Electrical conductivity (EC) represents a material’s ability to conduct electric current. Soil EC has been used as a soil quality attribute related to soil pH, nutrient availability, crop suitability and soil microbial activity. Time domain reflectometry (TDR) estimates soil water content and EC based on the propagation/reflection and energy attenuation of voltage signals along a waveguide. To maximize the data use efficiency, waveform interpretations for simultaneous water content and EC determination are needed. A tangent line/bounded mean oscillation (TL-BMO) model is available to estimate soil water content from TDR waveforms, but an associated EC model is not yet available. The objectives of this study are (1) to introduce a piecewise analysis method for TDR waveform interpretation, and (2) to develop a model for EC computation along a TDR waveguide under homogeneous water content. The proposed model sequentially fits a TDR waveform for the coaxial cable, the connection, and the waveguide according to the transmission line equation. A TDR waveguide can be discretized into multiple successive pieces for the determination of EC variations along the waveguide. Simplifications of the fitting procedures via (1) existing models, e.g., TL-BMO and Topp et al. (1988) models, and (2) analysis of waveforms obtained from controlled conditions, e.g., in distilled water under room temperature (~20 °C) and air pressure (~101 kPa), are also applied. Accuracy and stability of the proposed model are tested via observed TDR waveforms obtained under uniform EC conditions but perturbated with a range of noise levels. EC values computed with only one discretized piece (i.e., no discretization along the waveguide) are consistent with the theoretical EC values, and the results are robust for all of the tested noise levels. As the number of discretized pieces and the noise levels increase, numerical oscillations in the results increase. The maximum relative errors are <20%, occurring when the mean power of noise is as large as the mean power of waveforms (0 dB noise). Flexibility of the proposed model is tested using waveforms simulated under spatially varying EC, and the EC variations along a TDR waveguide can be detected by the proposed model. In summary, the proposed model provides reliable EC estimations, and it can evaluate uniform or varying EC distributions along a TDR waveguide under uniform moisture conditions. This model can be imbedded into the TL-BMO model for integrated water content and EC determination for commonly measured (251-scanning point) TDR waveforms.

电导率（EC）表示材料的导电能力。土壤EC已被用作与土壤pH值，养分利用率，作物适应性和土壤微生物活性有关的土壤质量属性。时域反射仪（TDR）基于电压信号沿波导的传播/反射和能量衰减来估算土壤含水量和EC。为了最大程度地提高数据使用效率，需要同时解释水含量和EC的波形解释。可以使用切线/有界平均振荡（TL-BMO）模型来从TDR波形估计土壤含水量，但是尚无相关的EC模型。这项研究的目的是（1）引入用于TDR波形解释的分段分析方法，（2）建立均匀水含量下沿TDR波导进行EC计算的模型。所提出的模型根据传输线方程依次拟合同轴电缆，连接和波导的TDR波形。可以将TDR波导离散化为多个连续的部分，以确定沿着波导的EC变化。通过（1）现有模型（例如TL-BMO和Topp等人）简化拟合过程。（1988）模型，以及（2）在受控条件下获得的波形分析，例如在室温（〜20°C）和气压（〜101 kPa）下的蒸馏水中。通过在均匀EC条件下获得的但受到一系列噪声级干扰的TDR波形来测试所提出模型的准确性和稳定性。仅用一个离散块计算出的EC值（即，沿波导不离散）与理论EC值一致，并且对于所有测试的噪声水平，结果都是可靠的。随着离散件的数量和噪声水平的增加，结果中的数值振荡也会增加。当噪声的平均功率与波形的平均功率（0 dB噪声）一样大时，最大相对误差小于20％。使用在空间变化的EC下模拟的波形测试了所提出模型的灵活性，并且所提出的模型可以检测到沿着TDR波导的EC变化。总而言之，所提出的模型提供了可靠的EC估计，并且它可以在均匀湿度条件下评估沿着TDR波导均匀或变化的EC分布。