Réactivités hydrologique et thermique de l’interface nappe-rivière pour des cours d’eau amont

Introduction

Understanding of the stream-aquifer interface functioning is of prime importance for the assessment of the stream ecological state and the associated biogeochemical processes (Stanford and Ward, 1988; Findlay, 1995; Brunke and Gonser, 1997; Marmonier et al., 2012; Flipo et al., 2014; Harvey and Gooseff, 2015). Its impact on biogeochemical processes is nowadays acknowledged and varies from upstream to downstream along a river network (Sauvage et al., 2018), with also a significant impact on large river metabolism (Vilmin et al., 2016). In river sediments, this significant impact corresponds to a large oxygen consumption (Flipo et al., 2007; Vieweg et al., 2016; De Falco et al., 2018) and nitrogen consumption (Mauclaire, et al., 2002; Caruso et al., 2017) by biofilm or bacterial colonies growth (Thullner, Zeyer, et al., 2002; Schmidt et al., 2018). The impact of such processes on in-stream water quality depends on hydrological conditions, especially for green house gas emissions (Newcomer et al., 2018). Understanding the vertical temperature distribution in the riverbed is Chapitre 3 : Sensibilité du fonctionnement hydrothermique de l’interface nappe-rivière 116 therefore of interest since the metabolism is very sensitive to the temperature (Wang et al., 2018), as well as denitrification rates (Bouletreau et al., 2012, 2014). Although the dynamics of water fluxes between streams and aquifers is better understood at the river network scale, including the effect of hydrological events on flow reversal (Saleh et al., 2011; Flipo et al., 2014; Pryet et al., 2015; Baratelli et al., 2016) as well as the bioclogging of the HZ (Newcomer et al., 2016), the relationship between hydrological conditions and temperature seasonality and heat fluxes is not fully conceptualized yet over a full range of hyporheic zone types, summarized by its hydrodynamic and thermal properties. Many in situ studies (Evans et al., 1995; Hannah et al., 2004; Anibas et al., 2011; Snyder et al., 2015; Bastola and Peterson, 2016) were carried on but are always site specific and do not propose a complete assessment of temperature profiles and energy fluxes responses to climatic and hydrological drivers. The thermal regimes of river reaches depend on drivers, such as the climatic conditions, the vegetation shading effect as well as hyporheic exchanges (Caissie, 2006). Hyporheic thermal exchanges depend on the hydrogeological context, the porous medium properties, and the temperature gradient between the aquifer and the stream. Usually stream-aquifer energy fluxes contribute to local cooling of streams in summer and warming in winter but are not predominant in the energy balance at the reach scale, the main driver being the heat exchanges at the air-water interface (Sinokrot and Stefan, 1993, 1994; Stefan and Preud’homme, 1993; Evans et al., 1998; Webb and Zhang, 1999; Bogan et al., 2003; Hannah et al., 2004, 2008; Hester et al., 2009; Hebert et al., 2011). However those general patterns may be different for small headwater streams were vegetation shadowing may hinder the predominance of the processes occurring at the water-air interface (Caissie, 2006; Webb et al., 2008). In such conditions the heat exchanges can reach around 20 % of the total energy budget (Moore et al., 2005; Cozzetto et al., 2006). Even though (Sinokrot and Stefan, 1993; Webb and Zhang, 1997, 1999) demonstrate the relative importance of the conductive heat flux through the riverbed for shallow streams, the conductive streambed heat flux has been first the only one considered and has then been neglected in some studies which assume implicitly the predominance of the advective heat flux, especially to interpret FO-DTS measurements (Selker et al., 2006; Westhoff et al., 2007; Briggs et al., 2012) or in large scale modeling of energy transfer in a whole river network (Beaufort et al., 2016). Heat fluxes at the stream-aquifer interface usually amount 10 to 100 W.m-2 . The share of those fluxes between conductive and advective flux is not straightforward (Hebert et al., 2011; Hester and Doyle, 2011; Caissie et al., 2014; Maheu et al., 2014) and depends on the many parameters that control river temperatures (Dugdale et al., 2017). For instance, based on high frequency combined measurements of vertical temperature and pressure difference in the stream bed of a small river, it was recently shown how a hydrological event due to a flood reverses the direction of the heat flux and switches the thermal regime of the hyporheic zone from conductive to advective (Cucchi et al., 2018). In this study, a synthetic case study, that mimics a headwater stream under temperate climatic conditions, is developed to characterize the behavior of the stream-aquifer interface submitted to climatic and hydrological forcings, taking into account various porous medium hydraulic and thermal properties, with the objective of quantifying the conductive and advective heat fluxes. A 2D finite element thermo-hydrogeological model (METIS) (Goblet, 1981; Mouhri et al., 2013) of a synthetic cross section is developed to: 1) quantify the heat fluxes between the stream and the subsurface under various stream-aquifer configurations corresponding to different climatic and  hydrological scenarios 2) quantify heat fluxes (conductive and advective) for a large range of streambed lithologies, 3) analyze the thermally active depth evolution as well as the dampening of the river temperature fluctuations with depth.

Materials and Methods

A 2D flow and heat transport model is developed to evaluate the effects of climatic and hydrological forcing as well as the porous media properties on the heat fluxes exchanged between surface and subsurface and to describe the factors controlling the temperature dynamics across the bed. The model simulates a synthetic case that mimics a 2nd order stream (Strahler, 1957). The water and heat fluxes at the stream-aquifer interface impact the riverbed temperature profile (Anderson et al., 2011). Therefore, a sensitivity analysis is performed to evaluate the various components of the heat flux through the HZ and their attenuation by depth under different climatic and hydrological configurations (Fig. 3.1). Figure 3.1: HZ heat gains and losses accross the stream aquifer interface 3.2.1 Governing equations Temporal and spatial water and heat fluxes in a two-dimensional domain (Fig. 3. 2) were simulated using METIS (Goblet, 1981, 2010, 2012). METIS is a 2D/3D flow, mass and heat transport finite element model. This model solves the classical coupled water flow (Eq. 3.1) and heat (Eq. 3.2) transport equations: 𝜵[ 𝑲𝜵𝒉] = 𝑺𝑺 𝝏𝒉 𝝏𝒕 (Equation 3.1) Where h is the head (m), K is the hydraulic conductivity (m s -1 ), Ss is the specific storage coefficient (m1 ) and t is time (s). 𝜵[ 𝝀𝜵𝑻 − 𝝆𝒘 𝑪𝒘 𝒒 𝑻] = 𝝆 𝑪 𝝏𝑻 𝝏𝒕 (Equation 3.2) Where T is temperature (K), λ is the thermal conductivity of the porous medium (W.m-1 K -1 ), ρw is the density of water (kg m-3 ) and ρ is the density of the porous medium (kg m-3 ), Cw is the specific heat capacity of water (J kg-1 K -1 ), C is the specific heat capacity of the porous medium (J kg-1K -1 ) and q is the specific discharge (m s-1 ). Chapitre 3 : Sensibilité du fonctionnement hydrothermique de l’interface nappe-rivière 118 To quantify the relative dominance of advective heat transport over heat conduction, we calculated the thermal Peclet number the ratio between heat transported by advection and heat transported by conduction (Eq. 3.3). Pe = 𝒒 𝑳𝒄𝝆𝒘 𝑪𝒘 𝝀 (Equation 3.3) Where Pe is the Peclet number for heat flow, q (m s-1 ) is the water flux within the stream-aquifer interface; Lc is the thermally characteristic length (m). Pe >1 suggests dominance of advective transport over conductive transport and Pe <1 suggests that conduction is the dominant mode of heat transport.

Simulations 

Model setup

The modeling domain represents a cross section of a stream embedded in its geological environment. The total cross section is 55 m-wide (x = 0 at the left boundary, positive in the right direction) and 15 m-deep (z, positive upwards). The grid size is gradually increased farther from the stream with a maximum node spacing of 1 m and a minimum node spacing of 0.01 m for the HZ (Fig. 3.2). The domain consists of 36894 elements. The width of the stream itself is only a few meters, which is representative of streams where heat transfer through the riverbed may be the predominant term of the energy budget (Caissie, 2006). An observation vertical profile is set up in the middle of the model to record temperature profiles that span the range from downwelling to upwelling.