will1: Model wind speed at a grid point for a storm track...
In geanders/stormwindmodel: Model Tropical Cyclone Wind Speeds

will1

R Documentation

Model wind speed at a grid point for a storm track observation

Description

Models the gradient wind speed at a certain radius from a storm's center. To do this, it uses different equations and subfunctions depending on how large the radius is (see details). This function requires, as inputs, Willoughby wind model parameters calculated using the add_wind_radii function.

Usage

will1(cdist, Rmax, R1, R2, vmax_gl, n, A, X1, X2 = 25)

Arguments

`cdist`	A numeric value with the distance between the grid point and the center of the storm (in km)
`Rmax`	A numeric value with the radius at which the maximum wind occurs (in km)
`R1`	A numeric value with the lower boundary of the transition zone (in km from the storm center)
`R2`	A numeric value with the upper boundary of the transition zone (in km from the storm center)
`vmax_gl`	A numeric value with the maximum gradient level 1-minute sustained wind, in (m/s)
`n`	A numeric value giving the power by which the wind is assumed to increase with radius within the center of the storm (i.e., from the center to the radius of maximum wind)
`A`	A numeric value that is a parameter between 0 and 1 for the Willoughby model
`X1`	A numeric value that is a parameter for the Willoughby model
`X2`	A numeric value as a parameter for the Willoughby model, set to 25 (Willoughby, Darling, and Rahn 2006)

Details

If r ≤ R1, this function is calculating the equation:

V(r) = Vi = vmax_gl (r / Rmax)^n

where:

V(r): Maximum sustained gradient wind speed at a radius of r from the storm's center
r: Radius from the storm center, in kilometers
vmax_gl: Maximum sustained gradient wind speed of the storm, in meters per second
R1: A parameter for the Willoughby wind model (radius to start of transition region)
Rmax: Radius (in kilometers) to highest winds
n: A parameter for the Willoughby wind model

If R2 ≤ r, this function is calculating the equation:

V(r) = Vo = vmax_gl[(1 - A) e^((Rmax - r) / X1) + A e^((Rmax - r) / X_2)]

where:

V(r): Maximum sustained gradient wind speed at a radius of r kilometers from the storm's center
r: Radius from the storm center, in kilometers
vmax_gl: Maximum sustained gradient wind speed of the storm, in meters per second
Rmax: Radius (in kilometers) to highest winds
A, X1, X2: Parameters for the Willoughby wind model

If R1 < r ≤ R2, this function uses the equations:

ξ = (r - R1) / (R2 - R1)

and, if 0 ≤ ξ < ≤ 1 (otherwise, w = 0):

w = 126 ξ^5 - 420 ξ^6 + 540 ξ^7- 315 ξ^8 + 70 ξ^9

and then:

V(r) = Vi (1 - w) + Vo w

where, for this series of equations:

V(r): Maximum sustained gradient wind speed at a radius of r kilometers from the storm's center
r: Radius from the storm center, in kilometers
w: Weighting variable
R1, R2: Parameters for the Willoughby wind model

Value

Returns a numeric vector with gradient wind speed at a radius of r from the storm's center, in meters per second.

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 Sept. 27, 2022, 6:47 a.m.