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Rainfall curves

A rainfall curve (or IDF — Intensity-Duration-Frequency curve) links the expected rainfall height \(h\) to a duration \(t\), for a fixed return period \(T\):

\[ h(t, T) = a(T) \cdot t^{\, n(T)} \qquad i(t, T) = a(T) \cdot t^{\, n(T) - 1} \]

with:

  • \(h\) in mm, \(i\) in mm/h, \(t\) in hours;
  • \(a(T)\) and \(n(T)\) derived from a log-log fit on the values \(h(t_i, T)\) provided by the probabilistic analyses.

How Runoff Lab computes it

  1. In the Curves panel → Add you select:
  2. source analysis (e.g. Gumbel-moments);
  3. return period (5, 10, 50, 100, 200 years or custom).
  4. For each station duration, the height \(h(t_i, T)\) is taken from the fitted distribution.
  5. Linear regression is applied in log-log space between \(\ln h\) and \(\ln t\):
\[ \ln h = \ln a + n \cdot \ln t \]

yielding \(a\) and \(n\). 4. The panel shows: - \(a\), \(n\), coefficient of determination \(R^2\); - table of observed vs curve values; - log-log plot with points and fitted line.

Interpreting \(a\) and \(n\)

  • \(\boldsymbol{a}\) = rainfall height for \(t = 1\) hour (for that \(T\)). Larger in wet climates or for high \(T\).
  • \(\boldsymbol{n}\) = exponent of the law, always in \([0, 1]\). Typically:
  • \(n \approx 0.20\text{–}0.30\) for highly convective rainfall (short and intense);
  • \(n \approx 0.40\text{–}0.55\) for persistent frontal rainfall.

Low \(n\) → rainfall "concentrates" in short durations → small basins prone to flash floods.

Multiple return periods

Create a curve for each \(T\) of interest: typically 5, 50, 200 years for hydraulic works. Overlay them on a single plot to show the "growth factor" between return periods.

Tip

Keeping at least T = 50 and T = 200 in the study is almost always required by a hydrological report for public works.

When the log-log fit isn't enough

If \(R^2 < 0.95\) the 2-parameter law doesn't represent the station well. Typical causes:

  • Sparse series on some durations → unstable analysis.
  • Discontinuities in the series (relocated rain gauge, historical vs recent period). Split the series and re-run analyses on sub-periods.
  • Scale effect: for stations at high elevation or close to the sea, a single 2-parameter law may fail. Use 3-parameter models (TCEV level 3) that better constrain the tail.

Export

Each curve enters the PDF report automatically with:

  • parameters \(a\), \(n\), \(R^2\);
  • observed vs predicted points table;
  • h-t plot (log-log) and i-t plot (lin-lin) for the chosen \(T\);
  • formula with numerical values substituted.