Once you've solved for \(\xi\), this function uses this value and the estimated \(R_{max}\) to determine \(R1\), the radius from the storm center to the start of the transition region.
calc_R1(Rmax, xi)Numeric vector of the radius at which the maximum wind occurs, in kilometers
A numeric value with the \(\xi\) value determined by
solve_for_xi
A numeric vector with the estimated value of \(R_1\), a parameter required for the Willoughby wind model.
This function is calculating the equation:
$$R_1 = R_{max} - \xi(R_2 - R_1)$$
where:
\(R_1\): A parameter for the Willoughby wind model (radius to start of transition region)
\(R_{max}\): Radius (in kilometers) to highest winds
\(R_2 - R_1\): Width of the transition region. This is assumed to be 25 kilometers if \(R_{max}\) is greater than 20 kilometers and 15 kilometers otherwise.
Willoughby HE, Darling RWR, and Rahn ME. 2006. Parametric representation of the primary hurricane vortex. Part II: A new family of sectionally continuous profiles. Monthly Weather Review 134(4):1102-1120.