Weather forecast uncentainty data
d = [[t_0 E_0], [t_1, E_1], ..., [t_{n-1}, E_{n-1}]]
is fitted with the model
E(t) = A tanh(a t + b ) + B for norm=false
E(t) = 1 + c[tanh(a t + b) − tanh(b)] for norm=true
where t is the time and E is the root-mean-square (r.m.s.) error. We consider two types of data:
normalized data with E(0)=1 (norm = true) and un-normalized/raw data (norm = false)
The routine fit_model in errorgrowth.py returns:
[a, b, c] for norm=true
[a, b, A, B] for norm=false
References:
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Lorenz, Edward (1996). "Predictability – A problem partly solved" Seminar on Predictability, Vol. I, ECMWF. link
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Nedjeljka Žagar, Martin Horvat, Žiga Zaplotnik & Linus Magnusson "Scale-dependent estimates of the growth of forecast uncertainties in a global prediction system" Tellus A: Dynamic Meteorology and Oceanography Vol. 69 , Iss. 1,2017 link