Assimilation of temperature and hydraulic gradients for quantifying the spatial variability of streambed hydraulics

Abstract

Understanding the spatial and temporal characteristics of water flux into or out of shallow aquifers is imperative for water resources management and eco-environmental conservation. In this study, the spatial variability in the vertical specific fluxes and hydraulic conductivities in a streambed were evaluated by integrating distributed temperature sensing (DTS) data and vertical hydraulic gradients into an ensemble Kalman filter (EnKF) and smoother (EnKS) and an empirical thermal-mixing model. The formulation of the EnKF/EnKS assimilation scheme is based on a discretized 1D advection-conduction equation of heat transfer in the streambed. We first systematically tested a synthetic case and performed quantitative and statistical analyses to evaluate the performance of the assimilation schemes. Then a real-world case was evaluated to calculate assimilated specific flux. An initial estimate of the spatial distributions of the vertical hydraulic gradients was obtained from an empirical thermal-mixing model under steady-state conditions using a constant vertical hydraulic conductivity. Then, this initial estimate was updated by repeatedly dividing the assimilated specific flux by estimates of the vertical hydraulic gradients to obtain a refined spatial distribution of vertical hydraulic gradients and vertical hydraulic conductivities.Our results indicate that optimal parameters can be derived with fewer iterations but greater simulation effort using the EnKS compared with the EnKF. For the field application in a stream segment of the Heihe River Basin in northwest China, the average vertical hydraulic conductivities in the streambed varied over three orders of magnitude (5 3 10 21 to 5 3 10 2 m/d). The specific fluxes ranged from near zero (q z < 60.05 m/d) to 61.0 m/d, while the vertical hydraulic gradients were within the range of 20.2 to 0.15 m/m. The highest and most variable fluxes occurred adjacent to a debris-dam and bridge pier. This phenomenon is very likely the result of heterogeneous streambed hydraulic characteristics in these areas. Our results have significant implications for hyporheic micro-habitats, fish spawning and other wildlife incubation, regional flow and hyporheic solute transport models in the Heihe River Basin, as well as in other similar hydrologic settings. (2016), Assimilation of temperature and hydraulic gradients for quantifying the spatial variability of streambed hydraulics, Water Resour. PUBLICATIONS measurements and differential stream gauging in series of synoptic surveys [Becker et al., 2004] can provide estimations over relatively large reaches. The most commonly used methods, seepage meters and piezometers can measure and/or estimate the seepage flux directly. Admittedly, these instruments only provide point-in-space measurements, but they can also provide localized estimates through averaging a relatively small representative area of a streambed.

Impacts of a beaver dam analogue complex on streambed vertical hydraulic gradients in a 1.2‐km stream reach in Wyoming, USA

“…VHG is a measure of water flux into or out of the stream via the stream bed. VHGs can be indicative of hyporheic exchange, as well as loss of stream water to groundwater or gain of groundwater into streams (Huang et al, 2016). Hyporheic exchange is characterized by bidirectional interaction between streamwater and shallow subsurface water (Bencala, 2005; Tonina & Buffington, 2009), which has been essential in downstream transport and in‐stream processes, solute transfer, nutrient dynamics, and biogeochemical cycling, and water temperature regulation (Bencala, 2005; Covino, 2017; Hester & Gooseff, 2010; Zarnetske et al, 2011).…”

Numerical Study of Coupled Water and Vapor Flow, Heat Transfer, and Solute Transport in Variably‐Saturated Deformable Soil During Freeze‐Thaw Cycles

“…TH models can simulate multiphase, non‐isothermal mass and energy transport in variably‐saturated, non‐deformable soils. Examples of these types of models include SHAW (e.g., Cui et al., 2020; Xie et al., 2021), Hydrus (Šimůnek et al., 2018), Sutra‐ice (Evans et al., 2018; Kurylyk et al., 2014; McKenzie et al., 2007) and PFLOTRAN‐ice (Karra et al., 2014), Smoker (Molson & Frind, 2015), among others (e.g., Grenier et al., 2018; Huang et al., 2016; Kelleners, 2020). This group does not consider mechanical deformation during the freeze‐thaw period or solute transport processes.…”

Identifying stream-aquifer exchange by temperature gradient in a Guarani Aquifer system outcrop zone

“…This method relies on differences in water temperature between surface and subsurface. These technique that have been applied in different regions worldwide (Lowry et al, 2007;Matheswaran et al, 2013;Vandenbohede et al, 2014;Yao et al, 2015;Huang et al, 2016). Additionally, it is possible to quantify the groundwater discharge in the stream by measuring the streambed temperature in multiple depths (Hatch et al, 2006;Schmidt et al, 2006;Schmidt et al, 2007;Swanson & Cardenas, 2011;McCallum et al, 2012;Luce et al, 2013).…”