SI calculation error

[daniel-caichac-DHI]

Hi all,
I think that here might be an error in the calculation of the scatter index. I have used another script and I got different results, so I decided to check and I think that the mean value is not being taken into account somewhere in the equation. I found that SI can also be interpreted as

with Xmean = Mean of observations
I reviewed a few comparer objects and the other script checks out but I don't get it in fmskill. I am computing SI with this formula

but the one in FMSkill is not taking into account 1/N

[ecomodeller]

Well... Scatter index according to for instance Mentaschi et al, 2013, Problems in RMSE-based wave model validations is defined like this:

Which is what we use in the fmskill at the moment:

I suppose there are several slightly different definitions for scatter index.

fmskill is pretty flexible in using custom metrics so you can use your definition or we could add it with a different name or change the definition of the existing one if we are really sure that is the commonly used definition.

[jsmariegaard]

The implemented formula for SI can be seen here: https://dhi.github.io/fmskill/api.html#fmskill.metrics.scatter_index - what is the best reference you have for the SI?

[daniel-caichac-DHI]

Alright no problem then, I thought it was an error but I agree with Henrik that there might be several slightly different definitions (The difference I got between my formula and the one implemented was ~0.02 or 0.01 so I will just close this post

[jsmariegaard]

Let's leave it open until we decide what to do. @ecomodeller and I are leaning towards changing the definition to be consistent with your other tool