rainfall-thresholds

Rainfall intensity-duration thresholds for shallow landslides: the Caine power law, the reconstruction of rainfall events from an hourly series, and the frequentist fit of a threshold to the events that triggered landslides. Pure Python, no dependencies.

What it does

A shallow landslide is triggered when rain is intense enough for long enough. The usual empirical model (Caine 1980) is a line in log-log space:

I(D) = alpha * D^(-beta)      I: mean intensity (mm/h), D: duration (h)

An event above the line is in the conditions that triggered landslides before. The package covers the three steps around that line:

It also ships T5 thresholds for Italy refitted on the e-ITALICA catalogue, with a test that refits them from the data.

Install

pip install rainfall-thresholds

Use

from datetime import UTC, datetime, timedelta

from rainfall_thresholds import ITALICA_T5, latest_event, reconstruct_events

start = datetime(2026, 10, 10, tzinfo=UTC)
hourly_mm = [0, 2, 8, 15, 22, 18, 9, 4, 0, 1, 3, 0, 0]
series = [(start + timedelta(hours=h), mm) for h, mm in enumerate(hourly_mm)]

event = latest_event(reconstruct_events(series, no_rain_break_hours=6, min_event_mm=2.0))
assert event is not None
threshold = ITALICA_T5["southern"]

print(f"{event.total_mm:.0f} mm in {event.duration_hours:.0f} h = {event.intensity_mm_h:.1f} mm/h")
print(f"T5 at that duration: {threshold.intensity(event.duration_hours):.1f} mm/h")
print(f"{threshold.exceedance(event.intensity_mm_h, event.duration_hours):+.2f} decades")

82 mm in 10 h = 8.2 mm/h
T5 at that duration: 2.0 mm/h
+0.62 decades

exceedance is log10(I / I(D)): 0 on the line, +1 at ten times the threshold intensity, negative below.

Fitting your own threshold

from rainfall_thresholds import fit_threshold

# (duration_h, intensity_mm_h) of rainfall events that triggered landslides
fit = fit_threshold(triggering_events, percentile=5)
fit.threshold  # PowerLawThreshold: 5 % of the events sit below it
fit.central  # the least-squares line before it is lowered

The method is the frequentist one of Brunetti et al. (2010) and Peruccacci et al. (2012): least squares on log I against log D, then the line is lowered by the chosen percentile of the residuals. One difference: they take the percentile from a Gaussian fitted to a kernel density of the residuals; this package takes it from the residuals themselves. The two agree when the residuals are close to normal.

Thresholds for Italy

Fitted with fit_threshold(percentile=5) on the 5,974 events of e-ITALICA v4 with a positive duration and cumulated rainfall:

MACROREGIONS lists the regions in each group. Abruzzo and Molise are in the centre, unlike the ISTAT "Sud": use macroregion_of(region) rather than an ISTAT table, or the threshold will not be the one fitted on that region's events.

These are not the thresholds published by the e-ITALICA authors, who use their own method and partitions: they are what this package's method gives on their data, and tests/test_italy.py checks that they still do.

Event reconstruction

An event runs from its first to its last wet hour; no_rain_break_hours dry hours in a row end it, and an event below min_event_mm is dropped. This is a simplified form of Melillo et al. (2018), whose CTRL-T tool also varies the dry gap with the season. The e-ITALICA durations come from that fuller procedure, so a threshold fitted on them and applied to events from reconstruct_events mixes the two: fine for monitoring, worth knowing for a study.

References

• Caine N. (1980). The rainfall intensity-duration control of shallow landslides and debris flows. Geografiska Annaler A 62, 23-27.
• Brunetti M.T. et al. (2010). Rainfall thresholds for the possible occurrence of landslides in Italy. NHESS 10, 447-458.
• Peruccacci S. et al. (2012). Lithological and seasonal control on rainfall thresholds for the possible initiation of landslides in central Italy. Geomorphology 139-140, 79-90.
• Melillo M. et al. (2018). A tool for the automatic calculation of rainfall thresholds for landslide occurrence. Environmental Modelling & Software 105, 230-243.
• Peruccacci S. et al. (2023). ITALICA: an ITAlian rainfall-induced LandslIdes CAtalogue. ESSD 15, 2863-2877.
• Brunetti M.T. et al. (2024). e-ITALICA (enhanced ITAlian rainfall-induced LandslIdes CAtalogue), v4. Zenodo, doi:10.5281/zenodo.14204473.

Data licence

The test fixture tests/fixtures/italica_v4_dur_rain.csv is e-ITALICA v4 (Brunetti et al. 2024), CC BY 4.0, reduced to four columns (id, region, duration, cumulated rainfall).

Extracted from Limen, which uses it for the rainfall component of its landslide score.

Development

uv sync
make check

License

Code: Apache-2.0.