Dylan J. Irvine

The effect of streambed heterogeneity on groundwater‐surface water exchange fluxes inferred from temperature time series

One-dimensional analytical heat transport equations based on temperature time series data have become popular tools to quantify groundwater-surface water interactions. The influence of nonideal field conditions on the use of these equations has been assessed for nonsinusoidal stream temperature signals, uncertainty in thermal parameters, sensor accuracy and multidimensional flow. Given that streambeds are often highly heterogeneous, the influence of streambed heterogeneity on flux estimates from temperature time series requires further investigation. Synthetic streambed temperatures were generated using two-dimensional numerical models with heterogeneous hydraulic conductivity distributions. Streambed temperatures were used to calculate fluxes using methods based on amplitude ratios (Ar), phase shifts (Δϕ) and both (ArΔϕ). Calculated fluxes were compared to known fluxes from the numerical models for flow fields analogous to losing streams. The influence of streambed structure, degree of heterogeneity, depth of the sensor pair, and location along a flow path were assessed. Errors in calculated fluxes increased with sensor pair depth, position along a flow path, and with the degree of heterogeneity. These errors were larger for streambeds with isotropic structures compared with anisotropic structures, and of the three methods tested; the Δϕ method produced the largest errors. The simultaneous estimation of strong fluxes using Δϕ, and an inability to obtain a flux estimate from Ar can suggest the presence of low hydraulic conductivity zones. Given the large errors and inability to determine flow direction from the Δϕ method, the Ar and ArΔϕ methods are recommended for downwelling fluxes.

Uncertainties in vertical groundwater fluxes from 1‐D steady state heat transport analyses caused by heterogeneity, multidimensional flow, and climate change

Steady state 1-D analytical solutions to estimate groundwater fluxes from temperature profiles are an attractive option because they are simple to apply, with no complex boundary or initial conditions. Steady state solutions have been applied to estimate both aquifer scale fluxes as well as to estimate groundwater discharge to streams. This study explores the sources of uncertainty in flux estimates from regional scale aquifers caused by sensor precision, aquifer heterogeneity, multidimensional flow and variations in surface temperature due to climate change. Synthetic temperature profiles were generated using 2-D groundwater flow and heat transport models with homogeneous and heterogeneous hydraulic and thermal properties. Temperature profiles were analyzed assuming temperature can be determined with a precision between 0.1°C and 0.001°C. Analysis of synthetic temperature profiles show that the Bredehoeft and Papadopulos (1965) method can provide good estimates of the mean vertical Darcy flux over the length of the temperature profile. Reliable flux estimates were obtained when the ratio of vertical to horizontal flux was as low as 0.1, and in heterogeneous media, providing that temperature at the upper boundary was constant in time. However, temporal increases in surface temperature led to over-estimation of fluxes. Overestimates increased with time since the onset of, and with the rate of surface warming. Overall, the Bredehoeft and Papadopulos (1965) method may be more robust for the conditions with constant temperature distributions than previously thought, but that transient methods that account for surface warming should be used to determine fluxes in shallow aquifers.

Heat and solute tracers: how do they compare in heterogeneous aquifers?

A comparison of groundwater velocity in heterogeneous aquifers estimated from hydraulic methods, heat and solute tracers was made using numerical simulations. Aquifer heterogeneity was described by geostatistical properties of the Borden, Cape Cod, North Bay, and MADE aquifers. Both heat and solute tracers displayed little systematic under- or over-estimation in velocity relative to a hydraulic control. The worst cases were under-estimates of 6.63% for solute and 2.13% for the heat tracer. Both under- and over-estimation of velocity from the heat tracer relative to the solute tracer occurred. Differences between the estimates from the tracer methods increased as the mean velocity decreased, owing to differences in rates of molecular diffusion and thermal conduction. The variance in estimated velocity using all methods increased as the variance in log-hydraulic conductivity (K) and correlation length scales increased. The variance in velocity for each scenario was remarkably small when compared to σ2 ln(K) for all methods tested. The largest variability identified was for the solute tracer where 95% of velocity estimates ranged by a factor of 19 in simulations where 95% of the K values varied by almost four orders of magnitude. For the same K-fields, this range was a factor of 11 for the heat tracer. The variance in estimated velocity was always lowest when using heat as a tracer. The study results suggest that a solute tracer will provide more understanding about the variance in velocity caused by aquifer heterogeneity and a heat tracer provides a better approximation of the mean velocity.

When can inverted water tables occur beneath streams

Decline in regional water tables (RWT) can cause losing streams to disconnect from underlying aquifers. When this occurs, an inverted water table (IWT) will develop beneath the stream, and an unsaturated zone will be present between the IWT and the RWT. The IWT marks the base of the saturated zone beneath the stream. Although a few prior studies have suggested the likelihood of an IWT without a clogging layer, most of them have assumed that a low-permeability streambed is required to reduce infiltration from surface water to groundwater, and that the IWT only occurs at the bottom of the low-permeability layer. In this study, we use numerical simulations to show that the development of an IWT beneath an unclogged stream is theoretically possible under steady-state conditions. For a stream width of 1 m above a homogeneous and isotropic sand aquifer with a 47 m deep RWT (measured in an observation point 20 m away from the center of the stream), an IWT will occur provided that the stream depth is less than a critical value of 4.1 m. This critical stream depth is the maximum water depth in the stream to maintain the occurrence of an IWT. The critical stream depth decreases with stream width. For a stream width of 6 m, the critical stream depth is only 1 mm. Thus while theoretically possible, an IWT is unlikely to occur at steady state without a clogging layer, unless a stream is very narrow or shallow and the RWT is very deep.

Using Diurnal Temperature Signals to Infer Vertical Groundwater-Surface Water Exchange

Heat is a powerful tracer to quantify fluid exchange between surface water and groundwater. Temperature time series can be used to estimate pore water fluid flux, and techniques can be employed to extend these estimates to produce detailed plan-view flux maps. Key advantages of heat tracing include cost-effective sensors and ease of data collection and interpretation, without the need for expensive and time-consuming laboratory analyses or induced tracers. While the collection of temperature data in saturated sediments is relatively straightforward, several factors influence the reliability of flux estimates that are based on time series analysis (diurnal signals) of recorded temperatures. Sensor resolution and deployment are particularly important in obtaining robust flux estimates in upwelling conditions. Also, processing temperature time series data involves a sequence of complex steps, including filtering temperature signals, selection of appropriate thermal parameters, and selection of the optimal analytical solution for modeling. This review provides a synthesis of heat tracing using diurnal temperature oscillations, including details on optimal sensor selection and deployment, data processing, model parameterization, and an overview of computing tools available. Recent advances in diurnal temperature methods also provide the opportunity to determine local saturated thermal diffusivity, which can improve the accuracy of fluid flux modeling and sensor spacing, which is related to streambed scour and deposition. These parameters can also be used to determine the reliability of flux estimates from the use of heat as a tracer.

Analytical solution and computer program (FAST) to estimate fluid fluxes from subsurface temperature profiles

This study details the derivation and application of a new analytical solution to the one-dimensional, transient conduction-advection equation that is applied to trace vertical subsurface fluid fluxes. The solution employs a flexible initial condition that allows for nonlinear temperature-depth profiles, providing a key improvement over most previous solutions. The boundary condition is composed of any number of superimposed step changes in surface temperature, and thus it accommodates intermittent warming and cooling periods due to long-term changes in climate or land cover. The solution is verified using an established numerical model of coupled groundwater flow and heat transport. A new computer program FAST (Flexible Analytical Solution using Temperature) is also presented to facilitate the inversion of this analytical solution to estimate vertical groundwater flow. The program requires surface temperature history (which can be estimated from historic climate data), subsurface thermal properties, a present-day temperature-depth profile, and reasonable initial conditions. FAST is written in the Python computing language and can be run using a free graphical user interface. Herein, we demonstrate the utility of the analytical solution and FAST using measured subsurface temperature and climate data from the Sendia Plain, Japan. Results from these illustrative examples highlight the influence of the chosen initial and boundary conditions on estimated vertical flow rates.

Groundwater flow estimation using temperature-depth profiles in a complex environment and a changing climate

Obtaining reliable estimates of vertical groundwater flows remains a challenge but is of critical importance to the management of groundwater resources. When large scale land clearing or groundwater extraction occurs, methods based on water table fluctuations or water chemistry are unreliable. As an alternative, a number of methods based on temperature-depth (T-z) profiles are available to provide vertical groundwater flow estimates from which recharge rates may be calculated. However, methods that invoke steady state assumptions have been shown to be inappropriate for sites that have experienced land surface warming. Analytical solutions that account for surface warming are available, but they typically include unrealistic or restrictive assumptions (e.g. no flow initial conditions or linear surface warming). Here, we use a new analytical solution and associated computer program (FAST) that provides flexible initial and boundary conditions to estimate fluxes using T-z profiles from the Willunga Super Science Site, a complex, but densely instrumented groundwater catchment in South Australia. T-z profiles from seven wells (ranging from high elevation to near sea level) were utilised, in addition to mean annual air temperatures at nearby weather stations to estimate boundary conditions, and thermal properties were estimated from down borehole geophysics. Temperature based flux estimates were 5 to 23mmy-1, which are similar to those estimated using chloride mass balance. This study illustrates that T-z profiles can be studied to estimate recharge in environments where more commonly applied methods fail.

Heat as a groundwater tracer in shallow and deep heterogeneous media: analytical solution, spreadsheet tool, and field applications

Groundwater flow advects heat, and thus, the deviation of subsurface temperatures from an expected conduction-dominated regime can be analysed to estimate vertical water fluxes. A number of analytical approaches have been proposed for using heat as a groundwater tracer, and these have typically assumed a homogeneous medium. However, heterogeneous thermal properties are ubiquitous in subsurface environments, both at the scale of geologic strata and at finer scales in streambeds. Herein, we apply the analytical solution of Shan and Bodvarsson (2004), developed for estimating vertical water fluxes in layered systems, in 2 new environments distinct from previous vadose zone applications. The utility of the solution for studying groundwater-surface water exchange is demonstrated using temperature data collected from an upwelling streambed with sediment layers, and a simple sensitivity analysis using these data indicates the solution is relatively robust. Also, a deeper temperature profile recorded in a borehole in South Australia is analysed to estimate deeper water fluxes. The analytical solution is able to match observed thermal gradients, including the change in slope at sediment interfaces. Results indicate that not accounting for layering can yield errors in the magnitude and even direction of the inferred Darcy fluxes. A simple automated spreadsheet tool (Flux-LM) is presented to allow users to input temperature and layer data and solve the inverse problem to estimate groundwater flux rates from shallow (e.g., <1 m) or deep (e.g., up to 100 m) profiles. The solution is not transient, and thus, it should be cautiously applied where diel signals propagate or in deeper zones where multi-decadal surface signals have disturbed subsurface thermal regimes.

Estimating the Spatial Extent of Unsaturated Zones in Heterogeneous River‐Aquifer Systems

The presence of unsaturated zones at the river-aquifer interface has large implications on numerous hydraulic and chemical processes. However, the hydrological and geological controls that influence the development of unsaturated zones have so far only been analyzed with simplified conceptualizations of flow processes, or homogeneous conceptualizations of the hydraulic conductivity in either the aquifer or the riverbed. We systematically investigated the influence of heterogeneous structures in both the riverbed and the aquifer on the development of unsaturated zones. A stochastic 1-D criterion that takes both riverbed and aquifer heterogeneity into account was developed using a Monte Carlo sampling technique. The approach allows the reliable estimation of the upper bound of the spatial extent of unsaturated areas underneath a riverbed. Through systematic numerical modelling experiments, we furthermore show that horizontal capillary forces can reduce the spatial extent of unsaturated zones under clogged areas. This analysis shows how the spatial structure of clogging layers and aquifers influence the propensity for unsaturated zones to develop: In riverbeds where clogged areas are made up of many small, spatially disconnected patches with a diameter in the order of 1 m, unsaturated areas are less likely to develop compared to riverbeds where large clogged areas exist adjacent to unclogged areas. A combination of the stochastic 1-D criterion with an analysis of the spatial structure of the clogging layers and the potential for resaturation can help develop an appropriate conceptual model and inform the choice of a suitable numerical simulator for river-aquifer systems.

Improved vertical streambed flux estimation using multiple diurnal temperature methods in series

Analytical solutions that use diurnal temperature signals to estimate vertical fluxes between groundwater and surface water based on either amplitude ratios (Ar ) or phase shifts (Δϕ) produce results that rarely agree. Analytical solutions that simultaneously utilize Ar and Δϕ within a single solution have more recently been derived, decreasing uncertainty in flux estimates in some applications. Benefits of combined (Ar Δϕ) methods also include that thermal diffusivity and sensor spacing can be calculated. However, poor identification of either Ar or Δϕ from raw temperature signals can lead to erratic parameter estimates from Ar Δϕ methods. An add-on program for VFLUX 2 is presented to address this issue. Using thermal diffusivity selected from an Ar Δϕ method during a reliable time period, fluxes are recalculated using an Ar method. This approach maximizes the benefits of the Ar and Ar Δϕ methods. Additionally, sensor spacing calculations can be used to identify periods with unreliable flux estimates, or to assess streambed scour. Using synthetic and field examples, the use of these solutions in series was particularly useful for gaining conditions where fluxes exceeded 1 m/d.