Forecasting at New Locations

Overview

krige_new() extends an estimated MCGF model to spatial locations that were not used for fitting. This is useful when:

a station is newly installed;
forecasts are required on a target grid;
some sites are intentionally held out for validation; or
future scenario generation is needed at additional locations.

There are two ways to describe the new sites:

provide their coordinates with locations_new, or
provide precomputed signed distances with dists_new.

This vignette demonstrates the coordinate workflow.

Prepare an MCGF object

The built-in sim1 data contain both observations and locations.

library(mcgf)
data(sim1)

x <- mcgf(
    sim1$data,
    locations = sim1$locations
)
#> `time` is not provided, assuming rows are equally spaced temporally.

x <- add_acfs(x, lag_max = 5)
x <- add_ccfs(x, lag_max = 5)

Fit the base covariance model

For a first new-location forecast, a separable base model is sufficient.

fit_sep <- fit_base(
    x,
    model = "sep",
    lag = 5,
    par_init = c(
        c = 0.001,
        gamma = 0.5,
        a = 0.3,
        alpha = 0.5
    ),
    par_fixed = c(nugget = 0)
)

x <- add_base(x, fit_base = fit_sep)

Define a new location

For illustration, place a new site near the centre of the existing network.

new_location <- matrix(
    colMeans(sim1$locations),
    nrow = 1
)
rownames(new_location) <- "New_site"

new_location
#>               [,1]     [,2]
#> New_site -109.9254 50.20862

Forecast with `krige_new()`

pred <- krige_new(
    x,
    locations_new = new_location,
    model = "base",
    interval = TRUE
)

dim(pred$fit)
#> [1] 1000   11

The output contains forecasts for the original sites and the appended new site. The new site is the last spatial column.

new_index <- dim(pred$fit)[2]

head(pred$fit[, new_index])
#>          1          2          3          4          5          6 
#>         NA         NA         NA         NA         NA 0.01776882
head(pred$lower[, new_index])
#>         1         2         3         4         5         6 
#>        NA        NA        NA        NA        NA -1.534888
head(pred$upper[, new_index])
#>        1        2        3        4        5        6 
#>       NA       NA       NA       NA       NA 1.570425

Forecast using new observed data

If you have a separate future period for the original locations, supply it with newdata:

pred_future <- krige_new(
    x,
    newdata = future_data,
    locations_new = new_location,
    model = "base",
    interval = TRUE
)

future_data must have the same columns, in the same order, as the fitted mcgf object.

If observations at the new location are available

You can also provide newdata_new. These observations are then included in the lagged information used for forecasting.

pred_with_new_history <- krige_new(
    x,
    newdata = future_data,
    locations_new = new_location,
    newdata_new = future_new_site,
    model = "base",
    interval = TRUE
)

The number of rows in newdata_new must match newdata, and the number of columns must match the number of new locations.

Supplying distances directly

If the object does not contain coordinates, calculate the distances yourself and pass them through dists_new.

d_new <- find_dists_new(
    locations = observed_locations,
    locations_new = new_location,
    longlat = TRUE
)

pred <- krige_new(
    x,
    dists_new = d_new,
    model = "base"
)

Do not supply both locations_new and dists_new.

General stationary model

Once a Lagrangian model has been fitted and added with add_lagr(), switch to:

pred_all <- krige_new(
    x,
    locations_new = new_location,
    model = "all",
    interval = TRUE
)

This extends both the base and directional Lagrangian covariance to the new location.

Regime-switching objects

krige_new() also has an mcgf_rs method. Use dists_new_ls and sds_new_ls when distance or marginal-variance assumptions differ by regime. For soft regime forecasts, supply regime probabilities using prob.

See vignette("mcgf_rs", package = "mcgf") for a complete RS-MCGF fit.