The reliability of a flood warning system can be characterized statistically in terms of two measures: (1) the relative operating characteristic (ROC), defined earlier, and (2) the performance trade-off characteristic (PTC), which shows feasible trade-offs that a given system offers between the expected number of detections per year and the expected number of false warnings per year. When the floodplain extends across a range of elevations, the ROC and PTC are defined for each zone of the floodplain [ Krzysztofowicz, 1992b].
Numerical procedures for computing the ROC and PTC have been derived and applied to flood warning systems serving three communities in Pennsylvania. The case of Milton demonstrates fundamental trade-offs between the reliability and the expected lead time of warnings. The case of Connellsville demonstrates synergistic gains in warning reliability due to a coupled solution: a flood warning system and a flood control dam upstream [ Krzysztofowicz et al., 1994].
In order to synthesize information for strategic planning and policy decisions, envelopes of ROCs have been constructed; they display graphically the overall reliability of flood warning systems within a region. A case study presents ROC envelopes of warning systems for uncontrolled rivers in Pennsylvania during the 1960--1980s [ Kelly and Krzysztofowicz, 1994b].
Finally, the BPF has provided a framework for studying the synergistic effect of a dam and forecasts. In essence, the dam changes not only (1) the natural regime of flood flows (and hence the prior distribution in the BPF), but also (2) the predictability of flood flows (and hence the likelihood function in the BPF). These changes affect the posterior probability of flood occurrence and the posterior distribution of the flood crest. These effects have been illustrated with a case study [ Kelly and Krzysztofowicz, 1994c].