The factors related to the joint probabilty of flooding on paired streams were investigated and quantified to provide information to aid in the design of hydraulic structures where the joint probabilty of flooding is an element of the design criteria. Stream pairs were considered to have flooded jointly at the design-year flood threshold (corresponding to the 2-, 10-, 25-, or 50-year instantaneous peak streamflow) if peak streamflows at both streams in the pair were observed or predicted to have equaled or exceeded the threshold on a given calendar day. Daily mean streamflow data were used as a substitute for instantaneous peak streamflow data to determine which flood thresholds were equaled or exceeded on any given day. Instantaneous peak streamflow data, when available, were used preferentially to assess flood-threshold exceedance.
Daily mean streamflow data for each stream were paired with concurrent daily mean streamflow data at the other streams. Observed probabilities of joint flooding, determined for the 2-, 10-, 25-, and 50-year flood thresholds, were computed as the ratios of the total number of days when streamflows at both streams concurrently equaled or exceeded their flood thresholds (events) to the total number of days where streamflows at either stream equaled or exceeded its flood threshold (trials).
A combination of correlation analyses, graphical analyses, and logistic-regression analyses were used to identify and quantify factors associated with the observed probabilities of joint flooding (event-trial ratios). The analyses indicated that the distance between drainage area centroids, the ratio of the smaller to larger drainage area, the mean drainage area, and the centroid angle adjusted 30 degrees were the basin characteristics most closely associated with the joint probabilty of flooding on paired streams in Ohio. In general, the analyses indicated that the joint probabilty of flooding decreases with an increase in centroid distance and increases with increases in drainage area ratio, mean drainage area, and centroid angle adjusted 30 degrees.
Logistic-regression equations were developed, which can be used to estimate the probability that streamflows at two streams jointly equal or exceed the 2-year flood threshold given that the streamflow at one of the two streams equals or exceeds the 2-year flood threshold. The logistic-regression equations are applicable to stream pairs in Ohio (and border areas of adjacent states) that are unregulated, free of significant urban influences, and have characteristics similar to those of the 304 gaged stream pairs used in the logistic-regression analyses.
Contingency tables were constructed and analyzed to provide information about the bivariate distribution of floods on paired streams. The contingency tables showed that the percentage of trials in which both streams in the pair concurrently flood at identical recurrence-interval ranges generally increased as centroid distances decreased and was greatest for stream pairs with adjusted centroid angles greater than or equal to 60 degrees and drainage area ratios greater than or equal to 0.01. Also, as centroid distance increased, streamflow at one stream in the pair was more likely to be in a less than 2-year recurrence-interval range when streamflow at the second stream was in a 2-year or greater recurrence-interval range.
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USGS Numbered Series
Factors related to the joint probability of flooding on paired streams
Water-Resources Investigations Report
U.S. Dept. of the Interior, U.S. Geological Survey ;
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