DFS Method
Depth-First Search converts daily high-temperature exceedances into reproducible three-dimensional event objects. This page separates the method into three operations: define active heat, connect adjacent space-time cells, and calculate event characteristics.
Method at a glance
Input and heat signal
DFS does not decide whether a temperature is extreme. It begins from a prepared active-cell mask. For the current ERA5 heatwave workflow, the mask is derived from daily maximum temperature and a calendar-day threshold, while daily magnitude \(M_d\) describes the strength of the heat signal at each active cell.
The current website description uses a centered 31-day sample around calendar day \(d\) across the 1981-2010 reference years.
A grid cell becomes a candidate heatwave voxel when daily maximum temperature exceeds the applicable threshold.
P90 determines whether a cell enters the event mask. The legacy HWMId formulation uses reference \(T_{25p}\) and \(T_{75p}\) values to standardize daily magnitude. They should not be read as interchangeable thresholds.
The production archive retains the legacy h1t05v4 threshold and magnitude provenance. Exact threshold files, calendar handling, and rounding belong to that production contract rather than to the DFS traversal itself.
DFS connectivity
Each active cell is a voxel in \((t, y, x)\) space. DFS starts from one unlabelled voxel, follows every valid neighbour until no new neighbour remains, and assigns all visited voxels to the same event. It then repeats from the next unlabelled active voxel.
Cells with a valid positive heatwave magnitude enter the candidate mask.
Spatially and temporally adjacent active voxels receive the same event label.
Daily horizontal slices reveal the complete footprint and lifetime of the event.
A three-dimensional connected-component problem.
All surrounding cells in the horizontal grid are considered.
Connectivity is evaluated across adjacent daily slices.
The global grid wraps across the date-line; latitude boundaries remain closed.
Shorter connected signals are excluded from the heatwave event catalog.
Labels are ordered consistently after connected components are formed.
Metric calculation
Once event membership is fixed, the event can be summarized without losing its three physical dimensions. Let \(E\) be the connected event, \(G_t\) its active grid cells on day \(t\), and \(a_g\) the area of grid cell \(g\).
Elapsed event time from the first to the final detected day, inclusive.
HWV accumulates daily affected area; HWMA is the mean daily footprint.
HWMS is cumulative area-weighted event magnitude; HWMM is mean magnitude per unit event volume.
This identity is why HWD, HWMA, and HWMM explain HWMS but should not be added to HPRI as separate hidden weights.
| Field | Calculation or role | Scientific reading |
|---|---|---|
maxHWA | \(\max_t(A_t)\) | Maximum daily affected area reached by the event. |
HWMD | HWV / maxHWA | Derived catalog measure retained for legacy output parity. |
sumofMd | Legacy magnitude accumulation field | Preserved in the source schema; use only with its production provenance. |
AREA | Climate-region code | The catalog can report one connected event by intersected region. |
tol_j, tol_i | Representative event coordinates | Useful for search; event boundary layers are preferred for exact spatial overlap. |
stT, edT | Start and end day index | Support timing, duration, and historical-day queries. |
Reading the characteristics
A larger value means the connected event lasts longer.
A larger value means the event covers a broader mean daily area.
A larger value means stronger average magnitude across the event volume.
A larger value can result from longer duration, wider area, stronger magnitude, or their combination.
Two events can have similar HWMS but very different structures. One may be brief and spatially extensive; another may be compact but persistent and intense. Read HWMS together with HWD, HWMA, and HWMM before interpreting the event.
Output and provenance
| Product | Current website source | Use |
|---|---|---|
| Event catalog | Heatwave/data/list_data.json | Event metrics used across Home, Data, Insights, Charts, and Risk. |
| Search source | event_data/ERA5_mxt2m_Heatwave_h1t05v4_20260129.csv | Spatial and calendar-date event search with the full legacy field set. |
| Event boundaries | boundary_data/ETid_<year>_boundaries.geojson | Footprint inspection and future asset-overlap analysis. |
| Validated coverage | 1940-2025; 15,634 records | Current local website validation status; revalidate after any archive refresh. |
The website preserves the event fields Year, Nu,
AREA, HWV, HWMA, maxHWA,
HWMD, HWMS, HWMM, sumofMd,
tol_j, tol_i, stT, edT,
and HWD. HPRI is added later as an interpretation layer.
Method boundaries
The archive follows the legacy h1t05v4 heatwave signal. Exact source files, leap-day treatment, calendar handling, and production rounding must accompany a reproducible release.
The current contract uses 8-neighbour spatial adjacency, adjacent time slices, periodic longitude, and a minimum three-day event. Other variables require their own signal and connectivity contract.
DFS describes physical event structure. Health, crop, power, water, labor, and financial effects require independent exposure and vulnerability evidence.
This event archive supports research and retrospective screening. It is not a substitute for operational high-temperature warnings.