In this paper, a bivariate model will be presented, using flood peak and flood volume of direct runoff as the two characteristic variables of a flood event. The model can also be applied to other bivariate problems in hydrology.The bivariate normal distribution was chosen as the parent bivariate distribution function, which seems to be suitable for the practical user. It is necessary to transform the marginal distributions of both samples into normal distributions. The theoretical bi-normal distributions is fitted and tested by using the equi-lines of probability density function (ISO-PDF-lines).The model offers various possibilities of probability interpretation ISO-PDF-lines show a range within which a certain percentage of events lie. The conditional distributions of one variable can be computed for a constant value of the other variable, which shows the probability by which the variable is reached or exceeeded for the other fixed variable. A useful calculation is given by the so called “Probability of quadrants” For instance, the “upper-right probability” of a certain pair of values defines the probability of events with both characteristics being higher than those of the presumed values.Applying this method to the planning of flood protection projects, design flood events of chosen probabilities are determined by a certain equi-line of quadrants probability.
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- A Bivariate Flood Model and Its Application
- Springer Netherlands