| Summary: | It is almost universally assumed in statistical hydroclimatology that relationships between large-scale climate indices and local-scale hydrometeorological responses, though possibly nonlinear, are monotonic. However, recent work suggests that northern-hemisphere atmospheric teleconnections to El Niño-Southern Oscillation (ENSO) and the Arctic Oscillation can be parabolic. The effect has recently been explicitly confirmed in hydrologic responses, though associations are complicated by land surface characteristics and processes, and investigation of water resource implications has been limited to date. Here, we apply an Akaike Information Criterion-based polynomial selection approach to investigate annual flow volume teleconnections for 42 of the northern hemisphere's largest ocean-reaching rivers. Though we find a rich diversity of responses, parabolic relationships are formally consistent with the data for almost half the rivers, and the optimal model for eight. These highly nonlinear water supply teleconnections could radically alter the standard conceptual model of how water resources respond to climatic variability. For example, the Sacramento river in drought-ridden California exhibits no significant monotonic ENSO teleconnection but a 0.92 probability of a quadratic relationship, reducing mean predictive error by up to 65% and suggesting greater opportunity for climate index-based water supply forecasts than previously appreciated.
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