MetFns (version 2.1.0)

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 vectors

start

factor Calendar date and time in UTC of left bound of time interval

stop

factor Calendar date and time in UTC of right bound of time interval

sollong

numeric Solar longitude corresponding to the middle of time interval

nINT

numeric Number of observing time intervals

nSHW

numeric Number of observed meteors. String SHW is replaced with the code of meteor shower.

ZHR

numeric Zenithal Hourly Rate

st.err

numeric Standard error of ZHR

density

numeric Spatial number density

dens.err

numeric Standard error of spatial number density

If add.plot is TRUE, additionally xy plot of Zenithal Hourly Rate is made. Solar longitude is on x-axis and population index on y-axis. ZHR 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

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 - total correction factor that accounts for all the imperfections in the observing period i such as clouds, low radiant, low limiting magnitude.

Total 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 field-of-view obstruction, 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 the 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 
## 27th July to 16th August, radiant elevation higher than 20 degrees,
## total correction factor smaller than 5, bin size 1 degree, population index 2.2
## First select rate data for Perseids activity - time period 15th July to 24th August, 
## radiant elevation higher than 20 degrees, total correction factor smaller than 5
## data(rate97)
## rate<-filter(rate97,year=1997,month.beg=7,month.end=8,day.beg=27,day.end=16,
## shw="PER",h.low=20)
## zhr(rate,year=1997,month.beg=7,month.end=8,day.beg=27,day.end=16,
## shw="PER",r=2.2,k1=1,num=300)

## make graphic of ZHR
## x-axis limits: min(sollong)=124.549, max(sollong)=144.110
## y-axis limits: min(ZHR-st.err)=5.1,max(ZHR+st.err)=68.6
## zhr(rate,year=1997,month.beg=7,month.end=8,day.beg=27,day.end=16,shw="PER",r=2.2,
## k1=1,num=300,add.plot=TRUE,xlim1=124,xlim2=145,xinc=1,ylim1=5,ylim2=70,yinc=5)



## calculate ZHR around maximum activity of 1997 Perseids, time period 10th August 19h
## to 14th August 7h, radiant elevation higher than 20 degrees, total correction 
## factor smaller than 5 and population index calculated from magnitude data
## data(magn97)
## magn<-filter(magn97,year=1997,month.beg=7,month.end=8,day.beg=15,day.end=24,
## shw="PER",h.low=20)
## zhr(rate,year=1997,month.beg=8,day.beg=10,day.end=14,time.beg=1900,time.end=700,
## shw="PER",data2=magn,num=300)

## make graphic of ZHR around max activity of 1997 Perseids
## x-axis limits: min(sollong)=138.252, max(sollong)=141.471
## y-axis limits: min(ZHR-st.err)=24.7,max(ZHR+st.err)=141.4
## zhr(rate,year=1997,month.beg=8,day.beg=10,day.end=14,time.beg=1900,time.end=700,
## shw="PER",data2=magn,num=300,add.plot=TRUE,xlim1=138.2,xlim2=141.5,xinc=0.1,
## ylim1=20,ylim2=150,yinc=10)