This function uses the Newton-Raphson method to solve equation 3 (the dual-exponential profile version) for \(\xi\) in Willoughby et al. (2006). This value of \(\xi\) can then be used to determine \(R_1\) for that storm observation.
solve_for_xi(xi0 = 0.5, eq3_right, eps = 0.001, itmax = 100)A numeric value giving the starting guess for \(\xi\)
A numerical value with the right-hand side of Willoughby
et al. (2006), Eqn. 3, the dual-exponential version. This value is
calculated at each storm observation point using the
will3_right function.
The convergence threshold for determining if the algorithm has converged.
The maximum number of iterations to try before deciding that the algorithm did not converge.
Jones O, Maillardet R, and Robinson A. 2009. Introduction to Scientific Programming and Simulation Using R. Boca Raton, FL: Chapman & Hall/CRC Press.
Press WH, Teukolsky SA, Vetterling WT, and Flannery BP. 2002. Numerical Recipes in C++: The Art of Scientific Computing. 2nd ed. Cambridge, UK: Cambridge University Press.
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.