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Before evaluating the models' simulations, we analyze the basic distribution features of GOCCP cloud (Fig. 1). The annual-mean TCC covers about 67% of the Earth's surface in GOCCP, slightly larger than the 64% given by (Cesana and Chepfer, 2012). The GOCCP TCC is also comparable with that observed by other spaceborne sensors (Stubenrauch et al., 2013). In addition, the spatial distributions are consistent between different observational platforms. Higher TCC in GOCCP is mainly located in the mid-latitude storm tracks and the ITCZ, with a peak at around 60#cod#x000b0; in the Southern Hemisphere (SH) from the zonal-mean perspective. Lower TCC mainly occurs over the subsidence region of the Hadley cell, especially the deserts over subtropical lands (Fig. 1a). HCC (Fig. 1b) contributes greatly to higher TCC along the ITCZ, where three highest-HCC regions exist. Consistent with the ITCZ, the maximum of zonal-mean HCC occurs a little north of the Equator. LCC is generally composed of optically-thick stratocumulus cloud over the oceans (Fig. 1d). Besides the above-mentioned mid-latitude storm tracks, subtropical stratocumulus decks can also be found anchored to the west coasts of continents, playing a crucial role in the surface radiation budget (Wood, 2012). Among the three types of cloud, MCC is the lowest (Fig. 1c), which has a similar distribution to HCC in the tropics and with LCC over the mid-latitude oceans, indicating that MCC may be seen as a downward (upward) extension of the HCC (LCC) in these regions.
Figure 2. BCC_AGCM2.1 (left) and BCC_AGCM2.2 (right) simulated (a, b) TCC, (c, d) HCC, (e, f) MCC, and (g, h) LCC biases as compared to GOCCP (units: %).
The biases of total and the three types of cloud cover between GOCCP and those simulated by BCC_AGCM2.1 and BCC_AGCM2.2 are shown in Fig. 2 and Table 1. Both BCC_AGCM2.1 and BCC_AGCM2.2 underestimate the global-mean TCC, with biases of about -11.8% and -19.0% for BCC_AGCM2.1 and BCC_AGCM2.2, respectively (Figs. 2a and b; also see Table 1), which is a common bias in climate models when compared to ISCCP observations (Zhang et al., 2005; Probst et al., 2012), and still exists in CMIP5 models compared with GOCCP data (Cesana and Chepfer, 2012). Underestimations also exist for HCC, MCC and LCC, except the HCC in BCC_AGCM2.1 (Figs. 2c-h). Further examination of the bias distribution in BCC_AGCM2.1 indicates two significant features. Firstly, HCC is significantly overestimated over the tropics, especially over equatorial eastern Africa to the tropical western Indian Ocean, and on both sides of the ITCZ in the central and eastern Pacific. Meanwhile, HCC is underestimated over western equatorial Africa and the Amazon basin where higher HCC can be observed (Figs. 2c and d; also see Fig. 1b), which is similar to other models such as NCAR CAM (Lin and Zhang, 2004; Kay et al., 2012) and ECHAM (Nam and Quaas, 2012). Clearly, the overestimation (underestimation) of HCC primarily arises from excessive (deficient) transport of the convective mass flux over tropical deep convective regions, which is closely associated with the performance of the convective scheme in the BCC_AGCM models. Secondly, LCC is generally overestimated over extra-tropical lands but underestimated over most of the oceans. The largest negative biases are associated with subtropical marine stratocumulus clouds (Figs. 2g and h), which mainly result from the large-scale subsidence in subtropical oceans and coastal-upwelling-induced cold SST, and controlled by planetary boundary layer (PBL) feedbacks between radiative driving, turbulence, surface fluxes, latent heat release and entrainment (Wood, 2012). Typically, oceanic stratocumulus clouds are not well represented in current climate models; they are frequently severely underestimated and the PBL depth is too shallow (Bony and Dufresne, 2005; Hannay et al., 2009). In addition, it should be noted that compensation between HCC and LCC may reduce the TCC bias, especially in the tropics, in spite of the unreasonable vertical structure (Zhang et al., 2005). In addition, we can see that the biases are larger over oceans than over land for TCC and LCC, but the MCC biases are smaller over oceans than over land in both models (Table 1).
Figure 3. Latitude-altitude cross section of annual cloud cover observed by (a) CALIPSO and simulated by (b) BCC_AGCM2.1 and (c) BCC_AGCM2.2 (units: %). Dashed lines denote boundaries of ISCCP cloud types at 3.36 and 6.72 km, respectively.
A significant systematic decrease in global-mean cloud for all cloud types can be found in BCC_AGCM2.2 as compared to BCC_AGCM2.1, and the maximum reduction is in HCC. This feature is mainly due to the increase in horizontal resolution from BCC_AGCM2.1 to BCC_AGCM2.2. HCC and MCC decrease almost globally, and the decrease in HCC is especially remarkable over the tropics where a reduction by over 15% can be found. In contrast, LCC moderately increases in the low latitudes and obviously decreases in the middle to higher latitudes (not shown). Further analysis reveals that the simulated zonal-mean air temperature in BCC_AGCM2.2 is generally higher in the troposphere than that in BCC_AGCM2.1 (not shown). Particularly in the upper troposphere, the warming can reach over 1 K, with a maximum over the tropics. Such a change in temperature tends to depress convection, leading to less convective mass flux transported to the upper troposphere and thus less HCC (Figs. 2c and d), and also a small increase of LCC between 30#cod#x000b0;N and 30#cod#x000b0;S. These responses of clouds to the increase in horizontal resolution have also been reported for other models (e.g., Hack et al., 2006; Roeckner et al., 2006). This implies that an increase in horizontal resolution only is not enough to improve simulations of cloud cover, indicating that refining both the horizontal and vertical resolution is needed for improvement (Roeckner et al., 2006).
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In the previous section, CVS was investigated by dividing clouds into three levels in terms of the cloud-top height. In this section, CVS is analyzed in more detail based on the finer-stratified GOCCP clouds. First, we examine the zonal mean of cloud cover as a function of latitude and altitude from the data presented in Fig. 3. We can see that three obvious high-value areas exist for GOCCP HCC, with the maximum at 12-15 km in the tropics and the other two areas located at lower altitudes of the mid-latitudes. Below 3 km, strong marine stratocumulus can be found over southern oceans and northern high latitudes. These features are also evident in horizontal HCC and LCC (Figs. 1b and d). Both BCC_AGCM versions can successfully capture an overall structure of zonal-mean cloud cover. However, large biases are characterized by an overestimation of high cloud, with maximum biases at 7-12 km in the mid-high latitudes and above 10 km in the tropics, and an underestimation of low cloud around 1.5 km with a maximum over southern oceans centered at 45#cod#x000b0;S (not shown). In BCC_AGCM2.2, the high-cloud bias decreases remarkably due to the great decrease in HCC in response to the improvement of horizontal resolution. A slight increase in cloud cover also can be found below 2 km between 60#cod#x000b0;N and 60#cod#x000b0;S, which provides further evidence for the above results for HCC, MCC and LCC.
Figure 3 depicts a zonal-mean cloud vertical profile and limited information is provided for the spatial variability of CVS. An EOF analysis or principal component analysis (PCA) was employed to extract the major modes along the vertical dimension. Then, the 3D cloud cover was decomposed into vertical and horizontal components by treating the horizontal distribution as time sampling in ordinary EOF analysis. Let Xmn be the cloud cover matrix with m vertical levels (m=40 in this study) and n horizontal grid points. Then Xmn can be decomposed as follows:
Xmn= VmmTmn, (2)
where Vmm denotes the eigenvector matrix which contains m eigenvectors at most, and Tmn represents the time coefficient matrix. It should be noted that Tmn does not mean the time coefficients in the traditional sense, but the horizontal loading distribution of vertical cloud cover modes.
Figure 4 shows the first three leading modes of vertical cloud cover, and it can be seen that the accumulated explained variances (EV) are 80.3%, 85.8% and 84.9% for GOCCP, BCC_AGCM2.1 and BCC_AGCM2.2, respectively. All the modes are significant at the 95% confidence level, through which the basic characteristics of annual cloud cover can be interpreted.
Figure 4. First three leading EOF modes of cloud cover for CALIPSO (solid line), BCC_AGCM2.1 (dashed line) and BCC_AGCM2.2 (dotted line). Dashed lines denote boundaries of ISCCP cloud types at 3.36 and 6.72 km, respectively.
Figure 5. Time coefficients of the first (upper row), second (middle row) and third (bottom row) EOFs for CALIPSO (left column), BCC_AGCM2.1 (central column) and BCC_AGCM2.2 (right column).
The first mode (EOF1) accounts for 42.1%, 53.3% and 51.7% of the total EV for GOCCP, BCC_AGCM2.1 and BCC_AGCM2.2, respectively (Fig. 4a). Both BCC_AGCM versions simulate EOF1 quite well, although their EVs are about 10% larger. It can be clearly seen that vertical cloud cover changes with an opposite sign above and below about 10 km, which means more (less) cloud cover above 10 km and less (more) cloud cover below 10 km. Combined with the spatial distribution of time coefficient (Figs. 5a-c), this mode indicates a significant discrimination of cloud top height between the tropics and the mid-latitudes (Kokhanovsky et al., 2011). In the tropics, EOF1 corresponds to high-thin cirrus detrained from deep convection, while in the mid-latitudes low and middle clouds prevail. In spite of the great consistency of eigenvectors between GOCCP and the two versions of BCC_AGCM, the horizontal loading of the vertical mode in the BCC_AGCMs is generally overestimated in the tropics, except for central Africa and the Amazon basin, indicating weaker deep convection in these regions.
The second mode (EOF2) shows a sign-consistent variation of eigenvector above 3 km, but with an opposite sign near the surface in GOCCP (Fig. 4b). However, in the BCC_AGCMs, the simulated eigenvectors have significant deficiencies. Firstly, the peak near 7 km is simulated about 2 km lower and weaker. Secondly, the models cannot reproduce the opposite-sign variation between the low and middle-high clouds, failing to capture the PBL cloud feature around 1-2 km. In addition, the BCC_AGCMs imitate an abnormal peak at around 18 km. The simulated EVs are 20.7% and 22.0% for BCC_AGCM2.1 and BCC_AGCM2.2 respectively, about 5% less than GOCCP. It is noteworthy that horizontal loading distributions are simulated somewhat reasonably (Figs. 5d-f), although there are large deficiencies in eigenvectors.
The third mode (EOF3) reflects the GOCCP eigenvector having a primary positive peak at around 10 km and a secondary positive peak below 3 km (Fig. 4c). On the contrary, two negative eigenvector peaks occur at around 16 km and 3 km. EOF3 indicates the coexistence of high and mid-low clouds in the main deep convective regions over the tropics and a 10-km-height high-cloud belt at around 45#cod#x000b0; latitude (Fig. 5g). The BCC_AGCMs simulate comparable EVs to GOCCP. However, the positive high-cloud peak is simulated more strongly, while the low cloud peak cannot be captured. The peak at around 16 km is also simulated at a higher altitude, and weakly by the BCC_AGCMs.
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Cloud radiative forcing (CRF) is commonly used to quantify the impact of clouds on the Earth's radiation budget at both the TOA and the surface (e.g., Harrison et al., 1990). However, CRF varies largely with location. Meanwhile, different heights generally correspond to different cloud types with distinct radiative properties (Chen et al., 2000b). It is more intuitive to introduce the relative SW cloud radiative forcing (RSCRF) to better represent the effect of CVS on surface SW radiation (Liu et al., 2011). RSCRF excludes the radiative effects of other factors such as surface albedo and seasonally- and geographically-varying incoming SW radiation. RSCRF is a measurement of a cloud's extinction (meaning absorption and backscattering of SW radiation by clouds) to incident SW irradiance at the surface, which may be defined as follows:
RSCRF = (Sdn,all−Sdn,clr)/Sdn,clr, (3)
where Sdn,all and Sdn,clr denote the all-sky and clear-sky surface downwelling SW radiation fluxes respectively, with positive values being indicative of downward fluxes.
Similarly, the relative longwave cloud radiative forcing (RLCRF) can be defined to illustrate the relative effects of clouds on TOA outgoing LW radiation, which is given as follows:
RLCRF = (Lup,all−Lup,clr)/Lup,clr, (4)
where Lup,all and Lup,clr denote the all-sky and clear-sky upwelling LW radiation fluxes at the TOA respectively, with positive values being indicative of upward fluxes.
Figure 6 presents the RSCRF and RLCRF calculated from the CERES observation. Clearly, clouds always exert a negative RSCRF at the surface and a negative RLCRF at the TOA. Maximum RSCRF is situated at the extra-tropical oceans, especially in the SH, generally exceeding 40% due to the large amount and optically-thick properties of low stratocumulus. On the other hand, minimum RSCRF mainly occurs in the subtropical subsidence regions, Greenland and the Antarctic (Fig. 6a). For RLCRF (Fig. 6b), the maximum is located in the ITCZ, indicating the important effect of high clouds on outgoing LW radiation. Overall, both BCC_AGCM versions tend to overestimate the global-mean RSCRF, by 5.5% and 3.9% for BCC_AGCM2.1 and BCC_AGCM2.2, respectively (Figs. 7a and b). That is, the BCC_AGCMs have stronger SW extinction ability, although they have less cloud in most cases (Fig. 2). This overestimation of RSCRF is also presented in the geographical distribution. Particularly in the high latitudes of the Northern Hemisphere, RSCRF is significantly overestimated, by about 20% (Figs. 7a and b). In addition, an apparent underestimation of RSCRF can be seen clearly in East Asia, particularly in BCC_AGCM2.2, corresponding to the significant cloud decrease. CRF simulation bias in East Asia commonly exists in climate models, due mainly to our limited understanding of the distinctive monsoon climate and its poor representation in climate models (Yu et al., 2001; Li et al., 2009). The bias of RLCRF is also overestimated by the BCC_AGCMs, but is much smaller than RSCRF (Figs. 7c and d). The RLCRF overestimation is about 1.3% and 0.8% for BCC_AGCM2.1 and BCC_AGCM2.2, respectively.
Figure 7. BCC_AGCM2.1 (left) and BCC_AGCM2.2 (right) simulated biases of RSCRF (upper row) and RLCRF (bottom row) as compared to CERES (units: %).
To what extent RSCRF and RLCRF can be interpreted by CVS is now investigated in both observations and the models. The commonly-used method for this is multiple linear regression analysis; however, there is always strong collinearity between cloud covers at different vertical layers, and thus the exploratory variables are not independent and may cause the regression coefficients to be unstable if 40-level vertical clouds are directly used in the regression analysis. As an alternative, the principal component regression (PCR) method is a more effective way to avoid the problem. First, we used previously-obtained eigenvectors (namely EOFs) to construct the principal components (PC), which are independent from each other, and can be expressed as follows:
where Vmi and Xin denote EOF eigenvectors and original 3D cloud cover field, with m, n and i representing the number of PC, horizontal spatial point and vertical level, respectively. Then, multiple linear regression was conducted (m=3) to obtain the following equation:
where a indicates regression coefficients and the other symbols have the same meanings as previously defined. Here, RCRF can refer to RSCRF or RLCRF. The regression coefficients are given in Table 2. Statistically, both the equation and the individual variable pass the 99% confidence level (F-test). The coefficients measure the variation of RSCRF and RLCRF with one unit change in PC when keeping the other two PCs constant. In GOCCP, PC1 and PC2 tend to reduce the RSCRF (note RSCRF is negative), and PC3 tends to increase RSCRF, corresponding to one unit PC change. Meanwhile, PC1 and PC3 tend to increase the RLCRF and PC2 tends to reduce the RLCRF.
Both BCC_AGCMs reproduce the sign of the coefficients successfully for RSCRF. In GOCCP, the largest RSCRF variation with unit PC change is from PC2. The coefficients of PC1 (a1) simulated by the BCC-AGCMs are substantially larger than those in CALIPSO, especially for BCC_ AGCM2.2, indicating that this cloud vertical mode of BCC_AGCM overestimates the SW extinction ability corresponding to unit change of PC1. Considering the good agreement in eigenvectors between CALIPSO and the BCC_AGCMs, it can be inferred that the extinction bias may primarily come from the difference in cloud microphysical optical properties. This feature may partly arise from the simulated bias of cloud water content (CWC), which can be interpreted by the underestimation of ice cloud water content (IWC) in the tropical upper troposphere and the overestimation of CWC in the extra-tropical middle and low troposphere as simulated by a coupled version of BCC_AGCM2.1 (i.e., BCC_CSM1.0) when compared to A-Train observations (Jiang et al., 2012). For PC2, the relative SW extinction ability is also overestimated for both BCC_AGCM versions. For PC3, the relative SW extinction ability is underestimated in both BCC_AGCM versions. Due to an existence of a deficiency in eigenvectors, the bias of the coefficients (a2 and a3) cannot be explained by either the eigenvector or an individual difference in optical properties, but rather by a combination of the two. It is important to note that the BCC_AGCMs tend to overestimate the extinction ability for unit cloud cover, which may be compensated for by inadequate cloud in the models resulting in less bias in CRF at the TOA. BCC_AGCM2.2 has stronger extinction with unit cloud cover change than the BCC_AGCM2.1, indicating that there may be an automatic compensation between cloud cover and extinction ability considering the systematic decrease in cloud cover with an increase in the horizontal resolution of BCC_AGCM2.2, which is proven by an overall increase in ice cloud water content in the low-middle latitudes and an increase in liquid cloud water content in the tropics (not shown).
Multiple regression coefficients for CALIPSO, BCC_ AGCM2.1 and BCC_AGCM2.2. a0 a1 a2 a3 RSCRF CALIPSO -8.11 0.34 0.43 -0.21 #cod#160; BCC_AGCM2.1 -10.07 0.46 0.49 -0.11 #cod#160; BCC_AGCM2.2 -11.42 0.60 0.53 -0.19 RLCRF CALIPSO 2.22 0.03 -0.28 0.08 #cod#160; BCC_AGCM2.1 0.58 -0.03 -0.16 0.17 #cod#160; BCC_AGCM2.2 0.62 -0.02 -0.27 0.22 As for RLCRF, both BCC_AGCM versions reproduce the correct sign of the coefficients for PC2 and PC3, but give the wrong sign for PC1, although its contribution is very small. The largest relative contribution to RLCRF is from PC2, which is underestimated by both the BCC_AGCM models. Meanwhile, the contribution from PC3 is overestimated in the BCC_AGCMs. Unlike SW radiation, cloud exerts its effect on RLCRF mainly through its absorption and re-emission to LW radiation. Apart from cloud cover and cloud water content, the RLCRF greatly depends upon the cloud-top temperature, which determines the LW emissivity to a large degree (i.e., the higher the cloud top, the larger the RLCRF). This is why PC2 has the smaller relative contribution to RLCRF if the eigenvector bias is considered in EOF2.
Equation (6) was used to calculate the actual contribution of PCs on RSCRF and RLCRF by multiplying the PC by the relevant coefficient. First, we analyze the global-mean contributions of PCs to RSCRF and RLCRF, as presented in Table 3. It can be seen that the largest global-mean RSCRF and RLCRF are both contributed by PC2. It is noteworthy that PC1 possesses the largest EV but does not make the largest contribution to RSCRF and RLCRF. This feature can be explained through the global distribution of actual RSCRF and RLCRF contribution by different PCs, where PC1 has an obvious opposite-sign contribution to RSCRF or RLCRF between the tropics and the middle latitudes, other than the consistent negative contribution by PC2 (not shown). As for the simulated biases (Figs. 8 and 9), the RSCRF and RLCRF contributions from PC1 are generally underestimated by the BCC_AGCMs between 30#cod#x000b0;N and 30#cod#x000b0;S and overestimated in the mid-latitudes, leading to a small bias in global-mean RSCRF and RLCRF from PC1. Combined with the simulated cloud bias relevant to PC1, this may imply that SW extinction by high cloud may be inadequate, while excessive SW radiation is absorbed or reflected by middle and low clouds, which is also the case for the LW radiation if the LW emission is considered rather than the extinction. Meanwhile, the RSCRF contribution from PC2 is overestimated in the tropics and underestimated mainly between 30#cod#x000b0; to 60#cod#x000b0; in both hemispheres, which may primarily come from the downward shift of the eigenvector peak in the BCC_AGCMs and failure to capture the PBL cloud features (Fig. 4b). The RLCRF from PC2 is generally underestimated in the extra-tropics and overestimated in some areas of the tropics. For PC3, the BCC_AGCMs cannot capture the spatial variation of the RSCRF and RLCRF sign in GOCCP, other than the consistent negative contribution for RSCRF and positive contribution for RLCRF (not shown), resulting in an overestimation of about 3% for RSCRF and #cod#62;4% for RLCRF.