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test_lorenz96_partial.jl
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test_lorenz96_partial.jl
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using Statistics
using LinearAlgebra
using Random
using Distributions
using BlockArrays
include("da.jl")
import .DA
include("ens_forecast.jl")
import .ens_forecast
include("models.jl")
import .Models
include("integrators.jl")
import .Integrators
Random.seed!(10)
D = 40
models = [Models.lorenz96_err, Models.lorenz96_err2, Models.lorenz96_err3,
Models.lorenz96_err4]
model_errs_prescribed = [nothing, nothing, nothing, nothing]
model_true = Models.lorenz96_true
n_models = length(models)
#half_I = Array{Float64}(I(D)[1:20, :])
H = diagm(ones(D))[1:2:D, :]
obs_ops = [H, H, H, H]
ens_sizes = [20, 20, 20, 20]
model_sizes = [D, D, D, D]
integrators = [Integrators.rk4, Integrators.rk4, Integrators.rk4, Integrators.rk4]
integrator_true = Integrators.rk4
da_method = DA.ensrf
localization_radius = 4
localization = DA.gaspari_cohn_localization(localization_radius, D, cyclic=true)
x0 = randn(D)
t0 = 0.0
Δt = 0.05
outfreq = 1
transient = 2000
x = integrators[1](models[1], x0, t0, transient*outfreq*Δt, Δt, inplace=false)
R = Symmetric(diagm(0.25*ones(20)))
ens_errs = [Symmetric(diagm(0.25*ones(D))), Symmetric(diagm(0.25*ones(D))),
Symmetric(diagm(0.25*ones(D))), Symmetric(diagm(0.25*ones(D)))]
gen_ensembles = false
assimilate_obs = true
save_Q_hist = false
save_P_hist = false
leads = 1
x0 = x[end, :]
n_cycles = 3000*leads
ρ = 1e-3
ρ_all = 1e-2
window = 4
all_Q_p = []
for i=1:4
for j=1:4
Q_p = mortar(reshape([zeros(10, 10) for i=1:16], 4, 4))
Q_p[Block(i, j)] = ones(10, 10)
append!(all_Q_p, [Matrix(Q_p)])
end
end
all_Q_p = Vector{Matrix{Float64}}(all_Q_p)
infos = Vector(undef, n_models)
for model=1:n_models
Random.seed!(10)
model_errs = [0.1*diagm(ones(D))]
ens_size = sum(ens_sizes)
ensembles = [x0 .+ rand(MvNormal(Symmetric(diagm(0.25*ones(D)))), ens_size)]
info = ens_forecast.da_cycles(x0=x0, ensembles=ensembles, models=[models[model]],
model_true=model_true, obs_ops=[obs_ops[model]], H_true=H,
model_errs=model_errs,
model_errs_prescribed=[model_errs_prescribed[model]],
integrators=integrators, integrator_true=integrator_true, da_method=da_method,
localization=localization, ens_sizes=[ens_size], Δt=Δt,
window=window, n_cycles=n_cycles, outfreq=outfreq,
model_sizes=model_sizes, R=R, ens_errs=ens_errs, ρ=ρ,
ρ_all=ρ_all,
gen_ensembles=gen_ensembles,
assimilate_obs=assimilate_obs, save_analyses=false,
leads=leads, save_Q_hist=save_Q_hist,
save_P_hist=save_P_hist, Q_p=all_Q_p)
infos[model] = info
end
Random.seed!(10)
ensembles = [x0 .+ rand(MvNormal(Symmetric(diagm(0.25*ones(D)))), ens_sizes[model]) for model=1:n_models]
model_errs = [0.1*diagm(ones(D)) for model=1:n_models]
info_mm = ens_forecast.da_cycles(x0=x0, ensembles=ensembles, models=models,
model_true=model_true, obs_ops=obs_ops, H_true=H,
model_errs=model_errs,
model_errs_prescribed=model_errs_prescribed,
integrators=integrators, integrator_true=integrator_true, da_method=da_method,
localization=localization, ens_sizes=ens_sizes, Δt=Δt,
window=window, n_cycles=n_cycles, outfreq=outfreq,
model_sizes=model_sizes, R=R, ens_errs=ens_errs, ρ=ρ,
ρ_all=ρ_all,
all_orders=false, combine_forecasts=true,
gen_ensembles=gen_ensembles, assimilate_obs=assimilate_obs,
leads=leads, save_Q_hist=save_Q_hist, Q_p=all_Q_p)
Random.seed!(10)
ensembles = [x0 .+ rand(MvNormal(Symmetric(diagm(0.25*ones(D)))), ens_sizes[model]) for model=1:n_models]
model_errs = [0.1*diagm(ones(D)) for model=1:n_models]
info_mm2 = ens_forecast.da_cycles(x0=x0, ensembles=ensembles, models=models,
model_true=model_true, obs_ops=obs_ops, H_true=H,
model_errs=model_errs,
model_errs_prescribed=model_errs_prescribed,
integrators=integrators, integrator_true=integrator_true, da_method=da_method,
localization=localization, ens_sizes=ens_sizes, Δt=Δt,
window=window, n_cycles=n_cycles, outfreq=outfreq,
model_sizes=model_sizes, R=R, ens_errs=ens_errs, ρ=ρ,
ρ_all=ρ_all,
combine_forecasts=false, gen_ensembles=gen_ensembles,
assimilate_obs=assimilate_obs, leads=leads,
save_Q_hist=save_Q_hist, Q_p=all_Q_p)
Random.seed!(10)
ensembles = [x0 .+ rand(MvNormal(Symmetric(diagm(0.25*ones(D)))), ens_sizes[model]) for model=1:n_models]
model_errs = [0.1*diagm(ones(D)) for model=1:n_models]
info_mm_all = ens_forecast.da_cycles(x0=x0, ensembles=ensembles, models=models,
model_true=model_true, obs_ops=obs_ops, H_true=H,
model_errs=model_errs,
model_errs_prescribed=model_errs_prescribed,
integrators=integrators, integrator_true=integrator_true, da_method=da_method,
localization=localization, ens_sizes=ens_sizes, Δt=Δt,
window=window, n_cycles=n_cycles, outfreq=outfreq,
model_sizes=model_sizes, R=R, ens_errs=ens_errs, ρ=ρ,
ρ_all=ρ_all,
all_orders=true, combine_forecasts=true,
gen_ensembles=gen_ensembles, assimilate_obs=assimilate_obs,
leads=leads, save_Q_hist=save_Q_hist, Q_p=all_Q_p)