The temporalBehaviour()
and the
spatialBehaviour()
functions allow computing wind speed and
direction along the lifespan of a tropical cyclone. The
temporalBehaviour()
function focuses on the temporal
variation at a specific location while the
spatialBehaviour()
function focuses on the spatial
variation over a given area. Both functions also allow to compute
summary statistics about the behaviour of the wind generated by
cyclones. Three summary statistics are available: maximum sustained wind
speed, power dissipation index, and the duration of exposure to winds
reaching defined speed thresholds.
The maximum sustained wind speed (MSW, in m.s−1) over the lifespan of a storm is computed as follows:
max
where t is the time of the
observation
T is the lifespan
of the storm
The power dissipation index (PDI, in J.m^{2}) or total power dissipated by a tropical storm over its lifespan (Emanuel 1999, 2005) is computed as follows:
\int_T \rho \times C_d \times v_r^3 \ dt
where t is the time of the
observation
T is the lifespan
of the storm
\rho is the air
density fixed to 1 kg.m^{-3} as in Emanuel (1999)
C_d is the drag coefficient of the storm
fixed to 2 X 10^{-3} as in Emanuel (1999)
The duration of exposure (in hours) to winds reaching defined speed thresholds is computed as follows:
\int_T c(v_t) dt
\left\{ \begin{aligned} c(v_t) &= 1 \quad if \quad v_t \geq Thd\\ c(v_t) &= 0 \quad if \quad v_t < Thd\\ \end{aligned} \right.
where
t is the time of the
observation
T is the lifespan
of the storm
v_t is the
maximum sustained wind speed at time t (in m.s^{-1})
Thd is the minimum wind sped threshold
(in m.s^{-1})
By default the duration of exposure is computed for each
Saffir-Simpson Hurricane Scale threshold values for tropical cyclone
categories (i.e., 33, 43, 50 ,58, and 70 m.s^{-1}, (Simpson
1974)) but can be defined using the wind_threshold
argument.