MetFns (version 2.1.0)

pop.index: Calculation of population index

Description

Calculates and plots population index of a meteor shower for a given magnitude data, specified time period, magnitude values and bin size.

Usage

pop.index(data,year,month.beg,month.end=month.beg,day.beg,day.end=day.beg,
time.beg=0,time.end=2359,shw,mag.range=-6:7,k,add.plot=FALSE,xlim1=NULL,
xlim2=NULL,xinc=NULL,ylim1=NULL,ylim2=NULL,yinc=NULL)

Arguments

data

data frame consisting of visual meteor magnitude data.

year

numeric vector of length 4 specifying year.

month.beg

numeric vector specifying the beginning month.

month.end

numeric vector specifying the ending month. By default, month.end is set to be equal to month.beg.

day.beg

numeric vector specifying the beginning day.

day.end

numeric vector specifying the ending day. By default, day.end is set to be equal to day.beg.

time.beg

numeric vector (0-2359) specifying lower boundary of time in hours and minutes, corresponding to day.beg. By default, time.beg is set to be equal to 0.

time.end

numeric vector (0-2359) specifying upper boundary of time in hours and minutes, corresponding to day.end. By default, time.end is set to be equal to 2359.

shw

character string consisting of three capital letters which represent meteor shower code.

mag.range

numeric vector specifying range of magnitudes. It should consist of at least 5 magnitude classes.

k

numeric vector specifying bin size in degrees of solar longitude.

add.plot

logical vector. If TRUE, the population index is plotted.

xlim1

numeric vector specifying minimum value on x-axis.

xlim2

numeric vector specifying maximum value on x-axis.

xinc

numeric vector specifying increment between labels on x-axis.

ylim1

numeric vector specifying minimum value on y-axis.

ylim2

numeric vector specifying maximum value on y-axis.

yinc

numeric vector specifying increment between labels on y-axis.

Value

Data frame containing following vectors

start

factor Calendar date and time in UTC at the time interval beginning

stop

factor Calendar date and time in UTC at the time interval end

sollong

numeric Solar longitude corresponding to the middle of time interval

mag

factor Range of magnitude values

nINT

numeric Number of observing time intervals

nSHW

numeric Number of observed meteors belonging to the shower

pop.index

numeric Population index

sigma.r

numeric Standard error of population index

If add.plot is TRUE, additionally xy plot of population index is made. Solar longitude is on x-axis and population index on y-axis. Population index is represented with black filled circles and 68% confidence intervals. Values of limits (minimum and maximum values) on x and y axis (xlim1,xlim2,ylim1,ylim2), as well as increments between the axis labels (xinc,yinc) should be provided to function call.

Details

Probabilities of perception are incorporated in magnitude distributions for each observing interval. Cummulative summarized magnitude distribution Phi(m) is formed by summing cummulative frequencies of all observers for each magnitude class m.

Using the relationship for population index r=Phi(m+1)/Phi(m) and substitutiong 0,1,...m magnitudes, equation Phi(m)=Phi(0)r^m (or ln(Phi(m))=ln(Phi(0))+r log(m) in logarithmic form) can be written. Then, population index r is calculated by the method of least squares, for chosen range of magnitude values.

Standard error of population index is approximated with

sigma_r= r sqrt(sum e_i^2/((n-2)sum_i m_i^2)),

where i=1,2,..n, n is number of magnitude values, e_i regression residuals, i=1,2,..n.

References

Koschack R. and Rendtel J. (1990). Determination of spatial number density and mass index from visual meteor observations (1). WGN, Journal of the IMO, 18(2), 44 - 58.

Koschack R. and Rendtel J. (1990). Determination of spatial number density and mass index from visual meteor observations (2). WGN, Journal of the IMO, 18(4), 119 - 140.

Rendtel J. and Arlt R., editors (2008). IMO Handbook For Meteor Observers. IMO, Potsdam.

See Also

mag.distr,pop.index2,zhr

Examples

## calculate population index for observations of 1997 Perseids, time period 
## 27th July to 16th August, radiant elevation higher than 20 degrees,
## total correction factor smaller than 5, bin size 1 degree
## First select magnitude data for Perseids activity - time period 15th July to 24th August, 
## radiant elevation higher than 20 degrees, total correction factor smaller than 5
## data(magn97)
## magn<-filter(magn97,year=1997,month.beg=7,month.end=8,day.beg=15,day.end=24,
## shw="PER",h.low=20)
## pop.index(magn,year=1997,month.beg=7,month.end=8,day.beg=27,day.end=16,shw="PER",k=1)

## make graphic of population index
## x-axis limits: min(sollong)=124.549, max(sollong)=144.111
## y-axis limits: min(pop.index-sigma.r)=1.94,max(pop.index+sigma.r)=2.81
## pop.index(magn,year=1997,month.beg=7,month.end=8,day.beg=27,day.end=16,shw="PER",
## k=1,add.plot=TRUE,xlim1=124,xlim2=145,xinc=1,ylim1=1.9,ylim2=2.9,yinc=0.1)