Dual-field-of-view Raman lidar measurements, detecting Raman-scattered light with two fields of view simultaneously, are used for the first time to retrieve cloud microphysical properties. The measurements are performed with the Multiwavelength Atmospheric Raman Lidar for Temperature, Humidity, and Aerosol Profiling (MARTHA) at the Leibniz Institute for Tropospheric Research in Leipzig, Germany. Light that is scattered in forward direction by cloud droplets and inelastically backscattered by molecules is detected. A forward iterative algorithm uses the measured signals to derive profiles of the effective cloud droplet radius, extinction coefficient, and liquid-water content of the investigated clouds. The setup, algorithm, error analysis, and a measurement example are presented. The obtained liquid-water path is validated by observations with a microwave radiometer. With the capability to retrieve aerosol properties as well as cloud microphysical properties, the Raman lidar MARTHA is an ideal tool for studies of the aerosol indirect effect.
© 2013 Optical Society of America
Uncertainties in the understanding of the aerosol influence on cloud properties are a major drawback for a satisfactory estimation of the anthropogenic radiative forcing . The complexity of aerosol–cloud interaction and the influence of meteorological conditions make it difficult to isolate and quantify the relevant effects . One major aerosol–cloud interaction process was described by Twomey . He suggested that an increased aerosol load leads to a higher concentration of cloud condensation nuclei that increases the cloud droplet concentration and thus decreases cloud droplet size under a constant liquid-water content (LWC). Consequently, the cloud albedo and therefore the radiative cooling effect of the cloud increase. Several investigations of the Twomey effect were performed that show a large spread of the obtained magnitudes of this effect . The corresponding uncertainty of the related radiative forcing is substantial relative to the total net anthropogenic radiative forcing , constituting the great demand for further field experiments of aerosol–cloud interaction.
There are several approaches to study the Twomey effect. In situ airborne observations permit detailed investigations of aerosol and cloud microphysical properties [5,6]. Nevertheless, these methods are too costly and are limited to case studies and thus are not suitable for statistically significant long-term studies. Satellite passive remote-sensing measurements have a global coverage [7,8], but do not provide information of the height distribution of the aerosol.
Active remote-sensing techniques promise a much deeper insight into the Twomey effect through the capability of long-term observations with a high spatial and temporal resolution. Lidar measurements, providing high-resolved profiles of various aerosol properties [9–13], are a valuable tool for aerosol studies. For active remote sensing of clouds, the usage of radar as well as lidar is feasible. Radars have a much greater penetration depth that may be important for measurements of clouds with a large vertical extent. On the other hand, signals of thin clouds are often below the radar detection threshold and can be better observed with lidar. The primary advantage of lidar studies is the higher sensitivity toward smaller droplets that leads to a greater accuracy at cloud base—the region where water droplets are formed and aerosol particles are mixed in. Thus lidar measurements are extremely valuable for studying aerosol–cloud interaction, either in combination with radar observations or even in a single-instrument approach.
Lidar studies of water clouds have been performed using light that is multiply scattered for the retrieval of the extinction coefficient and effective droplet radius [14,15]. Elastically scattered light was detected with several different fields of view (FOVs) to gain information on the angular distribution of the scattered photons. Thus cloud droplet radii were derived by making use of the bijective correlation between the width of the forward scattering peak and droplet size. However, the data analysis is complicated due to the nonisotropic backscattering at water droplets causing angle-dependent backscatter efficiencies. Therefore, the authors of  suggested the use of six FOVs for an optimum measurement. Lidars detecting multiple-scattered light with up to 32 FOVs are known . The drawback of the resulting complex measurement setup can be overcome by the detection of light being Raman scattered from molecules because the phase function for Raman scattering by nitrogen molecules is nearly isotropic in the backward direction. Thus the angular distribution of the received light depends on the forward scattering phase function and thus particle size only. When detecting Raman-scattered light, the usage of two FOVs is sufficient to derive profiles of the effective cloud droplet radius , which keeps the measurement setup as well as the data retrieval relatively simple.
With the dual-FOV Raman lidar technique, profiles of the single-scattering extinction coefficient can be retrieved as well. This capability is of great importance as the extinction coefficient calculated without considering multiple scattering [9,19] leads to errors of up to 50% in water clouds . Profiles of the extinction coefficient are important for retrievals of cloud microphysical properties using radar and lidar measurements .
In the second section the Multiwavelength Atmospheric Raman Lidar for Temperature, Humidity, and Aerosol Profiling (MARTHA) as well as the setup for the performance of dual-FOV measurements are presented. Section 3 describes the implemented forward iterative algorithm for the retrieval of cloud microphysical properties. Section 4 explains the data analysis scheme applied to the dual-FOV Raman measurements. In Section 5, a dual-FOV Raman measurement example is presented. Errors and uncertainties of the presented method are analyzed in Section 6. Section 7 provides a summarizing discussion and an outlook.
2. Setup of the Dual-Field-of-View Raman Lidar MARTHA
The Raman lidar MARTHA, being part of the Leipzig Aerosol and Cloud Remote Observations System (LACROS) is operated at the Leibniz Institute for Tropospheric Research (TROPOS) in Leipzig, Germany. It is used for long-term aerosol measurements in the framework of the European Aerosol Research Lidar Network (EARLINET)  as well as a laboratory environment for the application of novel lidar techniques [10,11,23,24]. The system is described in detail in . In 2008, MARTHA was upgraded to perform dual-FOV Raman measurements.
The transmitter of MARTHA consists of a pulsed, -switched Nd:YAG laser operating with a repetition rate of 30 Hz. By second and third harmonic generation light at wavelengths of 532 and 355 nm, respectively, is generated. The total pulse energy is 1.4 J, with 0.3 J at 355 nm, 0.6 J at 532 nm, and 0.5 J at 1064 nm. A beam expander with a magnification factor of 15 increases the beam diameter to 150 mm. Thus the beam divergence is decreased to a turbulence-limited full angle of 0.1–0.2 mrad. The receiver consists of a 0.8 m Cassegrain telescope with an effective focal length of 8974 mm. The emitted laser beam and the optical axis of the telescope are coaxial. The alignment of the laser beam is controlled with a camera displaying an image of the laser beam with respect to the telescope’s FOV. Thus, the pointing of the laser beam can be easily adjusted with two remotely controlled actuators.
The receiver consists of 14 detection channels as illustrated in Fig. 1. The channels 355, 532, and 1064 nm detect elastically backscattered light for the retrieval of profiles of the particle backscatter coefficient at the corresponding wavelength . For the determination of the profiles of the extinction coefficient the channels 387 and 607 nm detect light that is Raman scattered from molecules [9,19]. Further detection channels are employed to retrieve profiles of the depolarization ratio [532 nm (pp) and 532 nm (cp)], water-vapor-to-dry-air mixing ratio (407 nm) and temperature .
The capability to perform lidar measurements with two different FOVs simultaneously is realized by using a mirror diaphragm instead of a conventional field stop. The mirror diaphragm is illustrated in Fig. 1. It consists of a dielectric mirror, which is high-reflective at 532 and 607 nm, with an elliptical bore and an elliptical obstruction. The mirror diaphragm is placed under an angle of 45° in the optical path. The projections under this angle of the bore and the obstruction are circular. As the light from the narrow inner FOV is transmitted through the bore, the bore defines the inner FOV. Light from the annular wide outer FOV is reflected by the mirror. Thus the size of the obstruction defines the outer FOV. As the inner FOV constitutes a clearance for the outer FOV the shape of the outer FOV is not a full cone but has an annular cross section. Both ellipses are centered at the optical axis of the receiver. Hence the narrow and wide FOV are aligned to the same axis.
An exact knowledge of the overlap function is crucial for the retrieval algorithm described below. Therefore, we investigated the effect of employing a mirror diaphragm instead of a conventional field stop on the overlap function in detail. An ideal field stop has an infinite small thickness and is placed orthogonally to the optical axis in the optical path. The mirror diaphragm is 2 mm thick and is positioned under 45°. Ray-tracing simulations with the software ZEMAX were performed as described by Reichardt et al.  to compare the overlap functions of the Raman lidar MARTHA employing the mirror diaphragm as well as an ideal field stop. Figure 2 displays the obtained results: the simulated overlap functions (blue and green lines) agree very well. This demonstrates that the usage of a mirror diaphragm instead of an ideal field stop does not affect the overlap function and thus the measured lidar signals. Furthermore, the overlap function of the Raman lidar MARTHA was determined experimentally as described by Wandinger and Ansmann . This overlap function matches the simulated functions very well (see Fig. 2, red line), illustrating that the lidar system is well represented in the ray-tracing simulations.
The parameters used for the simulation are listed in Table 1. All angles given in Table 1 are to be understood as full angles. The same applies to all following angles if not stated otherwise. The given radius of the telescope’s secondary mirror is considered as an obstruction of the primary mirror in the ray-tracing simulations. The values for the FOV, radii of the telescope’s mirrors, and radius of the laser beam were either measured directly or calculated from measurements. The effective focal length of the telescope was given by the trader (Astro Optik Philipp Keller, Neutraubling, Germany). To obtain a steeper increase of the overlap function, the field stop of the Raman lidar MARTHA is not placed in the focal plane of the telescope but slightly behind. Due to the long focal length of the receiving telescope, it is difficult to obtain an exact measure for the distance between the focal plane of the telescope and the field stop. With the auto-collimation method, where a point light source is placed in the telescope’s focal plane and a plane mirror behind the telescope reflects its light back into the focal plane , it was determined to . The value was varied within this range to obtain the best fit of the overlap function obtained from the measurement and the ray-tracing simulations. Neither the divergence of the laser beam nor the tilt of the laser beam against the telscope’s optical axis were measured directly. The laser beam divergence was estimated from the manufacturer’s specification (1.5 mrad) divided by the beam’s expansion factor of 15. Still, the divergence obtained in this way is influenced, among other effects, by diffraction at optical elements of the transmitting unit, atmospheric turbulence, a nonperfect setup of the beam expander, and thermal effects within the laser cavity. Thus the laser beam divergence was varied within the boundaries of 0.08–0.3 mrad to obtain the best match between the measured and simulated overlap functions. Although the alignment of the laser beam is adjusted before every measurement, it is never perfect and thus a tilt of the laser beam against the optical axis of the telescope has to be considered as well. To find the best match of the measured and simulated overlap functions, the tilt of the laser beam was varied between 0 and 0.15 mrad.
Malinka and Zege  gave recommendations for the sizes of the employed FOVs to maximize the sensitivity of the measured signals to the cloud microphysical properties. The optimum for the inner FOV is
The recommended size for the inner as well as for the outer FOV depends on the cloud base height. The receiving unit of MARTHA is set up in a way that it is possible to choose between three differently sized mirror diaphragms to enable cloud measurements in an extended altitude range. The dimensions of the three different mirror diaphragms that can be employed and the corresponding pairs of FOVs are listed in Table 2. This table also shows altitude ranges for dual-FOV cloud measurements, which comply with Eqs. (1) and (4) and a penetration depth of .
In the derivation of Eqs. (1) and (4), a tilt of the laser beam against the optical axis of the telescope is not considered. However, a consideration of this tilt is necessary for a correct representation of the overlap function and thus the measurement geometry as mentioned before (see also Section 3). Figure 3 illustrates the effect of the tilt of the laser beam on the overlap function for the FOVs of 0.5 and 0.78 mrad with the help of ray-tracing simulations. The parameters utilized are listed in Table 1 and are identical to those used to derive the overlap functions displayed in Fig. 2. For the FOV of 0.5 mrad, the overlap function of a nontilted laser beam was compared to the overlap function with a tilt of the laser beam of 0.115 mrad as given in Table 1. The tilt used for the examination of this effect in the larger FOV of 0.78 mrad is 0.205 mrad (see Section 3 for the selection of this parameter). A tilt of the laser beam leads to a weaker increase of the overlap function and thus shifts the optimum altitudes for cloud measurements upward. At the altitudes relevant for cloud measurements, there is a height shift of 0.5–1.0 km between equivalent values of the overlap functions with and without the tilt of the laser beam. Thus, the altitude ranges of the clouds for the selection of the corresponding mirror diaphragm are corrected by these differences. In Table 2, the optimum cloud base heights for dual-FOV measurements with the corresponding mirror diaphragms, considering a tilt of the laser beam, are listed. These height requirements were applied for the performed dual-FOV cloud measurements.
For a proper performance of the interference filters and dichroic beam splitters in the receiver, small deviations from the nominal angles of incidence of 0° or 45° are required. In general, the deviations from the nominal angles of incidence increase with increasing FOV. In the dual-FOV technique, large FOVs are employed, especially for the outer FOVs. Thus a check of the angles of incidence on the optical elements in the beam separation unit is necessary. The distribution of these angles was investigated with help of ray-tracing simulations with ZEMAX. The lidar parameters for the simulations of the inner FOVs were the same as used for the retrieval of the overlap functions. The simulations for the outer FOVs were done with a virtual laser beam divergence of 2 and 4 mrad to account for the possible backscattering of photons from the entire volume of the outer FOV due to multiple scattering in clouds. Figure 4 shows the angular distribution for inner FOVs of 0.5 and 0.78 mrad and outer FOVs of 2.0 and 3.8 mrad on the interference filters of the detection channels for different backscattering heights. Rays from the outer FOV have much larger angles of incidence than rays from the inner FOV. Ray-tracing simulations show that the acceptance angles of the employed interference filters are of the order of 5° . Since all angles of incidence are well below this value, there is no effect of the limited angular acceptance of the interference filters on the measured signals.
The light from the outer FOV is collimated with an achromatic lens system having a clear aperture of 73.5 mm and a focal length of 300 mm. Raman-scattered light with a wavelength of 607 nm, as well as elastically scattered light at 532 nm, is detected. The detection channels are labeled 607 nm (out) and 532 nm (out) in Fig. 1. In both detection channels for the outer FOV a combination of an objective and eyepiece is employed to display an image of the primary mirror of the telescope on the photocathodes of the photomultipliers (PMTs) to avoid a dependence of the PMT sensitivity on backscattering height . The same principle is used for the detection channels of the inner FOV, except for the channels for the temperature measurement at 532 nm that work with fiber optics. The central wavelengths of the interference filters in the detection channels for the outer FOV are 532.0 and 607.3 nm with a full width at half-maximum of 5.0 and 3.0 nm, respectively. The signals from the outer FOV are detected with PMTs of the type R7400-U20 from Hamamatsu Photonics K.K., Hamamatsu City, Japan, which are employed in photomultiplier modules from Licel GmbH, Berlin, Germany and recorded with the Licel transient recorder TR20-160. The raw spatial resolution is 7.5 m. The temporal resolution is set to 4 s to limit the effect of cloud inhomogeneities. To increase the number of profiles which are detected within each 4 s interval, the maximum detection height is decreased to 30 km, which is far enough to do an accurate background correction of the measured signals. The signals from the inner FOV are recorded with the data acquisition system Purana from MEDAV, Uttenreuth, Germany, which is run synchronously with the Licel transient recorder and a temporal resolution of 4 s as well. The raw spatial resolution is 15 m covering an altitude range of 15 km.
As the Licel and Purana systems are triggered independently, the corresponding signals have to be corrected for a possible height shift. This shift was determined from cloud measurements by comparing the measured cloud base height. For the Purana system, the total signal at 532 nm (channel 532 nm in Fig. 1) was used for the study. For the Licel system, the channels detecting the cross- and parallel-polarized signals from the inner FOV at 532 nm [channels 532 nm (pp) and 532 nm (cp) in Fig. 1] were used. Hence, channels using the same FOV and thus the same measurement geometry were compared. Furthermore, the same wavelength was used for the comparison to avoid any effect of particle growth due to increased humidity below cloud base on the study. Five measurements were analyzed for the study of the height shift and consistently gave a height shift of 22.5 m, with the 0 m height of Purana corresponding to the height of 22.5 m in the Licel system.
To avoid effects of the PMT dead time on the measured signals, the intensity of the detected light is decreased with neutral-density filters in each detection channel separately. The optical density of the filters employed for the detection of light at 607 nm from the inner FOV is varied depending on cloud base height and aerosol properties between 0.2 and 1.1. For the detection of light at 607 nm from the outer FOV, filters with optical densities between 0 and 1.1 are used. With the appropriate setting of the neutral-density filters for each cloud measurement, a maximum penetration depth into the cloud is achieved.
Due to the small scattering cross section for Raman scattering and the large outer FOVs, the Raman signal from the outer FOV cannot be separated from the background lighting at daytime. Thus dual-FOV Raman measurements are restricted to night time.
3. Forward Iterative Algorithm
Malinka and Zege  presented a solution for analytical modeling of Raman lidar signals influenced by multiple scattering based on a small-angle approximation. The scattering process of one or multiple elastic scattering events in forward direction and an inelastic backscattering event, leading to signals at the Raman-shifted wavelength, is considered. The alternative scattering process with an inelastic scattering in forward direction and elastic backscattering is less probable by more than three orders of magnitude for scattering processes in clouds and thus can be neglected. The almost isotropic phase function for inelastic scattering simplifies the analytical solution because the angular distribution of the detected light is determined by forward scattering only.
The forward iterative algorithm, presented by Malinka and Zege , uses this analytical solution for the retrieval of the cloud droplet effective radius and extinction coefficient in water clouds. The algorithm is based on measuring Raman lidar signals synchronously with two FOVs. Photons being once or multiply forward scattered by cloud droplets and Raman backscattered by nitrogen molecules are detected. The retrieval of the droplet size is made possible by the nonambiguous dependence of the width of the forward scattering peak and thus the angular distribution on droplet size. No assumptions on cloud properties, as for example adiabaticity, are made for the retrieval.
In the algorithm, the investigated cloud is considered to consist of a number of homogenous cloud layers, each with its own characteristics regarding extinction and effective radius. For each layer the extinction and effective radius are determined, which constitute the resulting profiles of the derived quantities. The number of layers can be set manually to compromise the demands of a successful forward iteration and an adequate height resolution, which is necessary to resolve the cloud’s characteristics. Furthermore, the algorithm includes a function to set the number of cloud layers automatically according to the count rates of the measured lidar signals in each height range. The heights of the cloud base and top are set manually according to the signals from elastic scattering in the inner FOV. If the investigated cloud is too thick to be penetrated by the lidar, the upper height limit for the forward iteration is set to the maximum penetration depth.
The algorithm runs iteratively. In the first run, the effective radii in all cloud layers are set to 9 μm. The extinction coefficient is set to the values calculated from the signal measured in the inner FOV, applying the single-scattering approximation. From these cloud properties the expected lidar signals of both FOVs are calculated analytically. The results are compared with the measured signals. The assumed cloud microphysical properties are adapted according to the comparison and used for the next iteration step by calculating the resulting lidar signals again. The iteration is stopped when the calculated signals converge. The difference between the calculated and measured signal is calculated as
For analyzing dual-FOV measurements performed with the Raman lidar MARTHA, the forward iterative algorithm has to be adopted to the measurement geometry of the lidar, which is represented by the overlap function. A correct representation of the lidar parameters (e.g., tilt of laser beam, laser beam divergence, position of field stop) in the forward iterative algorithm is necessary, because the resulting measurement geometry has a strong effect on the dual-FOV lidar signals and thus the retrieved cloud microphysical properties. Functions of the forward iterative algorithm were used to calculate the overlap function analytically . Figure 5 shows a comparison of these overlap functions with the functions obtained experimentally and from ray-tracing simulations. The parameters for the ray-tracing simulation for the FOV of 0.5 mrad are identical to those in Section 2 and are listed in Table 1. The simulation for the FOV of 0.78 mrad uses the same parameters except for a larger uncertainty in the tilt of the laser beam. For a larger FOV, the image of the footprint of the FOV is larger, which makes it more difficult to adjust the displayed laser beam to the center of the image causing a larger tilt of the laser beam. To find the best match between the measured and simulated overlap functions, the tilt was varied between 0 and 0.23 mrad, giving the best match at a tilt of 0.205 mrad.
The parameters, used for the analytical calculation, that produced the best match with the overlap functions derived experimentally and from ray-tracing simulations, are utilized to represent the measurement geometry in the forward iterative algorithm. The radii of the telescope’s mirrors and the laser beam, the effective focal length of the telescope, as well as the distance between the focal plane of the telescope and the mirror diaphragm are set as listed in Table 1. In the ray-tracing simulation and the analytical calculation, the edge of the laser beam (cutoff intensity) is treated differently. Thus, the tilt and divergence of the laser beam were slightly varied from the corresponding values used for the ray-tracing simulation by . Table 3 shows the tilt and divergence for the analytical calculation and ray-tracing simulation that yield the best match of the overlap functions.
The forward iterative algorithm retrieves profiles of the effective droplet radius and the extinction coefficient of clouds. These two quantities together with the water density can be used to calculate the LWC , which is another important cloud microphysical property:6).
4. Scheme for Data Analysis
This section describes the pre- and postprocessing of the data for the forward iterative algorithm as well as the settings for running the cloud forward iterations. The signals at 607 nm from the inner and outer FOV are recorded with different data acquisition systems and have a different height resolution. Thus the signal from the outer FOV, recorded with the Licel transient recorder at a height resolution of 7.5 m, is averaged to a height resolution of 15 m that corresponds to the height resolution of the Purana system. The cloud base height often varies within a timespan of several seconds to minutes by 10–50 m. Averaging profiles with different cloud base heights would result in inaccurately retrieved cloud microphysical properties, especially at the cloud base where cloud-free and cloud-containing measurement points would be averaged. For each of the 4 s profiles, the height of the cloud base is determined from the derivative of the total signal at 532 nm automatically. For the averaging only profiles are considered for which the cloud base does not differ by more than 30 m.
For the analysis of a cloud measurement, the cloud forward iterations are performed with height resolutions of four, five, six, and seven layers as well as an automatically determined height resolution. Forward iterations with more than seven height layers often show oscillations in the retrieved results, indicating that the obtained solutions are not stable. For each case the algorithm is executed with a variety of lower and upper height limits. To account for uncertainties in the retrieved cloud base height, also due to its temporal variations, the cloud base height is varied by 30 m in steps of 15 m. The upper height limit for the forward iteration is set either where one of the measured signals reaches its background level or at the cloud top in case the cloud could be penetrated. However, the measured lidar signals close to that height limit are usually very weak and thus the forward iteration might not run successfully. In case of cloud penetration, the cloud top often cannot be exactly determined due to the weak lidar signals in the corresponding altitude. Thus, the upper height limit for the forward iteration is varied by 45 m toward lower altitudes in steps of 15 m.
The measurement error of the lidar signals used for the forward iteration is considered by input variation, using Monte Carlo simulations. Thus for a forward iteration run the algorithm is executed 14 times with count rates being varied within the range for each height in the 15 m signal resolution, according to the standard deviation of a Poisson distribution. The results of these forward iterations are used to compute for each cloud layer the mean value and its error from the standard deviation, yielding profiles of the effective radius and the extinction coefficient.
According to the five different height resolutions (number of layers) used for the forward iteration runs, as well as the three and four different heights for the lower and upper limit, respectively, a total of 60 forward iterative runs are performed for the analysis of a cloud measurement. The obtained profiles of cloud microphysical properties are checked for their quality. Profiles with a data point having a relative error of more than 60% are excluded as well profiles where the average error of two consecutive data points exceeds 45% and profiles where the average relative error of all data points exceeds 30%. Furthermore, profiles that are physically unrealistic are discarded. Thus profiles with effective radii greater than 30 μm are rejected as well as profiles that show oscillations. Moreover, profiles that show a strong difference between two consecutive data points are excluded. These profiles are defined as profiles with a data point that has a relative difference to its neighboring points larger than 5. On average, 30%–85% of the forward iterative results are accepted. These profiles are averaged to a common height resolution that corresponds to the lowest height resolution leading to successful cloud forward iterations. The resulting profiles are averaged with a weight according to the calculated statistical error from the input variation. The standard deviation of these data points in each height bin is regarded as the error of the corresponding mean.
5. Measurement Example
Figure 6 shows the time-height cross section of the range-corrected lidar signal at 532 nm from the inner FOV, measured during a dual-FOV Raman lidar measurement on 5 September 2011. Aerosol layers are indicated by yellowish colors. The measured cloud is shown in red colors. The orange line in the center of the cloud is due to the dead-time saturation effect of the PMT.
For the cloud retrieval, 132 profiles were summarized excluding profiles where cloud gaps or variations of the cloud base of more than 30 m occurred. The Raman signals at 607 nm, measured in the inner and outer FOV, are shown in Fig. 7. Furthermore Fig. 7 shows the signal at 532 nm from the inner FOV, which indicates the cloud base height at about 2.9 km and the cloud top height at approximately 3.07 km. The weak signal increase below 2.9 km is attributed to aerosol growth due to the increased humidity below the cloud. The signal decrease in the center of the cloud is due to dead-time effects of the PMT at high count rates. The cloud forward iteration is not affected by dead-time effects as the Raman signals have lower count rates of 0.8 and 5.0 mega counts per second (MC/s) in the cloud. In addition, Fig. 7 displays the Raman signals that were simulated with the forward iterative algorithm being in accordance with the measured signals.
Figure 8 presents the results obtained with the analysis scheme described in Section 4. On the left side, the extinction coefficient of the cloud is displayed. The profile retrieved with the forward iterative algorithm is compared with the extinction coefficient obtained from the conventional Raman method not considering multiple scattering . The extinction coefficient from the forward iterative algorithm exceeds the extinction coefficient calculated with the Raman method as expected because of the multiple-scattering effect. Light that is forward scattered under small angles remains in the inner FOV and is backscattered to the lidar instead of getting lost. The plot in the center shows the profile of the effective cloud droplet radius. Over the largest part of the cloud, the effective radius increases with penetration depth. This can be explained with the further condensation of water vapor due to the cooling of the ascending air parcel. The increase of the LWC, shown on the right side, is caused by the same process. The comparison of Figs. 7 and 8 shows that the upper cloud layer of the forward iterative results reaches the top of the measured cloud. Thus the decrease of the effective droplet radius and LWC at larger penetration depths can be explained with the downmixing of dry air from above the cloud leading to the evaporation of some liquid water. At penetration depths between 55 and 137.5 m, which correspond to the inner part of the cloud, the effective radius is between 10 and 16 μm. The LWC has values between 0.14 and in this height range. These values fit to effective radii and LWC from in situ measurements .
The microwave radiometer (MWR), being part of LACROS and situated only a few meters from MARTHA, was used for a verification of the forward iterative results. The MWR measured the liquid-water path (LWP) of the cloud. The MWR was calibrated to an LWP of in a cloud-free period from 20:02 to 20:06 UTC , which was identified with the measurement of MARTHA. As mentioned before, the forward iterative algorithm was capable to retrieve the microphysical properties of the cloud roughly up to the cloud top. Thus, the derived LWC profile can be used to calculate the LWP for a comparison with the corresponding measurement with the MWR. Figure 9 shows the LWP measured with the MWR during the time period used for the forward iteration as well as its average and the LWP obtained from the dual-FOV measurement. The average LWP measured with the MWR is . This value matches the LWP of from the dual-FOV measurement. A reason for the slightly smaller LWP from the forward iteration might be that eventually the cloud was not completely penetrated with the dual-FOV measurement. Furthermore, the measurement geometry might cause deviations: an MWR probes a much larger volume than the comparable narrow FOV of a lidar.
6. Error Analysis
This section deals with the accuracy and quality of the results retrieved from forward iterations. In the first section, the statistical error from the averaging of iteration results with differently set cloud boundaries and height resolutions is compared to the error obtained from the variation of the lidar signals as the input of the forward iteration. The second part investigates the influence of the measurement geometry, set in the forward iterative algorithm, on the retrieved results. Afterward, the minimal duration of a dual-FOV cloud measurement, which is necessary to obtain successful forward iteration runs, is determined.
A. Error from Averaging over Different Forward Iterative Runs and Input Variation
As explained in Section 4, the stated errors of the retrieved mircophysical properties are statistical errors, retrieved from the standard deviations of the forward iteration results from differently set cloud boundaries and height resolutions. Here, these errors are compared to the errors obtained through input variation of the utilized lidar signals of the inner and outer FOV. Figure 10 shows the relative statistical errors of the forward iteration results presented in Fig. 8 as well as the relative errors obtained from input variation averaged over all successful forward iterative runs. The relative statistical errors are largest at the cloud base with values of 0.41 and 0.53 for the effective radius and the extinction coefficient, respectively. This is due to the differently set lower cloud boundary. Thus profiles with values partially being zero are averaged with other profiles. At larger penetration depths, the corresponding relative errors are below 0.25.
The statistical errors are compared to the errors from input variation in Fig. 10. At the lowest penetration depth, the statistical errors are about nine times larger than the errors from input variation. The ratio of the relative statistical error to the relative error from input variation is much lower for the other penetration depths as illustrated in Fig. 10. Still, for most penetration depths the statistical error is slightly larger than the error from input variation and the magnitude of both errors is similar. Thus the statistical error is regarded as a reasonable measure for the uncertainty of the retrieved cloud microphysical properties. Not considering the errors of the lowest penetration depth, the average of the ratios of the statistical errors to the errors from input variation is 1.3 for the extinction coefficient and 1.0 for the effective radii. Taking the lowest penetration depth into account, the averaged ratios increase to 2.6 and 2.4, respectively.
B. Effects of Uncertainties of Measurement Geometry on Results of Forward Iteration
In Section 3 it was demonstrated that the dual-FOV measurement geometry of MARTHA is well represented in the forward iterative algorithm. In this section, the effect of uncertainties of parameters controlling the measurement geometry is investigated. Therefore, the tilt and divergence of the laser beam were varied as these parameters have a strong influence on the overlap function and have the largest uncertainty of the parameters affecting the measurement geometry (see Section 2). The varied as well as the original parameters are shown in Table 4. The corresponding overlap functions are displayed in Fig. 11. The cloud microphysical properties retrieved with the forward iteration using the original measurement geometry, as well as the varied geometries, are presented in Fig. 12. The mean deviation of the two forward iteration results, with the varied measurement geometry to the results obtained with the original measurement geometry, is calculated and averaged over height. Its value is compared with the height-averaged error of the corresponding cloud microphysical property, derived as described in Section 4. For the extinction coefficient, the ratio of the derivation to the errors is 0.31. The corresponding values for the effective radius and LWC are 0.43 and 0.26, respectively. This finding illustrates that the results of the forward iterative algorithm are dominated by the cloud microphysical properties, and the measurement geometry causes only minor uncertainties of the results.
C. Required Averaging Time for Forward Iteration
Due to the signal noise, several measured dual-FOV profiles have to be summed to obtain profiles suitable for running the forward iterative algorithm. The usage of weak, noisy signals results in forward iterations that do not run successfully. In this section, the neessary measurement time for dual-FOV cloud studies is examined. Different time periods for summation of measured dual-FOV profiles were utilized to check for successful runs of the forward iterative algorithm. To obtain representative results, this analysis was performed with four different dual-FOV cloud measurements, which are listed in Table 5. Altogether 49 forward iterations with summation time periods between 4 s and 22 min were run. The height resolution of the forward iterative algorithm was set automatically by the algorithm. Additionally, the algorithm was run with height resolutions of four and seven layers as well.
The signal-to-noise ratio of the summed signal depends not only on the measurement time but on the signal strength of the single profiles as well. To avoid an effect of a different signal strength because of different cloud heights, cloud microphysical properties, and neutral-density filter settings on the analysis, the study examines the success of the forward iterations regarding the signal strength of the summed signal. The success of the forward iterations is checked in dependence of the sum of the signals from the inner and outer FOVs because the success of a forward iteration depends on the signal quality in the inner as well as in the outer FOV. The sum of the signals is regarded below the cloud. Thus single-scattering signals are evaluated. These signals are a measure for the signal strength inside the cloud without being affected by the cloud properties. The signal strength at the cloud base is considered as suitable for running the forward iterative algorithm, if more than 25% of the forward iterations with the corresponding variations of cloud base and top height, as well as height resolution, produce successful runs. For less than 5% successful forward iterations, the signal strength is considered as not suitable. Measurements that do not fall in either of these categories are designated as ambiguous.
Figure 13 displays the results of the study. All measurements with more than 1100 counts below the cloud base were suitable for running the forward iterative algorithm. Below 80 counts, no measurement could be used for a forward iteration. As a threshold for obtaining a suitable dual-FOV measurement, 700 counts appears to be reasonable as the vast majority of the measurements, exceeding this value, turned out to be suitable for running the forward iteration. The performed dual-FOV measurements had a neutral-density filter setting that induced count rates of about directly below the cloud base in the detection channel for the outer as well as the inner FOV. With this signal strength, a measurement time of 116 s is required to detect 700 counts at the cloud base in both FOVs. Assuming that due to the variation of the cloud base height about every third measured profile has to be rejected, the required measurement time for running the forward iterative algorithm is about three minutes.
7. Discussion and Outlook
In the Introduction, the need for further investigations of aerosol–cloud interactions was explained. The Raman lidar MARTHA provides high-resolved profiles of various aerosol properties [9–12]. The capability to perform dual-FOV Raman measurements for the retrieval of the cloud droplet effective radius, extinction coefficient, and LWC without any assumptions on cloud properties makes MARTHA an ideal tool for studies of aerosol–cloud interactions. From 2010 to 2012, approximately 300 clouds were probed in about 280 h of measurements in Leipzig, Germany. The analysis of this dataset with regard to the Twomey effect is ongoing, considering meteorological aspects as well.
In Section 6C it was demonstrated that the minimum measurement time of a dual-FOV cloud measurement for running the forward iterative algorithm successfully is 3 min. For the analysis of aerosol–cloud interactions on the process scale, measurements with a spatial resolution of about 1 km are required . This demand is fullfilled with the dual-FOV technique for slowly moving clouds at a horizontal wind speed at cloud level of less than . This restriction does not hold true for the assessment of the impact of aerosol–cloud interactions on the earth’s radiation budget. Only changes of cloud properties prevailing over a larger time scale can induce considerable effects on the radiation budget.
In Section 4, it was stated that the error of the retrieved cloud properties is determined from the standard deviation from the averaging of the results of forward iterations with differently set cloud boundaries and height resolutions. Thus the rejection of some forward iterative results on the basis of the analysis of additional lidar signals may decrease the error of the retrieved cloud properties by reducing the statistical spread of the results of the forward iterative runs. Two pairs of signals, which are measured with the current setup of the Raman lidar MARTHA, suit this ambition very well as they strongly depend on cloud properties: one pair consists of the channels measuring cross- and parallel-polarized light in the inner FOV because the obtained depolarization ratio depends on the multiple-to-single-scattering ratio and thus cloud microphysical properties . Another possibility constitutes the signals detecting elastically scattered light at 532 nm from the inner and outer FOV. For each result of a successful forward iteration, the chosen pair of signals could be calculated from the derived cloud microphysical properties. On the basis of the deviations from the measured pair of signals, the corresponding result could be selected or discarded. Both, the approach using the depolarization as well as the method employing the elastical signals in both FOVs, will be investigated.
The Raman lidar MARTHA at the TROPOS in Leipzig, Germany was upgraded to perform dual-FOV Raman measurements. Thus Raman signals can be recorded with two FOV simultaneously by the usage of a mirror diaphragm. Replacing the conventional field stop with the mirror diaphragm does not influence the overlap function as shown by ray-tracing simulations. By switching between three different mirror diaphragms and thus different combinations of FOVs clouds in an extended altitude range of 1.3–6.0 km can be investigated. The cloud droplet effective radius, single-scattering extinction coefficient, and LWC can be retrieved without making any assumptions on cloud properties. A dual-FOV measurement and the retrieved microphysical properties were presented and an extended error discussion provided. A comparison of the derived LWP with an MWR measurement gave a first verification of the dual-FOV technique. Combining capabilities for retrieving cloud micropysical properties, as well as aerosol properties, the dual-FOV Raman lidar is an ideal device for a single-instrument approach to study aerosol–cloud interactions.
1. P. Forster, V. Ramaswamy, P. Artaxo, T. Berntsen, R. Betts, D. Fahey, J. Haywood, J. Lean, D. Lowe, G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R. V. Dorland, Climate Change 2007—The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge University, 2007), Chap. 2.
2. H. Guo, J. E. Penner, M. Herzog, and S. Xie, “Investigation of the first and second aerosol indirect effects using data from the May 2003 Intensive Operational Period at the Southern Great Plains,” J. Geophys. Res. 112, D15206 (2007). [CrossRef]
3. S. Twomey, “Influence of pollution on shortwave albedo of clouds,” J. Atmos. Sci. 34, 1149–1152 (1977). [CrossRef]
4. A. McComiskey and G. Feingold, “Quantifying error in the radiative forcing of the first aerosol indirect effect,” Geophys. Res. Lett. 35, L02810 (2008). [CrossRef]
5. J. L. Brenguier, P. Y. Chuang, Y. Fouquart, D. W. Johnson, F. Parol, H. Pawlowska, J. Pelon, L. Schüller, F. Schröder, and J. Snider, “An overview of the ACE-2 CLOUDYCOLUMN closure experiment,” Tellus 52, 815–827 (2000). [CrossRef]
6. M.-L. Lu, G. Feingold, H. H. Jonsson, P. Y. Chuang, H. Gates, R. C. Flagan, and J. H. Seinfeld, “Aerosol-cloud relationships in continental shallow cumulus,” J. Geophys. Res. 113, D15201 (2008). [CrossRef]
7. F.-M. Bréon, D. Tanré, and S. Generoso, “Aerosol effect on cloud droplet size monitored from satellite,” Science 295, 834–838 (2002). [CrossRef]
8. J. Quaas, O. Boucher, N. Bellouin, and S. Kinne, “Satellite-based estimate of the direct and indirect aerosol climate forcing,” J. Geophys. Res. 113, D05204 (2008). [CrossRef]
9. A. Ansmann, M. Riebesell, and C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990). [CrossRef]
10. A. Ansmann, M. Tesche, P. Seifert, S. Groß, V. Freudenthaler, A. Apituley, K. M. Wilson, I. Serikov, H. Linné, B. Heinold, A. Hiebsch, F. Schnell, J. Schmidt, I. Mattis, U. Wandinger, and M. Wiegner, “Ash and fine-mode particle mass profiles from EARLINET-AERONET observations over central Europe after the eruptions of the Eyjafjallajökull volcano in 2010,” J. Geophys. Res. 116, D00U02 (2011). [CrossRef]
11. D. Müller, A. Kolgotin, I. Mattis, A. Petzold, and A. Stohl, “Vertical profiles of microphysical particle properties derived from inversion with two-dimensional regularization of multiwavelength Raman lidar data: experiment,” Appl. Opt. 50, 2069–2079 (2011). [CrossRef]
12. Y. Sasano and E. Browell, “Light-scattering characteristics of various aerosol types derived from multiple wavelength lidar observations,” Appl. Opt. 28, 1670–1679 (1989). [CrossRef]
13. T. Murayama, N. Sugimoto, I. Uno, K. Kinoshita, K. Aoki, N. Hagiwara, Z. Liu, I. Matsui, T. Sakai, T. Shibata, K. Arao, B. Sohn, J. Won, S. Yoon, T. Li, J. Zhou, H. Hu, M. Abo, K. Iokibe, R. Koga, and Y. Iwasaka, “Ground-based network observation of Asian dust events of April 1998 in east Asia,” J. Geophys. Res. 106, 18345–18359 (2001). [CrossRef]
14. L. R. Bissonnette and D. L. Hutt, “Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements,” Appl. Opt. 34, 6959–6975 (1995). [CrossRef]
15. L. R. Bissonnette, G. Roy, L. Poutier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo Simulations and comparisons with in situ measurements,” Appl. Opt. 41, 6307–6324 (2002). [CrossRef]
16. I. Veselovskii, M. Korenskii, V. Griaznov, D. N. Whiteman, M. McGill, G. Roy, and L. Bissonnette, “Information content of data measured with a multiple-field-of-view lidar,” Appl. Opt. 45, 6839–6848 (2006). [CrossRef]
17. L. R. Bissonnette, G. Roy, and N. Roy, “Multiple-scattering-based lidar retrieval: method and results of cloud probings,” Appl. Opt. 44, 5565–5581 (2005). [CrossRef]
18. A. V. Malinka and E. P. Zege, “Possibilities of warm cloud microstructure profiling with multiple-field-of-view Raman lidar,” Appl. Opt. 46, 8419–8427 (2007). [CrossRef]
19. A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, and W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992). [CrossRef]
20. U. Wandinger, “Multiple-scattering influence on extinction-and backscatter-coefficient measurements with Raman and high-spectral-resolution lidars,” Appl. Opt. 37, 417–427 (1998). [CrossRef]
21. G. Martucci and C. D. O’Dowd, “Ground-based retrieval of continental and marine warm cloud microphysics,” Atmos. Meas. Tech. 4, 2749–2765 (2011). [CrossRef]
22. U. Wandinger, I. Mattis, M. Tesche, A. Ansmann, J. Bösenberg, A. Chaikovski, V. Freudenthaler, L. Komguem, H. Linne, V. Matthias, J. Pelon, L. Sauvage, P. Sobolewski, G. Vaughan, and M. Wiegner, “Air-mass modification over Europe: EARLINET aerosol observations from Wales to Belarus,” J. Geophys. Res. 109, D24205 (2004). [CrossRef]
23. I. Mattis, A. Ansmann, D. Althausen, V. Jaenisch, U. Wandinger, D. Müller, Y. F. Arshinov, S. M. Bobrovnikov, and I. B. Serikov, “Relative-humidity profiling in the troposphere with a Raman lidar,” Appl. Opt. 41, 6451–6462 (2002). [CrossRef]
24. Y. Arshinov, S. Bobrovnikov, I. Serikov, A. Ansmann, U. Wandinger, D. Althausen, I. Mattis, and D. Müller, “Daytime operation of a pure rotational Raman lidar by use of a Fabry–Perot interferometer,” Appl. Opt. 44, 3593–3603 (2005). [CrossRef]
25. J. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981). [CrossRef]
26. J. Reichardt, U. Wandinger, V. Klein, I. Mattis, B. Hilber, and R. Begbie, “RAMSES: the German Meteorological Service autonomous Raman lidar for water vapor, temperature, aerosol, and cloud measurements,” Appl. Opt. 51, 8111–8131(2012). [CrossRef]
27. U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002). [CrossRef]
28. R. N. Wilson, Reflecting Telescope Optics II (Springer, 2001).
29. J. Schmidt, “Aufbau und Test von Mehrfachstreukanälen zur Messung der Wolkentröpfchengröße mit einem Ramanlidar,” Master’s thesis (Friedrich Schiller University Jena, 2009).
30. V. Freudenthaler, “Effects of spatially inhomogeneous photomultiplier sensitivity on lidar signals and remedies,” in Reviewed and revised papers presented at the 22nd International Laser Radar Conference (ILRC) (ESA Publications Division, 2004), pp. 37–40.
31. A. V. Malinka and E. P. Zege, “Analytical modeling of Raman lidar return, including multiple scattering,” Appl. Opt. 42, 1075–1080 (2003). [CrossRef]
32. A. V. Malinka and J. Schmidt, “Overlap function of a lidar with a field stop shifted from the focal plane,” in Proceedings of the 25th International Laser Radar Conference (ILRC), G. Matvienko and A. Zemlyanov, eds. (Curran Associates, 2010), pp. 79–81.
33. N. Miles, J. Verlinde, and E. Clothiaux, “Cloud droplet size distributions in low-level stratiform clouds,” J. Atmos. Sci. 57, 295–311 (2000). [CrossRef]
34. N. Gaussiat, R. J. Hogan, and A. J. Illingworth, “Accurate liquid water path retrieval from low-cost microwave radiometers using additional information from a lidar ceilometer and operational forecast models,” J. Atmos. Ocean. Technol. 24, 1562–1575 (2007). [CrossRef]
35. A. McComiskey and G. Feingold, “The scale problem in quantifying aerosol indirect effects,” Atmos. Chem. Phys. 12, 1031–1049 (2012). [CrossRef]
36. Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809–1811 (2006). [CrossRef]