# Computing wind behaviour time series and summary statistics at given point locations

Source:`R/temporalBehaviour.R`

`temporalBehaviour.Rd`

The `temporalBehaviour()`

function allows computing wind speed and direction
for a given location or set of locations along the lifespan of a tropical cyclone.
It also allows to compute three associated summary statistics.

## Usage

```
temporalBehaviour(
sts,
points,
product = "TS",
windThreshold = NULL,
method = "Willoughby",
asymmetry = "Chen",
empiricalRMW = FALSE,
tempRes = 60,
verbose = 1
)
```

## Arguments

- sts
`StormsList`

object.- points
data.frame. Consisting of two columns names as "x" (for the longitude) and "y" (for the latitude), providing the coordinates in decimal degrees of the point locations. Row names can also be provided to named the locations.

- product
character. Desired output statistics:

`"TS"`

, for time series of wind speeds and directions (default setting),`"PDI"`

, for power dissipation index, or`"Exposure"`

, for the duration of exposure to defined wind thresholds.

- 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.- tempRes
numeric. Temporal resolution (min). Can be

`60`

(default setting),`30`

or`15`

.- verbose
numeric. Information displayed. Can be:

`2`

, information about the processes and outputs are displayed (default setting),`1`

, information about the processes are displayed, or`0`

, no information displayed.

## Value

For each storm and each point location, the `temporalBehaviour()`

function returns
a data.frame. The data frames are organised into named lists. Depending on the `product`

argument
different data.frame are returned:

if

`product == "TS"`

, the function returns a data.frame with one row for each observation (or interpolated observation) and four columns for wind speed (in \(m.s^{-1}\)), wind direction (in degree), the observation number, and the ISO time of observations,if

`product == "PDI"`

, the function returns a data.frame with one row for each point location and one column for the PDI,if

`product == "Exposure"`

, the function returns a data.frame with one row for the duration of exposure to winds above each wind speed threshold defined by the`windThreshold`

argument and one column for each point location.

## 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 temporalBehaviour() function, linear interpolations are
used to reach the temporal resolution specified in the `tempRes`

argument
(default value = 60 min).

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 \(Pa\)).

## 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

```
# \donttest{
# Creating a stormsDataset
sds <- defStormsDataset()
#> Warning: No basin argument specified. StormR will work as expected
#> but cannot use basin filtering for speed-up when collecting data
#> === Loading data ===
#> Open database... /home/runner/work/_temp/Library/StormR/extdata/test_dataset.nc opened
#> Collecting data ...
#> === DONE ===
# Geting storm track data for tropical cyclone Pam (2015) near Vanuatu
pam <- defStormsList(sds = sds, loi = "Vanuatu", names = "PAM")
#> === Storms processing ... ===
#>
#> -> Making buffer: Done
#> -> Searching for PAM storm ...
#> -> Identifying Storms: Done
#> -> Gathering storm(s) ...
#>
#> === DONE with run time 0.4751422 sec ===
#>
#> SUMMARY:
#> (*) LOI: Vanuatu
#> (*) Buffer size: 300 km
#> (*) Number of storms: 1
#> Name - Tropical season - Scale - Number of observation within buffer:
#> PAM - 2015 - 6 - 20
#>
pts <- data.frame(x = c(168.5, 168), y = c(-17.9, -16.3))
row.names(pts) <- c("point_1", "point_2")
# Computing time series of wind speed and direction for Pam
# over points 1 and 2 defined above
ts.pam <- temporalBehaviour(pam, points = pts)
#> === temporalBehaviour processing ... ===
#>
#> Initializing data ... Done
#>
#> Computation settings:
#> (*) Temporal resolution: Every 60 min
#> (*) Method used: Willoughby
#> (*) Product(s) to compute: TS
#> (*) Asymmetry used: Chen
#> (*) Points: lon-lat
#> 168.5 -17.9
#> 168 -16.3
#>
#>
#> Storm(s):
#> ( 1 ) PAM
#>
#>
#> === DONE ===
#>
# Computing PDI for Pam over points 1 and 2 defined above
pdi.pam <- temporalBehaviour(pam, points = pts, product = "PDI")
#> === temporalBehaviour processing ... ===
#>
#> Initializing data ... Done
#>
#> Computation settings:
#> (*) Temporal resolution: Every 60 min
#> (*) Method used: Willoughby
#> (*) Product(s) to compute: PDI
#> (*) Asymmetry used: Chen
#> (*) Points: lon-lat
#> 168.5 -17.9
#> 168 -16.3
#>
#>
#> Storm(s):
#> ( 1 ) PAM
#>
#>
#> === DONE ===
#>
# Computing the duration of exposure to wind speeds above the thresholds
# used by the Saffir-Simpson hurricane wind scale for Pam
# over points 1 and 2 defined above
exp.pam <- temporalBehaviour(pam, points = pts, product = "Exposure")
#> === temporalBehaviour processing ... ===
#>
#> Initializing data ... Done
#>
#> Computation settings:
#> (*) Temporal resolution: Every 60 min
#> (*) Method used: Willoughby
#> (*) Product(s) to compute: Exposure
#> (*) Asymmetry used: Chen
#> (*) Points: lon-lat
#> 168.5 -17.9
#> 168 -16.3
#>
#>
#> Storm(s):
#> ( 1 ) PAM
#>
#>
#> === DONE ===
#>
# }
```