A piecewise analysis model for electrical conductivity calculation from time domain reflectometry waveforms

Authors: WANG, Z - University Of Maryland; Timlin, Dennis; KOJIMA, Y - Gifu University; LUO, C - Beijing University Of Chinese Medicine; CHEN, Y - China Agricultural University; LI, S - Oak Ridge Institute For Science And Education (ORISE); Fleisher, David; TULLY, K - University Of Maryland; Reddy, Vangimalla; HORTON, R - Iowa State University

Submitted to: Computers and Electronics in Agriculture
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 1/20/2021
Publication Date: 2/12/2021
Citation: Wang, Z., Timlin, D.J., Kojima, Y., Luo, C., Chen, Y., Li, S., Fleisher, D.H., Tully, K., Reddy, V., Horton, R. 2021. A piecewise analysis model for electrical conductivity calculation from time domain reflectometry waveforms. Computers and Electronics in Agriculture. 182:106012. https://doi.org/10.1016/j.compag.2021.106012.
DOI: https://doi.org/10.1016/j.compag.2021.106012

Interpretive Summary: Knowledge of soil chemical properties is important for agricultural production. An understanding of solute movement within soils can provide information for soil salinity estimates, fertilizer application and contaminant tracing. We developed a method to measure the total concentration of dissolved chemical components (soil electrical conductivity- EC) in a soil. These components include soluble salts such as calcium and sodium as well as fertilizer related salts such as nitrate. Time domain reflectometry (TDR) is a commercial method used to measure water content in soil and can also provide an efficient way for the determination of soil EC. In this study, we developed a model for TDR data interpretation and EC calculation. A numerical implementation of the proposed model was tested, and the results showed the proposed model can provide accurate and stable evaluation of EC. This method can provide a measure of soil EC using an instrument already available to measure soil water content. This research is of interest to extension agents, crop consultants, growers and other scientists/engineers developing soil testing methods.

Technical Abstract: Electrical conductivity (EC) is a measure of solution ionic concentration, and it is related to a variety of soil physical and chemical properties. Time domain reflectometry (TDR) provides a simple way to measure bulk soil EC. Although a tangent line/bounded mean oscillation (TL-BMO) model is available to estimate soil water content from TDR waveforms, an associated analysis for EC is not yet developed. The objectives of this study are to (1) introduce a concept of piecewise analysis for TDR waveform analysis, and (2) to develop a model for EC computation along the TDR waveguides under homogeneous water content conditions, where EC values can be either uniform or contain (spatial) variations. The proposed model sequentially fits TDR waveforms for coaxial cables, connections, and waveguides based on the transmission line equation (telegraph equation). TDR waveguides can be discretized into multiple successive pieces for the determination of EC variations along the waveguides. Simplifications of the fitting procedures via (1) existing direct models, e.g., TL-BMO and Topp et al. (1988) equations, and (2) analysis of waveforms obtained from controlled conditions, e.g., in pure water, are also applied. The proposed model is implemented with a MATLAB-based computer program that can be executed in desktops or laptops. Consistency and stability of the proposed model are tested via observed TDR waveforms that are measured under uniform EC conditions but perturbed with a range of artificial noise levels. EC values computed with only one discretized piece (i.e., no discretization along the waveguides) 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, an increasing amount of numerical oscillations in the results are observed. However, the maximum relative errors are <20% in general, occurring when noise powers are as large as waveform powers (0 dB noise). Flexibility of the proposed model is tested using waveforms simulated under varying EC. The EC variations along the TDR waveguides are reported by the piecewise analysis results. In summary, the proposed model produces a reliable EC estimation method, and it can be embedded into the TL-BMO model for integrated water content and EC determination.