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a U.S. Geological Survey, Menlo Park, CA 94025
b University of Nevada, Reno, NV 89557
c Los Alamos National Laboratory, Los Alamos, NM, 87545
* Corresponding author (jconstan{at}usgs.gov)
Received 13 March 2002.
ABSTRACT
Percolation rates are estimated using vertical temperature profiles from sequentially deeper vadose environments, progressing from sediments beneath stream channels, to expansive basin-fill materials, and finally to deep fractured bedrock underlying mountainous terrain. Beneath stream channels, vertical temperature profiles vary over time in response to downward heat transport, which is generally controlled by conductive heat transport during dry periods, or by advective transport during channel infiltration. During periods of stream-channel infiltration, two relatively simple approaches are possible: a heat-pulse technique, or a heat and liquid-water transport simulation code. Focused percolation rates beneath stream channels are examined for perennial, seasonal, and ephemeral channels in central New Mexico, with estimated percolation rates ranging from 100 to 2100 mm d-1. Deep within basin-fill and underlying mountainous terrain, vertical temperature gradients are dominated by the local geothermal gradient, which creates a profile with decreasing temperatures toward the surface. If simplifying assumptions are employed regarding stratigraphy and vapor fluxes, an analytical solution to the heat transport problem can be used to generate temperature profiles at specified percolation rates for comparison to the observed geothermal gradient. Comparisons to an observed temperature profile in the basin-fill sediments beneath Frenchman Flat, Nevada, yielded water fluxes near zero, with absolute values <10 mm yr-1. For the deep vadose environment beneath Yucca Mountain, Nevada, the complexities of stratigraphy and vapor movement are incorporated into a more elaborate heat and water transport model to compare simulated and observed temperature profiles for a pair of deep boreholes. Best matches resulted in a percolation rate near zero for one borehole and 11 mm yr-1 for the second borehole.
BY THE EARLY 1900s, researchers intuitively understood that heat is transferred during the course of water movement through porous material, and that temperature profiles within the material are strongly influenced by water movement (Bouyoucos, 1915). As a consequence, temperature profiles above the water table might provide a basis for quantifying water fluxes. Challenges in collecting temperature profiles and the resources necessary to quantitatively solve complex heat and water transport models limited the utility of analyzing temperature patterns in the vadose zone. Recently both the measurement of temperature and the simulation of heat and water transport have benefited from significant advances in temperature acquisition and computer resources. These advances facilitate the measurement and analysis of temperature in the vadose zone, such that the link between temperature and water fluxes that was appreciated in the early 1900s is now being quantified in environments ranging from soils (e.g., Taniguchi and Sharma, 1993; Tabbagh et al., 1999) to sediments beneath stream channels to (e.g., Constantz et al., 1994; Izbicki and Michel, 2002) to deep basin-scale flow systems (e.g., Reiter, 2001).
Here we describe the general trends in temperature patterns common in the vadose zone of arid environments and the manner in which these patterns may be analyzed to estimate percolation rates. Temperature profiles for three common topographies in arid regions are examined to delineate several approaches for estimating vertical water fluxes at various depths, and to provide insight into the variability of percolation patterns with depth in arid regions. The first case examines the potential for determining focused percolation beneath stream channels, the second examines the potential for determining diffuse percolation within vast interchannel basin-fill material, and the third case examines the potential for determining deep percolation within fractured bedrock underlying mountainous terrain.
Temperature Profiles in the Vadose Zone of Arid Environments
On an annual time scale, temperature patterns in the shallow vadose zone are distinctly different from those in the deep vadose zone. Temperatures in the shallow vadose zone vary both with depth and time, while temperatures in the deeper vadose zone vary only with depth (i.e., show temporal stability). Below the depth of seasonal temperature variability, a region of uniformly increasing temperature with depth exists due to upward conduction of heat from the earth's warmer interior, termed the geothermal heat flux. There is a large spatial variation in the magnitude of this heat flux, primarily due to spatial variations in crustal heating and proximity to magmatic activity (Lachenbruch and Sass, 1977), as well as spatial variations in groundwater fluxes (Bredehoeft and Papadopulos, 1965). The resulting rate of temperature change with depth is commonly referred to as the geothermal gradient. If thermal conduction is the sole transport mechanism, the thermal conductivity of the solid, liquid, and gas phases, and the underlying geothermal heat flux determine the magnitude of the geothermal gradient for a given location. Processes such as percolation generally serve to alter the temperature gradient. (Note that infiltration is the flux of water into the vadose zone, percolation is the flux of water through the vadose zone, recharge is the flux of water into the underlying water table, and discharge is the upward flux of water from the water table.) Figure 1 (upper) depicts hypothetical temperature profiles between the surface and a depth of 200 m, for the case of groundwater discharge, no flux, and groundwater recharge. A distinct lineation is depicted between a shallow region of varying temperature profiles during the course of the year and a deeper region of time invariant temperature profiles during the year. In Fig. 1 (upper), the seasonal temperature extinction depth resides at approximately 30 m, below which no seasonal variation in temperature is observed. Within in the shallow region, the yearly temperature envelope encompasses the annual range of temperature at each depth above 30 m. Figure 1 (lower panel) depicts temperature profiles between the surface and a depth of 2 m, for winter vs. summer conditions, in the presence or absence of percolation. This creates daily temperature envelopes for each of the four separate conditions. For this hypothetical case, the daily temperature extinction depth is the location below which no daily variation in temperature is detected, or approximately 0.5 m in the absence of water flux, and approximately 2 m during percolation.
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The work of Philip and de Vries (1957) continues to stand today as the seminal work on water (both liquid and vapor) transport under temperature gradients encountered in the shallow vadose zone. Sophocleous (1979) developed coupled fluid and heat transport solutions for the vadose zone, demonstrating that inclusion of the coupling of the transport equations is necessary where thermal gradients are large and water fluxes significant. Scanlon (1994) and Scanlon and Milly (1994) simulated thermally driven water and vapor transport in shallow (15 m) vadose zone profiles in west Texas, demonstrating that vapor transport driven by seasonal temperature fluctuations is a significant transport mechanism in arid vadose zones. For temperature gradients encountered at greater depths, Sass et al. (1988) suggested that very small amounts of percolation could be responsible for large areas of anomalously low crustal heat flux in portions of the Great Basin of the western United States. Walvoord et al. (1999) suggested that upward vapor transport encountered at some locations in deep vadose zones may be responsible for the observations of nearly uniform capillary pressures with depth at these locations. Consequently, a comprehensive quantitative description of transient, multiphase flow in these types of arid environments requires a detailed knowledge of the thermal properties in the domain of interest, accurate definition of boundary and initial conditions, and detailed characterization of stratigraphy to fully describe heat and water transport in the liquid and vapor phases.
These stringent requirements have prompted alternative approaches, using simplifying assumptions, to develop a more tractable problem. We review several approaches as potential techniques for analysis of temperature profiles derived from a range of locations and depths in the vadose zone of the U.S. Southwest.
ANALYSIS OF SHALLOW TEMPERATURE PROFILES BENEATH STREAM CHANNELS IN ARID REGIONS
In the presence of streamflow, water and heat transport in the vapor phase can be assumed negligible within the underlying streambed, condensing the multiphase problem to a more computationally manageable expression. Suzuki (1960) and Stallman (1963)(1965) independently developed an expression for saturated vertical flow in the z-direction as follows:
 | [1] |
 | [2] |
s, w, and a are the densities (kg m-3) of the sediment, water, and air, respectively. The product of the specific heat capacity and the density is the volumetric heat capacity, which is approximately 0.8 x 106, 4.2 x 106, and 0.001 x 106 J m-3 °C-1 for sediments, water, and air, respectively (de Vries, 1963). Numerous researchers have demonstrated that Eq. [1] is quite successful in estimating saturated heat and groundwater flow in both shallow (e.g., Cartwright, 1974) and deep environments (e.g., Bredehoeft and Papadopulos, 1965).
A simplification of Eq. [1] is employed for the case where pore water velocities are sufficiently high, such that heat transport by conduction is negligible compared with heat transport by advection (e.g., Nightingale, 1975). This case is typical during flow events in many ephemeral streambeds in arid environments, especially near the mountain front. These high energy stream channels often possess highly permeable bed materials, which inhibit sustained streamflow except during atypically long events. For those cases where conduction is small compared with advection, ql is approximated by:
 | [3] |
A more comprehensive approach is warranted to account for simultaneous conductive and advective heat transport beneath streambeds that sustain longer duration streamflows. To implement this more comprehensive approach, a heat transport equation may be developed via the convective–dispersion equation (e.g., see Kipp, 1987) as follows:
 | [4] |
is percentage volumetric water content, 
is sediment porosity (dimensionless). Dh is the thermomechanical dispersion tensor (m2 s-1), ql is the liquid water flux (m s-1), and Q is the rate of fluid source (s-1). The left side of the equation represents the change in energy stored in a volume over time. The first term on the right side describes the energy transport by heat conduction through the bulk material. The second term on the right side accounts for thermomechanical dispersion. The third term on the right side represents advective heat transport, and the final term on the right side represents heat sources or sinks to mass movement into or out of the volume. To describe simultaneous water flow in the vadose zone, the variably saturated groundwater flow equation can be expressed as follows:
 | [5] |
is the water pressure head (m) and h is the total head (m) (Buckingham, 1907; Richards, 1931). Within Eq. [4] the thermomechanical dispersion tensor is defined as (Healy, 1990):
 | [6] |
l and t are longitudinal and transverse dispersivities, respectively (m); 
I,j is the Kronecker delta function; 
i and j are the ith and jth component of the velocity vector, respectively (m s-1), and |v| is the magnitude of the velocity vector (m s-1). Both the hydraulic conductivity, K, and the thermal conductivity, KT, vary with texture and degree of saturation; however, the total variation in KT is small compared with K and is more accurately predicted from texture and moisture content information (van Duin, 1963). Thus, KT is generally estimated, and K is varied in the course of matching observed temperatures through inverse simulation modeling. The two-dimensional forms of Eq. [4] and [5] are solved numerically in the computer simulation code, VS2DH (Healy and Ronan, 1996). VS2DH was developed specifically for stream channels and is restricted to environments in which heat and water transport in the vapor phase are small relative to transport in the liquid phase. Ronan et al. (1998) successfully applied VS2DH to simulate groundwater flow pattern below Vicee Canyon, Nevada, by inversely matching simulated sediment temperatures to observed temperatures.
Using this approach for temperature-based estimates of flux beneath channels, the primary uncertainty is a result of uncertainties in the thermal parameters, KT, Cs, and in extreme cases T. Niswonger and Rupp (2000) applied Monte Carlo analysis to VS2DH simulations for determining the relative impacts in random errors in the thermal parameters beneath streambeds. They concluded that errors in T produced significantly greater uncertainties in percolation rates compared with KT and Cs. Generally this does not present a problem, since T is routinely measured with great accuracy. However, as advective heat transport diminishes with decreasing percolation rates, the relative importance of the KT and Cs increases, such that their characterization is critical as ql approaches zero.
Results from three sites in central New Mexico are presented with a range of streamflow conditions to aid in demonstrating the various approaches necessary to derive streambed water fluxes for distinctly different streambed temperature signals.
Rio Grande, New Mexico
The Rio Grande is a wide, generally shallow (<3 m), perennial stream as it flows through central New Mexico. Traditional methods of determining seepage losses are hampered by undocumented withdrawals and return flows along virtually all reaches in the greater Albuquerque area. In this study, losses were monitored by direct estimates of streambed percolation using heat as tracer of groundwater flow. Temperatures were logged in several piezometers between the surface and depths of approximately 15 m below the streambed of the Rio Grande as described in Bartolino and Niswonger (1999). In a procedure similar to Lapham (1989), piezometers were temperature logged seven times at approximately 1-m vertical intervals from September 1996 to August 1998. Figure 2 shows the observed annual temperature envelope for a site 30 m north of the Paseo del Norte bridge. The temperature envelope in Fig. 2 possesses a tulip shape compared with the fanned out shape of the hypothetical envelope in Fig. 1. This shape suggests an abrupt decrease in the rate of heat transport below 5 m, as the slope sharply increases due to lack of transport. Also, note that the seasonal temperature extinction depth is below the depth of observation. Inverse modeling was performed using VS2DH and the parameter estimating code, PEST (Doherty et al., 1994). The stream stage and hydraulic gradient were measured along with stream and streambed temperatures; then simulated temperatures were fit to observed sediment temperatures by inverse modeling using PEST. Figure 3 gives an example of the excellent optimized fit achieved compared with observed sediment temperature at this site. The optimized fluxes yielded streambed fluxes ranging from 8 mm d-1 for September 1996 to 80 mm d-1 for January 1997. The higher percolation rates estimated in the winter were possibly the result of scour removal of summer fines and/or raised winter stages.
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In summary, the use of temperature profiles to examine shallow percolation appears to indicate a reasonable trend in terms of relative percolation rates. The temperature-derived percolation rates to a depth of 15 m for the perennial flows of the Rio Grande averaged in the 40 mm d-1 range. Shallow percolation rates to a depth of 3 m beneath Bear Canyon averaged in the 800 mm d-1 range during winter streamflows. Shallow percolation rates that were estimated between the surface and 2 m for ephemeral flows of the Santa Fe River ranged as high as 2000 mm d-1 during brief flow events lasting only hours. These trends were supported by surface water–based estimates of percolation that followed a similar trend. As shown below, these focused percolation estimates are orders of magnitude greater than deeper diffuse percolation rates estimated from temperature profiles.
ANALYSIS OF DEEP TEMPERATURE PROFILES IN ARID BASINS
Percolation rates generally vary slowly in deep vadose zones, and analytical solutions to the heat transfer equations may be appropriate. Beneath the region of temperature variations depicted in Fig. 1 (upper), heat transport is principally governed by the geothermal flux, advection associated with migration of water, conductive diffusion of sensible and latent heat, and long-term climate changes. In the deep vadose zones found in many arid regions, water flux may be very small, and it is often difficult to discern either its direction or magnitude. Thermal analysis can provide an assessment that is far less dependent on soil hydraulic properties and potentially reduce the uncertainty in the assessment of water flux direction and magnitude. The use of thermal data to quantify water flux direction and magnitude in deep vadose zones becomes less quantitative as the flux decreases; however, thermal analysis, when conducted along with soil hydraulic and tracer analysis, can be used as an independent check on these results and can add a significant level of confidence. The development of independent methods of estimating soil water flux, such as thermal analysis, in deep vadose zones is essential to improving our estimates of groundwater recharge (Scanlon et al., 1997). In this section, a brief review of thermal transport, with special emphasis on the geothermal gradient in deep vadose zones is discussed along with application to observations and limitations of the analysis.
In the deep vadose zone, the primary heat transport direction can be assumed to be vertical. In the saturated region where flow may be dominated by lateral flow, advective (transport by the flowing phase) or convective (transport driven by gradients in fluid density) heat transport may serve to significantly alter both the regional heat transport and the magnitude of the geothermal gradient in the vadose zone. The general approaches taken in this work follow the work of Lachenbruch and Sass (1977). Assuming that conduction, advection, and diffusive transport of latent heat by water vapor are the dominant processes of heat transport in deep vadose zones, the governing one-dimensional equation for heat transport (Sophocleous, 1979) is:
 | [7] |
This equation can be used in an inverse approach to estimate ql through a deep vadose zone if vadose zone temperatures are known. If the fluid flux is uniform, ql can be considered equivalent to the percolation rate (downward) or the discharge rate (upward) through the vadose zone. Solution of Eq. [7] requires initial and boundary conditions, soil thermal properties, and rates of fluid flux to derive the temperature distribution in the vadose zone. Under conditions of large thermal gradients and significant water flow, Eq. [7] must be coupled with the governing equation for the fluid (e.g., Eq. [5]) to obtain the correct thermal and fluid distributions. However, often the distribution of temperatures with depth, either from buried sensors or borehole logs, is the only environmental parameter monitored, such that Eq. [7] may be a reasonable option to obtain estimates of downward, upward, or negligible water flux.
Equation [7] may be simplified by assuming steady-state conditions and that the primary heat transport mechanisms are conduction and advection of heat by the liquid water phase. This represents a significant simplification relative to the previous analysis for stream-channel infiltration, where transient boundary conditions dominate. Tyler et al. (1996) showed that nonisothermal vapor transport in deep vadose zones of southern Nevada may be in the range of 0.02 mm yr-1. Considering the heat content of this amount of vapor, vapor phase latent heat transport would comprise <3% of 1 heat flow unit (where 1 heat flow unit is approximately equal to 4.2 x 10-4 J s-1 m-2) and can probably be ignored when only considering heat flux. Even when the nonisothermal vapor flux is a significant component of the heat budget, it may only vary slightly with depth, provided the thermal gradient is relatively constant and the range of temperature in the vadose zone is small. As a result, the diffusive transport of latent heat can be considered, to first order, to be a constant throughout the deep vadose zone and should not alter the shape of the geothermal gradient, only its magnitude. Therefore, thermal methods can be applied to vadose zones dominated by vapor transport, though the vapor phase component cannot be predicted. However, as shown by Walvoord et al. (1999), vapor transport may have significant impacts on the distribution of water potential in deep vadose zones. Further, if we limit our analysis to regions of small temperature gradients (i.e., deep in the vadose zone where the coupling between water and heat transport is limited), this leads to a more simplified analysis.
Under these assumptions and the assumptions of homogeneity of thermal properties and temporal stability, Eq. [7] can be reduced (Lachenbruch and Sass, 1977; Bredehoeft and Papadopulos, 1965) to the following energy balance for the vadose zone profile:
 | [8] |
Representing the boundary conditions correctly for Eq. [8] requires some discussion. The upper boundary condition can often be considered to be the average annual air temperature. The lower boundary temperature at the water table is more problematic. If the water table is treated as a constant temperature boundary condition, the thermal regime is mathematically decoupled from that of the saturated zone. This limits the need for specific hydraulic details of the saturation zone, with the observed temperature at the water table reflecting the combined effects of steady heat transport in the saturated and unsaturated zones. Such an approach is identical to that of Bredehoeft and Papadopulos (1965), who used the temperature distribution in an aquitard surrounded by aquifers of differing temperatures to estimate leakage through the aquitard. The aquifer temperatures were assumed to be unaffected by the transport of heat through the aquitard. Under conditions of no advective transport of heat in the vadose zone via fluid flux, such an assumption is valid. However, if the rate of water flux is large and hence the rate of advective transport to the water table is large, the groundwater temperatures can be altered by this transport. Sophocleous (1979) pointed out that the analysis of Bredehoeft and Papadopulos (1965) may have limited application in the saturated zone because of thermally driven liquid flow in the aquitard that may significantly affect the thermal distribution and lead to erroneous results. However, for the deep vadose zones at low water contents considered in this work, thermally driven liquid flow is likely to be insignificant because of the small hydraulic conductivity values and small thermal gradients.
Frenchman Flat, Nevada
Frenchman Flat, Nevada is typical of a sediment-filled basin of the Basin and Range Province and is given as an example of the analytical approach. For this deep setting, it is reasonable to assume that the temperature of the bottom water table boundary is constant, and subsequently unaffected by advective heat transport by fluid flux in from the vadose zone. The assumption is valid if groundwater temperatures are primarily governed by factors other than ql and if its value is small. There are many processes that will affect the temperature at the water table, including many that are independent of the vadose zone, such as local volcanic activity or groundwater flow paths, and these factors must be included in a comprehensive analysis of vadose zone temperatures. The vadose zone thermal properties are assumed to be uniform with depth, although they certainly will vary as saturation is approached at the water table. These assumptions may be limiting in some cases and clearly point out the need for additional numerical studies.
Under the above assumptions Eq. [8] can be solved easily to yield the temperature distribution as a function of the fluid flux and vadose zone thermal properties (Bredehoeft and Papadopulos, 1965):
 | [9] |
Temperature data from deep basin-fill vadose zones are relatively limited. Sass et al. (1988) presented a series of vadose and saturated zone temperatures from Yucca Mountain in southern Nevada, and reported generally linear profiles of temperature in this fractured rock vadose zone, suggesting primarily conductive heat transfer. Reynolds Electrical and Engineering Co. (1994) reported vadose zone temperatures from three boreholes completed in Frenchman Flat, which is two basins to the south of Yucca Mountain. Thermocouples were placed at 30- to 60-m intervals in boreholes drilled with air to minimize drilling impact on temperature, then backfilled. The water table is stable at a depth of approximately 240 m at this site. The vadose zone consists primarily of alluvial sediments with low volumetric water contents (8–12%) and was extensively sampled (both chemically and hydraulically) to determine the rate of water flux through the vadose zone. Tyler et al. (1996) reported that based on soil water tracers from these three boreholes, recharge through the vadose zone last occurred at 20 000 and 120 000 yr before present.
Figure 7 shows the vadose zone temperature distribution as measured by thermocouples from PW-1, one of the three boreholes in Frenchman Flat approximately a year after drilling and installation. Temperatures linearly increase from 18.45°C at a depth of 30 m to 20.74°C at a depth of 215 m. The calculated geothermal gradient (0.012°C m-1) is low and is consistent with the generally low heat fluxes observed in the southern Great Basin. The low heat fluxes are postulated to be the result of large-scale, lateral heat transfer in the confined carbonate aquifers at depth (Lachenbruch and Sass, 1977). In Fig. 7 the predicted vadose zone temperatures from Eq. [9] are plotted for downward flux conditions of 1, 10, and 50 mm yr-1. An effective thermal conductivity of 0.8 J s-1 m-1 °C-1 was assumed, which is representative of sand at water contents of approximately 8% by volume (Hillel, 1980; Sophocleous, 1979). The results are somewhat sensitive to the chosen value of effective thermal conductivity and point out the need to include laboratory testing of this parameter along with typical soil physical and hydraulic parameters. At recharge rates <10 mm yr-1 for the thermal properties chosen, the temperature distribution is essentially linear with depth, indicating the dominance of conductive heat transport over heat transported by percolation of cooler water. At higher rates of recharge, the heat transfer is dominated by advection and the shallow vadose zone approaches isothermal conditions. At these higher rates of recharge, it is important to note that the groundwater temperature (the assumed lower constant temperature boundary condition) may be reduced by the recharging waters. At these higher rates of recharge, the choice of a constant lower boundary condition is not entirely correct. However, the linearity in the observed temperature profiles (with a less mean square coefficient, R2 = 0.986) suggests that downward recharge rates are very small. Given the difficulty in resolving fluxes <10 mm yr-1 with Eq. [9], the thermal data indicates very low downward or upward fluxes of <10 mm yr-1. Previous work (Tyler et al., 1996) with chemical tracers suggested that downward migration was essentially zero. Water-potential data from the vadose zone show that hydraulic gradients are upward in the upper approximately 50 m, further reinforcing the concept of negligible recharge through this vadose zone. Recent work by Walvoord et al. (1999) and Phillips et al. (1999) further suggests that downward liquid flux in the vadose zone below 50 m may be balanced by upward vapor flux driven by the thermal gradient. In this case, thermal conduction is the dominant heat transport mechanism and serves to preserve the linear temperature gradient.
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ANALYSIS OF DEEP TEMPERATURE PROFILES UNDERLYING ARID MOUNTAINOUS TERRAIN
The third case study requires a full description of two-phase heat and groundwater transport because of the complex stratigraphy of the fractured bedrock typical beneath mountainous terrain in arid environments. For most deep vadose zone profiles, it is reasonable to assume steady-state conditions, and a heat-balance equation in a partially saturated porous or fractured media can be derived by considering heat-transport processes into and out of a control volume, much as the heat balance would be calculated for a computation cell in a finite difference model as expressed below:
 | [10] |
T is the temperature difference between elevations z2 and z1 (°C), ql,m and qg are the liquid and gas mass fluxes (kg s-1 m-2), cg is the specific heat of the bulk gas (1.1 x 103 J kg-1 0C-1), Hv is the heat of vaporization (2.45 x 106 J kg-1); 
v2 and v1 are the vapor mass fractions of the gas at elevations z2 and z1 (kg kg-1), Dv is the effective water vapor diffusity in air (m2 s-1), and v is the density of vapor (kg m-3). The term on the left side of the equation is the conductive heat flux at elevation z2, which can be thought of as a function of the conductive heat flux at a lower elevation z1 and the changes in the conductive heat flux resulting from the processes of liquid percolation, advective transport of sensible and latent heat in the gas phase, and diffusive transport of latent heat by water vapor. If the heat transport terms associated with gas and vapor transport are small relative to the percolation flux term, the liquid flux can be calculated directly from the temperature profile by considering the difference in the conductive heat flux at elevations z2 and z1 (Rousseau et al., 1999, p. 189). However, because the heat of vaporization (Hv) is quite large compared with other constants in Eq. [10], evaporation of what might normally be considered a small amount of water can have a large effect on the conductive heat flux, so processes that include the Hv term require careful evaluation. The potential significance of evaporative heat consumption can be illustrated by equating heat consumed to maintain thermal equilibrium between the rock and downwardly percolating water with that consumed by evaporation:
 | [11] |
Using the Eq. [10] approach, borehole temperature estimates of water flux suggest several possible advantages and disadvantages over other flux estimation methods. First, measurements of thermal conductivity and subsurface temperature are easy to make compared with measurements of unsaturated hydraulic conductivity and water potential. Second, thermal conductivity is a relatively linear function of saturation, and therefore subject to less uncertainty than other saturation-dependent quantities, such as hydraulic conductivity, that vary logarithmically with saturation. Also, temperature profiles may provide a meaningful long-term average of flux because temperatures below the depths affected by the annual temperature change respond slowly to changes in percolation flux because of the large mass and heat capacity of the rock. Finally, if thermal equilibrium is achieved between the rock and water, temperature measurements made in the rock will reflect the mass rate of water movement in both the matrix and fractures. The most significant disadvantage of deep temperature–based estimates of flux is that other heat transport processes, including vapor diffusion, convective gas transport, barometric pumping (particularly along faults), and topographic effects, may be operating in conjunction with advective liquid flux. Neglecting the effects of these processes without justification may significantly affect temperature-based estimates of flux. Data from beneath Yucca Mountain, Nevada provide an excellent case study of the advantages and limitations of this approach.
Yucca Mountain, Nevada
Mountainous terrain introduces complexities involving topography and air circulation not found when analyzing deep borehole temperature profiles in alluvial basin fill. Topographic effects result from the irregular nature of the surface boundary, which in itself results in a convergence or divergence of heat flow, and from microclimatic variations in ground-surface temperature related to slope aspect (Blackwell et al., 1980). Air circulation induced by topography (Weeks, 1987) increases the potential that the gas-phase transport of heat becomes a nonnegligible component of the overall heat balance.
Beneath Yucca Mountain the vadose zone consists of alternating layers of fractured, welded tuffs and relatively unfractured nonwelded tuffs (Scott et al., 1983). The welded tuffs have higher fracture permeabilities but lower intrinsic permeabilities than the nonwelded vitric tuffs (Montazer and Wilson, 1984; Flint, 1998). The thermal conductivities of the welded tuffs are about 2.0 J s-1 m-1 °C-1, or about twice those of the nonwelded tuffs (Sass et al., 1988). The generalized stratigraphy is shown for two boreholes in Fig. 8a and 8b, and the representative properties for different rock types and for the fracture network are given in Table 1.
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Subsurface convective gas flow at Yucca Mountain is thought to be the result of gas-density differences caused by differences in air temperature and relative humidity inside and outside of Yucca Mountain (Weeks, 1987). Gas chemistry data and borehole gas-flow measurements indicate rapid convection of gas takes place in the shallow welded tuffs above the PTn, but that convective gas flow is slow or absent below the PTn (Thorstenson et al., 1998; Yang et al., 1996). Therefore, although temperature data above the PTn may have been affected by gas flow, temperature data below and within the PTn have probably not been significantly affected by gas-flow processes.
The divergence of heat flux beneath ridges and convergence of heat flux toward washes also is a factor affecting borehole temperature profiles in rugged terrain (Blackwell et al., 1980; Rousseau et al., 1999). Unpublished two-dimensional heat transport simulations across Yucca Crest indicate these effects become less pronounced with depth, in part because the low thermal conductivity PTn obscures the effects of the surface topography on temperatures in the deeper rocks. Therefore, although the one-dimensional numerical simulations presented below cannot account for the effects of topography on heat flow, most of the data used in the percolation estimates originates from depths relatively unaffected by these processes.
Borehole temperature data have been used to estimate percolation flux at Yucca Mountain using both numerical models (Rousseau et al., 1999; Flint et al., 2002; Bodvarsson et al., 2002) and analytical solutions (Bodvarsson et al., 1997). In these analyses, percolation rate was considered to be the only uncertain parameter in the models, and although the sensitivity of the modeled borehole temperatures to percolation rate was examined, no attempts were made to quantify the effects of other uncertain variables. However, there is also some uncertainty in the ground-surface temperatures that are used as the upper boundary condition and in the thermal conductivity values used in the models because of gas-flow processes, seasonal effects in the shallow rocks (Fig. 1) not reflected in the one-time temperature measurements, and microclimatic effects (Blackwell et al., 1980). To investigate the effects of uncertainty in ground-surface temperatures and thermal conductivity on estimates of percolation rate, the numerical model FEHM (Zyvoloski et al., 1997) was coupled with the parameter estimation code PEST (Doherty et al., 1994). PEST provides measures of the uncertainty of the estimates in the form of 95% confidence limits that reflect the combined uncertainty in all estimated parameters and the effects of any correlations that exist between the estimated parameters. Although these are linear confidence limits (i.e., they only reflect the uncertainty near the estimated values) and these confidence limits could change as the estimated values change, these confidence limits provide some indication of the reliability of the estimates. Models were created with the FEHM and PEST codes at two of the 25 or so Yucca Mountain boreholes at which temperature data are available (Sass et al., 1988; Rousseau et al., 1999). The temperature profiles at these two boreholes, WT-2 and H-3, previously were used to estimate recharge rates (Flint et al., 2002). Borehole WT-2 is located in a short, east-trending wash in central Yucca Mountain, and Borehole H-3 is located on Yucca Crest. The models extended from the ground surface to the water table, with a constant vertical grid spacing of 5 m. Although more than 30 separate hydrogeologic units have been identified in the vadose zone at Yucca Mountain (Flint, 1998), the models presented here used a simplified stratigraphy that includes five units, with the properties given in Table 1. Information on the depths of the stratigraphic intervals, major welding changes, and zones of zeolite development were taken from unpublished lithologic logs compiled by the U.S. Geological Survey (R. Spengler, personal communication, 1997) and from geophysical logs (Nelson, 1994, 1996). The simulations assumed a passive gas phase.
Three simulation cases were completed sequentially. For Case 1, percolation and ground-surface temperature at each individual borehole were determined using data only from that borehole. For Case 2, percolation, ground-surface temperature, and thermal conductivity of the welded tuffs (kwelded) at each borehole were determined, using data only from that borehole. For Case 3, percolation, ground-surface temperature, and thermal conductivity of the welded tuffs were determined jointly at both boreholes. In Case 3, flux and ground-surface temperature were allowed to differ between boreholes, but the thermal conductivities of the welded tuffs at both boreholes were assumed to be the same. The estimated values and associated 95% confidence limits are given in Table 2. The measured temperature data and Case 1 simulation results are shown in Fig. 8a and 8b. The results indicate that although the estimated values of ground-surface temperature and percolation flux do not change much when kwelded is also estimated, the uncertainty in the flux and ground-surface temperature increases for Case 2 compared with Case 1, where kwelded is assumed to be known. When temperature data from both boreholes are used to estimate kwelded for Case 3, the uncertainty in each of the estimated parameters decreases compared with Case 2. Thus, if it can be assumed that thermal conductivity is relatively constant for a site, the simultaneous inversion of temperature profiles from multiple boreholes can reduce uncertainty in the percolation flux estimates at individual boreholes when the thermal conductivity and ground-surface temperature are also treated as uncertain parameters.
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CONCLUSIONS
Analysis of temperature profiles provides a promising tool for estimating percolation patterns for all three vadose environments examined in this work. Comparisons of shallow temperature profiles beneath stream channels for the perennial, seasonal, and ephemeral study reaches in New Mexico reveal a reasonable trend in terms of relative rates of focused percolation. Annual percolation rates beneath the perennial flows of the Rio Grande averaged in the 40 mm d-1 range. Seasonal percolation beneath Bear Canyon averaged in the 800 mm d-1 range during winter streamflows. Transient percolation rates beneath the Santa Fe River ranged as high as 2000 mm d-1 during brief flow events lasting only hours. These trends were supported by surface water–based estimates of streambed losses that followed a similar trend in magnitude when comparing the three sites.
A completely different flux pattern emerged from analysis of deep temperature profiles in southern Nevada. The temperature-derived diffuse percolation rates were estimated to be near zero in the deep basin sediments beneath Frenchman Flat and ranged from near zero to approximately 10 mm yr-1 deep beneath Yucca Mountain. Temperature profiles exhibited a robust, increasingly concave patterns as percolation rates reached 10 mm yr-1, in agreement with profiles predicted by both the analytical solution and the complex simulation model. Though the resulting magnitudes represent a negligible flux relative to the magnitudes estimated for focused percolation beneath New Mexico stream channels, the observed temporal stability of deep vadose zone temperature profiles indicates steady, long-term fluxes with potentially wide aerial extent.
ACKNOWLEDGMENTS
The authors would like to thank Jim Bartolino, USGS, for the Rio Grande Data; Amy Lewis, Sangre de Cristo Water, Santa Fe, NM, for surface water data for the Santa Fe River; Amy Stewart, Philip Williams and Associates, San Francisco, CA, for analysis of the Santa Fe River data; and Rich Niswonger, U.C. Davis and USGS, for analysis of the Bear Canyon data. The authors would also like to thank Joe Rousseau, USGS, and Paul "Ty" Ferre, University of Arizona, for thoughtful reviews. Efforts of the second author were funded in part by National Science Foundation Grant EAR-9614646.
REFERENCES
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  M. REITER Vadose Zone Temperature Measurements at a Site in the Northern Albuquerque Basin Indicate Ground-Surface Warming due to Urbanization Environmental and Engineering Geoscience, November 1, 2006; 12(4): 353 - 360. [Abstract] [Full Text] [PDF]
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 Y. Mori, J. W. Hopmans, A. P. Mortensen, and G. J. Kluitenberg Estimation of Vadose Zone Water Flux from Multi-Functional Heat Pulse Probe Measurements Soil Sci. Soc. Am. J., April 11, 2005; 69(3): 599 - 606. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 K. W. Blasch, T. P. A. Ferre, and J. P. Hoffmann A Statistical Technique for Interpreting Streamflow Timing Using Streambed Sediment Thermographs Vadose Zone J., August 1, 2004; 3(3): 936 - 946. [Abstract] [Full Text] [PDF]
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|
|
|
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M. Reiter Continuous Temperature Logging in Air across the Deep Vadose Zone Vadose Zone J., August 1, 2004; 3(3): 982 - 989. |
