R/vm_kappa.R

In Gi-Seop/ODA: Ocean Data Analysis package in R

  #kappa estimation (concentration parameter of von-Mises distribution)
  vm_kappa <- function(theta){
    
    theta <- na.omit(theta)
    n<-length(theta)
    C1 <- sum(cos(theta))
    S1 <- sum(sin(theta))
    R.bar <- sqrt((C1/n)^2+(S1/n)^2)
    
    kappa <- function(R.bar){
      if(R.bar<0.53){k<-2*R.bar+R.bar^3+5*R.bar/6
      return(k)}
      else if((R.bar>=0.53)&&(R.bar<0.85)){k <- -0.4+1.39*R.bar+0.43/(1-R.bar)
      return(k)}
      else if(R.bar>=0.85){k<- 1/(R.bar^3-4*R.bar^2+3*R.bar)
      return(k)}
      
    }
    
    kappa(R.bar)
    
  }