[15] Data collection and analysis progressed in 3 stages. First, stream discharge was continuously measured at 6 gauges and manually measured with 8 series of dilutiongauging experiments along 3 streams in the watershed. Second, topographic contributing areas were derived from elevation data, and then areal yields (or specific discharge) for the resulting contributing areas were calculated using the discharge data. Third, discharge and areal yield data were normalized to their associated watershed or subwatershed outlet values to facilitate assessment of changes in spatial patterns during the decrease in discharge over the summer.
3.1. Measurement of Stream Discharge and Lateral Inflow
[16] Main stem and subwatershed gauges used for this study were all flumes (Table 1), and stages in attached stilling wells were measured at 15 to 30 min intervals by capacitance rods (TruTrack, New Zealand, note that the use of trade or firm names in this publication is for reader information and does not imply endorsement by the U.S. Department of Agriculture or U.S. Geological Survey of any product or service). Discharges at watershed and subwatershed outlets (Q) were calculated from stage data using rating curves developed by the U.S. Forest Service, and daily average discharges were aggregated from the 15 to 30 min data. We report 2006 daily average outlet Q from all the headwaters within the TCEF watershed. Flow contributed by the Lower Tenderfoot Area for a given day was calculated as the difference between the TCEF watershed outlet Q and the sum of outlet Q from the five subwatersheds.
[17] Eight longitudinal series of stream discharge measurements were performed in the three largest subwatersheds of the TCEF watershed (Table 1, Figure 1): three series in Stringer Creek, three series in Upper Tenderfoot Creek, and two series in Spring Park Creek. Each series was performed during a different, relatively constant base flow discharge for the respective stream (Table 2). One Upper Tenderfoot Creek series was performed at higher base flow in 2005, and the remaining seven series were performed during the summer base flow recession of 2006. Each series consisted of multiple tracer dilution gauging measurements along the stream valley. This approach was part of a more detailed assessment of gains and losses in stream channel flow, and the presented flow data from Stringer Creek are derived from the same data set used for a 200 m reach water balance analysis [Payn et al., 2009].
Table 2. List of Stream Discharge DilutionGauging Series and the Corresponding Discharge Nearest the Subwatershed Outlet From the First Measurement in the SeriesDates  Q(0 m) (L s^{–1})  Q_{SP}(0 m) (mm h^{−1})  Q_{TCEF} (L s^{−1})  Q_{SP,TCEF} (mm h^{−1}) 

Stringer 
22–24 Jun 2006  101  0.066  515  0.081 
25–28 Jul 2006  21  0.014  151  0.024 
26 Aug to 4 Sep 2006  15  0.010  101  0.016 

Upper Tenderfoot 
30 Jun to 1 Jul 2005  89  0.072  722  0.113 
29 Jun to 2 Jul 2006  33  0.027  333  0.052 
2–3 Aug 2006  14  0.012  129  0.020 

Spring Park 
9–10 Jul 2006  28  0.025  221  0.035 
5–6 Aug 2006  14  0.013  122  0.019 
[18] We began each dilution gauging series by measuring discharge near the subwatershed gauge (Q(0 m)). Then, working upstream, we measured Q every 100 m of valley length (Q(100 m), Q(200 m), etc., Figure 2a). Series were completed near the origin of measurable channel flow during higher base flow conditions: at 2600 m in Stringer Creek, at 2300 m in Upper Tenderfoot Creek, and at 1200 m in Spring Park Creek. Measurement locations were occasionally moved less than 20 m to avoid locations where the tracer might be poorly mixed with inflows. Locations for discharge measurement were initially selected using measuring tape, then surveyed with an optical total station, and finally rectified with highresolution elevation data from airborne laser swath mapping. The 2005 measurements in Upper Tenderfoot Creek were performed according to a slightly different experimental design, such that the data are at less regular intervals and at a somewhat lower spatial resolution than 2006 data. However, 2005 data have sufficient resolution to allow direct comparisons of discharge distributions across a broader range of base flow conditions than 2006 data alone.
[19] Each dilution gauging measurement was made from an independent instantaneous tracer release, such that inaccuracy due to potential tracer mass loss over long transport distances was minimized (see Payn et al. [2009] for more details). A known mass of dissolved tracer was released a mixing length upstream of the location of tracer concentration measurement [Day, 1977]. Mixing lengths were selected to be long enough for complete mixing, but kept relatively short to minimize tracer mass loss. Mixing lengths included at least three transitions between convergent and divergent channel flow (e.g., poolriffle sequences) and ranged between 5 and 30 m in valley length, depending on channel structure and flow conditions. We selected dilution gauging over velocity gauging because dilution gauging is likely more accurate in the irregular, tortuous channels of mountain headwaters [Day, 1977; Zellweger et al., 1989]. Sodium chloride (NaCl) was used as a conservative tracer, and tracer concentrations were estimated by calibrating temperaturecorrected electrical conductivity measurements (EC) to bracketing standard NaCl concentrations made with stream water from the corresponding stream [Gooseff and McGlynn, 2005; Wondzell, 2006]. EC measurements were made with Campbell CR510 or CR10X data loggers and CS547AL temperature/conductivity probes (Campbell Scientific, Inc., Logan, UT, USA). Each probe was independently calibrated in 2006, and a single calibration curve was used for all probes in 2005. All stream EC measurements were corrected for background EC before determining NaCl concentration from the calibration slope.
[20] Dilution of the released tracer mass was used to estimate the discharge at a given valley location (Q(x m)) from each concentration breakthrough curve [Day, 1977], which assumes steady discharge and complete mass recovery:
where C(τ) is the tracer concentration breakthrough curve at the base of the reach due to slug mass M, τ is the time variable of integration, and t is the time of EC measurement between the release time (τ = 0) and the return to background EC (τ = t). Breakthrough curves consisted of discrete concentration measurements at 2 s intervals, and trapezoidal numerical approximation was used for breakthrough curve integration. Net lateral inflow per valley distance for a given reach location (Q_{L}(x m)) was calculated as the net change in flow over the reach (ΔQ) divided by length of the valley (L) along the reach (Q_{L}(x m) = ΔQ/L). “Lateral” is applied in a radial sense, where any surface or subsurface exchange that causes changes between upstream and downstream channel flow is considered lateral. “Inflow” implies the sign convention for the channel water balance, i.e., water contributed to channel flow over a reach is a positive lateral inflow and water lost from the channel over a reach is a negative lateral inflow. In this sense, sources or sinks of lateral inflow may include any combination of surface water, groundwater, or hyporheic flow [Kuraś et al., 2008].
[21] Ideally, longitudinal “snapshots” of discharge measurements would be carried out at exactly the same time. This was impractical for this study, so longitudinal patterns from our sequential method are subject to some bias due to temporal changes in stream discharge [Kuraś et al., 2008]. In this case, discharge tended to decrease over a given series of measurements, due to both diel and seasonal patterns. Therefore, individual dilution gauged measurements somewhat underestimated the true longitudinal snapshot that corresponded to the time of the first tracer experiment at 0 m. The fraction of underestimation was likely to increase with distance up the valley, due to the cumulative time necessary to complete the sequential tracer experiments.
[22] The “worstcase” scenario for temporal bias would coincide with the largest change in discharge during a series of dilution gauging experiments. For example, the maximum temporal bias in a series of experiments in Stringer Creek would have occurred on 22–24 June 2006 (Table 2), when discharge at the outlet gauge (∼0 m) was at its steepest decline (Figure 3) and decreased by 20% during the 52 h it took to complete the series. To evaluate temporal bias in this series, we calculated the fractional temporal change in discharge at the outlet gauge corresponding to the time between each upstream dilution gauging measurement (at 100 m, 200 m, etc.) and the dilution gauging measurement nearest the outlet (0 m). Then, each dilution gauged measurement as “corrected” for temporal bias by dividing it by the corresponding fractional temporal change in discharge at the outlet. The result was an average absolute bias of −5 L s^{−1} across the longitudinal series, where the negative value indicates underestimation. This temporal bias is small relative to the 86 L s^{−1} longitudinal change in discharge observed from 2600 m to 0 m, such that the relative patterns of spatial variability were nearly identical between the measured and “corrected” data. We conclude from this worstcase analysis that temporal bias in the data has little influence on our interpretation of spatial patterns along our study streams. Furthermore, the temporal change in discharge during a few days of experiments is small relative to the change in discharge over the entire summer, such that temporal biases in individual series have little influence on our analysis of changes in spatial patterns during the recession. Finally, we choose not to report the “corrected” data in this analysis, because the assumptions behind the above estimate of bias are not consistent with our findings. During a given period of time, the fractional temporal change in discharge measured at a subwatershed outlet was not necessarily uniform along the full length of the stream.
3.2. Derivation of Topographic Contributing Area and Areal Yields
[23] Topographic contributing areas were calculated for each location where discharge was measured (Figure 2), including all dilutiongauged (outlet A) and flumegauged (A(x m)) locations. Topographic analyses were based on digital elevation models (DEM) derived from airborne laser swath mapping. We calculated cumulative contributing area using a multipleflowdirection analysis of the DEM with 10 m grid cells (MD Infinity, [Seibert and McGlynn, 2007]). Multipleflowdirection algorithms are able to allocate output flow from a single grid cell into multiple adjacent cells, providing a more realistic quantification of topographic divergence in hillslopes along a stream valley. The Lower Tenderfoot contributing area was calculated by subtracting the sum of subwatershed areas from the total TCEF watershed area (Table 1). We also used a singleflowdirection algorithm [O'Callaghan and Mark, 1984] to derive the approximate boundaries of contributing areas for map visualizations (Figures 1 and 2).
[24] We calculated specific discharges at continuous gauges (outlet Q_{SP}) and at locations along stream valleys (Q_{SP}(x m)). In both cases, Q_{SP} was calculated by dividing flow measurements by their respective topographic contributing area (Q_{SP} = Q/A and Q_{SP}(x m) = Q_{SP}(x m)/A(x m)). Lateral contributing areas to stream reaches were calculated from the change in cumulative contributing area (ΔA) over each reach. Lateral specific discharges (Q_{SPL}(x m)) were then calculated from the net change in flow over each reach (ΔQ) divided by its lateral contributing area (Q_{SPL}(x m) = ΔQ/ ΔA). Because this definition of specific discharge is flow normalized to topographic contributing area, we interpret Q_{SP} as topographic “areal yield” and Q_{SPL} as topographic “lateral areal yield” for the purposes of this analysis.
3.3. Normalization of Data to Discharge at the Watershed Outlet
[25] During a seasonal recession uninterrupted by storms, two ubiquitous temporal patterns are expected: (1) flow will decrease at all locations and (2) absolute spatial variability in flow will thus necessarily decrease across all locations. Dominant temporal trends such as these tend to obscure whether contributions to streamflow from a given location have an increasing or decreasing influence on discharge at the watershed outlet through time. Thus, normalization to discharge at the outlet provides a straightforward spatial reference frame for direct interpretation of dynamics in these relative contributions. However, as with all normalization schemes, care should be taken that inferences made from increasing relative contributions are not artificially extended to the ubiquitously decreasing absolute trends.
[27] Similarly, Q(x m) and Q_{SP}(x m) measured by dilution gauging along streams (at x m along a valley) were normalized to the Q(0 m) and Q_{SP}(0 m) from the dilutiongauged discharge measurement nearest the subwatershed outlet from the same measurement series (Q*(x m) = Q(x m)/Q(0 m) and (x m) = Q_{SP}(x m)/Q_{SP}(0 m), Table 3). Q_{L}(x m) and Q_{SPL}(x m) were also normalized to the associated Q(0 m) and Q_{SP}(0 m), to quantify the relative lateral contribution to flow ( (x m) = Q_{L}(x m)/Q(0 m)) and relative lateral areal yield ( (x m) = Q_{SPL}(x m)/Q_{SP}(0 m), Table 3) for stream reaches. In this case, (x m) is the fraction of outlet discharge gained (+, net gaining reach) or lost (−, net losing reach) per 100 m of valley length, and (x m) is the fraction of the subwatershed areal yield associated with a given lateral contributing area. As with for subwatersheds, values of (x m) > 1.0 indicate lateral areas with disproportionately larger yields than the corresponding subwatershed, and values of (x m) < 1.0 indicate lateral areas with disproportionately smaller yields.
[28] Finally, A(x m) at each dilution gauged location was similarly normalized to the A(0 m) of the corresponding subwatershed (A*(x m) = A(x m)/A(0 m), Table 1, Figure 2). The resulting topographic area accumulation curves (A*(x m) versus x) can be compared directly with longitudinal Q*(x m) distributions on the same scale. In this comparison, correlation of Q*(x m) with A*(x m) would suggest a linear topographic control of streamflow generation, and the local slope of Q*(x m) versus A*(x m) is equal to (x m). We quantified the fraction of variability in stream discharge linearly described by accumulated contributing area by calculating the coefficient of determination (R^{2}) of Q*(x m) versus A*(x m) along valleys. Q*(x m) and A*(x m) along the same valley are inherently cumulative and nonindependent data, so the R^{2} statistic is always relatively near 1 in generally gaining streams. Therefore, this statistic is used only for description of relative changes in the relationship and not for direct inference.