scientimate.hurricanewavemax#

Hsmax, Tmax, RVmax = scientimate.hurricanewavemax(xCenter, yCenter, Pc, Vmax, Rknown, VgRknown, Pn=101325, Rhoa=1.204, VgToVCoeff=0.8, G=0.88, Vt=0, CalcMethod='young13', RVmaxCalcMethod='holland', dispout='no')

Description#

Calculate hurricane maximum wave height and wave period at a location of maximum wind

Inputs#

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 wind velocity at surface level in (m/s)

It can be estimated from Vmax=3.44*(1010-Pc*1e-2)^0.644; where Pc is in (Pa)

and, 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 Vgmax
VgRknown: Hurricane wind velocity at the gradient level which is known at radius Rknown in (m/s)
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 at the gradient level in (kg/m3)
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
G=0.88: Wind gust factor to convert 1-min averaged wind to 10-min averaged wind

e.g. Young (2017); Liu et al. (2017)

G=U(600s)/U(60s), therefore U(600s)=G*U(60s)

G=1/1.1; based on Powell and Houston (1996)

G=1/1.08; based on Harper (2013)

G=0.88; based on World Meteorological Organization (2015)

G=1/1.08 to 1/1.16; based on Liu et al. (2017)
Vt=0: Hurricane central translational velocity in (m/s)
CalcMethod=’young13’: Hurricane maximum wave height and period calculation method

‘spm’: Use method by Shore Protection Manual (SPM),

U.S. Army Corps of Engineers (1984) in deep water

‘young88’: Use method by Young (1988)

‘young13’: Use method by Young & Vinoth (2013)
RVmaxCalcMethod=’holland’: Method for calculating a hurricane radius of the maximum wind from known velocity and its radius

‘rankine’: Velocity is calculated using modiﬁed Rankine vortex model, Depperman (1947)

‘holland’: Velocity is calculated using using Holland (1980)

‘demaria’: Velocity is calculated using using DeMaria (1987)

‘slosh’: Velocity is calculated using using SLOSH model by Jelesnianski et al. (1992)

‘emanuel’: Velocity is calculated using using Emanuel and Rotunno (2011)
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

‘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

Outputs#

Hsmax: Hurricane maximum significant wave height in (m)
Tmax: Hurricane maximum wave period in (s)

For all methods excepth for ‘spm’: Tmax=Tpmax where, Tpmax is a maximum peak wave period

For ‘spm’ method: Tmax=Tsmax, where Tsmax is a maximum significant wave period (Ts=0.95Tp)
RVmax: Distance (radius) from hurricane center to a location of maximum hurricane wind velocity (m)

Examples#

import scientimate as sm
import numpy as np


#EXAMPLE 1

#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 1-min sustained maximum velocity (m/s) at max velocity
Vmax=76.5
Vmax=Vmax-Vt #Removing hurricane translation velocity from Vgmax

#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)

Hsmax,Tmax,RVmax=sm.hurricanewavemax(longCenter,latCenter,Pc,Vmax,Rknown,VgRknown,Pn,Rhoa,0.8,0.88,Vt,'young13','holland','yes')


#EXAMPLE 2

#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 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

#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

Pn=101325 #Ambient surface pressure (external pressure) in (Pa)
Rhoa=1.204 #Air density in (kg/m3)

Hsmax,Tmax,RVmax=sm.hurricanewavemax(longtrack[3:27],lattrack[3:27],Pc[3:27],Vmax[3:27],Rknown[3:27],VgRknown[3:27],Pn,Rhoa,0.8,0.88,Vt[3:27],'young13','holland','yes')


#EXAMPLE 3

longCenter=0 #(Degree)
latCenter=20 #(Degree)
Pc=90200 #(Pa)
Vt=5.18467 #(m/s)
Vmax=76.5 #(m/s)
Vmax=Vmax-Vt
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)
Vmax=Vmax-Vt

Hsmax,Tmax,RVmax=sm.hurricanewavemax(longCenter,latCenter,Pc,Vmax,Rknown,VgRknown,Pn,Rhoa,0.8,0.88,Vt,'young13','holland','yes')

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

Atkinson, G. D., & Holliday, C. R. (1977). Tropical cyclone minimum sea level pressure/maximum sustained wind relationship for the western north Pacific. Monthly Weather Review, 105(4), 421-427.

Batke, S. P., Jocque, M., & Kelly, D. L. (2014). Modelling hurricane exposure and wind speed on a mesoclimate scale: a case study from Cusuco NP, Honduras. PloS one, 9(3), e91306.

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.

Graham and Numm (1959) Meteorological Conditions Pertinent to Standard Project Hurricane, Atlantic and Gulf Coasts of United States. National Hurricane Research Project. U.S. Weather Service, Report no. 33.

Harper, B.A. (2013) Best practice in tropical cyclone wind hazard modelling: In search of data and emptying the skeleton cupboard. In Proceedings of the 16th Australasian Wind Engineering Society Workshop, Brisbane, Qld, Australia, 18–19 July 2013

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

Hu, K., Chen, Q., & Kimball, S. K. (2012). Consistency in hurricane surface wind forecasting: an improved parametric model. Natural hazards, 61(3), 1029-1050.

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.

Liu, Q., Babanin, A., Fan, Y., Zieger, S., Guan, C., & Moon, I. J. (2017). Numerical simulations of ocean surface waves under hurricane conditions: Assessment of existing model performance. Ocean Modelling, 118, 73-93.

Moon, I. J., Ginis, I., Hara, T., Tolman, H. L., Wright, C. W., & Walsh, E. J. (2003). Numerical simulation of sea surface directional wave spectra under hurricane wind forcing. Journal of physical oceanography, 33(8), 1680-1706.

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., & Houston, S. H. (1996). Hurricane Andrew’s landfall in South Florida. Part II: Surface wind fields and potential real-time applications. Weather and Forecasting, 11(3), 329-349.

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

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. (1988). Parametric hurricane wave prediction model. Journal of Waterway, Port, Coastal, and Ocean Engineering, 114(5), 637-652.

Young, I. R. (2006). Directional spectra of hurricane wind waves. Journal of Geophysical Research: Oceans, 111(C8).

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.

Young, I.R. (2017) A Review of Parametric Descriptions of Tropical Cyclone Wind-Wave Generation. Atmosphere 2017, 8, 194.

scientimate.hurricanewavemax

Contents