A new thermo-time domain reflectometry approach to quantify soil ice content at temperatures near the freezing point

Soil ice content (theta(i)) is an important property for many studies associated with cold regions. In situ quantification of theta(i) with thermo-time domain reflectometry (TDR) at temperatures near the freezing point has been difficult. The objective of this study is to propose and test a new thermo-TDR approach to determine theta(i). First, the liquid water content (theta(l)) of a partially frozen soil is determined from a TDR waveform. Next, a pulse of heat is applied through the thermo-TDR sensor to melt the ice in the partially frozen soil. Then, a second TDR waveform is obtained after melting to determine the theta(l), which is equivalent to the total water content (theta(t)) of the partially frozen soil. Finally, theta(i) is calculated as the difference between theta(t) and theta(l). The performance of the new approach was evaluated in sand and loam soils at a variety of theta(t) values. The new approach estimated theta(t), theta(l), and theta(i) accurately. The root mean square errors (RMSE) of estimation were 0.013, 0.020, and 0.023 m(3) m(-3) for sand, and 0.041, 0.026, and 0.031 m(3) m(-3) for loam. These RMSE values are smaller than those reported in earlier thermo-TDR studies. Repeating the thermo-TDR measurements at the same location on the same soil sample caused decreased accuracy of estimated values, because of radial water transfer away from the heater tube of the thermo-TDR sensor. Further research is needed to determine if it is possible to obtain accurate repeated measurements. The use of a dielectric mixing model to convert the soil apparent dielectric constant to theta(l) improved the accuracy of this approach. In our investigation, application of a small heat intensity until the partially frozen soil temperature became larger than about 1 degrees C was favorable. The new method was shown to be suitable for estimating ice contents in soil at temperatures between 0 degrees C and -2 degrees C, and it could be combined with the volumetric heat capacity or thermal conductivity thermo-TDR based methods, which measured ice content at colder temperatures. Thus, the thermo-TDR technique could measure theta(i) at all temperatures.

土壤含冰量（θ(i)）是许多寒区相关研究的一个重要特性。在接近冰点的温度下，利用热 - 时域反射仪（TDR）对θ(i)进行原位量化一直很困难。本研究的目的是提出并测试一种新的热 - TDR方法来测定θ(i)。首先，根据TDR波形确定部分冻结土壤的液态水含量（θ(l)）。接着，通过热 - TDR传感器施加一个热脉冲，使部分冻结土壤中的冰融化。然后，在融化后获取第二个TDR波形以确定θ(l)，它等同于部分冻结土壤的总含水量（θ(t)）。最后，θ(i)通过θ(t)和θ(l)的差值计算得出。在不同θ(t)值的砂土和壤土中对新方法的性能进行了评估。新方法能准确估算θ(t)、θ(l)和θ(i)。对于砂土，估算的均方根误差（RMSE）分别为0.013、0.020和0.023立方米/立方米，对于壤土则分别为0.041、0.026和0.031立方米/立方米。这些RMSE值小于早期热 - TDR研究中所报道的值。在同一土壤样本的同一位置重复进行热 - TDR测量会导致估算值的准确性下降，这是因为水从热 - TDR传感器的加热管径向转移。需要进一步研究以确定是否有可能获得准确的重复测量值。利用介电混合模型将土壤表观介电常数转换为θ(l)提高了该方法的准确性。在我们的研究中，施加较小的热强度直至部分冻结土壤温度高于约1℃是有利的。新方法被证明适用于估算0℃到 -2℃之间土壤的含冰量，并且它可与基于热 - TDR的体积热容量或热导率方法相结合，这些方法可测量更低温度下的含冰量。因此，热 - TDR技术可在所有温度下测量θ(i)。