Abstract Diurnal heat signal has been widely used to infer the seepage flux and thermal diffusivity in streambeds. The theoretical basis is the one-dimensional (1-D) analytical solution of heat advection-dispersion equation with sinusoidal boundary condition and homogeneous initial condition (Stallman, 1965). However, the assumption of homogeneous initial condition made in Stallman (1965) is physically unrealistic and the assumption of steady flow is often violated when water level changes rapidly (e.g., flooding). To incorporate the realistic initial condition, an innovative solution for 1-D heat transport with sinusoidal boundary condition and arbitrary initial condition is proposed. This solution makes it possible to accurately simulate heat transport with transient flux by sequentially applying the new solution at small time interval. Synthetic temperature signals at different depth of streambeds are generated to study the impact of transient flux to the estimation of water flux and thermal diffusivity. Here are some major findings. Firstly, the calculated flux is sensitive to the flux dynamics. The faster the flux increases or decreases, the less accurate the calculated flux is. Secondly, using temperature time series from deep sensor pair is more likely to cause erroneous estimation of flux because heat signal damps fast with depth. Thirdly, the heat tracer method for estimating water flux is sensitive to the thermal properties of saturated sediments. Large thermal diffusivity leads to high uncertainty for flux estimation.

中文翻译：

---

具有任意初始条件的河床昼夜热传递的创新解决方案及其对瞬态条件下水通量和热扩散率估计的影响

摘要 昼夜热信号已被广泛用于推断河床的渗流通量和热扩散率。理论基础是具有正弦边界条件和齐次初始条件的热对流-色散方程的一维（1-D）解析解（Stallman，1965）。然而，Stallman (1965) 提出的均匀初始条件的假设在物理上是不现实的，当水位快速变化（例如，洪水）时，稳定流的假设经常被违反。为了结合现实的初始条件，提出了具有正弦边界条件和任意初始条件的一维热传输的创新解决方案。该解决方案可以通过以小时间间隔顺序应用新解决方案来准确模拟瞬态通量的热传递。生成不同深度河床的合成温度信号，研究瞬态通量对水通量和热扩散率估计的影响。以下是一些主要发现。首先，计算的通量对通量动力学很敏感。通量增加或减少的速度越快，计算的通量就越不准确。其次，使用来自深度传感器对的温度时间序列更有可能导致错误的通量估计，因为热信号随深度衰减很快。第三，估算水通量的伴热法对饱和沉积物的热特性很敏感。大的热扩散率导致通量估计的高度不确定性。