calc_psid Subroutine

public subroutine calc_psid(rtc, r, theta, thetad, psid)

Calculate the nonlinear angle psid at a centain radius
From the geometry,
$\sin{\psi_d} = (R_{TC}/r) \sin{\theta _d}.$ --(1)
$R^2_{TC} = r^2 + D^2 - 2rD\cos{\psi_d} , D=r\dfrac{\sin{\theta}}{\sin{\theta _d}}.$ --(2)
From Eq. (2),
$\cos{\psi_d} = (r^2 + D^2 - R_{TC}^2) / (2rD).$ --(3)
From Eqs. (1) and (3),
$\tan{\psi_d} = 2\rho \dfrac{\sin{\theta}}{\rho ^2+a\rho ^2-1},$
$\rho =r/R_{TC}, a=\dfrac{\sin{\theta}}{\sin{\theta _d}} .$

Arguments

Type	Intent	Optional	Attributes		Name
double precision,	intent(in)			::	rtc	Distance from the radar to TC center [m]
double precision,	intent(in)			::	r	Radius [m]
double precision,	intent(in)			::	theta(:)	azimuthal angle [deg]
double precision,	intent(in)			::	thetad(size(theta))	Azimuthal angle for radar [rad]
double precision,	intent(out)			::	psid(size(theta))	Nonlinear angle $\psi _d$ [rad]