Method for estimating spatially variable seepage loss and hydraulic conductivity in intermittent and ephemeral streams



[1] A method is presented for estimating seepage loss and streambed hydraulic conductivity along intermittent and ephemeral streams using streamflow front velocities in initially dry channels. The method uses the kinematic wave equation for routing streamflow in channels coupled to Philip's equation for infiltration. The coupled model considers variations in seepage loss both across and along the channel. Water redistribution in the unsaturated zone is also represented in the model. Sensitivity of the streamflow front velocity to parameters used for calculating seepage loss and for routing streamflow shows that the streambed hydraulic conductivity has the greatest sensitivity for moderate to large seepage loss rates. Channel roughness, geometry, and slope are most important for low seepage loss rates; however, streambed hydraulic conductivity is still important for values greater than 0.008 m/d. Two example applications are presented to demonstrate the utility of the method.

1. Introduction

[2] Streambed seepage and hydraulic conductivity are important for hydrological and ecological studies. High seepage loss rates along a stream are indicative of focused groundwater recharge [Winter et al., 1998]. Seepage controls mixing between surface water and groundwater, which is important for biological cycling of nutrients and sustaining near-stream ecosystems [Brunke and Gonser, 1997]. Estimates of streambed hydraulic conductivity also are important for parameterizing hydrologic models that are used for water resources decision making [Sophocleous and Perkins, 2000].

[3] Typical methods for estimating streambed seepage and hydraulic conductivity are best applied to perennial streams. There are three basic approaches for estimating streambed seepage. The first approach provides estimates of seepage loss or gains by differencing flows at multiple locations along a river's course [Riggs, 1972]. This approach is limited by streamflow measurement accuracy and only provides a net seepage loss or gain over relatively large channel distances. The second approach uses changes in natural or artificial tracer concentrations to estimate seepage loss or gain indirectly [McCord et al., 1997; Constantz et al., 2003; Niswonger and Prudic, 2003; Böhlke et al., 2004; Gooseff and McGlynn, 2005; Cox et al., 2007]. Tracer approaches can provide high-resolution seepage loss or gain information for streambed areas of 1 m2 or more; however, data collection and analysis can be difficult and expensive and it is often difficult to determine tracer flow paths. This method is commonly used to evaluate flow into and out of the hyporheic zone [Harvey and Bencala, 1993]. The third approach is to directly measure the flow of water across the sediment–stream water interface over a scale less than 1 m2 using seepage meters [Lee, 1977]. Seepage meters work well for measuring large seepage loss or gain in small, slow moving streams but they are difficult to employ in larger streams and are inaccurate when used in moving water [Shinn et al., 2002].

[4] The three basic approaches generally do not work for intermittent and ephemeral channels in semiarid and arid regions because periods of streamflow are unpredictable, typically of short duration, and because seepage losses are unsteady in initially dry channels. During the past 50 years, semiarid and arid regions of the United States have been experiencing tremendous population growth that has resulted in the need to know the frequency of flow and seepage loss rates in many ungauged intermittent and ephemeral channels for evaluating both surface water and groundwater resources.

[5] A method is presented for determining seepage loss rates and streambed hydraulic conductivity using the streamflow front velocity (SFV) during flow initiation in a dry channel. Until recently, SFV values were difficult to determine; however with recent advancements in low-cost temperature and pressure loggers, the SFV in intermittent and ephemeral channels can be measured accurately at reasonable cost [Constantz et al., 2001; Blasch et al., 2002; Prudic et al., 2003]. Variations in the SFV along a channel can be used to provide variations in the estimates of seepage losses and streambed hydraulic conductivity over different reach lengths of an intermittent or ephemeral stream (i.e., from less than 100 m to several kilometers). This approach is similar in concept to a method used for estimating infiltration into agricultural fields [Philip and Farrell, 1964; Elliott and Walker, 1982; Shepard et al., 1993]. For the agricultural engineering application, the travel time of surface flow over the length of an irrigation furrow is used for estimating parameters that describe infiltration into the furrow. In the present work the approach is applied more broadly to natural stream channels to estimate variations in seepage loss and streambed hydraulic conductivity along a channel.

[6] The SFV can be diminished significantly by high streambed seepage loss rates at the advancing edge of flow due to initially dominant capillary pressure gradients. Capillary pressure gradients have been shown to enhance seepage loss rates by 1–2 orders of magnitude in dry streambeds as compared to steady seepage loss that occurs following several hours of flow in a stream [Ronan et al., 1998; Blasch et al., 2006]. Enhanced seepage loss due to capillary pressure gradients reduces streamflow disproportionately at the stream front and slows the front relative to the already flowing part of the stream. The sensitivity of the SFV to streambed seepage loss rates forms the basis of the approach being presented herein. In the context of this paper, the streambed represents the sediment surrounding a stream to a depth of a few meters beneath the channel surface. Sediment beneath the streambed region may affect streambed infiltration; however, the model formulation assumes that the hydraulic properties of the streambed control stream infiltration when there is an unsaturated zone beneath the stream.

[7] Previously published equations are combined into a numerical model for simulating streamflow and seepage loss in streams that become dry and then rewet. A sensitivity analysis of model parameters identifies the parameters that have the greatest effect on the simulated SFV. Results from a controlled experiment along an intermittent reach of the Cosumnes River in the Central Valley of California and a natural flow event along the ephemeral Amargosa River in southern Nevada were used to evaluate the approach for estimating seepage losses and streambed hydraulic conductivity.

2. Theory

2.1. Streamflow Routing

[8] Most modeling applications use shallow water equations to simulate free-surface flows in natural channels in one or two dimensions (1-D or 2-D) [Tchamen and Kahawita, 1998; Heniche et al., 2000]. However, flow initiation is difficult to model because the shallow water equations are discontinuous through zero depth and, in their standard forms, are difficult to use for problems involving zero depths. Several studies have addressed the problem of wetting and drying in stream channels and have developed techniques for simulating dry stream conditions with the shallow water equations [Tchamen and Kahawita, 1998; Heniche et al., 2000; Valiani et al., 2002; Niswonger et al., 2005].

[9] Methods used to simulate zero depths with the Saint-Venant equations are difficult to apply when considering high seepage loss rates at the streamflow front during flow initiation in a dry channel. This is partly due to the relatively high seepage loss rates at the streamflow front and the added nonlinearity caused by the interdependencies between seepage losses, stream wetted perimeter, and stream depth. Consequently, this study uses a kinematic wave approximation of the 1-D form of the shallow water (Saint-Venant) equations to simplify the simulation of flow in initially dry streams. The 1-D kinematic wave equation can simulate wetting and drying of stream channels during high streambed seepage loss without any special numerical treatment. However, the kinematic wave equation neglects the effects of dynamic waves, only is applicable to subcritical flow conditions, and does not consider backwater effects [Woolhiser, 1974]. The applicability of the kinematic wave equation to the streams studied here was evaluated with the kinematic wave number of the observed flow as demonstrated by Woolhiser [1974]:

equation image



is the kinematic wave number,


is the channel slope,


is the channel reach length (L),


is the normal flow depth (L),


is the Froude number.

Kinematic wave numbers greater than 10 indicate that the kinematic wave model is applicable.

[10] The kinematic wave approximation to the Saint-Venant equations assumes that waves possess only one velocity at each point, such that the continuity equation governs wave movement [Lighthill and Whitham, 1955]:

equation image



is the streamflow (L3T−1),


is time (T),


is the distance along the longitudinal axis of the stream (L),


is the cross-sectional area (L2),


is the cross-sectional area of channel depressions with dead storage (L2),


is the seepage loss per unit length along the longitudinal axis (L2T−1),


is the rate at which dead storage is filled. qd is equal to equation image, which is nonzero during flow initiation and zero after channel depressions are filled (L2T−1).

[11] If streamflow is adequately represented by a single-valued function of the channel cross-sectional area, A, and location, x, then the wave celerity, c, is equal to the slope of the flow concentration curve [Lighthill and Whitham, 1955]:

equation image

[12] The typical representation of momentum in the kinematic wave equation assumes that gravitational forces are balanced by frictional forces:

equation image

where Sf is the friction slope and S0 is the channel slope.

[13] Thus, momentum can be represented by Manning's equation in combination with equation (4):

equation image



is a constant, which is 1.0 for cubic meters per second and 1.486 for cubic feet per second (units depend on the units used in the model),


is Manning's roughness parameter, and


is the hydraulic radius of the stream, which is equal to the stream cross-sectional area divided by the wetted perimeter, (L).

[14] The wave celerity (equation (3)) can be calculated by taking the derivative of equation (5) with respect to the channel area, A. Because the hydraulic radius, R, is a function of A, a relationship must be defined to relate A and R; however, there is no universal function for this relationship that applies to all channels. Consequently, the derivative of equation (5) is calculated numerically, and the relationship between A and R is calculated by integrating their values over specified cross sections perpendicular to the stream axis.

[15] Equation (2) was solved numerically by using an implicit four-point, finite difference solution technique [Fread, 1993]. The spatial derivative in equation (2), ∂Q/∂x, is approximated by a forward difference quotient that includes time weighting of the quotient at the previous time step. The time derivative in equation (2), ∂A/∂t, was approximated by a forward difference quotient centered between the end of the previous and current time steps. The finite difference approximations are solved iteratively using Newton's method [Burden and Faires, 1997].

[16] Streamflow must be defined at the upstream boundary for the duration of the simulation period. Finite difference nodes that represent the stream are numbered as k = 1, N, where N is the total number of finite difference nodes, with k = 1 at x = 0. x denotes distance along the stream axis from the upstream end of the model. k = N at x = L, where L is the location at the downstream end of the model. Streamflow is routed for times j = 1, M, where M is the total number of time steps in the simulation. The boundary condition at x = 0 is specified on the basis of the measured flow at k = 1 (Q1) for all M time steps. The boundary condition at k = N is defined as QN = constant and initial conditions are defined as Qj=1,M = constant for all stream nodes in the model, where constant can be zero or nonzero.

2.2. Seepage Model

[17] A relatively simple approach was adopted for simulating transient seepage loss coupled to the kinematic wave equation for channel flow. Transient infiltration into a dry streambed begins at high rates driven by large capillary potential gradients. Following several hours of streamflow inundation, the capillary potential gradients subside and infiltration decreases to a steady rate. These two periods of infiltration were simulated using the equation developed by Philip [1957]:

equation image



is the cumulative infiltration (L),


is the time since channel inundation by streamflow (T),

S0, θi)

is sorptivity (LT−1/2), which is a function of physical sediment characteristics and the initial water content (θi) and wetting front water content (θ0), and Ag is the coefficient for the gravity component of infiltration in Philip's model.

[18] It is prudent to mention that Philip's equation has limitations in its applicability because of truncation of terms in the analytical solution to the partial differential equation [Parlange, 1973]. Because the problem addressed herein only concerns instantaneous ponding, the main limitation of Philip's equation is its accuracy during gravity dominated infiltration. However, because early time infiltration has the largest effect on the SFV, and because the parameters in the infiltration equation are fitted, the Philip equation provides a simple equation for testing the new approach. Future studies on this topic might benefit from adopting more accurate infiltration equations.

[19] Streams exert pressure on the channel bottom surface that can enhance seepage loss. The effects of stream depth on infiltration have been incorporated into analytical infiltration equations [Philip, 1958a, 1958b; Parlange, 1973; Freyberg et al., 1980]. The approach of Philip [1958a and 1958b] was adopted whereby stream depth has the effect of enhancing sorptivity, S. In order to incorporate the effects of stream depth into the seepage model, the following representation of sorptivity was adopted [Smith et al., 1993]:

equation image



is the saturated water content of the sediment,


is the initial water content of the sediment,


is the capillary pressure potential (L), and


is the capillary pressure potential corresponding to the initial sediment water content (L).

[20] Incorporating the effects of stream depth in a similar manner to Philip [1958b], the sorptivity is

equation image



is the stream depth for an unsaturated flow column that is calculated on the basis of the kinematic wave equation (L), and


is the relative hydraulic conductivity as a function of capillary pressure potential.

[21] The Brooks and Corey [1964] model was chosen to define the relative hydraulic conductivity as

equation image



is the air entry potential (L), and


is the Brooks-Corey exponent.

[22] The Brooks and Corey [1964] model also was used to relate the sediment water content to capillary pressure:

equation image



is the water content corresponding to the capillary pressure ψ, and


is the residual water content.

[23] Infiltration is calculated separately for each stream section that spans the distance between adjacent finite difference nodes and for each unsaturated flow column within the stream cross section (Figure 1). The wetting front depth, z, for a particular unsaturated flow column is calculated assuming I = P*cz, where Pc is the wetted perimeter of the unsaturated flow column (Figure 2). The vertical saturated hydraulic conductivity minus the unsaturated hydraulic conductivity at antecedent capillary pressure, KsK(ψ0), is used to represent the gravity term coefficient, Ag, from equation 8. Representing Ag with KsK(ψ0) has been shown to be a reasonable approximation [Hsu et al., 2002]; however, it also has been shown that Ag will be slightly less than KsK(ψ0) because of the effects of entrapped air [Bouwer, 1966]. The seepage loss is calculated for a discrete time period between times tw,j−1 and tw,j, Δtw, according to

equation image


Figure 1.

Diagram showing spatial increments for surface and subsurface flow calculations.

Figure 2.

Diagram showing separate unsaturated flow compartments for calculating infiltration and internal drainage.

[24] image is the volume of infiltrated water per unit area of the unsaturated flow column during the time period Δtw.

2.3. Coupled Streamflow Routing and Seepage Loss

[25] Equation (11) is coupled to equation (2) by relating the cumulative infiltration, I, to the seepage term, q, from equation (2):

equation image

where qc is the seepage loss for a single inundated unsaturated flow column. The total seepage loss, q, for a stream section is equal to the sum of the individual seepage losses, qc, for all inundated unsaturated flow columns.

2.4. Channel Drying During Streamflow Cessation

[26] After cession of streamflow, water drains from the streambed by a process often referred to as internal drainage. Internal drainage determines the sorptivity during reinitiation of flow (equation 8). Internal drainage was simulated using a simplified approximation of the process that assumes similarity of the infiltration front (i.e., the infiltration front remains nearly rectangular). Similarity is expressed by the solution of the absorption equation [Smith et al., 1993]. However, greater than a few meters below the streambed surface, gravity results in internal drainage that does not produce similarity in shape of the water content profile. Because the model is used to represent the shallow streambed sediment only, absorption is dominant in the model domain where streambed redistribution is calculated.

[27] The model used to simulate internal drainage is based upon mass conservation. It assumes a nearly rectangular infiltration front that decays over the profile equally as a function of time following the cessation of flow. This approach has been used by several researchers in the past. Gardner et al. [1970], Dagan and Bresler [1983], Milly [1986], and Smith et al. [1993] provide a more complete description of the approach. Smith et al. [1993] compared the simplified redistribution model to results from a numerical solution of Richards' equation and found the results to be within 10% for a variety of cumulative infiltration values and soil types; however, this error increases with the number of redistribution cycles.

[28] During a streamflow hiatus following a period of flow, the sediment water content in the streambed decays according to the following equation [Smith et al., 1993]:

equation image



is the streambed water content during the streamflow hiatus,


is the time since the previous flow event ceased (T),


is the initial water content prior to the streamflow event,


is the unsaturated hydraulic conductivity for water content θi (L/T),


is the unsaturated hydraulic conductivity for water content θ0 (L/T),


is the cumulative infiltrated water during the hiatus, (L),


is a scaling constant to account for deviations in the shape of the infiltration front—a value of 1 represents a rectangular front; a value of 0.9 is typical and was used in this study,


is the fraction of the infiltration front depth that is elongating, (2 was used in this study to represent half of the front elongating), and

Gi, θ0)

is the capillary drive at the front of the infiltration front, and is calculated directly from sorptivity (L).

Equation (13) was solved using an adaptive time step size Runge-Kutta-Fehlberg method [Patel, 1994].

[29] Seepage loss in the stream section is calculated for separate compartments in the direction perpendicular to the channel to consider variable hydraulic properties and sediment saturations in the thalweg, stream banks, and floodplain (Figure 2). The benefit of dividing the channel into separate columns is that during continuous low-flow conditions seepage losses can occur because of gravity potential gradients, and if flooding occurs, capillary pressure gradients in the stream bank and floodplain can be considered. Internal drainage also can occur within the riverbank while infiltration occurs beneath the thalweg (Figure 2).

[30] The modeling procedure for estimating seepage losses and streambed hydraulic conductivity consists of assigning reasonable estimates or measured values for all model parameters, and then adjusting Ks until the simulated SFV matches the measured values for a particular reach of the stream (a stream reach can include multiple stream sections). The process is then repeated for each downstream reach. The equations presented herein were added to the Streamflow Routing (SFR2) package [Niswonger and Prudic, 2005] of MODFLOW-2005 [Harbaugh, 2005] as an additional option for simulating routing down channels and infiltration through initially dry channels. The program can be attained through the U.S. Geological Survey's public Web page

3. Sensitivity Analysis

[31] Because the model requires input of several parameters, a sensitivity analysis was done to determine the relative sensitivity of parameters. Sensitivities were estimated as the change in an objective function resulting from a 5% perturbation in each of the input parameter values. The objective function was calculated as

equation image



is the objective function value (L/T);


is the weight applied to the difference between the measured and simulated velocity at location k;


is the measured SFV at location k (L/T);


is the simulated SFV at location k (L/T); and


is the total number of measured (and simulated) streamflow front velocities.

[32] The sensitivities were calculated for seven model input parameters, including those used for calculating seepage and those used for routing streamflow. Hypothetical simulations were done consisting of a 25-km long river that was divided into 50-m long stream sections (distance between finite difference nodes). Table 1 shows the eight model input parameter values used for the hypothetical simulation, seven of which affect vs. The objective function value was calculated by running a reference simulation to establish hypothetical measured streamflow front velocities, vmk. The model was run repeatedly with each of the input parameter values perturbed by 5% to establish hypothetical simulated values, vsk. Model results were sensitive to five parameters (Figure 3). The weighted squared difference for each velocity pair was summed for all five velocity pairs. Weights for all velocities were set to a value of 1.0 (i.e., no weighting). This process was repeated, while each time perturbing a different input parameter. Figure 3 shows the resulting sensitivities for each model parameter. The sensitivity analysis was repeated for two different reference simulations, one with a small Ks value of 0.01 m/d and another with a larger Ks value of 1.75 m/d.

Figure 3.

Change in objective function for a 5% perturbation in model input parameters. Sensitivity estimated for two reference simulations, including a low-Ks reference simulation and a high-Ks reference simulation. Objective function was calculated as the sum of the squared errors for five streamflow front velocities.

Table 1. Initial Seepage and Streamflow Parameters Used for Sensitivity Analysis
Seepage ParametersStreamflow Parameters
Ksθsaψa, mηAd, m2Sow at Bankfull Flown
  • a

    Saturated water content was not varied in the sensitivity analysis because it did not affect the SFV.

0.01 and 1.75 m/d0.33−

[33] The sensitivity analysis indicates that for small seepage loss rates (i.e., Ks reference value of 0.01 m/d), the SFV is most sensitive to the Manning's roughness parameter, n; however, for larger seepage loss rates (i.e., a Ks reference value of 1.75 m/d) the streamflow front velocity is most sensitive to Ks (Figure 3). The SFV is at least twice as sensitive to Ks as compared to any other input parameter used for calculating seepage. The sensitivity for all input parameters related to routing streamflow decreased for larger seepage loss rates. The sensitivity of the SFV to Ks is especially significant because Ks can vary over several orders of magnitude, whereas all other parameters that affect SFV vary over a much smaller range.

4. Field Applications

[34] The location of flood waves moving down initially dry channels was monitored in two rivers, the Cosumnes River in California and the Amargosa River in Nevada. The intermittent Cosumnes River flows from the Sierra Nevada into the Central Valley south of Sacramento (Figure 4). The ephemeral Amargosa River flows from Oasis Valley into the Amargosa Desert near Beatty, Nevada before ending at Death Valley in California (Figure 5).

Figure 4.

Distribution of streamflow detection loggers for measuring streamflow front velocity during flow initiation along the Cosumnes River.

4.1. Description of Field Sites

4.1.1. Cosumnes River

[35] The Cosumnes River drains approximately 1900 km2. Elevations vary from 2,400 m above mean sea level (amsl) in the headwaters to less than 10 m amsl at the confluence with the Mokelumne River in the Central Valley. The riverbed consists mostly of sand and gravel upstream of C3 (Figure 4). Downstream of C3, the gravel and sand in the riverbed is interrupted by discontinuous sections of a sandy, silty, and clayey paleosol. The climate is Mediterranean with strong seasonal rainfall. During July–September the river is usually dry in its alluvial reaches. Depth to groundwater beneath the study reach is more than 15 m below the channel thalweg.

4.1.2. Amargosa River

[36] The Amargosa River drainage ranges from 2,350 m amsl at its headwaters in Pahute Mesa, Nevada to 90 m below mean sea level (bmsl) in Death Valley, California [Tanko and Glancy, 2001]. Riverbed deposits overlie older (Tertiary) deposits and are about 2 m thick at site A2. The channel remains incised until where it splits upstream of sites A3A and A3B (Figure 5). Downstream of the split, the riverbed and alluvial deposits are moderately sorted coarse sand and gravel to a depth of at least 14 m. The Amargosa River is ephemeral throughout the study reach [Stonestrom et al., 2004]. Depth to groundwater beneath the Amargosa River is in excess of 100 m, except upstream of the site A0 where depth to groundwater is less than 30 m [Kilroy, 1991]. More than half the annual precipitation (56 percent) falls from December through March. Most of the rest (40 percent) falls from July through September [Stonestrom et al., 2004].

Figure 5.

Distribution of streamflow detection loggers for measuring streamflow front velocity during flow initiation along the Amargosa River.

4.2. Experimental Design and Model Input

4.2.1. Cosumnes River

[37] A controlled flow experiment was done from 17–31 October 2005 when approximately 0.6 m3/s of water was released at a steady rate from the nearby Folsom South Canal. Prior to the release, temperature loggers and pressure transducers were staked to the channel surface at approximately 0.7 km increments over an 11-km study reach (Figure 4). The onset of flow at each temperature logger was determined from an abrupt change in the thermograph. The pressure transducers were used in the stream channel to monitor temporal changes in the stage hydrograph. The temperature loggers and pressure transducers are referred to as “streamflow detection loggers” hereafter. Progression of the leading edge of flow was monitored for the first 4 d of the experiment. Streamflow of 0.32 m3/s was measured 10 October 2005 using a handheld velocity meter near site C3 following 2 d of continuous flow. Additionally, a streamflow of 0.04 m3/s was measured 26 October 2005 at 1 km downstream of site C12 following several days of flow.

[38] The study reach was divided into 12 river reaches that were subdivided into 100 stream sections. Each river reach was defined by streamflow detection loggers at the upstream and downstream ends, whereas stream sections were approximately 100 m long. Some small variations in stream section lengths (±10 m) were necessary to correspond to length of each river reach. The stream sections were used to construct the spatial discretization of the finite difference equations. River reach lengths were determined from measurements taken along the channel prior to flow using a handheld GPS.

[39] Channel cross sections and slopes used in the analysis were obtained from Constantine [2003]. Additional cross section and slope measurements were collected during installation of streamflow detection loggers. Because the measured cross sections and slopes along the channel were nearly the same at all locations, a single channel cross section and slope were used for all stream sections. The channel cross-sectional geometry used in the numerical model was approximated by 8 points (1 altitude and lateral distance from left bank for each point). Channel cross sections included seven compartments for simulating seepage losses and internal drainage (Figure 2).

[40] Measurements of channel depressions also were done during installation of streamflow detection loggers and were used to estimate the volume of dead storage in the channel for each river reach. Generally, more dead storage volume was estimated upstream of C3 than downstream. Manning's roughness parameter values were estimated by comparing the surfaces of channels to the surfaces of channels with known roughness presented by Barnes [1967].

[41] Measured streamflow of 0.6 m3/s at C0 was used to define the upstream boundary condition for simulating flow in the Cosumnes River. Time steps used in the simulation were approximately 1 h, with small deviations to match arrival times at streamflow detection loggers. Parameters used in the model to estimate seepage losses and streambed hydraulic conductivity are listed in Table 2.

Table 2. Streamflow and Seepage Parameters Used for Estimating Seepage Loss Rates and Streambed Hydraulic Conductivity Along the Cosumnes River
River ReachLength, kmStream SectionsStreamflow ParametersSeepage Parameters
NumberLength, mSonAd, m2w,a mθsψa, mη
  • a

    Stream width at bankfull.


4.2.2. Amargosa River

[42] Streamflow in the Amargosa River is solely a function of precipitation in the drainage. The channel in the study reach is dry more than 99% of the time [Stonestrom et al., 2004]. Pressure transducers and temperature loggers were installed in the channel at several locations downstream of Beatty beginning in 1997 to determine the frequency and duration of flow along the channel. Streamflow detection loggers measured the SFV at 5 locations along a 43-km length of the river. Stream depth was measured at 20-min intervals at the four locations where pressure transducers were installed in the channel thalweg (Figure 5).

[43] Sufficient precipitation occurred in the mountains north and east of Beatty, Nevada during January 2005 that resulted in streamflow throughout the study reach. Although tributaries can contribute additional flow to the channel, none was observed during the period of flow. Streamflow lasted about 2.5 d at site A0 (Figure 5). Peak streamflow was estimated at all five locations in February 2005 using high-water marks along the banks of the channel and stream conveyance and slope–slope area methods [Benson and Dalrymple, 1967]. At each site, cross-sectional data were collected at one or two locations for the stream conveyance method and two to four locations for the slope-area method. Peak streamflow ranged from 4.2 m3/s at site A0 to 1.5 m3/s at sites A3a and A3b. Additional indirect streamflow measurements were made following at least three other periods of flow. Rating curves were developed for the four sites with pressure transducers so as to approximate flow from measurements of stream depth.

[44] The study reach was divided into five river reaches that were subdivided into 116 stream sections. Stream sections were 256 to 350 m long. Channel lengths and slopes were estimated from 30 m by 30 m DEM data [U.S. Geological Survey, 2000]. Channel slopes from the DEM data were checked against measured slopes at places of indirect streamflow measurements. Two channels were simulated where the Amargosa River splits downstream of site A2. The two channels have similar lengths to where peak flow was estimated from indirect measurements. The onset of flow at sites A3a and A3b were nearly the same (within the 20 min measurement frequency) as were peak discharges and cross-sectional geometries.

[45] The channel cross-sectional geometry was measured at each of the streamflow detection logger locations (Figure 5) and was approximated by 8 points per cross section. The channel cross section was represented by 7 compartments for simulating seepage and internal drainage. The cross-sectional geometry of stream sections between measured locations was assumed the same as that measured at the upstream location except where the channel split into two. The cross-sectional geometry of all stream sections representing the east and west branches (river reaches 4 and 5) were assumed the same as the measured cross sections at sites A3a and A3b, respectively.

[46] The streamflow hydrograph developed for site A0 was used to define the upstream boundary condition for simulating flow. Time steps were 20 min and correspond to the frequency of pressure transducer data. Parameters used in the model to estimate seepage losses and streambed hydraulic conductivity are listed in Table 3.

Table 3. Streamflow and Seepage Parameters Used for Estimating Seepage Loss Rates and Streambed Hydraulic Conductivity Along the Amargosa River
River ReachLength, kmStream SectionsStreamflow ParametersSeepage Parameters
NumberLength, mSonAd, m2w,a mθsψa, mη
  • a

    Stream width at bankfull.


5. Results

5.1. Cosumnes

[47] The kinematic wave number (equation (1)) was used to evaluate the applicability of the kinematic wave equation for routing streamflow. Streamflow remained subcritical throughout the study period and estimated Froude numbers were consistently less than 0.09. The calculated kinematic wave numbers were greater than 20, indicating that the kinematic wave equation is appropriate.

[48] The streamflow front reached site C12 approximately 101 h after the release began. SFVs computed for each river reach had two distinct ranges (Table 4). The higher range was between 6.5 and 14.5 km/d for river reaches 3, 6, and 9, whereas the lower range was between 1.4 and 3.5 km/d for all the other river reaches (Figure 6). Qualitatively, the three river reaches in the higher SFV range reflect where the streambed seepage losses are less, and the stream sections in the lower SFV range reflect sections where the seepage losses are more. SFV provides a good qualitative assessment of the relative variations streambed seepage loss, which could be invaluable for quickly locating areas of focused recharge from a river at very low cost.

Figure 6.

Streamflow front velocities measured between water detection loggers located at approximately 0.7 km increments along the Cosumnes River (Figure 4).

Table 4. Measured Streamflow Front Velocities and Estimated Saturated Hydraulic Conductivities for the Cosumnes River
River ReachStreamflow Detection LoggersStreamflow Front Velocity, km/dKs, m/d
  • a

    SFV for this section was insensitive for Ks less than this value.


[49] Streamflow along the Cosumnes River decreased downstream because of seepage losses. If the seepage loss rate was constant with time and distance down the channel, the SFV would have decreased down channel proportional to the constant seepage loss rate. The three higher SFVs at reaches 3, 6, and 9 show such a decrease SFVs downstream (Figure 6). However, SFVs at the other locations do not show a similar decrease downstream, which first indicate great variability in the streambed hydraulic conductivity and second suggests that the overall hydraulic conductivity generally decreases down the channel.

[50] A quantitative analysis of changes in SFVs required numerical modeling to account for effects caused by changes in seepage loss rates, mean velocity of streamflow, and dead storage. The numerical model used to estimate seepage loss rates and streambed hydraulic conductivity was calibrated by adjusting Ks for each river reach while keeping all other parameters at estimated values. A single value for Ks was used for each river reach. The model was able to match all of the measured SFVs by adjusting Ks for each of the 12 river reaches, with the exception of river reach 3 (between sites C2 and C3). The model under predicted the high SFV for this reach, even when Ks was set to zero. To attain a better match, the values of dead storage (Ad) were increased by 15% and the values of Ks were decreased by 5% for river reaches 1–3. This result was consistent with an observed increase in dead storage upstream of site C3 relative to downstream of site C3. Following these small changes, the model was able to fit the SFV for river reach 3. Streamflow-routing parameters (Figure 3) other than Ad could have been adjusted as well; however, unlike the dead storage parameter, there were no notable changes observed in the field to justify changing their values. The changes to Ad and Ks for river reaches 1–3 caused a relatively small change in the estimates of seepage and Ks and are noted here only to document the single instance of a less than perfect fit to the measured SFVs for the Consumnes River.

[51] The Ks values display a qualitative correspondence to the SVFs (Table 3). Generally, Ks and the corresponding seepage loss rates are greater for the upper river sections. The decrease in Ks down the channel corresponded to an observable decrease in sediment texture over the lower sections of the river. Two streamflow measurements were made during the experiment that can be used to evaluate the simulated streamflow, seepage loss rates, and estimated Ks values. The simulated and measured streamflow at 1 km and 12.5 km differed by less than 0.02 m3/s, indicating that the cumulative seepage once the streamflow front had passed beyond site C12 was reasonably simulated in the model (Figure 7).

Figure 7.

Simulated and measured streamflow in the Cosumnes River.

5.2. Amargosa River

[52] Streamflow during the January event was subcritical and the Froude numbers were less than 0.36. The kinematic wave numbers for the January event were greater than 65, indicating that the kinematic wave equation was appropriate for simulating streamflow down the channel. Measured SFVs between streamflow detection loggers indicate that there is variability in the seepage loss rates down the channel (Table 1). Data was available to provide SFV from sites A0 to A1, A1 to A2, and A2 to A3a (Figure 5). River reaches 3 and 4 were combined obtain an estimate of the SFV between A2 and A3a. Although simulated in the model, the SFV between sites A2 and A3b was similar to that between sites A2 and A3a. Thus, results are presented only at the end of river reach 4. No data were collected at the site where the Amargosa River splits because that site is not accessible.

[53] River reach 1 had the lowest SFV and the greatest estimated Ks (Table 5). River reach 2 had a very low estimate of Ks, where the seepage loss rate was essentially zero compared to the other reaches. The combined reach between sites A2 and A3a (river reaches 3 and 4) had a much higher Ks value than river reach 2 but it was still just 1% of river reach 1. The simulated and measured SFVs were in good agreement following adjustment of the Ks values for each river reach except the SFV for river reach 2 was too low even when the Ks was set to zero (Figure 8). Manning's roughness had to be decreased to a value of less than 0.004, which is unrealistic for natural channels. Modification of the channel cross-sectional geometry did improve the model fit and suggests that the cross-sectional geometry at site A1 may not adequately represent the mean cross-sectional geometry for the reach. The final Ks value estimated for river reach 2 was increased until the SFV became sensitive to Ks. Thus, the Ks value estimated for this section represents an upper bound. The low seepage loss rate and estimated Ks for river reach 2 is further supported because the SFV is nearly the same as the estimated mean velocity at peak discharge at sites A1 and A2. The SFV for the other river reaches were much smaller than the estimated mean velocity at peak flow (Table 5).

Figure 8.

Simulated streamflow in the Amargosa River; circles represent the time when the streamflow front reached the streamflow detection loggers, and squares represent the time of peak flow measured with pressure transducers. Peak streamflow was indirectly measured at each water detection logger using slope conveyance and slope-area methods.

Table 5. Measured Streamflow Front Velocities, Mean Water Velocity at Peak Flow, and Estimated Saturated Hydraulic Conductivities for the Amargosa River
River ReachStreamflow Detection LoggersMeasured Streamflow Front Velocity, km/dMean Water Velocity at Peak Flow,a km/dEstimated Ks, m/d
  • a

    Mean velocities at peak flow were estimated indirectly on the basis of the slope conveyance and slope area methods.


[54] The difference between simulated and measured peak streamflow is less than 10% at A1, A2, and A3a (Figure 8). However, this is not a rigorous evaluation of the simulation results because uncertainties in the estimates of peak streamflow from indirect measurements are difficult to quantify. Generally, the SFVs were much higher in the Amargosa River as compared with those estimated for the Cosumnes River. The higher SFVs in the Amargosa River may have resulted from greater streamflow and streambed slopes.

6. Discussion

[55] Results for the Cosumnes River indicate that the simplified model can match measured variations in the SFV along the channel following a 15% increase of the channel dead storage upstream of site C3. Although there was an observable increase in dead storage upstream of site C3, the measured increase apparently was not sufficient to explain the SFV for river reach 3 (between sites C2 and C3). Even if the fit to the SFV for river reach 3 was left imperfect, the estimated Ks was only 5% greater than the simulation with the increase in channel dead storage.

[56] The model of streamflow and seepage losses in the Amargosa River had difficulty in simulating the SFV in river reach 2 (Figure 8). Changing the dead storage in reaches 1 and 2 did not result in a better fit. The model was better able to simulate the SFV at the end of this reach only when the channel cross-sectional geometry was modified. The small estimated value for streambed hydraulic conductivity is consistent with the lack of difference between the mean streamflow velocity estimated from peak streamflow using indirect methods and the SFV at the end of reach 2. Furthermore, even though the peak streamflow was 10% less at end of reach 2 than at the beginning, the total runoff estimated at the end of reach 2 was only 3% less, indicating the seepage loss was minimal in this reach compared with reach 1. The channel of the Amargosa River in reach 2 flows across a tectonically uplifted block of older basin fill that consists of poorly sorted mixture of clay, silt, sand, and gravel [Stonestrom et al., 2004], which may explain the small estimates of streambed hydraulic conductivity. Finally, because the channel is much wider than stream depth (channel is about 15 m wide when the stream depth is 0.3 m), the streambed hydraulic conductivity had to be small in the simulation in order to simulate the estimated SFV and the estimated peak discharge. Additional measurements of cross-sectional geometries and SFVs within this reach would provide a better basis for evaluating seepage loss rates and streambed hydraulic conductivity in an area where seepage loss rates are minimal.

[57] These results indicate that changes in the velocity of the leading edge of streamflow (SFV) down a previously dry channel of intermittent and ephemeral channels can be used to estimate seepage loss rates and streambed hydraulic conductivity. The method requires measuring the mean velocity of the leading edge of streamflow as it progresses down the channel along with measurements of channel cross-sectional geometries, channel slope, and dead storage. The method provides an advantage over the standard methods used to estimate seepage losses and streambed hydraulic conductivity because the advancement of the streamflow front can be monitored using temperature loggers and/or pressure transducers placed in the thalweg along the channel. Streamflow measurements upstream of the front add additional information that can be used to refine model input parameters.

[58] Because the SFV is dependent on changes in channel characteristics and seepage loss rates, a simple numerical model was developed for simulating seepage loss and streambed hydraulic conductivity. The model was able to reasonably replicate the SFV as streamflow progressed down two previously dry channels. The simplifications used in the model introduce errors that may affect the accuracy of the predicted seepage loss and streambed hydraulic properties for some rivers. The model presented herein would be inappropriate for simulating supercritical flow or flow in streams affected by backwater.

[59] The method of estimating seepage loss rates and hydraulic conductivity from SFV was insensitive to Ks values less than 0.008 m/d. Consequently, this value represents the lower limit for estimating Ks. However, because of uncertainty in other sensitive parameters, the accuracy of the estimated Ks is dependent on the accuracy of other input parameters, including channel length and slope, channel cross-sectional geometry, and Manning's roughness as well as the streamflow specified at the upstream boundary. The upper bound of Ks values maybe limited by the streamflow entering the reach. Model results indicate that the method for estimating Ks becomes more accurate as seepage loss and Ks increase. Although not fully evaluated, it is likely that the SFV becomes less sensitive to seepage loss with increased streamflow. Results from data collected in the Amargosa River indicate that the method is applicable for peak streamflow of at least 4.2 m3/s.

[60] The accuracy of the kinematic wave model used to simulate streamflow with seepage losses down a channel was not addressed in this paper and requires further testing and evaluation. Smaller-scale experiments consisting of detailed independent estimates of streamflow and seepage loss using flumes would be particularly useful. Results of the modeling in this study provide an indication that the method is viable and may produce reasonable estimates of streambed conductivity and seepage loss rates over stream lengths of 100 m and possibly less. Estimating seepage loss rates and streambed hydraulic conductivities over lengths of about 100 m are useful because such a length is typical for groundwater flow models that include stream interactions. This is in contrast to the seepage run approach that requires much longer channel lengths to make an estimate, and to tracer and seepage meter approaches that determine seepage for a small area of the channel.

[61] The method of estimating seepage loss rates and streambed hydraulic conductivities from SFV in channels where the streambed is saturated has not been tested. Whether the estimated Ks will be useful for predicting seepage for streamflow events when the streambed is saturated remains to be tested and evaluated.

7. Summary and Conclusions

[62] Seepage losses near the front of streamflow progressing down initially dry stream channels significantly slow the streamflow front velocity (SFV). Changes in SFV down the channel can be used to evaluate the spatial variability of seepage losses rates and streambed hydraulic conductivity in intermittent and ephemeral streams. The model developed for this study required six input parameters for simulating streamflow and streambed seepage. However, as demonstrated using sensitivity analysis, the SFV is most sensitive to streambed hydraulic conductivity for moderate to large seepage loss rates (>0.008 m/d). The SFV was most sensitive to parameters related to routing streamflow for small seepage loss rates. Sensitivity of the SFV to seepage loss rates was cumulative in the downstream direction. Thus, the estimated seepage loss rates and streambed hydraulic conductivity were more constrained as additional downstream SFVs were considered in the model. The method was successfully applied to an intermittent river with steady release of water from a canal and an ephemeral river with runoff generated from precipitation in an upland area. Model estimated variations in streambed hydraulic conductivity corresponded to observed changes in sediment texture within the river channels. At a minimum, the method is useful for locating reaches of a stream where high and low seepage loss rates occur, which could be invaluable for resource management. The method also provides information on the variability of streambed hydraulic conductivity over distances of kilometers to less than 100 m along the channel, which is not easily measured by traditional methods.


[63] Funding was provided by U.S. Geological Survey's Groundwater Resources Program through the Office of Groundwater. This research also was supported by California Bay–Delta Authority Ecological Restoration Program (award ERP-01-NO1) and through funding provided by Larry Rodriguez of Robertson-Bryan Inc. The authors are thankful for the reviews from John R. Nimmo and Jim Constantz from the U.S. Geological Survey, T. P. A. Ferré from the University of Arizona, John L. Rupp from Water Consultants, and Justin L. Huntington from the Nevada State Engineers Office as well as two anonymous reviewers.