review mainly to works in which lidar could operate as an isolated instrument, but clearly the integration of multi-platform observations greatly increases its capacity. Combining data from various remote sensing instruments offers a more holistic view of ACI. By combining weather radars in the millimeter range and lidars, it is possible to detect a wider range of particle sizes and to more accurately determine cloud boundaries. Lidars, due to their shorter wavelength emissions, are capable of detecting particles from a few nanometers up to a few micrometers in size, but they may miss cloud droplets that are in the tens of micrometers range when their concentration is low. Conversely, radar backscatter is basically dependent on the sixth power of the droplet diameter, making it insensitive to small particles [194,195], hence the synergy between lidars and cloud radars enhances atmospheric observations by combining lidar’s high-resolution profiling of aerosols and cloud particles with cloud radar’s ability to detect larger hydrometeors and cloud structures, providing a comprehensive view of cloud microphysics and dynamics. IR [196], visible spectrometers [197] and microwave radiometers [198] further enhance such synergy, allowing a seamless retrieval between regions of the cloud detected by both radar and lidar and regions detected by just one of these two instruments, or helping separate cloud and drizzle modes, or profiling the environmental temperature and LWC. Furthermore, the integration of remote sensors with in-situ measurements within and around clouds, either airborne [199,200] or from high mountain research stations [175,201], greatly supports the ACI study.

Satellite observations provide global coverage, aiding in the understanding of large-scale phenomena and their long term evolution [202]. Leading the way was the CALIOP lidar, which operated in the A-Train and C-Train sun-synchronous orbits at an altitude of around 700 km for 17 years (2006-2023). The Cloud-Aerosol Transport System (CATS) followed, operated from the International Space Station for two and a half years (2015-2017), showcasing innovative technologies such as high repetition frequencies. The now operational EarthCARE mission by ESA and JAXA includes the 355 nm HSR lidar ATLID, planned to operate for three or more years (2024-2027) and, lastly, NASA’s AOS initiative, launched in 2022, aims to deploy at least one lidar on orbital platforms, scheduled for launch around 2030. Additionally, the Cloud and Aerosol Lidar for Global Scale Observations of the Ocean-Land-Atmosphere System (CALIGOLA), an advanced multi-purpose space lidar mission developed by the Italian Space Agency (ASI), is anticipated to launch around 2031 [94,203]. These ongoing and future space-based lidar missions will significantly enhance our understanding of aerosol-cloud interactions by providing high-resolution, three-dimensional measurements of aerosol distribution and cloud properties on a global scale.

At the same time, ground based observation with large multiwavelength lidar systems with Raman or HSRL capabilities, innovative use of multiple FOV systems, possibly sided by radars and radiometers, will remain crucial for for formulating and validating inversion techniques. These techniques, once validated, can then be applied to less advanced but more widely deployable systems and measurement stations. The detailed, continuous, and high-resolution vertical profiles provided by these systems are invaluable for distinguishing different types of aerosols, measuring the optical and microphysical properties of clouds and aerosols, and assessing their vertical distribution and temporal evolution.

6. Conclusion

This paper has presented a survey of diverse lidar techniques utilized to study ACI, emphasizing the capabilities and advancements in multiwavelength, Raman, and HSRL systems. Both ground-based and satellite lidar platforms have been discussed, highlighting their respective contributions to our understanding of aerosol properties and their role in cloud formation and dynamics. Multiwavelength Lidar provides critical insights into the size distribution and optical properties of aerosols, allowing for detailed characterization of different aerosol types and their potential as cloud condensation nuclei (CCN). HSRL and Raman lidars enables precise separation of aerosol and molecular scattering components, delivering accurate aerosol optical depth (AOD) and backscatter profiles, as well as accurate aerosol classification. Raman WV Lidar by measuring water vapor and other gas profiles with high sensitivity, enhances our understanding of the humidity conditions under which aerosols interact with clouds, offering valuable data for modeling cloud microphysical processes. Dual-FOV depolarization lidars allows continuous measurements not limited to low light background conditions and is delivering precise characterization of aerosols and droplets within clouds, thus providing insights into the processes of aerosol-induced cloud nucleation.

The implementation of these lidar techniques has significantly advanced our knowledge of ACI, and, while ground-based lidar systems provide high-resolution, localized observations, which are critical for process-level studies, model validation and tests of new data interpretation schemes, satellite-based lidar extends the observation capability to a global scale, offering comprehensive coverage and the ability to monitor long-term trends and variability in aerosol-cloud interactions.

In conclusion, lidar technology has proven to be an indispensable tool in ACI studies. The advancements in multiwavelength, Raman, and HSRL techniques, combined with comprehensive ground-based and satellite observations, and more accurate inversion and interpretation schemes for the data, provide a robust framework for addressing critical scientific questions about the role of aerosol in climate. Continued innovation and collaboration in this field will undoubtedly lead to deeper insights and more accurate climate predictions.