MetFns (version 1.0)

zhr: Calculates zenithal hourly rate (ZHR)

Description

Calculation of average zenithal hourly rate of a meteor shower for a given rate data, specified shower, period of days, population index, length of time interval and ZHR correction.

Usage

zhr(data,year, month, day.beg,day.end,shw, r=NULL, Ralpha=NULL, Delta=NULL, k,c=1)

Arguments

data

data frame consisting of visual meteor rate data.

year

numeric vector of length 4 specifying year.

month

numeric vector specifying month of the year.

day.beg

numeric vector specifying beginning day.

day.end

numeric vector specifying ending day.

shw

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

r

numeric vector specifying population index of a meteor shower.

Ralpha

numeric vector with value between 0 and 360, specifying right ascension of the radiant, in degrees.

Delta

numeric vector with value between -90 and +90, specifying declination of the radiant, in degrees.

k

numeric vector specifying length of time interval in hours.

c

numeric vector specifying value of ZHR correction. By default, it is equal to 1.

Value

• Data frame containing following numeric vectors [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Details

Average zenithal hourly rate is calculated by the formula ZHR=(c+sum_i n_i)/(sum_i T_{eff,i}/C_i), i=1,2,...,k where k is the number of observing periods, n_i - the raw number of meteors seen by each observer in observing period i, T_{eff,i} - the effective time or amount of time an observer actually scans the sky for meteors during observing period i, and C_i - a correction factor that accounts for all the imperfections in the observing period i such as clouds, low radiant, low limiting magnitude. Correction factor is equal to C_i=r^(6.5-lmg_i)F_i/sin(h_i), where r is population index, lmg_i limiting magnitude, F_i correction factor for clouds, h_i radiant elevation for each observer in observing period i. In the numerator, c is included to correct for the asymmetric high and low end possibilities in a Poisson distribution (distribution of number of observed meteors). Standard error of the average zenithal rate is calculated by the formula sigma=ZHR/sqrt(c+sum_i n_i). The spatial number density of meteoroids producing meteors of magnitude at least 6.5 is (per 10^9km^3) rho=(10.65r-12.15)ZHR/(3600 178700r^(-1.82)V), where V is stream's geocentric velocity. Standard error of spatial number density is approximated with sigma_{rho}=sigma rho/ZHR. If right ascension and declination of shower radiant are not specified, the values from the data frame radiant are used. Day is divided in subintervals of k hours. For example, if k=12, subintervals are [0,12) and [12,24). Zenithal hourly rate is calculated for each subinterval in the following manner: If middle of observing time period belongs to the subinterval, corresponding data values are used in calculation of ZHR.

References

Rendtel J. and Arlt R., editors (2008). IMO Handbook For Meteor Observers. IMO, Potsdam. Koschack R. and Rendtel J. (1990a). Determination of spatial number density and mass index from visual meteor observations (1). WGN, Journal of the IMO, 18(2), 44 - 58. Bias, P.V. (2011). A Note on Poisson inference and extrapolations under low raw data and short interval observation conditions. WGN, Journal of the IMO,39:1, 14-19.

See Also

zhr.graph,pop.index

Examples

## select visual meteor data for observation of Orionids,period 20-24th October 2006, 
## 12hrs time intervals, and calculate ZHR 
data(rate06)
rateOri<-filter(rate06,shw="ORI",year=2006, month=10, day.beg=20,day.end=24)
zhr(rateOri,year=2006,month=10,day.beg=20,day.end=24,shw="ORI",r=2.5,k=12)