Although flood estimation at a confluence is one of the simpler collective risk problems to understand, general solutions are hard to find.
Confluences of lowland rivers are often characterised by shallow gradients, shifting channels, and a wide floodplain: conditions that make flood measurement problematic. It is not uncommon to have extensive flood records on each tributary, and a requirement to estimate flood flows for the town at, or close to, the confluence. There are plenty of them: from Kidderminster, Leicester & Malton to Rotherham, Salisbury & Tamworth.
Where the tributary catchments are of similar character, the rivers will often flood more or less in unison. Where the catchments are as different as chalk and cheese, they will flood together only exceptionally. Particularly in the latter situation, the exceptions are likely to be important in establishing flood frequency.
Comprehensive studies of flood risk at a confluence generally require a modelling approach, with a detailed hydraulic model of the interacting reaches. For the hydrological component, a more detailed description is required than flood peak data alone can provide, and some kind of rainfall-runoff approach will usually be invoked. A design event method is likely to be less convincing than one based on continuous simulation, but neither is straightforward.
Nevertheless, a statistical representation of the degree of dependence in tributary floods could be a useful prelude to, or ingredient of, studies of basin-wide flood risk. There is a potential tie-in with certain reinsurance problems.
If you are interested in any of the above, please do get in touch.