Calc metric over init or member - how to make it flexible

It would be nice to have the compute functions in a way that they only check for predictability over the member dimension, so the ensemble dimension is free to be plotted.

Now compute results only time as lead time. Then it would also give ensemble or initialization, so we can get a Lead year timeseries over the ensemble space.

This nicely shows how prediction skill is not constant but very dependent of initialization state. http://hdl.handle.net/21.11116/0000-0002-0A63-4 Fig. 6.1

Need to adapt computes and remove mean over all ensembles.

Propose: add flag mean_forecast=True as is, as we compute the mean forecast over all init states, and mean_forecast=False for the new part.

[bradyrx]

I like this idea a lot; I think you should open a PR just to implement this when you have time.

So if I understand this correctly, we take each initialization year and run a metric. So, say, we choose ensemble=1970. I now have 40 members with 10 lead years each. Do we then construct a vector of the first lead year for all 40 members and compare to 1971 in the reference? Then do the same for each lead year?

E.g. (example typed out here; not real):

A = DPLE['SST'].sel(ensemble=1970)
print(A)
[0.2, 0.1, 0.3, -0.2, 0.4, ...] # size is member size
B = FOSI['SST'].sel(ensemble=1970)
print(B)
[0.15] # actual anomaly from the hindcast
xr.corr([B]*DPLE.member.size, [A])

Hopefully that makes some sense…

[aaronspring]

pearson_r gives 0 if applied over members only

for other metrics both works