Throwing the Numbers out with the Bathwater
Originally published in the ASFPM February 2025 Insider
The importance of flood modeling cannot be overstated. Our abilities as stormwater managers, hydrological engineers, and floodplain administrators rely on a simple question; ‘How bad can flooding realistically get?’ Without a baseline to plan mitigation activities around, preparedness essentially becomes a guessing game based on past disasters, which does not adequately prepare for worsening conditions exacerbated by climate change and urban sprawl.
Flooding is Not Like Filling a Bath, published in Earth’s Future Volume 12, Issue 12, authors Brett F. Sanders, Oliver E.J Wing, and Paul D. Bates describe the methodology hydrologists use to determine flood risk. The article dives into the problems associated with theoretical flood behavior described as “level pool” or “bathtub modeling”, which is the premise that inundation events react as a horizontal free surface. In other words, bathtub modeling relies on the assumption that floods are perfectly level as they move through a variety of terrains.
Bathtub Modeling Methods and Practice
As reported by historical sources, displacements in a level pool of water can be used to establish volume based on the object submerged (Archimedes of Syracuse in the mid-200s BC was able to calculate the purity of a gold crown submerged in water and the subsequent change in water level). Still liquid volume changes are used in modern times to estimate water levels based on the surface area displaced. This approach fails when a fluid is no longer contained and is free moving because of fundamental physics, like friction, pressure gradients and inertia.
Current research relies on the assumption that flood events “behave as a level pool”. Coastal calculations consider ocean water heights over land to be perfectly level in order to calculate the extent of flooding. Similarly, inland (including fluvial) studies derive their guidance by spreading stream heights over floodplains using Height Above Nearest Drainage (HAND) methods.
These simplified approaches remove complex physics that are difficult to apply. The convenience of bathtub modeling allows for quick calculations over large areas. But the inherent problem is that water, and subsequently flooding events, do not behave this way. Approximations that ignore the laws of motion affect what land will or won’t be flooded. The levels of uncertainty, especially when human life is often in the balance, is uncomfortably high and “unacceptable”, as the paper states. Moreover, inaccurate data undermines the credibility of climate change in the eyes of the public, research, and policy.
Why Bathtub Modeling Fails
As high-intensity and unprecedented flooding events are seen around the world, a “one size fits all” approach does not conform with the often nuanced areas inundation affects. Many models overlook critical factors such as obstructions from structures, infrastructure, severe elevation changes and even natural consequences like soil runoff after inundation events — all of which significantly influence flood hazard predictions.
Additionally, the paper reports that episodic floods do not have the “unlimited time to propagate across extensive floodplains before the tide turns or the flood water peaks…”. Bathtub modeling operates under the assumption that floods move at a uniform rate and are not slowed by natural or artificial factors. The height of flood waters in coastal areas can contribute to this inaccuracy, and areas protected by flood defenses can similarly slow the movement of water. The paper cites Didier et al. (2019), which describes that flood depths resulting from bathtub modeling may be overestimated by 100% when compared to dynamic modeling.
Urban areas are disproportionately affected due to biases in both directions; susceptibility to flooding due to impervious surfaces, and resistance to flooding because of engineered hydrologic defenses. Topographical features like roadways can compound inaccuracies. These problems can result in incorrect hotspot determination and inequalities in exposure.
Bathtub Models Stir Panic
Bathtub modeling studies often appear in high-profile journals because they address large-scale flood risk. This makes them appealing for climate and policy discussions. However, when these journals are reported on by major media outlets, the oversimplification of bathtub modeling rarely makes it off the cutting room floor, leading to exaggerated predictions. More technical journals are less likely to accept these studies without stronger verification.
Improvement Recommendations
Physics-based flood inundation software has been ubiquitous in mitigation planning and design, as well as general construction activities. However, local flood modelling fails to take into account the details mentioned above, and is difficult to apply to large scale metropolitan areas. In recent years, this class of physics-based software has emerged to make better use of available data. Continental-scale models are able to take advantage of global datasets, and have been rolled out across large inland domains, as well as coastal areas. Regional scale models can use finely detailed topographical and infrastructure data to accurately map predicted inundation. Areas are calculated in grid-based chunks to reduce computational bottlenecks and slowdowns. With this more dispersed approach, complex calculations can be done more efficiently, allowing a wider audience to utilize software of these types.
