# 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 \(m.s^{-1}\)) over the lifespan of a storm is computed as follows:

\[ \max(v(t) | t \in [0,T]) \]

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 Disaster—Potential Scale.” Weatherwise, July. https://doi.org/10.1080/00431672.1974.9931702.