vmperception {vismeteor}

Perception Probabilities of Visual Meteor Magnitudes

Description

Provides the perception probability of visual meteor magnitudes and its first derivative.

Usage

vmperception(m, deriv.degree = 0L)

Arguments

m

numerical; difference between the limiting magnitude and the meteor magnitude.

deriv.degree

integer; degree of derivative of the perception probability. Currently, valid values of deriv.degree are 0, 1 and 2.

Details

The perception probabilities of Koschack R., Rendtel J., 1990b are estimated with the formula

p(m) = \begin{cases} 1.0 - \exp\left(-z(m + 0.5)\right)\ & \text{ if } m > -0.5,\\ 0.0 \ & \text{ otherwise,} \end{cases}

where

z(x) = 0.003 \, x + 0.0056 \, x^2 + 0.0014 \, x^4

and m is the difference between the limiting magnitude and the meteor magnitude.

Value

This function returns the visual perception probabilities. If deriv.degree is specified, it will return the deriv.degree-th order derivative of the perception probability.

References

Koschack R., Rendtel J., 1990b Determination of spatial number density and mass index from visual meteor observations (II). WGN 18, 119–140.

Examples

# Perception probability of visually estimated meteor of magnitude 3.0
# with a limiting magnitude of 5.6.
vmperception(5.6 - 3.0)

# plot
old_par <- par(mfrow = c(1,1))
plot(
    vmperception,
    -0.5, 8,
    main = paste(
        'perception probability of',
        'visual meteor magnitudes'
    ),
    col = "blue",
    xlab = 'm',
    ylab = 'p'
)
plot(
    function(m) {
        vmperception(m, deriv.degree=1L)/vmperception(m)
    },
    -0.3, 8,
    main = paste(
        'q-values of',
        'visual meteor magnitudes'
    ),
    col = "blue",
    log = 'y',
    xlab = 'm',
    ylab = 'q'
)

par(old_par)