The conceptual deconstruction of the GREB model to understand interactions in the climate system that lead to mean climate characteristics is achieved by defining 11 processes (switches; see Fig. 1). For each of these switches, a term in the model equations is set to zero or altered if the switch is OFF. The processes and how they affect the model equations are briefly listed below (with a short summary in Table 1). The model equations relevant for the experiments in this study are briefly restated in Appendix A1 for the purpose of explaining each experimental set-up in the MSCM.

Ice albedo. The surface albedo (αsurf) and the heat capacity over ocean points (γsurf) are influenced by snow and sea ice cover. In the GREB model these are a direct function of Tsurf. When the ice–albedo switch is OFF the surface albedo of all points is constant (0.1), and for ocean points γsurf follows the prescribed ocean mixed layer depth independent of Tsurf (i.e. no ice-covered ocean).

Clouds. The cloud cover, CLD, influences the amount of solar radiation reaching the surface (αclouds in Eq. A5) and the emissivity of the atmospheric layer, εatmos, for thermal radiation (Eq. A8). When the cloud switch is OFF, the cloud cover is set to zero.

Oceans. The ocean in the GREB model simulates subsurface heat storage with the surface mixed layer (∼ upper 50–100 m). When the ocean switch is OFF, the Focean term in Eq. (A1) is set to zero, Eq. (A3) is set to zero, and the heat capacity of all ocean points is set to that of land points.

Atmosphere. The atmosphere in the GREB model simulates a number of processes: the hydrological cycle, horizontal transport of heat, thermal radiation, and sensible heat exchange with the surface. When the atmosphere switch is OFF, Eqs. (A2) and (A4) are set to zero, the heat flux terms, Fsense and Flatent in Eq. (A1) are set to zero, and the downward atmospheric thermal radiation term in Eq. (A6) is set to zero.

Diffusion of heat. The atmosphere transports heat by isotropic diffusion (fourth term in Eq. A2). When this process is switched OFF, the term is set to zero.

Advection of heat. The atmosphere transports heat by advection following the mean wind field, u (fifth term in Eq. A2). When this process is switched OFF, the term is set to zero.

CO2. The CO2 concentration affects the emissivity of the atmosphere, εatmos (Eq. A9). When this process is switched OFF, the CO2 concentration is set to zero.

Hydrological cycle. The hydrological cycle in the GREB model simulates the evaporation, precipitation, and transport of atmospheric water vapour (Eq. A4). It further simulates latent heat cooling at the surface and heating in the atmosphere. When the hydrological cycle is switched OFF, Eq. (A4) is set to zero, the heat flux term Flatent in Eq. (A1) is set to zero, and viwvatmos in Eq. (A9) is set to zero. Subsequently, atmospheric humidity is zero.

It needs to be noted here that the atmospheric emissivity in the log-function parameterization of Eq. (A9) can become negative if the hydrological cycle, cloud cover, and CO2 concentration are switched OFF (set to zero). This marks an unphysical range of the GREB emissivity function and we will discuss the limitations of the GREB model in these experiments in Sect. 3b.

Diffusion of water vapour. The atmosphere transports water vapour by isotropic diffusion (third term in Eq. A4). When this process is switched OFF, the term is set to zero.

Advection of water vapour. The atmosphere transports water vapour by advection following the mean wind field, u (fifth term in Eq. A2). When this process is switched OFF, the term is set to zero.

Model corrections. The model correction terms in Eqs. (A1), (A3), and (A4) artificially force the mean Tsurf, Tocean, and qair climate to be as observed. When the model correction is switched OFF, the three terms are set to zero. This will allow the GREB model to be studied without any artificial corrections and therefore help to evaluate the GREB model equations' skill in simulating climate dynamics.

It should be noted here that the model correction terms in the GREB model have been introduced to study the response to doubling the CO2 concentration for the current climate, which is a relatively small perturbation if compared against the other perturbations considered above. They are meaningful for a small perturbation in the climate system but are less likely to be meaningful with large perturbations to the climate system (e.g. cloud cover set to zero).

Each different combination of the above-mentioned process switches defines a different experiment. However, not all combinations of switches are possible because some of the process switches depend on each other (see Table 1 and Fig. 1). The total number of experiments possible with these process switches is 656. For each experiment, the GREB model is run for 50 years, starting from the original GREB model climatology, and the final year is presented as the climatology of this experiment in the MSCM database.

In a similar way as described above for the mean climate, the climate response to a doubling of the CO2 concentration can be conceptually deconstructed with a set of GREB model experiments. These experiments help us to understand interactions in the climate system that lead to the climate response to a doubling of the CO2 concentration. However, there are a number of differences that need to be considered.

A meaningful deconstruction of the response to a doubling of the CO2 concentration should consider the reference control mean climate since the forcings and the feedbacks controlling the response are mean state dependent. We therefore ensure that all sensitivity experiments in this discussion have the same reference mean control climate. This is achieved by estimating the flux correction term in Eqs. (A1), (A3), and (A4) for each sensitivity experiment to maintain the observed control climate. Thus, when a process is switched OFF, the control climatological tendencies in Eqs. (A1), (S3), and (S4) are the same as in the original GREB model, but changes in the tendencies due to external forcings, such as doubling the CO2 concentration, are not affected by the disabled process. This is the same approach as in DF11.

For the 2×CO2 response deconstruction experiments, we define 10 boundary conditions or processes (switches; see Fig. 2). The ice albedo, advection and diffusion of heat and water vapour, and the hydrological cycle processes are defined in the same way as for the mean climate deconstruction (Sect. 2a). The remaining boundary conditions and processes are briefly listed below (and a short summary is given in Table 2).

The following boundary conditions are considered.

Topography. The topography in the GREB model affects the amount of atmosphere above the surface and therefore affects the emissivity of the atmosphere in the thermal radiation (Eq. A9). Regions with high topography have lower greenhouse gas concentrations in the thermal radiation (Eq. A9). It further affects the diffusion coefficient (κ) for the transport of heat and moisture (Eqs. A2 and A4). When the topography is turned OFF, all points of the GREB model are set to sea level height and have the same amount of CO2 concentration in the thermal radiation (Eq. A9).

Clouds. The cloud cover in the GREB model affects the incoming solar radiation and the emissivity of the atmosphere in the thermal radiation (Eq. A9). In particular, it influences the sensitivity of the emissivity to changes in the CO2 concentration. A clear-sky atmosphere is more sensitive to changes in the CO2 concentration than a fully cloud-covered atmosphere. When the cloud cover switch is OFF, the observed cloud cover climatology boundary conditions are replaced with a constant global mean cloud cover of 0.7. It is not set to zero to avoid an impact on the global climate sensitivity and to focus on the regional effects of inhomogeneous cloud cover.

Humidity. Similarly to the cloud cover, the amount of atmospheric water vapour affects the emissivity of the atmosphere in the thermal radiation and, in particular, the sensitivity to changes in the CO2 concentration (Eq. A9). A humid atmosphere is less sensitive to changes in the CO2 concentration than a dry atmosphere. When the humidity switch is OFF, the constraint to the observed humidity climatology (flux correction in Eq. A4) is replaced with a constant global mean humidity of 0.0052 kg kg-1. It is again not set to zero to avoid an impact on the global climate sensitivity and to focus on the regional effects of inhomogeneous humidity.

Ocean heat uptake. The ocean heat uptake in GREB is done in two ocean layers. The largest part of the ocean heat is in the subsurface layer, Tocean (Eq. A3). When the ocean switch is OFF the Focean term in Eq. (A1) is set to zero, Eq. (A3) is set to zero, and the heat capacity (γsurf) of all ocean points in Eq. (A1) is set to that of a 50 m water column.

The total number of experiments with these process switches is 640. For each experiment, the GREB model is run for 50 years, starting from the original GREB model climatology, with a doubling of the CO2 concentrations in the first time step. The changes over the 50-year period relative to the original GREB model climatology of these experiments are presented in the MSCM database.

There are a number of different scenarios for external boundary condition changes in the MSCM experiment database. They include different changes in the CO2 concentration and in the incoming solar radiation. A complete overview is given in Table 3. A short description follows below.

The skill of the GREB model is illustrated in Fig. 4 by running the GREB model without the correction terms. For reference, we compare this GREB run with the observed mean climate and seasonal cycle (this is identical to running the GREB model with correction terms) and with a bare world. The latter is the GREB model with all switches OFF (radiative balance without an atmosphere and a dark surface). In comparison with the full GREB model, this illustrates how much all the climate processes affect the climate.

The GREB model without correction terms captures the main features of the zonal mean climate, the seasonal cycle, the land–sea contrast, and even smaller-scale structures within continents or ocean basins (e.g. seasonal cycle structure within Asia or zonal temperature gradients within ocean basins). For most of the globe (<50∘ from the Equator), the GREB model root mean square error (RMSE) for the annual mean Tsurf is less than 10 ∘C relative to the observed (see Fig. 4g). This is larger than for state-of-the-art CMIP-type climate models, which typically have an RMSE of about 2 ∘C (Dommenget, 2012). In particular, the regions near the poles have high RMSE. It seems likely that the meridional heat transport is the main limitation in the GREB model given tropical regions that are too warm, polar regions that are generally too cold, and a seasonal cycle in the polar regions that is too strong in the GREB model without correction terms.

The GREB model performance can be put in perspective by illustrating how much the climate processes simulated in the GREB model contribute to the mean climate relative to the bare world simulation (see Fig. 4). The GREB RMSE to observed is about 20 %–30 % of the RMSE of the bare world simulation (not shown), suggesting that the GREB model has a relative error of about 20 %–30 % in the processes that it simulates or due to processes that it does not simulate (e.g. ocean heat transport).

Understanding what is causing the mean observed climate with its regional and seasonal difference is often central to understanding climate variability and change. For instance, the seasonal cycle is often considered as a first-guess estimate for climate sensitivity (Knutti et al., 2006). In the following analysis, we will give a short overview of how the 10 processes of the MSCM experiments contribute to the mean climate and its seasonal cycle. For these experiments, we use the GREB model without flux correction terms.

In the discussion of the experiments, it is important to consider the fact that climate feedbacks are contributing to the interactions of climate processes. The effect of a climate process on the climate is a result of all the other active climate processes responding to the changes that the climate process under consideration introduces. It also depends on the mean background climate. Therefore, the particular combination of switches with which GREB model experiments are discussed does matter. For instance, the effect of ice–snow cover is stronger in a much colder background climate, but it is also affected by feedback in other climate processes, such as the water vapour feedback. We will therefore consider different experiments or different experiment sets to shed some light on these interactions.

In Figs. 5 and 6 the contributions of each of the 10 processes (except the atmosphere) to the annual mean climate (Fig. 5) and its seasonal cycle (Fig. 6) are shown. In each experiment, all processes are active, but the process of interest and the model correction terms are turned OFF. The results are compared against the complete GREB model without the model correction terms (all processes active; expect model correction terms). For the hydrological cycle we will discuss some additional experiments in which the ice–albedo feedback is turned OFF as well.

The ice–snow cover (Fig. 5a) has a strong cooling effect, mostly at high latitudes in the cold season, which is due to the ice–albedo feedback. However, in the warm season (not shown) the insulation effect of the sea ice actually leads to warming, as the ocean cannot cool down as much during winter as it does without sea ice.

The cloud cover in the GREB model is only considered as a given boundary condition but does not simulate the formation of clouds. Therefore, it does not include cloud feedbacks. However, mean cloud cover influences the radiation balance of solar and thermal radiation and therefore affects the mean climate and its seasonal cycle. Figure 5b illustrates the fact that cloud cover has a large net cooling effect globally due to the solar radiation reflection effect dominating over the thermal radiation warming effect. Previous studies on the cloud cover effect on the overall climate mostly focus on radiative forcings estimates, but to our best knowledge, they do not discuss how much the mean surface temperature is affected by the mean cloud cover (e.g. Rossow and Zhang, 1995).

It is interesting to note that the strongest cooling effect of cloud cover is over regions with fairly little cloud cover (e.g. deserts and mountain regions). Here it is important to point out that the climate system response to any external forcing or changes in the boundary conditions, such as CO2 forcing or removing the cloud cover, is dominated by internal positive feedback rather than the direct local forcing effect (e.g. see the discussion of the global warming pattern in DF11).

The most important internal positive feedback is the water vapour feedback, which amplifies the effect of removing the cloud cover. This feedback is stronger over dry and cold regions (DF11) and therefore amplifies the effects of removing the cloud cover over deserts and mountain regions.

The large ocean heat capacity slows down the seasonal cycle (Fig. 6c). Subsequently, the seasons are more moderate than they would be without the ocean transferring heat from warm to cold seasons. This is, in particular, important in the middle and higher latitudes. The effect of the ocean heat capacity, however, also has an annual mean warming effect (Fig. 5c). This is due to the non-linear thermal radiation cooling. The non-linear black-body negative radiation feedback is stronger for warmer temperatures, which are not reached in a moderated seasonal cycle with the larger ocean heat capacity. Studies with more complex climate models find similar impacts of the ocean heat capacity on the annual mean and seasonal cycle (e.g. Donohoe et al., 2014).

The diffusion of heat reduces temperature extremes (Fig. 5d). It therefore warms extremely cold regions (e.g. polar regions) and cools the hottest regions (e.g. warm deserts). In global averages, this is mostly cancelled out. The advection of heat has strong effects where the mean winds blow across strong temperature gradients. This is mostly present in the Northern Hemisphere (Fig. 5e). The most prominent feature is the strong warming of the northern European and Asian continents in the cold season. On global average, warming and cooling mostly cancel each other out.

Literature discussions of heat transport are usually based on heat budget analysis of the climate system (in observations or simulations) instead of “switching off” the heat transport in fully complex climate models, since such experiments are difficult to conduct. A similar heat budget analysis of the GREB model experiments is beyond the scope of this study, but the results of these experiments appear to be largely consistent with the findings of heat budget analyses. For instance, the regional contributions of diffusion and advection are similar to those found in previous studies (e.g. Peixoto and Oort, 1992; Yang et al., 2015).

The CO2 concentration leads to a global mean warming of about 9 ∘C (Fig. 5f). Even though it is the same CO2 concentration everywhere, the warming effect is different at different locations. This is discussed in more detail in DF11 and in Sect. 3c.

The input of water vapour into the atmosphere by the hydrological cycle leads to a substantial amount of warming globally (Fig. 5g). However, we need to consider the fact that the experiment with switching OFF the hydrological cycle is the only experiment in which we have a significant amount of global cooling (by about -44 ∘C). As a result, most of the Earth is below freezing temperatures and therefore has a much stronger ice–albedo feedback than in any other experiment. This leads to a significant amplification of the response.

It is instructive to repeat the experiments with the ice–albedo feedback switched OFF (see Supplement Fig. S1). In these experiments, all processes show a reduced impact on the annual mean temperatures, but the hydrological cycle is most strongly affected by it. The ice–albedo effect almost doubles the hydrological cycle response, while for all other processes the effect is about a 10 % to 40 % increase. In the following discussions, we will therefore consider the hydrological cycle impact with and without ice–albedo feedback. In the average of both responses (Figs. 5g and S1g) the hydrological cycle has a global mean impact of about +34 ∘C, with the strongest amplitudes in the tropics. It is still the strongest of all processes.

Similar to the oceans, the hydrological cycle dampens the seasonal cycle (Fig. 6g), but with a much weaker amplitude. The transport of water vapour away from warm and moist regions (e.g. tropical oceans) to cold and dry regions (e.g. high latitudes and continents) leads to additional warming in the regions that gain water vapour and cooling in those that lose water vapour (Fig. 6h). The effect is similar in both hemispheres. The transport of water vapour along the mean wind directions has stronger effects on the Northern Hemisphere than on the Southern Hemisphere, since the northern hemispheric mean winds have more of a meridional component, which creates advection across water vapour gradients (Fig. 6i). This effect is most pronounced in the cold seasons.

Most processes have a predominately zonal structure. We can therefore take a closer look at the zonal mean climate and seasonal cycle of all processes to get a good representation of the relative importance of each process; see Fig. 7. The annual mean climate is most strongly influenced by the hydrological cycle (here shown as the mean of the response with and without the ice–albedo feedback). The cloud cover has an opposing cooling effect but is weaker than the warming effect of the hydrological cycle. The warming effect by the ocean's heat capacity is similar in scale to that of the CO2 concentration.

An interesting aspect of the climate system is that the Northern Hemisphere is warmer than the southern counterpart (by about 1.5 ∘C; not shown), which may be counterintuitive given the warming effect of the ocean heat capacity (see above discussion; Kang et al., 2015). The GREB model without flux correction also has a warmer Northern Hemisphere than the southern counterpart (by about 0.3 ∘C; not shown), whereas the bare Earth (pure black-body radiation balance; GREB all switches OFF) would have the Northern Hemisphere colder than the southern counterpart (by about -0.6 ∘C; not shown). A number of processes play into this inter-hemispheric contrast, with the most important contribution coming from cross-equatorial heat and moisture advection (see Fig. 7a). This is largely consistent with Kang et al. (2015).

The seasonal cycle is damped most strongly by the ocean's heat capacity and by the hydrological cycle. The latter may seem unexpected but is due to the effect of increased water vapour having a stronger warming effect in the cold seasons, similarly to the greenhouse effect of CO2 concentrations. In turn, ice–snow cover and cloud cover lead to an intensification of the seasonal cycle at higher latitudes. Again, the latter may seem unexpected but is due to interaction with other climate feedbacks such as the water vapour feedback, which also makes the climate more strongly respond to changes in cloud cover in regions where there actually is very little cloud cover (e.g. deserts).

As an alternative way of understanding the role of the different process we can build up the complete climate by introducing one process after the other; see Figs. 8 and 9. We start with the bare Earth (e.g. like our Moon) and then introduce one process after the other. The order in which the processes are introduced is mostly motivated by giving a good representation of each of the 10 processes. However, it can also be interpreted as a build-up of the Earth climate in a somewhat historical way: we assume that initially the Earth was a bare planet and then the atmosphere, ocean, and all other aspects were built up over time.

The bare Earth (all switches OFF) is a planet without atmosphere, ocean, or ice. It has an extremely strong seasonal cycle (Fig. 9a) and is much colder than our current climate (Fig. 8a). It also has no regional structure other than meridional temperature gradients. The combination of all climate processes will create most of the regional and seasonal differences that make up our current climate.

The atmospheric layer in the GREB model simulates two processes if all other processes are turned off: a turbulent sensible heat exchange with the surface and thermal radiation due to residual trace gases other than CO2, water vapour, or clouds. However, as mentioned in Appendix A1 the log-function approximation leads to negative emissivity if all greenhouse gas (CO2 and water vapour) concentrations and cloud cover are zero. The negative emissivity turns the atmospheric layer into a cooling effect, which dominates the impact of the atmosphere in this experiment (Fig. 8b, c). This is a limitation of the GREB model and the result of this experiment as such should be considered with caution. In a more realistic experiment we can set the emissivity of the atmosphere to zero or a very small value (0.01) to simulate the effect of the atmosphere without CO2, water vapour, and cloud cover; see Fig. S2. Both experiments have very similar warming effects in polar regions, suggesting that sensible heat exchange warms the surface. The residual thermal radiation effect from the emissivity of 0.01 has only a minor impact (Fig. S2f and g).

The warming effect of the CO2 concentration is nearly uniform (Fig. 8d, e) and without much of a seasonal cycle (Fig. 9d, e) if all other processes are turned OFF. This accounts for a warming of about +9 ∘C.

The large ocean heat capacity reduces the amplitude of the seasonal cycle (Fig. 9f, g). The effective heat capacity of the oceans is proportional to the observed mixed layer in the GREB model, which causes some small variations (differences from the zonal means) as seen in the seasonal cycle of the oceans. Land points are not affected, since there is no atmospheric transport (advection and diffusion turned OFF). The different heat capacity between oceans and land is already a significant element of the regional and seasonal climate differences (Fig. 8f, g).

Introducing the turbulent diffusion of heat in the atmosphere now enables interaction between points, which has the strongest effects along coastlines and in higher latitudes (Fig. 8h, i). It reduces the land–sea contrast and has strong effects over land with warming in winter and cooling in summer (Fig. 9h, i). The extreme climates of the winter polar region are most strongly affected by turbulent heat exchange with lower latitudes. The turbulent heat exchange makes regional climate differences a bit more realistic.

The advection of heat is strongly dependent on the temperature gradients along the mean wind field directions. It provides substantial heating during the winter season for Europe, Russia, and western North America (Figs. 8j, k, 9j, k). The structure (differences from the zonal mean) created by this process is mostly caused by the prescribed mean wind climatology. In particular, the milder climate in Europe compared to northeast Asia at the same latitudes is created by wind blowing from the ocean onto land. The same is true for the differences between the west and east coasts of northern North America. The climate regional and seasonal structures are now quite realistic, but the overall climate is much too cold. The ice–snow cover further cools the climate, in particular the polar regions (Fig. 8n, o). This difference illustrates the fact that the ice–albedo feedback primarily leads to cooling in higher latitudes and mostly in the winter season.

Introducing the hydrological cycle brings the most important greenhouse gas into the atmosphere: water vapour. This has an enormous warming effect globally (Fig. 8l, m) with a moderate reduction in the strength of the seasonal cycle (Fig. 9l, m). The resulting modelled climate is now much too warm, but introducing cloud cover cools the climate substantially (Fig. 8p, q) and leads to a fairly realistic climate.

The atmospheric transport (diffusion and advection) brings water vapour from relatively moist regions to relatively dry regions (Fig. 8r, s). This leads to enhanced warming in the dry and cold regions (e.g. the Sahara or polar regions) by the water vapour thermal radiation (greenhouse) effect and cooling in the regions where it came from (e.g. tropical oceans). The heating effect is similar to the transport of heat and also has a strong seasonal cycle component.

In the above discussion on how individual climate processes affect the climate we have to keep in mind the limitations of the GREB model and the experimental set-ups. The climate response to changing a single climate element is more complex in the real world than simulated in these GREB experiments. For instance, if the ocean heat capacity is turned OFF it will not just have an effect on the effective heat capacity, but the resulting changes in surface temperature gradients will also affect the atmospheric circulation patterns and subsequently the cloud cover. Such effects on the atmospheric circulation and cloud cover are neglected in the GREB model, as they are given as fixed boundary conditions. Regionally, such effects can be significant and CGCM simulations are required to study such effects.

The doubling of the CO2 concentrations leads to a distinct warming pattern with polar amplification, a land–sea contrast, and significant seasonal differences in the warming rate. These structures in the warming pattern reflect complex interactions between feedbacks in the climate system and regional differences in the CO2 forcing pattern. The MSCM 2×CO2 response experiments are designed to help us understand the interactions causing this distinct warming pattern. DF11 discussed many aspects of these experiments with a focus on the land–sea contrast, the seasonal differences, and the polar amplification. We will therefore focus here only on some aspects that have not been previously discussed in DF11.

In the GREB model, we can turn OFF the atmospheric transport and thereby study the local interaction without any lateral interactions. Figure 10 shows three experiments in which the atmospheric transport and other processes (see figure caption) are inactive. The three experiments highlight the regional difference in the CO2 forcing pattern and in the two main feedbacks (water vapour and ice albedo).

In the first experiment (Fig. 10a) without feedback processes, the local Tsurf response is approximately directly proportional to the local CO2 forcing. The regional differences are caused by differences in cloud cover and atmospheric humidity, since both influence the thermal radiation effect of CO2 (DF11; Kiehl and Ramanathan, 1982; Cess et al., 1993). This causes, on average, the land regions to see a stronger forcing than oceanic regions (see Fig. 10b). However, even over oceans we can see clear differences. For instance, the warm pool of the western tropical Pacific sees less CO2 forcing than the eastern tropical Pacific.

The ice–albedo feedback is strongly localized, and it is strongest over the mid-latitudes of the northern continents and at the sea ice edge around Antarctica (Fig. 10c and d). The water vapour feedback is far more widespread and stronger (Fig. 10e and f). It is strongest in relatively warm and dry regions (e.g. subtropical oceans) but also shows some clear localized features, such as strong Arabian and Mediterranean Sea warming.

The set of scenario experiments in the MSCM simulations allows us to study the response of the climate system to changes in the external boundary conditions in a number of different ways. In the following, we will briefly illustrate some results from these scenarios and organize the discussion by the different themes in scenario experiments.

The CMIP has defined a number of standard CO2 concentration projection simulations that give different RCP scenarios for future climate change; see Fig. 11a. The GREB model sensitivity in these scenarios is similar to those of the CMIP database (Forster et al., 2013).

Idealized CO2 concentration scenarios help us to understand the response to the CO2 forcing. In Fig. 11b, we show the global mean Tsurf response to different scaling factors of CO2 concentrations. To first order, we can see that the global mean Tsurf response follows a logarithmic CO2 concentration (e.g. any doubling of the CO2 concentration leads to the same global mean Tsurf response; compare 2×CO2 with 4×CO2 or with Fig. 11b) as suggested in other studies (Myhre et al., 1998). However, this relationship does break down if we go to very low CO2 concentrations (e.g. zero CO2 concentration), illustrating the fact that the log-function approximation of the CO2 forcing effect is only valid within a narrow range far away from zero a CO2 concentration.

The transient response time to CO2 forcing can be estimated from idealized CO2 concentration changes; see Fig. 11c. The stepwise change in CO2 concentration illustrates the response time of the global climate. In the GREB model, it takes about 10 years to get 80 % of the response to a CO2 concentration change (see step function response; Fig. 11c). In turn, the response to a CO2 concentration wave time evolution is a lag of about 3 years. The fast versus slow response also leads to different warming patterns with strong land–sea contrasts (not shown) that are largely similar to those found in previous studies (Held et al., 2010).

The regional aspects of the response to a CO2 concentration can also be studied by partially increasing the CO2 concentration in different regions; see Fig. 12. The warming response mostly follows the regions where we partially changed the CO2 concentration, but there are some interesting variations in this. The partial increase in the CO2 concentration over oceans has a stronger warming impact than the partial increase in the CO2 concentration over land for most Southern Hemisphere land regions. In turn, the land forcing has little impact for the ocean regions. The boreal winter forcing has a stronger impact on the Southern Hemisphere than boreal summer forcing, suggesting that the warm season forcing is, in general, more important than the cold season forcing. The only exception to this is the Tibetan Plateau region.

A series of scenarios focus on the impact of solar forcing. In Fig. 11d, we show the response to an idealized 11-year solar cycle. The global mean Tsurf response is 2 orders of magnitude smaller than the response to a doubling of the CO2 concentration, reflecting the weak amplitude of this forcing. This result is largely consistent with the response found in GCM simulations (Cubasch et al., 1997) but does not consider possible more complicated amplification mechanisms (Meehl et al., 2009). A change in the solar constant of +27 W m-2 has a global Tsurf warming response similar to a doubling of the CO2 concentration but with a slightly different warming pattern; see Fig. 13. The warming pattern of a solar constant change has a stronger warming when incoming sunlight is stronger (e.g. tropics or summer season) and a weaker warming in regions with less incoming sunlight (e.g. higher latitudes or winter season). This is in general agreement with other modelling studies (Hansen et al., 1997).

On longer paleo-timescales (>10 000 years), changes in the orbital parameters affect the incoming sunlight. Figure 14 illustrates the response to a number of orbital solar radiation changes. Incoming radiation (sunlight) typical of the ice age (231 kyr ago) has less incoming sunlight in the northern hemispheric summer. However, it has every little annual global mean change (Fig. 14a) due to increases in sunlight over other regions and seasons. The Tsurf response pattern in the zonal mean in different seasons is very similar to the solar forcing, but the response is slightly more zonal and seasonal differences are less dominant (Fig. 14b). The response is also amplified at higher latitudes. However, in the global mean there is no significant global cooling as observed during ice ages. If the solar forcing is combined with a reduction in the CO2 concentration (from 340 to 200 ppm), we find a global mean cooling of -1.7 ∘C (Fig. 14c), which is still much weaker than observed during ice ages but is largely consistent with previous simulations of ice age conditions (Weaver et al., 1998; Braconnot et al., 2007). This is not unexpected since the GREB model does not include an ice sheet model and, therefore, does not include glacier growth feedbacks that would amplify ice age cycles.

A better understanding of the orbital solar radiation forcing can be gained by analysing the response to idealized orbital parameter changes. We therefore vary the Earth distance to the Sun (radius), the Earth axis tilt to the Earth orbit plane (obliquity), and the shape of the Earth orbit around the Sun (eccentricity) over a wider range; see Fig. 14d–f. When the radius is changed by 10 %, the Earth climate becomes essentially uninhabitable, with either global mean temperature above 30 ∘C (approx. summer mean temperature of the Sahara) or a completely ice-covered snowball Earth. This suggests that the habitable zone of the Earth radius is fairly small due to the positive feedbacks within the climate system simulated in the GREB model (not considering long-term or more complex atmospheric chemistry feedbacks) and largely consistent with previous studies (Kasting et al., 1993).

When the obliquity is zero, the tropics become warmer and the polar regions cool down further than today's climate, as they now receive very little sunlight throughout the whole year. In the extreme case, when the obliquity is 90∘, the tropics become ice covered and cooler than the polar regions, which are now warmer than the tropics today and ice free. The polar regions now have an extreme seasonal cycle (not shown), with sunlight all day during summer and no sunlight during winter. Any eccentricity increase in amplitude would lead to a warmer overall climate. Thus, a perfect-circle orbit around the Sun has, on average, the coldest climate, and all of the more extreme eccentricity (elliptic) orbits have warmer climates. This suggests that the warming effect of the section of the orbit that has a closer transit around the Sun in an eccentricity orbit relative to the perfect-circle orbit overcompensates for the cooling effect of the more remote transit around the Sun in the other half of the orbit relative to the perfect-circle orbit.