Explaining the physics behind regional peak flow equations using the scaling theory of floods and river network descriptors

The development of regional flood-frequency equations is a key component of engineering infrastructure design and flood risk assessment at ungauged sites. These equations are constructed based on regression analysis techniques to study the connection between peak flow observations and different explanatory variables. However, many regions of the world remain poorly gauged or have experienced dramatic changes in land use or climate that make past observations less useful. To remedy this situation, we need to interpret and construct these regional equations based on physical principles of water movement and general knowledge of the geographic and geomorphologic setting of the upstream catchment at the location of interest. Several studies have examined these regional equations through the scaling theory of floods, making physical interpretations of the equation parameters (or scaling parameters) with respect to rainfall properties and geomorphologic variables. However, despite the advances of these previous works, the scaling theory of floods must be concerted with different, well-known problems in statistical hydrology for a proper engineering application in flood regionalization. These problems can vary from limitations in peak flow observations (sampling errors) to selection of an inadequate model structure of peak flows (epistemic errors). I present a series of studies based on hydrologic simulations and peak flow observations that illustrate several aspects related to the application and use of the scaling theory of floods, which include the following: (1) description of spatial patterns of scaling parameters; (2) inclusion of river network descriptors in flood frequency equations; and (3) evaluation of sampling errors and epistemic errors in the construction of flood frequency equations. The results presented in this dissertation contribute to the development of a more complete regional flood frequency analysis framework that leverages the physics of peak flow scaling and river network descriptors.