1.

## Introduction

The Fifth Assessment Report (AR5) of the Intergovernmental Panel of Climate Change (IPCC) reports that human impacts on the climate system are extremely likely the main reason for the global warming observed since the 1950s. Observations show that the global surface temperature over land and ocean increased from 1880 to 2012 by 0.85 K (IPCC, 2013) and that snow and sea ice masses have reduced significantly. It has also been observed that this warming is amplified in the Arctic (e.g., Serreze and Francis, 2006; Wendisch et al., 2017), where surface temperatures have increased at twice the rate of the global average (Meehl et al., 2007). This pronounced climate change is referred to as Arctic amplification.

Apart from changes in heat transports in atmosphere and ocean, physical climate feedbacks are thought to play an important role (Winton, 2006). The surface albedo feedback driven by the positive coupling between increasing temperature and melting snow and sea ice has long been suggested to be the main driver of this amplification (e.g., Manabe and Wetherald, 1975; Screen and Simmonds, 2010; Crook et al., 2011; Taylor et al., 2013).

However, other studies have demonstrated that there can also be an Arctic amplification without changes in snow and ice (Hall, 2004; Graversen and Wang, 2009). Thus, it has been shown that the surface albedo feedback is an important contributor to current Arctic amplification, but it is not necessarily the most dominant mechanism (Pithan and Mauritsen, 2014).

Lately the focus has shifted to other radiative feedbacks, especially to temperature feedbacks (e.g., Winton, 2006; Graversen and Wang, 2009; Langen et al., 2012; Pithan and Mauritsen, 2014). The Planck feedback, determined by the Stefan–Boltzmann law, is a rather natural contributor to polar amplification, as the change of emitted longwave radiation with respect to temperature is approximately proportional to the initial temperature to the power of three. Thus, in order to balance a radiative perturbation, larger temperature increases are necessary in regions with colder initial temperatures, such as the Arctic (Pithan and Mauritsen, 2014).

Special attention has also been given to the lapse rate feedback which, in contrast to the well mixed lower latitudes, turns positive in the stably stratified Arctic atmosphere (Payne et al., 2015) and is responsible for a rapid warming occuring near the surface. It has been suggested that, instead of the surface albedo feedback, the lapse rate feedback might be the dominant driver of Arctic amplification as it additionally reduces tropical warming (Lu and Cai, 2010; Bintanja et al., 2011; Pithan and Mauritsen, 2014; Payne et al., 2015).

Depending on which methodology is applied to which models and which experiments are performed, different relative contributions of surface albedo (Taylor et al., 2013), water vapour (Graversen and Wang, 2009), temperature (Pithan and Mauritsen, 2014) and cloud feedback [Vavrus, 2004] to Arctic warming are found.

Intermodel differences of these contributions lead to an increased spread of Arctic warming. This can be seen in Figure 1 which shows the zonal mean warming from 13 models of the fifth coupled model intercomparison project (CMIP5; Taylor et al., 2012) as a response to a forcing from CO2. Additionally, to the produced Arctic warming also the intermodel spread is very much amplified in comparison to lower latitudes. This underlines the complexity of the system and the need to assess the different model behaviours.

Fig. 1.

Multimodel zonal mean surface temperature change between the abrupt4xCO2 and the piControl experiment for the last 50 years of a 150-year simulation. The black line shows the multimodel average and the shaded area includes all individual model surface temperature changes. The box-whisker plots show the minimum, the 25th percentile, the median, the ${75}^{\text{th}}$ percentile and the maximum of surface temperature change of all models for the Arctic (70–90° N) [red], the Tropics (20° S - 20° N) [green] and Antarctica (70-90° S) [blue], respectively.

Analyses of feedback uncertainties associated with the equilibrium climate sensitivity (ECS) have been carried out for global means (e.g., Soden and Held, 2006; Klocke et al., 2013; Tomassini et al., 2013; Vial et al., 2013). It has been found that the cloud feedback exhibits the largest intermodel uncertainty and determines the intermodel spread of ECS (e.g., Bony et al., 2006; Vial et al., 2013). However, it cannot be deduced that this also holds for the local Arctic warming even though the modeling of clouds remains most uncertain there as well.

Pithan and Mauritsen (2014) have performed an uncertainty analysis regarding the contribution of various feedbacks and advection mechanisms to Arctic warming. They find that the intermodel spread is dominated by local feedbacks (mostly albedo and temperature feedbacks) and not by meridional heat transport changes, which instead reduces intermodel differences. They also find that intermodel differences of clouds play a minor role for the spread in modeled Arctic warming.

Because feedbacks are so important in explaining the rapid Arctic warming, a quantitative analysis of their uncertainties should be useful to explain the spread in modeled Arctic warming as well. Therefore, a quantitative assessment of intermodel differences of climate feedbacks and their implications on Arctic warming is the focus of this study. A comparison of feedback uncertainties in the Arctic and in the Tropics should help to understand characteristic differences and underlying origins. Therefore, this study follows the study by Pithan and Mauritsen (2014), but with a methodology in which the cloud feedback is computed explicitly.

2.

## Materials and methods

When an external radiative forcing (F) is applied to a climate system which is in radiative equilibrium, the radiation imbalance ($\Delta R$) occuring at the top of the atmosphere (TOA) is compensated by a corresponding change in global mean surface temperature ($\Delta {T}_{\mathrm{s}}$). This relationship can be considered to be linear in a first order approximation:

((1))
$\Delta R={F}_{{\text{CO}}_{2}}+\lambda \Delta {T}_{\mathrm{s}}$

In the context of global warming, the CO2 forcing (${F}_{{\text{CO}}_{2}}$) acts to decrease longwave outgoing radiation at TOA ($\Delta R>0$), so that the surface temperature has to rise in order to restore the radiative balance. Since the atmospheric structure and corresponding field variables are not fixed, the radiative relaxation of the climate system can be dampened or amplified by feedback processes (in units of ${\text{Wm}}^{-2}{\mathrm{K}}^{-1}$) which solely depend on changes of surface temperature. Relevant feedbacks correspond to changes in surface albedo (A), temperature (T), clouds (C) and water vapour (WV). The atmospheric temperature feedback can further be separated into contributions from a vertically homogeneous temperature change associated with the change in surface temperature, called the Planck feedback (PL), and the change of the vertical temperature gradient in the troposphere with respect to the vertically uniform temperature change, called the lapse rate feedback (LR). The global mean net or total feedback factor λ (in Equation 1) needs to be negative in order to decrease the global mean $\Delta R,$ however locally this does not have to be the case as advective processes can contribute to restore $\Delta R$ by redistributing the extra energy.

For each feedback process x, the feedback parameter can be written as

((2))
${\lambda }_{\mathrm{x}}={\left[\frac{\partial R}{\partial x}\right]}_{y}\frac{dx}{d{T}_{\mathrm{s}}}$
with y denotes all other feedback parameters held fixed. In a classical sense, feedback processes are regarded as linear and additive (Hansen et al., 1984), so that in Equation 1 we can write $\lambda ={\lambda }_{\mathrm{A}}+{\lambda }_{\mathrm{T}}+{\lambda }_{\mathrm{C}}+{\lambda }_{\text{WV}}.$ However, deviations from these assumptions can occur since Graversen et al. (2014) showed that the structure of the lapse rate feedback is to some extent dependent on the albedo feedback in high latitudes. Furthermore, Mauritsen et al. (2013) showed that synergy effects between feedbacks can occur which make the sum of them larger or smaller than the individual parts. Even though feedbacks cannot be regarded as completely independent, for a first order approximation we assume that the impact of their interactions is small and thus neglect higher order terms in Equation 2 (Klocke et al., 2013).

2.1

### Feedback computation

The computation of feedback factors is done here with the two sided “Partial Radiative Perturbation” method (PRP; Wetherald and Manabe, 1988; Colman and McAvaney, 1997). It has been used in previous studies to assess global climate feedbacks (e.g., Colman, 2003; Soden and Held, 2006; Klocke et al., 2013) and is employed here because it is close to the formal definition of the feedback factor as defined in Equation 2 and provides the possibility of a full feedback analysis even though computationally it is more elaborate than other methods. Especially, in contrast to the also widely used, more efficient Kernel technique (Kernel; Soden et al., 2008), the cloud feedback can be directly assessed here. In the Kernel method the cloud feedback can only be calculated as a residual from the cloud radiative forcing and allsky and clearsky Kernels from the other feedback parameters. It is therefore dependent on the uncertainties related to these parameters. Furthermore, the PRP method computes changes of radiation fluxes based on given changes in the field variables for each model, while the Kernel technique estimates these fluxes from a linearization around field variables in the mean climate state leading to larger deviations for larger forcings (Klocke et al., 2013; Block and Mauritsen, 2013).

The PRP method is a diagnostic technique, in which the change in TOA radiation with a certain perturbation x is computed in terms of finite differences between radiative fluxes when a certain perturbation x has been substituted (separately, one at a time) from the perturbed climate state into the reference state while all other components are hold fixed. To minimize biases by uncorrelated fields, this substitution is also done vice versa, from the control simulation into the perturbed simulation and the results are then averaged (therefore “two sided”, or forward and backward) (Colman and McAvaney, 1997).

This is done for 13 CMIP5 models (Table 1), using inputs from a preindustrial control run (“picontrol”) and a CO2–forced simulation (“abrupt4xCO2”) with fully coupled oceans. For each model, the feedback relevant parameters are used as inputs for the stand-alone radiative code (RRTMG; Iacono et al., 2008) from the atmospheric ECHAM6-model (Stevens et al., 2013; Pincus and Stevens, 2013), in which the radiative fluxes are computed offline.

The feedback parameter of the component x is computed via total derivatives in which the finite differences are resolved in space and time. This yields

((3))
${\lambda }_{\mathrm{x}}=\frac{{\Delta }_{\mathrm{x}}R}{\Delta x}\frac{\Delta x}{\Delta {T}_{\mathrm{s}}}=\frac{R\left({x}_{\text{ptrb}},{y}_{\text{ctrl}}\right)-R\left({x}_{\text{ctrl}},{y}_{\text{ctrl}}\right)}{{T}_{\mathrm{s},\text{ptrb}}-{T}_{\mathrm{s},\text{ctrl}}}$
with parameters are taken either from the control simulation (ctrl) or from the perturbed simulation (ptrb). The parameters which are substituted one by one in the radiative transfer code are upwelling and downwelling shortwave fluxes at TOA for the surface albedo feedback, relative and specific humidity for the water vapour feedback, surface and atmospheric temperatures for Planck and lapse-rate feedbacks, and cloud fractions as well as cloud ice and water mixing ratios for the cloud feedback.

The feedbacks factors are finally obtained by subsequently dividing the respective changes in radiation ${\Delta }_{\mathrm{x}}R$ in each grid cell of a model with the global mean change in surface temperature $\Delta {T}_{\mathrm{s}}.$ This allows for a quantitative comparison between the feedback strengths globally. Only means of the last 50 years from the 150–year simulation are used to reduce the influence of temporal variability of the resulting feedbacks.

Note, when Arctic mean feedbacks are analyzed, the feedback parameters retrieved in the Arctic are still normalised by the global mean surface temperature and not the Arctic mean temperature. This is done for two reasons, first, in order to scale regional radiation changes which makes them quantitatively comparable, and secondly, because local feedback parameters are not coupled to local temperature changes only but are also connected to remote changes via advective processes (Goosse et al., 2018).

For the Planck feedback, this yields

((4))
${\lambda }_{\text{PL},\text{polar}}=\frac{\Delta {R}_{\text{PL},\text{polar}}}{\Delta {T}_{\text{global}}}=-\frac{\Delta {T}_{\text{polar}}}{\Delta {T}_{\text{global}}}4ϵ\sigma {T}_{\text{ctrl},\text{polar}}^{3}$

From Equation 4 we can see, that both the polar amplification factor as well as the base-state surface temperatures play a role for the strength of Arctic Planck feedback. This is an important difference to other feedback definitions, where ${\Delta }_{\mathrm{x}}R$ is divided by local $\Delta {T}_{\mathrm{s}}$ (e.g., Crook et al., 2011; Pithan and Mauritsen, 2014) and therefore the Planck feedback would only be dependent on the derivative of the Stefan-Boltzmann law resulting in stronger (more negative) values in the Tropics than in the Arctic.

2.2

### Statistical analysis

In the next sections, feedbacks are compared between models and regions over the globe and we look at intermodel uncertainties, assuming that the models are independent from each other. For comparing regional means (e.g. Tropics versus Arctic), the results are area-weighted to avoid larger model spread in regions with smaller surface area, and as explained above, radiation differences are normalized by the global mean surface temperature change.

In the following sections two different statistical analyses are performed. The first one tests the significance of multimodel mean feedbacks. Because the sample size of 13 models is too small to prove a Gaussian distribution, multimodel mean feedbacks are considered to be significant if at least 90% of the sample (that is 12 out of 13 models) agree in sign. The second statistical analysis looks at the significance of linear regression slopes between feedback induced radiation changes $\Delta R$ and models’ exhibited global mean warmings $\Delta {T}_{\mathrm{s}}.$ For this a Student’s t-test with a two-tailed 95% significance level is used to test if the linear regression coefficient is significantly different from zero. Note here that the regression cannot be done for λ itself due to self-correlation artefacts.

3.

## Results

Global distributions of multimodel mean feedbacks are presented in Figure 2. Table 2 states the corresponding values of the feedbacks’ multimodel averages and intermodel standard deviations, calculated individually for global, Arctic, tropical and Antarctic regional averages. Hatched areas refer to points where less than 12 models (< 90% of the data sample) agree on the sign of the multimodel mean and which are therfore determined as insignificant.

Fig. 2.

Global distributions of multimodel-mean TOA radiation feedbacks [W m−2 K−1] from changes in surface albedo (a), clouds (b), water vapour (c), lapse rates (d), surface temperatures (e) and the sum of these components (f), which have been computed using the two sided PRP method for a quadrupling of CO2. Positive values denote increased downward radiation and thus an amplified surface warming. Hatching represents areas where less than 12 models (92% of data sample) agree with the sign of the multimodel-mean and are therefore considered to be insignificant.

In comparison with earlier studies on global feedbacks (Bony et al., 2006; Soden and Held, 2006; Tomassini et al., 2013; Vial et al., 2013; Klocke et al., 2013), the feedback estimates computed here are generally in good agreement in terms of distribution and intermodel spread. However, differences in their amplitudes may occur due to the use of different methods, spatial and temporal resolutions, and, in terms of multimodel means, on the selection of models.

The surface albedo feedback is significantly positive for the polar regions (and also in the global mean), while in the Tropics this feedback naturally is small as it is mainly driven by changes in sea ice coverage. Similar to the result of Pithan and Mauritsen (2014) (there, it is shown as a contribution to the Arctic warming), this feedback shows the largest absolute intermodel difference (see Table 2). Because it is the strongest positive feedback in the Arctic, the large spread has a large impact on modeled Arctic warming.

The overall negative Planck feedback is more than twice as strong in the Arctic as on the global scale since it is dependent on the amplification factor given in Equation 4. Together with the albedo feedback, the Planck feedback contributes most of the uncertainty to the total feedback estimate in the Arctic. This uncertainty is, however, not independent from uncertainties in sea ice feedback and in the lapse rate feedback as will be explained in later sections.

The overall positive water vapour feedback is temperature driven as the saturation water vapour pressure increases exponentially with temperature (Clausius-Clapeyron relationship) and therefore it is strongest in the Tropics. This component has only significant values all over the globe and has the lowest intermodel spread.

The global mean lapse rate feedback is dominated by its tropical contribution. In the tropical radiative–convective atmosphere, the decrease of the moist adiabatic lapse rate leads to a pronounced warming in the upper troposhere causing a negative lapse rate feedback. The polar regions however have a radiative–advective atmosphere characterised by a stably stratified boundary layer and strong inversions. Here, the warming is confined to the lower part of the troposhere, causing a positive lapse rate feedback. The lapse rate feedback shows more intermodel spread in the Arctic than in the Tropics and thus enhances the spread in Arctic warming simulations. In contradiction to Pithan and Mauritsen (2014), we find that the uncertainty of the Planck feedback contributes more to the spread in total feedback than do model differences of the lapse rate feedback.

The cloud feedback remains the most uncertain feedback with the largest intermodel spread resulting from its shortwave component. For the global mean value this is in agreement with previous studies (e.g., Soden and Held, 2006; Bony et al., 2006; Vial et al., 2013), which show that the intermodel spread in global mean equilibirum climate sensitivity (ECS) can be attributed to different representations of low tropical clouds. Also in the Arctic, the shortwave component is more uncertain than the longwave component. However, in terms of absolute values, the contribution of the Arctic cloud feedback is too small to have a relevant effect on the total feedback. This is in agreement with results from Pithan and Mauritsen (2014).

The multimodel mean total feedback (Figure 2 (f); Table 2), which is the sum of all feedback components, is negative in the global mean. The Planck feedback is the dominant contributor in leading the perturbed climate system to a new radiative equilibrium by dampening radiative imbalances at the TOA. In some regions, however, the Planck feedback is dominated by a combination of positive feedbacks. This is especially the case in regions with large albedo changes, along the ice edge in the Arctic and Antarctic, as well as in the Himalaya. Especially in these regions, where surface albedo, lapse rate and water vapour feedbacks act together to outweigh that of Planck, models very much disagree on the magnitude of total feedback. This is also the case in regions along the equator where the strong water vapour feedback counteracts the negative temperature feedbacks, leading to such small values that large intermodel uncertainties from clouds can have a large effect on the total result.

3.1

### Is the Arctic a local runaway system?

Because we are interested in model differences of feedback representation, we now want to compare the behaviour in regions with the largest intermodel spread, which are zonal bands in the Arctic, the Tropics and Antarctic as depicted in Figure 2. Figure 3 plots their feedback–induced radiation changes at TOA ($\Delta R$) as linear regressions against the global mean warming for each of the CMIP5 models used in this study. Figure 3 (a) shows spatial means in which all data points are included, while Figure 3 (b) presents the regional (and global) averages for which only grid cells have been selected which have insignificant multimodel mean values of total local $\Delta R.$ This comparison is done to see how much impact local multimodel uncertainties have on the entire region.

Fig. 3.

Feedback induced total TOA radiance change [W m-2] between the abrupt4xCO2 and the piControl experiment plotted against the global mean surface warming [K] from these experiments exhibited by 13 CMIP5 models. Area-weighted regional averages (markers) and corresponding linear regression lines are drawn for averages of the Globe, the Arctic (70-90° N), the Tropics (20° S - 20° N) and Antarctica (70-90° S). A comparison is made for (a), regional averages in which all data points are taken into account, and (b), regional averages in which only data points are used for which the multimodel mean total feedback has been shown to be insignificant (meaning that less than 12 of 13 models agree in sign). Regression lines are drawn solid for significant and dashed for insignificant regression coefficients at the 95% significance level.

Interestingly, the polar regions show a steep increase of $\Delta R$ with $\Delta T$ (Figure 3 (b)), while this is not the case in the Tropics where we even find a slight negative relationship. The spatially averaged multimodel mean total tropical feedback is significantly negative (also see Table 2), even if only these grid cells are selected which depict insignificant multimodel means. Apparently, model differences cancel each other in the Tropical mean while they can add up in the Arctic mean.

Figure 2 (f) reveals that areas with insignificant multimodel mean total feedbacks cover almost the entire Arctic. Thus, it is not surprising that the steep regression slope shown in Figure 3 (b) is also present for the entire regional average ($\mathrm{b}=2.52±1.11{\text{Wm}}^{-2}{\mathrm{K}}^{-1}$) in Figure 3 (a), while for all other regions the regression coefficients become insignificantly different from zero at the 95% significance level.

Very intriguing is however, that 7 out of 13 models show positive $\Delta R$ in the Arctic while the other 6 have negative values. This implies that half of the models analyzed here simulate local runaway climate systems in which the gain of energy is larger than the loss of energy if advection is not taken into account. These models increase the initial radiative perturbation rather than to reduce it. On the other hand, models exhibiting little warmings tend to be dominated by the negative Planck feedback and can be brought back to radiative balance without the contribution of advection.

Since all models have a similar tropical mean $\Delta R$ independent of $\Delta T$ and all models reach radiative balance in the global average, changes of heat transports must be fundamentally different for the two sets of models. This is already discussed in Pithan and Mauritsen (2014), who show a reversed warming contribution by atmospheric heat transport from positive to negative values with increasing Arctic warmings which therefore dampen the intermodel spread of Arctic warming. However, Pithan and Mauritsen (2014) do not attribute this behaviour of the atmospheric heat transport to differing total Arctic feedbacks.

Our findings show, that intermodel differences of meridional atmospheric heat transports are linked to regional atmospheric feedbacks, and that their respective roles regarding the relaxation of the radiative imbalance are not yet evident as they fundamentally differ between models. Whether meridional heat transports to the Arctic increase or decrease in the future is related to the sign of the total radiative feedback in the Arctic (based on energy budget arguments). Increasing vs. decreasing heat transport to the Arctic certainly implies fundamentally different effects of Arctic amplification on atmospheric dynamics. Therefore, a better understanding of Arctic radiative feedbacks seems imperative.

For the Antarctic, similar conclusions can be drawn, but only for the sea-ice covered area near the coast. Averaging over the entire Antarctic, we see from Table 2 and Figure 3 (a) that the total multimodel mean feedback is significantly negative, resulting from the negative feedbacks over the continent. Therefore, changes in atmospheric dynamics could be either weaker and/or more locally confined.

The strong dependance of $\Delta R$ on global mean temperature changes attributes to the increased feedback uncertainty in the Arctic compared to the uncertainty in the Tropics. This can arise from different regional feedbacks being involved and from regionally differing impacts of uncertainties associated with these feedback mechanisms such as model parameterizations or the accuracy of simulated initial conditions as will be discussed in the next section.

To explain some of the differences between the Arctic and the Tropics, we can split up the total radiance change from Figure 3 (a) into its contributions (Figure 4) where we can directly see the main contributors. In the Arctic, the Planck feedback dominates all others only in models which exhibit low warmings. For the other half of the models, the Planck component is overcome by the response from albedo, lapse rate and water vapour together. A simple test combining $\Delta R\mathrm{s}$ one at a time reveals, that for the two models with the largest ${\Delta }_{\mathrm{A}}R$ (MIROC5 and FGOALS-s2) albedo and lapse rate feedbacks are enough to outweigh the Planck feedback. For the other 4 models, the response by water vapour is additionally needed to turn the total feedback positive. But only by including the response from the longwave cloud component, which itself also has a weak but significant positive relation to $\Delta T,$ the regression slope becomes significant between $\Delta R$ and $\Delta T.$Figure 4 also shows that water vapour and temperature feedbacks oppose each other to almost the same degree in the Tropics, which leads to total feedbacks being rather insensitive to the amount of warming exhibited by the models (Figure 3).

Fig. 4.

Feedback induced total TOA radiance change [W m−2] between the abrupt4xCO2 and the piControl experiment plotted against the global mean surface warming [K] from these experiments exhibited by 13 CMIP5 models. The respective radiation changes induced from surface albedo (red), Planck (black), Lapse rate (green), water vapour (blue) and cloud feedbacks (net: light blue; shortwave: purple; longwave: orange) are area-weighted averages from the Tropics (a) and the Arctic (b), respectively. Please note the different scales on the y-axis. Related uncertainties to the individual δR are illustrated to the right of (a) and (b) showing the median (lines), 25th and 75th percentile (boxes), and the full ensemble spread (whiskers). Regression lines are drawn solid for significant and dashed for insignificant regression coefficients at the 95% significance level.

3.2

### Influence of initial climate state on intermodel spread

In addition to differing impacts of feedbacks occuring on a regional scale, also state dependencies can have an impact on the increased intermodel spread in the Arctic. Since the Stefan–Boltzmann law suggests larger warmings for lower initial temperatures (for the same perturbation in radiation), models with a cold control climate exhibit a larger warming (Figure 5 (a)) and thus a stronger Planck feedback. However, the range of Arctic temperatures (both horizontal as well as vertical) differs greatly between models. For comparison, the model span for Tropical near surface temperatures is roughly 298 K to 300 K (not shown here) while in the Arctic this range is tripled, ranging from 254 K to 260 K. This has severe consequences for the intermodel feedback spread, which can be explained for the example of the Planck feedback.

Fig. 5.

Relationships of (a) Arctic mean surface warming and (b) Arctic mean preindustrial (ctrl) sea ice cover (SIC) to Arctic mean preindustrial (ctrl) surface temperature. Red circles indicate models which show positive Arctic total feedbacks. Regression lines are drawn (dashed), but are insignificant at the 95% significance level.

Using Equation 4, regional uncertainties of the Planck feedback can be attributed to model differences in amplification factors and preindustrial temperature ranges. The amplification factors themselves are responsible for most of the multimodel spread within a certain region. When holding initial temperatures fixed at their multimodel mean values, the Arctic Planck feedback is increased by 65.6% from low to high Arctic amplification factors. The analogue increase in the Tropics is only 44.2%. Thus, the relative change of the Arctic Planck feedback range compared to the Tropics is increased by a factor of 1.4 owing to the different regional warming.

Even though the Planck feedback is primarily dependent on the degree of warming, this number is small compared to the impact that preindustrial temperatures have. When keeping the amplification factors fixed at their multimodel mean values, and only applying the range of initial temperatures, we find a 7.3% increase of the Planck feedback from low to high base temperatures in the Arctic, while in the Tropics it is only 1.9%. Thus, the uncertainty range of the Planck feedback in the Arctic compared to the Tropics is more than tripled (factor of 3.8) just because of the larger range in preindustrial temperatures.

Colder models also tend to simulate a larger sea ice fraction (Figure 5 (b)), and, the more sea ice there is to be melted the stronger the surface albedo feedback becomes. However, the representation of preindustrial sea ice fractions (annual means ranging from 46% to 85%) shows a wide spread, which is linked to the intermodel uncertainty of surface temperatures as the presence of sea ice strongly impacts the distribution of near surface temperatures and vice versa. Therefore, we can conclude that also the large uncertainty ranges associated with the Planck feedback and albedo feedback are connected.

Because of the large spread in initial conditions, the linear regression coefficients of total local $\Delta R$ to preindustrial Arctic mean surface temperature ($\mathrm{b}=-0.13±0.17{\text{Wm}}^{-2}{\mathrm{K}}^{-1},{\mathrm{R}}^{2}=0.04$) and to sea ice cover ($\mathrm{b}=0.02±0.02{\text{Wm}}^{-2}{\mathrm{K}}^{-1},{\mathrm{R}}^{2}=0.07$) are insignificant and we are not able to see whether models showing Arctic runaway effects (plotted in red) are linked to base states with low temperatures and high sea ice fractions. This result confirms the findings of Holland and Bitz (2003), for the case of sea ice extent.

A reduced intermodel spread of surface temperature and sea ice fields in the base state should help to decrease some of the models’ differences in both, albedo feedback and temperature feedbacks.

3.3

### Influence of seasonal variability on intermodel spread

As discussed above, the spread between modeled total feedbacks arises from the relation of the total radiative response to the degree of warming exhibited by the individual model. Therefore, it is reasonable to analyse the intermodel uncertainty of feedbacks in the two seasons in which the Arctic warming is weakest and strongest, which is the case for the Arctic summer and winter, respectively Pithan and Mauritsen (2014). The semiannual analysis of the individual intermodel feedback spread is presented in Figure 6.

Fig. 6.

The multimodel mean area-weighted feedback strengths of each individual feedback are shown for different time periods and regions. Blue represents the Arctic winter (December, January, February) and red the Arctic summer (June, July, August) average. The yearly average is shown in grey for the Arctic and in green for the global mean, for reference. The error bars show the extent of one standard deviation of the multimodel distribution.

The surface albedo feedback is, as expected and in agreement with previous results (e.g., Crook et al., 2011), strongest in summer, as it depends on incoming solar radiation. Cloud and water vapour feedbacks are also strongest in the summer season, which can be related to an increased atmospheric moisture transport during the summer season (Naakka et al., 2019).

Similar to the surface albedo feedback, the shortwave cloud feedback during winter is negligible to the lack of incoming solar radiation. Thus, the total cloud feedback is small but positive.

Lapse rate and Planck feedbacks are strongest in the winter months, in contrast to surface albedo, cloud and water vapour feedbacks. They are directly dependent on near-surface temperature changes, and those have been shown to be larger during the winter months than during the summer months (e.g., Boé et al., 2009). This leads to a stronger lapse rate and Planck feedback in absolute terms during polar night. The positive lapse rate feedback arises due to the stable stratification of the Arctic atmosphere. Temperature inversions and the lack of deep convection cause stronger warming in the lowest parts of the troposphere. Both seasonal feedbacks agree well with earlier results (e.g., Crook et al., 2011; Taylor et al., 2011).

As discussed above, yearly averaged surface albedo and Planck feedbacks are especially associated with the large intermodel spread in the Arctic. With the help of the semiannual analysis, we can now further confine these intermodel differences to be strongest in the summer regarding the albedo feedback, and in the winter regarding the Planck feedback.

The multimodel mean Arctic total feedback (not shown here) is significantly negative in the winter season ($-3.5±1.0{\text{Wm}}^{-2}{\mathrm{K}}^{-1}$) due to the dominating Planck feedback. In the summer season however, the multimodel average is insignificantly positive ($1.5±2.9{\text{Wm}}^{-2}{\mathrm{K}}^{-1}$), while in the global average it is significantly negative in both seasons since the impact of globally averaged albedo feedback is very small. The interplay between Arctic feedbacks remains uncertain in the summer and the total feedback is mostly determined by the intermodel spread of the albedo feedback as the largest source of uncertainty. This result indicates that not only the degree of warming determines the sign of the total feedback as is the case for the annual mean values, but related to that also the simulated change in sea ice extent.

The next largest contributions of intermodel uncertainty are summer shortwave cloud feedback and winter lapse rate feedback. Both are also related to intermodel differences in sea ice cover and near surface temperature which emphasizes the importance of reducing them in the base state.

4.

## Conclusions

The investigation of feedback uncertainties has produced several findings which confirm results of previous studies and some which give a new perspective on our understanding of Arctic amplification. In this study we have identified three regions with especially large intermodel uncertanties which locally influence the sign if the total feedback. These are both the Polar regions and the Tropics. However, only the Arctic shows a distinct intermodel spread which impact the sign of the total feedback for the entire region and therefore has a large-scale impact. In the Antarctic these uncertainties are similar but too localized to have a significant impact on the entire region and in the Tropics the intermodel uncertainties cancel each other leading to an overall robust response of the total radiative feedback.

A key point of this study is the realisation that half of the models investigated here show a positive total Arctic feedback, indicating a local runaway system if neglecting the contribution of advection. The strength of feedback induced radiative response has been found to be related to the degree of warming exhibited by the models. In models with very large warmings the gain of energy in the Arctic is larger than its loss and therefore local radiative feedbacks do not suffice to bring the Arctic system back into radiative equilibrium after being perturbed. Instead, fundamentally different changes of heat transports must come into play to stabilize the entire system globally in these models. An investigation of the dynamics of the two sets of models is therefore an interesting point in future studies.

An investigation of the regional individual feedback uncertainties reveals that different aspects are important in different regions. In agreement with previous studies, we have found that the cloud feedback has the largest intermodel uncertainties in the Tropics which locally influence the sign of the total feedback. The uncertainty of the cloud feedback in the Tropics has already been shown to determine the intermodel spread of climate sensitivity estimates and therefore plays an important role. In the Arctic however, it has a too small contribution on average to make a large impact on the overall model spread, even though relative uncertainties are of course still immense. This agrees with results from Pithan and Mauritsen (2014) who used a different technique to compute the cloud feedback. By considering achievements of observational campaigns (Wendisch et al., 2018), the interplay of Arctic clouds with surface properties and radiative fluxes could be improved in climate models and thus more certainty of the local cloud feedback may be obtained.

Intermodel differences in surface albedo and temperature feedbacks determine the spread of the Arctic total feedback, and thus, according to Pithan and Mauritsen (2014), also the spread in Arctic warming. A semiannual analysis reveals that the interplay of feedbacks during the Arctic summer when the warming is little contributes more to the annual mean intermodel spread of the Arctic total feedback than it does in winter when Arctic warming is strongest. This results from the large contribution from surface albedo uncertainties which are negligible in winter, while the uncertainties of the Planck feedback are dominating in the winter season.

Our results indicate that the large model spread does not only arise from different degrees of simulated Arctic warming and sea ice changes, but also from the dependency of these feedback components to largely different and incoherent representations of initial temperatures and sea ice fractions in the preindustrial control climate which inversely relate to the exhibited model warming. A comparison between the impact of Tropical and Arctic intermodel differences of preindustrial temperatures on the spread of the regional Planck feedback reveals that the uncertainty range is more than tripled in the Arctic just due to the larger range of base state temperature fields. However, further investigations of the dependency to the base state is needed to obtain significant and robust results. The lack of significant relationships of the radiative response to base state variables emphasizes the need to reduce intermodel differences in sea ice cover and near surface temperatures.

In conclusion, our results show that a reduction of intermodel differences of the preindustrial Arctic climate state in terms of sea ice fraction and surface temperature would lead to a better knowledge of Arctic local feedbacks. This is of utmost importance since these local feedbacks, if strong enough, can trigger an Arctic runaway system and lead to fundamental differences of meridional heat transport changes.