1DTempPro: Analyzing Temperature Profiles for Groundwater/Surface-water Exchange

Size: px

Start display at page:

Download "1DTempPro: Analyzing Temperature Profiles for Groundwater/Surface-water Exchange"

Byron Dalton
5 years ago
Views:

1 1DTempPro: Analyzing Temperature Profiles for Groundwater/Surface-water Exchange by Emily B. Voytek 1 *, Anja Drenkelfuss 2, Frederick D. Day-Lewis 1, Richard Healy 3, John W. Lane, Jr. 1, and Dale Werkema 4 1 U.S. Geological Survey, Office of Groundwater, Branch of Geophysics, 11 Sherman Place, Unit 5015, Storrs, CT 2 Formerly Department of Geodynamics and Geophysics, University of Bonn, Meckenheimer Allee 176, Bonn, Germany 3 U.S. Geological Survey, National Research Program, P.O. Box 25046, MS 418, Bldng., 53, Denver Federal Center, Denver, CO U.S. Environmental Protection Agency, 944 E. Harmon Ave., Las Vegas, NV * Corresponding Author: ebvoytek@usgs.gov, phone: x11, fax: Keywords: heat tracing, groundwater/surface-water interaction, model calibration, software Final copy as submitted to Ground Water for publication as: Voytek, E.B.; Drenkelfuss, Anja; Day-Lewis, F.D.; Healy, Richard; Lane, J.W., Jr.; and Werkema, Dale, 2013, 1DTempPro: Analyzing Temperature Profiles for Groundwater/Surface-water Exchange: Ground Water. Page 1 of 13

2 ABSTRACT A new computer program, 1DTempPro, is presented for analysis of vertical one-dimensional (1D) temperature profiles under saturated flow conditions. 1DTempPro is a graphical user interface to the U.S. Geological Survey code VS2DH, which numerically solves the flow and heat-transport equations. Pre- and post-processor features allow the user to calibrate VS2DH models to estimate vertical groundwater/surface-water exchange and also hydraulic conductivity for cases where hydraulic head is known. Introduction Temperature is a naturally occurring tracer, which can be exploited to infer the movement of water through subsurface saturated and unsaturated zones and between aquifers and surface-water bodies, such as estuaries, lakes, and streams. The interested reader is referred to reviews by Constantz (2008), Anderson (2005), and Constantz and Stonestrom (2003). As a result of burgeoning interest in the hyporheic zone, temperature data increasingly are used to estimate exchange rates through streambeds. One-dimensional (1D) vertical temperature profiles (Figure 1) commonly show amplitude decay and increasing phase lag of the temperature signal with depth; this behavior is predicted by the heat-transport equation, which can be solved analytically in 1D under simplifying assumptions (e.g., sinusoidal or steady boundary conditions and homogeneity of hydraulic and thermal properties). A number of methods based on analytical models have been proposed in the literature (Anderson, 2005) to calculate vertical groundwater flux based on amplitude decay or phase information. Although straightforward to implement (e.g., Swanson and Cardenas, 2011; Gordon et al., 2012), these methods are limited in application by the simplifying assumptions required for closed-form solution of the heattransport equation. Use of these methods is difficult or problematic in the presence of surface-water Page 2 of 13

3 stage fluctuations, non-sinusoidal or non-steady boundary conditions, or other complicated forcing mechanisms. The purpose of this Methods Note is to introduce a new computer program based on an existing numerical heat transport model that allows the analysis of vertical temperature profiles even if complicated forcing mechanisms are present. Analysis of 1D temperature profiles using numerical models has been demonstrated in a number of studies (e.g., Lappam, 1989; and Essaid et al., 2008). Numerical models readily can incorporate timevarying head boundary conditions (e.g., from stage fluctuations, dam releases, etc.), time-varying temperature boundary conditions (e.g., from precipitation events, weather systems, variable solar radiation), heterogeneity of bed materials, and 2D or 3D flow. 1D vertical temperature profiles are analyzed by calibrating the numerical model to match observed data. Calibration commonly focuses on adjustment of flux or, if head data are available, hydraulic conductivity. Other properties (e.g., thermal conductivity) also affect heat transport but are less variable by sediment or rock type. The VS2DH (Variably Saturated 2-Dimensional Heat Transport) model (Healy and Ronan, 1996) has been used in such studies (e.g., Essaid et al., 2008); however, the U.S. Geological Survey s (USGS) existing graphical user interface (GUI) (Hsieh et al., 2000) is not specifically designed to support such analysis, and thus users must manually generate boundary condition input files and manually parse output files in a time-consuming and labor-intensive procedure to compare model results to observed data. Although GUIs recently were published (Swanson and Cardenas, 2011; Gordon et al., 2012) for analytical methods (e.g., Stallman, 1965; Keery et al., 2007; and Hatch et al., 2006), the authors are aware of no GUI for analysis based on numerical models. Approach 1DTempPro is a GUI that allows users to manually calibrate a 1D VS2DH groundwater flow and heat-transport model to a set of temperature times-series data from different depths below a Page 3 of 13

4 sediment-water interface. The GUI functions as both a pre- and post- processor with capabilities including (1) graphical display of temperature data; (2) assignment of model parameters and settings; (3) generation of input files; (4) execution of the VS2DH executable from the Microsoft Windows GUI application; (5) reading and display of output files; and (6) iterative, manual adjustment of model parameters to match the model predictions to observed temperature data. Calibration is facilitated by immediate display of model results against measured data with each model run. Through this process, estimates of hydraulic conductivity (if head data are entered) or specific discharge (if no head data are provided) can be obtained. A flow chart (Figure 2) illustrates the iterative nature of the calibration procedure and links between pre- and post-processing features. 1DTempPro generates VS2DH input data for a 1D model, in which groundwater/surface-water exchange is modeled as a saturated-flow problem. The interested user is referred to Healy (1996) for a detailed description of the heat-transport equation and its numerical solution in VS2DH. 1DTempPro discretizes the model domain, spanning the distance between the uppermost and deepest temperature sensor locations, into a user-specified number of cells. The model assumes homogenous material conditions set in the main window. A library of sedimentary materials (e.g., silty sand, loam, etc.) is provided to initially define conditions prior to calibration. The active cells are surrounded by no-flow boundaries. Boundary conditions of specified temperature (and optionally specified-head difference) are applied to the top and bottom cells which correspond to the top and bottom temperature sensors. For initial conditions, a temperature profile is interpolated linearly between the sensor locations. Additional settings and model specifications are discussed in README and TUTORIAL files and documented in the model input files generated by 1DTempPro. Page 4 of 13

5 Using 1DTempPro 1DTempPro is written in C# for execution in a MS Windows.NET environment. Important model settings associated with calibration are specified by the user in the main window (Figure 3), which contains tabs to toggle between displays of simulated and observed data for each temperature sensor. Additional options and settings associated with the numerical solution (e.g., iterations per time step, length of recharge period, and the linear-system solver s convergence criteria) can be changed from default settings in the Advanced Settings menu. The code is installed by a Windows setup.exe provided in the distribution media. The normal progression of analysis includes the following steps: (1) read data; (2) set parameter values; (3) run VS2DH and read output; (4) repeat steps 2-3 until a satisfactory match is achieved. The execution of these steps in the GUI is explained in order below. (1) Read temperature data from a single comma-delimited file using the Read Data menu. The data file must include data from at least three sensors along the model profile. The data format is described in the software README file, and an example dataset is provided in the distribution media. The top and bottom sensors define boundary conditions, and interior sensors provide data for model calibration. The user has options for hydraulic data: (1) including no data; (2) specifying a time-invariant head difference across the model domain; or (3) reading time-varying head difference across the model domain from a file. Positive head difference values indicate a higher head at the surface location (downward flow and positive q, where q is flow rate), whereas negative values correspond to a higher head at the base of the model (upward flow and negative q). If head data are included in the model, estimation of hydraulic conductivity is possible. Otherwise, with only temperature data, only specific discharge can be estimated. Page 5 of 13

6 (2) Set model parameters using text boxes in the main window. Parameter assignments of specific discharge (or alternatively hydraulic conductivity), porosity, thermal conductivity, dispersivity and matrix heat capacity define the properties of the homogenous system. A selection of generic soil type properties is provided as a starting point when head difference across the model domain is provided, but all values can be entered manually. (3) Run the model by clicking the Run VS2DH button. Execution times are commonly less than a second. For each run, 1DTempPro creates a new folder, and generates VS2DH input files in this folder; invokes the VS2DH executable; saves model output to the folder; and reads and displays model output. The naming and structure of folders is designed to facilitate archiving of model input and results according to USGS policy. (4) Calibrate by repeating steps 2 and 3. Commonly, the calibration parameter is specific discharge, or, if head data are available, hydraulic conductivity; however, any other parameters (e.g., thermal properties) may also serve as calibration parameters. Example To demonstrate the operation of 1DTempPro, a simple synthetic example is provided. A plausible combination of hydraulic parameters, thermal parameters, and boundary conditions were assumed (Figure 3) and temperature data were simulated numerically; hence the true parameters are known, facilitating evaluation of the effectiveness of the calibration procedure and validating the code execution. A 1-m probe is assumed, with thermistors at 0, 0.15, 0.40, 0.75, and 1 m below the sedimentwater interface. The top thermal boundary condition is sinusoidal signal, with a 1-day period, maxima occurring mid-day, a diurnal temperature swing of 2 ºC, and a positive linear trend of 0.5ºC/day from Page 6 of 13

7 days 1-3 and a negative trend of identical slope from days 3-5. True hydraulic conductivity is assumed to be m/s; porosity, 0.33; thermal conductivity, 1.8 W/(mºC); matrix heat capacity, 3.2x10 6 J/(m 3 ºC); and dispersivity 0.1 m. To generate synthetic data, a static, a 11 ºC bottom boundary condition was placed at 5-m depth. The head difference across the 1-m probe is m for 3 days then drops to m thereafter; this gradient was extended to the bottom of the 5-m model. Synthetic data were taken from the model output for grid cells at the locations of the thermistors, and this dataset was downsampled to 10-minute intervals. To simulate noise, uniformly distributed random errors between ºC and 0.05 ºC were added to the synthetic data. As expected, the calibration procedure effectively recovers the true parameter values (Figure 3), and the simulated temperatures closely approximate the synthetic temperatures. Discussion & Conclusions The utility of 1DTempPro is subject to limitations including (1) 1D vertical flow for saturated porous media, (2) homogeneous, isotropic soil hydraulic and thermal properties, and (3) negligible feedback between temperature variation and hydraulic/thermal properties. Limitation (3) is inherent to the numerical solution coded in VS2DH, in which the flow problem is solved prior to the heat-transport problem. Limitations (1-2) may be relaxed in future releases of 1DTempPro, which may be extended to address heterogeneity, 2D flow, and unsaturated conditions. Users of the present version of 1DTempPro should check for potential 2D flow, which can be recognized as a degrading fit to temperature data with increasing depth. In analyzing a dataset, users also should evaluate parameter sensitivity and the potential for non-unique estimates by manual adjustment of parameter values and inspection of simulated temperatures. Future releases of 1DTempPro may include tools for automated model calibration and assessment of parameter sensitivity. The 1DTempPro code was written following objectoriented paradigm in C# to foster extensibility and future development. Page 7 of 13

8 Supporting Information Supplemental material available online includes the 1DTempPro installation, which also can be downloaded from and README and TUTORIAL files with information for installation, troubleshooting, and examples of code operation. Acknowledgments The authors are grateful for useful comments from USGS colleagues Jeannie Barlow, Martin Briggs, and Cheryl Miller. We acknowledge constructive comments from four anonymous reviewers. The first author also is grateful to Ethan Yang (U. Massachusetts, Amherst) for advice on development of graphical user interfaces. The second author is grateful to Andreas Kemna for supporting an internship at the USGS while studying at University of Bonn, Germany. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. This work was supported by the U.S. Environmental Protection Agency under contract EP10D000782, and the USGS Toxic Substances Hydrology and Groundwater Resources Programs. References Anderson, M.P Heat as a Ground Water Tracer. Ground Water 43, no. 6: Constantz, J Heat as a tracer to determine streambed water exchanges, Water Resources Research. 44, no. 4: 20 p. W00D10. Constantz, J. and D.A. Stonestrom Heat as a tracer of water movement near streams. In Heat as a Tool for Studying the Movement of Ground Water Near Streams, eds. D.A. Stonestrom and J. Constantz, 1-6. U.S. Geological Survey Circular 1260, 1-6. Reston, Virginia: USGS. Page 8 of 13

9 Essaid, H.I., C.M. Zamora, K.A. McCarthy, J.R. Vogel, and J.T. Wilson Using Heat to Characterize Streambed Water Flux Variability in Four Stream Reaches. Journal of Environmental Quality 37, no. 3: Gordon, R.P., L.K. Lautz, M.A. Briggs, and J.M. McKenzie Automated calculation of vertical pore-water flux from field temperature time series using the VFLUX method and computer program. Journal of Hydrology, : Hatch, C.E., A.T. Fisher, J.S. Revenaugh, J. Constanz and C. Ruehl Quantifying surface water groundwater interactions using time series analysis of streambed thermal records: Method development. Water Resources Research 42, no. 10. Healy, R.W., and A.D. Ronan Documentation of computer program VS2DH for simulation of energy transport in variably saturated porous media -- modification of the U.S. Geological Survey's computer program VS2DT. U.S. Geological Survey Water-Resources Investigations Report , 36. Reston, Virginia: USGS. Hsieh, P.A., W. Wingle, and R.W. Healy VS2DI--A graphical software package for simulating fluid flow and solute or energy transport in variably saturated porous media: U.S. Geological Survey Water-Resources Investigations Report , 16. Reston, Virginia: USGS. Keery, J., A. Binley, N.Crook, and J.W.N. Smith, Temporal and spatial variability of groundwater surface water fluxes: Development and application of an analytical method using temperature time series. Journal of Hydrology, 336: 16 p. Lappam, W Use of temperature profiles beneath streams to determine rates of vertical ground-water flow and vertical hydraulic conductivity. U.S. Geological Survery Water Supply Paper 2337, 35. Reston, Virginia: USGS. Stallman, R.W., Steady 1-dimensional fluid flow in a semi-infinite porous medium with sinusoidal surface temperature. Journal of Geophysical Research 70, no. 12: Page 9 of 13

10 Swanson, T.E. and M.B. Cardenas Ex-Stream: A MATLAB program for calculating fluid flux through sediment water interfaces based on steady and transient temperature profiles. Computers and Geosciences 37, no. 10: Page 10 of 13

11 Figure 1. (a) A schematic of data collection including a temperature probe with four sensors and a pair of pressure transducers; (b) measurements of temperature (T) and head difference (Δh = h1 h2) for use as boundary conditions and calibration data; (c) numerical model consisting of a single column of homogenous, fully saturated finite-difference cells; and (d) comparison of modeled and observed data. Page 11 of 13

12 Figure 2. Flowchart of the 1DTempPro program execution and data-analysis workflow. Page 12 of 13

13 Figure 3. Main window of the 1DTempPro interface, in which model parameters are adjusted and simulated temperatures are compared to data. Parameter values and plots reflect the calibrated model for the example dataset. Page 13 of 13

Study of heterogeneous vertical hyporheic flux via streambed temperature at different depths

168 Remote Sensing and GIS for Hydrology and Water Resources (IAHS Publ. 368, 2015) (Proceedings RSHS14 and ICGRHWE14, Guangzhou, China, August 2014). Study of heterogeneous vertical hyporheic flux via