MetFns (version 3.2.2)

pop.index: Calculation of population index

Description

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

Usage

pop.index(data,date.start,date.end,shw,mag.range=-6:7,k,gamma=1)

Arguments

data

data frame consisting of visual meteor magnitude data.

date.start

character vector or factor specifying start date, given in "%Y-%m-%d %H:%M:%S" format (UTC timezone).

date.end

character vector or factor specifying end date, given in "%Y-%m-%d %H:%M:%S" format (UTC timezone).

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. Minimum accepted value is 0.001 and maximum accepted value is 5.

gamma

numeric vector specifying zenith exponent. It takes value between 1 (default) and 2.

Value

Data frame containing following vectors

sollong

numeric Mean of observers' solar longitudes weighted by \(\frac{N_{obs}}{C_{obs}}\), observers' numbers of meteors divided by total correction factor

date

POSIXct Calendar date and time in UTC corresponding to sollong

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

r.error

numeric Standard error of population index

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 \(r=\frac{\Phi(m+1)}{\Phi(m)}\) and substitutiong \(0,1,...m\) magnitudes, equation \(\Phi(m)=\Phi(0)r^m\) (or \(ln(\Phi(m))=ln(\Phi(0))+r ln(m)\) 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

$$\sigma_r= r \sqrt{\exp{\left(\frac{\sum_j e_j^2}{(n-2)\sum_j m_j^2}\right)}\left(\exp{\left(\frac{\sum_j e_j^2}{(n-2)\sum_j m_j^2}\right)}-1\right)}$$

where \(n\) is number of magnitude values, \(m_j\) magnitude values, \(e_j\) regression residuals, \(j=1,2,...n\).

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

# NOT RUN {
##calculate population index for observations of 2015 Orionids, 
## time period 21th to 25th October, bin size 1 degree

## First select magnitude data for Orionids activity from 21th to 25th October, 
## limiting magnitudes above 5, radiant elevation above 20 degrees,
## percentage of clouds below 20
magnOri<-filter(magn2015,date.start="2015-10-21",date.end="2015-10-25",
shw="ORI",P.up=20,mag.low=5,h.low=20)
pop.index(magnOri,date.start="2015-10-21",date.end="2015-10-25",shw="ORI",k=1)

# }