1. Introduction

Clouds cover about 70% of the earth's surface, greatly affecting global climate change due to their strong radiative effects. The complexity of aerosol-cloud interactions (ACI) increases the difficulty of accurately quantifying clouds and brings large uncertainties to assess cloud radiative forcing [1,2]. Among many cloud microphysical properties, cloud effective radius (r_e) is perhaps the most important as it not only have a remarkable influence on cloud albedo [3], but is also a key proxy for assessing cloud lifecycle effects [4]. Additionally, clouds in different stages of their lifecycle have different sensitivity to aerosol loadings. Generally, growing clouds with updrafts near their tops reflect most directly the aerosol effects on cloud microphysical properties [5]. Therefore, monitoring r_e, especially for growing clouds, is of great significance for studying ACI and assessing global radiation forcing.

The importance of cloud r_e has motivated the development of satellite-based remote sensing for r_e retrieval, represented by MODIS (Moderate Resolution Imaging Spectroradiometer) onboard Aqua and Terra, which has provided much of the existent quantification of ACI [6]. MODIS provides r_e and cloud optical depth (COD) calculated by look-up tables (LUTs) based upon a plane-parallel radiative transfer algorithm [7,8]. The LUTs represent the nonlinear relationships between reflection functions at one non-absorbing visible wavelength (VIS, i.e., 0.65 µm or 0.86 µm used over lands and oceans respectively) and one absorbing near-infrared wavelength (NIR, i.e., 1.6, 2.1 or 3.7 µm) based on the assumption of plane-parallel homogeneous cloud properties [9]. However, MODIS can only provide daytime r_e observations. Even though many studies have been conducted to obtain cloud r_e using near-infrared channels at night, they are generally limited to the optically thin clouds [10,11].

The shortcoming of passive satellite observations promoted the application of active satellite remote sensing in cloud microphysical retrieval, e.g. CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization), which is unique in its ability to perform vertical profile measurements of clouds both during daytime and nighttime. Reference [11] firstly calculated cloud r_e using an artificial neural network model with the layer-integrated information derived from CALIOP Level-2 data, with an R² of 0.572 when compared with the simultaneous Aqua-MODIS measurements. This work is a good attempt, but the application of layer-integral information would introduce errors into r_e retrieval, especially for clouds with low homogeneity. In addition, there is no research using CALIOP observations to identify growing clouds as far as we know.

Growing convective clouds have much higher vertical continuity and homogeneity than aging ones or layer clouds, which is a key property that can be used to distinguish them well. At present, a large number of studies have been put forward to quantify cloud homogeneity based on MODIS observations. In Ref. [12], cloud horizontal homogeneity was characterized by a measure of MODIS COD variety within a spatial scale of 1° × 1°. An index (SPI) calculated by the 250 m MODIS reflectance observations was used to quantify sub-pixel inhomogeneity in 1 km in Ref. [13], and this method has since been widely used [14,15]. However, it is extremely difficult to distinguish whether cloud heterogeneity is caused by the varying cloud vertical structure or 3-D radiative effects (i.e., shadow in 1-D retrievals) using MODIS observations alone since one, or both, of the mechanisms could affect the observations and their occurrence may in fact be correlated [13,16].

Given the vertical detection ability of CALIOP, the key point of this study is using CALIOP profile measurements to quantify cloud vertical homogeneity and obtain more effective information for r_e retrieval. Here, we first put forward a method based on the relationship between cloud geometrical depth (CGT) and COD to classify water clouds into vertically homogeneous, mid-homogeneous, and non-homogeneous ones. Then, a two-stage model composed of a fully connected ANN and linear bias correction was developed to retrieve r_e for the three kinds of clouds using CALIOP optical signals excluding the strongly attenuated parts. Global maps of cloud vertical homogeneity and respective r_e are presented finally.

2. Data and methodology

This study focuses on the single-layer, liquid water clouds over oceans between the latitude of 60°N ∼ 60°S, as such clouds constitute much of the boundary layer clouds, which are of prime interest for aerosol cloud interactions. Data used here include CALIOP Level-1 dataset, Level-2 vertical feature mask (VFM), Level-2 5-km cloud profile dataset, and Level-2 5-km cloud layer dataset. All Level-2 datasets are Version 4.2, while the Level-1 dataset is Version 4.1 (updated to the version). The Level-1 dataset provides the attenuated backscatter coefficient (used to characterize echo intensity) at 532 nm and 1064 nm; VFM provides the cloud location and phase information. Profile Dataset can provide extinction coefficient, and layer dataset provides layer-integrated information and input parameters (such as lidar ratio) for extinction retrieval. Specific parameters will be described in the following content. All data used here covers four months (Jan., Apr., Jul., and Oct.) in 2016.

2.1 Cloud classification based on different vertical homogeneity

For vertically homogeneous clouds, the optical depth increases approximately linearly as the penetration depth increases from cloud top until the laser is fully attenuated. Therefore, the vertical correlation between CALIOP COD (i.e., integral of extinction coefficients from cloud top down to each vertical bin) and CGT (i.e., the geometrical thickness from cloud top down to each vertical bin in a profile) could be used to characterize cloud vertical homogeneity. Cloud extinction coefficient and layer height were obtained from Level-2 cloud profile and VFM dataset, respectively. The vertical resolution of the extinction coefficient was interpolated to 30 m from 60 m, but the horizontal resolution keeps unchanged (i.e., 5 km). When calculating the vertical correlation between COD and CGT (R_COD-CGT), vertical bins at the bottom end would be excluded if their corresponding COD is larger than 5 or the total attenuated backscatter (TAB) is less than 0.03 to avoid bias introduced by the strongly attenuated signals with low SNR. The uppermost bin was also excluded, because it is often partially filled with clouds. Figure 1 shows the variation of CALIOP optical signals grouped by R_COD-CGT as a function of CGT.

CALIOP backscatter signals consist of single and multiple scattering contributions of a similar order of magnitude in water clouds, and the latter would be larger in clouds with larger number of smaller cloud droplets [17]. Since the depolarization in water clouds is proportional to multiple scattering, the depolarization ratio also increases faster for denser clouds (i.e., having larger number of cloud droplets with a given effective radius) until saturation, which occurs at approximately COD = 2.5 (Fig. 1(c) and 1(f)). In water clouds, CALIOP TAB is generally larger than 0.05, with a maximum value from ∼0.15 to ∼0.6 (Fig. 1(b) and 1(e)). The day and night CALIOP optical signals within clouds present similar variations, which are the basis for nighttime retrieval based on the data characteristics during daytimes.

 

Fig. 1. Variation of CALIOP optical signals (COD, TAB and DR) grouped by R_COD-CGT (i.e., correlation coefficient between COD and CGT) as a function of CGT (i.e., geometrical depth from cloud top down to each vertical bin in a profile) during daytime (a ∼ c) and nighttime (d ∼ f).

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In terms of the variation of cloud microphysical properties showed in Fig. 1, the cases that have a R_COD-CGT larger than 0.995 and their TAB profiles have a unimodal distribution are considered as homogeneous clouds, indicating growing clouds identified by CALIOP as growing clouds have the highest homogeneity with largest multiple scattering contributions. When the R_COD-CGT is at a range of 0.975 and 0.995 or R_COD-CGT > 0.995 but TAB is not unimodal, the cases are judged as mid-homogeneous clouds. For the cases with a R_COD-CGT less than 0.975, they will be classified as non-homogeneous. Figure 2 shows TAB and COD examples varying with CGT in vertically homogeneous, mid-homogeneous, and non-homogeneous clouds, with a R_COD-CGT of 0.998, 0.994, and 0.974, respectively.

 

Fig. 2. Examples of TAB (i.e., the total attenuated backscatter coefficient, denoted by the blue line) and COD (i.e., the integral of extinction coefficients from cloud top down to each vertical bin, denoted by the orange line) varying with CGT in (a) vertically homogeneous, (b) mid-homogeneous, and (c) non-homogeneous clouds.

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2.2 r_e retrieval from CALIOP

In Ref. [17], an empirical formula was established based on Monte Carlo simulations, depicting the relationship among the mean extinction coefficient (α, in km⁻¹), the layer integrated depolarization ratios (δ’_layer), and r_e (in µm) in opaque water clouds, as expressed by Eq. (1). Theoretically, cloud r_e could be estimated if α and δ’_layer are both known. However, this solution would require to remove any effects imparted by a non-ideal transient response of the photo-detectors, which is almost impossible with current technology [17]. Therefore, considering the unique advantages of ANN in dealing with nonlinear problems, we established a two stage-model consisting of a fully connected ANN and linear bias correction to separately retrieve r_e from CALIOP for each type of cloud, as shown in Fig. 3.

ANN can explore the relationship between explanatory variables and dependent variables through experiential learning without prior knowledge. As a “connectionist” computing system, the basic elements of ANN are nodes (also called neurons). Every node has several weighted inputs and one output calculated from the transfer function. During training, the weights can be adjusted based on the learning rules and error propagation models until the error in predictions is minimized. More details about ANN can be found in [18].

 

Fig. 3. Schematic of r_e retrieval from CALIOP for water clouds.

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In this study, a fully connected ANN was established. According to Ref. [11], all the hidden layers adopted the “tan-sigmoid” transfer function, and the output layer adopted the linear transfer function. To quantify the performance of the network, we used the mean square error between the predicted value and the “real” value as the cost function. In addition, we attenuated weight parameters through L2 regularization to suppress model overfitting. The implementation of the neural network was based on Keras, a Python library built on TensorFlow (TensorFlow is a symbolic mathematical system based on dataflow programming, which has been widely used in the programming of machine learning algorithms).

The simultaneous Aqua-MODIS r_e measurements were used for model training and independent validation, which were provided by Level-2 1-km cloud dataset in Collection 6.1. Notably, the different absorption efficiency of water clouds determines the differences in the depth within clouds corresponding to retrieved r_e in the three NIR channels (i.e., 1.6, 2.1 and 3.7 µm) of MODIS. Given the widespread use of r_e3.7 and r_e2.1 [11] and the relatively high susceptibility of r_e1.6 to cloud heterogeneity [13,19], r_e3.7 and r_e2.1 were selected as training samples to explore the relationship between MODIS r_e and optical information detected by CALIOP, respectively. After the model is trained, r_e can be directly derived from CALIOP independently without MODIS input, which makes both day and night retrieval of r_e possible with CALIOP observations only [11]. There are four fundamental steps in the process: data matching, sample selection, model training, and bias correction.

2.2.1 Data matching

The horizontal resolution of CALIOP datasets was unified to 5 km, with a vertical resolution of 30 m, which means one CALIOP observation corresponds to five MODIS pixels based on the nearest pixel principle. According to cloud microphysics shown in Fig. 1, when CALIOP COD ≈ 2.5, the depolarization ratio starts saturating. With that, also the information content received by the lidar is approaching saturation. Therefore, we focus on the optical signals ending at COD ≈ 2.5 (the first vertical bin with COD not less than 2.5) to extract the information for r_e retrieval. Referring to studies of Ref. [11] and Ref. [17], 15 properties (Table 1) were eventually adopted as the ANN's inputs.

Table 1. The ANN inputs for CALIOP r_e retrieval

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Specifically, the ANN input properties include: extinction coefficient at 532 nm (Extinc₅₃₂), volume depolarization ratio at 532 nm (DR₅₃₂), multi-scattering factor at 532 nm (MSF₅₃₂), vertical COD at 532 nm (COD₅₃₂), slope of DR₅₃₂ to COD₅₃₂, altitude, vertical CGT, corrected TAB both at 532 and 1064 nm (CTAB₅₃₂, CTAB₁₀₆₄), total backscatter at 532 nm (TBS₅₃₂), LR₅₃₂, bin-integrated CTAB₅₃₂ (InteCTAB₅₃₂, i.e., CTAB₅₃₂ integrated from cloud top to the aimed bin in a profile), bin-integrated CTAB₁₀₆₄ (InteCTAB₁₀₆₄), bin-integrated DR₅₃₂ (InteDR₅₃₂), and bin-integrated attenuated CR (InteAttCR). The integral parameters are used to account for the impacts of upper layer parts on the following CALIOP signals inside clouds. Please refer to Eq. (S1)-(S9) for more details on the calculation of each parameter.

2.2.2 Sample selection

We set a series of criteria for sample selection to ensure the high precision of MODIS observations. If the five matched MODIS pixels meet all criteria, they would be averaged as an acceptable case. The criteria are as follows: (1) all of five matched pixels should be single-layer water clouds detected simultaneously by CALIOP and MODIS; (2) MODIS COD at 0.86 µm should be larger than 3, as the accuracy of MODIS retrieval is limited when COD$\; \le \; $ 3 [20]; (3) the pixel should be embedded by clouds; (4) given the significant influence of 3-D radiative effects and solar zenith angle (SZA) on MODIS measurements, the uncertainty of MODIS r_e should be less than 10%, with SZA smaller than 65° and sensor zenith angle at the range of −25° ∼ 50° [21]; (5) the standard deviation (std) of the five matched MODIS r_e values should not exceed 2 µm. Requirements (3) ∼ (5) can effectively filter out cloud pixels with low horizontal homogeneity, which is conducive to ensuring the stability of the model (Fig. S1 shows the influence of cloud horizontal inhomogeneity on r_e retrieval). Finally, there are 83,328 matched cases left.

2.2.3 ANN model training

Here, an improved 5-fold cross-validation method was used for model training and validation. The process is as follows: (1) all matched cases were evenly and randomly divided into five folds; four were used for model training (among them, 85% used as the training set, and 15% used as the validation set), and the remaining one was used as the test set. This step was repeated five times until every fold was independently predicted. The R², mean absolute error (MAE), root-mean-square error (RMSE), relative MAE (the ratio between MAE and the mean value of MODIS r_e, denoted by RMAE) and relative RMSE (the ratio between MAE and the mean value of MODIS r_e, denoted by RRMSE) were used to quantify the model performance.

By comparing the performance of ANN models with different number of nodes (layers) (Fig. S2), we finally adopted the model composed of one input layer, three hidden layers, and one output layer, with the number of nodes in each hidden layer of 80, 40 and 20, respectively. With the model complexity increasing (e.g., the node number of each hidden layer was doubled), the model accuracy would not get better.

2.2.4 Bias correction

The ANN model tends to overestimate small r_e (< 12.5 µm) and underestimate large ones (> 22.5 µm) (Fig. S3), which also has been concluded in Ref. [11]. Therefore, a simple linear regression method was proposed to fit the averaged MODIS- and CALIOP-retrieved r_e. The bias was corrected based on the relationship shown by Eq. (2), at the expense of some decrease in the correlation.

Where the parameter $\overline {{r_e}} $ is the mean values of fixed r_e intervals.

3. Results and discussion

3.1 Validation of CALIOP r_e retrieval

Based on the proposed classification method, all clouds detected simultaneously by CALIOP and MODIS were identified as vertically homogeneous, mid-homogeneous, and non-homogeneous cases, with the number of 51,983, 21,873, and 9,472, respectively. Figure 4 shows the statistics of MODIS r_e2.1, CALIOP TAB, the whole penetrated COD and CGT (i.e., COD and CGT from cloud top until full attenuation or cloud base) in each type of clouds, indicating the significant differences in microphysical and optical properties among those cases. Compared with mid- and non-homogeneous clouds, homogeneous ones have the smallest droplet size, the strongest backscatter, the largest optical depth, and the weakest lidar penetration. Specifically, approximately 75% of homogeneous cases have r_e2.1 smaller than 15 µm; 90% of cases have a maximum TAB larger than 0.5. However, for non-homogeneous clouds, about half of cases have r_e2.1 larger than 15 µm, and more than 80% of cases have the maximum TAB smaller than 0.5. The laser penetration depth until full attenuation increases with r_e increasing and cloud homogeneity decreasing (Fig. 4(d) ∼ 4(f). The mean penetration depth of homogeneous clouds is about 350 m and increases to 580 m in non-homogeneous ones.

 

Fig. 4. Statistics of microphysical and optical properties for vertically homogeneous, mid-homogeneous, and non-homogeneous clouds detected simultaneously by CALIOP and MODIS during daytime. (a) MODIS r_e2.1; (b) maximum TAB; (c) whole penetrated COD, i.e., integral of extinction coefficients from cloud top until laser full attenuation; (d) ∼ (f) whole penetrated CGT, i.e., geometrical thickness from cloud top until laser full attenuation. In subplots of (d) ∼ (f), the color represents the number of cases in the corresponding grid; the red lines represent the 1:1 reference; black dots are the mean values and the fine “I” type lines are the corresponding standard deviations in each MODIS r_e bin, which was partitioned based on a fixed interval. The sample number of each r_e bin showed in the subplots is larger than 100.

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Figure 5 shows the fitting relation between CALIOP and MODIS-retrieved r_e. To prove that the optical signals at COD ≈ 2.5 are the optimal for model input, we also compared with the model performance with input at COD of 1.5 and 3.5 respectively (Fig. S4, S5). The results show that the accuracy of the latter two solutions is relatively low, especially when COD ≈ 3.5. Notably, no matter what kind of the solution is, the model with MODIS r_e2.1 as the training sample always has higher accuracy compared with the model trained by MODIS r_e3.7. This is mainly due to the higher correlation between CALIOP signals and MODIS r_e2.1 (Fig. 6), especially at the optical depth of 2.5 ∼ 3.0, which further proves the reliability of using optical information at COD ≈ 2.5 for r_e retrieval.

 

Fig. 5. Validation of CALIOP r_e retrieval (after bias correction) for vertically homogeneous, mid-homogeneous, and non-homogeneous clouds detected simultaneously by CALIOP and MODIS during daytime. (a) ∼ (c) show the results using the ANN model trained by MODIS r_e2.1, and (d) ∼ (f) show the results using the ANN model trained by MODIS r_e3.7. The matched sample size (N), R², MAE, RMSE, relative MAE (i.e., RMAE) and relative RMSE (i.e., RRMSE) are given; the color represents the number of cases in the corresponding grid; the red lines represent the 1:1 reference; black dots are the mean values and the fine “I” type lines are corresponding standard deviations.

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Fig. 6. Absolute correlation coefficients between explanatory parameters derived from CALIOP and MODIS r_e3.7, as well as r_e2.1 at different COD bins (i.e., the vertical bin with COD closest to the target value).

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According to Ref. [22], the optical depth within clouds corresponding to MODIS-retrieved r_e3.7, r_e2.2, and r_e1.6 is about 2.1, 3.3 and 3.6 respectively when the whole COD (from cloud top to base) is not less than 5, and the strongest reflectance (denoted by the maximum vertical weighting for bidirectional reflectance) occurs at optical depths of approximately 0.25, 1.45, and 1.5 for bands of 3.7 µm, 2.2 µm, and 1.6 µm, respectively. Compared with MODIS, CALIOP has also shown a high sensitivity to cloud parts within optical depth < 3.5, and the most substantial photon scattering occurs in the region of optical depth near 1.5, more similar to the vertical weighting profiles of MODIS at 2.1 µm rather than 3.7 µm (Fig. 7). Therefore, it is reasonable to expect a higher correlation between cloud microphysics retrieved by CALIOP and MOIDS r_e2.1. Additionally, as MODIS r_e3.7 is much closer to cloud tops, it is more susceptible to the changes in the atmospheric environment. Thus, unless otherwise specified, the subsequent CALIOP r_e is calculated from the model trained by MODIS r_e2.1, which is different from MODIS r_e3.7 used in Ref. [11].

 

Fig. 7. Normalized vertical energy profiles of MODIS and CALIOP: (a) dependence of MODIS vertical weighting functions on optical depth for bidirectional reflectance, referred to Ref. [22]; (b) dependence of CALIOP total attenuated backscatter on optical depth. The different lines represent cases with different whole COD (i.e., from cloud top to base).

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It can be found from Fig. 5 that vertically homogeneous clouds have the highest estimation accuracy, with a R², RMSE and MAE of 0.72, 1.75 µm and 2.25 µm, followed by the mid-homogeneous. The model performs worst for non-homogeneous clouds, with a R², MAE and RMSE of 0.60, 2.90 µm and 3.70 µm. The low accuracy of r_e retrieval in non-homogeneous clouds should be attributed to the limited reliability of MODIS and CALIOP observations in those cases. Since MODIS r_e retrieval is based on the assumption of plane-parallel homogeneous clouds, heterogeneous clouds do not satisfy this assumption and hence r_e retrieval in those clouds has great uncertainty, although we have strictly screened the training samples in this study. According to Ref. [23], ignoring shadow in 1-D retrievals with high resolution would result in substantial positive bias in small droplets. Besides, vertically non-homogeneous clouds are usually aged open cells with significant sub-pixel inhomogeneity, and ignoring sub-pixel inhomogeneity would produce a negative bias in MODIS r_e retrieval, especially for large droplets [23]. As for CALIOP, despite of the small footprint (i.e., 70 m), CALIOP observations also could be affected by cloud inhomogeneity, especially for multilayer clouds or single-layer clouds with large vertical fluctuation of attenuated backscatter [24], and the latter are generally identified as non-homogeneous clouds here.

To verify the proposed algorithm's spatial stability, we compared MODIS- and CALIOP-retrieved r_e globally in the daytime (Fig. 8). Due to the sparse data caused by the narrow swath of CALIOP, all cases were mapped into 2° × 2° grids. As can be seen, the geographical distributions of MODIS- and CALIOP-retrieved r_e are very similar, with a global mean value of 14.2 ± 3.0 µm and 14.4 ± 3.4 µm, respectively. Relatively small droplets are distributed near coasts, where vertically homogeneous clouds accumulate (Fig. 8(c)). In contrast, large droplets are mainly located over remote oceans around the equator, where there are high fractions of non-homogeneous clouds (Fig. 8(d)). Except for the Southern Ocean near Antarctica, CALIOP r_e tends to be smaller than MODIS r_e2.1 in areas with large amounts of vertically homogeneous clouds, such as West Africa. Even though the difference seems small, the relative bias, calculated by $|{{r_e}({\textrm{CALIOP}} )- {r_{e2.1}}({\textrm{MODIS}} )} |/{r_{e2.1}}({\textrm{MODIS}} )\times 100\%$, is still large in those regions (Fig. 8(f)), which is due to the smaller droplet size distribution of homogeneous clouds. The mean value of global relative bias is about 8.1%, less than the uncertainty threshold (10%) of MODIS r_e adopted in this work. More than 40% of the grids have a relative bias of less than 5%; and the portion can be up to ∼70% if the relative bias threshold is set to 10%, indicating the high spatial consistency between CALIOP and MODIS retrievals.

 

Fig. 8. Global validation of CALIOP r_e retrieval for all cases detected simultaneously by CALIOP and MODIS in the daytime, with a grid of 2° × 2°: (a) MODIS r_e2.1; (b) CALIOP r_e; (c) fraction of vertically homogeneous clouds; (d) fraction of vertically non-homogeneous clouds; (e) difference (µm) of averaged CALIOP r_e minus MODIS r_e2.1 in each grid; (f) relative error (%) between CALIOP r_e and MODIS r_e2.1 in each grid, which was calculated by $|{{r_e}({\textrm{CALIOP}} )- {r_{e2.1}}({\textrm{MODIS}} )} |/{r_{e2.1}}({\textrm{MODIS}} )\times 100\%$.

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3.2 Global distributions of CALIOP r_e

Global distributions of day-night vertically homogeneous, mid-homogeneous, and non-homogeneous clouds detected by CALIOP are presented in Fig. 9, with a 2° × 2° grid. Each grid has at least 10 cases. Consistent with that shown in Fig. 8, geographical distributions of homogeneous and non-homogeneous clouds have significant spatial heterogeneity. Specifically, vertically homogeneous clouds are mainly distributed close to continents, especially near the coasts downwind of major landmasses, such as North America, Peruvian, Eastern Atlantic, and Western Africa. The Southern Ocean also has a higher fraction of homogeneous clouds. Non-homogeneous clouds are concentrated mainly over remote oceans around the equator, where the convection is strong. However, the mid-homogeneous clouds are more evenly distributed globally, especially during daytimes. Although the nighttime geographical distributions of each type of cloud present similar patterns with the daytime ones, the global mean fraction varies greatly. For homogeneous clouds, the nighttime global mean fraction is 25% ± 16%, approximately 10% less than the daytime one (35% ± 20%). The non-homogeneous clouds are also reduced at night, but only with −4% decrease in global mean fraction (33% ± 18% on daytime V.S. 29% ± 15% on nighttime). In contrast to homogeneous and non-homogeneous clouds, the proportion of mid-homogeneous clouds increases at night, with an increment of ∼14% (32% ± 11% on daytime V.S. 46% ± 13% at night). It may result from large amounts of homogeneous clouds developing at night and maturing into mid-homogeneous ones, as proved by the significantly increased fraction of mid-homogeneous clouds near coasts.

 

Fig. 9. Global distribution of vertically homogeneous, mid-homogeneous, and non-homogeneous clouds detected by CALIOP in 2° × 2° grids during the daytime and nighttime: (a) ∼ (b) homogeneous clouds; (c) ∼ (d) mid-homogeneous clouds; (e) ∼ (f) non-homogeneous clouds. The number in the caption of each subplot represent the averaged cloud proportion ± std.

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Figure 10 shows the day-night r_e distributions of clouds with different vertical homogeneity detected by CALIOP, also with a 2° × 2° grid. Significantly consistent with the geographical distribution of homogeneous clouds, small values of r_e-estimates are distributed close to continents, demonstrating the remarkable influence of aerosols on cloud microphysics. Large droplets are concentrated around the equator, especially over the Pacific and the Indian Ocean, determined by the strong convection and less aerosol disturbance in these regions. Compared with the daytime, cloud droplets get enlarged at night. Specifically, the global mean r_e of homogeneous clouds during the nighttime is 17.9 ± 3.1 µm, approximately 3.5 µm larger than the daytime one. For mid-homogeneous and non-homogeneous clouds, the global mean r_e is increased from 15.5 ± 3.3 µm to 18.7 ± 2.7 µm and from 16.3 ± 3.3 µm to 19.4 ± 2.8 µm, with a nighttime-daytime positive difference of approximately 3.2 µm and 3.1 µm respectively.

 

Fig. 10. Global r_e distribution of vertically homogeneous, mid-homogeneous, and non-homogeneous clouds detected by CALIOP in 2° × 2° grids during the daytime and nighttime: (a) ∼ (b) homogeneous clouds; (c) ∼ (d) mid-homogeneous clouds; (e) ∼ (f) non-homogeneous clouds. The number in the caption of each subplot represents the averaged r_e ± std.

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Since the advanced calibration algorithm of CALIOP used in the version 4.2 datasets makes the uncertainty of calibration processes greatly decreased [25,26], the bias caused by the system errors of CALIOP observations would be limited, especially during the nighttime. Therefore, the positive deviation of CALIOP r_e between nighttime and daytime should be mostly attributed to the cloud physical processes. As the dominant cloud type over oceans, stratiform clouds are driven by the radiative cooling at the marine boundary layer [27]. The larger cloud-top radiative cooling rate at night would invigorate the convection over oceans, as implied by the increased cloud top height (CTH) during nighttime (Fig. S4). According to statistics, the nighttime enhancement of global mean CTH in vertically homogeneous clouds is approximately 100 m. Enhanced convection would undoubtedly lead to an increase in LWP on nighttime [28]. According to Ref. [29], the diurnal peak of LWP occurs around 02–05 am local time; therefore, cloud r_e would be larger at that time. Additionally, the greater LWP and r_e are expected to increase precipitation to decrease cloud vertical homogeneity, which explains the decrease of homogeneous cloud fraction during the nighttime shown in Fig. 9(b).

4. Conclusions

Accurate retrieval of day-night cloud droplet effective radius, especially for vertically homogeneous growing clouds, is significant for ACI studies. Although MODIS r_e retrieval has made great progress, it only works during the daytime. Profiling measurements conducted by CALIOP have a great possibility for identifying vertically homogeneous clouds at a small scale and filling the MODIS gap of cloud retrieval at night. In this study, we explored CALIOP potential in r_e retrieval while accounting for cloud vertical homogeneity.

Vertically homogeneous, mid-homogeneous, and non-homogeneous clouds were classified based on the correlation of vertical COD and CGT detected by CALIOP. According to global ocean statistics, homogeneous clouds are mainly distributed near the coasts downwind of major landmasses, with a global mean fraction of approximately 35% and 25% during the daytime and nighttime, respectively. In contrast, non-homogeneous clouds are concentrated mainly over remote oceans around the equator determined by the strong convection, with a 4% decreased fraction at night. Mid-homogeneous clouds are more evenly distributed globally but with a significant increase in cloud fraction at night.

A two-stage model was developed to retrieve r_e from CALIOP. The validation results indicate that CALIOP r_e retrieval has the highest accuracy for vertically homogeneous clouds, with a R², MAE and RMSE of 0.72, 1.75 µm and 2.25 µm, followed by the mid-homogeneous and non-homogeneous ones. Furthermore, according to global statistics, more than 40% (up to 70%) of grids in 2° × 2° have a relative bias less than 5% (10%) when compared with MODIS r_e, indicating the high spatial consistency between CALIOP and MODIS retrievals.

Geographical distributions of CALIOP r_e indicate that significantly small values are distributed near coasts, where vertically homogeneous clouds accumulate. However, large droplets are concentrated around the equator, where there are high fractions of non-homogeneous clouds. Although the day-night cloud geographical distributions present similar patterns, the droplets get enlarged at night, which should be mainly attributed to the different cloud physical processes during the daytime and nighttime.

Since growing clouds with the highest vertical homogeneity reflect most directly the effects of aerosols on cloud properties, the improved accuracy of retrieved r_e in homogeneous clouds provides a basis application to possible breakthrough insights in ACI. More importantly, this study implies a powerful tool to depict the vertical microstructure of convective clouds if this method can be used for r_e retrieval at the full resolution of CALIOP in the future.