scientimate.hurricanewindh08

Vxgrid, Vygrid, Vgrid, Pgrid, Rgrid, RVmax, thetagrid, thetaVgrid, thetaVgridtan = scientimate.hurricanewindh08(xgrid, ygrid, xCenter, yCenter, Pc, Vmax, Rknown, VgRknown, dPcdt, Vt, Rmax=423e3, Pn=101325, Rhoa=1.204, SST=None, \
    VgToVCoeff=0.8, inflowdirCalcMethod='bretschneider', VtAzmdir=0, backwindCalcMethod='no', distCalcMethod='gc', flattendata='no', savedata='no', dispout='no')

Description

Generate hurricane wind and pressure data on (x,y) points using method from Holland (2008)

Inputs

xgrid

x (longitude) of points which outputs are calculated at

xgrid can be a single point or 1d or 2d array

ygrid

y (latitude) of points which outputs are calculated at

ygrid can be a single point or 1d or 2d array

xCenter

x (longitude) of hurricane center (track)

yCenter

y (latitude) of hurricane center (track)

Pc

Hurricane central surface pressure in (Pa)

Vmax

Maximum hurricane 1-min averaged surface wind velocity at 10m height from surface in (m/s)

It can be estimated by Vmax=3.44*(1010-Pc*1e-2)^0.644;

where, Vmax is 1-min averaged wind at a 10-m elevation in (m/s) (Atkinson & Holliday, 1977)

Hurricane translation velocity (forward velocity) needs to be removed from Vmax before applying (e.g. Hu et al., 2012)

Hurricane translation velocity (forward velocity) needs to be added after rotational velocity is calculated

Rknown

Radius that hurricane wind velocity is known at that radius in (m)

Rknown should be larger than radius associated to Vmax

VgRknown

Hurricane wind velocity at the gradient level which is known at radius Rknown in (m/s)

dPcdt

Hurricane central pressure (Pc) intensity change (dPc/dt) in (hPa/hr)

Convert from (Pa) to (hPa): hPa=0.01*Pa;

Vt

Hurricane translation velocity in (m/s)

Rmax=423e3;

Maximum radius of hurricane from hurricane center in (m)

Outputs for points with R>Rmax is set to zero

Median values of Rmax is 423 km (e.g. Chavas & Emanuel 2010; Lin & Chavas, 2012)

Pn=101325;

Ambient surface pressure (external pressure) in (Pa)

Standard atmosphere pressure is 101325 (Pa)

Typical value: Pn=101500 (Pa) for the western North Pacific, Pn= 101000 (Pa) for the North Atlantic

(Batke et al., 2014)

Rhoa=1.204;

Air density in (kg/m3)

SST=(28-3*(abs(yCenter)-10)/20)+1;

Sea surface temperature in (C), Holland (2008), Ts=SST-1, Ts=28-3*(abs(yCenter)-10)/20

VgToVCoeff=0.8;

Coefficient to convert gradient wind velocity to wind velocity at 10 m above surface as:

V=VgToVCoeff*Vg, if VgToVCoeff=1, then V=Vg

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)

VtAzmdir=0;

Hurricane center velocity azimuth (bearing) direction in (Degree)

azimuth (bearing) direction which is measured clockwise from the north:

0 (degree): toward North, 90 (degree): toward East, 180 (degree): toward South, 270 (degree): toward West

backwindCalcMethod=’no’;

Calculation method for adding background wind velocity due to hurricane motion

background wind velocity is added to points with R<=Rmax, e.g. Chavas & Emanuel (2010), Lin & Chavas (2012)

‘no’: background wind velocity is not added to hurricane velocities

‘constant’: background wind velocity is added as constant value to hurricane velocities

‘slosh’: Background wind velocity is calculated and added using SLOSH model by Jelesnianski et al. (1992)

‘lin’: Background wind velocity is calculated and added based on Lin & Chavas (2012)

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

flattendata=’no’;

Define if flat data or not

‘no’: does not flat the results, outputs are in 3d array

‘yes’: flat the results, outputs are in 2d array

savedata=’no’;

Define if save data in a file or not in working folder

‘no’: does not save,

‘yes’: save data as ascii ‘dat’ file, data are flatten regrdless of flattendata value

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 1-min averaged wind velocity at 10 m above surface in x (East) direction on defined mesh in (m/s)

Vygrid

Hurricane 1-min averaged wind velocity at 10 m above surface in y (North) direction on defined mesh in (m/s)

Vgrid

Resultant hurricane 1-min averaged wind velocity at 10 m above surface (Vx^2+Vy^2)^0.5 on defined mesh in (m/s)

Pgrid

Hurricane surface pressure on defined mesh in (Pa)

Rgrid

Distance (radius) from hurricane center to each point on the grid

RVmax

Distance (radius) from hurricane center to a location of maximum hurricane wind velocity (m)

thetagrid

Angle from hurricane center to each point on the grid in (Degree)

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

If flattendata=’yes’; then Outputs has dimension of [M*L,N]

Hurricane translation velocity needs to be added after rotational velocity is calculated

(e.g. Hu et al., 2012; Lin & Chavas, 2012)

1-min averaged wind velocity needs to be converted to standard duration such as

10-min averaged wind by using a gust factor

Examples

import scientimate as sm
import numpy as np
import matplotlib.pyplot as plt


#EXAMPLE 1

#Creating calculation mesh
xgrid,ygrid=np.meshgrid(np.linspace(-98,-68,100),np.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 centeral pressure (Pa) at max velocity
Pc=90200;

#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

#34 kt (17.49 m/s) wind radii maximum extent in northeastern quadrant in (m) for Hurricane Katrina at max velocity
Rknown=370400;
VRknown=17.49;
VRknown=VRknown-Vt; #Removing hurricane translation velocity from VRknown
VgRknown=VRknown/0.8; #Converting surface velocity to gradient velocity

Pn=101325; #Ambient surface pressure (external pressure) in (Pa)
Rhoa=1.204; #Air density in (kg/m3)
dPcdt=-1.16667; #Hurricane central pressure (Pc) intensity change in (hPa/hr)
SST=27.77; #Sea surface temperature in (C)

Vxgrid,Vygrid,Vgrid,Pgrid,Rgrid,RVmax,thetagrid,thetaVgrid,thetaVgridtan=sm.hurricanewindh08(xgrid,ygrid,longCenter,latCenter,Pc,Vmax,Rknown,VgRknown,dPcdt,Vt,423e3,Pn,Rhoa,SST,\
0.8,'bretschneider',VtAzmdir,'slosh','gc','no','no','quiver');

#Converting 1-min sustained wind to 10-min averaged wind using gust factor
#e.g. World Meteorological Organization (2015)
Vxgrid=Vxgrid*0.88;
Vygrid=Vygrid*0.88;
Vgrid=Vgrid*0.88;


#EXAMPLE 2

#Creating calculation mesh
xgrid,ygrid=np.meshgrid(np.linspace(-98,-68,100),np.linspace(16,44,100));

#Longitude of Hurricane Katrine best track
longtrack=[-75.1,-75.7,-76.2,-76.5,-76.9,-77.7,-78.4,-79.0,-79.6,-80.1,-80.3,-81.3,\
    -82.0,-82.6,-83.3,-84.0,-84.7,-85.3,-85.9,-86.7,-87.7,-88.6,-89.2,-89.6,\
    -89.6,-89.6,-89.6,-89.6,-89.1,-88.6,-88.0,-87.0,-85.3,-82.9];

#Latitude of Hurricane Katrine best track
lattrack=[23.1,23.4,23.8,24.5,25.4,26.0,26.1,26.2,26.2,26.0,25.9,25.4,\
    25.1,24.9,24.6,24.4,24.4,24.5,24.8,25.2,25.7,26.3,27.2,28.2,\
    29.3,29.5,30.2,31.1,32.6,34.1,35.6,37.0,38.6,40.1];

#Hurricane Katrina centeral pressure (Pa)
Pc=[100800,100700,100700,100600,100300,100000,99700,99400,98800,98400,98300,98700,\
    97900,96800,95900,95000,94200,94800,94100,93000,90900,90200,90500,91300,\
    92000,92300,92800,94800,96100,97800,98500,99000,99400,99600];

#Hurricane Katrina translational velocity (m/s)
Vt=np.array([0.00000,3.23091,3.13105,3.86928,4.99513,4.82816,3.27813,2.81998,2.77140,2.53041,\
    1.05928,5.30662,3.60661,2.98269,3.61863,3.43691,3.28168,2.85849,3.20404,4.26279,\
    5.31340,5.18467,5.39195,5.46121,5.66270,1.02958,3.60354,4.63312,8.02540,8.01558,\
    8.12721,8.31580,10.75406,12.28350]);

#Hurricane Katrina velocity azimuth (bearing) in (Degree)
VtAzmdir=[0.00000,298.67291,311.22135,338.70264,338.13626,309.94476,279.18860,280.65053,270.13245,\
246.10095,240.96690,241.20181,244.79591,249.93382,244.88325,252.71384,270.14459,280.49918,\
298.94148,299.05364,299.18896,306.76219,329.36839,340.59069,0.00000,0.00000,0.00000,\
0.00000,15.67775,15.42254,18.00215,29.63266,39.49673,50.29744];

#Hurricane Katrina 1-min sustained maximum velocity (m/s)
Vmax=np.array([15.3,15.3,15.3,17.850,20.4,22.950,25.5,28.050,30.6,35.7,35.7,33.150,\
    38.250,43.350,45.9,48.450,51.0,51.0,51.0,63.750,73.950,76.5,71.4,63.750,\
    56.1,56.1,53.550,40.8,25.5,20.4,15.3,15.3,15.3,12.750]);

Vmax=Vmax-Vt; #Removing hurricane translation velocity from Vmax
Vgmax=Vmax/0.8; #Converting surface velocity to gradient velocity

#34 kt (17.49 m/s) wind radii maximum extent in northeastern quadrant in (m) for Hurricane Katrina
RknownRaw=[0,0,0,111120,111120,111120,111120,111120,129640,np.nan,129640,138900,\
    138900,138900,166680,240760,240760,259280,259280,296320,333360,370400,370400,370400,\
    np.nan,370400,np.nan,185200,138900,138900,0,0,0,0];

#34 kt (17.49 m/s) wind radii maximum extent in northeastern quadrant in (m) for Hurricane Katrina
Rknown=[0,0,0,111120,111120,111120,111120,111120,129640,129640,129640,138900,\
    138900,138900,166680,240760,240760,259280,259280,296320,333360,370400,370400,370400,\
    370400,370400,277800,185200,138900,138900,0,0,0,0];
VRknown=np.ones(34)*17.49;
VRknown=VRknown-Vt; #Removing hurricane translation velocity from VRknown
VgRknown=VRknown/0.8; #Converting surface velocity to gradient velocity

Hurricane central pressure (Pc) intensity change in (hPa/hr)
dPcdt=[0.00000,-0.16667,0.00000,-0.16667,-0.50000,-0.50000,-0.50000,-0.50000,-1.00000,-0.66667,-0.16667,\
    0.66667,-1.33333,-1.83333,-1.50000,-1.50000,-1.33333,1.00000,-1.16667,-1.83333,-3.50000,-1.16667,\
    0.50000,1.33333,1.16667,0.50000,0.83333,3.33333,2.16667,2.83333,1.16667,0.83333,0.66667,\
    0.33333];

Pn=101325; #Ambient surface pressure (external pressure) in (Pa)
Rhoa=1.204; #Air density in (kg/m3)
SST=27.77; #Sea surface temperature in (C)

Vxgrid,Vygrid,Vgrid,Pgrid,Rgrid,RVmax,thetagrid,thetaVgrid,thetaVgridtan=sm.hurricanewindh08(xgrid,ygrid,longtrack[3:27],lattrack[3:27],Pc[3:27],Vmax[3:27],Rknown[3:27],VgRknown[3:27],dPcdt[3:27],Vt[3:27],423e3,Pn,Rhoa,SST,\
    0.8,'bretschneider',VtAzmdir[3:27],'slosh','gc','no','no','quiver');

#Converting 1-min sustained wind to 10-min averaged wind using gust factor
#e.g. World Meteorological Organization (2015)
Vxgrid=Vxgrid*0.88;
Vygrid=Vygrid*0.88;
Vgrid=Vgrid*0.88;


#EXAMPLE 3

xgrid=np.linspace(0,10,100); #(Degree)
ygrid=np.ones(100)*20; #(Degree)
longCenter=0; #(Degree)
latCenter=20; #(Degree)
Pc=90200; #(Pa)
Vt=5.18467; #(m/s)
VtAzmdir=306.76219; #(Degree)
Vmax=76.5; #(m/s)
Vmax=Vmax-Vt;
Vgmax=Vmax/0.8; #(m/s)
Rknown=370400; #(m)
VRknown=17.49; #(m/s)
VRknown=VRknown-Vt;
VgRknown=VRknown/0.8; #(m/s)
Pn=101325; #Ambient surface pressure (external pressure) in (Pa)
Rhoa=1.204; #Air density in (kg/m3)

dPcdt=3; #Hurricane central pressure (Pc) intensity change in (hPa/hr)
SST=27.77; #Sea surface temperature in (C)

Vxgrid,Vygrid,Vgrid,Pgrid,Rgrid,RVmax,thetagrid,thetaVgrid,thetaVgridtan=sm.hurricanewindh08(xgrid,ygrid,longCenter,latCenter,Pc,Vmax,Rknown,VgRknown,dPcdt,Vt,423e3,Pn,Rhoa,SST,\
    0.8,'bretschneider',VtAzmdir,'slosh','gc','no','no','no');
plt.plot(Rgrid,Vgrid)

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

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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.

Chavas, D. R., & Emanuel, K. A. (2010). A QuikSCAT climatology of tropical cyclone size. Geophysical Research Letters, 37(18).

Department of the Army, Waterways Experiment Station, Corps of Engineers, and Coastal Engineering Research Center (1984), Shore Protection Manual, Washington, D.C., vol. 1, 4th ed., 532 pp.

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Holland, G. J. (1980). An analytic model of the wind and pressure profiles in hurricanes. Monthly weather review, 108(8), 1212-1218.

Holland, G. (2008). A revised hurricane pressure–wind model. Monthly Weather Review, 136(9), 3432-3445.

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Jelesnianski, C. P., Chen, J., & Shaffer, W. A. (1992). SLOSH: Sea, lake, and overland surges from hurricanes (Vol. 48). US Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service.

Lin, N., & Chavas, D. (2012). On hurricane parametric wind and applications in storm surge modeling. Journal of Geophysical Research: Atmospheres, 117(D9).

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.

Powell, M. D., Vickery, P. J., & Reinhold, T. A. (2003). Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422(6929), 279.

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.

U.S. Army Corps of Engineers (2015). Coastal Engineering Manual. Engineer Manual 1110-2-1100, Washington, D.C.: U.S. Army Corps of Engineers.

Valamanesh, V., Myers, A. T., Arwade, S. R., Hajjar, J. F., Hines, E., & Pang, W. (2016). Wind-wave prediction equations for probabilistic offshore hurricane hazard analysis. Natural Hazards, 83(1), 541-562.

Wei, K., Arwade, S. R., Myers, A. T., Valamanesh, V., & Pang, W. (2017). Effect of wind and wave directionality on the structural performance of non‐operational offshore wind turbines supported by jackets during hurricanes. Wind Energy, 20(2), 289-303.

World Meteorological Organization. Tropical Cyclone Programme, & Holland, G. J. (2015). Global guide to tropical cyclone forecasting. Secretariat of the World Meteorological Organization.

Young, I. R., & Vinoth, J. (2013). An ‘extended fetch’ model for the spatial distribution of tropical cyclone wind–waves as observed by altimeter. Ocean Engineering, 70, 14-24.