There are quite a number of steps and additional data that you'd require before you can answer this question with a level of detail that is appropriate for such an important question. This is not just a question of emergency response, as it might first appear, but of rapid inundation which can cause a significant hazard to a wide area.
Note: I am a flood risk manager by profession; my answers are mostly linked to UK practice, and particularly practice in my firm. In general, my recommendation would be to seek professional advice in your own country, where standards and guidance may be different.
In general, there are three (or perhaps more) possible approaches to answer this question, which relates to time-varying, spatial-varying hydraulic flow:
- 1D analysis, using software such as Flood Modeller Free/Pro or HEC-RAS;
- 2D analysis, using software such as MIKE or HEC-geoRAS (as Fernando suggested);
- 3D analysis, using CFD software like OpenFOAM.
The nomenclature is slightly misleading: 1D analysis uses a series of 2D cross-sections to convey flow from upstream to downstream, in a time-varying way (and so is more like 3D); 2D analysis uses a ground model (e.g. LiDAR or river channel TINs) to do likewise, and is also time-varying; and CFD is often (but not always) time-varying as well.
I would deter anybody from doing 3D analysis as a first pass; it is hard, time-consuming and requires a level of expertise and verification that can be hard to come by.
2D analysis has its place, but can become computationally expensive if you are covering a wide area, as you would be in dam breach models such as this. This can make simulation times, and results storage, excessively large. In addition, software licenses can be very expensive.
My personal recommendation, at least as a first pass, would be to undertake a 1D analysis. This is not totally straightforward, and does require a little training (which can be self-guided), and additional data:
- River cross-sections at appropriate distances, usually by topographic survey;
- Photographs or other estimates of channel roughness;
- Flow data for the river, for verification purposes.
You should also have an understanding about how to schematise your dam in terms of 1D modelling, and about how to simulate a dam failure in your chosen piece of software. This is not quite my field of expertise, so I'm not best placed to advise on this.
All being well, your results will come out as a longitudinal profile along the river of maximum water levels throughout a dam break scenario.
You can now transpose these maximum water levels onto your DTM, using the location of your river cross-sections as a guide. There will be some interpolation between cross-sections, which is fine; fix a maximum water level at a location first, and follow the contours to the next section; then do the same at the next section and work backwards; finally, take an average line between them (I expect there's a programmatic way to do this, but I don't know it offhand). Actually Flood Modeller Pro (and perhaps its Free cousin) has some tools to help with this "1D Flood Mapping" exercise.
This will give you a spatial plot of maximum flood extents - but, be warned. This will be indicative only, because in reality the levels predicted by the 1D model will not take into account the loss of flow into the spatial domain, and so will overpredict water levels. Your flood mapping exercise may also give "wetted" areas where in practice overland flow routing would avoid these areas.
That said, as a high-level exercise to inform emergency response, it would be a good first pass.
I think it bears repeating that in practice it is really important to seek professional guidance on how this exercise should be undertaken, and perhaps employ a consultant to carry it out on your behalf. Failure to predict the high-depth, high-velocity and hence high-hazard flow of water out of a breaching dam is a serious matter, and should not attempted by those not familiar with flood risk management.