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test_lorenz96_twores.jl
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test_lorenz96_twores.jl
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using Statistics
using LinearAlgebra
using Random
using Distributions
include("da.jl")
import .DA
include("ens_forecast.jl")
import .ens_forecast
include("models.jl")
import .Models
include("integrators.jl")
import .Integrators
Random.seed!(1)
D1 = 220
D2 = 20
models = [Models.lorenz96_twoscale_err, Models.lorenz96_half_true]
model_errs_prescribed = [nothing, nothing, nothing, nothing]
model_true = Models.lorenz96_twoscale_true
n_models = length(models)
dd = zeros(D1)
dd[1:11:D1] .= 1
I1to2 = diagm(dd)[Vector{Bool}(dd), :]
I2to1 = I1to2'
obs_ops = [I(D1), I2to1]
mappings = Matrix{AbstractArray}(undef, n_models, n_models)
mappings[1, 1] = I(D1)
mappings[1, 2] = I1to2
mappings[2, 1] = I2to1
mappings[2, 2] = I(D2)
H = I(D1)
ens_sizes = [20, 20]
model_sizes = [D1, D2]
integrators = [Integrators.rk4, Integrators.rk4, Integrators.rk4, Integrators.rk4]
integrator_true = Integrators.rk4
da_method = DA.ensrf
localization = diagm(ones(D1))
indices = reshape(1:220, 11, :)
first_layer_indices = indices[1, :]
second_layer_indices = indices[2:end, :]
c = 4
for (ii, i) in enumerate(first_layer_indices)
for (ij, j) in enumerate(first_layer_indices)
r = min(mod(ii - ij, 0:20), mod(ij - ii, 0:20))/c
localization[i, j] = DA.gaspari_cohn(r)
localization[j, i] = DA.gaspari_cohn(r)
end
end
for (ii, i) in enumerate(first_layer_indices)
for j=second_layer_indices[ii]
localization[j, i] = localization[i, j] = 1
end
end
for (ii, i) in enumerate(vcat(second_layer_indices...))
for (ij, j) in enumerate(vcat(second_layer_indices...))
r = min(mod(ii - ij, 0:200), mod(ij - ii, 0:200))/40
localization[i, j] = DA.gaspari_cohn(r)
localization[j, i] = DA.gaspari_cohn(r)
end
end
x0 = rand(D1)
t0 = 0.0
Δt = 0.005
outfreq = 1
transient = 2000
x = integrators[1](models[1], x0, t0, transient*outfreq*Δt, Δt, inplace=false)
R = Symmetric(diagm(var(x, dims=1)[:]*0.1))
ens_errs = [R, R[first_layer_indices, first_layer_indices]]
gen_ensembles = false
assimilate_obs = false
all_orders = false
save_Q_hist = false
leads = 5
ref_model = 1
x0 = x[end, :]
n_cycles = 500*leads
ρ = 1e-3
ρ_all = 1e-2
window = 40
ensembles = [mappings[ref_model, 1]*x0 .+ rand(MvNormal(ens_errs[1]), sum(ens_sizes))]
info_a = ens_forecast.da_cycles(x0=x0, ensembles=ensembles, models=[models[1]],
model_true=model_true, obs_ops=[obs_ops[1]], H_true=I,
model_errs=[ens_errs[1]],
model_errs_prescribed=[model_errs_prescribed[1]],
integrators=[integrators[1]],
integrator_true=integrator_true, da_method=da_method,
localization=mappings[ref_model, 1]*localization*mappings[ref_model, 1]',
ens_sizes=[sum(ens_sizes)], Δt=Δt, window=window,
n_cycles=n_cycles, outfreq=outfreq,
model_sizes=[model_sizes[1]], R=R,
ens_errs=[ens_errs[1]], ρ=ρ, ρ_all=ρ_all,
gen_ensembles=gen_ensembles,
assimilate_obs=true, save_analyses=true, save_trues=true,
leads=1, save_Q_hist=save_Q_hist,
mappings=mappings[1:1, 1:1])
#x0 = integrators[1](model_true, x0, t0, window*outfreq*Δt, Δt)
infos = Vector(undef, n_models)
for model=1:n_models
model_errs = [ens_errs[model]]
ens_size = ens_sizes[model]
ensembles = [mappings[ref_model, model]*x0 .+ rand(MvNormal(ens_errs[model]), ens_size)]
if model == 2
analyses = permutedims(cat([mappings[1, 2]*info_a.analyses[c, :, :] for c=1:n_cycles]..., dims=3), [3, 1, 2])
mapping_true = mappings[1, 2]
else
analyses = info_a.analyses
mapping_true = I
end
info = ens_forecast.da_cycles(x0=x0, ensembles=ensembles, models=[models[model]],
model_true=model_true, obs_ops=[obs_ops[model]], H_true=I,
model_errs=model_errs,
model_errs_prescribed=[model_errs_prescribed[model]],
integrators=[integrators[model]],
integrator_true=integrator_true, da_method=da_method,
localization=mappings[ref_model, model]*localization*mappings[ref_model, model]',
ens_sizes=[ens_size], Δt=Δt, window=window,
n_cycles=n_cycles, outfreq=outfreq,
model_sizes=[model_sizes[model]], R=R,
ens_errs=[ens_errs[model]], 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,
mappings=mappings[model:model, model:model], mapping_true=mapping_true,
prev_analyses=analyses)
infos[model] = info
end
ensembles = [mappings[ref_model, model]*x0 .+ rand(MvNormal(ens_errs[model]), ens_sizes[model]) for model=1:n_models]
model_errs = ens_errs
info_mm = ens_forecast.da_cycles(x0=x0, ensembles=ensembles, models=models,
model_true=model_true, obs_ops=obs_ops,
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=all_orders, combine_forecasts=true,
gen_ensembles=gen_ensembles, assimilate_obs=assimilate_obs,
leads=leads, save_Q_hist=save_Q_hist, ref_model=ref_model,
mappings=mappings, prev_analyses=info_a.analyses)