1. Introduction
Observational evidence indicates that the global surface temperature (GST) has exhibited signs of a muted or stalled warming since the beginning of the twenty-first century (Easterling and Wehner 2009; Knight et al. 2009; Solomon et al. 2010; Liebmann et al. 2010; Cowtan and Way 2014). Several mechanisms have been proposed to account for the muted global warming, including external cooling forcing due to solar radiation (Lean and Rind 2009; Hansen et al. 2011; Kaufmann et al. 2011) and internal climate variability (Kosaka and Xie 2013; England et al. 2014; Maher et al. 2014; Watanabe et al. 2014). It has been suggested that the primary source of the climate variability responsible for the slowdown of warming is the increasing deep-ocean heat uptake during this period (Hansen et al. 2011; Meehl et al. 2011; Kuhlbrodt and Gregory 2012; Balmaseda et al. 2013; Guemas et al. 2013; Chen and Tung 2014; Drijfhout et al. 2014; Kosaka and Xie 2013, 2015). There are several recent studies indicating that the volcanic and aerosol forcing may contribute to the recent slowdown of warming (e.g., Solomon et al. 2011; Santer et al. 2014; Haywood et al. 2014; Schurer et al. 2015). Most recently, the work of Karl et al. (2015) and Hausfather et al. (2017) seems to suggest that the global warming rate in the last two decades could be significantly underestimated owing to biases in ocean measurements.
The recent studies of Wu et al. (2007), Semenov et al. (2010), DelSole et al. (2011), and Wu et al. (2011) present statistical evidence indicating that the warming phase of a multidecadal oscillation associated with the thermohaline is the main mechanism responsible for the unprecedented warming pace occurring in the last two decades of the twentieth century. Therefore, both the fast warming pace in the last two decades of the twentieth century and the slowdown of warming in the first decade of the twenty-first century can be interpreted by the combined effect of external forcing (Trenberth and Fasullo 2009) and internal climate variability (Fyfe et al. 2013; Maher et al. 2014; Schmidt et al. 2014). Trenberth and Fasullo (2013) further pointed out that the apparent hiatus could be attributed to an increasing trend in heat storage into deep oceans in the past decade. The main objective of this paper is to perform a process-based decomposition of the surface temperature difference between two decades: one at the beginning decade and the other at the end of the fast warming since the 1980s. Specifically, based on the energy balance principle, we attempt to quantify how much of the warming between the two periods is directly due to the increase of CO2 alone and how much of the additional warming is associated with oceanic heat storage and other climate feedback processes, such as the surface albedo, water vapor, clouds, surface evaporation, and sensible heat flux feedbacks, as well as changes in atmospheric circulation. Because the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) does not include information of natural and/or anthropogenic aerosols, our analysis presented below does not include information of the aerosol effect.
The remaining part of this paper is organized as follows. Section 2 describes the data and presents the key features of the difference in the climate mean states of the two periods. Section 3 describes the method for the process-based decomposition. The geographical distributions of process-based decompositions are given in section 4. Section 5 presents the results of process-based decompositions for the global mean of the surface temperature change and its global pattern. Section 6 discusses regional decompositions. The conclusions are given in section 7. The appendix discusses the main sources of the error term in our process-based decomposition analysis, corrections, and implications.
2. Data and the decadal mean surface temperature anomalies
All the data used in this study are obtained from the ERA-Interim (Uppala et al. 2008; Dee et al. 2011), as in Deng et al. (2012), Park et al. (2012, 2013), and Deng et al. (2013). The variables considered by us include temperature, specific humidity, ozone mixing ratio, cloud amount, cloud liquid/ice water content, downward solar energy flux at the top of the atmosphere (TOA), and surface albedo, surface sensible, and latent heat fluxes. The time series of the annual mean CO2 concentration from 1984 to 2013 is downloaded from the Earth System Research Laboratory website (http://www.esrl.noaa.gov/gmd/ccgg/trends/).
Figure 1 shows the annual mean and 5-yr running mean of global mean surface temperature anomalies (STAs) from 1979 to 2014, indicating a strong positive trend from the mid-1980s to the late 1990s but only a weaker positive trend in the first decade of the twenty-first century. The results vividly support the consensus in the literature that there are two distinct warming periods from the 1980s to the present (Knight et al. 2009; Liebmann et al. 2010). Based on Fig. 1, we will use the slowdown-warming decade (i.e., 2002–13) as the end decade of the fast warming and 1984–95 as the beginning decade. Therefore the difference between the two periods roughly represents the net warming during the fast warming period from the beginning of the 1990s (corresponding to the middle of 1984–95) to the middle of the 2000s (close to the middle of 2002–13). We calculate the temporal means of each variable for the periods of 1984–95 and 2002–13, referred to as the mean states of 1984–95 and 2002–13, respectively. The symbol Δ denotes the difference in the mean states between 2002–13 and 1984–95.
Time series of the annual global mean surface temperature anomalies (black solid line) and 5-yr running mean (red dashed line) from 1979 to 2014 based on the climatology of 1981–2010. The shadings highlight the analysis periods.
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
Figures 2a and 2b are the decadal mean surface temperature anomalies for the periods of 1984–95 and 2002–13, respectively (the anomalies are defined with respect to the 30-yr mean between 1981 and 2010). It is obvious that the decade of 2002–13 is still much warmer than 1984–95 over most places around the globe, despite the warming rate during the period 2002–13 being weaker. The difference between 2002–13 and 1984–95 (Fig. 2c) exhibits two salient patterns. The first one is the pronounced polar warming amplification (PWA) pattern over the Arctic and a weak PWA over the Antarctic. The PWA is one of the most recognized and well-defined global warming patterns in the trends derived from station observations and all reanalysis products (Polyakov 2002; Johannessen et al. 2004), as well as in all climate model simulations radiatively forced by anthropogenic greenhouse gases (e.g., Holland and Bitz 2003; Gillett et al. 2008; Bindoff et al. 2013; Bracegirdle and Stephenson 2012, 2013; Flato et al. 2013). The second is the relatively stronger warming over the tropical portion of the Indian, Pacific, and Atlantic Oceans than over midlatitude oceans (Hartmann et al. 2013). However, there are three regions that had colder surface temperature anomalies in 2002–13 than in 1984–95. As reported in IPCC Fifth Assessment Report (AR5; Bindoff et al. 2013), the first is the eastern tropical Pacific, the second over the Southern Ocean along the Antarctic Circumpolar Current, and the third over the west coastlines of North America and South America (Fig. 2a vs Fig. 2b; Fig. 2c). To the west of the cooling over the eastern tropical Pacific is a warming pattern over the western tropical Pacific, referred to as a La Niña–like pattern (Meehl et al. 2011; Sohn et al. 2013). The cooling trend over the Southern Ocean (Fan et al. 2014; Armour et al. 2016; Kostov et al. 2016) is surrounded by a weak warming trend in the Antarctic (Comiso 2000; Bertler 2004; Monaghan et al. 2008; Nicolas and Bromwich 2014) and southern subtropics, defined as the warm–cold–warm (WCW) pattern.
Surface temperature anomalies (K): time mean of (a) 1984–93 and (b) 2004–13, (c) their differences, and (d) the sum of partial temperature anomalies (see text for details). The regions marked with black dots in (a) and (b) indicate regions where the results exceed the 0.1 level of statistical significance. The anomalies are defined with respect to the climatology of 1981–2010.
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
3. The process-based decomposition method
The majority of existing methods for studying climate feedback and sensitivity are built on the premise that the temperature change is the response to radiative energy exchange with outer space, and therefore they consider primarily the radiation perturbations at the TOA. Accordingly, the climate forcing and feedback agents are mechanisms that directly affect the radiative budget at the TOA, namely, the incoming solar energy flux at the TOA, changes in the atmospheric composition (e.g., CO2), water vapor, cloud, surface albedo, and lapse rate of atmospheric temperature. The popular TOA-based climate feedback analysis methods include the partial radiative perturbation (PRP) method (Wetherald and Manabe 1988), the cloud forcing analysis method (Cess et al. 1990), and the radiative kernel method (Soden and Held 2006; Soden et al. 2008). Readers may refer to Bony et al. (2006) for a comprehensive review on these methods and Flato et al. (2013) for their applications in assessing climate sensitivity and climate feedbacks in CMIP5 climate simulations. Boer and Yu (2003) extend the PRP method to study spatial patterns of climate sensitivity. However, none of these TOA-based methods calculates the partial temperature changes due to individual feedback processes. In addition, the TOA-based feedback analysis framework cannot explicitly take into consideration the internal nonradiative processes (e.g., oceanic heat storage, convective and large-scale atmospheric energy transport, and surface turbulent fluxes such as evaporation and sensible heat fluxes). Bates (2007) further pointed out that the usage of an equation similar to the amplification formula of electronics in the PRP method is only figurative since the climate system does not follow the physical principles invoked for the electronics application.
The online feedback suppression method is designed to calculate partial temperature change due to a specific feedback process. It requires running a climate model twice: one with all processes on (original climate system) and the other with one specific process turned off (virtual climate system). The difference between such a pair of simulations corresponds to the partial temperate change due to the process under consideration (Hall and Manabe 1999; Schneider et al. 1999). However, the difference between two different systems inferred from the online feedback suppression method does not reflect exactly the effect of the suppressed feedback in the original climate system because the difference also includes the compensating effects from the other feedbacks (Cai and Lu 2009). As a result, the partial temperature change due to a specific feedback inferred by the online feedback suppression method also includes the difference in the other feedbacks between the original and virtual climate system.
































Replacing Δ
Maps of direct energy flux perturbations at the surface [
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
Here, we wish to add that like any other offline feedback analysis methods, our feedback analysis is a postprocessing diagnostic that cannot predict changes in other fields. The majority of other offline methods also need the information of the total temperature change as the input field for the feedback analysis. However, the CFRAM method allows us to explicitly calculate partial temperature changes associated with individual processes without requiring the information of the total temperature change. The sum of these partial temperature changes can be directly compared to the total temperature change in observations. It is seen in Fig. 2d that the spatial pattern of
Because ERA-Interim does not include information of natural and/or anthropogenic aerosols, our method does not allow us to make a direct estimate of the aerosol effect, as we have done for other variables. According to Cai and Kalnay (2005), a reanalysis made with a frozen model is still capable of capturing the temperature trend as well as its variations due to an anthropogenic forcing at its full strength (at least 95% level) after a few hundred analysis cycles, even though the forcing itself is never directly assimilated in the analysis. Therefore, the temperature fields derived from ERA-Interim can still capture the temporal cooling due to volcanic forcing and the cooling trend due to anthropogenic aerosol forcing. In our analysis, we obtain all of these partial temperature changes using non-temperature fields (e.g., atmospheric water vapor) derived from ERA-Interim except for three terms: the atmospheric dynamics, oceanic heat storage/dynamics, and offline calculation error terms. Because (i) these three terms use ERA-Interim’s temperature information and (ii) the sum of all partial temperature changes is convergent to the (total) temperature change derived from the reanalysis, we believe that the signals from the volcanic and anthropogenic aerosol forcings are blended in these three terms.
4. Direct forcings, air temperature feedbacks, and surface temperature changes
Displayed in Fig. 3 are the energy flux perturbations at the surface due to the direct effect of individual processes.2 As discussed in Cai and Tung (2012) and Sejas et al. (2016), the enhancement of the downward longwave radiative flux at the surface due to a spatially uniform increase CO2 tends to be stronger over the regions where atmospheric water vapor and/or clouds are scarce, such as polar regions and high elevation areas (Fig. 3a). The reduction of the solar energy flux reaching to the surface (Fig. 3b) is due to the upward trend of the stratosphere ozone (Fig. 4b). Because of a stronger increase of the stratosphere ozone in the tropics as well as more available incoming solar energy, the reduction in the downward solar energy flux at the surface is stronger in the tropics. The melting of sea ice over the Arctic Ocean, as indicated by a substantial reduction of surface albedo (Fig. 4b), results in more solar energy absorbed there (Fig. 3f). The increase of sea ice coverage over most regions along the Antarctic continental shelf leads to a reduction of solar energy absorption due to the increase of surface albedo. The direct effect of an increase (decrease) in atmospheric water vapor is the strengthening (reduction) of the downward longwave radiative fluxes at the surface (Fig. 3g vs Fig. 4c). The relationship of the direct effect of cloud changes strongly depends on the spatial distribution of the incoming solar energy flux. In general, the increase (decrease) of clouds in high latitudes where the incoming solar energy flux is much weaker leads to a stronger (weaker) downward longwave radiative flux at the surface (Fig. 3h vs Fig. 4d). Because of the stronger incoming solar energy flux outside high latitudes, cloud-albedo-induced changes of downward shortwave fluxes at the surface are stronger than their longwave effects. As a result, in the tropics and midlatitudes, the net of the clouds’ direct effect is positive (negative) over the regions where clouds decrease (increase). The remaining four panels in Fig. 3 (i.e., Figs. 3c,d,e,i) are the direct effect of the nonradiative processes and are obtained directly from ERA-Interim. Note that the direct effect of the atmospheric dynamics term (Fig. 3i) is zero everywhere because the energy transport by the atmospheric motions by itself, by definition, has no direct contribution to energy fluxes at the surface.
Maps of differences in radiative feedback agents between 2002–13 and 1984–95: (a) total column-integrated stratosphere ozone (kg m−2),
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1











As in Fig. 3, but for maps of partial surface temperature changes [
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
As in Fig. 3, but for maps of downward thermal radiative energy flux perturbations at the surface or air temperature feedbacks [
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
To explain the linkages among individual direct forcings at the surface (Fig. 3), their air temperature feedbacks (Fig. 6), and surface temperature changes (Fig. 5) via the temperature feedback loop, we consider two special scenarios first and then the general situation [readers may consult Sejas and Cai (2016) for more detailed discussions on the importance of the temperature feedback loop]. The first special case is that most of the direct heating perturbation (without temperature feedbacks) is at the surface. Examples of the first special scenario include the change of the solar energy absorbed by the atmosphere and surface due to the change in the surface albedo Δ
The second special scenario is solely related to the atmospheric dynamics term, in which the energy flux convergence perturbations are caused by changes in atmospheric convections and large-scale atmospheric advective processes and its direct forcing at the surface is zero by definition. Obviously, changes in the surface temperature in this case are entirely through the thermal radiative coupling between the atmosphere and the surface or the air temperature feedback. The comparison of Fig. 4d and Fig. 6i indicates that in the tropics, negative (positive) values of the dynamics-induced air temperature feedback tend to be over the regions where cloud liquid/ice water content increases (decreases). An increase (decrease) of clouds is indicative of the intensification (weakening) of tropical convections, which acts to transport more (less) energy upward, causing warming (cooling) anomalies in the upper atmosphere at the expense of cooling (warming) in the lower atmosphere. As illustrated in Lu and Cai (2009) and Cai and Tung (2012), the dynamics-induced cooling (warming) in the lower troposphere results in a reduction (enhancement) of the downward thermal energy fluxes at the surface, giving rise to negative (positive) values of
For the general situation in which both atmospheric and surface components of a direct forcing Δ
5. Contributions to global mean and pattern
Figure 7a shows the global mean values of these individual
Contributions (ordinate; K) from individual partial surface temperature changes
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
It is seen that the partial surface temperature change due to the increase of CO2 from 1984–95 to 2002–13 alone (i.e., without any feedbacks) explains nearly half (0.15 K) of the observed global mean warming between the two periods. The largest term for the global mean of the surface temperature change turns out to be from the oceanic heat storage term (note that the global mean of oceanic dynamic term is zero), contributing as much as 1.29 K to 〈









For the global pattern contribution analysis, the area A is the entire global surface
6. Contributions to regional patterns
Our regional contribution analysis is focused on the four key differences between the two periods discussed in section 2: (i) relatively large warming over tropical oceans, (ii) a La Niña–like pattern over the tropical Pacific basin, (iii) the pronounced PWA pattern in the northern extratropics, and (vi) the WCW pattern in the southern extratropics.
a. Tropics
The amplitude of the spatial pattern of
As in Fig. 7b, except that the global domain is replaced by (a) the tropics (30°S–30°N), (b) the northern extratropics (north of 30°N), and (c) the southern extratropics (south of 30°S).
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
Some recent studies suggest that the La Niña–like trend of SST in the tropical eastern Pacific can be regarded as a combined effect of the internal climate variability and global warming (Zhang et al. 2011; Dong and Zhou 2014). The OCH process (Fig. 5c) shows a weak cooling effect in the equatorial central Pacific, which seems to be consistent with the strengthening of the upper-ocean meridional overturning circulation proposed by Zhang et al. (2011). Figure 4d shows that clouds have an upward trend in the central and eastern tropical Pacific from 1984–95 to 2002–13. The net effect of the increase in clouds acts to reduce the warming in the central and eastern tropical Pacific (Fig. 5h), thereby contributing positively to the La Niña–like trend of
b. Northern extratropics
The dominant feature of
The four three positive contributors are
c. Southern extratropics
As mentioned in section 2, the spatial pattern of
7. Discussion and conclusions
This study decomposes the climate difference between the periods of 2002–13 and 1984–95 into partial temperature differences due to external forcing and various internal climate processes by applying the climate feedback–response analysis method (CFRAM) to ERA-Interim. Despite that the warming rate during 2002–13 is much lower, the global mean surface temperature of the decade of 2002–13 is 0.27 K warmer than 1984–95. The surface temperature difference between the two periods is characterized by four distinct regional patterns: (i) a pronounced polar warming amplification (PWA) pattern over the Arctic and a relatively weaker PWA over the Antarctic, (ii) the relatively stronger warming over the tropical portion of the Indian, western Pacific, and Atlantic Oceans than over the midlatitude oceans, (iii) a La Niña–like pattern over the tropical Pacific, and (iv) a large-amplitude cooling trend over the Southern Ocean surrounded by a warming trend in the Antarctic and southern subtropics (referred to as the WCW pattern). All these features are consistent with other observational studies and IPCC AR5 climate simulations (Hartmann et al. 2013; Bindoff et al. 2013; Flato et al. 2013).
Our process-based decomposition indicates that the direct effect of the increase of CO2 (0.15 K) is the largest contributor to the global warming between the two periods (about 0.27 K). Changes in clouds contribute about 0.14 K to the global mean warming. Although the energy released by the oceanic heat storage term is partially canceled out by the enhancement of evaporation and sensible heat flux from the surface, the combined effect of these three surface processes still contributes 0.11 K to the global mean warming. The increase in atmospheric moisture adds another 0.1 K to the global surface warming, but the enhancement in tropical convections acts to reduce the surface warming by 0.17 K.
The oceanic heat storage term is responsible for most of the warming in the tropical oceans as well as the cooling over the southern oceans. More atmospheric water vapor and more deep clouds above the western tropical Pacific act to further strengthen the warming there, whereas the reduction of atmospheric water vapor and increase of clouds above the eastern tropical Pacific lead to a cooling trend there. The combined effects of water vapor and cloud feedbacks contribute positively to the La Niña–like pattern.
The ice-albedo feedback is the leading factor responsible for the Arctic PWA pattern, the warming along the coastline of the West Antarctic and Antarctic Peninsula, and the cooling along the coastline of the remaining portion of the Antarctic continent. The atmospheric dynamical feedback is the second largest contributor to the Arctic PWA pattern. The increase of atmospheric water vapor over the Arctic region also contributes substantially to the Arctic PWA pattern.
The period between 1984–95 and 2002–13 exhibits the fastest warming in the past three decades. Our process-based decomposition presented in this study suggests that the ocean heat storage term contributes most of the warming between 2002–13 and 1984–95. The results support the statistical analysis of the unprecedented warming pace occurring in the last two decades of the twentieth century to the ocean heat storage term reported in Wu et al. (2007), Semenov et al. (2010), DelSole et al. (2011), and Wu et al. (2011). Here we further conjecture that the heat release from the vast ocean surface, particularly from the tropical oceans, may have already reached a plateau in the first decade of the twenty-first century (i.e., 2002–13). As a result, the rate of heat release from oceanic storage is likely smaller or even turned negative in the last decade. The conjecture based on the results presented in this paper is consistent with the findings by Kosaka and Xie (2013, 2015), Chen and Tung (2014), and Drijfhout et al. (2014), which suggest that the increasing deep-ocean heat uptake is the predominant mechanism for the slowdown of the warming trend in the last decade.
Finally, we wish to comment on potential uncertainties in our decomposition analysis (see the appendix for more details). Besides having no explicit consideration of aerosol forcings, there are two main sources of errors in our decomposition analysis. One is associated with offline radiative transfer model calculations, which use the time mean fields as the inputs of the radiative transfer model instead of the instantaneous fields. In the appendix, we have explicitly identified the offline calculation errors and attributed them to be mainly associated with the use of longtime mean clouds in the offline radiative transfer calculations instead of the longtime mean radiative fluxes calculated from instantaneous clouds, as reported in Wetherald and Manabe (1988), Taylor and Ghan (1992), Kato et al. (2011), Song et al. (2014a,b), and Sejas et al. (2014). The spatial pattern of the offline calculation errors is negatively correlated with the partial radiative flux perturbations associated with clouds, indicating that the offline calculation overestimates the cloud feedback. In the appendix, we have applied the regression analysis to remove the portion of the offline calculation errors that are correlated with the partial radiative flux perturbations associated with clouds. However, the residual offline calculation errors are still relatively pronounced whose global mean is as large as 0.09 K. The second main source of errors is the uncertainty in some atmospheric components, variables, or surface fluxes provided by ERA-Interim. This type of error has little impact on our decomposition analysis as far as the convergence of individual partial temperature changes to the observed temperature change is concerned. However, this type of error could cause an overestimate of the effect of one individual process at the expense of an underestimate of other processes.
Acknowledgments
We are grateful for the editor (Mingfang Ting) and four anonymous reviewers’ insightful comments and constructive suggestions that led to significant improvements in the presentation. HXM, LYN, and YS are supported by the National Key Research Program of China (2014CB953900), the National Natural Science Foundation of China (41375081), China Special Fund for Meteorological Research in the Public Interest (GYHY201406018), and the Special Funds of Guangdong Province of China (YCJ2013-196). MC is supported by grants from the National Science Foundation (AGS-1354834) and NASA Interdisciplinary Studies Program (NNH12ZDA001N-IDS). YD is supported by the National Science Foundation (AGS-1354402 and AGS-1445956). Calculations for this study were supported by the High-Performance Grid Computing Platform of Sun Yat-sen University and the China National Supercomputer Center in Guangzhou. The datasets used in this study are all freely available on the official websites (http://apps.ecmwf.int/datasets/data/interim-full-mnth/).
APPENDIX
Quantifying Errors of Offline Radiative Transfer Calculations
We here wish to provide additional comments on sources of




Displayed in Figs. A1a,c,e are, respectively, the terms (a), (b), and [(a) + (b)] defined in (A1). It is seen that (i) the pattern of (a) is highly (or almost perfectly) correlated with (b) negatively and (ii) the range of numerical values of (a) is larger than that of (b). The collocation of the opposite sign of (a) and (b) with the magnitude of (a) greater than (b) is the trademark of radiative forcing of clouds at the surface, namely that an increase in clouds would reduce solar energy flux (due to more reflection) but increase longwave flux (due to cloud greenhouse effect) reaching to the surface and vice versa with shortwave effect greater than longwave.
Changes of radiative fluxes at the surface between 2002–13 and 1984–95 (W m−2): (a) the difference in changes of the net downward shortwave radiative fluxes at the surface between ERA-Interim and our offline calculations; (b) as in (a), but for the downward shortwave radiative flux perturbations at the surface due to changes of clouds; (c) as in (a), but for the net downward longwave radiative fluxes at the surface; (d) as in (b), but for the downward longwave radiative flux perturbations; (e) the sum of (a) and (c); and (f) the sum of (b) and (d).
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
To confirm that the source of offline errors is mainly due to using the decadal mean cloud fields as the inputs of the radiative transfer model in our offline calculations (instead of taking the decadal mean of the radiative heating rates calculated using instantaneous cloud fields), we also plot the partial radiative fluxes at the surface due to the decadal mean difference in the cloud fields obtained from our offline calculations. It is seen that the main centers of large values of both shortwave (Fig. A1b) and longwave (Fig. A1d) fluxes as well as the net flux (Fig. A1f), representing the key regions where the decadal changes in cloud fields are pronounced, also appear in Fig. A1a,c,e with the opposite polarity. Therefore, it is mainly the error in cloud fields in our offline calculations that is responsible for






Maps of (a) the shortwave component of the residual error term [i.e., fA1a(x, y) − correction_SW (W m−2)] and (b) correction_SW (W m−2). (c) As in (a), but for [fA1c(x, y) − correction_LW]. (d) As in (b), but for correction_LW. (e) The
Citation: Journal of Climate 30, 12; 10.1175/JCLI-D-15-0742.1
We note that
It should also be pointed out that
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It should be stressed here that the phrase “
The direct effect at the surface of a process is referred to as the corresponding surface energy flux perturbation without considering its associated changes in air and surface temperatures.
The air temperature feedback is akin to the lapse rate feedback, which is defined as the upward thermal radiative energy flux perturbation at the TOA due to the difference between the air temperature and surface temperature changes and commonly used in the PRP method. Here, the air temperature feedback is defined as the downward thermal radiative energy flux perturbation at the surface due to changes in air temperatures, which is one of the terms that directly affect the surface energy balance.