1. Measuring Arctic amplification R. Davy, L. Chen, E. Hanna, and I. Esau
Bjerknes Centre, norway
Bologna, Jan 2018.

2. Measuring Arctic amplification
Goal: Understand impact of Arctic warming on local climate, regional and global circulation
Need: Identify periods of Arctic amplification & control periods.
Example: Testing hypothesis about how AA affects extreme weather in the mid- latitutdes
What metrics to use?
One of the things that motivated this work was that in different ways we are wanting to understand the impact of Arctic warming on the local climate and explore the pathways whereby it can affect the regional and global circulation. So whether you’re looking at this in observations, reanalysis, or climate models you need to identify those periods with arctic amplification and periods without.
And one of the questions that arose in that discussion was what is the appropriate measure of Arctic amplification for a given study and what does it tell us about the sensitivity of the Arctic?

3. Choosing a metric A1 Temperature anomalies A2 Temperature trends
Arctic SAT anomaly vs. NH SAT anomaly
When is the Arctic anomalously warm?
A2 Temperature trends
Arctic SAT trend vs. NH SAT trend
When is the Arctic warming anomalously fast?
A3 Variability
Arctic variability vs. NH variability
When does the Arctic have anomalously high variability?
A4 Regression
Coefficient of regression of Arctic anomalies against NH anomalies
How much warmer does the Arctic become during warm periods in the northern hemisphere?
So when we dug around the literature we found four different ways that have been commonly used to measure Arctic amplification.
The first is the simplest: we simply take the temperature anomalies and average them for the Arctic and for some reference region, and compare the two. So this simply tells us when the Arctic is anomalously warm.

4. Choosing a metric A1 Temperature anomalies A2 Temperature trends
Arctic SAT anomaly vs. NH SAT anomaly
When is the Arctic anomalously warm?
A2 Temperature trends
Arctic SAT trend vs. NH SAT trend
When is the Arctic warming anomalously fast?
A3 Variability
Arctic variability vs. NH variability
When does the Arctic have anomalously high variability?
A4 Regression
Coefficient of regression of Arctic anomalies against NH anomalies
How much warmer does the Arctic become during warm periods in the northern hemisphere?
In the second metric we looked at you compare the rate of warming in the Arctic compared to the hemispheric average.
So you take your timeseries of Arctic and hemispheric-mean temperatures, you calculate the trends in each over some given period, and you take the ratio of these trends to tell you how much faster the Arctic is changing than the hemisphere as a whole.
Of course this method has limitations because of the uncertainties associated with the trends and the subsequent ratio of the trends. So one way round that is to instead look at the difference in the variability.

5. Choosing a metric A1 Temperature anomalies A2 Temperature trends
Arctic SAT anomaly vs. NH SAT anomaly
When is the Arctic anomalously warm?
A2 Temperature trends
Arctic SAT trend vs. NH SAT trend
When is the Arctic warming anomalously fast?
A3 Variability
Arctic variability vs. NH variability
When does the Arctic have anomalously high variability?
A4 Regression
Coefficient of regression of Arctic anomalies against NH anomalies
How much warmer does the Arctic become during warm periods in the northern hemisphere?
So for this metric you take the temperature anomaly time series for the Arctic and hemispheric-mean, and you calculate the variability of the two timeseries over a moving window.
Then taking the ratio of the two gives you a measure of Arctic amplification. Although the interpretation of changes in inter-monthly variability can be a little tricky.

6. Choosing a metric A1 Temperature anomalies A2 Temperature trends
Arctic SAT anomaly vs. NH SAT anomaly
When is the Arctic anomalously warm?
A2 Temperature trends
Arctic SAT trend vs. NH SAT trend
When is the Arctic warming anomalously fast?
A3 Variability
Arctic variability vs. NH variability
When does the Arctic have anomalously high variability?
A4 Regression
Coefficient of regression of Arctic anomalies against NH anomalies
How much warmer does the Arctic become during warm periods in the northern hemisphere?
And finally we have the regression method. So for this metric you plot your Arctic temperature anomalies against the hemispheric anomalies and you take a linear regression of the two to see how much stronger anomalies are in the Arctic, compared to the hemisphere as a whole. One of the advantages of this metric is that you look at the amplification of both warm and cold anomalies.
So we wanted to know how consistent these different metrics are within different datasets, so we were looking over the historical period. We took some gridded observations and some reanalysis products from the last century and we looked at the multidecadal variability in each of these metrics in turn.

7. Consistency of Metrics within observations and reanalysis (A1)
The difference in SAT anomalies
A1 = Arctic SAT anom –
NH SAT anom
Excellent agreement between gridded observations. Peak around 1940.
Small spread in reanalysis in current period.
So starting with the temperature anomalies, we mapped the difference in temperature anomalies for two different gridded observations and every reanalysis we could find from the last century using a 21 year moving window. So they all have pretty good agreement in the recent warming period, and both the observation datasets show that very clear warm anomaly in the early 20th century which is almost as strong as the warm anomaly from the last 20 years. This early warming peaks around 1940 or so. The reanalaysis on the other hand do not capture the amplification prior to the satellite observation era at all well.

8. Consistency of Metrics within observations and reanalysis (A2)
The ratio of SAT trends
A2 = |Arctic trend| / |NH trend|
Large number of non-significant trends.
Large spread in warming rates 1995 – present
So looking at the second metric, the ratio of the trends. While this metric might be quite intuitively appealing, looking at how much faster the Arctic is warming than the global average, it is quite limited when it comes to assessing temporal behaviour. Quite often the hemispheric trend is close to zero and the metric is non-significant, which leads to large gaps in the timeseries as you can see here. We see quite a jump in Arctic amplification in the mid-90s but you can see there are large differences in the degree of amplification even in the last twenty years.

9. Consistency of Metrics within observations and reanalysis (A3)
The ratio of SAT variability
A3 = SD Arctic SAT anom / SD NH SAT anom
Large differences in last 20 years.
Peaks around 1950.
This actually gets even worse when we look at the temperature variability. So this is the Arctic amplification as determined by the ration of temperature variability in the arctic compared to the hemispheric average. And we can see that while the different reanalysis agree reasonably well about the overall temporal pattern in the 20th century, they have very big differences in the degree of amplification, even in the relatively well-constrained period over the last twenty years.

10. Consistency of Metrics within observations and reanalysis (A4)
Coefficient of regression of SAT anomalies
A4 = regress [Arctic SAT anom,NH SAT anom]
Large differences in last 20 years.
Peak around 1940.
And the regression of the anomalies shows similar differences between the products. We have this quite consistent multi-decadal variability with a peak in the early 20th century around 1940; but there are large differences in the magnitude of the amplification. So even in the last few years the reanalysis can’t agree as to whether Arctic anomalies are two or three tiems larger than the hemispheric anomalies. So why are these different products not agreeing about the degree of amplification?

11. Why do they differ?
Gridded-observations – Which observations; processing; homogenization
Reanalyses – Which observations assimilated; model physics in under-sampled regions.
Climate models – Feedback processes – sea-ice-albedo, clouds, aerosols, humidity, lapse-rate,..
Don’t capture SAT sensitivity well (trends, variability)
Poor representation of mixing in the atmospheric boundary layer
Well for the gridded observations it comes down to which observations are included, how the station data are processed, and how they are homogenized into a gridded product.
But for the reanalysis it’s a combination of which observations are assimilated but also in these regions and times with limited observations, a lot comes down to the model physics.
And of course, these problems with model physics present an even bigger challenge when it comes to capturing arctic amplification in climate models.
But in general what we found with these different metrics is that they have quite good agreement in capturing the mean temperature, but they don’t do so well in capturing the senstivity of the surface temperature to changes in forcing. So we looked at one of the reasons why this is the case, related to how these models represent the atmospheric boundary layer. And I think this is easiest to see when we consider an energy budget model of the climate system.

12. Why do they differ?
Gridded-observations – Which observations; processing; homogenization
Reanalyses – Which observations assimilated; model physics in under-sampled regions.
Climate models – Feedback processes – sea-ice-albedo, clouds, aerosols, humidity, lapse-rate,..
Don’t capture SAT sensitivity well (trends, variability)
Poor representation of mixing in the atmospheric boundary layer
Well for the gridded observations it comes down to which observations are included, how the station data are processed, and how they are homogenized into a gridded product.
But for the reanalysis it’s a combination of which observations are assimilated but also in these regions and times with limited observations, a lot comes down to the model physics.
And of course, these problems with model physics present an even bigger challenge when it comes to capturing arctic amplification in climate models.
But in general what we found with these different metrics is that they have quite good agreement in capturing the mean temperature, but they don’t do so well in capturing the senstivity of the surface temperature to changes in forcing. So we looked at one of the reasons why this is the case, related to how these models represent the atmospheric boundary layer. And I think this is easiest to see when we consider an energy budget model of the climate system.

13. Energy-budget model Three components to SAT response:
Magnitude of forcing
Feedback effects
Effective heat capacity
ABL depth
So if we think about the near-surface energy balance, there are three components that determine the strength of the temperature response to a given forcing: The strength of the forcing, any feedback effects involved, and the effective heat capacity of the system.
So the temperature response is just linearly related to the forcings and feedbacks through this term, Q. But it is inversely related to the effective heat capacity of the system.
Now the effective heat capacity is just defined by the volume of air through which that heat is mixed, which is described by the planetary boundary-layer depth.
So this formulation tells us quite a lot about some patterns we might expect to see. We can expect that shallow boundary layers amplify the effect of climatological forcings and feedbacks such that we should get the strongest temperature responses in shallow boundary layers, whether we think of these as being trends or variability. Now, as we know, the climatology of the boundary layer is extremely varied. This is the average boundary-layer depth taken from reanalysis and we can see that it varies by about an order of magnitude across the globe. But it also can vary by an order of magnitude on diurnal and seasonal cycles. So
- Heat Q is mixed through a layer of depth h.
- For a given forcing, shallower layers have greater temperature change

14. Assessing the ABL in climate models
Dependent on vertical resolution
Bulk Richardson method
6hrly synoptic snapshots
Apply to CMIP5 archives to assess model spread.
Large bias over sea-ice (winter)
Strong SAT sensitivity dependency on PBL depth
Introduce PBL calculations

15. PBL controls sensitivity to forcings
Reanalysis
Amplified trends in shallow ABLs
High-latitude ABL
Climate model
Derived ABL depth
Amplification effect in high-latitude ABL
This is an example of the results from a reanalysis showing the inter-annual surface temperature trends as a function of the mean boundary layer depth, and we can see that clear amplification of the trends in shallow boundary layers. This bar chart below is showing you how often the given boundary layer depth occurs, and this strong amplification effect only occurs in relatively few places, principally in the high-latitudes.
Climate models have pretty low-resolution atmospheric models, but we can still derive the PBL depth in these models. And we find very similar results to the reanalysis with the strongest trends in shallow boundary layers.

16. Model biases damps SAT variability
Biased towards deep PBLs
Large spread in PBL depth
Introduce PBL calculations

17. Summary
Several metrics for Arctic amplification, highlight different aspects of amplification
Atmospheric Boundary Layer mixing defines SAT sensitivity
Biases in GCMs and reanalysis -> damped variability
Working to improve representation of:
- stable boundary layers
- convection over leads
in NorESM
Look out for Metrics of Arctic amplification (IJOC) and The climatology of the atmospheric boundary layer in CMIP5 (J. Clim).
Introduce PBL calculations

19. Definition of the Arctic
Introduce PBL calculations

20. Convection over leads Observations (Baltic Sea data)
Turbulence data (approximation of LES runs)
Parameterizations (flux-gradient approach)
So commonly we use some flux-gradient approximation to describe the heat flux from leads, but this ignores the organisation of convective structures. But we can explore the effects of turbulent structures using large eddy simulations which resolve the mixing. So we ran these simulations over sea-ice with leads in the ice of different widths.
When the leads are less than a km or so the turbulence is organised into chimney structures, whereas when we expand the leads to a few km, there is enough room for convective cells to form.
Now this is the heat flux as a function of the lead width. The blue data are from our large eddy simulations and you can see they agree well with the available observations in green, which were taken from observations made over the Baltic sea.
So we can clearly see an amplification of the heat flux for leads on the scale of a few km, and this is completely missed in conventional parameterization schemes.
Large open water patches – Convection is organized in cells
Small open water patches – Convection is organized in chimneys