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Band-integrated irradiance at one or more depths

Source: R/band_irradiance.R
band_irradiance.Rd

Propagates a spectrum from a known depth to one or more target depths via Beer-Lambert attenuation and integrates the result over a wavelength band. Works in both directions: set from > depths to recover shallower values (including the surface) from a deeper measurement.

Usage

band_irradiance(E_lambda, ...)

# S3 method for class 'numeric'
band_irradiance(
  E_lambda,
  Kd_lambda,
  lambda,
  depths,
  from = 0,
  lambda_min = NULL,
  lambda_max = NULL,
  photonic = FALSE,
  molar_unit = "umol",
  binwidth = NULL,
  allow_above_surface = FALSE,
  ...
)

# S3 method for class 'lux_spectrum'
band_irradiance(E_lambda, Kd_lambda, depths, lambda = NULL, ...)

Arguments

E_lambda

Spectral irradiance (W/m^2/nm) at depth from. Length-N vector, or a lux_spectrum object.

...

Ignored.

Kd_lambda

Diffuse attenuation coefficients (1/m) at the same wavelengths. Length-N vector.

lambda

Wavelengths in nm. Length-N vector (not needed when E_lambda is a lux_spectrum).

depths

Target depth(s) in metres. Scalar or vector.

from

Depth of the known spectrum in metres. Default 0 (surface). Set to a positive value to propagate from a subsurface measurement.

lambda_min

Lower wavelength bound in nm (inclusive). Defaults to min(lambda).

lambda_max

Upper wavelength bound in nm (inclusive). Defaults to max(lambda).

photonic

Logical; if TRUE the result is returned in \(\mu\)mol photons m\(^{-2}\) s\(^{-1}\) rather than W/m^2. Default FALSE.

molar_unit

Molar unit for photonic output. Default "umol".

binwidth

Wavelength bin width in nm. Inferred from lambda if not supplied.

allow_above_surface

Logical; permits target depths above the surface (negative values). Default FALSE.

Value

A data.frame with columns:

depth

Target depth in metres.

E

Band-integrated irradiance in W/m^2 (or \(\mu\)mol/m^2/s when photonic = TRUE).

Details

Two operations are applied in sequence. First, Beer-Lambert propagation at each wavelength: $$E(z,\,\lambda) = E_0(\lambda)\, \exp\!\bigl[-K_d(\lambda)\,(z - z_0)\bigr]$$ where \(z_0\) is the depth of the known spectrum (from) and \(K_d(\lambda)\) is the diffuse attenuation coefficient. Second, the propagated spectrum is integrated over the specified wavelength window [\(\lambda_{\min}\), \(\lambda_{\max}\)]: $$E_{\mathrm{band}}(z) = \int_{\lambda_{\min}}^{\lambda_{\max}} E(z,\,\lambda)\,d\lambda$$ approximated as \(\sum_i E(z,\lambda_i)\,\Delta\lambda\) over bins within the window. See propagate_spectrum for the full Beer-Lambert documentation.

See also

propagate_spectrum, par_irradiance

Examples

sp  <- solar_irradiance("clear_noon")
keep <- sp$wavelength >= 350 & sp$wavelength <= 700
lam <- sp$wavelength[keep]
E0  <- sp$irradiance[keep]
Kd  <- jerlov_Kd("II", lam)

# surface to depth profile, 500-600 nm band
band_irradiance(E0, Kd, lam, depths = c(0, 5, 10, 20, 50),
                lambda_min = 500, lambda_max = 600)
#>   depth          E
#> 1     0 198.300000
#> 2     5 134.985969
#> 3    10  93.620606
#> 4    20  47.073651
#> 5    50   7.323195

# recover surface from a 10 m measurement
E_10m <- E0 * exp(-Kd * 10)
band_irradiance(E_10m, Kd, lam, depths = 0, from = 10)
#>   depth   E
#> 1     0 535