Description Usage Arguments Details Value References
View source: R/willoughby2006eqs.R
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.
1 | will1(cdist, Rmax, R1, R2, vmax_gl, n, A, X1, X2 = 25)
|
cdist |
Distance (in km) from center of tropical cyclone to grid point. |
Rmax |
Numeric vector of the radius at which the maximum wind occurs, in kilometers |
R1 |
A numeric vector of one of the parameters of the Willoughby model. |
R2 |
A numeric vector of one of the parameters of the Willoughby model. |
vmax_gl |
Numeric vector of the tangential wind component of the maximum gradient wind speed, in meters per second |
n |
A numeric vector of one of the parameters of the Willoughby model. |
A |
A numeric vector of one of the parameters of the Willoughby model. |
X1 |
A numeric vector of one of the parameters of the Willoughby model. |
X2 |
A numeric vector of one of the parameters of the Willoughby model. |
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
Returns a numeric vector with gradient wind speed at a radius of r from the storm's center, in meters per second.
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.
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