Probability of detection in the study area at a fixed noise level

Answers the question that pDetInArea answers, but with the noise level held still rather than drawn from a distribution: if the noise were always exactly nl, what fraction of the calls in the study area would be detected?

Usage

pDetGivenNL(
  nl,
  detFun,
  SL,
  TL,
  truncationDistance = max(TL[[1]]),
  nSLnodes = 41,
  binWidth = 0.25
)

Arguments

nl

Vector of noise levels in dB.

detFun

Either a detFun object from fitDetFun, or a plain function of SNR returning probability of detection.

SL

List or data.frame containing the distribution of source levels, with elements named mean and sd.

TL

Data.frame of transmission losses. The first column contains ranges in metres, the remaining columns contain TL in dB for each radial transect at that range. Same format as cde expects.

truncationDistance

Scalar or vector of truncation distances in metres. If a vector, one value per transect. Cells beyond the truncation distance carry no weight, and the returned probability is relative to the truncated area.

nSLnodes

Number of quadrature nodes used to average over the source level distribution. Default 41.

binWidth

Width in dB of the transmission loss bins. The only approximation in this function. Default 0.25, which is conservative: results are typically stable to four significant figures at 1 dB.

Value

Numeric vector of the same length as nl, each between 0 and 1.

Details

Evaluated over a grid of noise levels this gives a curve, and that curve is what makes the noise levels measured at detections biased. Quiet periods are over-represented among detections by exactly the ratio the curve describes. See nlFromDetections for the use, and the noiseLevels vignette for the derivation.

Transmission loss enters only as a lookup table, so this makes no assumption about the propagation model. Under spherical spreading the curve falls by one decade per 10 dB, but that is a consequence rather than an input.