As the most important regulators of Earth's climate system, clouds significantly affect the radiation budget, the hydrological cycle and the large-scale circulation on Earth (Hartmann et al., 1992; Stephens, 2005). However, because of incomplete knowledge of their underlying physical processes, clouds are still poorly represented in climate and weather models (Zhang et al., 2005) and are considered a major source of uncertainty in climate change predictions by GCMs (general circulation models; Cess et al., 1990).

Cloudiness is composed of a variety of cloud types that are governed by different types of atmospheric motion and are associated with different microphysical properties; moreover, different cloud types have distinct cloud radiative effects and precipitation forms (Ackerman et al., 1988; Betts and Boers, 1990; Hartmann et al., 1992). However, multilayered cloud systems, in which two or more cloud types are simultaneously present over the same location but at different levels in the atmosphere, have been frequently reported by surface and aircraft observations (Tian and Curry, 1989). The frequent co-occurrences of different cloud types in the atmosphere increase the complexity of present cloud climatology studies. For example, the effects of individual cloud types on the surface and atmospheric radiation budgets depend on whether other clouds are also present above or below them. In addition, cloud overlap variations can significantly change atmospheric radiative heating/cooling rates, atmospheric temperatures, hydrological processes, and daily variability (Chen and Cotton, 1987; Morcrette and Jakob, 2000; Liang and Wu, 2005). Therefore, to improve radiation calculations of climate prediction models, understand cloud physical processes, and evaluate the schemes for generating clouds in those models, it is necessary to know the amount and distribution of each cloud type; in particular, a detailed description of the co-occurrence of different cloud types and their statistical properties.

Until recently, many related studies on cloud types and cloud overlap, which are based on several fundamentally different types of passive observational data sets (typically the International Satellite Cloud Climatology Project (ISCCP) and surface observer reports), have focused on the geographical distributions and long-term variations of cloud types (e.g., Rossow and Schiffer, 1991; Rossow and Schiffer,1999; Hahn et al., 2001; Warren et al., 2007; Eastman et al., 2011, 2013), cloud radiative effects (Hartmann et al., 1992; Chen et al., 2000; Yu et al., 2004), cloud-property retrievals in multilayered clouds using multichannel measurements from passive sensors (Chang and Li, 2005a, b; Huang, 2006; Huang et al., 2005, 2006a; Minnis et al., 2007), and the statistics of cloud overlap based on surface weather reports and measurements from ground-based cloud radar (Warren et al., 1985; Hogan and Illingworth, 2000; Minnis et al., 2005). However, these studies have different limitations and uncertainties. First, passive detection methods and cloud-classification algorithms generally fail to detect multilayered clouds effectively. For example, the existence of overlapping cloud layers may obscure the upper-level clouds from the perspective of a ground-based weather reporter, and lower clouds may be hidden from the view of a passive satellite. As a result, surface observer reports and the ISCCP significantly underestimate high and low cloud frequencies, respectively, and introduce significant biases into the trend analysis of cloud cover, retrievals of cloud properties and evaluations of cloud radiative effects for the multilayered cloud systems since passive satellite retrieval techniques are based on the typical single-layered cloud assumption. Second, although the cloud properties can be retrieved relatively accurately from ground-based lidar or radar signals, only one-dimensional observations are possible, and the sites are sparsely distributed, almost nonexistent over the oceans. Third, most of these studies are limited to specific locations and time periods or specific multilayered (or single-layered) cloud systems. Systematic studies on the statistical co-occurrence of different cloud types on a global scale have still received far less attention.

Fortunately, the millimeter-wavelength cloud-profiling radar (CPR) on CloudSat (Stephens et al., 2002) and the cloud-aerosol lidar with orthogonal polarization (CALIOP) (Winker et al., 2007) on CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation; launched in late April 2006) provide an unprecedented opportunity for detailed studies on the three-dimensional structures of clouds on a global scale. Since mid-June 2006, CALIPSO and CloudSat data have been widely used to investigate the three-dimensional distributions and structures of hydrometeors and to improve the cloud-overlap assumption used in GCMs (e.g., Barker, 2008; Luo et al., 2009; Kato et al., 2010; Li et al., 2011). By using a radar-only cloud-classification product (i.e., the 2B-CLDCLASS data set from CloudSat), Sassen and Wang (2008) presented the geographical distributions and global average frequency of each cloud type. In this study, we investigate the co-occurrence frequencies of different cloud types and analyze their along-track horizontal scales and radiative effects using the latest cloud-classification and radiative-flux products based on the combined measurements of the two active sensors mentioned previously. Finally, we perform a preliminary evaluation of how well cloud-overlap assumptions characterize the overlap of two apparently separate cloud types. Although some statistical results reasonably agree with previous studies, new insights are achieved in this investigation. These new results will hopefully be useful for future GCM evaluations and improvements.

The study is organized as follows. The data set for the research is described in Sect. 2. Section 3 provides the zonal distributions and global statistics of the co-occurrence frequencies of cloud types and discusses their along-track horizontal scales and radiative effects. An evaluation of the performance of cloud-overlap assumptions based on the co-occurrence frequencies of cloud types is presented in Sect. 4.

In the following study, 4 years (2007–2010) of data from the latest release of the CloudSat 2B-CLDCLASS-LIDAR (version 1.0) product (i.e., radar–lidar cloud classification) and the 2B-FLXHR-LIDAR product are collected to analyze cloud types and discuss their co-occurrence frequencies, horizontal scales and radiative effects.

The ISCCP uses a combination of cloud-top pressure and cloud optical depth to classify clouds into cumulus, stratocumulus, stratus, altocumulus, altostratus, nimbostratus, cirrus, cirrostratus, and deep convective clouds. However, traditional surface observations identify clouds by using basic features (e.g., base height, horizontal and vertical dimensions, and precipitation types) of the major cloud types (World Meteorological Organization, 1956; Parker, 1988; Moran et al., 1997). Based on these basic cloud characteristics, Wang and Sassen (2001) classified cloud types into eight classes by combining the range capabilities of active sensors (radar and lidar) and the auxiliary measurements from the other passive sensors (e.g., infrared and microwave radiometers); they further indicated the overall agreement (approximately 70 %) between the results from their algorithm and the surface visual observations from the southern Great Plains (SGP) CART (Cloud and Radiation Testbed) site.

Based on the algorithm presented by Wang and Sassen (2001), the radar–lidar cloud classification identifies the cloud types using two steps. First, combined radar and lidar cloud-mask results are used to find a cloud cluster according to cloud persistence in the horizontal and vertical directions. By performing the cloud clustering analysis, a CloudSat granule may be divided into a number of cloud clusters, depending on the cloud systems present. Once a cloud cluster is found, the cloud height and phase, maximum effective radar reflectivity factor (Ze) and temperature, and the occurrence of precipitation are determined. Second, the cluster mean properties and spatial inhomogeneities, in terms of the cloud-top heights and maximum signals of the radar and lidar, are sent to a fuzzy classifier to classify the cluster into one cloud type with an assigned confidence level. To improve the classification flexibility, a combination of rule-based and fuzzy-logic-based classification is used in this algorithm. The cloud-phase determination is based on rules, and the cloud-type classification is mainly based on fuzzy logic (see Wang et al., 2013; Level 2 Combined Radar and Lidar Cloud Scenario Classification Product Process Description and Interface Control Document, version 1.0, 2013, available at http://www.cloudsat.cira.colostate.edu/dataSpecs.php?prodid=12&pvid=12). The cloud types provided by this product (version 1.0) include high clouds (High), altostratus (As), altocumulus (Ac), stratus (St), stratocumulus (Sc), cumulus (Cu), nimbostratus (Ns) and deep convective (Dc) clouds. The High cloud type includes cirrus, cirrocumulus and cirrostratus, and the Cu cloud type represents cumulus congestus and fair weather cumulus. Following the study of Sassen and Wang (2008), we also combine two cloud types (St and Sc) into St + Sc in the present study. By combining the unique complementary capabilities of the CPR of CloudSat and the space-based polarization lidar (CALIOP), some CPR weaknesses (e.g., high surface contamination in the lowest three to four vertical bins of the CPR and a lower sensitivity to optically thin clouds) are minimized in the latest radar–lidar cloud classification product; thus, the identification of High (cirrus or cirrostratus) and low cloud types (such as St, Sc and Cu) is significantly improved in the 2B-CLDCLASS-LIDAR product.

By using CloudSat microphysical retrievals, a combined CloudSat/CALIPSO cloud mask and lidar-based aerosol retrievals as inputs for a broadband, two-stream, plane-parallel, adding-and-doubling radiative transfer model, the 2B-FLXHR-LIDAR product provides calculated radiative fluxes and atmospheric heating rates at 240 m vertical increments (Henderson et al., 2013). Incorporating the radiative influence of optically thin and low clouds that were undetected by CloudSat significantly improved the agreement between the 2B-FLXHR-LIDAR calculations and observations from the Clouds and the Earth's Radiant Energy System (CERES) experiment. Henderson et al. (2013) showed that the global mean outgoing shortwave radiation (OSR) and outgoing longwave radiation (OLR) estimated from the collocated CERES observations and 2B-FLXHR-LIDAR calculations agree within 4 and 5 W m-2, respectively, with root-mean-square differences of 6 and 16 W m-2 on monthly / 5∘ scales. Because the passive sensors largely fail to resolve the cloud overlap in the vertical, the 2B-FLXHR-LIDAR product derived from these two active sensors is considered a vital data set for examining the radiative heating features in the atmosphere and for studying the variations in fluxes and heating rate caused by vertically overlapping clouds (L'Ecuyer et al., 2008; Haynes et al., 2013). In this investigation, we only provide the results of the net radiative effect of different multilayered cloud types at the TOA (top of the atmosphere) and at the surface during the daytime by using the 2B-FLXHR-LIDAR. However, it needs to further explain that the radiative effects of different cloud types only are the instantaneous effects at the overpass time of the satellites during the daytime in this study.

The following cloud parameters in the 2B-CLDCLASS-LIDAR product are used in this study: cloud layer (CL) and cloud-layer type (CLTY). In the 2B-FLXHR-LIDAR product, only the TOACRE (cloud radiative effect at the TOA) and BOACRE (cloud radiative effect at the surface) are used. Here, we consider one data profile as a multilayered (or single-layered) cloud profile when two or more cloud layers (or only one layer) are present within the vertical profile based on the parameter “cloud layer”. To map the regional variability in the studied variable, we group the global area into 2∘ × 2∘ grid boxes to collect a sufficient number of samples in each grid box. Following the definitions of cloud fraction and cloud amount proposed by Hagihara et al. (2010), the cloud-type fractions and amounts in a given grid box are defined as the number of particular cloud-type profiles divided by the number of total sample profiles and the total cloud profiles within this box, respectively. For example, the cloud fraction for multilayered clouds is the ratio of the number of multilayered cloud profiles to the number of total sample profiles in a given grid box. In this investigation, we only provide the annual average cloud properties of different overlapping cloud types with small seasonal variations. In addition, comparisons of the 4-year average cloud fractions for different cloud types between daytime and nighttime are provided in tables. Notably, the day–night comparisons of cloud fractions are only represented by the two overpass times of the satellites. The full diurnal cycle cannot be captured by CALIPSO and CloudSat. Sassen et al. (2009) showed that the observed day–night variations in cirrus observed by CALIPSO mostly reflect real cloud processes, even when the strong solar noise signature impacts the comparisons of cloud types between day and night, particularly for cirrus. For other cloud types, the uncertainty caused by the daylight noise for lidar may be smaller. Thus, the calculated annual mean cloud fractions for different cloud types in this investigation are reliable.

Based on the advantages of the two active sensors, we preliminarily evaluate how well the cloud-overlap assumptions can characterize the overlap of two apparently separate cloud types using the 2B-CLDCLASS-LIDAR cloud type product. The cloud overlap assumption has been widely used to describe the actual vertical distribution of clouds and the parameterization of the total cloud fraction in a given model grid box. Several basic cloud-overlap assumptions have been proposed, such as maximum, random, random-maximum and minimum overlaps (Hogan and Illingworth, 2000). The most common cloud-overlap scheme in current GCMs is called “random-maximum” overlap, which assumes that cloud layers separated by clear layers are randomly overlapped, while vertically continuous cloud layers have maximum overlap (Stephens et al., 2004). When the cloud fractions of the upper and lower layers are C1 and C2, the total cloud fractions of the two cloud layers based on the overlap assumptions are given by Crandom=C1+C2-C1×C2,Cmax=max(C1,C2),andCmin=min(1,C1+C2). In addition, if we know the actual overlap fraction Coverlap, then the observed total cloud fraction Creal can be written as Creal=C1+C2-Coverlap. However, Hogan and Illingworth (2000) proposed a simpler and more useful expression for the degree of cloud-layer overlap (exponential random overlap). In the expression, the mean observed cloud fraction of two cloud layers can be determined by the linear combination of the maximum and random overlap in terms of an “overlap parameter”a: Creal=a×Cmax+(1-a)×Crandom. Here, the overlap parameter a is considered a function of the layer separation and related to the vertical resolution and the horizontal domain size. a=0 is random overlap and a=1 is the maximum overlap. As Creal increasingly departs from Cmax (trending toward Cmin), a becomes negative, indicating a tendency for an even lower degree of overlap than that predicted by the random overlap assumption. In fact, previous studies already have shown that the cloud overlap parameter is sensitive to the spatial scale of the GCM's grid box. For example, Hogan and Illingworth (2000) found that a tends to increase with decreasing spatial and temporal resolution (that is, with an increasing vertical and horizontal scale of GCMs), but one interesting finding is that, with a temporal resolution of 3 h (that is, horizontal scale of 216 km in their study) and a level separation of between 6 and 8 km, a falls to -0.1. Mace et al. (2002) also found an increase in a with decreasing temporal resolution at all sites but the southern Great Plain (SGP) site while they found a decrease in a with decreasing spatial resolution. However, Naud et al. (2008) found a decrease in a with increasing spatial resolution by analyzing the cloud overlap at the SGP site for the winter months. These studies further implied that the degree of cloud overlap also may depend on the other factors, such as atmospheric vertical motion, convective stability and wind shear in different seasons besides vertical resolution and the horizontal domain size (Mace et al., 2002; Naud et al., 2008). For example, vertically continuous clouds tend to be more maximally overlapped in the presence of vertical motion in midlatitudes and decreased convective stability in the tropics. However, large wind shears were found to increase the randomness of the overlap, with the overlap becoming less than random in some cases (a<0). What changes from one high to low horizontal resolution is actually the increase of number of samples, which in turn may affect the averaged values of the vertical velocity, convective stability and wind shear, thus, further affecting the way cloudy layers overlap.

Based on several months of data from ICESat/GLAS observations, Wang and Dessler (2006) showed that overlap differences between the observed and random overlaps exist when describing the actual overlap of two separated cloud types (vertical separation > 0.5 km). However, the authors' work focused on the tropics and was limited to simple cloud classifications using space-based lidar. We expand the study by Wang and Dessler (2006) by employing a global-scale analysis and a more complete cloud classification; the overlap of two separate cloud types (here, vertical separation > 0.24 km at least) in each combination of cloud types in each grid box is determined. Moreover, we evaluate the performances of the random overlap assumption and calculate the overlap parameter a for each multilayered cloud type in each 2∘ × 2∘ grid box.

We first group each multilayered cloud system. For example, for the all High + Cu multilayered cloud systems in the same 2∘ × 2∘ grid box, we consider two layers and group all high clouds into the upper layer and all cumulus clouds into the lower layer, regardless of the vertical separation between these two types and their heights. Then, four possible values for the combined total cloud fraction of the two cloud types at different layers are calculated by assuming random overlap, maximum overlap, minimum overlap and actually observed overlap. Because random cloud overlap is considered a better characterization of cloud overlap behavior than minimum overlap and maximum overlap when two cloud layers separated by clear layers, we only provide the difference in the cloud fractions between random overlap and actually observed overlap. Finally, the overlap parameter a for each multilayer in each grid is calculated based on Eq. (3). Notably, because we do not group multilayered cloud types into multiple layers according to the vertical separation of two types, only one value for the overlap parameter a for each multilayered cloud system in each grid is obtained. a may be considered the mean value of all overlap parameters at different layer separations. Here, we define the relative difference (RD) between the random and actual overlap for one of the multilayered cloud types as RD=(Crandom-Creal)/Creal. In addition, the cumulative relative difference (CRD) between the random and actual overlap for all multilayered cloud types (here, 17 different combinations of different cloud types are considered) in each 2∘ × 2∘ grid box is given by CRD=∑i=117RDi×wii=1,2,3,…,17. Similar to the definition of CRD, we define the cumulative overlap parameter (COP) in each 2∘ × 2∘ grid box as COP=∑i=117ai×wii=1,2,3,…,17, where w is the weight coefficient for one multilayered cloud type in each 2∘ × 2∘ grid box as follows: wi=fi∑i=117fii=1,2,3,…,17. f is the cloud fraction of each multilayered cloud type in every grid box.

Figure 8a and b show the zonal distributions of the relative differences between the random and actual overlap for 10 of the main multilayered cloud types and the cumulative relative differences for all multilayered cloud types (gray line). The results show that differences exist, even though the random-cloud-overlap assumption is thought to better describe cloud-overlap behavior than other schemes when the cloud layers appear to be separate. The cloud fractions based on the random-overlap assumption are underestimated for High + St/Sc, As + St/Sc and Ac + St/Sc at all latitudes; these differences can exceed -5 %. The cloud fraction of the High-over-Ac system is overestimated at all latitudes. The peak values of the difference are mainly located in mid and high latitudes in both hemispheres and are of up to 5 %. For other types, the relative differences are smaller and change with latitude. In summary, the cumulative relative difference of all multilayered cloud types is small (gray lines), and most values are negative at all latitudes. In Fig. 8c and d, we further show the zonal distributions of the overlap parameter for 10 of the main multilayered cloud types and the cumulative overlap parameter of all multilayered cloud types. Clearly, the overlap parameters for High + St/Sc, As + St/Sc and Ac + St/Sc at all latitudes are negative, indicating a Creal departure from Cmax (trending toward Cmin) and a tendency for an even lower degree of overlap than predicted by the random overlap assumption. Thus, the linear combination of maximum and random overlap assumptions is problematic due to the negative overlap parameters in those regions, where the three multilayered cloud types mentioned above are dominant, particularly over the major Sc-dominated oceanic areas. However, the overlap parameters are positive for High + Ns and High + Ac. Thus, Creal has a value between Cmax and Crandom,and the exponential random overlap can predict the actual overlap of these two types very well. These results are intuitive, as cloud types are governed by different types of atmospheric motion and state. The formation of cumuliform clouds may be related to the strong ascent or convectively unstable atmosphere which result in clouds that increase in height more quickly, and increasing the degree of overlap with other cloud types. However, random or minimum overlap occurs preferentially in regions of subsidence or convective stability (favors stratiform cloud). Therefore, it is not difficult to understand why the zonal distributions of cloud overlap parameters are very different for similar cloud overlap systems (e.g., middle-over-low). For example, the overlap parameters of As + St/Sc and Ac + St/Sc over the Southern Ocean are obviously distinct from As + Cu and Ac + Cu. In summary, the cumulative overlap parameters of all multilayered cloud types (gray lines) are negative at nearly all latitudes. However, two points still require further interpretation. First, the cumulative overlap parameters in the tropics and in the Northern Hemisphere have small values (and possibly positive values); thus, random overlap or exponential random overlap is representative of the actual conditions. Second, in the Southern Hemisphere, the cumulative overlap parameters trend toward Cmin; thus, a better prediction using random overlap or exponential random overlap is difficult. This finding partially explains why the climate model errors in the TOA fluxes over the Southern Ocean are the largest (Trenberth and Fasullo, 2010). Based on the global results from this study, we also further support the findings of Naud et al. (2008) that factors such as dynamics could be connected to the way cloudy layers overlap. As a result, we suggest that a linear combination of minimum and random overlap assumptions may further improve the predictions of real cloud fractions for the multilayered cloud types in the Southern Hemisphere (e.g., As + St/Sc and Ac + St/Sc), particularly poleward of 40∘ S over the ocean. However, only three cloud types (e.g., low-level marine stratus, convective clouds and layered clouds) are diagnosed by the cloud scheme in current GCMs. To be useful for parameterization design, it is necessary for the overlap behavior we observe to be related to quantities predicted by a GCM. In view of the cloud types that are governed by different types of atmospheric motion and state, we thus consider environmental conditions related to cloud formation as a means to parameterize the overlap characteristics in numerical models. However, before that, statistical connection between multilayered cloud types and the environmental conditions should be established in the future studies by using global cloud-overlap and meteorological reanalysis data sets.

The global distributions and statistical results of the cumulative relative difference and the cumulative overlap parameter for all multilayered cloud types are shown in Fig. 9 and Tables 3 and 4, respectively. Figure 9a shows the cumulative relative difference, whereas Fig. 9b shows the cumulative overlap parameter. In Fig. 9a, we find that the cloud fractions based on the random overlap assumption are underestimated over the vast ocean, except over the west-central Pacific Ocean warm pool. Obvious overestimations occur over tropical and subtropical land masses, particularly where low multilayered cloud fractions are found, such as in equatorial central South America, southern and northern Africa, Australia and the Antarctic. In these regions, the High-over-Ac system is the dominant multilayered cloud type. This pattern indicates that land surface effects may favor an exponential random overlap. In Fig. 9b, the distributions of the cumulative overlap parameter are similar to the results of the cumulative relative difference. Negative overlap parameters also occur over the vast ocean, except over the west-central Pacific Ocean warm pool. The typical negative high-value centers correspond to the major Sc-dominated oceanic areas very well. The positive overlap parameters are mostly located over tropical and subtropical land masses and Antarctica. Globally, by using random overlap, the overlap percentages are overestimated by 24, 21.9, 30 and 133.3 % for High clouds over As, St/Sc clouds, Ns, and Ac over St/Sc clouds, respectively, over land during the daytime (Table 3). An overestimation also occurs for As over Cu and St/Sc clouds. However, the overlap of High clouds with Ac and Cu is underestimated by -32.6 and -25 % over land during the daytime, respectively. Regardless of vertical separation of two types, the absolute errors of cloud-type fractions (See Tables 3 and 4) seem small for the global mean, but we should recall the previous finding that a 4 % increase in low cloud cover would be sufficient to offset the warming effect of a doubling of CO2 (Randall et al., 1984); therefore, these bias errors in cloud cover possibly induce a substantial bias error in the regional radiation budget. The underestimations (or overestimations) of the cloud fraction by the random overlap assumption ultimately cause overestimations (or underestimations) of cloud radiative effects. Globally, the overestimations of the net cloud radiative effect are obvious for High + St/Sc and Ac + St/Sc (approximately 3.9 W m-2 at the surface, about 3.3 % of the mean cloud forcing), whereas the underestimations of the net cloud radiative effect are obvious for High + Ac and High + Cu (Table 3). Generally speaking, change in cloud forcing caused by these bias errors in cloud cover is about 11 W m-2 at the surface, about 10 % of the mean cloud radiative effect at the surface. Thus, if these bias errors in cloud cover were codified in GCMs, models could bias climate feedbacks resulting from increasing trace gasses or natural variability.

Although cloud types and their co-occurrence variations are the most significant components of the global climate system and cloud climatology studies, systematic and global studies on statistical properties of clouds have not received much attention. This study quantitatively evaluates the co-occurrence frequencies of different cloud types, analyzes their along-track horizontal scales and radiative effects by using the latest cloud classification (2B-CLDCLASS-LIDAR) and radiative flux products (2B-FLXHR-LIDAR) based on 4 years of combined measurements from CALIPSO and CloudSat. We also preliminarily evaluate cloud-overlap assumptions. Although some statistical results reasonably agree with previous research, new insights are also achieved in this paper.

The statistical results clearly show that High clouds, As, Ac and Cu tend to coexist with other cloud types. However, St/Sc, Ns and convective clouds are much more likely to exhibit individual features than other cloud types. The zonal variations in along-track horizontal scales are distinct for different multilayered cloud systems. On average over the globe, As + St/Sc has a maximum scale of 17.4 km and SD of 23.5 km, while Ac + Cu has a minimum scale of 2.8 km and SD of 3.1 km. By considering the weight of each multilayered cloud type, the global mean instantaneous net cloud radiative effects of all multilayered cloud systems during the daytime are approximately -41.3 and -50.2 W m-2, which account for 40.1 and 42.3 % of the global mean total net CREs at the TOA and at the surface, respectively. However, the net radiative effects of 10 multilayered cloud types in our study are -22.7 and -27.1 W m-2 (a radiative contribution of 22 %) at the TOA and at the surface, respectively. High + Ac and High + Sc/St (or Cu) cloud systems dominate the weighted global mean net CREs of multilayered cloud types because they are most frequent.

Active sensors allow us to preliminarily evaluate how well the overlap assumptions describe the actual overlap of two separate cloud types. In summary, the cloud fractions based on the random overlap assumption are mainly underestimated over the vast ocean, except over the west-central Pacific Ocean warm pool. Obvious overestimations occur over tropical and subtropical land masses, particularly in regions with low multilayered cloud fractions. These bias errors in cloud cover may induce a substantial bias error in the regional radiation budget. Globally, change in cloud forcing caused by these bias errors is about 11 W m-2 at the surface, and contributes about 10 % of the mean cloud radiative effect at the surface. Considering that negative overlap parameters occur over the vast ocean, particularly poleward of 40∘ S, we suggest that a linear combination of minimum and random overlap assumptions may further improve the predictions of actual cloud fractions for multilayered cloud types (e.g., As + St/Sc and Ac + St/Sc) over the Southern Ocean. In fact, negative overlap parameters indicate that fractions of cloud overlap are overestimated by random overlap assumption at mid and high latitudes of both hemispheres, and that a tendency for an even more minimal degree of overlap than that predicted by the random overlap assumption is exists. Due to passive sensors (such as ISCCP) usually fail to effectively detect the cloud overlap; the minimum overlap is what ISCCP or another passive sensor would observe. However, why do the active sensors in our results and in previous studies (Hogan and Illingworth, 2000; Mace et al., 2002) also tend to function similarly over those regions? One possible reason is that cloud features in one bigger grid box (here, 2∘ × 2∘) are associated with vertical wind shears (or other dynamical factors in those regions) that are sloped in space to become more grouped together, thus trending toward increasing cloud cover. However, a similar trend whether can be observed by active sensors on a smaller spatial scale (such as, 1∘ × 1∘), which still needs to be confirmed in future studies using this data set. Generally speaking, this study further verifies that factors such as dynamics related to cloud formation could be connected to the way cloudy layers overlap. Therefore, we may consider environmental conditions as a means to parameterize the overlap characteristics in order to be useful for parameterization design in numerical models. In addition, the seasonal variations of cloud overlap must also be studied, as one would expect if cloud systems are driven by processes related to convection during the warm season and synoptic-scale systems during winter (Mace et al., 2002).

Previous studies have quantitatively evaluated the global mean cloud fraction of each cloud type using various data sets (such as ISCCP). However, we identify new features that were not observed with the ISCCP D1 data set (Doutriaux-Boucher and Seze, 1998). For example, As and Ac prevail over the arid/semiarid land of the Northern Hemisphere (northwestern China and North America) and Southern Hemisphere (Australia and southern Africa), respectively. Although the representations and simulations of these mid-level clouds in global climate models are poor and under-predicted (Zhang et al., 2005), the balance of phases for these mixed-phase clouds (mid-level clouds) due to cloud-layer temperature or ice nuclei (IN) changes will certainly have a potentially large radiative impact in local regions (Sassen and Khvorostyanov, 2007). Thus, to quantify the feedback of an individual cloud type in these regions and document the local cloud climatology, related studies on mid-level clouds in these arid/semiarid regions should focus on the impacts of dust aerosols on radiative effects and “cold rain processes” (Huang et al., 2006b, c; Su et al., 2008; Wang et al., 2010).