Distributed function analysis of ice jam flood frequency

River ice jams can cause extreme flood events with major socio-economic and ecological impacts. A major practical question is how to quantify and assess ice-jam flood risk. Ideally, this question can be answered by means of historical ice-influenced water level peaks. More commonly, however, the available historical information is scarce and determination of ice-jam flood frequencies or probabilities must rely on a synthetic method. After noting that empirical evidence does not support the assumption of discrete stage outcomes, which is central to the existing methodology, a new synthetic method is developed. It hinges on the fact that the peak stage can take on any value between discharge-dependent envelopes and is thence called the distributed-function method, or DFM, and successfully tested by means of four case studies. It is shown further that the DFM produces more realistic results relative to those of the existing approach. Practical limitations are common to both methods and arise primarily from the need to use the peak runoff discharge, rather than the unknown value that prevails at the time of the peak stage. Resulting errors in probability estimates are evaluated in an extreme case and shown to be both conservative and tolerable. Analysis of additional case studies is recommended as a means of enhancing the utility of the DFM.