The Atlantic Multidecadal Oscillation
Low frequency variability has been observed in sea surface temperatures in the North Atlantic. This variability has a time scale in the range of 30 - 70 years and a particular spatial pattern [1,2] and has been named the "Atlantic Multidecadal Oscillation" or AMO . Due to this variability the North Atlantic was unusually warm in the 1940s and 50s as well as after the mid 1990s, and anomalously cool around 1920 and during the 1970s.
The influence of the AMO extends beyond the ocean alone, affecting the climate of the surrounding land. The positive phase of the AMO (warmer than normal temperatures in the North Atlantic) has been linked to warmer temperatures in Europe, less rainfall over the central United States, more rainfall in Florida and the Sahel, a stronger Indian monsoon as well as stronger and more frequent hurricanes in the North Atlantic [4,5]. Greater understanding of the AMO would thus be very useful for weather and climate prediction. The AMO also plays a role in the variability of the global mean temperature. Apart from the increase associated with anthropogenic forcings, the global mean temperature shows variability on multidecadal time scales which may be at least partially explained by the AMO .
There are two different approaches to modelling and understanding the physics of the AMO. In one method we can use Coupled General Circulation Models (CGCMs) to simulate the entire climate and then try to understand the processes which cause variability. This method has lead to the idea that the AMO is linked to variations in the strength of the overturning circulation of the ocean, although the time scale seems to be dependent on the model used. The drawback of this approach is that in these complex models there are always many different fields varying at the same time which makes it difficult to separate cause from effect. This has lead to numerous different descriptions of the physics of the AMO [7-14].
The other approach to studying the AMO uses a so-called "minimal model", the simplest possible model which can still simulate the fundamental physics of the system. Additional processes may later be included in the model to make it more realistic and to allow comparisons with more complex models as well as with observations, but these additions do not change the underlying physical processes. This is the approach described here.
A minimal model for the AMO
The minimal model for the AMO is a coarse resolution ocean only model representing the North Atlantic. The model is spun up to equilibrium using boundary conditions in which temperature at the surface is restored to a sinusoidal profile (temperature decreasing with increasing latitude). Salinity is constant and there is no wind forcing. Once at equilibrium, the surface heat flux is diagnosed and the model is switched to prescribed heat flux boundary conditions. Under these conditions the equilibrium state is no longer steady - instead we find a periodic oscillation [15,16].
Figure 1: Temperature anomalies at the surface in the sector ocean model at three different time steps, showing westward propagation.
This oscillation appears as westward propagating temperature anomalies at the surface. Figure 1 shows SSTs at the beginning of the oscillation (t=0), a quarter of the way through (t=π/2), and half way through (t=π, where the SST pattern is the opposite to that at t=0).
Figure 2: Illustration of the mechanism of the oscillation (from ).
The mechanism of the variability is depicted in figure 2 and can be described as follows: An initial anomaly in the meridional temperature gradient leads to an anomaly in the zonal overturning anomaly. The temperature anomaly propagates westward and is thus referred to as a "thermal Rossby wave", since it propagates along a background temperature gradient in the same way that a regular Rossby wave travels along a background vorticity gradient. The resulting zonal temperature gradient anomaly leads to an anomaly in the meridional overturning circulation, which leads to a temperature anomaly the opposite sign of the original one, beginning the second half of the oscillation.
The minimal model can be expanded to include salinity, wind, continental geometry and bathymetry without significant changes to the physics . Including other ocean basins shows that the variability is localised in the North Atlantic [18,19]. Figure 3 shows that the comparison of model results to observations improves once continental geometry is included.
Figure 3: Spatial pattern of the AMO in observations (upper; differences in observed SST between 1950-1964 (warm) and 1970-1984 (cold); from ) and the simple model with the inclusion of continental boundaries (lower).
The AMO mode
This change from a steady equilibrium state under restoring boundary conditions to an oscillation under prescribed flux boundary conditions is indicative an internal mode in the ocean , specifically a Hopf bifurcation, where the steady equilibrium solution becomes unstable to a periodic solution.
examine the appearance of the oscillation by making boundary conditions that are
a combination of restoring (Qrest, in which damping of temperature
anomalies is very large) and prescribed flux (Qpres, in which damping of
temperature anomalies is zero):
where γ is the control parameter, measuring the strength of the damping. Figure 3 shows that oscillations appear for values of γ greater than 0.85.
Figure 3: Standard deviation of variability in the minimal model for different damping strengths (from ).
Atmospheric damping is estimated to be less than 0.85, indicating that this oscillatory mode would be damped in the real ocean. However, this does not take the additional effect of atmospheric variability into account.
Addition of noise in the minimal model
An oscillatory mode may be excited for values of the control parameter less than the critical value when noise is present in the system. To implement this in the minimal model a white noise term is included in the surface boundary condition. The noise may be uncorrelated in space or may be given a spatial pattern.
Figure 4: Standard deviation of variability in the minimal model for different damping strengths when noise is added to the surface boundary condition (from ).
Figure 5: The variability excited by the noisy forcing has a particular frequency (from ).
Figure 4 shows that different types of noise are more efficient at exciting the variability, and figure 5 shows that the variability excited by the noise has the particular frequency associated with the internal mode. When EOFs of the variability are calculated we find the same spatial patterns as in the minimal model under prescribed flux boundary conditions. This indicates that the noise excites the internal mode, i.e. the variability is not just the typical red noise response of the ocean to white noise forcing.
Observations of the AMO
The view of the AMO which arises from the minimal model has several distinctive features, most notably the westward propagation of temperature anomalies across the North Atlantic. Associated with this propagation is a lag between the temperature at the surface and deeper layers (with SST leading) and a lag between the variability on either coast of the North Atlantic, with variability on the eastern (European) coast leading variability on the western (North American) coast.
Figure 6: Observed temperature at different depths in the North Atlantic (from ).
Figure 7: Observed westward propagation of temperature anomalies in the North Atlantic (from ).
Due to the influence of atmospheric noise it is difficult to distinguish the propagation of temperature anomalies at the surface. However, if we use the temperatures measured by XBTs then both the lag of temperature with depth (figure 6) and the westward propagation (figure 7) can be observed. In addition to large signal attributed to anthropogenic global warming, the XBT time series is rather shorter than would be necessary to make any estimates of the period of the variability. However the time scale that is observed seems to be closer to 20-30 years than to the 50-70 year period that is normally associated with the AMO.
Figure 8: Variation of SSH as measured by tide gauges along the coasts of (a) Europe and (b) North America on either side of the North Atlantic (from ).
A longer time series is available in the form of tide gauge records from around the North Atlantic. Figure 8 shows a composite of tide gauge records from the east and west coasts of the North Atlantic. Once again the time scale seems to be 20-30 rather than 50-70 years.
The 20-30 year time scale is also observed elsewhere, most notably in the Central England Temperature record and in δ18O records from Greenland. Along with the range of time scales found in GCMs, this leads to the hypothesis that there is more than one type of variability occurring in the North Atlantic. If the AMO mode from the minimal model is responsible for variability on the 20-30 year time scale (as indicated by the XBT and tide gauge data), the what is the source of the longer period variability?
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