1 Introduction

The global climate model (GCM) is a unique tool for simulating Earth’s climate in a physically-based manner. GCMs have been improved for the past decades (Reichler and Kim 2008) and extensively used in the Intergovernmental Panel on Climate Change (IPCC) Assessment Reports (Solomon et al. 2007). While many aspects of the climate simulated in GCMs, such as temperature and wind fields, are much more realistic than in the past, the representation of clouds remains one of their largest limitations. Indeed, the current IPCC-class models show a substantial divergence in terms of sign and magnitude of the cloud-radiative feedback in response to increase in atmospheric CO2 concentration (e.g., Bony and Dufresne 2005; Soden and Held 2006; Webb et al. 2006). In particular, shortwave radiative feedbacks associated with changes in low clouds (combination of stratiform, stratocumulus, and shallow cumulus clouds) remain largely unknown; they act as negative feedback in some GCMs, but vice versa in the others.

It is widely recognized that the tropical low-level cloud fraction (C l ), a major player in the global cloud shortwave forcing, is partly controlled by the large-scale environment, especially over the subsidence regime. Klein and Hartmann (1993), and later Wood and Bretherton (2006), revealed that the inversion strength above the planetary boundary layer (PBL) provides a good measure of the distribution and seasonal cycle of C l . This thermodynamic constraint is typically measured in terms of lower-tropospheric stability (LTS), defined by the difference in potential temperature (θ) between the 700 and 1,000 hPa levels. There is also a dynamic constraint that affects C l as measured by the vertical pressure velocity at 500 hPa (ω500) or the low-level divergence (Zhang et al. 2009). Several studies have shown that the cloud properties sorted using these quantities reveal well the distinct cloud regimes in the GCMs (Wyant et al. 2006; Su et al. 2008; Medeiros and Stevens 2011).

In reality, the physics of low clouds are complex phenomenon involving mutual interaction between the large-scale environment and the local processes of turbulence, cloud microphysics, convection, and radiation. Therefore, it is difficult to construct a simple theory of low-cloud physics and their response to climate change. Yet, several works have proposed a simplified model for low clouds (Miller 1997; Larson et al. 1999; Caldwell and Bretherton 2009). They argue a possible negative low-cloud feedback in a warmed climate. When there is non-uniform change in sea surface temperature (SST) in the tropics, this negative feedback results from shoaling of the PBL, increased LTS, and thickened cloud layer. These changes are not fully investigated in the climate change simulation by GCMs.

There have been attempts to estimate climate sensitivity and cloud-radiative feedback based solely on observations, which, if possible, greatly reduce the uncertainty in climate change projections. However, these observational estimates still suffer from large errors due to the short periods covered by the data as well as the uncertainty in the measurements (Forster and Gregory 2006; Murphy et al. 2009). A more critical question is whether the climate feedback estimated for the natural variability that dominates the short record is applicable to the feedback in long-term climate change due to radiative forcing. Clement et al. (2009), who followed analyses by Burgman et al. (2008), discussed low-cloud feedback associated with the Pacific decadal oscillation, by combining satellite cloud products and GCM simulations. They concluded that the low clouds over the northeastern Pacific serve as a positive feedback, and further suggested a similar feedback at work over the entire Pacific under global warming. Such an extrapolation may, however, be controversial since the metric constructed over a particular regime is used for arguing the cloud feedback in other regimes. Dessler (2010) identified a positive cloud shortwave feedback in short-term variations in satellite and reanalysis data and also in climate models, but found that they are not correlated with the cloud feedback in response to long-term climate change. Thus, cloud feedback is apparently dependent on the time scale, which is the major focus of the present study.

Gregory and Webb (2008) demonstrated that, in GCMs, clouds can change without any change in the global-mean surface air temperature (SAT). This occurs rapidly as part of the tropospheric adjustment due directly to the radiative forcing caused by increased CO2 levels. In contrast to this rapid adjustment, cloud changes in response to changing SAT are often called ‘slow feedback’. However, the above observational studies and a recent GCM study by Held et al. (2010) suggest that cloud feedback can also be classified according to the time scales. In the present study, the cause and timescale-dependence of tropical low-cloud feedback are examined using two GCMs, the Model for Interdisciplinary Research on Climate (MIROC) versions 3.2 and 5, which show an opposite sign of the cloud shortwave feedback to climate change (Watanabe et al. 2010). As described later, MIROC5 is a newer version that adds more physical constrains in representing clouds; nevertheless, we cannot say it providing more ‘reliable’ cloud feedback in the climate change simulation because we do not yet understand how the cloud feedbacks are controlled and whether the responsible processes are adequately represented in the model. Therefore, we intend to examine the extent to which the C l change can be constrained by properties of the model’s natural variability, but not to conclude which version gives the correct C l change. Furthermore, we try to demonstrate that change in lower-tropospheric stability is a robust part of the climate change related to C l by analysing outputs from six other GCMs.

The present paper is organized as follows. In Sect. 2, two versions of MIROC and abrupt 4 × CO2 experiments are described. Several observational data sets for validating the simulated cloud fields are also explained. In Sect. 3, the natural low-cloud variability and its mechanism are examined using the model control runs and observations. The results are then applied in Sect. 4 to understand the low-cloud response to changes in radiative forcing. In particular, we emphasize the multiple time scales of the response, in which the property of the natural low-cloud variability plays a partial role. In Sect. 5, the analysis is extended to the multi-model outputs obtained from the Coupled Model Intercomparison Project phase 3 (CMIP3), in order to identify a robust portion of the low-cloud response. Section 6 presents the concluding discussion.

2 Model and experiments

2.1 MIROC3.2

MIROC version 3.2 (denoted as MIROC3.2) is a full atmosphere–ocean–land–sea-ice coupled model, jointly developed at the Center for Climate System Research (CCSR),Footnote 1 the University of Tokyo, National Institute for Environmental Studies (NIES), and the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) (K-1 model developers 2004). This version of MIROC contributed to the IPCC Fourth Assessment Report (AR4). The atmospheric component model, including a multi-layer land model, employs a spectral dynamical core and implements a standard physics package which also incorporates a simplified aerosols module. The ocean and sea-ice models comprise the CCSR ocean component model (COCO). The resolution of the atmospheric model is T42L20 and the ocean component has approximately 1° grid spacing. They correspond to the ‘MIROC3.2med’ abbreviated in the IPCC AR4.

2.2 MIROC5

We have upgraded MIROC3.2 to the latest version 5.0, denoted as MIROC5, which will be used for the IPCC Fifth Assessment Report (AR5). The basic framework of MIROC5 follows that of MIROC3.2, but many of the parameterization schemes in the atmospheric model have been replaced either by implementing recent ones or by schemes newly developed by our group. In particular, it is important to state for the present study that the following significant changes were made in the treatment of turbulence and clouds in MIROC5: the level 2.5 turbulence closure, prognostic cloud scheme, cloud microphysics, and a prognostic scheme for number concentrations of cloud droplets and ice crystals (see Watanabe et al. 2010 for details). The ocean and sea-ice fields are also calculated with an updated COCO. The standard resolution of the atmospheric model is T85L40, which is double that of MIROC3.2, while the ocean component employs almost the same horizontal resolution as that used in MIROC3.2. We conducted a 500-year pre-industrial control simulation, which shows improvements in both the mean state and natural climate variability (Watanabe et al. 2010). For example, the features of the El Niño-Southern Oscillation (ENSO) are more realistic in MIROC5. Furthermore, the importance of a new cumulus convection scheme in the ENSO simulation was identified through perturbed parameter experiments (Watanabe et al. 2011a).

2.3 4 × CO2 experiments

The pre-industrial control experiments are first carried out with atmospheric CO2 concentration of 285 ppm. We then take the initial conditions from the control runs, which are at least 20 years apart to avoid overlapping of the 4 × CO2 experiments. From each of the initial states, the models are integrated for 20 years with an abrupt quadrupling of the CO2 concentration from 285 to 1,140 ppm. This concentration does not mimic the possible level of CO2 in climate change scenarios but rather sets to increase the signal-to-noise ratio, as recommended in CMIP5 (cf. experiments 6.3 and 6.3E). A ten- and six-member ensemble is made with MIROC3.2 and MIROC5, respectively. The period of integration is short for the model’s climate to be equilibrated, but long enough to estimate the effective climate sensitivity (Gregory et al. 2004). However, these ensembles do not represent a slowly evolving response of the climate system; therefore, we extended one member up to 150 years. The response of the variable x to the radiative forcing due to the quadrupled CO2 concentration is evaluated using annual-mean fields and is denoted as Δx. We recognize the uncertainty associated with clouds due to interaction of clouds with both the radiation and meteorological fields, but focus in this study on the latter without arguing the cloud-radiative processes.

2.4 CFMIP1 database

A systematic comparison of clouds simulated in GCMs has been proposed in the Cloud Feedback Model Intercomparison Project phase 1 (CFMIP1; http://cfmip.metoffice.com), which collected a dataset of equilibrium control and 2 × CO2 experiments using coupled atmosphere-slab ocean models. The CFMIP1 data have so far been extensively used to analyse the cloud regime in control experiments as well as to examine cloud feedback in climate change simulation (Webb et al. 2006; Williams et al. 2006; Ringer et al. 2006; Tsushima et al. 2006; Williams and Tselioudis 2007). We use the CFMIP1 data in this study and compare them with the cloud response identified in our two models; note that data from MIROC3.2 has also been submitted to CFMIP1. The data used are obtained from six models: the Canadian Centre for Climate Modelling and Analysis (CCCma) low-resolution version, National Center for Atmospheric Research (NCAR) CCSM3, Geophysical Fluid Dynamics Laboratory (GFDL) CM2.0, Goddard Institute for Space Studies (GISS) ER, Institute for Numerical Mathematics (INM) CM3.0, and the Meteorological Research Institute (MRI) CGCM2.3.2. Each model provides a single member integrated for 20 years, from which we define Δx as in the MIROC outputs.

2.5 Observational data

To validate the cloud fields in the control experiments, we use two satellite-based low-cloud datasets. One is obtained from the International Satellite Cloud Climatology Project (ISCCP) (Rossow and Schiffer 1999). The ISCCP provides the longest term satellite cloud data, for 1984–2007 on a regular 2.5º grid. The other is derived from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) (Winker et al. 2009). The CALIPSO data are limited for the recent few years from January 2006 to November 2008, but are able to capture a fine horizontal structure of clouds.

In addition to the satellite-derived cloud data, we use observations of SST for 1945–2006 derived from Ishii et al. (2006) and of the atmospheric fields obtained from two reanalyses: the Japanese 25-year reanalysis (JRA25) (Onogi et al. 2007) for 1979–2009 and the European Centre for Medium Range Weather Forecasts (ECMWF) 40-year reanalysis (ERA40) (Uppala et al. 2005) for 1979–2001. These are all monthly basis and analysed in order to identify environmental conditions associated with past low-cloud variability.

For the cloud regime analysis performed in Sect. 5, we newly compiled the cloud data using CloudSat and CALIPSO and the cloud mask scheme C4, ‘CloudSat or CALIPSO’ scheme, in which clouds are detected by at least one of these two satellites (Hagihara et al. 2010). The scheme was developed on the basis of cloud masks derived from shipborne 95 GHz cloud radar and lidar observations in the western Pacific Ocean near Japan and in the tropical western Pacific (Okamoto et al. 2010, references therein). Radar reflectivity was derived from the CloudSat 2B GEOPROF product (release R04), in which a confidence level value ≥20 was applied to determine cloudy pixels from CloudSat (Marchand et al. 2008). The minimum detectable signal radar reflectivity is about −30 dBZ, implying that some cloud regions were not detected. This underestimation of cloud detection may account for more than 10% of low-level clouds, based on ship-based radar measurement. CALIPSO lidar level 1B (version 2.01) products were used as lidar backscattering coefficients for co- and cross-polarization at 532 nm wave length. The CALIPSO cloud mask C2 used in this study is different from the standard cloud mask, vertical feature mask (VFM) (http://eosweb.larc.nasa.gov/PRODOCS/calipso/Quality_Summaries/). We first applied a threshold of the total backscattering coefficient at 532 nm to the target grid. The threshold depended on the background noise signal (estimated at 19–20 km altitude), the molecular signal derived from the ECMWF data. Next, the spatial continuity was tested using the surrounding 5 × 5 bins at altitudes <5 km, and 9 × 9 bins at altitudes >5 km. The cloud mask results were then averaged to obtain the same vertical and horizontal resolutions as the CloudSat data (1.1 km and 240 m). It is worth noting that the cloud mask results for CALIPSO have less contamination by noise and aerosols at low altitude levels compared with the CALIPSO standard VFM (Hagihara et al. 2010; Okamoto et al. 2010).

3 Natural low-cloud variability

As a prelude to the low-cloud response to increasing CO2 in GCMs, the property of natural low-cloud variability is compared between the observations and the models. The definition of low cloud (hereafter denoted as C l ) follows ISCCP (Rossow and Schiffer 1999). As stated in the introduction, the formation and dissipation of stratocumulus and shallow cumulus clouds, the major components in C l , are partly controlled by large-scale environmental factors such as vertical motion and inversion strength. We therefore compare the local correlation between the monthly C l anomalies and the anomalies of either ω500 or LTS. The ω500 field represents a dynamic constraint whereas LTS provides a thermodynamic constraint on C l .

The observed correlation maps for 1984–2007 based on ISCCP and JRA reanalysis reveal that the C l anomaly is overall positively correlated with both ω500 and LTS (Fig. 1a, b). In particular, the C l variability is strongly coupled with the in-situ ω500 over the equatorial regions where the mean SST is higher than roughly 26°C. Likewise, the C l variability is associated with the local LTS over the subtropical regions where the mean SST is lower than 26 °C. While the influence of ω500 and LTS to C l is generally complementary in terms of the geographical distribution, both factors affect C l in some regions such as the subtropical western Pacific and the southern Indian Ocean.

Fig. 1
figure 1

Local correlation maps of monthly anomalies: a C l and ω500 in observations, b C l and LTS in observations, c–f same as a, b but for 150-year control runs of MIROC3.2 and MIROC5, respectively. The observed C l data are derived from ISCCP, and both ω500 and LTS are calculated from the JRA reanalysis for 1984–2007

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Correlation maps for the 150-year control runs using MIROC3.2 and MIROC5 are shown in the remaining panels of Fig. 1. The C l -ω500 and C l -LTS relationships show several discrepancies compared to the observations: weak dynamical coupling over the tropical western Pacific and stronger thermodynamic coupling near the equator in MIROC3.2 (Fig. 1c, d), and a banded structure in the C l -LTS relationship in MIROC5 (Fig. 1f). Yet, the broad features of the dynamic and thermodynamic coupling with C l appear to be reproduced in the two models.

Given the strong local coupling of C l with ω500 and LTS, which are ultimately maintained by the underlying SST, we attempt to extract the leading mode of variability in the natural C l variability together with the dominant pattern of the SST variability. For this purpose, singular value decomposition (SVD) analysis is applied to the monthly C l and SST anomalies over the tropical oceans between 30ºS and 30ºN. To obtain robust observational estimates, two sets of cloud and SST data are used: monthly SST by Ishii et al. (2006) and ISCCP cloud productsFootnote 2 from July 1983 to June 2005 (Fig. 2a, b), and NOAA OISST and CALIPSO data from June 2006 to November 2008 (Fig. 2c, d). Despite the different sources and periods of data, both sets show the leading SVD very similar to each other; the SST anomaly pattern clearly represents the ENSO warm phase and the associated C l fields show the reduction over the positive SST anomaly and vice versa. Because the SST and C l anomalies are not uniform in space, the tropical-mean C l anomaly associated with the leading SVD is small but slightly negative.

Fig. 2
figure 2

Heterogeneous regression maps of the monthly SST (K) and C l (%) anomalies associated with the leading SVD between them: a, b observations for the period from July 1983 to June 2005 based on Ishii et al. (2006) SST and the ISCCP cloud data, c, d observations from June 2006 to November 2008 based on NOAA OISST and CALIPSO, e, f 150 years control run of MIROC3.2, and g, h 150 years control run of MIROC5. The values of squared covariance fraction and correlation between the corresponding expansion coefficients are shown at the top of each panel

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Figure 2a–d suggests that the dominant C l variability in the tropics is the response to ENSO, so that the reproducibility in the GCMs may depend on the quality of the ENSO simulation. It has been reported that MIROC5 produces a more realistic ENSO in terms of the spatial structure and amplitude (Watanabe et al. 2010). This, in fact, is seen in the difference in the leading SVD patterns (Fig. 2e–h). The SST anomaly pattern in MIROC3.2 lacks the horse-shoe shaped cooling in the western Pacific and thereby the uniform negative anomaly dominates the C l field (Fig. 2e, f). The anomaly patterns in MIROC5 have more resemblance to the observational counterparts (Fig. 2g, h).

The leading SVDs, possibly representing ENSO and its driving of C l , account for 40–70% of the total covariance; this suggests that a measure for ENSO can be used to explain the tropical-mean C l anomaly. This idea is tested by plotting the area-weighted, tropical-mean C l anomaly (30ºS and 30ºN over oceans, denoted as \( \left\langle {C_{l}^{\prime } } \right\rangle \)) against the Niño 3 SST anomaly (Fig. 3a–c). The tropical average is affected by regional errors and a bias in the ISCCP C l field, so we used the monthly \( \left\langle {C_{l}^{\prime } } \right\rangle \) time series from January 2006 to November 2008 based on the CALIPSO data. It shows a negative correlation with the Niño 3 SST anomaly (r = −0.47) and reveals a 0.44% decrease per 1 K increase in SST (Fig. 3a). A similar negative correlation is found in the two GCMs, but the regression slope in MIROC3.2 is larger and indicative of higher sensitivity of \( \left\langle {C_{l}^{\prime } } \right\rangle \) to ENSO (Fig. 3b, c).

Fig. 3
figure 3

Scatter plot of the monthly tropical-mean C l anomaly (%) against the Niño 3 SST anomaly (K): a NOAA OISST and CALIPSO C l data, b, c 150-year control runs of MIROC3.2 and MIROC5, respectively. The regression slope and correlation coefficient are also shown. d, f Contribution of dynamic (blue) and thermodynamic (red) components to the C l anomaly as revealed by the scatter plot against the reconstructed C l (denoted as \( \tilde{C}_{l} \)) anomaly corresponding to a–c

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The C l response to ENSO will be partly generated via changes in the large-scale environment. By referring to ω500 as an environmental variable, the C l anomaly, \( C_{l}^{\prime } \), is expressed following Bony et al. (2004):

$$ \tilde{C}_{l}^{\prime } \simeq \int\limits_{\omega } {P_{\omega }^{\prime } \bar{C}_{l} (\omega )d\omega } + \int\limits_{\omega } {\bar{P}_{\omega } C_{l}^{\prime } (\omega )d\omega } , $$
(1)

where \( \tilde{C}_{l}^{\prime } \) denotes the reconstruction of \( C_{l}^{\prime } \), \( \bar{P}_{\omega } \) and \( P^{\prime}_{\omega } \) are the probability density functions (PDFs) of the ω500 climatology and anomaly, respectively, and \( \bar{C}_{l} (\omega ) \) and \( C_{l}^{\prime } (\omega ) \) are the climatology and anomaly of the composite C l with respect to ω500. The first term is often called the dynamic component whereas the second term is known as the thermodynamic component of the cloud regime. When Eq. (1) is applied to the ENSO-related anomalies, \( \left\langle {C_{l}^{\prime } } \right\rangle \) is well reproduced both in observations and models (root mean square errors are 0.27, 0.12, and 0.39% for Fig. 3a–c). The contribution of each component can then be seen in the scatterplot of the two terms in Eq. (1) against \( \left\langle {\tilde{C}_{l}^{\prime } } \right\rangle \), which shows that the observed \( \left\langle {C_{l}^{\prime } } \right\rangle \) variability mostly occurs thermodynamically, i.e., without change in \( P_{\omega } \) (Fig. 3d). This thermodynamic driving of \( \left\langle {C_{l}^{\prime } } \right\rangle \) is qualitatively reproduced in MIROC5, but not in MIROC3.2 (Fig. 3e, f).

To summarize, the above results indicate that the tropical-mean C l variability in the absence of any change in radiative forcing, i.e., the natural variability, is governed by ENSO and occurs through thermodynamic processes. These observed features are better reproduced in MIROC5. However, it may not guarantee that the response of C l to the change in radiative forcing in MIROC5 is more reliable than that in MIROC3.2. The question of how the natural variability is related to the externally induced climate change is examined in the next section using the 4 × CO2 experiments.

4 Three timescales of the low-cloud response

4.1 Adjustment, fast and slow responses

Following previous studies that showed a quasi-linear relationship between the changes in the global-mean radiative budgets and in SAT under the doubling of CO2 (Gregory et al. 2004; Gregory and Webb 2008), we use the global-mean SAT response, denoted as ΔSATg, defined by the annual- and ensemble-mean difference between the control and 4 × CO2 experiments for each model. Assuming that the radiatively forced response of x, i.e., Δx, can be represented by a linear function of ΔSATg, we write

$$ \Updelta x \approx \alpha_{x} \Updelta {\text{SAT}}_{g} + \Updelta x_{0} $$
(2)

where α x is the regression slope of Δx against ΔSATg while Δx 0 is the interception. By definition, Δx 0 represents a component of Δx occurring without change in SATg and hence is referred to as the ‘adjustment’. The rate of response proportional to ΔSATg, α x , measures the sensitivity of x to the global-mean surface warming and is called ‘feedback’ throughout the paper. Specifically, a change in x may not necessarily feedback to SAT, but we use the term (except for αSAT) in an analogical sense to the change in radiative fluxes. Both the adjustment and feedback are evaluated on an annual basis using 20-year ensemble runs, so that the number of samples becomes 200 and 120 for MIROC3.2 and MIROC5, respectively.

The local αSAT is first presented in Fig. 4a, c. The surface warming patterns are similar to each other in several aspects: larger warming over land than over the ocean, well-known polar amplification around the Arctic, and less warming or slight cooling over the Antarctic circumpolar region. These features have been identified in realistic climate change simulations (Solomon et al. 2007). Given the fact that the change in global-mean radiative fluxes either at the top of atmosphere or on the surface is well fitted by Eq. (2), and that the change in cloud shortwave radiation is greatly affected by the change in low cloud (Klein and Hartmann 1993), we would expect a quasi-linear relationship between the global-mean ΔC l and ΔSATg, which is, however, not observed (Fig. 4b, d). For the first 20 years, the ensemble- and global-mean ΔC l tends to show a monotonic decrease in MIROC3.2 and increase in MIROC5 (blue symbols). Afterwards, ΔC l appears to fluctuate more independently of ΔSATg, as indicated by the weak correlation of r = −0.21 and −0.23.

Fig. 4
figure 4

Differences in annual-mean fields between the 4 × CO2 and control runs (Δ): a, c regression of the annual-mean ΔSAT (K K−1) on ΔSATg in the 10-member ensemble of MIROC3.2 and the 6-member ensemble of MIROC5, b, d scatter plot of the global-mean oceanic ΔC l (%) against ΔSATg in MIROC3.2 and MIROC5. Blue triangles are the ensemble-means from the 20 years integration whereas red crosses denote the values from a single 150 years run

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We calculated the correlation of the local ΔSAT and the global-mean ΔC l using the 150-year single run, which revealed that the global-mean ΔC l is highly correlated with ΔSAT over the eastern equatorial Pacific (not shown). This suggests that the global-mean ΔC l is better explained in terms of the projection on to the natural variability shown in Fig. 2. Because of a great similarity in the temporal evolution between the global-mean and tropical-mean ΔC l , we use ΔC l averaged over the tropical oceans (30º S - 30º N) and plot it against ΔSST in the Niño 3 region (Fig. 5). It is evident that ΔC l is more coherent with the Niño 3 ΔSST than ΔSATg; the correlation after 20 years reaches r = −0.86 and −0.69 in MIROC3.2 and MIROC5, respectively. It is interesting to note that the regression slope, −0.59 and −0.25% K−1, is nearly identical to the slope obtained from the natural variability presented in Fig. 3b, c (also represented by the dashed lines in Fig. 5). This coincidence implies that ΔC l on a time scale longer than 20 years can be constrained by the natural variability associated with ENSO, which has observational counterparts. By referring to Fig. 3a as the observational estimate, the slow negative C l feedback may be overestimated in MIROC3.2. Since the annual-mean changes in a single run include natural variability, one may suspect that the slope of the slow change simply reflects the internal fluctuation in a quasi-equilibrated climate but not the forced response. It is, however, not true, and the decadal-mean changes (red circles in Fig. 5) indeed show the decreasing/increasing tendency well fitted by the slope of the internal variability.

Fig. 5
figure 5

Same as Fig. 4b, d but for the tropical-mean ΔC l (%) against ΔSST (K) in the Niño 3 region. Blue triangles are the annual- and ensemble-averages from the 20 years integration whereas yellow stars indicate the values at the first month. Green crosses, red circles, and thick lines denote the annual- and decadal-mean values and the regression slope for the single 150 years run. The background dashed lines are the slopes for the intrinsic variability shown in Fig. 3b, c

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While it is encouraging that a part of ΔC l can be constrained by natural variability, Fig. 5 reveals that the total ΔC l averaged over the entire period is not determined by the slow response. During the first few years, ΔC l tends to be negative in MIROC3.2 while positive in MIROC5, as seen in the ensemble-mean response for the 20-year runs (blue symbols in Fig. 5). It is this fast response that determines the sign of the low-cloud response in the two models. The mechanism of the fast response is therefore the heart of the low-cloud change to 4 × CO2 as will be elaborated in Sect. 4.2.

It is clear that ΔC l depends on ΔSST in a nonlinear fashion, hence Δx 0 in Eq. (2) may not be a good measure for the initial adjustment of clouds. We therefore used ΔC l at the initial month of the ensemble, as presented by stars, which show a slight reduction of −0.23 and −0.28% in MIROC3.2 and MIROC5. This decrease is almost independent of both ΔSATg and the Niño 3 ΔSST, and is discussed further in this section.

In simple models for low clouds, the change in C l is often argued to be coupled with changes in the PBL thickness, Z PBL (Larson et al. 1999; Caldwell and Bretherton 2009). The adjustment component of Z PBL is shown in Fig. 6a, b. Because of the different turbulence scheme, the mean Z PBL is somewhat different between MIROC3.2 and MIROC5, the latter showing deeper PBL (contours in Fig. 6a, b). Nevertheless, the patterns of ΔZ PBL0 appear to be similar to each other in terms of sign and magnitude; they both show the initial shoaling of the PBL. Interestingly, the ‘feedback’ component of Z PBL is much smaller (not shown), indicating that Z PBL is sensitive to the direct radiative forcing but not so to slow SST increases.

Fig. 6
figure 6

Adjustment components of the response in the 20 years ensemble: a ΔZPBL (m) in MIROC3.2, b ΔZPBL in MIROC5, c ΔQ (W m−2) in MIROC3.2, d ΔQ in MIROC5. White contours in a, b indicate climatological-mean ZPBL in the control run

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Among the various factors controlling Z PBL, such as buoyancy flux at the surface, cumulus mass flux, and LTS, the buoyancy input from the surface plays a dominant role over the tropical oceans (Medeiros et al. 2005). Indeed, the adjustment components of the surface heat flux (sum of the sensible and latent fluxes, denoted as Q) are negative over most of the tropical oceans (Fig. 6c, d). They indicate the reduction of buoyancy production required for deepening the PBL and thereby seem to explain the negative ΔZ PBL0. In the tropospheric adjustment process, Q is known to change without any change in SATg (Gregory and Webb 2008). Andrews et al. (2009) demonstrated that the positive downward radiative forcing is smaller at the surface than at the tropopause, which results in a rapid reduction in Q to accomplish the energy balance in the troposphere (cf. their Fig. 8). The results shown in Fig. 6c, d are consistent with this argument and a thinner PBL and low-cloud layer are thus a robust part of the tropospheric adjustment at least in the two models.

4.2 Mechanism for fast response

We need to elucidate the reasons why the tropical-mean \( \Updelta C_{l} \) decreases in MIROC3.2 and increases in MIROC5 on a fast time scale (Fig. 4b, d). For this purpose, the ‘feedback’ components, α in Eq. (2), are calculated for C l , ω500, LTS, and SST using the ensemble of 20-year runs. It should be noted that a positive C l feedback means an increase of C l in response to the positive ΔSATg, corresponding to a negative cloud shortwave feedback.

Figure 7a, b compares the feedback for C l over the tropical oceans in MIROC3.2 and MIROC5. As SATg increases, C l decreases over the equatorial Pacific while increasing over the southern subtropics in both models. A major difference is found over the Indian Ocean and the northern subtropical Pacific, where C l decreases in MIROC3.2 but increases in MIROC5. The C l feedback patterns are consistent with feedbacks in both ω500 and LTS (Fig. 7c–f). The ω500 feedback, αω, is negative over the equatorial Pacific and positive over the mean ascending regions, indicating a slowdown of the tropical circulation. This response is similarly found in the two models as well as being reported in realistic scenario experiments (e.g., Vecchi et al. 2006). The LTS feedback, αLTS, is overall positive in the tropics, but shows a horizontal inhomogeneity in its magnitude; αLTS is relatively small near the equator while large over the southern subtropical Pacific. They match well the negative and positive feedbacks due to C l changes (Fig. 7a, b). Over the western off-equatorial Pacific, both αω and αLTS are large in MIROC5 compared to MIROC3.2, which appears to match the greater increase in C l (Fig. 7b, d, f).

Fig. 7
figure 7

Feedback components of the response in the 20y ensemble: a, b ΔC l (% K−1) in MIROC3.2 and MIROC5, respectively, c, d Δω500 (hPa dy−1 K−1), e, f ΔLTS (K K−1), and g, h ΔSST (K K−1). The solid and dashed contours in c, d indicate the climatological-mean ω500 in the control run (+20 and −20 hPa dy−1), and the contours in e, f denote the mean LTS of 15 K in the control run

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The fast response of the atmosphere occurring over several years can ultimately be attributed to changes in the tropical SST that responds to the radiative forcing even on such a time scale. Figure 7g, h shows that SST warms as much as SATg during the 20-year period, i.e., \( \alpha_{\text{SST}} \sim 1 \). Yet, the warming is not uniform and a greater SST increase accompanies a smaller increase in LTS and an ascending tendency in ω500, for example, over the central-eastern equatorial Pacific in MIROC5. This correspondence of the spatial patterns between changes in SST, LTS, ω500 and C l has been identified in realistic climate change simulations as well (Watanabe et al. 2011b). Despite the warming of the ocean surface everywhere in the tropics, αLTS is positive, which indicates more warming of the lower troposphere above the PBL. The entirely positive αLTS is in contrast to the pattern of αω, which cannot be uniformly positive or negative in accordance with the mass conservation of the tropical air mass. This suggests that the tropical-mean, but not regional C l response is primarily controlled by the change in stability but not the circulation.

In order to verify the above inference, the cloud regime composite used in Sect. 3 is applied to the fast response. Namely, Eq. (1) is rewritten for Δ:

$$ \Updelta \tilde{C}_{l} \simeq \int\limits_{\omega } {\Updelta P_{\omega } C_{l}^{\text{CTL}} (\omega )d\omega } + \int\limits_{\omega } {P_{\omega }^{\text{CTL}} \Updelta C_{l} (\omega )d\omega } $$
(3a)
$$ \quad\quad \simeq \int\limits_{s} {\Updelta P_{s} C_{l}^{\text{CTL}} (s)ds} + \int\limits_{s} {P_{s}^{\text{CTL}} \Updelta C_{l} (s)ds} $$
(3b)

where \( \Updelta \tilde{C}_{l} \) is the reconstruction of \( \Updelta C_{l} \), \( P_{\omega }^{\text{CTL}} \) the mean PDF in the control run, \( \Updelta P_{\omega } \) the PDF difference between the control and the 4 × CO2 runs, \( C_{l}^{\text{CTL}} (\omega ) \) and \( \Updelta C_{l} (\omega ) \) are similar to \( P_{\omega }^{\text{CTL}} \) and \( \Updelta P_{\omega } \) but for the composite of C l with respect to ω500. The subscript of ω in (3a) can be replaced with LTS, denoted as s in (3b). When we choose ω500 as a reference, the first and second terms represent the dynamical and thermodynamic components of \( \Updelta \tilde{C}_{l} \), respectively. The physical meaning of the terms becomes opposite for s. It is possible to construct a joint PDF using ω500 and s, but we carried out the calculation separately because the two variables are not independent (not shown). The regime composite of the observed C l anomaly on the two-dimensional phase plane has been computed by Medeiros and Stevens (2011), who show that the C l anomaly depends more on s (cf. their Fig. 2).

The regime composite \( C_{l}^{\text{CTL}} (\omega ) \), and \( P_{\omega }^{\text{CTL}} \) are represented by blue curves in Fig. 8a, c. As is well known, most of the tropics are occupied by weak subsidence except for a small area having a strong ascent; \( P_{\omega }^{\text{CTL}} \) is thus skewed in both models. When \( C_{l}^{\text{CTL}} (\omega ) \) is compared with satellite observations (cf. Fig. 1 of Bony and Dufresne 2005), MIROC3.2 is found to underestimate the amount of C l in the subsidence regime while MIROC5 overestimates in the convective regime. Nevertheless, the C l responses, i.e., \( \Updelta C_{l} (\omega ) \), in each regime resemble each other: increasing for ω500 < 0 and decreasing for ω500 > 0. This indicates that, in spite of the opposite sign of the tropical-mean ΔC l , low cloud is suppressed in the 4 × CO2 runs over the subtropical cool oceans where \( C_{l}^{\text{CTL}} (\omega ) \) dominates. The tropical-mean ΔC l is determined by a subtle residual; the \( C_{l} (\omega ) \) reduction in the subsidence regime is prevailing over the enhancement in the ascent regime, leading to the net decrease in MIROC3.2, and vice versa in MIROC5. A certain difference between \( C_{l}^{\text{CTL}} (\omega ) \) and \( C_{l}^{\text{CTL}} (\omega ) \) + \( \Updelta C_{l} (\omega ) \), together with a similarity between \( P_{\omega }^{\text{CTL}} \) and \( P_{\omega }^{\text{CTL}} \) + \( \Updelta P_{\omega } \), clearly indicates that the thermodynamic change in each cloud regime is the major factor for \( \Updelta \tilde{C}_{l} \).

Fig. 8
figure 8

Low-cloud regime diagrams: a, b C l composites (%) with respect to ω500 (hPa dy−1) and LTS (K) in MIROC3.2, c, d same as a, b but for MIROC5. Blue (red) curves indicate the composite average in the control (4 × CO2) run, and the shading denotes one std dev. The PDF in the control run (4 × CO2) is also shown by the blue (red) curve at the bottom

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The thermodynamic constraint to ΔC l is expressed in terms of the PDF for LTS, ∆P s , in (3b). Indeed, \( P_{s}^{CTL} + \Updelta P_{s} \) is displaced toward a higher value in both models, resulting in a positive contribution to \( \Updelta \tilde{C}_{l} \) (Fig. 8b, d). The composite of \( \Updelta C_{l} (s) \) is negative for large LTS, indicating that the second term in (3b) works to reduce C l . The shift in P s is small in MIROC3.2. Because of this and underrepresentation of the mean \( C_{l} (s) \), the thermodynamic contribution \( \Updelta P_{s} C_{l}^{\text{CTL}} (s) \) will be small and thus cannot overcome the negative effect due to the dynamic component in MIROC3.2. To summarize, both similarities and differences are identified in the cloud regime changes in the two models. The major similarity is the dominant thermodynamic driving of ΔC l in which a more stable condition, as represented by ∆P s , should favour a positive ΔC l . The differences are mostly in the quantitative sense, e.g., smaller ∆P s in MIROC3.2 which, however, determines the sign of the tropical-mean ΔC l . In order to examine the extent to which the similarity found between the two models is generally valid, we analyse the multi-model outputs obtained from the CFMIP1 in the next section.

5 Robust thermodynamic changes in CFMIP models

Given the dominant thermodynamic effect on ΔC l in MIROC, we extend the regime analysis to outputs from the CFMIP1 models. We use cloud fraction but not C l because the models providing temperature and/or ω500 lack the C l data obtained from the ISCCP simulator. The composite cloud fraction sorted by LTS is calculated either on the model level or on the pressure level and then collectively plotted in Fig. 9. For reference, we computed a similar composite diagram using the CALIPSO data (see Sect. 2.5 for the method).

Fig. 9
figure 9

Regime composite of the cloud fraction in the lower troposphere over the tropical oceans as sorted by LTS (shading), together with its PDF (curves at the bottom of each panel): a CloudSAT/CALIPSO from June 2006 to May 2007, b MIROC3.2, c MIROC5, d–i CFMIP1 models, all from control runs. The vertical axis is the normalized pressure. In b–i, contours indicate the difference between the control and either 4 × CO2 or 2 × CO2 runs (intervals ±1, 2, 4, 6, 8, 10%), and blue (red) curves in the bottom panels are the PDF for the control (4 × CO2 or 2 × CO2) run. The grey shading in the PDF gives the definition of stable regime (see text)

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Before examining the cloud changes in 2 × CO2 and their differences among the models, we compare the mean cloud fraction between CALIPSO and GCMs (shading in Fig. 9). The satellite-based estimate of the cloud fraction (Fig. 9a) reveals the following characteristics: a maximum of more than 30% occurring at the highest value of LTS, and a gradual increase of the cloud layer altitude as LTS decreases. These features of the mean low-cloud fraction may also be seen when we make the longitude-height section along the subtropical eastern oceans (Wang et al. 2004). All the GCMs not only fail to reproduce the cloud distribution derived from CALIPSO but also show different types of bias. Namely, low clouds are overestimated for low LTS in MIROC5, CCSM3, and GISS ER, whereas overall they are underestimated in MIROC3, CCCma, and GFDL CM2.0. The cloud layer is too thin in MRI GCM. The causes of these biases would involve various factors and are beyond the scope of this study, but we need to bear them in mind when comparing the cloud change in the 2 × CO2 runs.

The divergence of the mean cloud distribution in GCMs prevents us from detecting and understanding the consistent change in the cloud fraction in the 2 × CO2 experiments (contours in Fig. 9). Yet, we can identify some consistency although it may not necessarily explain the different magnitude and sign of the total low-cloud change. For example, a relatively large change in the cloud fraction is found at small LTS in models that overestimate the mean cloud there (e.g., MIROC5, CCSM3, and GISS ER). At large LTS, many models show an increase and decrease of clouds above and below the mean cloud layer, suggesting an upward shift of the cloud layer. This accompanies an asymmetry in the cloud amount change, either a greater increase (e.g., MIROC5, CCSM3, and GISS ER) or decrease (e.g., MIROC3, INM, and MRI), probably resulting in a non-zero change of the low-cloud amount.

Despite large differences in the mean cloud fraction and its changes among GCMs, the change in the thermodynamic condition P s has a common structure, which represents a shift of the PDF peak to larger values (bottom panels in Fig. 9). While the degree of the PDF shift depends on the model (for example, it is large in CCSM3 but small in INM), this coincidence indicates that the changing thermodynamic constraint as found in the two MIROC models (Fig. 8b, d) is a robust part of the climate change. If the cloud change at a given LTS (contours) does not prevail, this thermodynamic effect should act to increase the low cloud in all the models.

The positive shift of P s , i.e., increased stability, can also be represented on a geographical map by defining the frequency of the stable condition:

$$ f_{s} = \frac{1}{N}\sum\limits_{n} {\delta _{n}} ,\quad \delta _{n} = \left\{ {\begin{array}{*{20}c} {1\quad {\text{for }}s_{n} \ge s_{0} } \\ {0{\text{ }}\quad {\text{otherwise }}} \\ \end{array} } \right. $$
(4)

where N indicates the number of samples at a grid point (N = 240), and s 0 is the threshold of the LTS. In the reanalysis, we may set s 0 = 15 K (shaded region in Fig. 9a). For the GCMs, we need to take the mean bias into account, so that the value is defined for each model: s 0 = 15 K for CCCma, INM CM3.0, and MRI CGCM2.3.2, s 0 = 16 K for NCAR CCSM3, and s 0 = 13 K for GFDL CM2.0, GISS ER, and MIROC. The choice of s 0 is somewhat subjective, but the area of f s greater than 0.9 in the control runs (contours in Fig. 10) indicates that it is indeed capturing the mean subtropical low-cloud regions in all the models.

Fig. 10
figure 10

Difference in the occurrence frequency of stable regime, ∆f S, between the control and increased CO2 runs: a MIROC3.2, b MIROC5, c–h CFMIP1 models. The grey contours indicate f S = 90% in the control run. The values of ∆f S in a, b have been divided by factor two for comparing with the other panels based on 2 × CO2 runs. The threshold for f S is indicated in Fig. 9

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As expected, the change in f s to the radiative forcing, i.e Δf s, is overall positive in the tropics, and shows similar spatial patterns among the models. Remarkably, a weak positive Δf s is commonly found over the subtropical Pacific and Atlantic. In contrast to the diversity in magnitude and sign of Δf s near the equator, this robust response in the subtropics suggests that the shallow trade cumulus clouds are stimulated by the frequent occurrence of stable conditions. It is somewhat surprising that Δf s is small or even negative over the eastern subtropical oceans where the mean f s is large. These areas mostly satisfy a condition of high LTS in the control runs, which may therefore not change drastically under the warmed climate.

6 Concluding discussion

Motivated by the fact that the two different versions of the climate model MIROC show opposite signs of cloud shortwave feedback to global warming (positive feedback in MIROC3.2 and negative feedback in MIROC5), we investigated the mechanisms of the tropical low-cloud response to abrupt increases in atmospheric CO2 concentration using two sets of ensemble 4 × CO2 experiments based on those models. The major results are summarized as follows.

  1. 1.

    An initial reduction in the tropical-mean C l occurs in both models, which is likely the cause of the positive cloud shortwave forcing (Fig. 18 of Watanabe et al. 2010). The decrease of C l is accompanied by a shoaling of the PBL due to suppressed surface heat fluxes (Fig. 6), possibly as a part of the tropospheric adjustment.

  2. 2.

    The feedback of C l can be separated into two timescales: fast and slow components, emerging during the first several years and after about 20 years, respectively. The slow component commonly shows a gradual decrease of the tropical-mean C l , the rate of which matches well with the slope determined by the C l response to ENSO in the control runs.

  3. 3.

    The fast component in the two models shows an opposite sense of decrease in MIROC3.2 and increase in MIROC5, which are crucial for the total C l response and consistent with the different cloud shortwave feedbacks between the two models. However, changes in the C l regime diagram, i.e., the decrease over the subsidence regime and increase over the other subtropical regions where a thermodynamic condition favourable for C l happens more frequently, are qualitatively similar to each other. The sign of the tropical-mean C l is thus determined by a subtle residual of the increase and decrease of the regional C l .

  4. 4.

    The frequency change in the thermodynamic condition measured by LTS is similarly found in six other climate models despite a large difference of both the mean and the changes in the low-cloud fraction for a given LTS. This suggests that the response of the thermodynamic constraint for C l to increasing CO2 concentration is a robust part of the climate change.

The second finding partly coincides with conclusions in Dessler (2010). The cloud response to radiative forcing shows up primarily on the fast time scale in our experiments and is distinct from the cloud response to natural climate variability. This implies that the ENSO-related C l variability cannot be used to constrain the C l response to climate change. At the same time, there might be confusion about the time scale of these responses. Namely, Dessler (2010) discussed the observational constraint on short-term variability, which corresponds to the natural variability which appeared on the long time scale in our 4 × CO2 experiments (Fig. 5). This apparently opposite result could arise from the experimental design of the abrupt CO2 increase. Since the time scale of the fast response depends not only on the system’s inertia (cf. Held et al. 2010) but also on the time scale of the change in the radiative forcing, the fast response identified in this study appears on much longer time scales in realistic twentieth century and future scenario runs (Watanabe et al. 2011b).

On one hand, the above arguments may be somewhat discouraging because they suggest that the radiatively forced C l response can hardly be constrained from the observed natural variability. On the other hand, the response of the thermodynamic condition to the abrupt CO2 increase, i.e., ΔLTS, which shows a large similarity among the models both in terms of sign and horizontal distribution (Fig. 10), is encouraging to the modelling groups. This suggests that the LTS change is not crucially dependent on the details of cloud representation such as sub-cloud layer and coupling between cloud physics and turbulence. Yet, the magnitude of ΔLTS was largely different among the eight models analysed here, so that further studies are needed to deepen our understanding of the LTS change under global warming.

In contrast to the robust thermodynamic change discussed above, the change in the vertical structure of low clouds for a given LTS is complex and is still divergent among the models (Fig. 9). Even though the thermodynamic contribution to ΔC l (first term in Eq. 3b) is positive in all the models, any cloud structure change due to other processes (second term in Eq. 3b) would have a positive contribution to ΔC l in some models but negative in others. It is not clear what processes are responsible for the latter, and a systematic approach, not simply comparing the GCM outputs, is desirable to pursue this question. For example, a single column model derived from a GCM and therefore including all the physical processes represented therein will be a useful tool to examine the cloud response to a prescribed large-scale forcing (Zhang and Bretherton 2008). At the same time, we anticipate that the ongoing second phase of CFMIP based on newer versions of GCMs will provide another set of multi-model ensemble. It is thus imperative to analyse and compare the cloud response between the two CFMIP ensembles when they become available. We will attempt to contribute to such activity, and also plan to generate another model ensemble based on a hybrid version of MIROC3.2 and MIROC5 in which individual parameterization schemes can be interchangeable. The results will be reported elsewhere.