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Abstract
Cloud droplet effective radius (CER) and number concentration (CDNC) are two critical microphysical properties of liquid water clouds, which play essential roles in the Earth’s radiative energy balance and atmospheric hydrological cycle. Even though many satellite remote sensing techniques have been developed to obtain these two properties, the observations are often limited to the daytime. In this study, a method to estimate CER and CDNC of liquid water clouds over global ocean area during both daytime and nighttime from CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) measurements is presented. The size sensitivity of the dual-wavelength (532 nm & 1064 nm) layer-integrated attenuated backscattering signals from CALIOP is checked and information content for liquid water cloud CER retrieval is found. Taking use of the artificial neural network (ANN) technique, the CER and then the CDNC are estimated from CALIOP by combining the polarization ratio and the dual wavelength attenuated backscattering signals. The comparisons with CER and CDNC estimated from MODIS (Moderate Resolution Imaging Spectroradiometer) during daytime demonstrate the feasibility of this new method. Both the daytime and nighttime CER and CDNC derived from CALIOP observations are presented in this paper and the day-night variation of liquid water cloud is discussed which would provide useful day-night variation of liquid water cloud properties.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It has been long recognized that clouds play a critical role in the Earth’s radiation budget as the presence of clouds increases the reflection of the incoming short-wave solar radiation and reduces the outgoing long-wave radiation [1–3]. The cloud-aerosol-radiation interaction is one of the largest uncertainty sources in climate prediction [4,5]. Aerosol would affect the properties of clouds through various ways [3], including the cloud albedo effect [6], cloud lifetime effect [7], and cloud thermal emissivity effect [8]. Among the various effects, the most direct effect of aerosol on cloud is that aerosol can serve as cloud condensation nuclei (CCN) modifying the cloud droplet number concentration (CDNC) and cloud effective radius (CER) and altering the radiative and precipitation properties of clouds. Reliable information about the CER and CDNC would lead to a better parameterization of cloud-aerosol-radiation interactions in global climate models [9].
Satellite remote sensing is a critically important technique for acquiring cloud observations over large domains. Passive satellite measurements of solar and infrared (IR) spectral images have been widely used to retrieve optical and micro/macro physical properties of clouds with large spatial and temporal coverage. The cloud optical depth (COD) and CER can be obtained from the bi-spectral method with the combination of solar and infrared channels from satellite images during day time [10], and the typical representative is the MODIS (Moderate Resolution Imaging Spectroradiometer) onboard Aqua and Terra [11]. Then, under the “adiabatic cloud model” assumption, the CDNC of warm water cloud could be further retrieved from COD and CER [12]. However, both day and night optical and micro/macro physical properties of clouds are crucial for weather and climate models as the understanding of diurnal variations of clouds are important to the determination of Earth radiation budget [13]. Many attempts have been put forward for the cloud properties detection during night time recent years. The Visible Infrared Imaging Radiometer Suite (VIIRS) instrument on board Suomi-National Polar Partnership (S-NPP), extends the application of bi-spectral retrieval method to the nighttime by adding a day/night band channel with high sensitive observations in the visible spectral region to lunar reflectance during night [14]. However, the retrieval is only effective for a range of lunar illuminating conditions over nonurban regions where no static background signals disturb the retrieval [15]. It is also possible to retrieve COD and CER only using near-infrared channels during the night, but the retrieval is limited to optically thin clouds with visible optical depth no more than 5 or so [2,11].
Satellite active remote sensing measurements, such as Cloud Profile Radar (CPR) on board CloudSat [16] and CALIOP (Cloud-Aerosol LIdar with Orthogonal Polarization) [17] on board CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation), can provide a special insight to the vertical structure of clouds during both day and night [18]. CloudSat and CALIPSO were launched at the same time in April 2006, and are still working on orbit now. CPR is a 94 GHz Radar which shows a more powerful ability for cloud profiling than CALIOP as it uses a much longer wavelength electromagnetic wave as probe. The CER and COD retrieved from CPR alone is found not consistent with that from MODIS which somehow limits its application [19]. And what’s more, CPR can no longer work during night time since 2011 due to the battery anomaly [20]. CALIOP is a space-borne dual-wavelength (532 nm & 1064 nm) polarized (532 nm only) lidar which has been quasi-continuous working for more than ten years. The retrieval technique of CDNC from CALIOP was also proposed [21], but it needs the CER from collocated passive satellite measurements (such as MODIS) as input which limited the retrieval only available during day time [21,22]. The retrieval of CDNC from CALIOP alone is mainly hampered by the transient response of photomultiplier tubes (PMTs for short) at 532 nm channels (the PMTs exhibit a decaying noise tail after a strong signal) [23,24]. Deconvolution technique was proposed to correct the effects of transient response to retrieve extinction coefficients from CALIOP, but the retrieval is limited to extinction less than 60 km-1 and is challenging to be applied to the CDNC retrievals [24]. A reliable retrieval algorithm that can estimate the CER and CDNC during night time based on CALIOP measurements alone is highly desirable, particularly considering the availability of more than ten years observations from CALIOP.
In this paper, the relationship between the dual-wavelength (532 nm & 1064 nm) polarization (532 nm only) observations of CALIOP with the collocated CER measurements from MODIS is examined and an artificial neural-network (ANN) based method is proposed to retrieve CER and CDNC of liquid water clouds from CALIOP observations alone. This study not only extends the application of CALIOP data to provide a dataset on the day-night variations of liquid water cloud microphysical properties, but also proposes a possible remote sensing method for retrieval of liquid water cloud properties during both day and night using dual-wavelength polarization lidar.
The rest of this paper is arranged as follow. Some basic optical properties of liquid water clouds used in this study are briefly introduced in Section 2. In Section 3, the possibility to retrieve CER of liquid water clouds from CALIOP is examined using the coincident measurements from CALIOP and MODIS and then the ANN based method for CER estimation is presented. The CER and CDNC retrieved from CALIOP are given along with corresponding MODIS product and the day-night differences of micro-physical properties of water clouds are discussed in Section 4. Finally, a short summary is addressed in section 5.
2. Lidar observation of cloud optical properties
The layer-integrated attenuated backscatter coefficient is defined as
As for liquid water cloud, the lidar ratio varies little for most cases and is around 18.2 sr or so at 1064 nm [27]. And the transmittance of the opaque liquid cloud layers can be treated as 0. Then we can get the multi-scattering factor of the cloud layer as
Another important relationship for CALIOP measurements is concluded by Hu et al. from Monte Carlo simulations as [21]
3. Methodology
3.1 The CER information implied in the CALIOP dual-wavelength measurements
It is well known that the multi-scattering effect is related to the size parameter $x = {{2\pi {r_e}} \mathord{\left/ {\vphantom {{2\pi {r_e}} \lambda }} \right.} \lambda }$ [29,30]. Under the quasi-small-angle (QSA) approximation, the multiply scattered photons returned to the lidar receiver encountered only one large-angle scattering event along with several times of forward scattering events [30]. As the angle width of the forward scattering is scaled to ${\lambda \mathord{\left/ {\vphantom {\lambda {({2{r_e}} )}}} \right.} {({2{r_e}} )}}$ [29], the multi-scattering effect in lidar is related to the CER and also wavelength of incident laser. But for the spaceborne lidar, such as CALIOP, the QSA approximation is no longer satisfied and much stronger multi-scattering effects are expected. In order to examine the relationship between the multi-scattering effects and CER, the CER products from coincident measurements of MODIS are used in this study.
The dual wavelength layer-integrated attenuated backscatter coefficients (${\gamma ^{\prime}_{532}}$ and ${\gamma ^{\prime}_{1064}}$), layer-integrated depolarization ratio ($\delta $), cloud top altitude (${z_{top}}$), cloud top temperature (${T_{top}}$), the opacity flag, the number of layers and the cloud phase information from CALIOP level-2 5 km cloud layer products(v4.1) were used in this study. The collocated Aqua-MODIS Collection 6.1 level-2 cloud product (MYD06) provides the CER from 3.7 µm and 0.86 µm bands (refer to as ${r_{e,3.7}}$ hereafter), cloud optical depth (τ), cloud multi-layer flag (CMLF) as well as cloud phase information determined from optical properties during daytime. ${r_{e,3.7}}$ is considered more representative for the situation of the top of cloud and less sensitive to the horizontal heterogeneity of clouds. Satellite lidar is also only sensitive to the cloud top as lidar usually can only penetrate into cloud of COD about 3. Thus, the ${r_{e,3.7}}$ is considered as more consistent with the lidar observations and is adopted for the analysis in this paper [21,24].
In this study, we focus only on the upmost, single-layered, opaque liquid water cloud layers as the cloud products of MODIS is usually more accurate for single layer cases. The cloud phase information both from CALIOP and MODIS are adopted to make sure only liquid water cloud layers are included and the number of layers from CALIOP and CMLF from MODIS were used to choose only the upmost, single-layered cloud layers. Because the retrieval of CER from MODIS by the bi-spectral method is causally less convincing for clouds with COD less than 3, the cloud samples used here are restricted to those cases that are opaque for lidar detections and have a MODIS COD estimated larger than 3 [31]. The cloud samples are restricted to the cases with layer integrated depolarization less than 0.35 as Eq. (4) is valid only when the layer-integrated depolarization ratio is smaller than 0.35 [24] and no additional constrain on the optical properties of those cloud layers is applied in this study. For the data processing, each lidar profile of the CALIOP level-2 5 km cloud layer product is first matched with a MODIS pixel-level observation in both space (distance < 1 km) and time (time difference 70∼80 s) in order to ensure they point to the same clouds. As the spatial resolution of MYD06 cloud products is 1 km × 1 km, the five pixels of MODIS along CALIOP track are averaged. Also, the partly cloudy pixels of MODIS are not included in the analysis.
Four-month coincident measurements from MODIS and CALIOP (Jan./Apr./Jul./Oct. 2016) are used to generate the two-dimensional histogram of the CER- ${{{\eta _{532}}} \mathord{\left/ {\vphantom {{{\eta_{532}}} {{\eta_{1064}}}}} \right.} {{\eta _{1064}}}}$, as shown in Fig. 1. The multi-scattering factor of 532 nm is estimated from Eq. (4) and the multi-scattering factor of 1064 nm is estimated from Eq. (3) with constant lidar ratio of 18.2 sr [32]. ${R_\eta }$ denotes the ratio of ${{{\eta _{532}}} \mathord{\left/ {\vphantom {{{\eta_{532}}} {{\eta_{1064}}}}} \right.} {{\eta _{1064}}}}$. The data samples used in this study are restricted to the subsurface of Ocean between [60°S-60°N] as the retrieval of MODIS is more reliable over these areas [12].
Fig. 1. Two-dimensional histogram of CER-Rη. The black dashed line gives the linear regression results.
There is an approximate linear relationship between CER and ${R_\eta }$. And the linear regression is
where the 95% confidence bounds of the slope is (0.01759,0.01778), and the 95% confidence bounds of the intercept is (0.9338,0.9364). The coefficient of determination ${R^2}$ of the linear regression is 0.336 or so and most CER-Rη sample pairs are located around the linear regression line as can be seen from Fig. 1. The multi-scattering factor can be estimated from Eq. (4), and then the lidar ratio at 532 nm can be derived as ${S_{532}} = {1 \mathord{\left/ {\vphantom {1 {({2{\eta_{532}}{{\gamma^{\prime}}_{532}}} )}}} \right.} {({2{\eta_{532}}{{\gamma^{\prime}}_{532}}} )}}$. Here we also checked the relationship between ${S_{532}}$ and CER from the synergetic measurements of MODIS and CALIOP. The data used here are the same as that of Fig. 1 and the results are shown in Fig. 2.Fig. 2. Two-dimensional histogram of CER-S532. The black dashed line gives the linear regression results.
There is also an approximate linear relationship between CER and S532 and the linear regression gives a result as
where the 95% confidence bounds of the slope is (-0.374,-0.3701), and the 95% confidence bounds of the intercept is (23.74,23.79). The linear regression line is shown as the dashed line in Fig. 2 and the CER-S532 sample pairs compared favorably to the linear regression result with the coefficient of determination ${R^2}$ of the linear regression as 0.336.3.2 Retrieval methodology
In Sec. 3.1, we estimate the ratio of ${{{\eta _{532}}} \mathord{\left/ {\vphantom {{{\eta_{532}}} {{\eta_{1064}}}}} \right.} {{\eta _{1064}}}}$ using a constant lidar ratio at 1064 nm. However, the estimated results of lidar ratio at 532 nm may change with CER. If we make an assumption that, the ratio of lidar ratios of liquid water cloud at 532 nm and 1064 nm are independent of the CER, then a new estimation of ${R_\eta }$ can be obtained as ${R_\eta } \approx k \cdot {{{{\gamma ^{\prime}}_{1064}}} \mathord{\left/ {\vphantom {{{{\gamma^{\prime}}_{1064}}} {{{\gamma^{\prime}}_{532}}}}} \right.} {{{\gamma ^{\prime}}_{532}}}}$, where k is a CER independent constant. We examined the relationship of CER-${{{{\gamma ^{\prime}}_{1064}}} \mathord{\left/ {\vphantom {{{{\gamma^{\prime}}_{1064}}} {{{\gamma^{\prime}}_{532}}}}} \right.} {{{\gamma ^{\prime}}_{532}}}}$ and the results are shown in Fig. 3.
Fig. 3. Two-dimensional histogram of CER-χ. The black dashed line gives the linear regression results.
As we can see, the attenuated layer-integrated color ratio $\chi = {{{{\gamma ^{\prime}}_{1064}}} \mathord{\left/ {\vphantom {{{{\gamma^{\prime}}_{1064}}} {{{\gamma^{\prime}}_{532}}}}} \right.} {{{\gamma ^{\prime}}_{532}}}}$ is dependent on the CER, but the linear fit result demonstrates a relatively lower ${R^2}$. However, the tendency that layer-integrated attenuated color ratio $\chi $ decreases with the increase of CER is clear. Actually, this can also be expected from Fig. 25 and Fig. 26(a) of Ref. [32]. The variation of mean CER from MODIS along the latitude nearly has a reverse correlation with that of mean $\chi $ between the latitude of 60°N∼60°S. As there is no depolarization measurement at 1064 nm from CALIOP, the multi-scattering factor ${\eta _{1064}}$ cannot be derived directly. However, it seems still quite reasonable to make a conclusion that the dual-wavelength measurements from CALIOP contain more information for CER of liquid water clouds when comparing with that of single wavelength measurements. Along with the multi-scattering effects information contained in the depolarization measurements at 532 nm, it is possible to estimate CER from CALIOP directly.
However, the explicit relationship between CER and the layer information detected from CALIOP is hard to derive. Instead, it might be possible to derive the relationship between these parameters indirectly under the help of some non-linear analysis method, such as the ANN method.
The ANN method does not use a representative physical model, but tries to identify the relationship between input and output variables by learning from a set of observed or simulated data. More detailed introduction to ANN can refer to [33] and references therein. An ANN is a ‘connectionist’ computational system and its basic elements are the neurons. The output response of a single neuron to the inputs can be modeled as
where the ${x_i}$ ($0 < i \le n$, n is the number of inputs) is the input stimulation; ${W_i}$ stands for the weight for each input and b is an additive bias for the neuron and $F({\cdot} )$ represents the transfer function (also called activation function). An ANN may consist of multi-layers of neurons and every neuron is connected with all of the neurons in neighboring layers through ‘weights’. The ANN can be trained by supervised learning technique to obtain the ‘weights’ and ‘biases’. In order to quantify the performance of the network, the mean square error between the predicted value and the ‘real’ value is used as the cost function. The dataset is divided into three parts: training, validation and test dataset [34]. The training dataset is used for the training of the network according to the cost function and the validation dataset is used to avoid over-fitting of the network. And the performance on the validation dataset is the criteria to determine the architecture of the ANN. The test dataset is used to assess the performance of a fully-trained model on unseen new data.In this study, a neural network with one input layer, two hidden layers and one output layer is chosen according to the performance of the network on the validation dataset after testing networks with different transfer functions and number of neurons. There are 9 neurons in the input layers to receive the input vector $[{{{{\eta_{532}}} \mathord{\left/ {\vphantom {{{\eta_{532}}} {{\eta_{1064}}}}} \right.} {{\eta_{1064}}}},{S_{532}},\delta ,{\eta_{532}},\chi ,{{\gamma^{\prime}}_{532}},{{\gamma^{\prime}}_{1064}},{T_{top}},{z_{top}}} ]$. The number of neurons for the two hidden layers is 80 and 40, respectively. And tan-sigmoid [$t(x )= {2 \mathord{\left/ {\vphantom {2 {({1\textrm{ + }{e^{2x}}} )- 1}}} \right.} {({1\textrm{ + }{e^{2x}}} )- 1}}$] transfer function is applied to both hidden layers. The CER is set as the only output in the output layer and the linear function [that is, $t(x )= x$] is adopted as transfer function for the output layer.
An ANN is an adaptive system and it can change its ‘weights’ between different neurons and ‘biases’ for different neurons from the matched input and output dataset. After the ANN is trained, the CER can be directly derived from the input vector constructed from CALIOP independently without the input of MODIS anymore. This makes both day and night retrieval of CER possible with CALIOP observations only.
4. Results
4.1 CER estimated from CALIOP
As we mentioned in Sec. 3.2, an ANN is used to set up a bridge between CER and CALIOP measurements. Four-month coincident measurements during daytime from MODIS and CALIOP (Jan./Apr./Jul./Oct. 2016) are used to train and validate the ANN. The data samples are randomly divided into three datasets for training (70%), validation (15%) and test (15%), respectively. Bayesian regulation backpropagation method [35] is adopted in the training of this multi-layer ANN. When the weight and bias values of the ANN are learned after the training process, the performance of the ANN is estimated by comparing the retrieved CER (hereafter refer to as ${r_{e,c}}$) with collocated CER products from MODIS, which is shown in Fig. 4. The red solid line denotes the line y = x, the black points are the mean values of CER from CALIOP and the vertical black short lines are the statistic standard deviations.
Fig. 4. Two-dimensional histogram of the CERs retrieved from MODIS and CALIOP for the four-month matched data samples. The red line is the 1-1 line, black dots are the mean values and vertical shorter lines are the corresponding standard deviations.
The sample densities of scatterplots in Fig. 4 do not fully coincide with the 1:1 line, but the coefficient of determination of the linear fitting seems quite high (R2=0.572). The ${r_{e,c}}$ is apt to overestimate the CER in the small range of CER and tend to underestimate the CER in the big range of CER. This divergence may stem from the dampening effects of the ANN [36] or too few data samples for this range, or both. But as for $8\mu m < {r_{e,3.7}} < 24\mu m$, the biases between these two different CERs are less than 1.8 µm. And in the whole, the relative deviation of CERs is almost below 50% (most no more than 25%). For all the samples, the mean bias and the root-mean-square (RMS) of the relative deviation of CERs from two different methods are about 3.3% and 27.3%, respectively. The relative deviation of CERs seems acceptable comparing with the standard uncertainties of the effective radius retrieved from MODIS which is estimated as 27% or so according to Ref. [37].
4.2 Statistic results of CER from CALIOP and comparison with MODIS
According to the trained ANN, the CER can be derived from the CALIOP measurements during both day and night. With this retrieval algorithm, we obtained the CER for both day and night time in 2015 and the cloud samples are constraint to the uppermost opaque water clouds with $\delta < 0.35$. We first investigate the geographical distributions of averaged CER from this retrieval algorithm in 2015. Due to the sparse dataset caused by the narrow orbit of CALIOP, the CER of liquid water clouds over ocean between 60°S and 60°N is averaged into 2° latitude × 3° longitude grid. In order to make a comparison, the geographical distribution of average daytime CER in 2015 from MODIS level-3 dataset (MYD08) is also averaged into this grid resolution.
Figure 5 shows the geographic distributions of averaged CER in 2015 retrieved from MODIS during day time, CALIOP during day time, and CALIOP during night time. As we can see, the geographical distributions of CER from MODIS and CALIOP have the similar patterns and they agree with each other during day time. The global mean CER over ocean derived from MODIS during daytime and from CALIOP during daytime and nighttime are around 14.65 ± 1.46 µm, 14.20 ± 2.03 µm and 16.67 ± 2.23 µm, respectively. The absolute relative deviation of the daytime CERs from CALIOP and MODIS is less than 10% in most regions (about 75.0% percent of all the grids) and the proportion would be up to 92.7% if we set the threshold as 15%. Here, the relative deviation of these two averaged CERs is defined as ${{({{r_{e,c}} - {r_{e,3.7}}} )} \mathord{\left/ {\vphantom {{({{r_{e,c}} - {r_{e,3.7}}} )} {{r_{e,3.7}}}}} \right.} {{r_{e,3.7}}}} \times 100\%$. As for geographical distribution of CER during nighttime, the distribution pattern is similar to that during daytime. However, the global mean nighttime CER is approximately 2.47 µm larger than the daytime one. Even though the uncertainty of the calibration coefficients of CALIOP channels, especially the day-night differences [38,39], would contribute to the day-night difference of the CER, a larger CER during nighttime still seems reasonable according to some existing observations, for example, the diurnal variation of liquid water path (LWP) has a peak value around 02-05 am local time [40], the cloud top altitude is usually higher during nighttime than daytime [41], and also the finding regarding the diurnal variation of CER from surface site observations [42–44].
Fig. 5. Geographical distributions of the CER estimated from MODIS (a), CALIOP daytime measurements (b), and CALIOP nighttime measurements(c). The data used to generate this figure are both from year of 2015. (units: µm)
The monthly variations of CER show the similar trends between MODIS and CALIOP for different regions as shown in Fig. 6, particularly for daytime retrievals. Different color lines denote the monthly mean value of different CERs and the accompanying semitransparent belts with similar colors account for the relative standard deviations. The seasonal variation of CER over four classic subtropical stratocumulus regions (the Californian, Canarian, Namibian, and Peruvian) as shown in the blue boxes in Fig. 5 are taken as an example here [24,45]. The correlation coefficients of daytime CERs from CALIOP and MODIS calculated from the monthly averaged CERs are 0.89, 0.85, 0.93, and 0.68 for these four regions, respectively. The monthly mean daytime CERs are also similar between CALIOP and MODIS for all 12 months. The nighttime CER from CALIOP are larger than that of daytime but still demonstrate a similar seasonal variation trend. We have to clarify that the day and night differences are different from the diurnal cycle, which are not able to be provided by the CALIOP due to the orbits of its platform.
Fig. 6. Monthly variations of MODIS (solid line) and CALIOP daytime(dashed line) and nighttime(dot-dash line) CERs of year 2015 for four different regions: (a)Californian (10°N-30°N; 150°W-110°W), (b)Namibian (30°S-0°S; 25°W-15°E), (c)Canarian (10°N-30°N; 45°W-20°W) and (d) Peruvian (30°S-0°S; 120°W-70°W). These four regions are corresponding to the four regions shown in blue box of Fig. 5.
4.3 Discussions
As we mentioned in Sec. 4.2, the nighttime averaged CER is larger than the daytime one. Is it caused by the cloud physical process or just due to the artifacts of the ANN algorithm? A short discussion will be given here. First, we examined the day-night variations of the optical properties of the cloud layers, as shown in Table 1.
Table 1. The day-night variations of the optical and micro-physical properties of the cloud layers for four classic subtropical stratocumulus regions
The “Statistic” results in Table 1 is the statistical results from CALIOP retrievals and the “Calculated” results of ${R_\eta }$, ${S_{532}}$ and $\chi $ is estimated from the regression relationship in Sec. 3 using the statistical results of CERs. As we can see that the day-night variation is related to the variation of the optical properties. Thus, we can exclude the possibility of the artificial output of the ANN algorithm. The differences of the calibration coefficients between daytime and nighttime may also contribute to the CER differences. The calibration algorithm of CALIOP version 4 data products has greatly improved which makes the uncertainty of the calibration process greatly decrease [32,38,39]. The numerical sensitive analysis performed through disturbing optical properties of clouds (${\gamma ^{\prime}_{532}},{\gamma ^{\prime}_{1064}},\delta $) with systematic error of 3% demonstrates that the CER differences introduced by 3% systematic error would be less than 1 µm. The day-night differences of CER from CALIOP retrieval at least cannot be explained by the systematic error only. Thus, larger CER during nighttime at least is partially due to the physical process of clouds. Moreover, the LWP, cloud top height, as well as cloud fraction all present day-night variations [40,45]. Actually, nighttime temperature is generally lower than that during daytime, making the condensation growth of droplets in stratus clouds larger at night. Considering that the dominant cloud type is stratiform over marine areas, it is reasonable that the CER should be larger during nighttime than daytime. Correspondingly, the day-night differences of 1064 nm calibration using opaque water clouds [32] and lower lidar ratio during night [38] at least partially attribute to the day-night variations of the CERs as we cannot fully exclude the instrument–related reasons now [38]. While a more thorough analysis is beyond the scope of this current paper, further research could be rewarding.
The average cloud top extinction coefficient and CDNC of liquid water cloud can also be estimated from CALIOP according to Eq. (5) and Eq. (7). As the average extinction coefficient α is proportional to $r_e^{{1 \mathord{\left/ {\vphantom {1 3}} \right.} 3}}$, the relative uncertainty of α would be ${1 \mathord{\left/ {\vphantom {1 3}} \right.} 3}$ less than that of CER and better retrieval results of α can be obtained. As we focus on the micro-physical properties of liquid water cloud in this study, the extinction coefficient would not be discussed here. Similarly, the CDNC is proportional to $r_e^{ - {5 \mathord{\left/ {\vphantom {5 3}} \right.} 3}}$ and the uncertainty of CER would be propagating to the CDNC. In contrast, the CDNC retrieval from MODIS is related to $r_e^{ - {5 \mathord{\left/ {\vphantom {5 2}} \right.} 2}}$ which shows an even more sensitivity to the uncertainty of CER [37]. Thus, it is reasonable to expect more reliable CDNC results from CALIOP. Figure 7 shows a scatter plot between the CDNCs estimated from CALIOP only using the CER retrieved from the ANN (the y-axis) and the CDNCs estimated from Hu’method [21] where using CER from MODIS as an input (the x-axis). The notation (the red solid line, the black points and the short black vertical lines) is similar to that of Fig. 4. In all these calculations, the width of the size distribution parameter a in Eq. (7) is set as 12.3 which is consistent with the assumption of CDNC retrieval from MODIS [12,46].
Fig. 7. Two-dimensional histogram of the CDNCs estimated form CALIOP using the CER retrieved from the ANN and CER from MODIS (the Hu’s method). The data used are the four-month matched data samples. The red line is the 1-1 line, black dots are the mean values and vertical shorter lines are the corresponding standard deviations.
As we can see, the CDNC estimated from CALIOP data only according to the method proposed in this paper is in agreement with the CDNC from Hu’s method when the CDNC is smaller than 200 cm-3. The underestimation of CDNC using the proposed method for larger CDNC is due to the overestimation of CER when CER is small as shown in Fig. 4. The uncertainty of CDNC is indeed enlarged when comparing with that of CER. However, the coefficient of determination of the linear fitting (R2=0.71) demonstrates rather good linear relationship and the standard deviations between these two CDNCs are less than 40% overall even for CDNC large as 300 cm-3.
Figure 8 shows the geographical distributions of average CDNC in 2015 for both day and night estimated from CALIOP, along with the daytime CDNC average in 2015 estimated form MODIS (available from https://ir.vanderbilt.edu/handle/1803/8374) [46]. The statistical results of daytime CDNC from CALIOP show similar geographical patterns to that of MODIS. The CDNCs are much larger along coastal regions of the continental and relatively smaller in the open ocean regions, which is likely related to the anthropogenic aerosol pollution. The global mean CDNC derived from MODIS is greater than that derived from CALIOP during daytime, which is also consistent with the results from other researches [22,37,47]. The CDNC over east China retrieved from CALIOP is much underestimated when comparing with that of MODIS [47], but for the typical subtropical stratocumulus regions (the Californian, Canarian, Namibian, and Peruvian) the differences are much smaller for these two methods. The underlying reasons for these results have not been definitively ascertained, but they are likely partially linked to the feasibility of adiabatic assumptions for different cloud regimes. The nighttime CDNC estimated from CALIOP also shows the similar geographical distribution patterns with that of daytime and the mean CDNC during nighttime is slightly lower than daytime one.
Fig. 8. Geographical distributions of the CDNC derived from MODIS (a), CALIOP daytime measurements (b), and CALIOP nighttime measurements(c). The data used to generate this figure are both from year of 2015. (units: cm-3)
5. Conclusions
Inspired by the possibility to retrieve CER from different multi-scattering effects at dual-wavelength, the size sensitivity of dual-wavelength measurements from lidar is examined using coincident measurements from Aqua-MODIS and CALIOP. A nearly linear relationship between CER and CALIOP measured cloud optical properties is found which provides a possibility to retrieve CER from CALIOP dual-wavelength detections. An ANN based approach using the layer optical properties measured from CALIOP has been developed to estimate the CER of liquid water clouds. The feasibility of the ANN-based method for CER and CDNC estimation from CALIOP is evaluated by comparing with the CER from MODIS and CDNC retrieved using Hu’s method. The CER estimated from CALIOP in this paper has small biases comparing with that of MODIS for $8\mu m < {r_{e,3.7}} < 24\mu m$ and the overall relative standard deviation is about 27.3% which is similar to that of CER products from MODIS [37]. We have to admit that the uncertainties of CER products from MODIS may have an influence on the retrieval results of CALIOP and a more reliable CER reference would improve the CER retrieval behavior of CALIOP. The CDNC estimated from CALIOP shows larger deviations when comparing with results from Hu’s method and larger deviations may be found for single cases. However, the standard deviations between the CDNC estimated from CALIOP alone and that from Hu’s method are less than 40% overall which seems acceptable in a statistical sense.
The spatial and seasonal variations of CER derived from CALIOP daytime measurements show the similar geographical distributions to that from MODIS over ocean. The nighttime CER derived from CALIOP is larger than the daytime CER in most regions which seems related to the diurnal variations of air temperature and condensation growth of liquid water cloud droplets and more thorough analysis is rewarding to figure it out. CER retrievals allow independent assessments of CDNC from CALIOP and provide a global comprehensive dataset of CDNC during both daytime and nighttime. Over all, the CALIOP-based CDNC is lower than the MODIS based one during day time, but similar geographical distribution patterns are still found between them. The CDNC during nighttime is slightly smaller than the CDNC during daytime over all. As the corresponding aerosol variation is not performed in this study, the underlying reasons for the day-night variations will be examined in the future studies. Moreover, the ANN-based method for CER retrieval would also provide a new point of view for liquid water cloud study and more work should be done to validate whether it is also feasible for the ground based dual-wavelength polarized lidars.
Funding
National Key Research and Development Program of China (2016YFC1400900, 2016YFC0200700); National Natural Science Foundation of China (41775023, 91837204); Excellent Young Scientist Program of Zhejiang Provincial Natural Science Foundation of China (LR19D050001); Public Welfare Project of Zhejiang Province (2016C33004); Fundamental Research Funds for the Central Universities; State Key Laboratory of Modern Optical Instrumentation Innovation Program.
Acknowledgments
The authors would like to thank the science teams of MODIS and CALIOP for providing excellent and accessible data products used in this investigation. The data used for this study were got from MODIS Atmosphere website (https://modis-atmos.gsfc.nasa.gov/) and CALIOP website (https://www-calipso.larc.nasa.gov/). Special appreciation should be given to Professor Ralf Bennartz from Vanderbilt University who provides a MODIS derived CDNC dataset (https://ir.vanderbilt.edu/handle/1803/8374) to the science research community. We thank the two anonymous reviewers for their pertinent comments on this paper and their valuable advice to promote the quality of this paper.
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