Calculate Modified Two-Step Floating Catchment Area (M2SFCA) accessibility scores

Implements the Modified Two-Step Floating Catchment Area (M2SFCA) method (Delamater, 2013). M2SFCA is identical to [spax_e2sfca()] in step 1, but in step 2 the supply-to-demand ratios are weighted by the **squared** distance decay. This discounts accessibility in sub-optimally configured systems – where demand and supply are both far apart yet still within the catchment – which standard 2SFCA/E2SFCA cannot distinguish.

Usage

spax_m2sfca(
  demand,
  supply,
  distance,
  decay_params = list(method = "gaussian", sigma = 30),
  demand_normalize = "identity",
  id_col = NULL,
  supply_cols = NULL,
  indicator_names = NULL,
  snap = FALSE
)

Arguments

demand

SpatRaster representing spatial distribution of demand

supply

vector, matrix, or data.frame containing supply capacity values

distance

SpatRaster stack of travel times/distances to facilities

decay_params

List of parameters for decay function:

method: "gaussian", "exponential", "power", or "binary"
sigma: decay parameter controlling the rate of distance decay
Additional parameters passed to custom decay functions

demand_normalize

Character specifying normalization method:

"identity": No normalization (original weights)
"standard": Weights sum to 1 (prevents demand inflation)
"semi": Normalize only when sum > 1 (prevents deflation)

id_col

Character; column name for facility IDs if supply is a data.frame

supply_cols

Character vector; names of supply columns if supply is a data.frame

indicator_names

Character vector; custom names for output accessibility layers

snap

Logical; if TRUE enable fast computation mode (default = FALSE)

Value

A spax object (see [spax_e2sfca()]); `type` is "M2SFCA".

Details

Step 1 (unchanged from E2SFCA): \(R_j = S_j / \sum_i P_i W(d_{ij})\).

Step 2 (modified): \(A_i = \sum_j R_j \, W(d_{ij})^2\).

M2SFCA is not a separate engine here: it is the shared FCA recipe with the access-side kernel squared. It is exactly equivalent to `compute_fca(demand, supply, demand_kernel = W, access_kernel = W^2)`.

References