We confirm that energy dissipation weighting provides the most accurate approach to determining the effective hydraulic conductivity (Keff) of a binary K grid. Machine learning and deep learning algorithms of varying complexity (decision tree, vanilla CNN, UNET) can infer Keff with extremely high accuracy (R2 > 0.99), even given only the fraction of the grid occupied by the high K medium. Adding information derived from the energy dissipation distribution improved each algorithm. However, all methods failed to infer Keff accurately for outlier cases, all of which were inferred accurately using energy dissipation weighting directly. The UNET architecture could be trained to infer the energy dissipation weighting pattern from an image of the K distribution with high fidelity, although it was less accurate for cases with highly localized structures that controlled flow. Furthermore, the UNET architecture learned to infer the energy dissipation weighting even if it was not trained on this information. However, the weights were represented within the UNET in a way that was not immediately interpretable by a human user. This reiterates the idea that even if ML/DL algorithms are trained to make some hydrologic predictions accurately, they must be designed and trained to provide each user-required output if their results are to be used to improve our understanding of hydrologic systems most effectively.

Electromagnetic induction (EMI) is used widely for environmental studies. The apparent electrical conductivity (ECa), which can be mapped efficiently with EMI, correlates with a variety of important soil attributes. EMI instruments exist with several configurations of coil spacing, position, and height. There are general, rule-of-thumb guides to choose an optimal instrument configuration for a specific survey. The goal of this study was to use machine learning to improve this design optimization task. In this investigation, we used machine learning as an efficient tool for interpolating among the results of many forward model runs. Specifically, we generated an ensemble of 100,000 EMI forward models representing the responses of many EMI configurations to a range of three-layer subsurface models. We split the results into training and testing subsets and trained a decision tree (DT) with gradient boosting (GB) to predict the subsurface properties (layer thicknesses and EC values). We further examined the value of prior knowledge that could limit the ranges of some of the soil model parameters. We made use of the intrinsic feature importance measures of machine learning algorithms to identify optimal EMI designs for specific targets. The optimal designs identified using this approach agreed with those that are generally recognized as optimal by informed experts for standard targets, giving confidence in the ML-based approach. The approach also offered insight that would be difficult if not impossible to offer based on rule-of-thumb optimization. We contend that such ML-informed design approaches could be applied broadly to other survey design challenges.

We demonstrate the application of two simple machine learning tools - regression tree and gradient boosting analyses - to a hydrologic inference problem to address two objectives. The first goal was to infer the flux between a river and the subsurface based on high temporal resolution (5-minute) observations of subsurface pressure and temperature. The second goal was to identify an optimal set of observations to support these inferences. Specifically, we examine how many and what type of observations (pressure and/or temperature) were necessary and at what depths. Using synthetic observations and surface fluxes provided by a fully resolved three-dimensional flow and heat transport model, we found that both machine learning tools could identify the flux well using pressure and temperature measurements collected at three depths, even when considerable noise was added to the synthetic observations. Neither method could provide reasonable flux estimates given only noisy temperature data. A shallow, collocated temperature and pressure observations performed as well as the complete data set. The results show the promise of using machine learning tools to design hydrologic measurement networks - both for determining whether a proposed data set can constrain inversion and for optimizing monitoring networks comprised of multiple measurement types.

Catchment-scale response functions, such as transit time distribution (TTD) and evapotranspiration time distribution (ETTD), are considered fundamental descriptors of a catchment’s hydrologic and ecohydrologic responses to spatially and temporally varying precipitation inputs. Yet, estimating these functions is challenging, especially in headwater catchments where data collection is complicated by rugged terrain, or in semi-arid or sub-humid areas where precipitation is infrequent. Hence, we developed practical approaches for estimating both TTD and ETTD from commonly available tracer flux data in hydrologic inflows and outflows without requiring continuous observations. Using the weighted wavelet spectral analysis method of Kirchner and Neal [2013] for δ18O in precipitation and stream water, we specifically calculated TTDs that contribute to streamflow via spatially and temporally variable flow paths in a sub-humid mountain headwater catchment in Arizona, USA. Our results indicate that composite TTDs most accurately represented this system for periods up to approximately one month and that a Gamma TTD was most appropriate thereafter. The TTD results also suggested that some contribution of subsurface water was beyond the applicable tracer range. For ETTD and using δ18O as a tracer in precipitation and xylem waters, a Gamma ETTD type best matched the observations, and stable water isotopes were capable tracers for the majority of vegetation source waters. This study contributes to a better understanding of a fundamental question in mountain catchment hydrology; namely, how tracer input fluxes are modulated by spatially and temporally varying subsurface flow paths that support evapotranspiration and streamflow at multiple time scales.