Propagate a known irradiance to any other depth (bidirectional).

Computes E(to) = E_known * exp(-Kd * (to - from)). Works forward (to > from), inverse (to < from, recovering a shallower value), and between any two depths.

Usage

propagate_depth(E_known, Kd, from = 0, to, allow_above_surface = FALSE)

Arguments

E_known: Irradiance at depth from. Scalar or vector.
Kd: Diffuse attenuation coefficient in 1/m. Scalar.
from: Depth of the known measurement in metres. Default 0 (surface).
to: Target depth(s) in metres. Scalar or vector.
allow_above_surface: Logical; permits negative absolute depths (above the surface). Default FALSE.

Value

Irradiance at to, in the same units as E_known.

Note

Un-attenuating with a negative depth delta assumes the water column is homogeneous above the measurement point. For stratified water bodies (thermocline, chlorophyll layer) the result will be approximate. Inverse propagation also amplifies measurement noise and can overflow for long or strongly attenuating paths. This model does not cross the air-water interface; use surface_transmittance explicitly or a high-level workflow such as light_at_depth.

Examples

propagate_depth(112400, Kd = 0.062, from = 0, to = 30)
#> [1] 17497.6
propagate_depth(8260,   Kd = 0.062, from = 22, to = 0)
#> [1] 32311.54