Uncertainty in Estimation of Field-scale Variability of Soil Saturated Hydraulic Conductivity

Saturated hydraulic conductivity (Ks) is among the most important soil properties that influence the partitioning of rainfall into surface and subsurface waters and is needed for understanding and modeling hydrologic processes at the field-scale. Field-scale variability of Ks is often represented as a lognormal random field, and its parameters are assessed either by making local- or point-scale measurements using instruments such as permeameters and infiltrometers or by calibrating probabilistic models with field-scale infiltration experiments under natural/artificial rainfall conditions. This research quantifies the uncertainty in the Ks random field when using observations from the above techniques and provides recommendations as to what constitutes a good experiment to assess the field-scale variability of Ks. Infiltration experiments with instruments sampling larger areas (or volumes) are typically expected to be more representative of field conditions than those sampling smaller ones; hence, the uncertainty arising from the field-scale natural rainfall-runoff experiments was evaluated first. A field-averaged infiltration model and Monte Carlo simulations were employed in a Bayesian framework to obtain the possible Ks random fields that would describe experimental observations over a field for a rainfall event. Results suggested the existence of numerous parameter combinations that could satisfy the experimental observations over a single rainfall event, and high variability of these combinations among different events, thereby providing insights regarding the identifiable space of Ks distributions from individual rainfall experiments. The non-unique parameter combinations from multiple rainfall events were subsequently consolidated using an information-theoretic measure, which provided a realistic estimate of our ability to quantify the spatial variability of Ks in natural fields using rainfall-runoff experiments. With the resolving ability from rainfall-runoff experiments constrained due to experimental limitations, the Ks estimates from in-situ point infiltration devices could provide additional information in conjunction with the rainfall-runoff experiments. With this hypothesis, the role of three in-situ point infiltration devices --- the double-ring infiltrometer, CSIRO version of tension permeameter, and Guelph constant-head permeameter --- was then evaluated in characterizing the field-scale variability of Ks. Results suggested that Ks estimates from none of the instruments could individually represent the field conditions due to the presence of measurement and structural errors besides any sampling biases; hence any naive efforts at assimilating their data (e.g., data pooling, instrument-specific transforms, etc.) and augmenting with field-scale rainfall-runoff observations as informative prior distributions would not be fruitful. In the absence of benchmarks establishing the true Ks field, it is also impossible to quantify these errors; therefore, a posterior coarsening method was used to alleviate their impact when estimating the field-scale variability of Ks. Finally, the impact of censored moments on the maximum likelihood (ML) estimates of the Ks distribution parameters was studied. Results highlighted the rainfall event's ability to only be able to resolve a fraction of the Ks field, and that the time and duration of peak rainfall intensity play a role in resolving the Ks field, besides the peak rainfall intensity. The reliability of the ML estimates is a function of the fraction of the Ks field resolved by the rainfall event, until a limit when the estimates start to overfit the calibration data. Rainfall-runoff experiments for which the ML estimates resolve 30--80 % of the Ks distribution are likely to be good calibration events.

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