由温度时序资料反演地下水流速的两种解析解及其比较

应用河床温度时序资料对地表水与地下水交换过程进行评价。首先假设半无限空间上部温度边界按正弦波动，由1D地下水渗流传热模型，得到采用温度衰减规律计算地下水流速的解析模型；典型的解析模型求解有Hatch解析解和Keery解析解， Hatch解考虑了热弥散效应所引入的误差，因此其计算精度优于Keery解。然后基于典型渗透性介质，通过算例讨论了解析模型的适用性和局限性。研究结果表明：只有研究区能简化为均质多孔介质、地下水的1D垂向运动占主导地位时，才能采用解析法确定地下水流速；采用常规的测点距离（1.0 m左右），振幅比法能有效评价流速在(-1.0～8.0)×10^-5 m/s的地下水活动，而相位滞后法能有效评价流速在(0.0～1.6)×10^-4 m/s的地下水活动；采用温度时序资料解析模型计算地下水流速时，2个测点间必须存在振幅衰减或相位滞后，因此需要预估研究区地下水流速以便设置合理的测点间距。实例研究表明,该解析方法能够有效地评价地表水与地下水交换的时域特征。

Analysis and Contrast of Two Analytic Solutions of Inversing Groundwater Velocity by Temperature Time-Series Records

Temperature time-series records were used to determine groundwater-surface water (GW-SW) exchange. If it is assumed that the temperature on the top boundary is oscillated in a sinusoidal pattern, the analytic model to calculate the seepage velocity by temperature damping can be obtained. Two typical analytic solutions are Hatch solution and Keery solution. The study shows that the Hatch solution is more accurate due to taking thermal diffusion into account. So it’s recommended that Hatch solution should be adopted to calculate seepage velocity. A typical permeable medium is taken as a case, and limitations and applicability of the model were discussed. It is shown that only when the study area can be simplified as a homogeneous medium and vertical seepage is dominant, the analytic model can be used. For the common interval of test points (around 1.0 m), it’s more effective to compute seepage velocity from -1.0×10^-5 m/s to 8.0×10^-5 m/s by using amplitude damping method and from 0.0 m/s to 1.6×10^-4 m/s by using phase lagging method, respectively. For the analytic model, the two test points must have amplitude damping and phase lagging. So the seepage velocity in the domain should be estimated firstly, and the reasonable interval of test points be designed then. It is shown from a case study that this method is available for evaluating the temporal variation of GW-SW exchange.