Analytical solutions to the 1D heat transport equation can be used to derive point measurements of flux between surface water and groundwater from streambed temperature time series. Recent studies have used empirical relationships between measured flux and point-in-time observations of streambed temperatures to produce detailed plan view maps of flux from instantaneous temperature maps. Here, the accuracy of such flux maps, derived using streambed temperatures as a quantitative proxy, was assessed from synthetic streambed temperature data generated by numerical flow and transport simulations. The use of numerical simulations is advantageous because maps of flux from the temperature proxy method can be compared to known flux maps to quantify error. Empirical flux-temperature relationships are most accurate if developed from data collected when stream temperatures are at a maximum. The true relationship between flux and streambed temperature will generally be non-linear and well approximated as a cubic function, although linear relationships may be applied when data density is low. Intermediate fluxes (±1.0. m/day) returned by the temperature proxy method have errors typically less than ±0.1. m/day. Errors in estimated flux increase for strong upwelling (>1.0. m/day) or downwelling (<-1.0. m/day), although the direction of flux is still accurate.
- Heat tracing
- Hyporheic zone
- Numerical modeling
- Surface water-groundwater interaction