Simulation of Heat Flow in a Synthetic Watershed: The Role of the Unsaturated Zone
2.1. Representation of Warming Conditions
2.2. Model Construction: Groundwater Flow
2.3. Representation of Unsaturated Zone Processes
- NO_UZ_THK: no UZ processes are simulated by the model. Instead, a monthly infiltration of water and heat is applied directly to the water table, using the Recharge (RCH)  and Source/Sink Mixing (SSM)  packages, respectively. Note that the NO_UZ_THK and MID_UZ_THK models (explained below) are dimensionally identical (i.e., cell geometries (thicknesses) are the same), meaning that an overlying UZ is present in the NO_UZ_THK, although the grid cells above the water table are inactive. The NO_UZ_THK designation does not imply that the water table is near the land surface throughout the model domain.
- MID_UZ_THK: a model with the same grid cell dimensions as the NO_UZ_THK simulation but simulates UZ processes with the UZF1 and unsaturated zone transport (UZT) [11,27] packages. The UZ average thickness is approximately 11 ft, with a maximum of 62 ft. The land surface slope from surface water features to “upland” locations is low (1.5 ft/300 ft, or 0.005 ft/ft; Figure 3A).
- HI_UZ_THK: the UZ is approximately three times thicker than the MID_UZ_THK setup, averaging approximately 31 ft thick with a maximum thickness of approximately 150 ft. The land surface slope from surface water features is steeper than the MID_UZ_THK model (3.0 ft/300 ft, or 0.01 ft/ft; Figure 3B).
2.4. Model Construction—Heat Transport
3.1. Water Table Temperatures
3.2. Groundwater System Temperatures
3.3. Stream Baseflow Temperatures
4. Discussion and Implications for Watershed Heat Transport Modeling
- A potential effect of warming climate on groundwater temperatures in a watershed depends on the relative heat flux—the product of infiltration rate and associated temperature—that determines the amount of heat entering the subsurface. For example, if the temperature of infiltrating water increases during a warming climate, the net change in groundwater temperature may be lessened if drought conditions cause the rate of infiltration to be reduced;
- The UZ acts as a low-pass filter. Both the magnitude and timing of water and heat pulses entering the subsurface and migrating downward to the water table, are attenuated by the UZ. Neglecting the UZ from a model simulation (as in the NO_UZ_THK version of the synthetic model) effectively “short circuits” the dampening and lag time influences of the UZ;
- The effect of a warming climate is buffered in a watershed by the total thickness of the groundwater system. A relatively thick groundwater system gives rise to mixed water temperatures at natural discharge points where shallow and deep flow lines converge. The convergence of flow lines dampens the heat signal carried by recharge that eventually discharges as baseflow to surface water;
- The spatial extent of riparian zones plays an important role in determining the flashiness of a stream’s response to heat forcing. That is, the riparian zone sheds (or shunts) precipitation to the surface water network, without the low-pass filtering of the UZ;
- Additional vertical discretization to more accurately simulate the movement of wetting and heat fronts did not change simulation results. However, omission of the UZ and its effects on heat transport in a watershed-scale model produces erroneous results;
- A sensitivity analysis of the flow and heat transport parameters showed an appreciable influence on simulated temperatures in both the saturated and unsaturated components of the subsurface, as well as on simulated stream temperatures (Supplementary Material Section S3).
5. Limitations of the Methodology
- Root zone processes (i.e., evapotranspiration) are neglected; therefore, the infiltration rate is equated with the water that drains out of the root zone and enters the top of the UZ.
- As noted above, the UZF1 package in MODFLOW implements simplifying assumptions that neglect capillary forces. As a result, UZF1 simulates downward-only gravitational flow. This simplification is generally considered acceptable at a watershed scale .
- With the UZF1 package active in MODFLOW, one of three potential states is simulated for any active cell. They are either (1) unsaturated (i.e., partially-saturated over the entire thickness of the active grid cell), (2) a mix of unsaturated and saturated conditions (i.e., the water table is present within the cell), or (3) fully saturated. For water table cells, a single water content value is calculated that is equivalent to a volume average of both the unsaturated and saturated portions of the cell. Ambiguity arising from this mixed condition appears to have minimal effect on the heat flux solution, insofar as refined layer discretization hardly changes model results (Supplementary Material Section S3).
- Although conduction occurs through the matrix material of an aquifer and may transport heat more rapidly than in the fluid phase in low convection environments, MT3D-USGS simulates a single “bulk” diffusion term that approximates heat transport through both phases. In other words, the conductive propagation of heat through the solid and fluid phases is represented as a conjoined movement that is slower than thermal diffusion through a pure solid but faster than thermal diffusion through a pure fluid. In a predominantly horizontal flow-field, the upward or downward thermal diffusion is generally secondary, compared with the convection in humid temperate climates . It is conceivable that the conductive flux through matrix material is dominant when the temperature gradient is unusually strong.
- The methods applied in this study were designed for temperate climate regions. It neglects processes such as mountain-front recharge in settings with deep water tables (>30 m), long flow paths (>2–3 km), and long UZ residence times, which are characteristic of arid and semi-arid regions.
- The effects of changes in viscosity owing to temperature changes are not considered in this study. However, variations in viscosity over the relatively small temperature changes simulated in the model are expected to be small.
- Temporal smoothing of system dynamics via the use of a monthly climate forcing.
- Simplification of the thermal influence of storm runoff to streams was ignored/not simulated: that is, the restriction of the simulation to monthly average baseflow conditions.
- Inadequate representation of lake energy budget considerations as important for lake temperature. For example, neglecting the formation of ice during the winter months, energy changes related to evaporation, and lake thermal stratification.
- Whereas specification of infiltration is critical for representative groundwater flow models, specification of the heat forcing function, represented by the product of the infiltration rate added to the top of UZ multiplied by the infiltration temperature (the relative heat influx) is critical for developing a representative heat transport model.
- Heat transport in watershed models stand to benefit from a discretization scheme with at least one unsaturated layer. This approach enables the simulation to store, dampen, and/or lag the heat pulse before it is mixed with an underlying water table cell.
Data Availability Statement
Conflicts of Interest
- IPCC. Climate Change 2022: Impacts, Adaptation, and Vulnerability, Technical Summary; Cambridge University Press: Cambridge, UK, 2022. [Google Scholar]
- Hunt, R.J.; Walker, J.F.; Selbig, W.R.; Westenbroek, S.M.; Regan, R.S. Simulation of Climatechange Effects on Streamflow, Lake Water Budgets, and Stream Temperature Using GSFLOW and SNTEMP, Trout Lake Watershed, Wisconsin; U.S. Geological Survey Scientific Investigations Report 2013-5159; U.S. Geological Survey Scientific: Reston, VA, USA, 2013; p. 118. Available online: http://pubs.usgs.gov/sir/2013/5159/ (accessed on 15 January 2022).
- Hunt, R.J.; Westenbroek, S.M.; Walker, J.F.; Selbig, W.R.; Regan, R.S.; Leaf, A.T.; Saad, D.A. Simulation of Climate Change Effects on Streamflow, Groundwater, and Stream Temperature Using GSFLOW and SNTEMP in the Black Earth Creek Watershed, Wisconsin; 2328-0328; U.S. Geological Survey, Scientific Investigations Report 2016-5091; U.S. Geological Survey Scientific: Reston, VA, USA, 2016; p. 117. [CrossRef]
- Niswonger, R.G.; Prudic, D.E.; Regan, R.S. Documentation of the Unsaturated-Zone Flow (UZF1) Package for Modeling Unsaturated Flow between the Land Surface and the Water Table with MODFLOW-2005; 2328-7055; U.S. Geological Survey Scientific: Reston, VA, USA, 2006; p. 62. [CrossRef]
- Niswonger, R.G.; Panday, S.; Ibaraki, M. MODFLOW-NWT, a Newton Formulation for MODFLOW-2005; U.S. Geological Survey Scientific: Reston, VA, USA, 2011; p. 44. [CrossRef][Green Version]
- Hunt, R.J.; Prudic, D.E.; Walker, J.F.; Anderson, M.P. Importance of unsaturated zone flow for simulating recharge in a humid climate. Groundwater 2008, 46, 551–560. [Google Scholar] [CrossRef]
- Morway, E.D.; Feinstein, D.T.; Hunt, R.J.; Healy, R.W. New capabilities in MT3D-USGS for Simulating Unsaturated-Zone Heat Transport. Groundwater 2022. [Google Scholar] [CrossRef] [PubMed]
- Anderson, M.P.; Bowser, C. The role of groundwater in delaying lake acidification. Water Resour. Res. 1986, 22, 1101–1108. [Google Scholar] [CrossRef]
- USDA-NRCS. HUC10: USGS Watershed Boundary Dataset of Watersheds. Available online: https://datagateway.nrcs.usda.gov (accessed on 25 May 2022).
- Harbaugh, A.W. MODFLOW-2005, the U.S. Geological Survey Modular Ground-Water Model: The Ground-Water Flow Process; U.S. Geological Survey Scientific: Reston, VA, USA, 2005. [CrossRef][Green Version]
- Bedekar, V.; Morway, E.D.; Langevin, C.D.; Tonkin, M.J. MT3D-USGS Version 1: A U.S. Geological Survey Release of MT3DMS Updated with New and Expanded Transport Capabilities for Use with MODFLOW; 2328-7055; U.S. Geological Survey Scientific: Reston, VA, USA, 2016. [CrossRef][Green Version]
- USGS. National Climate Change Viewer. Available online: https://www2.usgs.gov/landresources/lcs/nccv/maca2/maca2_watersheds.html (accessed on 31 January 2022).
- Niswonger, R.G.; Prudic, D.E. Documentation of the Streamflow-Routing (SFR2) Package to Include Unsaturated Flow Beneath Streams—A Modification to SFR1; 2328-7055; U.S. Geological Survey, Techniques and Methods 6-A13; U.S. Geological Survey Scientific: Reston, VA, USA, 2005. [CrossRef][Green Version]
- Merritt, M.L.; Konikow, L.F. Documentation of a Computer Program to Simulate Lake-Aquifer Interaction Using the MODFLOW Ground-Water Flow Model and the MOC3D Solute-Transport Model; U.S. Geological Survey Water-Resources Investigations Report 00–4167; U.S. Geological Survey Scientific: Reston, VA, USA, 2000; p. 146. Available online: https://pubs.er.usgs.gov/publication/wri004167 (accessed on 15 May 2020).
- Niswonger, R.; Prudic, D.E. Comment on “evaluating interactions between groundwater and vadose zone using the HYDRUS-based flow package for MODFLOW” by Navin Kumar, C. Twarakavi, Jirka Simunek, and Sophia Seo. Vadose Zone J. 2009, 8, 818–819. [Google Scholar] [CrossRef]
- Markstrom, S.L.; Niswonger, R.G.; Regan, R.S.; Prudic, D.E.; Barlow, P.M. GSFLOW-Coupled Ground-Water and Surface-Water FLOW Model Based on the Integration of the Precipitation-Runoff Modeling System (PRMS) and the Modular Ground-Water Flow Model (MODFLOW-2005); U.S. Geological Survey Techniques and Methods 6-D1; U.S. Geological Survey Scientific: Reston, VA, USA, 2008; p. 240. Available online: https://pubs.usgs.gov/tm/tm6d1/pdf/tm6d1.pdf (accessed on 15 May 2020).
- Morway, E.D.; Gates, T.K.; Niswonger, R.G. Appraising options to reduce shallow groundwater tables and enhance flow conditions over regional scales in an irrigated alluvial aquifer system. J. Hydrol. 2013, 495, 216–237. [Google Scholar] [CrossRef]
- Woolfenden, L.R.; Nishikawa, T. Simulation of Groundwater and Surface-Water Resources of the Santa Rosa Plain Watershed, Sonoma County, California; 2328-0328; U.S. Geological Survey, Scientific Investigation Report 2014-5052; U.S. Geological Survey Scientific: Reston, VA, USA, 2014. [CrossRef][Green Version]
- Haserodt, M.J.; Hunt, R.J.; Fienen, M.N.; Feinstein, D.T. Groundwater/Surface-Water Interactions in the Partridge River Basin and Evaluation of Hypothetical Future Mine Pits, Minnesota; 2328-0328; U.S. Geological Survey, Scientific Investigations Report 2021-5038; U.S. Geological Survey Scientific: Reston, VA, USA, 2021. [CrossRef]
- Feinstein, D.T.; Hart, D.J.; Gatzke, S.; Hunt, R.J.; Niswonger, R.G.; Fienen, M.N.J.G. A simple method for simulating groundwater interactions with fens to forecast development effects. Groundwater 2020, 58, 524–534. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Khadim, F.K.; Dokou, Z.; Bagtzoglou, A.C.; Yang, M.; Lijalem, G.A.; Anagnostou, E. A numerical framework to advance agricultural water management under hydrological stress conditions in a data scarce environment. Agric. Water Manag. 2021, 254, 106947. [Google Scholar] [CrossRef]
- Kitlasten, W.; Morway, E.D.; Niswonger, R.G.; Gardner, M.; White, J.T.; Triana, E.; Selkowitz, D. Integrated Hydrology and Operations Modeling to Evaluate Climate Change Impacts in an Agricultural Valley Irrigated with Snowmelt Runoff. Water Resour. Res. 2021, 57, e2020WR027924. [Google Scholar] [CrossRef]
- Dunne, T.; Black, R.D. An experimental investigation of runoff production in permeable soils. Water Resour. Res. 1970, 6, 478–490. [Google Scholar] [CrossRef]
- Muldoon, M.A.; Madison, F.M.; Lowery, B. Variability of Nitrate Loading and Determination of Monitoring Frequency for a Shallow Sandy Aquifer, Arena, Wisconsin. 1998. Available online: https://wgnhs.wisc.edu/catalog/publication/000810/resource/wofr199809 (accessed on 25 January 2022).
- Feinstein, D.T.; Hunt, R.J.; Morway, E.D. Simulation of heat flow in a synthetic watershed: Lags and damping across multiple pathways under a climate-forcing scenario. Water 2022, 14, 2810. [Google Scholar] [CrossRef]
- Zheng, C.; Wang, P.P. MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems; Documentation and User’s Guide; Contract Report SERDP-99-1; U.S. Army Engineer Research and Development Center: Vicksburg, MS, USA, 1999; Available online: http://hydro.geo.ua.edu/mt3d (accessed on 22 June 2022).
- Morway, E.D.; Niswonger, R.G.; Langevin, C.D.; Bailey, R.T.; Healy, R.W. Modeling variably saturated subsurface solute transport with MODFLOW-UZF and MT3DMS. Groundwater 2013, 51, 237–251. [Google Scholar] [CrossRef] [PubMed]
- Zheng, C.; Hill, M.C.; Hsieh, P.A. MODFLOW-2000, the U.S. Geological Survey Modular Ground-Water Model: User Guide to the LMT6 Package, the Linkage with MT3DMS for Multi-Species Mass Transport Modeling; 2331-1258; U.S. Geological Survey Scientific: Reston, VA, USA, 2001. [CrossRef]
- Zheng, C.; Bennett, G.D. Applied Contaminant Transport Modeling, 2nd ed.; John Wiley & Sons, Inc.: New York, NY, USA, 2002. [Google Scholar]
- Harter, T.; Hopmans, J.W. (Eds.) Role of Vadose-Zone Flow Processes in Regional-Scale Hydrology: Review, Opportunities and Challenges; Kluwer Academic Publishers: Wageningen, The Netherlands, 2004; pp. 179–208. [Google Scholar]
- Healy, R.W.; Ronan, A.D. 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 96-4230 36; United States Environmental Protection Agency: Washington, DC, USA, 1996. [CrossRef]
- Van Duin, R.H.A. The Influence of Soil Management on the Temperature Wave Near the Soil Surface. Wageningen University & Research, Technical Bulletin no. 29, Institute for Land and Water Management Research. 1963. Available online: https://edepot.wur.nl/417072 (accessed on 22 June 2022).
- Westenbroek, S.M.; Engott, J.A.; Kelson, V.A.; Hunt, R.J. SWB Version 2.0—A Soil-Water-Balance Code for Estimating Net Infiltration and Other Water-Budget Components; Book 6; U.S. Geological Survey Techniques and Methods: Lakewood, CO, USA, 2018; Chapter A59; p. 118. [CrossRef]
- Zheng, C. MT3DMS V5.3: A Modular Three-Dimensional Multispecies Transport Model For Simulation Of Advection, Dispersion, And Chemical Reactions Of Contaminants In Groundwater Systems: Supplemental User’s Guide. 2010. Available online: https://hydro.geo.ua.edu/mt3d/index.htm (accessed on 25 August 2021).
- Morway, E.D.; Feinstein, D.T.; Hunt, R.J. MODFLOW-NWT and MT3D-USGS Models for Appraising Parameter Sensitivity and Other Controlling Factors in a Synthetic Watershed Accounting for Variably-Saturated Flow Processes. Available online: https://doi.org/10.5066/P99NUKIX (accessed on 25 January 2022).
|MODFLOW-NWT Package||Parameter Name||Value|
|Horizontal hydraulic conductivity||42.5 ft/day (12.95 m/day)|
|Vertical hydraulic conductivity||1 ft/day (0.30 m/day)|
|Specific yield||0.26 (unitless)|
|Specific storage||1 × 10−5 1/day|
|Vertical hydraulic conductivity||1 ft/day (0.30 m/day)|
|Surface infiltration hydraulic conductivity||0.1 ft/day (0.0305 m/day)|
|Saturated water content||0.30 (unitless)|
|Residual water content||0.04 (unitless)|
|Brooks-Corey epsilon||3.87 (unitless)|
|Monthly infiltration rate||See Figure 1A|
|Channel width||25 ft (7.62 m)|
|Channel bed thickness||1 ft (0.30 m)|
|Channel bed hydraulic conductivity||20 ft/day (6.10 m/day)|
|Channel slope||0.0002 (ft/ft)|
|Channel incision (streambed elevation below top of cell)||2.5 ft (0.76 m)|
|Conductance||90,000 ft2/day (8362 m2/day)|
|Lakebed conductance||90,000 ft2/day (8362 m2/day)|
|Conductance||11.37 ft2/day (1.06 m2/day)|
|MT3D-USGS Package||Parameter Name||Value|
|Saturated thermal conductivity||52,669 Joules/(day·ft·°C) [2.0 Joules/(sec·m °C)]|
|Residual thermal conductivity||13,167 Joules/(day·ft °C) [0.5 Joules/(sec·m °C)]|
|Fluid density||28.3166 kg/ft3 (1000 kg/m3)|
|Fluid heat capacity||4183 Joules/(kg °C)|
|Residual water content||0.04 (unitless)|
|Longitudinal dispersivity||3.0 ft (0.91 m)|
|Transverse horizontal dispersivity||0.30 ft (0.091 m)|
|Transverse vertical dispersivity||0.30 ft (0.091 m)|
|Monthly infiltration temperature||see Figure 4|
|Bulk density of solid||51.849 kg/ft3 (1830 kg/m3)|
|Distribution coefficient||2.68 × 10−3 ft3/kg (7.59 × 10−5 m3/kg)|
|Source temperature||8.55 °C during spin-up (raised 0.03 °C/yr during warm-up)|
|Initial temperature||8.55 °C|
|Initial temperature||8.55 °C|
|Precipitation temperature||see Figure 4 (temperature the same as infiltration, with following exceptions) |
April: +0.5 °C; May: +1.0 °C; June: +1.5 °C; July: +2.0 °C; August: +1.5 °C; September: +1.0 °C; October: +0.5 °C
|Figure 4 Subplot ID||Warming Year||Month||Relative Heat Influx for Current Month||Relative Heat Influx for Proceeding 12 Months||Infiltration Rate (in/mo)||Infiltration Temperature (°C)|
|Base Model Version||Stream Gage||Contributing Area (Fraction of Model Domain)||Riparian Area (Percent of Contributing Area)|
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Morway, E.D.; Feinstein, D.T.; Hunt, R.J. Simulation of Heat Flow in a Synthetic Watershed: The Role of the Unsaturated Zone. Water 2022, 14, 3883. https://doi.org/10.3390/w14233883
Morway ED, Feinstein DT, Hunt RJ. Simulation of Heat Flow in a Synthetic Watershed: The Role of the Unsaturated Zone. Water. 2022; 14(23):3883. https://doi.org/10.3390/w14233883Chicago/Turabian Style
Morway, Eric D., Daniel T. Feinstein, and Randall J. Hunt. 2022. "Simulation of Heat Flow in a Synthetic Watershed: The Role of the Unsaturated Zone" Water 14, no. 23: 3883. https://doi.org/10.3390/w14233883