Abstract

Pithan and Mauritsen argue that the 2009 results of Boé et al. are not consistent with current understanding of the lapse-rate feedback in the Arctic. They also argue that these results arise to an important extent from self-correlation issues. In this response, the authors argue that their results are not inconsistent with current understanding of lapse-rate feedback and demonstrate that the conclusions remain unchanged when all possibilities of self-correlation are excluded.

1. Introduction

In Boé et al. (2009, hereafter B09), we concluded that models from the World Climate Research Programme's phase 3 of the Coupled Model Intercomparison Project (CMIP3) dataset with stronger present-day climatological temperature inversions in the Arctic are characterized by a stronger negative longwave feedback. The comment by Pithan and Mauritsen (2013, hereafter PM13) about this paper makes two main points. First, they argue this result is not consistent with the common understanding of a positive lapse-rate feedback in the Arctic. Second, they argue that this result is to an important extent an artifact related to self-correlation issues. These two points are examined in this reply. We will first argue that our results are consistent with current understanding of longwave feedback in the Arctic. Then we will demonstrate that our conclusions remain unchanged when all possibilities of self-correlation issues are excluded.

2. Current understanding of longwave feedback

First, we examine the claim that the results in B09 are not consistent with the common understanding of the lapse-rate feedback and its spatial variations.

Feedbacks are usually defined in terms of surface temperature change. Yet, given the high infrared opacity of the atmosphere in the tropics, changes in outgoing longwave radiation (OLR) there are controlled not by surface temperature change but by the temperature change in the upper troposphere. As the temperature change in the upper troposphere in the tropics is generally larger than at the surface, more longwave radiation escapes to space than would be expected for a given amount of surface warming. Therefore, a negative lapse-rate feedback must be introduced.

The situation is different in the Arctic as the atmosphere is drier and its infrared opacity above the boundary layer smaller, especially in late fall and winter, the time of year when longwave feedbacks are most active (e.g., see Fig. 2a of B09). The change in OLR is therefore much more controlled by the near-surface temperature change in the Arctic than in the tropics. This is confirmed by the large and significant intermodel anticorrelation between the change in longwave radiation at the top of atmosphere (TOA) and surface warming seen in the Arctic (−0.70 for annual mean and −0.80 for winter mean) and the fact that such a large anticorrelation does not hold in the tropics (Fig. 1). The concept of lapse-rate feedback is therefore probably more necessary to understand climate change in the tropics than in the Arctic, and more generally in high latitudes. (Because the tropics dominate the globe in area, the concept of lapse-rate feedback is still highly applicable to changes in global-mean temperature.)

In any event, B09 never dealt specifically with the lapse-rate feedback in the Arctic, and the term “lapse rate” is never used in the paper. Instead, the relationship between the inversion and the total negative longwave feedback (to use the same terminology as the paper) was investigated. The temperature inversion in the Arctic does not simply impact the lapse-rate change; it also influences surface air temperature and humidity change, through at least a modulation of vertical mixing. To understand longwave feedbacks, one should therefore not think solely in terms of lapse-rate feedback (what is shown in Fig. 1 in PM13), but rather in terms of the total longwave feedback.

In fact, the lapse-rate feedback is overwhelmed by other longwave feedback components. The total temperature feedback turns out to be strongly negative in the Arctic, almost as negative as in the tropics [see Figs. 1 and 3 in Zelinka and Hartmann (2012)]. Moreover, there is a strong link between the change in temperature and change in specific humidity that results from the very small change in relative humidity. Thus, the inversion directly influences not only temperature change but also the specific humidity change and therefore the water vapor feedback. It is therefore useful to consider temperature and water vapor feedbacks together, as done in B09. Large near-surface warming in the Arctic is associated with a large increase of water vapor there. As shown for example by Soden et al. (2008), the increase in water vapor near the surface in regions characterized by a temperature inversion can lead to an increase rather than a decrease in OLR. The vertical temperature structure in the Arctic therefore explains to an important extent why the Arctic is characterized by a very small water vapor feedback compared to other regions [Antarctica excepted; see, e.g., Figs. 1 and 3 in Zelinka and Hartmann (2012)].

In the end, the total water vapor plus temperature feedback—what is investigated in B09—is more negative in the Arctic than anywhere else in the world [see Fig. 3 in Zelinka and Hartmann (2012)]. Although this peculiarity of Arctic climate is not only due to its temperature inversion, the inversion does clearly play a large role. Arguing that a stronger inversion could lead to a more negative longwave feedback in the Arctic as in B09 is therefore consistent with current understanding of the lapse-rate feedback, and is more generally consistent with current understanding of overall longwave feedbacks, including temperature and water vapor components.

3. Self-correlation issues

In B09, a classical framework to define the feedback parameters was used. It consisted of dividing the change in radiative fluxes at the TOA by the change in temperature (oceanic temperature in our case, for reasons explained in the paper and mentioned below). PM13 make the point that self-correlation issues can arise when relations between the feedback parameters and change in temperature or variables constructed from the change in temperature are studied.

The choice to define the feedbacks in terms of ocean warming (in the uppermost 70 m of ocean, ΔToc) was motivated by an important specificity of Arctic climate change, as shown for example in B09. In the Arctic, there is a large difference between the change in the system's heat content, as captured by ΔToc, and the change in surface temperature ΔTas. Surface temperature change is therefore not representative of the change in system's heat content. Very large surface temperature changes can be obtained without particularly large increase in oceanic temperature: the ratio ΔTocTas is much smaller than one in the Arctic, with a large intermodel spread.

The ratio ΔTasToc appears in the longwave feedback parameter with our definition [Eq. (6) in B09]. All else being equal, a larger ΔTasToc ratio is associated with a larger longwave negative feedback. The heat that enters in the system (mostly during summer because of sea ice retreat) would be lost to space as infrared radiation during winter more effectively in models with a large ΔTasToc ratio. In B09, we showed that models with large inversion strength are generally characterized by larger ΔTasToc ratio. Consistent with the previous reasoning, we found that models with larger inversion strength are also generally characterized by smaller ocean warming. Although not mentioned in B09, greater inversion strengths are associated with larger negative longwave feedbacks (r = −0.73 without the outlier noted in Fig. 7 in B09, −0.43 with this model included), also consistent with the previous reasoning. Note that there is no possibility for self-correlation to play any role in any of these relationships.

With this background, we deal directly with the self-correlation issues mentioned by PM13. First, we note that PM13 do not contradict the fact that there is a significant link between the total feedback parameter we defined and the change in oceanic temperature.

PM13 report no significant correlation between ΔTasToc and the longwave feedback parameter (λLW = ΔRLWToc, with ΔRLW being the change in net longwave radiation at the top of atmosphere minus the forcing) using a test based on randomized data. When the link between two variables (such as ΔTas and ΔRLW) divided by a same third one (such as ΔToc) is studied, a significant correlation can be found even if there is no relation between the first two original variables simply because of the common divisor (i.e., self-correlation). First, it is important to note there actually is a significant anticorrelation between ΔRLW and ΔTas (r = −0.63) prior to any normalization by ΔToc. This relationship between change in longwave radiation and surface warming is a feature of high-latitude climate change (Fig. 1), as noted earlier. Second, one can also limit the potential influence of self-correlation without affecting physical interpretation by looking at the link between the inverse of the ratio previously defined (i.e., ΔTocTas) and the longwave feedback parameter, as ΔToc in that case is not in the denominator of the two quantities whose link is studied. The correlation is found to be significant compared to randomized data (r = 0.86, p < 0.02, with an average correlation for randomized data of 0.72, using the same approach as in PM13). Models with smaller ΔTocTas are therefore significantly associated with larger negative longwave feedbacks.

An additional concern of PM13 is the respective importance of the longwave and shortwave feedback parameters and therefore our choice to focus on the longwave feedback parameter in B09. They find that the correlation between shortwave feedback parameters (λSW = ΔRSWToc, with ΔRSW being the change in net shortwave radiation at the top of atmosphere) and ΔToc is less negative than the correlation obtained using randomized data most of the time. They conclude from this result that the true correlation between shortwave feedbacks and ocean warming is positive. We do not agree with this conclusion. Indeed, the reduction of the negative correlation with true data compared to randomized data can be attributed to the significant positive correlation between the change in shortwave radiation and oceanic temperature change (r = 0.63).

First, imagine an extreme case where ΔRSW and ΔToc are perfectly correlated (with ΔRSW = kΔToc): All the models would have the exact same shortwave feedback parameter (defined as ΔRSWToc) and therefore there would be no link between the shortwave feedback parameter and ocean warming. More negative correlations would still generally be obtained with most randomized data, but it would clearly be wrong to conclude that there is a true significant relation between the shortwave feedback parameter and ocean warming.

More concretely, if among the randomized data we only select cases where the correlation between values of ΔRSW and ΔToc is greater than 0.5, small negative correlations between randomized shortwave feedbacks and ocean warming are found (−0.54 on average). In this context, the correlation obtained with real data (−0.51) is not exceptional. (In more than a quarter of the cases of this subset, correlations greater than −0.51 are found.) Conversely, larger negative correlations between randomized values of shortwave feedbacks and ocean warming are obtained when the randomized values of ΔRSW and ΔToc have a strong (nonphysical) anticorrelation. (For the subset of cases with a correlation between randomized ΔRSW and ΔToc smaller than −0.5, correlations of −0.71 are obtained on average.) In conclusion, we do not agree that the analysis in PM13 leads to the conclusion that there is a true positive relation between the shortwave feedback parameter and ΔToc.

It is true, as PM13 pointed out, that these types of statistical arguments do not highlight the importance of the longwave feedback parameter either. However, the importance of the longwave feedback parameter is highlighted by its larger intermodel spread compared to that of the shortwave feedback parameter, as noted in B09 (14.3 vs 6.5 W m−2 K−1). This suggests another way to think about the question of the relative importance of longwave and shortwave processes. Arctic climate change is characterized by both a very large increase in the energy entering the system during summer as shortwave radiation (hence ocean warming) and a very strong increase of the energy leaving during winter as longwave radiation (e.g., Fig. 2a in B09) because of a large increase in surface temperature. Those changes are both strongly modulated by the decrease in sea ice cover. In the case of the shortwave change, this is because of the optical properties of sea ice, while in the case of the longwave change it is because of the insulating effect of sea ice separating a relatively warm ocean and frigid atmosphere. A decrease in sea ice cover leads to more solar energy absorbed in summer, but also to a larger oceanic heat loss and increase in surface air temperature in winter (Screen and Simmonds 2010) and consequently a greater loss of energy to space as longwave radiation. An important question is therefore which is more uncertain when a given decrease in sea ice cover occurs: the increase in net shortwave radiation or the increase in OLR. To answer this, it is possible to look at the change in the fluxes at the TOA (minus the forcing for longwave radiation) normalized by the change in sea ice extent in the various models. The spread in these quantities is larger for longwave than for shortwave radiation: 1.67 W m−2 (106 km2)−1 versus 0.75 W m−2 (106 km2)−1. Thus for a given change in sea ice cover, it is more uncertain how much more energy leaves the system as longwave radiation than how much more enters as shortwave radiation.

Because longwave and shortwave feedbacks are anticorrelated in the Arctic, what ultimately matters is the compensation between those feedbacks, rather than their relative importance. This compensation is measured by the total feedback parameter. The correlation of ΔTocTas with the total feedback parameter is highly significant, even when self-correlation is taken into account (r = 0.87, p < 0.003 following the test of PM13 based on randomized data, with an average correlation of 0.56 for randomized data). The models with small ΔTocTas and large inversion strength given in Fig. 7 in B09 are therefore generally associated with more negative total feedbacks.

4. Conclusions

In conclusion, complementary approaches that avoid or limit potential self-correlation issues confirm what was argued in B09 (i.e., the importance of the oceanic temperature change to surface warming ratio and the inversion strength for Arctic climate change uncertainty). Moreover, those results are perfectly consistent with current understanding of longwave feedbacks in the Arctic. The wintertime Arctic inversion strength does not simply affect the lapse rate. It plays an important role in modulating the total temperature and water vapor feedbacks. These other components are dominant, and lead to a strongly negative total longwave feedback parameter for the Arctic in all models.

Acknowledgments

We are grateful for valuable discussions with Felix Pithan. We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP's Working Group on Coupled Modelling (WGCM), for their roles in making available the WCRP CMIP3 multimodel dataset. The authors thank two anonymous reviewers for their constructive comments.

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Footnotes

The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/2009JCLI2885.1.