def L63_gen():
from dapper.mods.Lorenz63.sakov2012 import HMM as _HMM
HMM = _HMM.copy()
HMM.t.BurnIn = 0
HMM.t.KObs = 10
dpr.set_seed(3000)
# xps
xps = dpr.xpList()
xps += da.Climatology()
xps += da.OptInterp()
xps += da.Var3D(xB=0.1)
xps += da.ExtKF(infl=90)
xps += da.EnKF("Sqrt", N=3, infl=1.30)
xps += da.EnKF("Sqrt", N=10, infl=1.02, rot=True)
xps += da.EnKF("PertObs", N=500, infl=0.95, rot=False)
xps += da.EnKF_N(N=10, rot=True)
xps += da.iEnKS("Sqrt", N=10, infl=1.02, rot=True)
xps += da.PartFilt(N=100, reg=2.4, NER=0.3)
xps += da.PartFilt(N=800, reg=0.9, NER=0.2)
xps += da.PartFilt(N=4000, reg=0.7, NER=0.05)
xps += da.PFxN(xN=1000, N=30, Qs=2, NER=0.2)
# Run
xps.launch(HMM, False, store_u=True)
return xps
def L96_table():
import dapper.mods.Lorenz96 as model
from dapper.mods.Lorenz96.sakov2008 import HMM as _HMM
model.Force = 8.0 # undo pinheiro2019
HMM = _HMM.copy()
HMM.t.BurnIn = 0
HMM.t.KObs = 10
dpr.set_seed(3000)
# xps
xps = dpr.xpList()
xps += da.Climatology()
xps += da.OptInterp()
xps += da.Var3D(xB=0.02)
xps += da.ExtKF(infl=6)
xps += da.EnKF("PertObs", N=40, infl=1.06)
xps += da.EnKF("Sqrt", N=28, infl=1.02, rot=True)
xps += da.EnKF_N(N=24, rot=True)
xps += da.EnKF_N(N=24, rot=True, xN=2)
xps += da.iEnKS("Sqrt", N=40, infl=1.01, rot=True)
xps += da.LETKF(N=7, rot=True, infl=1.04, loc_rad=4)
xps += da.SL_EAKF(N=7, rot=True, infl=1.07, loc_rad=6)
xps.launch(HMM, store_u=True)
table = xps.tabulate_avrgs(statkeys, decimals=4)
return table.splitlines(True)
# #### Imports
# %matplotlib notebook
from mpl_tools import is_notebook_or_qt as nb
import dapper as dpr
import dapper.da_methods as da
# #### Load experiment setup: the hidden Markov model (HMM)
from dapper.mods.Lorenz63.sakov2012 import HMM # isort:skip
# #### Generate the same random numbers each time this script is run
seed = dpr.set_seed(3000)
# #### Simulate synthetic truth (xx) and noisy obs (yy)
HMM.t.T = 30 # shorten experiment
xx, yy = HMM.simulate()
# #### Specify a DA method configuration ("xp" for "experiment")
xp = da.EnKF('Sqrt', N=10, infl=1.02, rot=True)
# xp = da.Var3D()
# xp = da.PartFilt(N=100, reg=2.4, NER=0.3)
# #### Assimilate yy, knowing the HMM; xx is used to assess the performance
xp.assimilate(HMM, xx, yy, liveplots=not nb)
"""Prettier, static illustration of Lorenz two-speed/scale/layer model.""" # Sorry for the mess. import matplotlib as mpl import numpy as np from matplotlib import pyplot as plt import dapper as dpr from dapper.mods.LorenzUV.lorenz96 import LUV from dapper.tools.math import ccat # Setup sd0 = dpr.set_seed(4) # from dapper.mods.LorenzUV.wilks05 import LUV nU, J = LUV.nU, LUV.J dt = 0.005 t0 = np.nan K = int(10 / dt) step_1 = dpr.with_rk4(LUV.dxdt, autonom=True) step_K = dpr.with_recursion(step_1, prog=1) x0 = 0.01 * np.random.randn(LUV.M) x0 = step_K(x0, int(2 / dt), t0, dt)[-1] # BurnIn xx = step_K(x0, K, t0, dt) # Grab parts of state vector ii = np.arange(nU + 1) jj = np.arange(nU * J + 1) circU = np.mod(ii, nU)
def set_X0_and_simulate(hmm, xp):
dpr.set_seed(3000)
hmm.X0 = X0(TRUTH, 0)
xx, yy = hmm.simulate()
hmm.X0 = X0(GUESS, 0.1**2)
return xx, yy
"""Illustrate usage of DAPPER to benchmark multiple DA methods."""
import dapper as dpr
dpr.set_seed(3000)
##############################
# DA method configurations
##############################
xps = dpr.xpList()
from dapper.mods.Lorenz63.sakov2012 import HMM # Expected rmse.a:
xps += dpr.Climatology() # 7.6
xps += dpr.OptInterp() # 1.25
xps += dpr.Var3D(xB=0.1) # 1.03
xps += dpr.ExtKF(infl=90) # 0.87
xps += dpr.EnKF('Sqrt', N=3, infl=1.30) # 0.82
xps += dpr.EnKF('Sqrt', N=10, infl=1.02, rot=True) # 0.63
xps += dpr.EnKF('PertObs', N=500, infl=0.95, rot=False) # 0.56
xps += dpr.EnKF_N(N=10, rot=True) # 0.54
xps += dpr.iEnKS('Sqrt', N=10, infl=1.02, rot=True) # 0.31
xps += dpr.PartFilt(N=100, reg=2.4, NER=0.3) # 0.38
xps += dpr.PartFilt(N=800, reg=0.9, NER=0.2) # 0.28
# xps += dpr.PartFilt( N=4000, reg=0.7 , NER=0.05) # 0.27
# xps += dpr.PFxN(xN=1000, N=30 , Qs=2 , NER=0.2) # 0.56
# from dapper.mods.Lorenz96.sakov2008 import HMM # Expected rmse.a:
# xps += dpr.Climatology() # 3.6
# xps += dpr.OptInterp() # 0.95
# xps += dpr.Var3D(xB=0.02) # 0.41
###########################
# Setup
###########################
PRMS = 'Lorenz'
if PRMS == 'Wilks':
from dapper.mods.LorenzUV.wilks05 import LUV
else:
from dapper.mods.LorenzUV.lorenz96 import LUV
nU = LUV.nU
K = 400
dt = 0.005
t0 = np.nan
dpr.set_seed(30) # 3 5 7 13 15 30
x0 = np.random.randn(LUV.M)
true_step = with_rk4(LUV.dxdt, autonom=True)
model_step = with_rk4(LUV.dxdt_trunc, autonom=True)
true_K = with_recursion(true_step, prog=1)
###########################
# Compute truth trajectory
###########################
x0 = true_K(x0, int(2 / dt), t0, dt)[-1] # BurnIn
xx = true_K(x0, K, t0, dt)
###########################
# Compute unresovled scales
###########################
