Application of probability plots

A probability plot shows the magnitude of an event (e.g. flood or rainfall) against its probability of exceedance, or return period, on a paper designed so that the assumed distribution plots as a straight line (normal, log-normal, Gumbel paper). Plotting positions are $P=m/(N+1)$ or $T=(N+1)/m$.

 Q
  |                     o  <- extrapolated
  |                  /
  |               o/
  |            o /
  |         o  /
  |      o   /
  |   o    /     (best-fit line)
  +--+-----+-----+-----+---- T (yr) or P (%)
    1.1    2     10    100

Applications

1. Flood estimation: read the flood of a required return period (e.g. 50 or 100 years) by extending the straight line beyond the record (extrapolation) for design of dams, bridges and culverts.
2. Choice of distribution: the closeness of the points to the line shows whether Gumbel, normal, log-normal or log-Pearson III fits the data.
3. Return period of a past event: read T for an observed flood or rainfall.
4. Risk and reliability: the probability of a design value being exceeded in the structure's life.
5. Design rainfall and low-flow (drought) analysis, and comparison between stations or regions.
6. Checking the parameters, e.g. the mean flood plots at about T = 2.33 years on Gumbel paper.