UBERN Report 9/02/2006
D11 – Assessment of time varying influence of SST and atmospheric circulation on European surface T and precipitation. (Author Chris Folland)
Granger causality of North Atlantic SSTs on the NAO
We used a Vector AutoRegression (VAR) model to examine the feedback process between north Atlantic Sea Surface Temperature (SST) and the first principle component (PC) of EMSLP on the monthly timescale. The first PC shows the well known dipole pattern referred to as the North Atlantic Oscillation (NAO), known to influence mainly winter temperature and precipitation patterns over northern and western Europe.
V AR is a linear statistical model incorporating the memory effects and feedback between multiple variables. A VAR model consisting of two variables X1 and X2 considering lagged values up to one time step before may be presented as:
The magnitude of the coefficients, 12 and 21 control the amount of feedback between the two variables whereas 11 and 22 indicate the amount of natural predictability there exists from persistence. This can be stated more concisely: A variable X1 is causal for another variable X2 if knowledge of the past history of X1 is useful for predicting the future state of X2 over and above knowledge of the past history of X2 itself (Mosedale et al. 2005; Granger 1969)
The coefficients, written:
If 12 is significantly different from zero then X2 is Granger causal of X1. Whereas if 21 is significantly different from zero then X1 is Granger causal of X2.
O ne way to test the significance of is with the Omega statistic which compares the full model given in the first equation and a restricted model with no feedback allowed.
Where RSS_{r} and RSS_{u} are the Residual Sum of Squares of the restricted and unrestricted model respectively. N is the number of time points and p the maximum lag value. The Omega statistic is Fdistributed.
Figure 1 shows the Omega statistic pvalue of North Atlantic SSTs influence on the NAO. Areas in red are highly significant indicating that SST in these areas influences the NAO up to 6 months prior to the current NAO. The pattern of significant influence reveals the well known north Atlantic tripole SST pattern. A possible advantage of the VAR approach over simple linear analysis is that the model removes the influence of intrinsic autocorrelation in each variable.
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