dapper.mods.Lorenz96.pinheiro2019

 1"""Settings from `bib.pinheiro2019efficient`."""
 2
 3import dapper.mods as modelling
 4import dapper.mods.Lorenz96 as model
 5from dapper.mods.Lorenz96 import LPs, step, x0
 6from dapper.mods.utils import linspace_int
 7from dapper.tools.localization import nd_Id_localization
 8
 9model.Force = 8.17
10tseq = modelling.Chronology(0.01, dko=10, K=4000, Tplot=10, BurnIn=10)
11
12Nx = 1000
13
14Dyn = {
15    "M": Nx,
16    "model": step,
17    # It's not clear from the paper whether Q=0.5 or 0.25.
18    # But I'm pretty sure it's applied each dto (not dt).
19    "noise": 0.25 / tseq.dto,
20    # 'noise': 0.5 / t.dto,
21}
22
23X0 = modelling.GaussRV(mu=x0(Nx), C=0.001)
24
25jj = linspace_int(Nx, Nx // 4, periodic=True)
26Obs = modelling.partial_Id_Obs(Nx, jj)
27Obs["noise"] = 0.1**2
28Obs["localizer"] = nd_Id_localization((Nx,), (1,), jj, periodic=True)
29
30HMM = modelling.HiddenMarkovModel(Dyn, Obs, tseq, X0)
31
32HMM.liveplotters = LPs(jj)
33
34
35# Pinheiro et al. use
36# - N = 30, but this is only really stated for their PF.
37# - loc-rad = 4, but don't state its definition, nor the exact tapering function.
38# - infl-factor 1.05, but I'm not sure if it's squared or not.
39#
40# They find RMSE (figure 8) hovering around 0.8 for the LETKF,
41# and conclude that "the new filter consistency outperforms the LETKF".
42# I cannot get the LETKF to work well with so much noise,
43# but we note that optimal interpolation (a relatively unsophisticated method)
44# scores around 0.56:
45#                                                   # Expected rmse.a:
46# xps += da.OptInterp()                                        # 0.56
47#
48# The following scores were obtained WITHOUT model noise.
49# They can be used as an indication of how much noise there is in the system.
50# xps += da.EnKF('Sqrt', N=500, infl=1.04)                     # 0.06
51# xps += da.LETKF(N=10, loc_rad=4, infl=1.05, rot=False)       # 0.07
52# xps += da.LETKF(N=30, loc_rad=4, infl=1.05, rot=False)       # 0.07