A one-dimensional (1-D) analytic solution is developed for heat transport through an aquifer system where the vertical temperature profile in the aquifer is nearly uniform. The general anisotropic form of the viscous heat generation term is developed for use in groundwater flow simulations. The 1-D solution is extended to more complex geometries by solving the equation for piece-wise linear or uniform properties and boundary conditions. A moderately complex example, the Eastern Snake River Plain (ESRP), is analyzed to demonstrate the use of the analytic solution for identifying important physical processes. For example, it is shown that viscous heating is variably important and that heat conduction to the land surface is a primary control on the distribution of aquifer and spring temperatures. Use of published values for all aquifer and thermal properties results in a reasonable match between simulated and measured groundwater temperatures over most of the 300 km length of the ESRP, except for geothermal heat flow into the base of the aquifer within 20 km of the Yellowstone hotspot. Previous basal heat flow measurements (110 mW/m2) made beneath the ESRP aquifer were collected at distances of >50 km from the Yellowstone Plateau, but a higher basal heat flow of 150 mW/m2 is required to match groundwater temperatures near the Plateau. The ESRP example demonstrates how the new tool can be used during preliminary analysis of a groundwater system, allowing efficient identification of the important physical processes that must be represented during more-complex 2-D and 3-D simulations of combined groundwater and heat flow.

Groundwater temperature changes will lag surface temperature changes from a changing climate. Steady state solutions of the heat-transport equations are used to identify key processes that control the long-term thermal response of springs and other groundwater discharge to climate change, in particular changes in (1) groundwater recharge rate and temperature and (2) land-surface temperature transmitted through the vadose zone. Transient solutions are developed to estimate the time required for new thermal signals to arrive at ecosystems. The solution is applied to the volcanic Medicine Lake highlands, California, USA, and associated springs complexes that host groundwater-dependent ecosystems. In this system, upper basin groundwater temperatures are strongly affected only by recharge conditions. However, as the vadose zone thins away from the highlands, changes in the average annual land-surface temperature also influence groundwater temperatures. Transient response to temperature change depends on both the conductive time scale and the rate at which recharge delivers heat. Most of the thermal response of groundwater at high elevations will occur within 20 years of a shift in recharge temperatures, but the large lower elevation springs will respond more slowly, with about half of the conductive response occurring within the first 20 years and about half of the advective response to higher recharge temperatures occurring in approximately 60 years.