bin_average_weight: Bin-average the weight of a size-spectrum integral

In mizer: Dynamic Multi-Species Size Spectrum Modelling

Bin-average the weight of a size-spectrum integral

Description

Prepares the weight K(w) of an integral over the size spectrum so that the integral is evaluated with the quadrature scheme the model is actually using. Use this when writing your own indicator or diagnostic function; the built-in summary and indicator functions call it for you.

Usage

bin_average_weight(K, params)

Arguments

K	A numeric vector of weights indexed over the size grid, or a numeric array whose last dimension runs over the size grid (e.g. a species-by-size matrix or a gear-by-species-by-size array).
params	A MizerParams object whose second_order_w slot controls the gating.

Details

An integral \int N(w) K(w)\, dw is discretised on mizer's finite-volume grid as \sum_j N_j \bar K_j \Delta w_j, where N_j is the cell average of the density over bin [w_j, w_{j+1}]. Only the weight is approximated: N_j is already a cell average and \Delta w_j is exact, so neither the abundance nor the bin widths should ever be passed through this function.

Whether the point weight K(w_j) is replaced by the bin average

\bar K_j = \frac{1}{\Delta w_j}\int_{w_j}^{w_{j+1}} K(w)\,dw \approx \tfrac12\big(K(w_j) + K(w_{j+1})\big)

is controlled by the bin_average entry of the model's second_order_w() slot. When it is FALSE (the default) K is returned unchanged, so an indicator written with this function reproduces the left-edge Riemann sums of previous mizer versions byte-for-byte. When it is TRUE the trapezoidal bin average is returned, which is uniformly second order and exact whenever K is linear in w (e.g. the first moment K = w, for which it equals (w_{j+1}^2 - w_j^2)/(2\Delta w_j)).

Because the gating happens inside, always call this rather than averaging unconditionally: a hard-coded bin average silently changes the results of models that are on the default scheme.

If K is a product of several size-dependent factors, average the product and not the individual factors — the average of a product is not the product of the averages. Spawning stock biomass, for example, averages maturity * w as a single weight.

The top bin has no right-hand neighbour on the grid, so its weight is left unaveraged (one-sided); the density there is negligible, so this does not affect the second-order accuracy of the totals.

Value

The weight K, bin-averaged when params@second_order_w[["bin_average"]] is TRUE, otherwise returned unchanged.

See Also

second_order_w(), get_size_range_array(), encounter_kernel()

Examples

# Biomass of each species above 10g -- what getBiomass() does internally.
params <- NS_params
K <- get_size_range_array(params, min_w = 10)   # species x size, 0/1
K <- sweep(K, 2, params@w, "*")                 # weight by w to get biomass
K <- bin_average_weight(K, params)              # gated on second_order_w
rowSums(sweep(initialN(params) * K, 2, params@dw, "*"))

mizer documentation built on Aug. 24, 2026, 9:08 a.m.