How does flood damage increase with flood water depth? That’s the question explored in a recent Nature Communications paper by Oliver Wing (University of Bristol) and colleagues.
Observed flood losses are not monotonic functions of depth, but instead better follow a beta function, with bimodal distributions for different water depths.
In other words, if you look at the median damage claims (as % of property value) across many properties for a selection of different depths (say 1, 2, 3, 4, 5, 6 feet) you would indeed find that deeper water leads to more damage. But the uncertainty around the median is huge. It’s also constrained to a maximum of the value of the property and a minimum of zero damage. Interestingly, for any given depth you get a disproportionate number of properties at either end of the spectrum. Lots survive undamaged, others are a total write-off. This seems pretty important for putting a dollar value on flood damage:
This variability in depth–damage is not adequately described by any central tendency. For example, if 100 buildings were flooded to a depth of 4 feet, assuming that all 100 uniformly incur the median of 38% damage is very different from a bimodal or beta distribution in which 22 buildings experienced <10% damage, 16 buildings experienced >90% damage, and the remaining 62 something in between (10–90%).
It’s a neat study. I also love this killer statement:
… even a hydraulic model based on state-of-the-science lidar topography and multibeam bathymetry and calibrated to within millimeters may yield damage estimates off by an order of magnitude after translation through the depth-damage bottleneck.
By extension, valuation of flood protection measures must also be a stab in dark.