Shallow groundwater thermal sensitivity to climate change and land cover disturbances: derivation of analytical expressions and implications for stream temperature modeling

Climate change is expected to increase stream temperatures and the projected warming may alter the spatial extent of habitat for cold-water fish and other aquatic taxa. Recent studies have proposed that stream thermal sensitivities, derived from short-term air temperature variations, can be employed to infer future stream warming due to longterm climate change. However, this approach does not consider the potential for streambed heat fluxes to increase due to gradual warming of the shallow subsurface. The temperature of shallow groundwater is particularly important for the thermal regimes of groundwater-dominated streams and rivers. Also, recent studies have investigated how land surface perturbations, such as wildfires or timber harvesting, can influence stream temperatures by changing stream surface heat fluxes, but these studies have typically not considered how these surface disturbances can also alter shallow groundwater temperatures and streambed heat fluxes. In this study, several analytical solutions to the onedimensional unsteady advection–diffusion equation for subsurface heat transport are employed to estimate the timing and magnitude of groundwater temperature changes due to seasonal and long-term variability in land surface temperatures. Groundwater thermal sensitivity formulae are proposed that accommodate different surface warming scenarios. The thermal sensitivity formulae suggest that shallow groundwater will warm in response to climate change and other surface perturbations, but the timing and magnitude of the subsurface warming depends on the rate of surface warming, subsurface thermal properties, bulk aquifer depth, and groundwater velocity. The results also emphasize the difference between the thermal sensitivity of shallow groundwater to short-term (e.g., seasonal) and longterm (e.g., multi-decadal) land surface-temperature variability, and thus demonstrate the limitations of using short-term air and water temperature records to project future stream warming. Suggestions are provided for implementing these formulae in stream temperature models to accommodate groundwater warming.