Paper in Press

WATER RESOURCES RESEARCH, doi:10.1029/2012WR012380

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

- A new equation is presented to analyze temperature time series from streambeds
- Explicit solutions calculate both water flux and thermal diffusivity directly
- Additional applications, error estimation, and validation are provided

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 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 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.

Received 15 May 2012; accepted 21 November 2012.

Citation:
(2012),
Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds
from temperature time series,
*Water Resour. Res.*,
doi:10.1029/2012WR012380, in press.