Flooding is a major hazard to lives and infrastructure, but trends in flood hazard are poorly understood. The capacity of river channels to convey flood flows is typically assumed to be stationary, so changes in flood frequency are thought to be driven primarily by trends in streamflow. We have developed new methods for separately quantifying how trends in both streamflow and channel capacity have affected flood frequency at gauging sites across the United States Flood frequency was generally nonstationary, with increasing flood hazard at a statistically significant majority of sites. Changes in flood hazard driven by channel capacity were smaller, but more numerous, than those driven by streamflow. Our results demonstrate that accurately quantifying changes in flood hazard requires accounting separately for trends in both streamflow and channel capacity. They also show that channel capacity trends may have unforeseen consequences for flood management and for estimating flood insurance costs.

It has long been suggested that climate shapes land surface topography, through interactions between rainfall, runoff, and erosion in drainage basins 1-4. The longitudinal profile of a river (elevation versus distance downstream) is a key morphological attribute that reflects the history of drainage basin evolution, so its form should be diagnostic of the regional expression of climate and its interaction with the land surface 5-9. However, both detecting climatic signatures in longitudinal profiles and deciphering the climatic mechanisms of their development have been challenging due to the lack of relevant data across the globe, and due to the variable effects of tectonics, lithology, land-surface properties, and humans 10,11. Here we present a global dataset of river longitudinal profiles (n = 333,502), and use it to explore differences in overall profile shape (concavity) across climate zones. We show that river profiles are systematically straighter with increasing aridity. Through simple numerical modeling, we demonstrate that these global patterns in longitudinal profile shape can be explained by hydrological controls that reflect rainfall-runoff regimes in different climate zones. The most important of these is the downstream rate-of-change in streamflow independent of drainage basin area. Our results illustrate that river topography inherits a signature of aridity, suggesting that climate is a first-order control on drainage basin evolution. Conventional theory presents river longitudinal profiles (long profiles) as having a generally concave-up shape, with knickpoints and other fluctuations expressing the interactions of several independent variables: climate, tectonics, lithology, and human impacts 11-13. This characteristic shape of long profiles has been interpreted to arise due to downstream flow increase with drainage area, which erodes the riverbed, transports sediment from upstream to downstream, and produces fining profiles in bed material grain size 13,14. However, there are long profiles with overall concavity much closer to zero (straighter) than the typical concave-up profile shape 15-17 , yet there is limited understanding of the global distribution of long profile concavities and their relation to climate. Stream power incision theory states that channel erosion is intrinsically tied to an assumed relationship between river discharge (Q) and drainage area (Q~A c). Based on this theory, an expression has been derived that links supply-limited river long profile concavity to the exponent c 18 , illustrating that profiles will be concave up for c > 0, straight for c = 0, and convex for c < 0, and a similar dependency of profile concavity on the Q-A relationship has been derived for transport-limited fluvial systems 19. Previous work has largely emphasized long profile concavity for cases where c > 0, despite evidence that c in many river basins, especially in drylands, may vary flood to flood between negative, zero, and positive values 8,17,20. Of particular interest here is to ascertain whet...

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