Generate a synthetic 4D soil-dynamics cube (Pillar 3 helper)

Builds a small spatio-temporal cube with realistic-looking dynamics of Soil Organic Carbon (SOC) driven by monthly precipitation over a static elevation field. The governing update is a minimalist mass-balance

Usage

temporal_synth_soc_cube(
  H = 16L,
  W = 16L,
  T_total = 18L,
  seed = 1L,
  k_in = 0.03,
  k_out = 0.015,
  noise = 0.2
)

Arguments

H, W

Integer, spatial grid size.

T_total

Integer, total number of months.

seed

Integer, RNG seed for reproducibility.

k_in, k_out

Numeric rate coefficients (defaults are tuned so SOC stays in a physically plausible 10-50 g/kg range).

noise

Numeric, standard deviation of Gaussian process noise on the SOC evolution (per pixel, per month).

Value

A list with elements

elev

Numeric matrix H x W.

precip

Numeric array T x H x W.

soc

Numeric array T x H x W.

Details

$$ \mathrm{SOC}_{t+1} = \mathrm{SOC}_t + k_{\text{in}}\, P_t - k_{\text{out}}\,\mathrm{SOC}_t\, P_t / \bar{P} + \varepsilon $$

with k_in, k_out small, \(P_t\) the monthly precipitation, and \(\bar P\) the long-term mean. Precipitation itself is a sinusoidal seasonal cycle modulated by a west-east gradient so the cube shows both temporal memory and spatial heterogeneity.

Use the resulting object to train temporal_convlstm_fit() and forecast forward with temporal_convlstm_rollout() in the Pillar 3 vignette.

Examples

cube <- temporal_synth_soc_cube(H = 8, W = 8, T_total = 12, seed = 1)
dim(cube$soc)  # 12 x 8 x 8
#> [1] 12  8  8