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Retrieval of Water Cloud Optical and Microphysical Properties from Combined Multiwavelength Lidar and Radar Data

: The remote sensing of water clouds is useful for studying their spatial and temporal variations and constraining physical processes in climate and weather prediction models. However, radar-only detection provides inadequate information for the cloud droplet size distribution. Here, we propose a novel lookup-table method, which combines lidar (1064, 532 nm) and radar (8.6 mm) to retrieve proﬁles of cloud optical (backscatter coefﬁcient and extinction coefﬁcient) and microphysical properties (effective diameter and liquid water content). Through the iteration of the extinction-to-backscatter ratio, more continuous cloud optical characteristics can be obtained. Sensitivity analysis shows that a 10% error of the lidar constant will lead to a retrieval error of up to 30%. The algorithm performed precise capture of the ideal cloud signal at a speciﬁc height and at full height and the maximum relative error of the backscatter coefﬁcients at 1064 nm and 532 nm were 6% and 4%, respectively. With the application of the algorithm in the two observation cases on single or multiple cloud layers, the results indicate that the microphysical properties mostly agree with the empirical radar measurements but are slightly different when larger particles cause signal changes of different extents. Consequently, the synergetic algorithm is capable of computing the cloud droplet size distribution. It provides continuous proﬁles of cloud optical properties and captures cloud microphysical properties well for water cloud studies.


Introduction
In the atmosphere, clouds cover about 67% of the globe and play a critical role in regulating the energy budget of the Earth [1]. In particular, the optical and microphysical properties of water clouds affect their capability to absorb and scatter radiation, and this poses a major challenge leading to uncertainty in numerical weather forecasts and climate simulations [2,3]. Testing and improving parameterization schemes for cloud variations and physical processes requires knowledge of cloud properties [4,5]. Hence, the current techniques will be validated and new ones will be developed for retrieving water properties. One of the best ways to collect cloud properties is using aircraft-mounted in situ probes, which are able to perform measurements of cloud microphysical properties directly and accurately. This approach is hampered by the scarcity of aircraft measurements by volume and is temporally and spatially limited [6][7][8]. Therefore, some active sensors are used alone or combined to generate a large amount of observational information about cloud characteristics [9,10]. Radar remote sensing is routinely operated from ground-based observations [11,12] and a variety of ship-based and satellite platforms [13,14]. Some radar-based studies use the empirical power-law relations between radar reflectivity factor ∞ 0 α t (λ L,R , z)dz (1) where the subscripts of L and R represent lidar and radar. P is the received power detected at the wavelength of λ L and λ R . C L,R is the constant that takes into account the instrument parameters. β t (λ L,R ,z) and α t (λ L,R ,z) are the total backscatter coefficients and extinction coefficients from the instrument to distance z.
Although the principles of lidar and radar are similar, radar signals are most commonly specified in terms of the radar reflectivity factor Z in Equation (2). The backscatter coefficient β t (λ R ,z) can be calculated by Z and then converted into the form of Equation (1). K w is calculated by the refractive index of water at the radar wavelength [21]: The mentioned total extinction and backscatter coefficients consist of molecules and particles. In this study, we mainly focus on the extinction and backscatter for cloud particles that are defined as β p (λ L,R ) and α p (λ L,R ) and are presented in Equations (3) and (4) [25]: α p (λ L,R ) = The σ b and σ ext are backscatter and extinction scattering cross-sections and n(D) is the DSD of the cloud particles. As Equations (3) and (4) show, the σ b is a function of the Mie backscattering efficiency Q b and particle diameter D. Similarly, the σ ext is a function of the Mie extinction efficiency Q ext and D.
The relationship between α p (λ L,R ) and β p (λ L,R ) is defined by the extinction-to-backscatter ratio, which is the lidar ratio (LR λ ) [23]. Analogous to the definition of the LR λ , we defined the radar ratio (RR) as: To model the DSD of water clouds, we chose lognormal distribution as the function form of the DSD. The literature shows that the lognormal distribution function can be used to approximate empirical water cloud DSD [26,27]. Therefore, the cloud droplet size distribution n(D) is given by Equation (6): The n(D) is characterized by the cloud number concentration N 0 , the dispersion parameter of the logarithmic distribution σ, and the median diameter D log .
Through the parameterized DSD, the microphysical properties of the cloud, especially the LWC and D eff , can be given in terms of the moment of the DSD using Equations (7) and (8) [20] as follows, where ρ w is the density of water, and the angle brackets denote averaging over the size distribution.
Remote Sens. 2021, 13 The implementation of the lidar-radar synergetic algorithm incorporates three observables-the radar reflectivity factor Z and the lidar signals at wavelengths of 1064 nm and 532 nm, P 1064 and P 532 . It mainly consists of five steps: data interpolation, cloud detection, optical retrieval, microphysical retrieval, and LR λ /RR iteration. The schematic of the algorithm is expressed in Figure 1 and explained below.

Backscatter Statistic Model (BSM)
In this section, we propose a BSM that aims to transfer cloud optical properties to microphysical properties and validate the accuracy of the model. In detail, we first calculate the backscatter coefficient based on nature's DSD distribution. Then, we establish a model relationship between the backscatter coefficient and parameters of DSD (Dlog and σ). Finally, we confirm the accuracy of the BSM.
The theoretical calculations of the particle backscatter coefficients βR, β1064, and β532 is achieved using Mie theory. Since only cloud droplets are considered in this research, the β 532 β 1064 β R  Figure 1. Schematic of the algorithm for the retrieval of optical and microphysical properties of clouds by multiwavelength lidar and cloud radar.

LRλ(i) = LRλ(i + 1)， RR(i) = RR(i + 1)
Firstly, lidar and radar data are averaged to the same time and range resolution. In this study, the range resolution and the time resolution are set to 30 m and 10 min, respectively.
Layers of clouds are then identified from the lidar and radar overlap region. Due to the distinguished ability of lidar to capture cloud bases, we use a simple multiscale Remote Sens. 2021, 13, 4396 5 of 18 algorithm (SMA) [28] for cloud masking detection. Afterward, layers with a volume linear depolarization ratio (δ) at 1064 nm of less than 0.1 are selected as water cloud layers [29]. The range is recorded from the cloud base to the top.
Next, backscatter coefficients of clouds at lidar and radar wavelengths are retrieved by the Fernald forward integral method [30]. This algorithm uses pre-calibrated lidar constants and does not require the assumption of the backscatter coefficient at the reference height, thereby reducing the uncertainty of the inversion. The initial value of the lidar ratio (LR λ,I ) and radar ratio (RR ,I ) need to be assumed before obtaining β at the beginning. The detailed methods to retrieve lidar/radar backscatter coefficients and lidar constant are supplied in Appendix A.
After deriving β for cloud particles at three wavelengths, two backscatter ratios, R1 = β R /β 1064 and R2 = β 1064 /β 532 , are defined for cloud microphysical property retrieval. A look-up backscatter statistical model (BSM) has been established through electromagnetic simulations to bridge the gap between the optical and microphysical properties. The DSD parameters, D log and σ, can be looked up in BSM with the pairwise ratio R1 and R2 as inputs. The details of the BSM are introduced in Section 2.2.2.
Once D log and σ are derived, LR λ and RR can be calculated theoretically with the retrieved DSD. If the differences between the newly calculated and the previously used LR λ /RR exceed the thresholds, the newly calculated LR λ and RR are used to retrieve β and the subsequent DSD until the LR λ and RR are stable at this height. After looping the iterative process from the cloud base to the cloud top, the profiles of cloud optical and microphysical properties can be retrieved eventually.

Backscatter Statistic Model (BSM)
In this section, we propose a BSM that aims to transfer cloud optical properties to microphysical properties and validate the accuracy of the model. In detail, we first calculate the backscatter coefficient based on nature's DSD distribution. Then, we establish a model relationship between the backscatter coefficient and parameters of DSD (D log and σ). Finally, we confirm the accuracy of the BSM.
The theoretical calculations of the particle backscatter coefficients β R , β 1064 , and β 532 is achieved using Mie theory. Since only cloud droplets are considered in this research, the particle shape is assumed to be spherical. The range of droplet diameters D is assumed to be 0.5-100 µm for this study. β p (λ L,R ) and α p (λ L,R ) can be calculated using Equations (3) and (4). The parameters are defined below. The Q ext and Q b are also implicit functions of the refractive index of water. The refractive index of water clouds at 20 • C at the wavelengths 532 nm, 1064 nm, and 8.6 mm are 1.33-j(1.32 × 10 −9 ), 1.32-j(2.89 × 10 −6 ), and 5.25-j(2.81), respectively [31,32].
As for the range of the parameters (N 0 , D log , σ) of n(D), they are set to be N 0 = 200 cm −3 , 0.1035 ≤ σ ≤ 0.8, and 0.3 ≤ D log ≤ 66.7 µm, which are converted by a series of observations [14,[33][34][35]. Figure 2a shows the backscatter cross section for each wavelength using the above parameters. The relation of the LR λ /RR with the D eff is shown in Figure 2b. The single-colored lines represent the condition of the same D log but different σ values. The parameters of DSD lead to a rapid change in LR λ /RR and present a unique trend in LR λ /RR along with the D eff . Admittedly, the LR λ and RR can characterize the changes in the cloud's microphysical properties.
Remote Sens. 2021, 13, 4396 6 of 18 [14,[33][34][35]. Figure 2a shows the backscatter cross section for each wavelength using the above parameters. The relation of the LRλ/RR with the Deff is shown in Figure 2b. The single-colored lines represent the condition of the same Dlog but different σ values. The parameters of DSD lead to a rapid change in LRλ/RR and present a unique trend in LRλ/RR along with the Deff. Admittedly, the LRλ and RR can characterize the changes in the cloud's microphysical properties. After the theoretical calculation of the optical properties from the microphysical properties, how to convert the optical properties to microphysical properties is the main problem due to there being no algebraical formula describing these relationships with DSD known in advance. Therefore, we calculate the backscattering through theoretical simulation and construct a statistical table to assess the relationship between β and DSD. Because three variables influence the DSD, we determine the R1 and R2 when ignoring the influence of N0 in the algorithm. The range of R1 and R2 differ by several orders of magnitude, hence they are set at exponential and linear intervals, respectively. The center median of Dlog and σ is calculated using Equation (9) as the final value for each interval where N is the numbers of parameters in the specific interval, and Xi are the parameters in that interval. Finally, the BSM has been organized as shown in Figure 3. After the theoretical calculation of the optical properties from the microphysical properties, how to convert the optical properties to microphysical properties is the main problem due to there being no algebraical formula describing these relationships with DSD known in advance. Therefore, we calculate the backscattering through theoretical simulation and construct a statistical table to assess the relationship between β and DSD. Because three variables influence the DSD, we determine the R1 and R2 when ignoring the influence of N 0 in the algorithm. The range of R1 and R2 differ by several orders of magnitude, hence they are set at exponential and linear intervals, respectively. The center median of D log and σ is calculated using Equation (9) as the final value for each interval where N is the numbers of parameters in the specific interval, and Xi are the parameters in that interval. Finally, the BSM has been organized as shown in Figure 3. Figure 3a shows that the D log has a proportional relationship with R1 when R2 is constant. On the contrary, σ exhibits a complex relationship between R1 and R2. Thus, constructing the BSM can easily yield the sophisticated DSD based on R1 and R2. The standard deviation of the D log and σ is shown in Figure 3c,d. The large deviation between the two shows the uncertainty between the model values and the real parameters.
To evaluate the accuracy of the BSM, we compared the look-up BSM results to simulation results (SIM). The four microphysical parameters are located at the 1:1 line (black line) in Figure 4. The correlation coefficients (R 2 ) for σ, D log , D eff , and LWC are 0.89, 0.97, 0.96, and 0.87, respectively. Other metrics, such as the Nash-Sutcliffe efficiency (NSE) [36], measure how well predictions are relative to the observed average. The NSE for D log , σ, D eff , and LWC are 0.94, 0.78, 0.94, and 0.72, respectively. RMSE standard deviation ratio (RSR) is defined as the standardized RMSE using the simulations' standard deviations, which makes all variables comparable. The RSR for D log , σ, D eff , and LWC are 0.47, 0.25, 0.29, and 0.53, respectively. Among all the parameters, the D log and D eff show the best fit to the model, and the smallest deviation belongs to σ and D eff . In summary, all the parameters of BSM highlight its great performance for the conversion of optical to microphysical properties.  Figure 3a shows that the Dlog has a proportional relationship with R1 when R2 is constant. On the contrary, σ exhibits a complex relationship between R1 and R2. Thus, constructing the BSM can easily yield the sophisticated DSD based on R1 and R2. The standard deviation of the Dlog and σ is shown in Figure 3c,d. The large deviation between the two shows the uncertainty between the model values and the real parameters.
To evaluate the accuracy of the BSM, we compared the look-up BSM results to simulation results (SIM). The four microphysical parameters are located at the 1:1 line (black line) in Figure 4. The correlation coefficients (R 2 ) for σ, Dlog, Deff, and LWC are 0.89, 0.97, 0.96, and 0.87, respectively. Other metrics, such as the Nash-Sutcliffe efficiency (NSE) [36], measure how well predictions are relative to the observed average. The NSE for Dlog, σ, Deff, and LWC are 0.94, 0.78, 0.94, and 0.72, respectively. RMSE standard deviation ratio (RSR) is defined as the standardized RMSE using the simulations' standard deviations, which makes all variables comparable. The RSR for Dlog, σ, Deff, and LWC are 0.47, 0.25, 0.29, and 0.53, respectively. Among all the parameters, the Dlog and Deff show the best fit to the model, and the smallest deviation belongs to σ and Deff. In summary, all the parameters of BSM highlight its great performance for the conversion of optical to microphysical properties.

Sensitivity Analysis
Considering the robustness of the inversion results, we analyze the sensitivity of the initial value of lidar/radar ratio (LR 532 , I LR 1064 , I RR ,I ) and the instrument constant (C 532 , C 1064 , C rad ) to the uncertainty of the lidar/radar ratio (LR 532 , LR 1064 , RR), backscatter coefficient (β 532 , β 1064 ), radar reflectivity (Z), and microphysical properties (D eff , LWC).
We assumed the parameters of DSD with a typical water cloud condition [34]. The change range for the initial value of lidar/radar ratio and instrument constant are set between ±30% and ±10%, individually. The maximum relative error induced by the LR λ,I and RR ,I is less than 1%, so the error of these input parameters can be ignored. The sensitive test for the instrument constant is shown in Figure 5. As Figure 5a,b shows, the lidar constant (C 532 , C 1064 ) has a more significant impact on microphysical properties than the radar constant (C rad ), especially for the C 532 where a 10% error results in a retrieval error of up to 30%. Therefore, a cautious restriction for the error of lidar constant should be considered.

Sensitivity Analysis
Considering the robustness of the inversion results, we analyze the sensitivity of the initial value of lidar/radar ratio (LR532,I LR1064,I RR,I) and the instrument constant (C532, C1064, Crad) to the uncertainty of the lidar/radar ratio (LR532, LR1064, RR), backscatter coefficient (β532, β1064), radar reflectivity (Z), and microphysical properties (Deff, LWC).
We assumed the parameters of DSD with a typical water cloud condition [34]. The change range for the initial value of lidar/radar ratio and instrument constant are set between ±30% and ±10%, individually. The maximum relative error induced by the LRλ,I and RR,I is less than 1%, so the error of these input parameters can be ignored. The sensitive test for the instrument constant is shown in Figure 5. As Figure 5a,b shows, the lidar constant (C532, C1064) has a more significant impact on microphysical properties than the radar constant (Crad), especially for the C532 where a 10% error results in a retrieval error of up to 30%. Therefore, a cautious restriction for the error of lidar constant should be considered

Application to the Ideal Cloud Signal
The feasibility and stability of the algorithm had been proven in preliminary testing. We simulated the ideal cloud signal to verify the inversion results at a specific height and at full height. Here, we used a thin cloud located from 3 to 3.3 km with a lognormal DSD

Application to the Ideal Cloud Signal
The feasibility and stability of the algorithm had been proven in preliminary testing. We simulated the ideal cloud signal to verify the inversion results at a specific height and at full height. Here, we used a thin cloud located from 3 to 3.3 km with a lognormal DSD of water particles as our example. With the implementation of the look-up BSM, the LR λ and RR iteration at cloud base is shown in Figure 6. The inversion results for full height are shown in Figures 7 and 8.
The iteration results with the fixed D log and σ at cloud base are shown in Figure 6. The initial values of lidar/radar ratio were set as 20, 15, and 10 6 for LR 532,I , LR 1064,I , and RR ,I , respectively. It can be seen in Figure 6a that the LR λ and RR were stable after three iterations. Similar results were shown for the larger particles. The iteration was stopped for lookup BSM twice (Figure 6b).

Application to the Ideal Cloud Signal
The feasibility and stability of the algorithm had been proven in preliminary testing. We simulated the ideal cloud signal to verify the inversion results at a specific height and at full height. Here, we used a thin cloud located from 3 to 3.3 km with a lognormal DSD of water particles as our example. With the implementation of the look-up BSM, the LRλ and RR iteration at cloud base is shown in Figure 6. The inversion results for full height are shown in Figures 7 and 8.
The iteration results with the fixed Dlog and σ at cloud base are shown in Figure 6. The initial values of lidar/radar ratio were set as 20, 15, and 10 6 for LR532,I, LR1064,I, and RR,I, respectively. It can be seen in Figure 6a that the LRλ and RR were stable after three iterations. Similar results were shown for the larger particles. The iteration was stopped for lookup BSM twice (Figure 6b). For optical properties, the LR λ /RR results were similar to the simulation for different parameters of DSD (Figures 7a,b and 8a,b). Compared to the result assuming constant LR λ,I /RR ,I for β λ,I and Z ,I profile, the results after iteration showed a significant change for β λ and Z in profile. Especially for Figure 8c, the algorithm showed a better ability to capture complete profiles and improved the detection capability of lidar. The maximum relative error of the backscatter coefficient in profiles is 4% and 6% for β 1064 and β 532 , respectively.
The performance of the microphysical property retrieval depends on nature's conditions. The results were compared with a series of empirical formulas for LWC, which was attached to Atlas [37], Fox [16], and Baedi [15]. Likewise, the D eff was attached to Atlas, Continent (C) [34], and Marine (M) [34] as stipulated in the literature. Figure 7d,e shows that the retrieved LWC and D eff were located between the empirical formula Z-LWC and Z-D eff . However, a large deviation between the LWC and D eff occurred in Figure 8d,e due to the presence of large particles. It should be emphasized that when only a small number of large particles are present, the contribution of the LWC and D eff as determined by Z could be challenging.

Application to Lidar and Radar Observation
In this section, the newly proposed algorithm was applied to the observation of a water cloud using lidar with 532 nm, 1064 nm, and cloud radar with 8.6 mm. These two instruments are collocated at the Haidian meteorological station, Beijing, China (39.983 • N 116.283 • E). The 60-day observation campaign was from September 2019 to October 2019. The technical specification of the lidar was used in Wang's studies [15]. The cloud radar was produced by the Meteorological Observation Center of the China Meteorological Administration and Huateng Microwave Co. Ltd. Radar provided measurements of the reflectivity (Z), mean Doppler velocity (V D ), and Doppler spectrum width (W D ). It operated continuously in meteorological stations [38]. The Chinese Academy of Meteorological Sciences (CAMS) AERONET station (39.933 • N 116.317 • E) was used to calibrate the lidar constant, which was at a distance of 3 km from the observation stations.
For optical properties, the LRλ/RR results were similar to the simulation for different parameters of DSD (Figures 7a,b and 8a,b). Compared to the result assuming constant LRλ,I/RR,I for βλ,I and Z,I profile, the results after iteration showed a significant change for βλ and Z in profile. Especially for Figure 8c, the algorithm showed a better ability to capture complete profiles and improved the detection capability of lidar. The maximum relative error of the backscatter coefficient in profiles is 4% and 6% for β1064 and β532, respectively.
The performance of the microphysical property retrieval depends on nature's conditions. The results were compared with a series of empirical formulas for LWC, which was attached to Atlas [37], Fox [18], and Baedi [17]. Likewise, the Deff was attached to Atlas [37], Continent (C) [34], and Marine (M) [34] as stipulated in the literature. Figure 7d,e shows that the retrieved LWC and Deff were located between the empirical formula Z-LWC and Z-Deff. However, a large deviation between the LWC and Deff occurred in Figure  8d,e due to the presence of large particles. It should be emphasized that when only a small number of large particles are present, the contribution of the LWC and Deff as determined by Z could be challenging.

Application to Lidar and Radar Observation
In this section, the newly proposed algorithm was applied to the observation of a water cloud using lidar with 532 nm, 1064 nm, and cloud radar with 8.6 mm. These two  Figure 9 shows the time height profile for radar reflectivity (Z) and 1064 nm lidar ranged-correct signal (RCS) on October 10, 2019. There was a water cloud 3 km above ground between 00:00-10:00 local standard time (LST). Two moments at 2:30 a.m. and 4 a.m. were selected to show the results of the inversion.

Observation in a Layer of the Cloud
At 2:30 a.m. (Figure 10), the LR λ and RR had significant changes in the same region, and the β and Z rose to the same range. The algorithm had a significant effect on the lidar retrieval, which was calibrated using the β from the initial value (Figure 10c). It has the same effect as the simulation mentioned above. Compared with the microphysical retrieval, results were close to Baedi's LWC and Marine's D eff at most heights. A difference appeared at the height of 3.9-4.5 km, where Z increased rapidly and β increased slowly, indicating the existence of large particles, which is verified in Figure 10e. Another difference can be seen at a height of 5-6 km, with the instantaneous decrease in Z and a nearly unchanged β. As a result of the decreased R1 and the fixed R2 for BSM, the lookup-table value of D log was reduced.
At 4 a.m. (Figure 11), the LR λ /RR changed with almost the same trend. Figure 11c shows that the Z and β contributed to the same range but to different extents. Specifically, lidar was more sensitive at a height of 4-4.6 km, while radar changed rapidly at all other heights. The results in Figure 11e verified this condition. The D eff was relatively small at low altitudes and larger at the top, which caused a large deviation between the empirical relations. The LWC was smaller than the unique Z-LWC relations at this moment because the large particles contribute less to the LWC.     Figure 12 shows the time height profile for Z and RCS on 16 October 2019. A water cloud was 4 km above ground between 12:00 and 00:00 LST. The two moments at 13:00 and 20:30 were selected to observe the inversion results of multiple cloud layers.

Observation in Multiple Layers of the Cloud
At 13:00 (Figure 13), the LRλ/RR had significantly changed in the same heights. Additionally, the rapid change of LRλ/RR corresponds to the change of Deff in the same region. The radar and lidar showed several peaks in the profile representing different DSD information. Notably, the lidar has a peak at 4.5 km, but with such peak in the radar data at the different height. This is evidence for the existence of a large number of small particles. The reduced Deff at that height verified the observation in Figure 13e. The microphysical characteristic of LWC coincides with Fox's at 4.4 km but closer to Baedi's immediately above. The Deff was close to the continent's Deff at this moment. At 20:30 (Figure 14), LRλ/RR had significantly changed in a similar region. The radar showed a similar intensity at two layers, but the lidar had a smaller intensity at the lower one than the upper one ( Figure  14c), suggesting that there is a larger Deff at the top. This conclusion is supported by Figure   Figure 11. The inversion results at 4:00 a.m. on 10 October 2019: (a) lidar ratio at different wavelengths (LR 532 , LR 1064 ); (b) radar ratio (RR); (c) lidar backscatter at different wavelengths (β 532 , β 1064 ) and radar reflectivity factor (Z) (initial value subscript I); (d) liquid water content (LWC); (e) effective diameter (D eff ). Figure 12 shows the time height profile for Z and RCS on 16 October 2019. A water cloud was 4 km above ground between 12:00 and 00:00 LST. The two moments at 13:00 and 20:30 were selected to observe the inversion results of multiple cloud layers.

Observation in Multiple Layers of the Cloud
At 13:00 (Figure 13), the LR λ /RR had significantly changed in the same heights. Additionally, the rapid change of LR λ /RR corresponds to the change of D eff in the same region. The radar and lidar showed several peaks in the profile representing different DSD information. Notably, the lidar has a peak at 4.5 km, but with such peak in the radar data at the different height. This is evidence for the existence of a large number of small particles. The reduced D eff at that height verified the observation in Figure 13e. The microphysical characteristic of LWC coincides with Fox's at 4.4 km but closer to Baedi's immediately above. The D eff was close to the continent's D eff at this moment. At 20:30 (Figure 14), LR λ /RR had significantly changed in a similar region. The radar showed a similar intensity at two layers, but the lidar had a smaller intensity at the lower one than the upper one (Figure 14c), suggesting that there is a larger D eff at the top. This conclusion is supported by Figure 14e. The microphysical characteristic of LWC was close to Baedi's formula and Atlas's D eff at this moment.

Strengths and Limitations of the Application of the Combination Algorithm to Observation Cases
The cloud radar is the most suitable instrument with which to observe clouds in day and nighttime. It shows the best continuity of the data and the complete data volume for all kinds of cloud layers. As for lidar, although it is very precise at detecting the cloud base, it cannot penetrate the thick optical depth cloud due to the attenuation of the beam in the cloud. Consequently, the limitation of the efficiency of the lidar-radar combining algorithm is restricted by the capability of lidar detection. Nevertheless, the lidar-radar algorithm has less data volume than the radar-only detection, and it advances atmospheric observation capabilities substantially. It is useful for the accurate detection of cloud optical and microphysical properties in further scientific research. In addition, the problem of the insufficient dataset can be complemented by a nearby wavelength radar system, for example, 95 GHz radar (3.2 mm).

Conclusions
Lidar and cloud radar are excellent instruments in the routine observation of temporal and spatial water cloud properties. Synergizing lidar and radar measurements of clouds advance atmospheric observation capabilities on many frontiers. We offer new insights on combined lidar (1064, 532 nm) and cloud radar (8.6 mm) to complete the three parameters of DSD, which is a long-standing dilemma in the observation of water clouds. The algorithm mainly consists of five parts: (a) data interpolation, (b) cloud detection, (c) optical retrieval, (d) microphysical retrieval, and (e) LRλ/RR iteration. This algorithm proposes a forward technique to establish BSM to transfer the backscatter coefficient to the parameters of DSD.
The feasibility of the BSM is discussed in the simulation. The correlation coefficients (R 2 ) for σ, Dlog, Deff, and LWC are 0.89, 0.97, 0.96, and 0.87, respectively. The NSE for Dlog, σ, Deff, and LWC are 0.94, 0.78, 0.94, and 0.72, and the RSR are 0.47, 0.25, 0.29, and 0.53, respectively. This indicates that the Dlog and Deff show the best fit of the model and the smallest deviation belongs to σ and Deff. All the parameters show the excellent performance for BSM to establish a model relationship between backscatter to clouds' microphysical variables. Through iteration of the extinction-to-backscatter ratio, the accuracy

Strengths and Limitations of the Application of the Combination Algorithm to Observation Cases
The cloud radar is the most suitable instrument with which to observe clouds in day and nighttime. It shows the best continuity of the data and the complete data volume for all kinds of cloud layers. As for lidar, although it is very precise at detecting the cloud base, it cannot penetrate the thick optical depth cloud due to the attenuation of the beam in the cloud. Consequently, the limitation of the efficiency of the lidar-radar combining algorithm is restricted by the capability of lidar detection. Nevertheless, the lidar-radar algorithm has less data volume than the radar-only detection, and it advances atmospheric observation capabilities substantially. It is useful for the accurate detection of cloud optical and microphysical properties in further scientific research. In addition, the problem of the insufficient dataset can be complemented by a nearby wavelength radar system, for example, 95 GHz radar (3.2 mm).

Conclusions
Lidar and cloud radar are excellent instruments in the routine observation of temporal and spatial water cloud properties. Synergizing lidar and radar measurements of clouds advance atmospheric observation capabilities on many frontiers. We offer new insights on combined lidar (1064, 532 nm) and cloud radar (8.6 mm) to complete the three parameters of DSD, which is a long-standing dilemma in the observation of water clouds. The algorithm mainly consists of five parts: (a) data interpolation, (b) cloud detection, (c) optical retrieval, (d) microphysical retrieval, and (e) LR λ /RR iteration. This algorithm proposes a forward technique to establish BSM to transfer the backscatter coefficient to the parameters of DSD.
The feasibility of the BSM is discussed in the simulation. The correlation coefficients (R 2 ) for σ, D log , D eff , and LWC are 0.89, 0.97, 0.96, and 0.87, respectively. The NSE for D log , σ, D eff , and LWC are 0.94, 0.78, 0.94, and 0.72, and the RSR are 0.47, 0.25, 0.29, and 0.53, respectively. This indicates that the D log and D eff show the best fit of the model and the smallest deviation belongs to σ and D eff . All the parameters show the excellent performance for BSM to establish a model relationship between backscatter to clouds' microphysical variables. Through iteration of the extinction-to-backscatter ratio, the accuracy profiles of the optical properties and microphysical properties can be obtained. The features of the algorithm do not rely on the unique relationship of observations and can derive the LWC and D eff in particular. Moreover, this method does not require an assumption about the parameters (N 0 , D log , σ) of DSD and is applicable over a broad range of Z. In addition, the uncertainty of β has been improved by the iterative LR λ /RR ratio. Consequently, these algorithms are more effective in observing continuous optical and precise microphysical properties in water clouds.
We performed a sensitivity test for the initial value of lidar/radar ratios (LR 532,I , LR 1064,I , RR ,I ) and the instrument constant (C 532 , C 1064 , C rad ) to the uncertainty of the lidar/radar ratio (LR 532 , LR 1064 , RR), backscatter coefficient (β 532 , β 1064 ), radar reflectivity (Z), and cloud microphysical properties (D eff , LWC). Among these parameters, the lidar constant is the most sensitive in the test. This highlights the cautiousness necessary in constraining the error of the lidar constant (C 532 , C 1064 ). Because the lidar constant can change slightly over time, we suggest using the same day or nearest day's lidar constant to reduce the error of the measurement.
Application to the ideal cloud signal shows that both iterations result in specific clouds and full heights. The iteration results for cloud bases show that both small particles and larger particles can approach stability after several iterations. The iteration results for the maximum relative error of the backscatter coefficient in profiles is 6% and 4% for β 532 and β 1064 , respectively. It improves the continuous lidar signal through the iteration of the lidar ratio. However, due to the presence of larger particles, the empirical relations are challenging.
The implementation of the algorithm in observation cases shows that the results of Z and β are proportional to D eff and LWC in usual cases. However, the lidar supplies additional information for the complete DSD, which caused deviations in the empirical relationship of radar measurements. The synergetic algorithm shows an excellent ability to obtain cloud droplet spectrum information with a single peak or multiple peaks. Consequently, this technique can be developed in the observation of the cloud's spatial and temporal variations.
The limitation of the lidar-radar combined system requires only the lidar-radar overlap region, which means that the amount of efficiency in the dataset is smaller than the radar-only detection. This technique is important to supplement the DSD in principle and fill the gaps in this research field. In addition, the problem of an insufficient dataset can be complemented to combine other wavelength results of remote sensing instruments. Moreover, if the airborne probes could be observed instantaneously, this technique could be validated.
With the development of routine observations, observational stations have been installed at multiwavelength lidar and cloud radar stations for further scientific research. This algorithm could collect long-term water cloud properties and improve parameterization schemes for climate and weather prediction models.