Calibration of hydra impedance probes using electric circuit theory

Impedance probes are an attractive electromagnetic technique to measure water content and bulk electrical conductivity (EC) in the same volume of soil. In this study, we developed an electric circuit model for Hydra probes that explains how the output voltages can be related to the soil real and imaginary permittivity. Internal probe transmission line sections were modeled using either a distributed approach or a lumped approach. The distributed approach resulted in seven circuit model parameters, while the lumped approach resulted in six parameters. Optimization of all the parameters using probe readings in air, ethanol, methanol, deionized water, and saline water solutions did not result in physically realistic parameter values. In contrast, fixing four parameters (distributed approach) and two parameters (lumped approach), while optimizing others, did yield realistic parameter values. Both the parameter optimization method and the default probe algorithm performed well during model verification. The parameter optimization method resulted in improved real permittivity measurements when nonsaline fluids at different temperatures were used in the optimization process.