The green circles and red Xs represent the observed event pairs for each scenario. Green circles indicate observed annual peak 3-day precipitation paired with near-coincident flows, while red Xs indicate observed annual peak 1-day flow paired with near-coincident precipitation.
The small gray points represent a subsample of the 1 million randomly generated event pairs simulated from the fitted copulas.
An isoline represents a constant joint-exceedance probability. Each isoline traces the combinations of variables A and B that produce the same joint probability, defined by the "AND" condition:
P(A > a, B > b)
The dashed purple and dotted green isolines each represent a separate copula. The dashed purple isoline is conditioned on flow, representing extreme flows paired with near-coincident precipitation. The dotted green isoline is conditioned on precipitation, representing extreme precipitation paired with near-coincident flows.
The shaded envelope curve represents the worst-case combination of the two copula-based isolines. Specifically, it is the outer envelope of the two "AND" isolines, such that the resulting curve encompasses the more extreme combination of variable values from either copula.
The blue-to-yellow-to-red shading along the isolines indicates the relative, normalized likelihood of different combinations of variables A and B. Warmer colors indicate combinations with a higher relative likelihood of occurrence.
The design event is defined as the point along each envelope curve with the highest relative likelihood of occurrence. These design events are shown as open black diamonds, and their corresponding variable values are provided in the accompanying table.
Coincident Frequency vs. Copulas
- The output of a coincident frequency analysis is a response variable's frequency curve.
- The output of a copula analysis are isolines and design points for joint probabilities. The values of the design point must be applied in a model to describe the response variable at that joint probability.
