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TECHNICAL REPORTS

Vadose Zone Processes and Chemical Transport

Determining Long-Term (Decadal) Deep Drainage Rate Using Multiple Tracers

Dep. of Soil Science, Univ. of Saskatchewan, Saskatoon, SK, Canada

^* Corresponding author (Bing.Si{at}usask.ca).

Received for publication January 14, 2007.

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 
The deep drainage rate is a critical hydrological parameter in understanding contamination mechanisms of soil and groundwater. Little research has been conducted on the temporal variations in deep drainage rate during the last century. The objective of this study was to determine the long-term deep drainage rate on a cultivated loamy soil in the Canadian Prairies. Three tracers were used: KCl applied in 1971, fallout tritium in 1963, and NO₃^– released during the initial cultivation of the field (1923). Two soil cores to a depth of 3.6 m were taken along a flat portion of the field, and soil Cl^–, ³H, and NO₃^– concentrations were measured as a function of depth. An additional four cores were taken for soil water content measurements between 2000 and 2003. Distinct peaks in the depth distribution of these three tracers were located at 1.27 m for Cl^–, 1.31 m for ³H, and 1.52 m for NO₃^–, 32, 40, and 80 yr after the application of Cl^–, ³H, and NO₃^–, respectively. The average deep drainage rates, calculated as the product of the estimated tracer velocity and volumetric soil water content below the active root zone, were 2.0 mm yr^–1 from the Cl^– tracer, 2.2 mm yr^–1 from ³H, and 2.5 mm yr^–1 from the NO₃^– tracer. Therefore, there was little temporal variability in the groundwater recharge over the eight decades that the field has been cultivated. The recharge rates are less than 1% of the mean annual precipitation (333 mm).

Abbreviations: MPA, mass per unit area • ZFP, zero flux plane

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 
DEEP drainage rate is the downward water flux at the bottom of the root zone, and is a critical hydrological parameter for understanding soil and groundwater contamination (Scanlon and Cook, 2002). Reports indicate that the deep drainage rate varies considerably in different climate zones and geomorphologic settings (Allison and Forth, 1982; Gee and Hillel, 1988; Hayashi et al., 1998; La Salle et al., 2001; Phillips, 1994). Methods for measurement of recharge rate are well developed for humid regions because groundwater is shallow and the recharge rate is high. However, in arid and semiarid regions, an unsaturated zone generally occurs between the groundwater and the soil surface and the groundwater recharge rate is very small and difficult to quantify (Gee and Hillel, 1988).

Recharge rates in semiarid zones have been determined with a variety of techniques, including estimates based on the water balance of bodies of surface water and groundwater (Allison et al., 1994; Scanlon et al., 2002). Groundwater balance methods based on the dilution of tracers or groundwater level rise, provide reasonable estimates of recharge rates. However, they integrate over a large area, which makes the method inappropriate for estimation of the recharge rate at a specific location. The water balance of a surface water body can give an accurate estimate of ground water recharge underneath that body, but does not provide an estimate of recharge rate in other landscape positions or during periods when the depression is dry. Methods for measurement of the soil water flux in unsaturated soil below the root zone are desirable.

Unsaturated zone methods can be classified into water balance, Darcy's law, zero flux plane, lysimeter, flux meter (Gee et al., 2002), and tracer methods. Water balance or numerical modeling may require estimates of unsaturated hydraulic parameters, especially the hydraulic conductivity, which can vary over orders of magnitude. Water balance or numerical modeling methods are generally applied to large areas because of difficulty of measuring local rainfall and evaporation rates (Gee and Hillel, 1988). Moreover, a long time series of data is needed to obtain a long-term average of the recharge. Lysimeter and flux meter methods have been used for estimation of local groundwater recharge (Scanlon et al., 2005), but are destructive during initial installation. The zero-flux plane (ZFP) is the plane in the soil profile where the vertical hydraulic gradient is zero and groundwater recharge rate should be equal to the decrease in soil water storage below ZFP. To locate the position of the ZFP, we need accurate soil matric potential and soil water content measurements, which are not possible with current technologies. The ZFP method is most applicable to locations with high recharge rates (Scanlon et al., 2002) where measurement errors in soil water and matric potential are relatively small.

Environmental tracer methods estimate the infiltration rate or age of water at a given depth based on in situ concentrations of a natural tracer. Natural tracers like different forms of water (²H, ³H, and ¹⁸O) (Phillips, 1994) and some other presumably conservative solutes (³⁶Cl^–, Cl^–, NO₃^–), have been used to determine soil water flux. Precipitation ³H and ³⁶Cl^– are radioactive and present in the fallout of open-air atomic bomb tests; ³H peaked in 1963, and ³⁶Cl in 1955. Environmental tracers can provide information on current water fluxes and long-term net water fluxes for up to thousands of years (Allison and Forth, 1982). A complication in the interpretation may arise when a tracer occurs in both the liquid and vapor phases (Scanlon, 1992; Phillips, 1994).

Because of many uncertainties in determining water fluxes in arid areas, and extensive spatial and temporal variability in soil properties, vegetation, and precipitation, generalized conclusions about recharge rates at a specific site are difficult to draw (Scanlon et al., 2002). Detailed investigations are required to determine the nature, magnitude, and direction of water fluxes at specific locations. Research has indicated the strong spatial variability and long-term variation (e.g., over thousands of years) of deep drainage rate (Scanlon et al., 2002), but temporal variation of groundwater recharge on decadal scales is not well documented. The latter information is important because information from the last century is more pertinent to decision making and management than the recharge rate thousands of years ago. The objectives of this article are to determine the deep drainage rate from multiple tracers and to examine the temporal variation of deep drainage rate.

	Materials and Methods

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 
The study site, located at Laura, Saskatchewan, Canada (51°52' N, 107°18' W; Fig. 1 ) is described by Dyck et al. (2003). Surficial sediments were deposited by a glacial lake during the Wisconsin deglaciation (Christiansen, 1979), resulting in a thick glacial-lacustrine formation. The site is classified as semiarid (Lloyd, 1986), with an average annual precipitation of 333 mm (40% in the form of snow) and annual monthly average temperature of 2.1°C (Fig. 2 ). The growing season is from May to September, and temperature is generally below zero from November to March. Air temperatures warm up in April, resulting in quick snowmelt.

View larger version (74K): [in this window] [in a new window]   Fig. 1. Geographic location of the research site at Laura, Saskatchewan, Canada.

View larger version (29K): [in this window] [in a new window]   Fig. 2. Difference between (a) annual precipitation and long-term annual average and (b) annual average temperature and long-term average. Dashed lines represent the long-term average. Climate data are collected from a nearby location Saskatoon, Saskatchewan, Canada (Environment Canada, 2007).

More than 70% of the cultivated land in the Canadian Prairies is in rolling landscape. The selected site is very typical of a knoll in the Canadian Prairies, and was investigated intensively by Dyck et al. (2003) and Woods et al. (2006). Dyck et al. (2003) showed small spatial variability in the mean Cl^– travel distance from 50 soil cores along a 10-m-long transect, suggesting two cores will suffice to characterize groundwater recharge rate. In the summer of 2003, 32 yr after the last tracer application, two 53-mm-diameter cores were taken to 4-m depth with a drill rig along the same transect. The two cores were taken at the south end of the plot that had a total KCl application of 33.6 Mg ha^–1. Our sampling locations were within the 10-m-long transect that was sampled by Dyck et al. (2003) in 2000 and are 2 and 6 m, respectively, into the transect from the south end. Each core was sliced immediately into 0.15-m segments that were wrapped with aluminum foil to prevent moisture loss due to evaporation, as recommended by the Environmental Isotope Laboratory (EIL) at the University of Waterloo.

For each core, 14 to 15 0.15-m segment samples were selected for tritium analysis. For the two cores, a total of twenty-nine samples were sent to EIL for tritium analysis. Water was extracted from each sample using toluene and tritium content was determined by liquid scintillation counting (LSC). Tritium measurements [counts per minute (cpm)] were converted directly into tritium units (TU = 1 tritium atom per 10¹⁸ water molecules). The system had a detection limit of 6 TU.

All samples were subsequently air-dried, homogenized, and analyzed for air-dry water content, bulk density, and Cl^– and NO₃^– concentration. For Cl^– and NO₃^–, 5 g of the air-dried soil sample was put into a test tube and 10 g of water was added, and the tube was then shaken for 30 min. The suspension in the test tube was filtered through #42 (0.7 µm) Whatman filter paper (Whatman, Brentford, England) into another clean container and the 2:1 (weight based) water/soil extract was analyzed for Cl^– and NO₃^–concentration using an auto analyzer (Technicon Corp., Terrytown, NY). The Cl^– and NO₃^– concentrations were corrected to oven-dry based concentration and expressed as g g^–1 soil, which was subsequently converted to volume-based concentration (µg cm^–3) by multiplying the weight-based concentration by the bulk density of the segment.

To examine the temporal variation of soil water content and to determine the active root zone, soil water content as a function of depth at the same transect near the two soil cores taken for Cl^–, ³H, and NO₃^–, was measured at different times in 2000, 2001, 2002, and 2003 by taking undisturbed soil cores to a depth of 3.6 m. Soil water content and bulk density were determined using the gravimetric method.

Mass-balance and depth-to-peak methods are the two most popular methods for calculating groundwater recharge rate from the measured depth distribution of Cl^–, ³H, and NO₃^– (Scanlon et al., 2002; Heilweil et al., 2006). The mass-balance approach requires that the input be known exactly. However, for ³H, it is not possible because tritium input varies with geographic locations and we do not have measurements of tritium concentration in precipitation in a nearby location. For NO₃^–, the original mass of release from the first cultivation is unknown. However, we know the application rate of Cl^–; there is always some pedogenetic Cl^– in the soil profile. The background Cl^–, albeit minute and having minimal effect on mass balance, could affect the mean travel distance because mean travel distance is strongly affected by the long tail of a breakthrough curve. For all these reasons, the depth to peak method is considered to be more accurate than the mass balance methods (Heilweil et al., 2006) and is widely used (Scanlon et al., 2002). Therefore, we choose the depth to peak method to calculate recharge rates for all three tracers.

Different methods have been used in the literature to calculate the peak locations of the tracers including curve fitting (Joshi and Maule, 2000) and the intersection of two tangent lines, one on each arm of the curve (Ward, 2003). To reduce uncertainty, we used a log-normal distribution curve to fit the measured concentration as a function of depth. We used a log-normal distribution curve, because it is widely used (Dyck et al., 2003) and fits our data very well. The peak depth is defined as the depth that has the highest concentration, and is determined from the fitted log-normal distribution curve. The calculated peak location for the three tracers is shown in Table 1 along with the soil water content for that depth. Having identified the peak depth of each of the three tracers (Cl^–, ³H, and NO₃^–) and their corresponding time of entering the soil, we can calculate their residence time and travel velocity (or pore water velocity; defined as the flow rate of water and calculated by dividing the water flux density by the volumetric soil water content) in the soil profile. There are many methods available for determining the travel velocity; we used the active root zone method (Scanlon et al., 2002) in this study. The pore water velocity was calculated by dividing the difference between the depth of peak location and the active root zone depth by the residence time. We assumed a negligible travel time from the soil surface to the bottom of active root zone. This is justified because an average precipitation rate is 333 mm yr^–1, a root zone depth is about 1 m, and typical moisture content is about 0.30 m³ m^–3, implying that water in the root zone should have a mean residence time of about one year. The recharge rate was then obtained by multiplying pore water velocity by the average soil water content within the zone between the peak and the bottom of the active root zone. Therefore, thickness of the active root zone affects the recharge rate calculated with this active root zone method. We also used a differential method: pore velocity was obtained by dividing the difference between the two tracer peak depths by the difference in residence times. Then, the recharge rate was calculated as the product of pore water velocity and the average soil water content between the two peak depths. Recharge rates calculated using the differential method do not depend on the defined thickness of the active root zone (Joshi and Maule, 2000).

	Results and Discussion

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

View larger version (16K): [in this window] [in a new window]   Fig. 3. Depth distribution of sand content and soil water content () at different times in 4 yr.

View larger version (15K): [in this window] [in a new window]   Fig. 4. Depth distribution of (a) 3H, (b) Cl–, and (c) NO3– concentration in the two cores (pooled data).

The NO₃^– profile distribution was more complex than the ³H and Cl^– profiles. The NO₃^– concentration decreased with depth from 0 to 0.8 m, consistent with the degradation of plant residue during the 2002 fallow year (Fig. 4c). The NO₃^– concentration increased from 0.8 to about 1.7 m, and then NO₃^– decreased with increasing depth to about 15 µg NO₃^––N cm^–3 at the 3-m depth. The NO₃^– bulge was unlikely to have originated from chemical fertilizer: in summer fallow–crop rotation, less than 5 kg fertilizer N ha^–1 was usually applied every second year. Therefore, the NO₃^– bulge must originate from a natural source. The NO₃^– bulges were also found in desert soils (Walvoord et al., 2003). Because a Cl^– bulge was at the same depth as the NO₃^– bulge, Walvoord et al. (2003) attributed both to NO₃^– and Cl^– accumulation in subsoil zones of arid regions throughout the Holocene. In our study, the natural Cl^– bulge was between 2.0 and 2.5 m (Fig. 5 ), which was well below the NO₃^– bulge. Therefore, the NO₃^– bulge, in contrast to the natural Cl^– bulge, was not likely a result of 10,000 yr of accumulation since deglaciation. Research at 150 km south of Laura, Saskatchewan, indicated that the cultivation of native grassland caused a bulge of NO₃^– in the soil profile (Campbell et al., 1975). The NO₃^– bulge at about 1.6 m was thus attributed to the initial breaking of the native grassland; however, the exact time for conversion of native grassland to cultivated land is unknown. The field was sold to a farmer in 1920 by the Canadian government and we assumed that the land was broken in about 1923.

View larger version (13K): [in this window] [in a new window]   Fig. 5. Depth distribution of natural Cl– concentration at a plot. The soil core was taken to the depth of 6 m. The sampling interval was 0.3 m. Landscape position of the core was similar to Fig. 4.

The above method assumed that the tracers move to the base of the active root zone in a short time (negligible compared to the total travel time). This assumption is justified for long-term tracer studies. While the assumed thickness of the active root zone is close to the value used by others (1.20 m) in the Canadian Prairies, significant errors could be introduced if the peak depth is not far below the rooting depth. To reduce the uncertainty associated with these assumptions, we also used the differential method for determining the recharge rate (Table 2 ): we calculate groundwater recharge rate (J, mm yr^–1) as: J=t^–1·(z)dz, where z₁ (mm) and z₂ (mm) are the depths to peak of two tracers introduced at time t₁ (yr)and t₂ (yr), respectively; and t = t₂–t₁. The calculated recharge rates varied between 1.3 to 1.7 mm yr^–1 (Table 2), similar to the active root zone recharge rate estimates in Table 1. This suggests that the tracers spent only a fraction of their residence time in the root zone.

In humid regions, preferential flow is reported as one of the major components contributing to groundwater recharge (Carey and Feng, 2004). However, preferential flow may be negligible at the site. First, the site consists of a loamy soil and the clay content is not high enough for the formation of continuous deep cracks; the active root zone is only 1 m, precluding the presence of significant root channels below that depth. Second, the site was under conventional tillage, which tends to destroy vertical cracks near the soil surface, diminishing the possibility for rainfall entering continuous deep cracks. Furthermore, the rainfall intensity and duration may be able to wet the soil surface, but there is a lack of the continuous deep cracks and root channels to transport water from soil surface to below the root zone. Therefore, the lack of continuous deep flow channels and the rainfall characteristics suggests that preferential flow may not be important for this site.

Scanlon (1992) and Phillips (1994) found that in desert soils, the ³H peak depth was deeper than ³⁶Cl^–, even though the peak of ³⁶Cl^– release was ten year earlier than ³H. Deeper penetration of ³H relative to that of ³⁶Cl^– was attributed to enhanced downward movement of ³H in the vapor phase. The vapor flux was calculated as 6 mm yr^–1 while the liquid water flux was 1.4 mm yr^–1 (Scanlon, 1992). We calculated the non-isothermal vapor diffusion rate in the soil based on soil temperature measurements at a near weather station (Fig. 6 ; Environment Canada, 2007). The annual net vapor flux is 0.02 mm yr^–1 (Appendix B), indicating the net downward flow of vapor is <5% of the liquid water flux (Tables 1 and 2). Considering the measurement errors, the annual net vapor flux is negligible. In addition, the calculated fluxes based on the three tracers are similar, further supporting the conclusion that vapor transport is negligible. The difference in the magnitude of vapor vs. liquid water flux between Scanlon (1991) and our study may be attributed to the soil and climate characteristics in the prairies region. At depth, soil water content was much higher than that of a sandy soil in the desert, resulting in smaller air-filled porosity, diffusion coefficient, and vapor fluxes. In addition, the longer summer in the desert may cause a prolonged period of high surface temperature and thus higher downward vapor flow in the desert.

View larger version (11K): [in this window] [in a new window]   Fig. 6. Monthly soil temperature at 100- and 150-cm depth and the vapor water flux based on soil temperature gradient between the two depths. The soil temperature data are the monthly normal from 1971 to 2003, obtained from the Saskatoon SRC weather station.

[1]

where K_h is the Henry's constant of vapor (K_h = 1.75 x 10^–5 at 293K), D_A (m² yr^–1) is the vapor diffusion coefficient in air, is the tortuosity, and f_a is the air-filled porosity (m³ m^–3). The calculated diffusion coefficient is five orders of magnitude smaller than that of ¹H vapor. The negligible vapor diffusion rate (0.02 mm yr^–1), plus the much smaller diffusion coefficient of ³H than vapor, suggest that ³H movement in our soil is mainly through the liquid form and that vapor diffusion is negligible for groundwater recharge rate determination in this study.

The Cl^– profile has very steep concentration gradients. This may lead to enhanced molecular diffusion in the liquid phase. The diffusion coefficient D_L (m² yr^–1) in the liquid phase can be calculated as (Hu and Wang, 2003):

[2]

where D₀ (m² yr^–1) is the diffusion coefficient in water. Assuming soil water content is 0.3 m³ m^–3, the calculated diffusion coefficient for Cl^– at 25°C is 1.9 x 10^–6 cm² s^–1, well within the measured range (10^–5 to 10^–6 cm² s^–1) of diffusion coefficients collected from a variety of materials (Hu and Wang, 2003). The large diffusive coefficient, supported by Nye and Tinker (1977), resulted from the large soil water content (= 0.30 m³ m^–3). Cubic splines were fitted to the observed Cl^– concentration profiles (C(z)) and the first-order derivatives with respective to depth z were calculated. The diffusive flux was estimated as the product of D_L and the maximum first-order derivative of C(z) with respect to z. The calculated soil water flux due to diffusion is 0.01 mm yr^–1, which is quite small relative to the water flux calculated from the displacement of peak location. Furthermore, the water flux above the peak is upward and has the same magnitude as the downward flux, suggesting that the diffusive flux has a minimum effect on the peak location. Therefore, it is reasonable to assume that the peak location is dominated by convective water movement. Scanlon (1991) also reported a negligible diffusive soil water flux in the sandy desert soils.

It is not surprising that the recharge rates obtained in humid regions are much higher than what we obtained at the research site. The recharge rate estimated in this study is at the lower limit of the recharge rate estimated in the Canadian Prairies (Meyboom, 1966; Zebarth et al., 1989). Hayashi et al. (1998) estimated the recharge rate below a prairie pothole is about 2 to 6 mm yr^–1 based on natural chloride cycles. Lower landscape positions will have higher recharge rates than the upslope positions due to accumulation of snow and runoff in depressions (Derby and Knighton, 2001; Hayashi et al., 2003). Remenda et al. (1996) reported a negligible recharge rate at Warman (15 km north of Saskatoon). This is because there are thick tills in Warman, while the Laura site has only a relatively thin varved layer (Appendix A). Woods et al. (2006) observed strong topography dependence of mean travel depth of applied Cl^– at the same site as our study, suggesting that for the same hydrogeological setting, topography is an important factor controlling deep drainage rates. Dyck et al. (2003) obtained a recharge rate of 3 mm yr^–1 for the study site. Their estimates were based on moment analysis of the depth distribution of applied chloride. We did not use the moment analysis for determination of solute travel velocity, because depth distribution of chloride shows that not all the chloride is below the active root zone, which may give rise to errors (Tyler and Walker, 1994).

The uncertainty associated with the recharge rate estimates was also analyzed. From the 50 cores taken along the 10-m-long transect, Dyck et al. (2003) found that the horizontal coefficient of variation of the calculated mean Cl^– travel depths was 4%. Since the two cores were taken along the same transect and same methods of soil sampling and laboratory analysis were used in this study and in Dyck et al. (2003), we expect the same spatial variability for Cl^– as Dyck et al. (2003). Given the similar transport properties of ³H, NO₃^–, and Cl^–, we expect similar spatial variability for all three tracers in this study. However, there may be higher uncertainty associated with ³H and NO₃^– because of larger measurement errors in ³H and stronger spatial variability in NO₃^– than in Cl^–. The standard deviation of soil water content measured along the 10 m transect is about 0.02 m³ m^–3 (Dyck et al., 2003). Given =0.02 cm³ cm^–3, and coefficient of variation (CV) of peak depth = 4%, the calculated standard deviations of recharge rates (Appendix C; Eq. [C2]) are given in Table 2. At the 90% confidence level, there were no statistically significant differences between the recharge rates, suggesting that at the same location the difference between the recharge rates calculated from two tracers introduced at two different times is similar to the spatial variability of the recharge rates. However, we would expect that the spatial variability of recharge rates in rolling landscapes is much larger than that for the transect of our study because the transect represents a land element (knoll) in the landscape and recharge rates in depressions will be larger than that on a knoll (Zebarth et al., 1989; Hayashi et al., 1998).

The measured Cl^–, ³H, and NO₃^– concentrations are the average of 0.15-m-long soil core segments. The effect of this averaging on calculated depth-to-peak was evaluated. For Cl^– and NO₃^– distribution as shown in Fig. 4b and 4c, we expect negligible averaging errors associated with the 0.15-m increments (Appendix D). For ³H distribution in soil, the 0.15-m increment averaging may introduce an error of 0.01 m. However, considering measurement error in slicing the soil core and compaction during taking soil cores, the error introduced by averaging over a 0.15-m increment is still negligible.

We assumed steady-state, vertical, downward flow in soils below the active root zone. The recharge might be episodic and dominated by extreme wet events. However, the long-term nature of this study may justify this assumption.

The result of this study has important implications. The long-term average annual precipitation is 333 mm at the study site. The calculated groundwater recharge rates are between 1.1 and 1.9 mm yr^–1 (Tables 1 and 2). Therefore, groundwater water recharge is less than 1% of the precipitation and exhibits small temporal variability on decadal scales. The small temporal variation can be explained by the fact that the crop utilized most of the available water in soils. In the root zone, the field capacity is about 0.2 to 0.3 m³ m^–3 and the permanent wilting point is about 0.10 to 0.15 m³ m^–3, which is equivalent to 100 to 150 mm of water. In the fall of the crop year, soil water is exhausted by plants. Most of the over-winter precipitation falls as snow and accumulated until it melted in spring. Average snowfall at the site is 135 mm and even if all of this entered the soil, there would be little water penetrating below the active root zone because of its large storage capacity. From May to October, evapotranspiration exceeds precipitation, and soil water content would decrease if a crop is present and increase slightly if the field is in fallow; there is usually a small further gain in the fall and winter following the fallow summer. Therefore, crops cycle the water in the root zone back to the atmosphere through evapotranspiration (de Jong, 1988). Only in wet years may there be significant snowmelt water and intense rainfall in the summer and fall, giving excess water in the soil profile. The excess water can penetrate through the active root zone and become recharge water. However, in the Canadian prairies, the situation may happen once in every 10 yr. Again, we want to indicate that the study site is on a knoll, therefore, the recharge rate obtained on a knoll may be quite different from that in a depression. The recharge rates in a depression may be much higher, according to Hayashi et al. (1998), ranging from 6 to 12 mm yr^–1 below an ephemeral wetland. Therefore, the recharge rate in a depression may account for 2 to 3% of the annual precipitation.

	Summary

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 
Deep drainage rate is important for groundwater and soil management in semiarid zones. In this study, soil water fluxes were calculated from three tracers NO₃^– (80 yr residence time), ³H (40 yr residence time), and Cl^– (32 yr residence time). The effective root zone was found to be 1.0 m from the soil surface and the peaks of the tracers were at 1.27, 1.31, and 1.52 m for Cl^–, ³H, and NO₃^–, respectively. Average drainage water fluxes since the release of the tracers were 1.5, 1.9, and 1.8 mm yr^–1. The recharge rates calculated by the differential methods are not subject to errors arising from the assumed active root zone thickness. The recharge rates are 1.3 mm yr^–1 from tritium/Cl^–, 1.6 mm yr^–1 from NO₃^–/Cl^–, and 1.7 mm yr^–1 from NO₃^–/tritium. All these recharge estimates are less than 1% of the mean annual precipitation. The calculated water flux is smaller than those reported in nearby locations, but showed very small temporal variation.

	Appendix A

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 

	Appendix B

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

[B1]

where p (kPa) is the saturated vapor pressure; T (K) is the soil temperature; z (m) is depth (downward positive); is the enhancement factor accounting for the increase in vapor diffusion over that predicted by the simple diffusion theory; H_v is the latent heat of vaporization for water (2.45 MJ kg^–1); R is the gas constant (8.3143 J mol^–1 K^–1); D_A (m² yr^–1) is the diffusion coefficient of vapor in air at temperature T. In soils, p is approximately equal to saturated vapor pressure p* (kPa), which can be approximated by p^*=610.7·exp(7.5·(T–273.15)/(T–35.7)) at different air temperatures (Monteith and Unsworth, 1990). The diffusion coefficient D_A also depends on air temperature and its dependence on air temperature can be expressed as (Gates, 1980):

[B2]

where c = 2.17 x 10^–5 m² s^–1. The average air-filled porosity was 0.12 m³ m^–3 with a minimum of 0.06 m³ m^–3 at depth of 1.2 to 1.6 m for the site. Soil temperature at the 1.5-m depth is higher than that of 1-m depth from October to March and then is lower than that at the 1-m depth from April to September in a year. Therefore, on average, upward and downward vapor movement lasted for roughly 6 mo each. Since the temperature gradient is larger in the summer than in the winter and daily fluctuations within a month may be small, the vapor fluxes were calculated on a monthly basis. The enhancement factor is generally unknown; however, Cass et al. (1984) obtained values between 1 and 16. Here we used = 8. In addition, we used the largest air-filled porosity between the 1- and 1.5-m depths (0.12 m³ m^–3) and tortuosity factor of 0.66 (Hillel, 1980). The calculated vapor flux is negative (upward) from October to March and becomes positive (downward) from April to September (Fig. 5). The annual net vapor flux is 0.02 mm yr^–1.

	Appendix C

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 
Soil water flux (J, mm yr^–1) can be calculated as:

[C1]

where W (mm) is soil water storage between the depth to peak (z₁) at time t₁ and the depth to peak (z₂) at time t₂, z = z₂ – z₁, is soil water content between z₁ and z₂, and t = t₂ – t₁.

Based on the perturbation principle, the variance of J,

[C2]

where and _z are the spatial standard deviations of water content () and difference between depths to peak, respectively. For simplicity, we assume that two tracers applied at different time t₁, and t₂ travel at the same speed locally, thus, z₁ and z₂ measured at different spatial locations are perfectly correlated. Then,

[C3]

	Appendix D

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 
Since the Cl^– distribution is approximately log-normal, we used a log-normal distribution for simulating point concentration distribution of a conservative tracer as a function of depth at 0.01-m intervals. The point concentrations were averaged over 0.15-m increments (integration of concentrations within an increment divided by the length of the increment) from the soil surface to a depth of 4 m for log-normal distributions with a mean of 5 ln(cm) and standard deviations of 0.1, 0.2, 0.3, 0.4, and 0.5 ln(cm), respectively. The log-normal distribution with a mean of 5 ln(cm)and 0.1 ln(cm) represents a very spiky distribution with a peak location at 1.47 m and the spread mainly between 1.00 and 2.00 m. The log-normal distribution with a mean of 5 ln(cm) and standard deviation of 0.5 (ln(cm) represents a broad, left-skewed tracer distribution with a peak depth at 1.16 m and the spread between 0.3 m and beyond 4.00 m. Then the mean and standard deviation of the tracer concentrations of 0.15-m increments were determined by fitting the concentrations of 0.15-m increments to a log-normal depth distribution function using a nonlinear least square method. The peak depth was determined as the depth that had the highest Cl^– concentration from the log-normal distribution with the fitted mean and standard deviation. The difference between the theoretical (point concentration) and fitted (from the average concentrations of 0.15-m increments) peak depths are 0, 0, 0, 0, and 0.01 m with standard deviations of 0.1, 0.2, 0.3, 0.4, and 0.5 ln(cm). The averaging over 0.15-m increments did not affect the calculated peak depth, particularly for distribution with a mean of 5 ln(cm) and standard deviation < 0.5 ln(cm).

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 
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	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Summary Appendix A Appendix B Appendix C Appendix D REFERENCES

 

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