[1] Work over the last decade has documented methods for estimating fluxes between streams and streambeds from time series of temperature at two depths in the streambed. We present substantial extension to the existing theory and practice of using temperature time series to estimate streambed water fluxes and thermal properties, including (1) a new explicit analytical solution to predict one-dimensional fluid velocity from amplitude and phase information; (2) an inverse function, also with explicit formulation; (3) methods to estimate fluid velocity from temperature measurements with unknown depths; (4) methods to estimate thermal diffusivity from the temperature time series when measurement depths are known; (5) methods to track streambed elevation between two sensors, given knowledge of the thermal diffusivity from (4) above; (6) methods to directly calculate the potential error in velocity estimates based on the measurement error characteristics ; and (7) methods for validation of parameter estimates. We also provide discussion and theoretical insights developed from the solutions to better understand the physics and scaling of the propagation of the diurnal temperature variation through the streambed. In particular, we note that the equations developed do not replace existing equations applied to the analysis, rather they are new equations representing new aspects of the process, and, as a consequence, they increase the amount of information that can be derived from a particular set of thermal measurements.Citation: Luce, C. H., D. Tonina, F. Gariglio, and R. Applebee (2013), Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series, Water Resour. Res., 49,

[1] Stream water enters and exits the streambed sediment due to hyporheic fluxes, which stem primarily from the interaction between surface water hydraulics and streambed morphology. These fluxes sustain a rich ecotone, whose habitat quality depends on their direction and magnitude. The spatiotemporal variability of hyporheic fluxes is not well understood over several temporal scales and consequently, we studied their spatial and temporal variation over a pool-riffle-pool sequence at multiple locations from winter to summer. We instrumented a pool-riffle-pool sequence of Bear Valley Creek, an important salmonid spawning gravel-bed stream in central Idaho, with temperature monitoring probes recording at high temporal resolution (12 minute intervals). Using the thermal time series, weekly winter season seepage fluxes were calculated with a steady-state analytical solution and spring-summer fluxes with a new analytical solution that can also quantify the streambed thermal properties. Longitudinal pool-riffle-pool conceptualizations of downwelling and upwelling behavior were generally observed, except during the winter season when seepage fluxes tended toward downwelling conditions. Seepage fluxes near the edges of the channel were typically greater than fluxes near the center of the channel, and demonstrated greater seasonal variability. Results show that the interaction between streamflow and streambed topography has a primary control near the center of the channel, whereas the interaction between stream water and groundwater table has a primary control on seepage fluxes near the banks of the stream.

[1] We propose a new method based on temperature time series of surface and streambed pore waters to monitor local changes in streambed surface elevations at a nominally daily time scale. The proposed method uses the naturally occurring daily temperature signal changes in amplitude and phase between stream water and the water flowing within the streambed sediment. Application of the method in a fine-bedded stream predicts the timing and magnitude of a prescribed sequence of scour and deposition. This provides a new, effective, easy to use, and economic methodology to monitor the temporal evolution of erosion and depositional patterns in rivers.Citation: Tonina, D., C. Luce, and F. Gariglio (2014), Quantifying streambed deposition and scour from stream and hyporheic water temperature time series, Water Resour. Res., 50,[287][288][289][290][291][292]

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