zhr: Calculates zenithal hourly rate (ZHR)
In MetFns: Analysis of Visual Meteor Data

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates 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.

1 2	zhr(data,date.start,date.end,shw,r=NULL,kmin=0.01,kmax=1,num,c.zhr=0.5, rdata=NULL,gamma=1)

`data`	data frame consisting of visual meteor rate 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.
`r`	numeric vector specifying population index of a meteor shower.
`kmin`	numeric vector specifying minimum bin size, in degrees of solar longitude. By default, it is equal to 0.01. Minimum accepted value is 0.001.
`kmax`	numeric vector specifying maximum bin size, in degrees of solar longitude. By default, it is equal to 1. Maximum accepted values is 5.
`num`	numeric vector specifying total number of meteors per interval. Minimum accepted value is 1.
`c.zhr`	numeric vector specifying value of ZHR correction. By default, it is equal to 0.5. Accepted values are 0.5 and 1.
`rdata`	data frame consisting of population index values calculated on corresponding visual meteor magnitude data.
`gamma`	numeric vector specifying zenith exponent. It takes value between 1 (default) and 2.

Optimal bin size algorithm is used. It searches for an optimal bin size between minimum bin size kmin and maximum bin size kmax with total number of meteors per bin num. If there are not enough meteors, a maximum bin size is used. For further calculations, only observing intervals with lengths smaller or equal to optimal bin are 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))^gamma)

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 and γ zenith exponent gamma.

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=sqrt(c+sum_i N_i)/(sum_i T_{eff,i}/C_i), i=1,2,...,k

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

Values from the data frame radiant are used for right ascension and declination of shower radiant. If population index is not specified, it should be calculated using functions pop.index or pop.index2 and then incorporated in the calculation of ZHR (through data frame rdata).

Data frame containing following vectors

sollong: numeric Mean of observers' solar longitudes weighted by T_{eff,obs}/C_{obs}, observers effective time divided by total correction factor
date: POSIXct Calendar date and time in UTC corresponding to sollong
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.error: numeric Standard error of ZHR
density: numeric Spatial number density
dens.error: numeric Standard error of spatial number density

Kristina Veljkovic

Rendtel J. and Arlt R., editors (2014). 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.

zhr.plot,pop.index2

## calculate ZHR for observations of 2015 Orionids, 
## time period around maximum 21th to 25th October, 
## min bin size 0.16 degrees (4 hours), max bin size 1 degree, 
## number of meteors equals 100, population index calculated from magnitude data

## First select rate data for Orionids activity from 21th to 25th October, 
## limiting magnitudes above 5, radiant elevation above 20 degrees, 
## percentage of clouds below 20
ori2015<-filter(rate2015,date.start="2015-10-21",date.end="2015-10-25",
shw="ORI",P.up=20,mag.low=5,mag.up=8,h.low=20)
ori2015mag<-filter(magn2015,date.start="2015-10-21",date.end="2015-10-25",
shw="ORI",P.up=20,mag.low=5,h.low=20)

oripop<-pop.index2(ori2015mag,date.start="2015-10-21",date.end="2015-10-25",
shw="ORI",kmin=0.16,kmax=1,num=100)
zhr(ori2015,date.start="2015-10-21",date.end="2015-10-25",shw="ORI",
kmin=0.16,kmax=1,num=100,rdata=oripop)

Loading required package: astroFns
Loading required package: lubridate

Attaching package: 'lubridate'

The following object is masked from 'package:base':

    date

Loading required package: plotrix
Loading required package: pracma

Attaching package: 'MetFns'

The following object is masked from 'package:stats':

    filter

  sollong                date nINT nORI  ZHR st.error density dens.error
1 207.137 2015-10-21 01:52:52   37  211 16.1      1.1     7.4        0.5
2 207.616 2015-10-21 13:26:40   11  100 17.8      1.8     8.1        0.8
3 208.278 2015-10-22 05:25:16    7   67 17.5      2.1     8.0        1.0
4 209.375 2015-10-23 07:53:05    7   87 18.2      1.9     8.3        0.9
5 210.276 2015-10-24 05:36:35    8   83 14.8      1.6     6.8        0.7