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Behaviour

2024-07-24

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.

Maximum sustained wind speed

The maximum sustained wind speed (MSW, in m.s1) 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

Power Dissipation Index

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)

Duration of exposure

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.

References

Emanuel, Kerry A. 1999. “The Power of a Hurricane: An Example of Reckless Driving on the Information Superhighway.” Weather 54 (4): 107–8. https://doi.org/10.1002/j.1477-8696.1999.tb06435.x.
———. 2005. “Increasing Destructiveness of Tropical Cyclones over the Past 30 Years.” Nature 436 (7051): 686–88. https://doi.org/10.1038/nature03906.
Simpson, R. H. 1974. “The Hurricane DisasterPotential Scale.” Weatherwise, July. https://doi.org/10.1080/00431672.1974.9931702.