IDF fitting & intensity retrieval

HDAT uses a segmented log-log fitting approach on standard durations to retrieve intensity at a target duration (typically \(T_c\)).

Standard durations

Durations (minutes):

\[ [5, 10, 15, 30, 60, 120, 180, 360, 720, 1440] \]

Segmented power-law model

The model is a power law per segment:

\[ I(x) = e^{C_0}\cdot x^{C_1} \]

where:

• \(x\): duration (minutes)
• \(C_0, C_1\): fitted coefficients in log space

Segments:

• A: 5–60 min (first 5 points)
• B: 60–120 min (2 points)
• C: 120–1440 min (last 5 points)

Segment selection for a requested duration \(x\):

• \(x \le 60\) → A
• \(60 < x \le 120\) → B
• \(x > 120\) → C

Fit quality

Legacy stores a goodness-of-fit metric as \(R^2\). Recommended practice is to:

• store \(R^2\) per return period
• flag poor fits (low \(R^2\)) for engineer review
• ensure intensity is monotonic/non-increasing with duration for sanity