hurricanewindinflowangle#

[Vxgrid, Vygrid, thetaVgrid, thetaVgridtan, thetagrid, Rgrid] = hurricanewindinflowangle(xgrid, ygrid, Vgrid, xCenter, yCenter, RVmax, inflowdirCalcMethod, distCalcMethod, dispout)

Description#

Calculate hurricane velocity tangential and inflow angle and inflow velocity in x (East) and y (North) directions

Inputs#

xgrid: x (longitude) of points which outputs are calculated at as a [M*N] array

xgrid can be a single point or 1d or 2d array
ygrid: y (latitude) of points which outputs are calculated at as a [M*N] array

ygrid can be a single point or 1d or 2d array
Vgrid: Resultant hurricane wind velocity (Vx^2+Vy^2)^0.5 on (xgrid,ygrid) as a [M*N*L] array in (m/s)

L is a number of time steps

If only angle values are required, then set Vgrid equal to an arbitary constant such as Vgrid=1

For demonstaration purpose, set Vgrid equal to an arbitary constant such as Vgrid=1
xCenter: x (longitude) of hurricane center (track) as a [L] array
yCenter: y (latitude) of hurricane center (track) as a [L] array
RVmax: Distance (radius) from hurricane center to a location of maximum hurricane wind velocity as a [L] array in (m)
inflowdirCalcMethod=’bretschneider’;: Inflow angle calculation method

‘no’: Inflow angle are not calculated, thetaVgrid=thetaVgridtan

‘bretschneider’: Inflow angle are calculated based on Bretschneider (1972)

‘sobey’: Inflow angle are calculated based on Sobey et al. (1977)
distCalcMethod=’gc’;: Distance calculation method

‘cart’: Distances are calculated on cartesian coordinate

‘gc’: Distances are calculated on Great Circle based on Vincenty formula, Vincenty (1975)

Earth radius coonsidered as mean earth radius=6371000 m
dispout=’no’;: Define to display outputs or not

‘imagesc’: 2 dimensional plot using imagesc or imshow

‘pcolor’: 2 dimensional plot using pcolor

‘contour’: 2 dimensional contour plot, number of contour=ncolor

‘quiver’: 2 dimensional vector plot

‘no’: not display

Use dispout=’no’ if calculation mesh is not 2d array

if there is more than one time step, only the last one is plotted

if flattendata=’yes’; then dispout is set as dispout=’no’;

Outputs#

Vxgrid: Hurricane wind velocity after applying inflow angle in x (East) direction on defined mesh in (m/s)
Vygrid: Hurricane wind velocity after applying inflow angle in y (North) direction on defined mesh in (m/s)
thetaVgrid: Inflow angle (trigonometric direction) of hurricane velocity at each grid point in (Degree)

Inflow angle: angle between the inwardly spiraling surface wind

and the circular isobars around the hurricane center (Boose et al., 2004)
thetaVgridtan: Angle (trigonometric direction) of hurricane velocity at each grid point in (Degree)

thetaVgridtan is tangential angle respect to radius.

Note: Outputs has dimension of [M,N,L] where [M,N] is size of the x-y grid and [L] is number of time steps
thetagrid: Angle from hurricane center to each point on the grid in (Degree)
Rgrid: Distance (radius) from hurricane center to each point on the grid

Examples#

%Creating calculation mesh
[xgrid,ygrid]=meshgrid(linspace(-98,-68,100),linspace(16,44,100));

%Longitude of Hurricane Katrine center at max velocity
longCenter=-88.6;

%Latitude of Hurricane Katrine center at max velocity
latCenter=26.3;

%Hurricane Katrina translational velocity (m/s) at max velocity
Vt=5.18467;

%Hurricane Katrina velocity azimuth (bearing) in (Degree) at max velocity
VtAzmdir=306.76219;

%Hurricane Katrina 1-min sustained maximum velocity (m/s) at max velocity
Vmax=76.5;
Vmax=Vmax-Vt; %Removing hurricane translation velocity from Vmax
Vgmax=Vmax/0.8; %Converting surface velocity to gradient velocity

%Calculating distance using spherical law of cosines
Rgrid=(acos(sin(deg2rad(latCenter)).*sin(deg2rad(ygrid))+cos(deg2rad(latCenter)).*cos(deg2rad(ygrid)).*cos(deg2rad(xgrid)-deg2rad(longCenter)))).*6371000; %Radius

%Calculating hurricane velocity at each radius using SLOSH model
RVmax=32197; %Radius from hurricane center to a location of maximum hurricane wind
Vgrid=Vgmax.*(2.*RVmax.*Rgrid)./((RVmax)^2+(Rgrid).^2); %Hurricane wind velocity at radius R

[Vxgrid,Vygrid,thetaVgrid,thetaVgridtan,thetagrid,Rgrid]=hurricanewindinflowangle(xgrid,ygrid,Vgrid,longCenter,latCenter,RVmax,'bretschneider','gc','quiver');

References#

Data

www.nhc.noaa.gov/data/
www.nhc.noaa.gov/data/hurdat/hurdat2-format-nencpac.pdf
coast.noaa.gov/hurricanes
www.aoml.noaa.gov/hrd/data_sub/re_anal.html

Boose, E. R., Serrano, M. I., & Foster, D. R. (2004). Landscape and regional impacts of hurricanes in Puerto Rico. Ecological Monographs, 74(2), 335-352.

Bretschneider, C. L. (1972, January). A non-dimensional stationary hurricane wave model. In Offshore Technology Conference. Offshore Technology Conference.

Phadke, A. C., Martino, C. D., Cheung, K. F., & Houston, S. H. (2003). Modeling of tropical cyclone winds and waves for emergency management. Ocean Engineering, 30(4), 553-578.

Sobey, R. J., Harper, B. A., & Stark, K. P. (1977). Numerical simulation of tropical cyclone storm surge. James Cook University of North Queensland, Department of Civil & Systems Engineering.

hurricanewindinflowangle

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