Fraction of downwelling irradiance transmitted across the water surface.

The fraction of above-surface downwelling irradiance that enters the water after Fresnel reflection at a flat air-water interface — the surface term of an above-vs-below-water light budget: \(E_{\text{below}} \approx \tau\,E_{\text{above}}\) (Johnsen 2012, ch. 5).

Usage

surface_transmittance(angle = NULL, n = 1.333, source = c("direct", "diffuse"))

Arguments

angle: Solar/incidence angle from the surface normal, in degrees (0-90). Required for source = "direct"; ignored for "diffuse".
n: Refractive index of water relative to air. Default 1.333.
source: "direct" (collimated beam at angle) or "diffuse" (isotropic sky).

Value

Transmitted fraction of downwelling irradiance (0-1).

Details

For a "direct" (collimated, e.g. solar-beam) source at a given incidence angle, \(\tau = 1 - R(\theta)\). For a "diffuse" (isotropic sky) source it is the cosine-weighted hemispherical average of \(1 - R(\theta)\), about 0.93 for seawater (i.e. ~7% is reflected). This is the planar-irradiance transmittance; in-water radiance is additionally boosted by \(n^2\) because the refracted beam is compressed into snells_window.

References

Johnsen S (2012) The Optics of Life. Princeton University Press, ch. 5.

Examples

surface_transmittance(angle = 0)              # overhead sun: ~0.98
#> [1] 0.9796268
surface_transmittance(source = "diffuse")     # isotropic sky: ~0.93
#> [1] 0.9335942