Correlation for a 3dimensional field of time series (MATLAB)

I have a 4 dimensional matrix with for example absolute values of a flow velocity. Just to get a picture of it:

the first two dimensions are longitude and latitude, the third dimension is the depth and the forth dimensions is time. So for every point in a 3dim space I have a time series. Now I want the correlation of each of these points with some external variable (here it's the nao-index as a function of time)

Is there some way to get a threedimensional matrix full of correlation coefficients without using a loop? (My matrices are very big, so a loop takes hours in computing time)

I have the following test code:

%produce some flow matrix:

flow(:,:,1,1) = [0.5 0.2 0.6

0.4 0.7 0.3

0.6 0.1 0.8

0.4 0.2 1.1];

flow(:,:,2,1) = flow(:,:,1,1)+0.1;

flow(:,:,1,2) = flow(:,:,1,1)-0.2;

flow(:,:,2,2) = flow(:,:,1,1)+0.2;

flow(:,:,1,3) = flow(:,:,1,1)-0.3;

flow(:,:,2,3) = flow(:,:,1,1)+0.3;

flow(:,:,1,4) = flow(:,:,1,1)-0.4;

flow(:,:,2,4) = flow(:,:,1,1)+0.4;

flow(:,:,1,5) = flow(:,:,1,1)-0.5;

flow(:,:,2,5) = flow(:,:,1,1)+0.5;

nao = [4 5 6 7 8];

C = corrcoef(flow(1,1,1,:),nao)

%but I need: matrix which contains the non-diagonal element of the correlation matrix for all points