will3_deriv_func: Calculate the function value and derivative for Willoughby...

In geanders/stormwindmodel: Model Tropical Cyclone Wind Speeds

Calculate the function value and derivative for Willoughby Eqn. 3

Description

Calculates values of both the function and the derivative of the function for which you are trying to solve the root in Eqn. 3 (the version using the dual exponential profile) of Willoughby et al. (2006).

Usage

will3_deriv_func(xi, eq3_right)

Arguments

xi	A numerical value for \xi from Willoughby et al. (2006), Eqn. 2
eq3_right	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, defined in C++ code for this package.

Value

A numeric vector of length two. The first value is the calculated value of f'(x) for x = \xi, while the second value is the calculated value of f(x) for x = \xi. These two values are used in iterating through the Newton-Raphson method to determine \xi.

References

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.

geanders/stormwindmodel documentation built on Feb. 10, 2025, 11:58 a.m.