## 1. Introduction

[2] As freshwater supplies become scarcer in many parts of the world and the need to quantify overall water availability grows more important, it has become increasingly clear that surface water and groundwater indeed represent one connected, finite, and dynamic source of water [*Winter et al.*, 1998]. Therefore, it is important to understand where, and how much, water is moving between the aquifer and the surface water expressions above it. Several methods have been explored for this purpose, including seepage meters, differential-discharge measurements, shallow piezometers, tracer experiments, and temperature-tracer measurements. Several recent papers have compared the use of streambed temperatures with other methods to determine seepage [*Anderson*, 2005; *Kalbus et al.*, 2006; *Constantz*, 2008; *Rosenberry and LaBaugh*, 2008] and found this method to produce acceptable results for a wide variety of conditions. Moreover, temperature measurements have the advantages of being comparatively cost-effective to collect with readily available data loggers, even over relatively long periods of time and with fine temporal resolution.

[3] Several methods of solving the coupled water and heat advection-dispersion equation have been employed to calculate streambed seepage using temperature measurements [*Constantz*, 2008; *Anderson*, 2005]. *Stallman* [1965] proposed a one-dimensional (1-D) solution in which the change in the amplitude of the diel temperature signal, with depth and lag in the response time to temperature variation at the surface, is used to directly calculate seepage flux when all other parameters are known. This analytical solution assumes 1-D, uniform vertical flow, sinusoidal behavior of diel surface temperature, and no change in average temperature with depth. Several studies have used Stallman's approach to calculate seepage rates from thermal time series data [see, e.g., *Goto et al.*, 2005; *Hatch et al.*, 2006; *Keery et al.*, 2007; *Fanelli and Lautz*, 2008; *Lautz*, 2010]. *Hatch et al.* [2006] developed a useful, semiautomated set of Matlab routines to filter field data, derive amplitude and phase-shift information, and use these values to iteratively solve for time-varying seepage rates. *Lautz* [2010] evaluated the impact of nonideal field conditions on flux estimates from this analytical model. *Vogt et al.* [2010] used fine-resolution vertical temperature measurements to determine differences in velocity along a vertical profile. However, there has been little investigation as to the influence of uncertainty in input parameters on the accuracy of predicted seepage velocities and the range of applicability of this method.

[4] Monte Carlo simulation is a useful technique for testing uncertainty in seepage estimates from temperature measurements [*Keery et al.*, 2005; *Niswonger and Rupp*, 2000; *Constanz et al.*, 2002]. In this paper, we use a Monte Carlo analysis to explore the effects of sensor accuracy and uncertainty in the input parameters' thermal diffusivity (*Ke*) and sensor spacing on the predicted velocity estimates over a wide range of both gaining and losing streambed conditions. We explore the effects of uncertainty on velocity estimates for each parameter separately, as well as the cumulative effects of uncertainty in several parameters concurrently.