spatialBehaviour {StormR}

Computing wind behaviour and summary statistics over given areas

Description

The spatialBehaviour() function allows computing wind speed and direction for each cell of a regular grid (i.e., a raster) for a given tropical cyclone or set of tropical cyclones. It also allows to compute three associated summary statistics.

Usage

spatialBehaviour(
  sts,
  product = "MSW",
  windThreshold = NULL,
  method = "Willoughby",
  asymmetry = "Chen",
  empiricalRMW = FALSE,
  spaceRes = "2.5min",
  tempRes = 60,
  verbose = 2
)

Arguments

sts

StormsList object

product

character vector. Desired output statistics:

• "Profiles", for 2D wind speed and direction fields,

• "MSW", for maximum sustained wind speed (default setting),

• "PDI", for power dissipation index, or

• "Exposure", for duration of exposure.

windThreshold

numeric vector. Minimal wind threshold(s) (in m.s^{-1}) used to compute the duration of exposure when product="Exposure". Default value is to set NULL, in this case, the windthresholds are the one used in the scale defined in the stromsList.

method

character. Model used to compute wind speed and direction. Three different models are implemented:

• "Willoughby", for the symmetrical model developed by Willoughby et al. (2006) (default setting),

• "Holland", for the symmetrical model developed by Holland (1980), or

• "Boose", for the asymmetrical model developed by Boose et al. (2004).

asymmetry

character. If method="Holland" or method="Willoughby", this argument specifies the method used to add asymmetry. Can be:

• "Chen", for the model developed by Chen (1994) (default setting),

• "Miyazaki", for the model developed by Miyazaki et al. (1962), or

• "None", for no asymmetry.

empiricalRMW

logical. Whether (TRUE) or not (FALSE) to compute the radius of maximum wind (rmw) empirically using the model developed by Willoughby et al. (2006). If empiricalRMW==FALSE (default setting) then the rmw provided in the StormsList is used.

spaceRes

character. Spatial resolution. Can be "30 sec" (~1 km at the equator), "2.5 min" (~4.5 km at the equator), "5 min" (~9 km at the equator) or "10 min" (~18.6 km at the equator). Default setting is "2.5 min".

tempRes

numeric. Temporal resolution (min). Can be 60 ( default setting), 30 or 15.

verbose

numeric. Whether or not the function should display informations about the process and/or outputs. Can be:

• 2, information about the processes and outputs are displayed (default setting),

• 1, information about the processes are displayed, pr

• 0, no information displayed.

Details

Storm track data sets, such as those extracted from IBRTrACKS (Knapp et al., 2010), usually provide observation at a 3- or 6-hours temporal resolution. In the spatialBehaviour() function, linear interpolations are used to reach the temporal resolution specified in the tempRes argument (default value = 60 min). When product = "MSW", product = "PDI", or product = "Exposure" the focal() function from the terra R package is used to smooth the results using moving windows.

The Holland (1980) model, widely used in the literature, is based on the 'gradient wind balance in mature tropical cyclones. The wind speed distribution is computed from the circular air pressure field, which can be derived from the central and environmental pressure and the radius of maximum winds.

v_r = \sqrt{\frac{b}{\rho} \times \left(\frac{R_m}{r}\right)^b \times (p_{oci} - p_c) \times e^{-\left(\frac{R_m}{r}\right)^b} + \left(\frac{r \times f}{2}\right)^2} - \left(\frac{r \times f}{2}\right)

with,

b = \frac{\rho \times e \times v_m^2}{p_{oci} - p_c}

f = 2 \times 7.29 \times 10^{-5} \sin(\phi)

where, v_r is the tangential wind speed (in m.s^{-1}), b is the shape parameter, \rho is the air density set to 1.15 kg.m^{-3}, e being the base of natural logarithms (~2.718282), v_m the maximum sustained wind speed (in m.s^{-1}), p_{oci} is the pressure at outermost closed isobar of the storm (in Pa), p_c is the pressure at the centre of the storm (in Pa), r is the distance to the eye of the storm (in km), R_m is the radius of maximum sustained wind speed (in km), f is the Coriolis force (in N.kg^{-1}, and \phi being the latitude).

The Willoughby et al. (2006) model is an empirical model fitted to aircraft observations. The model considers two regions: inside the eye and at external radii, for which the wind formulations use different exponents to better match observations. In this model, the wind speed increases as a power function of the radius inside the eye and decays exponentially outside the eye after a smooth polynomial transition across the eyewall.

\left\{\begin{aligned} v_r &= v_m \times \left(\frac{r}{R_m}\right)^{n} \quad if \quad r < R_m \\ v_r &= v_m \times \left((1-A) \times e^{-\frac{|r-R_m|}{X1}} + A \times e^{-\frac{|r-R_m|}{X2}}\right) \quad if \quad r \geq R_m \\ \end{aligned} \right.

with,

n = 2.1340 + 0.0077 \times v_m - 0.4522 \times \ln(R_m) - 0.0038 \times |\phi|

X1 = 287.6 - 1.942 \times v_m + 7.799 \times \ln(R_m) + 1.819 \times |\phi|

A = 0.5913 + 0.0029 \times v_m - 0.1361 \times \ln(R_m) - 0.0042 \times |\phi| and A\ge0

where, v_r is the tangential wind speed (in m.s^{-1}), v_m is the maximum sustained wind speed (in m.s^{-1}), r is the distance to the eye of the storm (in km), R_m is the radius of maximum sustained wind speed (in km), \phi is the latitude of the centre of the storm, X2 = 25.

Asymmetry can be added to Holland (1980) and Willoughby et al. (2006) wind fields as follows,

\vec{V} = \vec{V_c} + C \times \vec{V_t}

where, \vec{V} is the combined asymmetric wind field, \vec{V_c} is symmetric wind field, \vec{V_t} is the translation speed of the storm, and C is function of r, the distance to the eye of the storm (in km).

Two formulations of C proposed by Miyazaki et al. (1962) and Chen (1994) are implemented.

Miyazaki et al. (1962) C = e^{(-\frac{r}{500} \times \pi)}

Chen (1994) C = \frac{3 \times R_m^{\frac{3}{2}} \times r^{\frac{3}{2}}}{R_m^3 + r^3 +R_m^{\frac{3}{2}} \times r^{\frac{3}{2}}}

where, R_m is the radius of maximum sustained wind speed (in km)

The Boose et al. (2004) model, or “HURRECON” model, is a modification of the Holland (1980) model. In addition to adding asymmetry, this model treats of water and land differently, using different surface friction coefficient for each.

v_r = F\left(v_m - S \times (1 - \sin(T)) \times \frac{v_h}{2} \right) \times \sqrt{\left(\frac{R_m}{r}\right)^b \times e^{1 - \left(\frac{R_m}{r}\right)^b}}

with,

b = \frac{\rho \times e \times v_m^2}{p_{oci} - p_c}

where, v_r is the tangential wind speed (in m.s^{-1}), F is a scaling parameter for friction (1.0 in water, 0.8 in land), v_m is the maximum sustained wind speed (in m.s^{-1}), S is a scaling parameter for asymmetry (usually set to 1), T is the oriented angle (clockwise/counter clockwise in Northern/Southern Hemisphere) between the forward trajectory of the storm and a radial line from the eye of the storm to point $r$ v_h is the storm velocity (in m.s^{-1}), R_m is the radius of maximum sustained wind speed (in km), r is the distance to the eye of the storm (in km), b is the shape parameter, \rho = 1.15 is the air density (in kg.m^{-3}), p_{oci} is the pressure at outermost closed isobar of the storm (in Pa), and p_c is the pressure at the centre of the storm (pressure in Pa).

Value

The spatialBehaviour() function returns SpatRaster objects (in WGS84). The number of layers in the output depends on the number of storms in the inputs, on the desired product, as well as the tempRes argument:

• if product = "MSW", the function returns one layer for each Storm. The names of the layer follow the following terminology, the name of the storm in capital letters and “MSW” separated by underscores (e.g., "PAM_MSW"),

• if product = "PDI", the function returns one layer for each Storm. The names of the layer follow the following terminology, the name of the storm in capital letters and “PDI” separated by underscores (e.g., "PAM_PDI"),

• if product ="Exposure", the function returns one layer for each wind speed values in the windThreshold argument and for each Storm. The names of the layer follow the following terminology, the name of the storm in capital letters, "Exposure", and the threshold value separated by underscores (e.g., "PAM_Exposure_18", "PAM_Exposure_33", ...),

• if product = "Profiles" the function returns one layer for wind speed and one layer for wind direction for each observation or interpolated observation and each Storm. The names of the layer follow the following terminology, the name of the storm in capital letters, "Speed" or "Direction", and the indices of the observation separated by underscores (e.g., "PAM_Speed_41", "PAM_Direction_41",...).

References

Boose, E. R., Serrano, M. I., & Foster, D. R. (2004). Landscape and regional impacts of hurricanes in Puerto Rico. Ecological Monographs, 74(2), Article 2. https://doi.org/10.1890/02-4057

Chen, K.-M. (1994). A computation method for typhoon wind field. Tropic Oceanology, 13(2), 41–48.

Holland, G. J. (1980). An Analytic Model of the Wind and Pressure Profiles in Hurricanes. Monthly Weather Review, 108(8), 1212–1218. https://doi.org/10.1175/1520-0493(1980)108<1212:AAMOTW>2.0.CO;2

Knapp, K. R., Kruk, M. C., Levinson, D. H., Diamond, H. J., & Neumann, C. J. (2010). The International Best Track Archive for Climate Stewardship (IBTrACS). Bulletin of the American Meteorological Society, 91(3), Article 3. https://doi.org/10.1175/2009bams2755.1

Miyazaki, M., Ueno, T., & Unoki, S. (1962). The theoretical investigations of typhoon surges along the Japanese coast (II). Oceanographical Magazine, 13(2), 103–117.

Willoughby, H. E., Darling, R. W. R., & Rahn, M. E. (2006). Parametric Representation of the Primary Hurricane Vortex. Part II: A New Family of Sectionally Continuous Profiles. Monthly Weather Review, 134(4), 1102–1120. https://doi.org/10.1175/MWR3106.1

Examples

# Creating a stormsDataset
sds <- defStormsDataset()

# Geting storm track data for tropical cyclone Pam (2015) near Vanuatu
pam <- defStormsList(sds = sds, loi = "Vanuatu", names = "PAM")

# Computing maximum sustained wind speed generated by Pam (2015) near Vanuatu
# using default settings
msw.pam <- spatialBehaviour(pam)

# Computing PDI generated by Pam (2015) near Vanuatu using the Holland model without asymmetry
pdi.pam <- spatialBehaviour(pam, method = "Holland", product = "PDI", asymmetry = "None")

# Computing duration of exposure to Saffir-Simpson hurricane wind scale threshold values
# during Pam (2015) near Vanuatu using default settings
exp.pam <- spatialBehaviour(pam, product = "Exposure")

# Computing wind speed and direction profiles  generated by Pam (2015) near Vanuatu
# using Boose model
prof.pam <- spatialBehaviour(pam, product = "Profiles", method = "Boose")