StochasticWeatherGenerators.jl

fit_mle_stations(df::DataFrame, K, T, degree, local_order)

Given a DataFrame df with known hidden states column z ∈ 1:K. The rain occurrences of the new station are fitted conditionally to the hidden state. For local_order>0 the model is also autoregressive with its past.

fit_mle_RR(df::DataFrame, K, local_order; maxiter=5000, tol=2e-4, robust=true, silence=true, warm_start=true, display=:none, mix₀=mix_ini(T))

mix_allE = fit_mle_RR.(data_stations, K, local_order)

fit_TN(df_full::DataFrame, 𝐃𝐞𝐠, T; kwargs...)

Fit the variable TN (daily minimum temperature). In fact it fits the difference ΔT = TX - TN to ensure a positive difference between TX and TN

fit_AR1(df_full::DataFrame, X, 𝐃𝐞𝐠, T, K)

Fit a Seasonal AR(1) model of period T and with K hidden states for the variable X of the DataFrame df_full. $X_{n+1} = \mu(t_n) + \phi(t_n) X_t + \sigma(t_n)\xi$

VCX3(df; y_col, nb = 3)

Yearly Max of nb = 3 days sliding mean for y for every year. By default, y_col is the first column not with a Date type

using DataFrames, Dates, RollingFunctions
time_range = Date(1956):Day(1):Date(2019,12,31)
df = DataFrame(:DATE => time_range, :Temperature => 20 .+ 5*randn(length(time_range)))
VCX3(df)

VCX3(y, idxs; nb = 3)

Yearly Max of nb = 3 days sliding mean for y. Here idxs can be a vector of vector (or range) corresponds to the index of every year.

using DataFrames, Dates, RollingFunctions
time_range = Date(1956):Day(1):Date(2019,12,31)
year_range = unique(year.(time_range))
df = DataFrame(:DATE => time_range, :Temperature => 20 .+ 5*randn(length(time_range)))
idx_year = [findall(x-> year.(x) == m, df[:, :DATE]) for m in year_range]
VCX3(df.Temperature, idx_year)

cum_monthly(y::AbstractArray, idxs)

using DataFrames, Dates, RollingFunctions
time_range = Date(1956):Day(1):Date(2019,12,31)
year_range = unique(year.(time_range))
df = DataFrame(:DATE => time_range, :Temperature => 20 .+ 5*randn(length(time_range)))
idx_year = [findall(x-> year.(x) == m, df[:, :DATE]) for m in year_range]
idx_month = [findall(x-> month.(x) == m, df[:, :DATE]) for m in 1:12]
idx_all = [intersect(yea, mon) for yea in idx_year, mon in idx_month]
cum_monthly(y, idx_all)

corTail(x::AbstractMatrix, q = 0.95)

Compute the (symmetric averaged) tail index matrix M of a vector x, i.e. M[i, j] = (ℙ(x[:,j] > Fxⱼ(q) ∣ x[:,i] > Fxᵢ(q)) + ℙ(x[:,i] > Fxᵢ(q) ∣ x[:,j] > Fxⱼ(q)))/2 where Fx(q) is the CDF of x. Note it uses the same convention as cor function i.e. observations in rows and features in column.

longuest_spell(y::AbstractArray; value=0)

Compute the length of the longuest consecutive sequence of value in y

pmf_spell(y::AbstractVector, value)

Return the distribution of spells (consecutive sequence of with the same value) length of value in y

rand_RR(mixs::AbstractArray{<:MixtureModel}, n2t::AbstractVector, z::AbstractVector, y::AbstractMatrix, Σk::AbstractArray)

Generate a (nonhomegenous) sequence of length length(n2t) of rain amounts conditionally to a given dry/wet matrix y and (hidden) state sequence z. Univariate distribution are given by mixs while correlations are given by covariance matrix Σk.

rand_cond(ϵ, z, θ_uni, θ_cor, n2t, T)

Genererate a random variable conditionnaly to another one Using Copula

\[X_1 \mid X_2 = ϵ \sim \mathcal{N}\left(\mu_1 + \dfrac{\sigma_1}{\sigma_2}\rho (a - \mu_2), (1-\rho^2)\sigma_1^2 \right)\]

For two N(0,1)

\[X_1 \mid X_2 = ϵ \sim \mathcal{N}\left(\rho a , (1-\rho^2) \right)\]

Compute and fit the `cor` between two `var` with a smooth function for each `z`.

Compute and fit the `cor` between `:TX` and `:TX-:TN` with a smooth function for each `z`.

Fit residual to constant (in time) cov matrices for each weather regime Example:

cov_ar1(data_stations, ar1sTX, :TX, K)

cov_RR(dfs::AbstractArray{<:DataFrame}, K)

Each df must have :DATE, :RR, :z (same :z for each df)

Σ²RR = cov_RR(data_stations, K)

Σ_Spearman2Pearson(M::AbstractMatrix)

Compute the Pearson correlation coefficient i.e. the classic one from the Spearman correlation #TODO Add ref

Σ_Kendall2Pearson(M::AbstractMatrix)

Compute the Pearson correlation coefficient i.e. the classic one from the Kendall correlation #TODO Add ref

joint_rain(M::AbstractMatrix, j1::Integer, j2::Integer, r = 0)

Select all the rows of M with values for (two) columns above some value r.

distance_x_to_y

Distance in km between two stations.

dms_to_dd(l)

Convert Degrees Minutes Seconds to Decimal Degrees. Inputs are strings of the form

• LAT : Latitude in degrees:minutes:seconds (+: North, -: South)
• LON : Longitude in degrees:minutes:seconds (+: East, -: West)

collect_data_ECA(STAID::Integer, path::String, var::String="RR"; skipto=19, header = 18)

path gives the path where all data files are stored in a vector

collect_data_ECA(STAID, date_start::Date, date_end::Date, path::String, var::String="RR"; portion_valid_data=1, skipto=19, header = 18, return_nothing = true)

• path gives the path where all data files are stored in a vector
• Filter the DataFrame s.t. date_start ≤ :DATE ≤ date_end
• var = "RR", "TX" etc.
• portion_valid_data is the portion of valid data we are ok with. If we don't want any missing, fix it to 1.
• skipto and header for csv files with meta informations/comments at the beginning of files. See CSV.jl.
• return_nothing if true it will return nothing is the file does not exists or does not have enough valid data.

select_in_range_df(datas, start_Date, interval_Date, [portion])

Select station with some data availability in dates and quality (portion of valid data). Input is a vector (array) of DataFrame (one for each station for example) or a Dict of DataFrame. If 0 < portion ≤ 1 is specified, it will authorize some portion of data to be missing.

shortname(name::String)

Experimental function that returns only the most relevant part of a station name.

long_name = "TOULOUSE-BLAGNAC"
shortname(long_name) # "TOULOUSE"

my_color(k, K)

Convenience for plot colors pattern and hidden states to blue for k=1 (∼wetter) and orange for k=K (∼driest)