Figure 1a shows the linear trends in total cloud cover (ΔTCC/Δt) derived from the corrected ISCCP D2 data set (1983–2009). The general pattern of trends over the oceans is in excellent agreement with those reported by Chen et al. (2019). The pattern is also consistent with those derived by Eastman and Warren (2013) from the Extended Edited Cloud Reports Archive (EECRA) data set for 1971–2009. The linear trends in annual total precipitation (ΔTP/Δt) derived from GPCP pentad V2.2, (1983–2009) are shown in Fig. 1b. These trends are in good agreement with results of previous studies (Zhou et al., 2011; R. Liu et al., 2016). The climatological average annual precipitation rates are shown in green contours in both Fig. 1a and b to facilitate comparison between the patterns of clouds and precipitation.

There is a high degree of consistency between the general patterns of Fig. 1a and b. This can be seen by first noticing a prominent feature of a loose circle of warm color patches (increases in cloud cover and precipitation) in both Fig. 1a and b centered around Kalimantan, Indonesia, starting in northern Australia and circling counterclockwise to the Philippines and to western China and turning southward along the western Indian Ocean all the way to about 50∘ S, covering nearly half of the eastern hemisphere (0–180∘ E). This loose circle of warm color patches exists in both Fig. 1a and b, albeit not at the exactly same location, and has an obvious effect of broadening the center of precipitation (ascending/wet zone of Hadley cells) over the Maritime Continent in all directions (Zhou et al., 2011; R. Liu et al., 2016). There are also significant and extensive enhancements/broadenings of precipitation centers over Central America and equatorial Africa. These enhancements/broadenings have been interpreted to be an essential part of the widening of Hadley circulation and poleward shifts of the jet streams associated with global warming (Reichler and Held, 2005; Hu and Fu, 2007; Zhou et al., 2011; Davis and Rosenlof, 2012; Eastman and Warren, 2013; R. Liu et al., 2016; Norris et al., 2016).

As a measure of the broadening of the major ascending zone of Hadley circulation, we calculate and illustrate the expansion of cloud cover and precipitation as a function of 16 rectangular belts centered in the middle of Kalimantan, Indonesia, which is located near the major ascending/wet zone of the Hadley cell (Fig. 2). Each rectangular belt is 2.5∘ wide in both latitude and longitude except that the first rectangle is 5∘ wide in latitude and 55∘ wide in longitude. The summing up was done for each rectangle independently; the inner rectangles were not included. Figure 3a and e depict their “climatology” (black curve) and “climatology + change during 1983–2009” (blue curve) for annual precipitation and total cloud cover, respectively. It can be seen that, for a specific value of the y axis, the blue curve is characterized by a shift horizontally (x axis direction) to the right (i.e., higher number of belts) of the black curve for most of Fig. 3a and e. In comparison, there is very little upward shift in the vertical or y axis direction, especially at low-end (belts 1 and 2) and high-end belts (belts 15 and 16). As a result, there is hardly any enhancement in total cloud cover and total precipitation. These characteristics can be interpreted as an expansion to higher latitudes and wider longitudes, i.e., a broadening of the major ascending zone of Hadley circulation, but without any significant enhancement in total cloud cover or total precipitation during the period of 1983–2009. Remarkably one can see that the expansion of the major ascending zone of the Hadley cell as measured by clouds (Fig. 3e) starts at belt 2 (3.75∘ latitude). Meanwhile, the expansion of the major ascending zone of the Hadley cell as measured by precipitation (Fig. 3a) starts at belt 5 (12.5∘ latitude). The reason for the difference is unknown; one possible reason could be the constraint on the total annual precipitation, which is equal to global evaporation and determined by the global surface energy budget, increases with global temperature at a rather small rate of about 2–3 %K-1 (Cubasch et al., 2001). Quantitatively the degree of expansion depends on the selected value of the y axis, increasing quickly when the value is near the 1000 mm precipitation level (Fig. 3a) or 55 % of TCC (Fig. 3e). The value of the shift is typically within the range of one-quarter to three-quarters of a belt width (2.5∘) or about 0.6–1.9∘. These annual values are comparable to the poleward shift of the subtropical dry zones (up to 2 ∘decade-1 in June–July–August (JJA) in the Northern Hemisphere and 0.3–0.7 ∘decade-1 in June–July–August and September–October–November in the Southern Hemisphere) found by Zhou et al. (2011). As a summary of this and the last paragraphs, a logical conclusion can be drawn that the linear trends in TCC and TP are mainly characterized by a broadening of the major ascending zone of Hadley circulation in both latitude and longitude associated with global warming. These characteristics will be used in the following as key criteria for the evaluation of relative contributions of individual climate indexes to the linear trends in total cloud cover (TCC) and total precipitation (TP).

A critical question remaining is whether climate parameters other than global warming may also contribute to the linear trends in TCC and TP, particularly AMO and PDO, which also have significant linear trends (Fig. S2 in the Supplement) during the relatively short period of 1983–2009 of this study. This is addressed in the following. Figure 4a and b depict slopes of linear regressions of TCC and TP against the annual average global temperature anomaly (GT) at each grid point, i.e., ΔTCC/ΔGT and ΔTP/ΔGT, respectively. The circle of warm-color patches around Kalimantan, which symbolizes the broadening of the major ascending zone of Hadley circulation, is highly visible in both Fig. 4a and b. The broadening as a function of the 16-rectangular belts is illustrated in Fig. 3b for TP and Fig. 3f for TCC. The enhancement/broadening of the precipitation centered over equatorial Africa can also be clearly seen. These agreements between Figs. 1a and 4a and between Figs. 1b and 4b are substantiated by the relatively high correlation coefficients of 0.82 and 0.93, respectively (Table 1), suggesting that global warming can explain 67 % and 86 %, respectively, of the spatial variabilities of linear trends in cloud cover and precipitation. It is important to note that these high degrees of correlation do not establish a causal relationship; they merely suggest there are probabilities of finding a causal relationship. The slopes of linear regressions of TCC and TP against AMO at each grid point are plotted in Fig. 5a and b. The general patterns also match reasonably well with those of Fig. 1a and b. The correlation coefficients between Figs. 1a and 4a and between Figs. 1b and 4b are slightly less than those of global temperature at 0.70 and 0.77, respectively (Table 1), implying that AMO can explain about 49 % and 59 %, respectively, of the spatial variabilities of linear trends in cloud cover and precipitation. Due to limited space, figures for PDO and Niño3.4 corresponding to Fig. 4a and b are presented in the Supplement (Figs. S3 and S4 in the Supplement). The correlation coefficients of Niño3.4 with Fig. 1a and b are very low at -0.20 and 0.02, respectively (Table 1). A major reason for the low correlation coefficient is the lack of any linear trend in Niño3.4 during 1983–2009. Correlation coefficients of PDO with Fig. 1a and b are 0.62 and 0.73 (Table 1), respectively, slightly less than those of AMO. These correlation coefficients imply that PDO can explain approximately 38 % and 53 %, respectively, of the spatial variability of linear trends in cloud cover and precipitation.

It should be noted that considering PDO together with AMO and GT, there obviously is a problem of over 100 % explanation of the spatial variabilities of linear trends in cloud cover and precipitation. Since the trend in global SST has been removed from the PDO and AMO indexes in this study, in theory the trend in GT should be orthogonal to those of PDO and AMO. In practice the orthogonality is not attained because the trend in global SST does not equal the real influence of GT on PDO or AMO. It is difficult to completely remove the influence of GT from the PDO or AMO index, which is likely the main reason of the problem of over 100 % explanation. Table 1 presents the correlation coefficients with Fig. 1a and b for various linear combinations of GT and three other climate indexes. Significant improvements of the correlation with Fig. 1a (TCC) are attained when GT is paired with AMO (0.86) or Niño3.4 (0.89). The correlation with Fig. 1b (TP) is not improved by any combination, which is understandable as the correlation coefficient of GT alone (0.93) is already very high.

Table 1 has also been evaluated for detrended data of TCC, TP, GT, AMO, PDO and Niño3.4 (Table S1 in the Supplement). The correlation coefficients are all less than 0.33, implying that consecutive yearly variabilities contribute insignificantly to the high correlation coefficients in Table 1, and the high correlation coefficients are nearly entirely contributed by the long-term linear trends in GT on PDO and AMO. One of the reasons for the lack of correlation could be due to the small consecutive yearly variabilities relative to the long-term linear trends (about 1 to 10) for GT, PDO and AMO (Fig. S2).

Based on Table 1, we can conclude that the linear trends in GT, AMO and PDO all have a good probability in contributing to the observed linear trends in total cloud cover and precipitation in 1983–2009. However, the results of Table 1 do not provide any clue indicating which one of the three is the primary contributor. To address this question, we examine Fig. 3b–d and f–h to evaluate how the trends in GT, AMO and PDO influence the observed linear trend in the broadening of the major ascending zone of Hadley circulation as shown in precipitation and total cloud cover in 1983–2009. Figure 3b–d shows the changes (blue curve) from the climatology (1983–2009) (black curve) in the annual total precipitation (mm) of the 16 belts of Fig. 2 as a function of GT, AMO and PDO. The formula for calculating the blue curve, for instance for the changes in precipitation as a function of global temperature (Fig. 3b), is d(TP)/d(GT)×ΔGT, where ΔGT denotes a difference in the global temperature between 1983 and 2009. It can be seen that Fig. 3b (GT) agrees very well with Fig. 3a both qualitatively and quantitatively, while Fig. 3c and d have significantly greater positive values (broadening) compared to the small negative values (contraction) of Fig. 3a for the inner five belts, resulting in a significant enhancement of the overall precipitation. This discrepancy is crucial, as the quantity of global total annual precipitation, which is equal to global evaporation and determined by the global surface energy budget, increases with global temperature at a rather small rate of about 2–3 %K-1 (Cubasch et al., 2001), which is manifested in Fig. 3a and b by the small/negligible change in the net area between blue and black lines, while both Fig. 3c and d have significant enhancements. Therefore, based on the results of Fig. 3a–d, we propose that the trend in global temperature, rather than that of AMO and PDO, is the primary contributor to the observed linear trend in precipitation in 1983–2009. Likewise, Fig. 3e and f both have small/negligible changes in the net areas between blue and black lines, while both Fig. 3g and h have significant enhancements of cloud cover. Accordingly, we propose that the trend in global temperature, rather than that of AMO and PDO, is the primary contributor to the observed linear trend in cloud cover in 1983–2009.

A comparison of Fig. 1b with 3e reveals that the enhancements in precipitation in the tropics (Fig. 1b) are the major contributor to the broadening of the major ascending zone of Hadley circulation in observed precipitation (Fig. 3e). Since it has been shown by R. Liu et al. (2016) that the enhancements in precipitation in the tropics are nearly entirely driven by heavy precipitation (strong convections), we propose that the broadening of the major ascending zone of Hadley circulation is primarily driven by the moisture–convection–latent-heat feedback cycle.

To summarize Sect. 3.1, the spatial distributions of the linear trends in total cloud cover and precipitation are characterized primarily by a broadening of the center of precipitation (ascending/wet zone of Hadley cells) over the Maritime Continent in all directions (Zhou et al., 2011; R. Liu et al., 2016). Our correlation studies show that GT, AMO and PDO can each explain significant spatial variabilities of the linear trends in cloud cover (67 %, 49 % and 38 %, respectively) and precipitation (86 %, 59 % and 53 %, respectively). Contribution by Niño3.4 itself is insignificant because it does not have any trend in 1983–2009. A linear combination of GT and AMO can explain as much as 74 % and 79 %, respectively, of the spatial variabilities of linear trends in cloud cover and precipitation. Further analysis of the broadening of the major ascending zone of Hadley circulation (Fig. 3a–h) shows that the trend in global temperature, rather than that of AMO and PDO, is the primary contributor to the observed linear trend in total cloud cover and precipitation in 1983–2009. The underlying mechanism driving this broadening is proposed to be the moisture–convection–latent-heat feedback cycle under global warming conditions.

The effects of anthropogenic aerosols on clouds and precipitation acting as cloud condensation nuclei (CCN) is a highly controversial issue, which has been discussed extensively in a number of studies as well as one of our earlier papers (Liu et al., 2015). We defer the discussion on this issue to future studies and acknowledge here that the CCN effects could introduce an unknown degree of uncertainty into this study. The long-term radiative effect of aerosols on the global temperature and other climate parameters is expected to be imbedded in the observed changes in these climate parameters and thus is included in this study.

Our results suggest that the global temperature contributes the most to the trends in cloud cover, which is more in line with the view of Eastman and Warren (2013), rather than with that of Chen et al. (2019), who suggested that AMO and PDO contributed more than the global temperature. However, it is well known that correlation method does not imply any cause–effect relationship and certainly not a quantitative cause–effect relationship. Our analysis in this section has used a correlation method, as did the study by Chen et al. (2019) and many studies on attributing the broadening of the major ascending zone of Hadley circulation to global warming cited by Eastman and Warren (2013). In this context, we note that Eastman and Warren's analysis covered a longer period 1971–2009, in which PDO did not have any significant linear trend and hence could not have any contribution to the linear trends in cloud cover. This conclusion, which does not rely on the correlation method, should override those derived from correlation studies, including those associated with PDO in this section and those derived by Chen et al. (2019).

The global analysis is extended in this section by investigating connections between clouds and precipitation in China, where there is a large number of long-running, high-quality surface weather stations for the period of 1957–2005. The long-running data enable the analysis to be carried out over a period in which the linear trends in AMO and PDO have both diminished to insignificant values. More importantly, the high-quality data allow us to make meaningful analysis without using the correlation method, which has an intrinsic weakness because it confuses associations between variables and causal relationships as discussed above.

Data on cloud cover and precipitation from 477 surface meteorological stations provide significantly higher spatial and temporal resolution over a longer time period (1957–2005 for TCC, 1957–2017 for TP) than satellite data, such that detailed analysis can be carried out to reveal fine features for different periods of time. Figure 6 shows linear trends in annual precipitation amount (ΔP) falling within each of the 10 bins of equal rain rate with increasing precipitation intensity during 1957–2005. There is a significant overall shift toward higher precipitation intensity, in agreement with previous studies (Liu et al., 2005, 2009, 2015; Zhai et al., 2005; Sun et al., 2007; Qian et al., 2007; Wang and Zhai, 2008; Shiu et al., 2012; Wu and Fu, 2013; Jiang et al., 2014; R. Liu et al., 2016). Specifically, the bottom 10 % light precipitation decreases by -1.5 ± 0.5 %decade-1 and the top 10 % heavy precipitation increases by 2.7 ± 1.0 %decade-1, both significant at the 99 % confidence level. These values are robust over different time periods; for example for the period (1983–2009) overlapping with satellite data, the bottom 10 % light precipitation decreases by -2.8 ± 1.7 %decade-1 and the top 10 % heavy precipitation increases by 8.0 ± 3.4 %decade-1. The latter is significant at the 95 % confidence level. For the period 1957–2017, the bottom 10 % light precipitation decreases by -2.0 ± 0.4 %decade-1 and the top 10 % heavy precipitation increases by 3.0 ± 0.7 %decade-1, both significant at the 99 % confidence level.

The linear trend in the non-precipitation days is 4.5 ± 0.2 ddecade-1, which is significant at the 99 % confidence level (Table 2 and Fig. 7a). During the 49-year period, non-precipitation days have increased by about 22 d, which is nearly completely compensated for by the decrease in light-precipitation days. The bottom 10 % precipitation alone has decreased by about 21 d, accounting for ∼ 95 % of the change in non-precipitation days. Note that the value of the bottom 10 % precipitation days in Fig. 7 has been multiplied by -1 to better compare with the non-precipitation days; the same is true for the bottom 10 % ∼ 30 % precipitation days. This value quickly approaches 100 % when changes in the bottom 10 %–40 % precipitation days are included. This is fully expected as the number of bottom 40 % precipitation days (147) account for ∼ 90 % of total precipitation days (163). In the meantime, the top 60 % precipitation days barely change.

During the 49-year period, the number of cloud-free days has increased by about 11 d, accounting for one-half of the increase in non-precipitation days (Fig. 7b and Table 2). This value quickly approaches 21 d when changes in the (0–50)% cloud cover days (CCDs) are included. Twenty-one days account for 95 % of the increase in non-precipitation days. This is reasonable as precipitation usually does not occur when the cloud cover is less than 50 %. Linear trends in the cloud-free days (CFDs) and CCDs are 2.3 ± 0.1 and 4.3 ± 0.2 d per decade, respectively, both significant at the 99 % confidence level (Table 2). This is compensated for by a reduction of 50 %–100 % in cloud cover days (Fig. 8), mostly by the 90 %–100 % overcast days. This is also logical because precipitation tends to occur when the sky is heavily overcast (see also Fig. 1). Since light-precipitation days account for most of precipitation days, their decrease should approximately equal the decrease in overcast days.

So far in Sect. 3.2, we have used observed cloud cover and precipitation data from Chinese surface meteorological stations to successfully establish a quantitative matching relationship starting from the reduction in light-precipitation days, to the increase in non-precipitation days, then to the increase in cloud-free days and finally to the reduction in total cloud cover in China. This relationship is established via a straightforward arithmetic analysis, which is more robust than the correlation analysis, as the correlation analysis tends to introduce extra uncertainties (e.g., the causal relationship problem) as discussed in the last section. A critical remaining question is what the cause of the reduction in light-precipitation days in China is. Liu et al. (2015) proposed that the reduction in light-precipitation days in China is part of the extensive worldwide reports of enhancements in heavy precipitation and reductions in light and moderate precipitation (Karl and Knight, 1998; Manton et al., 2001; Klein Tank and Können, 2003; Fujibe et al., 2005; Groisman et al., 2005; Liu et al., 2005, 2009, 2015; Zhai et al., 2005; Goswami et al., 2006; Qian et al., 2007; Sun et al., 2007; Wang and Zhai, 2008; Shiu et al., 2012; Wu and Fu, 2013; Jiang et al., 2014; R. Liu et al., 2016), and the primary driving mechanism is the MCL–feedback cycle in a global warming environment proposed by Trenberth et al. (2003). We check this proposal by making the following evaluation of the trend in the bottom 10 % light precipitation (B10LP) using its slope of linear regression against various climate oscillation indexes. For example, the trend in B10LP can be calculated from the trend in PDO as follows: Calculated trend in B10LP from PDO for 1957–2005=(ΔB10LP/ΔPDO)×(trend in PDO)=(-0.33±0.09)%decade-1, where ΔB10LP/ΔPDO is the slope of linear regression between B10LP and PDO during 1957–2005. This calculated trend should be interpreted as the maximum possible contribution to the trend in B10LP from PDO because there may be other climate parameters contributing to the slope (ΔB10LP/ΔPDO). Table 3 lists the trends in B10LP calculated from PDO, AMO and GT for three time periods of interest in this study: 1957–2005, 1957–2017 and 1983–2009. Niño3.4 is not listed because it has no linear trend during these periods and thus by definition no significant contribution.

Calculated trends in B10LP from GT agree remarkably well with the observed trends in all three periods. Calculated trends in B10LP from PDO are more than a factor of 5 too low for both periods 1957–2005 and 1957–2017, while no significant trend is found for 1983–2009. The calculated trend in B10LP from AMO agrees with the observed value during 1983–2009, but no significant trend is found for the two longer periods 1957–2005 and 1957–2017. Since the trends in longer periods should carry more weight, results in Table 3 suggest that GT is the primary contributor to the linear trends in B10LP, the maximum possible contribution from PDO is about 10 %, while contribution from AMO and Niño3.4 is negligible. These results are consistent with the proposal by Liu et al. (2015) that the reduction in light-precipitation days in China is part of the extensive worldwide reports of enhancements in heavy precipitation and reductions in light and moderate precipitation under global warming environment. Finally, it is worth mentioning that the value of ΔB10LP/ΔGT calculated from detrended data is consistent with those shown in Table 3.

In summary of Sect. 3.2, our study suggests that the reduction in cloud cover in China is primarily driven by the MCL–feedback cycle under a global warming environment, PDO plays a secondary role, while the contribution from AMO and Niño3.4 is insignificant. This finding lends strong albeit regional support to the findings in Sect. 3.1 because it is derived primarily via an arithmetic analysis; the only exception is in attributing the cause of the reduction trend in the bottom 10 % light precipitation to GT, which is adopted from extensive investigations cited in Trenberth et al. (2003) and Liu et al. (2015).