Calibration of time domain reflectometry for measurement of liquid water in frozen soils

The amount of liquid water (θL) present in soils at sub-freezing temperatures affects soil infiltrability, soil solution migration, and soil-atmosphere energy exchange. For these reasons, a number of frozen soil simulation models calculate θL. Time domain reflectometry (TDR) is the most practical technique available for field measurement of θL. In the course of monitoring θL, we have observed that TDR-measured θL often conflicted with modeled values. Specifically, models generally assume that θL is essentially independent of the total (ice plus liquid) soil water content (θW) at a constant temperature, whereas we have observed increases in θL with θW. This conflict may be the result of the TDR calibration equations used for frozen soils, which implicitly assume that the dielectric constant of ice (3.2) equals that of air (1) and ignore the effects of temperature on the liquid water dielectric constant. Less empirical, dielectric mixing-model calibration equations, which incorporate the individual dielectric contributions of soil constituents, have successfully described other inclusion responses and, therefore, may account for these effects. We applied six calibration equations to three soils under frozen and unfrozen conditions to determine if θL, as calculated with the alternative equations, was consistent with modeling approaches (i.e., if ice and temperature effects were accounted for). Two mixing-model and two empirical equations described water contents of the unfrozen soil well. The empirical equation results exhibited the expected changes in θL with θW for all three soils. The mixing-model equations calculated no change in θL with θW for the sand, indicating that ice effects were well accounted for. However, calculated θL changed with θW in the other soils. Thus, we found that, in general, the mixing-model equations did not incorporate ice and/or temperature effects in a manner consistent with modeling approaches. At this point, it is not clear whether the TDR-measured θL changes are real or the result of dielectric effects that are not accounted for in the calibration equations. We provide evidence that the measured trends are realistic and the model assumptions should be questioned. Resolution of this question requires use of rather specialized instrumentation, which can provide an independent check of θL measurements under unsaturated conditions.