Four years (2007–2010) of data from the CloudSat 2B-GEOPROF-LIDAR, ECMWF-AUX, and the daily 6 h ERA-Interim reanalysis are used to analyze the impacts of atmospheric states and dynamics on the cloud overlap over the TP (27–39^∘ N; 78–103^∘ E) region (Fig. 1a).

2.3 The overlap parameter and its dependence on the spatial scale

Previous studies have shown that the overlap parameter α and decorrelation length L are sensitive to the spatial scale of the general circulation models (GCMs) grid box (Hogan and Illingworth, 2000; Oreopoulos and Khairoutdinov, 2003; Oreopoulos and Norris, 2011; Pincus et al., 2005). For example, Hogan and Illingworth (2000) found that the cloud overlap parameter tends to increase with decreasing spatial and temporal resolutions (i.e., increasing vertical and horizontal grid scales) of GCMs.

Figure 2The dependence of α on the layer separation and its sensitivity to the spatial scale for (a) noncontiguous and (b) contiguous cloud pairs; the horizontal bars correspond to means ± 3 standard errors, which represent the upper and lower endpoints of the 99 % confidence interval. (c) The probability distribution functions (PDFs) of the along-track horizontal scales of the cloud system at a different height over the TP region. (d) The variations in cloud sample number and the cumulative percentages with cloud layer separations for both noncontiguous and contiguous clouds at a given spatial scale of 50 km. The cumulative percentages represent the proportions of cloud sample below the corresponding layer separation to all samples.

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To examine the dependence of the overlap parameter on the spatial scale, each CloudSat orbit over the TP region is divided into segments with different horizontal lengths including 25, 50, 100, and 200 km. Hereafter, this horizontal length is referred to as the effective spatial scale of the GCM's grid box. Figure 1b shows an example of cloud mask from the 2B-GEOPROF-LIDAR dataset over the TP region. This cloud mask includes eight, four, two, and one segments, which correspond to the horizontal resolution of 25, 50, 100, and 200 km, respectively. Given the threshold of 99 % for cloud fraction, the segment-average cloud cover profile of each segment is first derived. Here, it is important to emphasize that cloud fraction and cloud cover are different variables in our study. The Cloud fraction reports the fraction of lidar volumes in each radar vertical bin that contains hydrometeors and is used to identify a cloudy atmospheric bin based on the chosen threshold of 99 %. When averaging all cloud fraction profiles in the along-track direction for a given CloudSat data segment, we derive the segment-average cloud cover profile, which represents the percentage of clouds in a given spatial scale and certain height. Then, the vertical overlap between any two atmospheric layers in this profile is calculated if the cloud covers (C_i and C_j) of both layers exceed 0. Layers are analyzed in pairs and there is no “double-counting”. If cloud layer pairs have the same separation distance but different altitudes, they will be categorized as belonging to the same statistic group. Following Hogan and Illingworth (2000) and Di Giuseppe and Tompkins (2015), we consider the non-adjacent layers to be a contiguous cloud pair when all layers between them are classified as cloud layers. Otherwise, these layers are classified as a noncontiguous cloud pair (Hogan and Illingworth, 2000; Di Giuseppe and Tompkins, 2015).

Based on the definitions of different overlap assumptions and α in the introduction section, Fig. 1c and d show an example of the observed and calculated segment-average cloud cover profiles based on maximum and random assumptions, and corresponding overlap parameters of contiguous cloud pairs for the 25, 50, 100, and 200 km spatial scale in a given cloud mask sample (Fig. 1b). It is clear that the observed and calculated cloud covers and corresponding overlap parameters tend to increase as the spatial scale increases. In the meantime, the observed cloud covers tend to transform from the maximum to the random overlap assumption with increasing layer separations.

By collecting 4 years of cloud sample from the 2B-GEOPROF-LIDAR dataset, Fig. 2a and b further show the dependence of α on the layer separation and its sensitivity to the spatial scale for both noncontiguous and contiguous cloud layers. Many studies have used ground- and space-based radars to examine the validity of the random overlap assumption for vertically noncontiguous clouds (Hogan and Illingworth, 2000; Mace at al., 2002; Naud et al., 2008; Di Giuseppe and Tompkins, 2015). Figure 2a shows that the degree of cloud overlap of the noncontiguous clouds over the TP region is lower than the random overlap, especially when the layer separation is smaller than 2 km. Given the spatial scale of 50 km, almost all of the α values are negative and fall between −0.25 and −0.05. Thus, the total cloud cover would still slightly be underestimated for noncontiguous cloud pairs by using the random overlap assumption. Assuming a cloud layer separation of less than 9 km, α for noncontiguous cloud pairs increases as the spatial scale increases (e.g., from 25 to 200 km). For a contiguous cloud pair (Fig. 2b), α decreases from 0.95 to 0 with an increasing separation. In the meantime, a slight dependence of α on the spatial scale is also observed for contiguous cloud pairs when they are separated by a distance of about 1 to 4 km. This indicates that the maximum overlap is slightly more common for a larger horizontal domain, which is consistent with previous studies (Hogan and Illingworth, 2000; Oreopoulos and Khairoutdinov, 2003; Oreopoulos and Norris, 2011).

2.4 Selection of thresholds for cloud cover and spatial scale

Regarding the dependence of α on a spatial scale, Tompkins and Di Giuseppe (2015) theorized that some overcast or single cloud layers would be removed from the samples when the spatial scale is smaller than the cloud system scale, thus biasing α and its decorrelation length L. Given a spatial scale of 50 km, the ratio of the spatial scale to the cloud system scale decreases strongly from the equator to the poles because many of the frontal cloud systems of the middle and high latitudes are larger than the convective cloud systems over the tropics. Ultimately, the corresponding bias in α would increase with latitude. For these reasons, regional atmospheric models should account for the typical cloud system scale in their parameterization schemes when using a fixed horizontal resolution.

Figure 2c depicts the probability distribution functions (PDFs) of the horizontal scales of the along-track cloud systems at different heights over the TP region. Here, the horizontal scale of a cloud system at a given height along the CALIPSO/CloudSat track is determined by calculating the number of continuous cloud profiles (N) at a given height. Using a 1.1 km along-track resolution for the CPR measurements, the along-track scale (S) of a cloud system is S=N × 1.1 km (Zhang et al., 2014; Li et al., 2015). It is clear that the probability of a cloud system with a small-scale decreases with increasing height (Fig. 2c). The mean horizontal scale of 59.2 km for a cloud system at a height of 15 km is almost 12 times greater than that (i.e., 4.6 km) at a height of 2 km. For the TP region, we can see that the horizontal scales of cloud system below 10 km are smaller than the spatial scale of 50 km; thus, we apply the spatial scale of 50 km to perform the following analysis, although this scale would still result in significant errors in α at greater atmospheric heights (e.g., 15 km), where clouds have a larger horizontal scale.

Figure 3The monthly variations in the pentad-averaged (a) cloud overlap parameter, α, (c) conditional instability to moist convection, $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ (K km⁻¹), (e) wind shear, dV∕dz (m s⁻¹ km⁻¹), and (g) vertical velocity ω (hPa day⁻¹) at 500 hPa, for the contiguous cloud layers over the TP. The monthly variations in the pentad-averaged (b) α, (d) $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$, (f) dV∕dz, and (h) ω for the contiguous clouds for the layer separation of 2 km (red) and 3 km (black).

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In addition, to further reduce the sensitivity of α to the spatial scale caused by data truncation, we follow the study from Tompkins and Di Giuseppe (2015) and apply a simple data filter so that only atmospheric layers with segment-average cloud cover below a given threshold of 50 % are retained. As stated by Tompkins and Di Giuseppe (2015), data might still be truncated with this filter, but the sensitivity of the results to the spatial scale should largely be reduced. Here, we need to emphasize that the thresholds of 99 and 50 % used in our study correspond to the cloud fraction and cloud cover, respectively. After limiting the spatial scale (50 km) and upper limit of cloud cover (50 %), the number of available cloud layer pair samples is still at least 1 million, thus ensuring representative sampling. Figure 2d shows the variations in sample number and the cumulative percentage with cloud layer separation for both noncontiguous and contiguous clouds at a given spatial scale of 50 km. It shows that the cumulative proportion of cloud sample significantly increases with increasing layer separation. For the contiguous cloud, the cumulative percentage accounts for 90 % of all samples when layer separation is smaller than 4 km. Given the 1.1 km along-track resolution of the CPR measurements and a spatial scale of 50 km (that is, about 50 CloudSat profiles), each cloudy CloudSat profile has a cloud cover of about 2 % (Di Giuseppe and Tompkins, 2015).

Figure 3a shows the monthly variations in α for the contiguous cloud pairs based on pentad averages over the TP. In Fig. 3a, the maximum separation of contiguous cloud layers gradually increases from January (approximately 6 km) to August (beyond 8 km) and then gradually decreases, indicating that the cloud systems over the TP during summer are thicker than those clouds during other seasons due to frequent strong convective motions. When the cloud layer separation is less than 1 km, the overlap parameter α has little monthly variation and is always large (even beyond 0.7). However, the monthly variation in α becomes manifest when the layer separation is larger than 1 km. For a 2 km cloud separation, for example, α reaches its maximum of 0.45 in August and a minimum of 0.1 in February (see Fig. 3d). For a separation of 3 km, α is generally lower but has the similar monthly variation to those seen for a 2 km separation. The negative values of α in Fig. 3a show that even the random overlap assumption could underestimate the total cloud cover between two cloud layers with large separation during all seasons except summer. These cloud overlap features may be associated with the unique topographical forcing and corresponding thermodynamic and dynamic environment of the TP. In summer, the TP is usually considered an atmospheric heat source or “air pump” due to its higher surface temperature compared with surrounding regions at the same altitude (Wu et al., 2015). Additionally, humid and warm air intrudes from the South Asia monsoon into the lower atmosphere over the TP, which intensifies the atmospheric instability of moist convection when combined with the enhanced surface heating (Taniguchi and Koike, 2008). This process further promotes the transport of water vapor to high altitudes and favors the development of convective clouds. Indeed, satellite observations have indicated that cumulus prevails over the TP during the summer (Wang et al., 2014; Li and Zhang, 2016).

In view of the small horizontal scale of cumulus, a 50 km-spatial scale from CloudSat should not bias the α estimate too much in our study. However, previous studies have pointed out that precipitation may bias the cloud overlap statistics toward maximum overlap (Mace et al., 2009; Di Giuseppe and Tompkins, 2015), which is not accounted for in the present study. If we exclude the samples with precipitation from the analysis, the overlap parameter α would become smaller. The feature may be even more obvious during summer due to more frequent precipitation over the TP during this season (Yan et al., 2016). The seasonal variation in α is also found at different ground sites (Mace and Benson-Troth, 2002; Naud et al., 2008). For example, Oreopoulos and Norris (2011) indicated that cloud overlap tends to be more random in the winter and mostly maximum during the summer. In fact, these overlap properties are associated with the cloud system scale, which is dominated by the large-scale dynamical situation (Tompkins and Di Giuseppe, 2015).

Figure 4The zonal variations in the (a) α, (c) $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ (K km⁻¹), (e) dV∕dz (m s⁻¹ km⁻¹), and (g) ω (hPa day⁻¹) for the contiguous cloud layers over the TP. The zonal variations in the (b) α, (d) $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$, (f) dV∕dz, and (h) ω for the contiguous cloud layers for the layer separation of 2 km (red) and 3 km (black).

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Figure 3b and c show the monthly variations in pentad-averaged conditional instability of moist convection ($\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$) and wind shear (dV∕dz) for the contiguous cloud pairs over the TP, respectively. Both $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ and dV∕dz exhibit clear monthly variations for all cloud-layer separations. The atmospheric stability and wind shear gradually decrease from January to August and then steadily increase (see Fig. 3c, d, e, and f). From Fig. 3c, we can see that the adjacent atmospheric layers during May to September tend to be more unstable and have weak wind shear. These atmospheric states favor the development of clouds and result in maximum overlap between cloud layers. During other months (e.g., December), clouds also tend to follow the maximum overlap more although adjacent atmospheric layers are stable with large $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ and dV∕dz. It might be the case that vertical velocities are large because of extratropical cyclones or other sources of baroclinic instability. When the layer separation increases, atmospheric layers become more stable and then favor random overlap, especially during the summer season. These results verify that a more unstable atmosphere tends to favor a maximum overlap of cloud layers over a random one, as shown in previous studies (Mace and Benson-Troth, 2002; Naud et al., 2008). Note that Fig. 3d and f might reveal an inconsistency between the wind shear and atmospheric stability. For example, we can see that the wind shear for a 2 km layer distance is greater than that for a 3 km distance, but the atmosphere is also more unstable. This inconsistency is probably because two cloud layers with the same separation but occurring at different altitudes are sorted into the same statistical group. Or it is also possible that other large-scale forcings might influence the overlap. In addition, we find the monthly variations in pentad-averaged vertical velocity (ω) at 500 hPa (see Fig. 3g and h) are also consistent with the monthly cycle of α. It means that vigorous ascent tends to favor maximum overlap. This result agrees well with the previous studies (Naud et al., 2008).

Figure 5The sensitivities of median overlap parameter α to the (a) wind shear, (b) instability, and (c) vertical velocity at 500 hPa at a given upper limit of cloud cover (50 %) and spatial scale (50 km) for the contiguous cloud layers. The horizontal bars correspond to means ± 3 standard errors, which represent the upper and lower endpoints of the 99 % confidence interval.

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Figure 4 shows the zonal variations in α, $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$, dV∕dz, and ω over the TP. Figure 4a and b indicate that α is larger in the south part of the TP and smaller in the north. This is mainly because atmospheric instability in the southern part of the TP enhances convective activity (Fujinami and Yasunari, 2001). Due to the weakening of the monsoon and the blocking by topography, less water vapor may reach the northern part of the TP, and thus fewer clouds form there (You et al., 2014). Compared with the southern TP, the stability and wind shear are both larger over the northern part, especially for those cloud layers with large separation (e.g., > 2 km). These meteorological conditions will result in more frequent negative α, indicating that the random overlap assumption used in models would underestimate the total cloud cover and thus bias the surface radiation over these regions (see Fig. 4a). The most significant warming occurring over the northern part of the TP has been attributed to pronounced stratospheric ozone depletion (e.g., Guo and Wang, 2012). However, a more recent study indicates that the accelerated warming trend over the Tibetan Plateau may be due to the rapid cloud cover increases at nighttime over the northern Tibetan Plateau and the sunshine duration increase in the daytime over the southern Tibetan Plateau (Duan and Xiao, 2015). Therefore, an accurate representation of cloud overlap and its relations to atmospheric thermodynamic and dynamic conditions in models are critically important to the understanding of rapid warming over the TP. Although it is still difficult for models to capture the cloud overlap properties, especially for those cloud layers with large separation over the north TP, our results confirm that the α is well related to wind shear and instability. However, the zonal variation in α is inconsistent with the variation in vertical velocity (see Fig. 4g and h).

To facilitate the parameterization of α for cases of contiguous clouds, we further investigate the sensitivity of α to the different meteorological conditions. Here, each meteorological factor over the TP region is grouped into one of four bins as follows. The four bins for $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ are $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ > 5 K km⁻¹, 2.5 < $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ < 5 K km⁻¹, 0 < $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ < 2.5 K km⁻¹, $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$ < 0 K km⁻¹. For wind shear, the four bins are dV∕dz < 0.5 m s⁻¹ km⁻¹, 0.5 < $\mathrm{d}V/\mathrm{d}z<\mathrm{2}$ m s⁻¹ km⁻¹, 2 < dV∕dz < 3.5 m s⁻¹ km⁻¹, and dV∕dz > 3.5 m s⁻¹ km⁻¹. For vertical velocity, the four bins are ω < −40 hPa day⁻¹, −40 < ω < 0 hPa day⁻¹, 0 < ω < 40 hPa day⁻¹, and ω > 40 hPa day⁻¹. These groupings ensure that a statistically representative number of samples fall within each bin (i.e., at least 1 000 000 samples per bin). In addition, Li et al. (2015) indicated that the overlap properties between different cloud types are also important for the Earth's climate system. Although this study does not include the information on cloud type, the dependence of α on meteorological parameters found in our analysis actually demonstrates the effects of cloud types on the α because different combinations of cloud type with the same layer separation possibly occur in distinct wind shear and stability conditions.

Table 1Parameterizations of decorrelation scale length L from the exponential fit as a function of atmospheric stability $\partial {\mathit{\theta }}_{\mathrm{es}}/\partial z$, wind shear dV∕dz or latitude Φ.

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Figure 6The monthly differences in total cloud cover (unitless) between calculation and observation for different schemes (see Table 1) and their dependence on the layer separation.

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Figure 5 illustrates the sensitivity of α to wind shear, instability, and vertical velocity at a given upper limit of cloud cover (50 %) and spatial scale (50 km) for the contiguous clouds. Since the cloud samples with layer separation below 3.5 km account for 90 % of all samples for contiguous clouds, we only present the results for layer distances smaller than 3.5 km. Naud et al. (2008) tested the sensitivity of α to wind shear at three sites and found that wind shear slightly affects α when the layer distance is larger than 2 km. In a recent study, Di Giuseppe and Tompkins (2015) demonstrated the important effect of wind shear on the global cloud overlap by using a combination of the CloudSat-CALIPSO cloud data and the ECMWF reanalysis dataset. Our results along with previous studies suggest that the cloud overlap strongly depends on atmospheric conditions, but their relationship displays some variability, in particular spatially and seasonally. The effect of the atmospheric stability on cloud overlap may be more important over convective regions (e.g., the intertropical convergence zone and the TP during the summer season), while the effect of wind shear may be dominant over the midlatitudes. Besides the wind shear and instability, some studies also tested the sensitivity of the overlap parameter to the large-scale vertical velocity. For example, Naud et al. (2008) indicated that vertical velocities in the tropics are not captured in the reanalysis dataset when convection occurs; thus, they only discussed the impact of vertical velocity on the cloud overlap parameter over the midlatitudes and found that vigorous ascent tends to favor maximum overlap. Fig. 5c shows that vertical velocity at 500 hPa has some effect on the cloud overlap parameter. However, by combining the effects of wind shear, instability, and vertical velocity into parameterization of decorrelation length scale L, we find that this scheme is not superior to a scheme which only includes the wind shear and instability.

Here, we derive the decorrelation length scale L values (km) from the least squares exponential fit to the original α curve at given wind shear and instability bin. Then, we further parameterize L as a function of wind shear or both wind shear and atmospheric instability based on a (multiple) linear regression. The regression formula of L can be written as

Here, L_α, L_α1, b1, b2, and c1 are the fitting parameters. Table 1 lists several parameterization schemes for the decorrelation length scale L. The scheme with wind shear from Di Giuseppe and Tompkins (2015) using the global CloudSat-CALIPSO cloud data and ECMWF reanalysis dataset is shown for comparison. Di Giuseppe and Tompkins (2015) discussed the uncertainties from fitting methods and the calculation of wind shear. Related to the observational orbit, the impact of cross-track wind shear is neglected in our study, which would exclude many large wind shears associated with jet structures (Di Giuseppe and Tompkins, 2015). The parameterization scheme of Shonk et al. (2010) is also shown in Table 1, which is an empirical linear relationship between L and latitude based on CloudSat and CALIPSO data. Our parameterization schemes in terms of wind shear or both wind shear and instability are given in Table 1. Note that the R-squared values (R²) for our wind shear and wind-shear–instability schemes are 0.88 and 0.96, respectively.

Figure 7The zonal differences in total cloud cover (unitless) between calculation and observation for different schemes (see Table 1) and their dependence on the layer separation.

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After deriving the regression formula of decorrelation length scale L, we reapply it to all contiguous cloud samples and retrieve the L and corresponding α based on the formula $\mathit{\alpha }=e^{-D/L}$ and dynamical conditions. Finally, the retrieved overlap parameter α is used to calculate the total cloud cover between any two cloud layers by using Eq. (1) and definitions of random and maximum overlap assumptions. Figure 6 presents the monthly difference between calculated and observed cloud covers using various overlap parameterization schemes. It is seen that the maximum and random overlap assumptions result in large cloud cover biases, especially for layer separations greater than 1 km for maximum overlap and less than 2 km for random overlap where the bias exceeds 5 %. Compared with random and maximum assumptions, the differences between total cloud cover caused by other schemes are small and range from −3 to 3 %. In addition, the wind shear scheme and the wind-shear–instability scheme from the present study overall show less biases than other schemes. However, several points should be further noted. First, the wind shear scheme from Di Giuseppe and Tompkins (2015) significantly underestimates the cloud cover for layer separations above 1 km (e.g., by up to 3 %). This large bias may be because it is based on the global CloudSat-CALIPSO measurements and ECMWF reanalysis dataset for a short period (January–July 2008); as such, some obvious regional or seasonal cloud overlap properties are easily obscured by global averaging. Furthermore, the role of atmospheric stability is not considered in this scheme. However, the scheme from Di Giuseppe and Tompkins (2015) shows little bias for layer separations below 1 km. This is because this scheme retrieves much larger L and overlap parameter values than other schemes. An interesting finding is that the latitude scheme from Shonk et al. (2010) leads to a bias comparable to new schemes from this study. The bias is even smaller for the latitude scheme when the layer separation is below 1 km. In fact, Fig. 5 has demonstrated that the sensitivity of α to wind shear and instability is rather weak when cloud layers are very close. Our wind-shear–instability scheme further combines the impact of atmospheric instability and has a relatively lower bias at large layer separations with higher R-squared values (R²=0.96).

Figure 7 shows the zonal difference between calculated and observed cloud covers for the aforementioned schemes. The differences between cloud cover caused by different overlap schemes are obvious. Similar to Fig. 6, the maximum and random overlap assumptions still result in the most prominent cloud cover biases (exceeding ±5 %) at most of the layer separations. Compared with our wind shear scheme and wind-shear–instability schemes, the scheme from Di Giuseppe and Tompkins (2015) and latitude scheme from Shonk et al. (2010) cause a clear underestimation of total cloud cover when cloud layer separations exceed 1 km, especially for scheme from Di Giuseppe and Tompkins (2015) (bias reaching −3 %). Only if cloud layer separations are smaller than 1 km, do these two schemes produce a better cloud cover simulation than our schemes. In summary, these results indicate that a new parameterization (that is, our wind-shear–instability scheme) of decorrelation length scale L, which includes the effects of both wind shear and atmospheric stability on cloud overlap, may improve the simulation of total cloud cover over the TP.

The CloudSat datasets are available from the CloudSat website: (http://www.cloudsat.cira.colostate.edu/order-data, CloudSat dataset, 2018). The ERA-Interim reanalysis daily 6 h products are downloaded from the ERA-Interim website: http://www.ecmwf.int/en/research/climate-reanalysis/era-interim (ERA-Interim, 2018).

The authors declare that they have no conflict of interest.