IDF curve and DAD curve

IDF curve (Intensity-Duration-Frequency)

An IDF curve shows the relationship between rainfall intensity $i$, duration $D$ and frequency (return period) $T$ of storms at a place. Intensity decreases with duration, and for the same duration a rarer storm (higher $T$) has a higher intensity.

Development: From annual maximum rainfall of various durations (5 min to 24 h), a frequency analysis (Gumbel, Log-Pearson III) gives the depth for each return period. Intensity = depth / duration is plotted against duration on log scales, one curve per return period.

 i (mm/h)
  |\
  | \\   T = 100 yr
  |  \\\  T = 25 yr
  |    \\\ T = 5 yr
  +-------------- D (min)

An empirical form is $i = \dfrac{K T^x}{(D + a)^n}$. IDF curves are used to get design rainfall for storm drains, culverts and small catchments (rational method).

DAD curve (Depth-Area-Duration)

A DAD curve shows the average rainfall depth over an area for storms of different durations. For a given duration, the average depth decreases as the area increases, and for the same area a longer duration gives a larger depth.

Development: From isohyetal maps of a storm for 6, 12, 24 h, etc., the average depth within each isohyet and the area enclosed are computed, and plotted as depth against area for each duration.

 Depth
  | \____  24 h
  |  \____ 12 h
  |   \____ 6 h
  +-------------- Area (km2)

DAD curves are used to estimate the probable maximum precipitation (PMP) and the design storm for large catchments, flood control and spillway design.