Temperature trend amplification in shallow boundary layers

Here we have identified the relationship between the boundary layer depth and the trend in θ v during the recent warming period, as seen in different re-analyses, and in two state-of-the-art global climate models (Fig. 3). There is a distinctly inverse relationship, where the strongest warming trends are found in shallow boundary layers, and correspondingly low atmospheric heat capacity. The strength of the trends decrease rapidly as we go towards deeper boundary layers and then remain relatively constant across a wide range of boundary layer depths. This amplified temperature trend in the shallowest boundary layers can also be seen in climate models with very different climatologies of the PBL depth. The Norwegian Earth System Model and Geophysical Fluid Dynamic Laboratories Coupled Model 3 have very different climatologies of the PBL depth compared with the re-analyses (Supplementary Fig. 1); both have biases towards deeper PBLs, but they still show a significant correlation between inverse boundary layer depth and the magnitude of trends in θ v (R = 0.35, P < 0.05 and R = 0.32, P < 0.05, respectively). This process where heat gets trapped in a shallow layer near the surface by stable stratification in the boundary layer has been shown to be one of the dominant causes of Arctic amplification30,31, but it also has a crucial implication for how we assess the efficacy of different forcings in affecting the SAT. Given the large differences between the climatology of the PBL depth in re-analyses and the global climate models shown here, and the controlling influence the boundary layer depth has on the surface climate32, this is clearly an area that requires more attention, especially in future model development.

Figure 3: The amplification of temperature trends in shallow boundary layers. The bin mean and s.d. of the inter-annual trend in the virtual potential temperature at a height of 2 m above the ground, as a function of the climatological monthly mean planetary boundary layer depth for (a) ERA-Interim reanalysis, (b) CFSR reanalysis, (c) the Geophysical Fluid Dynamic Laboratories Coupled Model 3 (GFDL-CM3) and (d) the Norwegian Earth System Model (NorESM1-M) climate model simulations. The ERA-Interim and CFSR data are taken over the period 1979–2014 and the climate model data from 1979–2005. Full size image

Variability in the strength of the boundary layer effect

Owing to its varied climatology (Supplementary Fig. 2), there are some geographical differences as to when the boundary layer depth becomes important in determining the strength of temperature trends. For deep boundary layers the relationship between boundary layer depth and temperature trends is expected to be small, and it is the strength of the local forcing factors themselves, which will principally determine the variations in the rate of warming. However, in shallower boundary layers the strength of temperature trends may be expected to become increasingly dependent on the boundary layer depth. This can be seen in the correlation between the magnitude of temperature trends and the inverse boundary layer depth for different geographical regions (Fig. 4). In high-latitude continental regions such as North America, North Asia and Antarctica, where we frequently get very shallow boundary layers in autumn and winter, there is a strong correlation between inverse boundary layer depth and θ v trends. Whereas in more tropical regions such as Africa, South Asia and South America, where cases of shallow boundary layers are less frequent, there is no evidence of this amplification effect.

Figure 4: Geographical variations to the planetary boundary layer effect. The inter-annual trend in the virtual potential temperature at a height of 2 m above the ground as a function of the climatological monthly mean planetary boundary layer depth is shown for nine different regions: (a) Africa, (b) Antarctica, (c) Europe, (d) North America, (e) South America, (f) South Asia, (g) North Asia, (h) Sea-ice and (i) Ocean, as illustrated on the (j) map of the Earth. The thick red line indicates the bin-mean and the shaded area shows the region of 1 s.d. The correlation between the magnitude of the temperature trends and the inverse boundary layer depth is given for each region. Full size image

There is also a strong seasonal variation in the PBL amplification effect: in the boreal spring and summer, the boundary layer is relatively deep and so the amplification effect is relatively weak. However, during the boreal autumn and winter, we can see that the PBL depth is very small over land (Supplementary Fig. 2); thus, during these periods the amplification effect of the PBL depth can become important and should be taken into account. This is why studies that have chosen to focus on the mid-latitudes during the summer seasons have had some success in demonstrating a relationship between a given forcing process and changes to the SAT9, whereas more global analysis of the same processes have shown weaker relationships8. From the ERA-Interim results, we can see that the amplification effect becomes very apparent for boundary layers less than a few hundred metres (Fig. 3). This is quite common, with PBL depths <400 m occurring >46 % of the time in ERA-Interim. This is a good indication of the fraction of time that the PBL depth becomes important in determining the strength of temperature trends.

Including the boundary layer effect in signal detection

One way to account for the PBL depth in the analysis of climate processes is by considering the integrated temperature response within a co-variability framework (Fig. 5). In this framework, the net temperature change is proportional to the time integration of the product of the perturbations in the forcing, dQ, with the inverse boundary layer depth, h−1. In this regard, the conventional methodology is a limit of the co-variability framework, when the variations in the heat capacity can be neglected and we can directly relate perturbations in the forcing to perturbations in the surface temperature (case A, Fig. 5). This is a reasonable approximation only if that forcing is applied solely to deep or weakly varying boundary layers such as the tropical marine boundary layer17. The other limit of the co-variability framework occurs when we have a uniformly applied perturbation to the climate forcing (case B, Fig. 5). In this limit, it is the climatology of the boundary layer depth that principally determines the pattern of warming/cooling in response to a perturbation in the surface heating. The enhanced concentration of GHGs is one such example of a near-uniform perturbation in the surface heating and, as such, there is a strong relationship between the inverse boundary layer depth and the strength of temperature trends in re-analysis (Fig. 3), and both within and between global climate models32.

Figure 5: Relationship of proposed co-variability method to existing methodology. Schematic of the proposed co-variability method and the relation to: (a) current methodology where variations in the PBL depth, h, are neglected and we directly relate surface temperature trends, , with climate perturbations, dQ; (b) a uniform climate-forcing perturbation where it is the climatology of the PBL depth, which is the best predictor of temperature trends; and (c) intermediary conditions where both the PBL depth and the perturbation in the forcing are significant in determining the temperature response. Full size image

However, in most cases it is both the PBL depth and the strength of the forcing that will be important in determining the spatial and temporal variations of climate change. In these cases, it is necessary to account for the nonlinear amplification effect of the PBL depth. Let us take the example of the influence of cloud cover on surface temperatures. We expect that an increase in cloud cover during the day will damp incoming solar radiation and thus decrease surface temperatures9. However, an increase in cloud cover at night is expected to reduce longwave cooling and hence result in warmer surface temperatures. Thus, the net effect of changes to the cloud cover on the surface climate is determined by the balance between the cooling effect of damped shortwave radiation and the warming effect of reduced longwave cooling. The cooling effect principally applies during conditions with strong surface heating (when the surface energy balance is dominated by shortwave radiation) and applies to deep PBLs, compared with the warming effect that dominates when there is a net longwave cooling and relatively shallow PBLs. Therefore, when we consider the effect of changes in cloud cover on the atmospheric heat content, rather than on the surface temperature, we expect the cooling effect to become more apparent. This can be seen in the regressions of the cloud cover anomalies, , against surface temperature anomalies, , and against normalized atmospheric heat content anomalies, (Fig. 6). If we look at the sensitivity of surface temperature to cloud cover we can see that in the high latitudes the strong winter-time warming effect of increased cloud cover dominates on the inter-annual scale and we get a strong positive relationship, whereas when we consider the effect of cloud cover on heat anomalies we find a more widespread cooling effect of increased cloud cover, even in these high-latitude continental interiors.This may be expected, as the warming effect of positive cloud cover perturbations on the surface temperature that occurs during the winter months only has a small impact on the atmospheric heat content compared with the cooling that occurs in deep PBLs in the summer months. Thus, when we account for variations in the effective heat capacity, we get a significantly stronger damping of atmospheric heat content from increased cloud cover than we found when assessing surface temperatures: the globally averaged overland temperature sensitivity to cloud cover is −12 (±17) × 10−3 K %−1, compared with a sensitivity of normalized heat content to cloud cover of −32 (± 16) × 10−3 K %−1. This marks a much clearer signal of an overall cooling effect of increased cloud cover on the surface climate.