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Synthetic hyetographs (Chicago design storm)

A synthetic hyetograph is the time distribution of rainfall height within a design event. While the IDF curve only tells you how much it rained over a given interval, the hyetograph tells you how it was distributed in time: this is the information needed to apply rainfall-runoff transformation.

Runoff Lab NX uses the Chicago Design Storm (Keifer & Chu, 1957), the standard method for building synthetic hyetographs from an IDF curve.

Method idea

Instant intensity on either side of the peak is obtained directly from the IDF inversion:

\[ i(t_b) = a \cdot \left(\frac{t_b}{r}\right)^{\!n-1} \qquad i(t_a) = a \cdot \left(\frac{t_a}{1-r}\right)^{\!n-1} \]

with:

  • \(r\) peak position (\(r = 0.4\) typical);
  • \(t_b\) time before the peak;
  • \(t_a\) time after the peak;
  • \(a\), \(n\) parameters of the source curve.

Result: a sequence of intensities centred on the peak, asymmetrically decreasing toward head and tail.

Building it in Runoff Lab

  1. Go to the Synthetic hyetographs panel → Add.
  2. Set:
  3. source curve (e.g. Gumbel — T=100 years);
  4. event total duration \(D\) in minutes (60, 120, 360, …);
  5. peak position \(r\) in \([0, 1]\);
  6. time step \(\Delta t\) (1, 5, 10 min — default 1 min).
  7. Confirm → the chart shows the bar-chart hyetograph, the table shows values \(\big(t_i, i(t_i)\big)\).

Choosing \(r\)

\(r\) Interpretation
0.0 Peak at start — decreasing rainfall. Saturated urban basins.
0.3 Early peak.
0.4 (default) Compromise adopted by Italian guidelines (PAI, basin authorities).
0.5 Symmetric — overestimates peak discharge on ordinary basins.
1.0 Peak at end — increasing rainfall.

When to use it

The synthetic hyetograph is used to:

  • feed the rainfall-runoff model (see SCS-CN Hydrographs);
  • document the design hyetograph in hydraulic reports;
  • test work sensitivity to different scenarios (\(D\), \(r\)).

Alternative hyetographs

Chicago is one standard but alternatives exist (Huff, Sifalda, alternating blocks). Runoff Lab NX currently implements only the Chicago method; for almost all practical uses it's sufficient.

Bibliography

  • Keifer C.J., Chu H.H. (1957), Synthetic Storm Pattern for Drainage Design, ASCE Hydraulic Division 83.
  • Watt W.E., Chow K.C.A. (1985), A general expression for basin lag time, Canadian Journal of Civil Engineering 12(2).