Jim Constantz

Quantifying surface water–groundwater interactions using time series analysis of streambed thermal records: Method development

[1] We present a method for determining streambed seepage rates using time series thermal data. The new method is based on quantifying changes in phase and amplitude of temperature variations between pairs of subsurface sensors. For a reasonable range of streambed thermal properties and sensor spacings the time series method should allow reliable estimation of seepage rates for a range of at least ±10 m d � 1 (±1.2 � 10 � 2 ms � 1 ), with amplitude variations being most sensitive at low flow rates and phase variations retaining sensitivity out to much higher rates. Compared to forward modeling, the new method requires less observational data and less setup and data handling and is faster, particularly when interpreting many long data sets. The time series method is insensitive to streambed scour and sedimentation, which allows for application under a wide range of flow conditions and allows time series estimation of variable streambed hydraulic conductivity. This new approach should facilitate wider use of thermal methods and improve understanding of the complex spatial and temporal dynamics of surface water–groundwater interactions.

Influence of diurnal variations in stream temperature on streamflow loss and groundwater recharge

We demonstrate that for losing reaches with significant diurnal variations in stream temperature, the effect of stream temperature on streambed seepage is a major factor contributing to reduced afternoon streamflows. An explanation is based on the effect of stream temperature on the hydraulic conductivity of the streambed, which can be expected to double in the 0° to 25°C temperature range. Results are presented for field experiments in which stream discharge and temperature were continuously measured for several days over losing reaches at St. Kevin Gulch, Colorado, and Tijeras Arroyo, New Mexico. At St. Kevin Gulch in July 1991, the diurnal stream temperature in the 160-m study reach ranged from about 4° to 18°C, discharges ranged from 10 to 18 L/s, and streamflow loss in the study reach ranged from 2.7 to 3.7 L/s. On the basis of measured stream temperature variations, the predicted change in conductivity was about 38%; the measured change in stream loss was about 26%, suggesting that streambed temperature varied less than the stream temperature. At Tijeras Arroyo in May 1992, diurnal stream temperature in the 655-m study reach ranged from about 10° to 25°C and discharge ranged from 25 to 55 L/s. Streamflow loss was converted to infiltration rates by factoring in the changing stream reach surface area and streamflow losses due to evaporation rates as measured in a hemispherical evaporation chamber. Infiltration rates ranged from about 0.7 to 2.0 m/d, depending on time and location. Based on measured stream temperature variations, the predicted change in conductivity was 29%; the measured change in infiltration was also about 27%. This suggests that high infiltration rates cause rapid convection of heat to the streambed. Evapotranspiration losses were estimated for the reach and adjacent flood plain within the arroyo. On the basis of these estimates, only about 5% of flow loss was consumed via stream evaporation and stream-side evapotranspiration, indicating that 95% of the loss within the study reach represented groundwater recharge.

Field study and simulation of diurnal temperature effects on infiltration and variably saturated flow beneath an ephemeral stream

Two experiments were performed to investigate flow beneath an ephemeral stream and to estimate streambed infiltration rates. Discharge and stream-area measurements were used to determine infiltration rates. Stream and subsurface temperatures were used to interpret subsurface flow through variably saturated sediments beneath the stream. Spatial variations in subsurface temperatures suggest that flow beneath the streambed is dependent on the orientation of the stream in the canyon and the layering of the sediments. Streamflow and infiltration rates vary diurnally: Streamflow is lowest in late afternoon when stream temperature is greatest and highest in early morning when stream temperature is least. The lower afternoon Streamflow is attributed to increased infiltration rates; evapotranspiration is insufficient to account for the decreased Streamflow. The increased infiltration rates are attributed to viscosity effects on hydraulic conductivity from increased stream temperatures. The first set of field data was used to calibrate a two-dimensional variably saturated flow model that includes heat transport. The model was calibrated to (1) temperature fluctuations in the subsurface and (2) infiltration rates determined from measured Streamflow losses. The second set of field data was to evaluate the ability to predict infiltration rates on the basis of temperature measurements alone. Results indicate that the variably saturated subsurface flow depends on downcanyon layering of the sediments. They also support the field observations in indicating that diurnal changes in infiltration can be explained by temperature dependence of hydraulic conductivity. Over the range of temperatures and flows monitored, diurnal stream temperature changes can be used to estimate streambed infiltration rates. It is often impractical to maintain equipment for determining infiltration rates by traditional means; however, once a model is calibrated using both infiltration and temperature data, only relatively inexpensive temperature monitoring can later yield infiltration rates that are within the correct order of magnitude.

Analysis of streambed temperatures in ephemeral channels to determine streamflow frequency and duration

Spatial and temporal patterns in streamflow are rarely monitored for ephemeral streams. Flashy, erosive streamflows common in ephemeral channels create a series of operational and maintenance problems, which makes it impractical to deploy a series of gaging stations along ephemeral channels. Streambed temperature is a robust and inexpensive parameter to monitor remotely, leading to the possibility of analyzing temperature patterns to estimate streamflow frequency and duration along ephemeral channels. A simulation model was utilized to examine various atmospheric and hydrological upper boundary conditions compared with a series of hypothetical temperature-monitoring depths within the streambed. Simulation results indicate that streamflow events were distinguished from changing atmospheric conditions with greater certainty using temperatures at shallow depths (e.g., 10–20 cm) as opposed to the streambed surface. Three ephemeral streams in the American Southwest were instrumented to monitor streambed temperature for determining the accuracy of using this approach to ascertain the long-term temporal and spatial extent of streamflow along each stream channel. Streambed temperature data were collected at the surface or at shallow depth along each stream channel, using thermistors encased in waterproof, single-channel data loggers tethered to anchors in the channel. On the basis of comparisons with site information, such as direct field observations and upstream flow records, diurnal temperature variations successfully detected the presence and duration of streamflow for all sites.

Temperature-Profile Methods for Estimating Percolation Rates in Arid Environments

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.

Stream bed temperature profiles as indicators of percolation characteristics beneath arroyos in the Middle Rio Grande Basin, USA

Stream bed temperature profiles were monitored continuously during water year 1990 and 1991 (WY90 and 91) in two New Mexico arroyos, similar in their meteorological features and dissimilar in their hydrological features. Stream bed temperature profiles between depths of 30 and 300 cm were examined to determine whether temporal changes in temperature profiles represent accurate indicators of the timing, depth and duration of percolation in each stream bed. These results were compared with stream flow, air temperature, and precipitation records for WY90 and 91, to evaluate the effect of changing surface conditions on temperature profiles. Temperature profiles indicate a persistently high thermal gradient with depth beneath Grantline Arroyo, except during a semi-annual thermal reversal in spring and autumn. This typifies the thermal response of dry sediments with low thermal conductivities. High thermal gradients were disrupted only during infrequent stream flows, followed by rapid re-establishment of high gradients. The stream bed temperature at 300 cm was unresponsive to individual precipitation or stream flow during WY90 and 91. This thermal pattern provides strong evidence that most seepage into Grantline Arroyo failed to percolate at a sufficient rate to reach 300 cm before being returned to the atmosphere. A distinctly different thermal pattern was recorded beneath Tijeras Arroyo. Low thermal gradients between 30 and 300 cm and large diurnal variations in temperature, suggest that stream flow created continuous, advection-dominated heat transport for over 300 days, annually. Beneath Tijeras Arroyo, low thermal gradients were interrupted only briefly during periodic, dry summer conditions. Comparisons of stream flow records for WY90 and 91 with stream bed temperature profiles indicate that independent analysis of thermal patterns provides accurate estimates of the timing, depth and duration of percolation beneath both arroyos. Stream flow loss estimates indicate that seepage rates were 15 times greater for Tijeras Arroyo than for Grantline Arroyo, which supports qualitative conclusions derived from analysis of stream bed temperature responses to surface conditions.

Monitoring moisture storage in trees using time domain reflectometry

Abstract Laboratory and field tests were performed to examine the feasibility of using time domain reflectometry (TDR) to monitor changes in the moisture storage of the woody parts of trees. To serve as wave guides for the TDR signal, pairs of stainless steel rods (13 cm long, 0.32 cm in diameter, and 2.5 cm separation) were driven into parallel pilot holes drilled into the woody parts of trees, and a cable testing oscilloscope was used to determine the apparent dielectric constant. A laboratory calibration test was performed on two sapwood samples, so that the relation between the volumetric water content and the apparent dielectric constant of the sapwood could be determined over a range of water contents. The resulting calibration curve for these sapwood samples was significantly different than the general calibration curve used for soils, showing a smaller change in the apparent dielectric constant for a given change in the volumetric water content than is typical for soils. The calibration curve was used to estimate the average volumetric water content to a depth of 13 cm in living trees. One field experiment was conducted on an English walnut tree ( Juglans regia ) with a diameter of 40 cm, growing in a flood-irrigated orchard on a Hanford sandy loam near Modesto, California (U.S.A.). Rods were driven into the tree at about 50 cm above the soil surface and monitored hourly for the month of August, 1988. The moisture content determined by TDR showed a gradual decrease from 0.44 to 0.42 cm 3 cm −3 over a two week period prior to flood irrigation, followed by a rapid rise to 0.47 cm 3 cm −3 over a four day period after irrigation, then again a gradual decline approaching the next irrigation. A second field experiment was made on ten evergreen and deciduous trees with diameters ranging from 30 to 120 cm, growing in the foothills of the Coast Range of central California. Rods were driven into each tree at 50 to 100 cm above the soil surface and monitored on a biweekly to monthly basis for over a year. Most trees showed an early spring maximum in moisture content determined by TDR associated with leaf growth, and a late summer minimum in moisture content associated with the end of the dry season. Moisture contents ranged from 0.20 to 0.70 cm 3 cm −3 , with an annual percentage change in moisture of 15% to 70% depending on species and environmental conditions. A final field test was performed in northern New Mexico (U.S.A.) to examine the effect of trunk freezing on TDR measurements. This test confirmed that freezing conditions were recorded as a total loss of liquid water by the TDR method. These results suggest that further TDR calibration for wood, plus some understanding of the relation between tree moisture and physiological stress could be useful to several disciplines, ranging from irrigation scheduling to watershed management to forest ecology.

The temperature dependence of ponded infiltration under isothermal conditions

Abstract A simple temperature-sensitive modification to the Green and Ampt infiltration equation is described; this assumes that the temperature dependence of the hydraulic conductivity is reciprocally equal to the temperature dependence of the viscosity of liquid water, and that both the transmission zone saturation and the wetting front matric potential gradient are independent of temperature. This modified Green and Ampt equation is compared with ponded, isothermal infiltration experiments run on repacked columns of Olympic Sand and Aiken Loam at 5, 25, and 60°C. Experimental results showed increases in infiltration rates of at least 300% between 5 and 60°C for both soil materials, with subsequent increases in cumulative infiltration of even greater magnitudes for the loam. There is good agreement between measured and predicted initial infiltration rates at 25°C for both soil materials, yet at 60°C, the predicted results overestimate initial infiltration rates for the sand and underestimate initial rates for the loam. Measurements of the wetting depth vs. cumulative infiltration indicate that the transmission zone saturation increased with increasing temperature for both soil materials. In spite of this increased saturation with temperature, the final infiltration rates at both 25 and 60°C were predicted accurately using the modified Green and Ampt equation. This suggests that increased saturation occurred primarily in dead-end pore spaces, so that transmission zone hydraulic conductivities were unaffected by these temperature-induced changes in saturation. In conclusion, except for initial infiltration rates at 60°C, the measured influence of temperature on infiltration rates was fully accounted for by the temperature dependence of the viscosity of liquid water.

Comparison of Isothermal and Isobaric Water Retention Paths in Nonswelling Porous Materials

Water in porous media near the Earths surface is subject to large fluctuations in pore water pressure and temperature, often causing significant changes in the degree of saturation. Quantitative comparisons of isothermal versus isobaric water retention are necessary to accurately predict changes in saturation due to the coupled influence of changes in the pore water matric potential ψ and temperature T. Yet there is a lack of experimental measurements of isobaric (i.e., constant ψ) water retention, inhibiting comparisons between isobaric and isothermal processes. In the present study the influence of the chronological sequence of changes in ψ and T is examined to determine whether the volumetric water content θ for any given final ψ-T condition is independent of the ψ-T sequence, when θ changes monotonically. To obtain the necessary data for these comparisons, isothermal water retention experiments were performed over a range in ψ from 0 to −100 kPa, and isobaric water retention experiments were performed at 20° and 80°C on core samples of a sandy soil and a nonwelded tuff. Results provide further evidence that the effect of T on ψ is considerably greater than estimates based on pore water capillary theory. For these materials the thermal enhancement of ψ was 4–12 times greater than capillary theory would predict. The effect of T on θ during isobaric water retention was several times greater for drying (warming) conditions than for wetting (cooling) conditions at a given ψ, resulting in net losses in θ ranging from 3 to 30%. For a given final ψ at 80°C, virtually identical θ values were obtained regardless of the chronological sequence of isothermal and isobaric drainage paths for both materials. This confirms the validity of unique θ (ψ, T) surfaces describing monotonic changes in θ as functions of both ψ and T in nonswelling porous materials. Determination of these θ (ψ, T) response surfaces for drying and wetting should yield water retention envelopes, useful in modeling water retention in near-surface environments where both ψ and T vary.

Confirmation of rate-dependent behavior in water retention during drainage in nonswelling porous materials

In the water retention process in porous material, changes in water content are assumed to be independent of the rate at which the matric potential varies. Periodically, researchers have presented results that do not support this assumption, indicating that water retention may be rate-dependent under certain conditions. In the present study, long-term experiments were performed on five porous materials in which core samples were drained at different rates down to matric potentials of −50 kPa. Comparisons of these results with previous results confirm that slight rate-dependent behavior occurs during drainage of porous materials in this matric potential range. Specifically, new and previous results indicate that on average 4–5% more water was retained for a slow, multistep drainage versus a fast, one-step drainage treatment. For the present study, average results for individual materials were variable, ranging from a 1 to a 10% difference in water content due to treatment. Several possible mechanisms for the observed rate-dependent behavior are discussed. The only plausible mechanism is related to variations in pore water salt concentrations that induce differences in the pore water surface tension for fast versus slow drainage. Regardless of the mechanism, results suggest that rate-dependent behavior during water retention may contribute to an enhanced temperature dependence of water retention, due to higher rates of water redistribution at higher temperatures.