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 (v(t)|t ∈ [0, T])
where t is the time of the
observation
T is the
lifespan of the storm
The power dissipation index (PDI, in J.m2) or total power dissipated by a tropical storm over its lifespan (Emanuel 1999, 2005) is computed as follows:
∫Tρ × Cd × vr3 dt
where t is the time of the
observation
T is the
lifespan of the storm
ρ
is the air density fixed to 1 kg.m−3
as in Emanuel (1999)
Cd 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:
∫Tc(vt)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
vt 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.