Heatwave Definition
Our heatwave definition follows Russo et al. (2015), where a heatwave is identified as more than three consecutive days
with the (Tmax) above a daily threshold which is defined as the 90th percentile of daily Tmax centered on
a 31-days window throughout the reference years.
For a given day d, the corresponding data pool, Ad, is defined by
$${A_d=\displaystyle\bigcup_{y=1981}^{2010}\displaystyle\bigcup_{i=d-15}^{d+15}T(y,i)}$$
where ⋃ denotes the union of sets and T(y,i) is the Tmax on day i in the year y.
The daily heatwave magnitude, Md, is defined as :
$$
M_d(T_d)=\Bigg\{\displaylines{
\begin{align*}
\frac{T_d-T_{25p}}{T_{75p}-T_{25p}}&, \; if \; T_d > T_{25p} \\
0&, \; if \; T_d \leq T_{25p}
\end{align*}
}$$
with Td being the Tmax on day d of a heatwave, T25p and T75p are the 25th and 75th percentile values chosen from the yearly Tmax in the 30 years base period.
Depth-First Search (DFS) Algorithm
We employ a Depth-First Search (DFS) algorithm to track heatwave events in both spatial and temporal dimensions.
This approach enables objective identification of heatwave event extents, allowing for advanced analysis and visualization.
The left figure illustrates how DFS is applied in a 3D grid, detecting connected regions of extreme temperature.
The adjacency list representation and tree-based traversal allow us to map out heatwave developments dynamically.