MetFns (version 2.0)

zhr: Calculates zenithal hourly rate (ZHR)

Description

Calculates and plots average zenithal hourly rate of a meteor shower for a given rate data, specified shower, period of days, population index, minimum and maximum bin sizes, number of meteors and ZHR correction.

Usage

zhr(data,year,month.beg,month.end=month.beg,day.beg,day.end=day.beg,
time.beg=0,time.end=2359,shw,r=NULL,Ralpha=NULL,Delta=NULL,k1=0.01,k2=1,num,C=1,
data2=NULL,add.plot=FALSE,xlim1=NULL,xlim2=NULL,xinc=NULL,ylim1=NULL,ylim2=NULL,
yinc=NULL)

Arguments

data

data frame consisting of visual meteor rate 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.

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.

k1

numeric vector specifying minimum bin size, in degrees of solar longitude. By default, it is equal to 0.01.

k2

numeric vector specifying maximum bin size, in degrees of solar longitude. By default, it is equal to 1.

num

numeric vector specifying total number of meteors per interval.

C

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

data2

data frame consisting of corresponding visual meteor magnitude data.

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 numeric vectors [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

code

xinc,yinc

emph

65%

Details

Adaptive-bin size algorithm is used. It tries to maintain a used-defined optimum meteor number per bin. For the case that not enough meteors are available, a maximum bin size is used. 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. If population index is not specified, it is calculated using the function pop.index2 and then incorporated in the calculation of ZHR.

References

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

pop.index2

Examples

##calculate ZHR for observations of 1997 Perseids, time period 10th August 19h to
##13th August 7h, radiant elevation higher than 20 degrees, total correction smaller than 5
##select 1997 Perseids, 28th July to 16th August, radiant elevation higher than 20 degrees
## data(rate97)
## rate<-filter(rate97,year=1997,month.beg=7,month.end=8,day.beg=28,day.end=16,
## shw="PER",h.low=20)
## zhr(rate,year=1997,month.beg=8,day.beg=10,day.end=13,time.beg=1900,time.end=700,
## shw="PER",r=2.2,num=300)

##make a graphic of ZHR
##x-axis limits: min(sollong)=138.252, max(sollong)=140.561
##y-axis limits: min(ZHR-st.err)=26.2, max(ZHR+st.err)=144.6

## zhr(rate,year=1997,month.beg=8,day.beg=10,day.end=13,time.beg=1900,time.end=700,
## shw="PER",r=2.2,num=300,add.plot=TRUE,xlim1=138.2,xlim2=140.6,xinc=0.1,
## ylim1=20,ylim2=160,yinc=20)

##calculate ZHR for the same data using population index calculated from 
##magnitude data
## data(magn97)
## magn<-filter(magn97,year=1997,month.beg=7,month.end=8,day.beg=28,day.end=16,
## shw="PER",h.low=20)
## zhr(rate,year=1997,month.beg=8,day.beg=10,day.end=13,time.beg=1900,time.end=700,
## shw="PER",num=300,data2=magn)

##make a graphic of ZHR
##x-axis limits: min(sollong)=138.252, max(sollong)=140.561
##y-axis limits: min(ZHR-st.err)=25.4, max(ZHR+1.96*st.err)=141.4
## zhr(rate,year=1997,month.beg=8,day.beg=10,day.end=13,time.beg=1900,time.end=700,
## shw="PER",r=2.2,num=300,data2=magn,add.plot=TRUE,xlim1=138.2,xlim2=140.6,xinc=0.1,
## ylim1=20,ylim2=160,yinc=20)