Can Simple Machine Learning Tools Extend and Improve Temperature-Based Methods to Infer Streambed Flux?

Abstract

Temperature-based methods have been developed to infer 1D vertical exchange flux between a stream and the subsurface. Current analyses rely on fitting physically based analytical and numerical models to temperature time series measured at multiple depths to infer daily average flux. These methods have seen wide use in hydrologic science despite strong simplifying assumptions including a lack of consideration of model structural error or the impacts of multidimensional flow or the impacts of transient streambed hydraulic properties. We performed a “perfect-model experiment” investigation to examine whether regression trees, with and without gradient boosting, can extract sufficient information from model-generated subsurface temperature time series, with and without added measurement error, to infer the corresponding exchange flux time series at the streambed surface. Using model-generated, synthetic data allowed us to assess the basic limitations to the use of machine learning; further examination of real data is only warranted if the method can be shown to perform well under these ideal conditions. We also examined whether the inherent feature importance analyses of tree-based machine learning methods can be used to optimize monitoring networks for exchange flux inference.

Machine Learning for Bayesian Experimental Design in the Subsurface

“…When working with data that must be collected through an experimental process, as is often the case in geoscience, one of the most important considerations is where to gather new observations: designing a monitoring network necessitates careful consideration of many factors, especially when measurements are costly or resources are limited (cf. Chapter 4; Moghaddam et al 2022). Controlling the experimental conditions for data acquisition is essential to maximize resource utilization and information gain because this process is typically expensive and/or time-consuming (Attia et al, 2018;Vilhelmsen and Ferré, 2018).…”

“…Chapter 5: Groundwater-surface water interaction. The groundwater-surface water (GW-SW) exchange fluxes are driven by a complex interplay of subsurface processes and their interactions with surface hydrology (Hermans et al, 2022), which have a significant impact on the water and contaminant exchanges (e.g., Dujardin et al, 2014;Ghysels et al, 2021;Hermans et al, 2022;Irvine et al, 2016;Kikuchi and Ferré, 2017;Kurylyk et al, 2019;Moghaddam et al, 2022). Due to the complexity of these systems, the accurate estimation of GW-SW fluxes is important for quantitative hydrological studies and should be based on relevant data and careful experimental design.…”

“…Methods for quantifying groundwater-surface water (GW-SW) exchange flux have long been of interest in order to better understand water and solute exchange across the sediment-water interface as well as the magnitude, spatial distribution, and temporal dynamics of fluxes between subsurface and surface compartments of the Earth (Hermans et al., 2022). Therefore, understanding and quantifying the exchange processes between rivers and groundwater is crucial for the best possible protection of our water resources: the provision of drinking water, the characterization and management of environmental flow regimes, the preservation or restoration of riverine ecosystem health and functions, the attenuation of contaminants and water storage in aquifers are some of the challenges that are impacted by processes that occur at the GW-SW interface (Dujardin et al, 2014;Ghysels et al, 2021;Hermans et al, 2022;Irvine et al, 2016;Kikuchi and Ferré, 2017;Kurylyk et al, 2019;Moghaddam et al, 2022).…”

“…Additionally, measuring temperature with conventional sensors such as thermistors or fiber-optic cables (Hare et al, 2015;Mamer and Lowry, 2013) is relatively simple and accurate (Irvine et al, 2016). As a result of their practical benefits and ability to provide flux estimates with varying resolutions, these thermal techniques have grown in popularity among alternative techniques (Anderson, 2005;Moghaddam et al, 2022).…”

“…During the last two decades, several methods have been developed to estimate water fluxes from temperature data, as reviewed by Anderson (2005); Constantz (2008); Irvine et al (2017); Rau et al (2014). Recent advances in machine learning (ML) in the field of hydrology (e.g., Nearing et al 2021) have enabled novel approaches to estimate fluxes from temperature data, as reviewed by Moghaddam et al (2022), who also applied and compared various state-of-the-art ML algorithms for this purpose. Additionally, Moghaddam et al (2022) examined approaches to extract information from ML methods that can be used to design efficient and effective monitoring networks.…”