Spatial and temporal trends in stream chemistry were investigated in a large (1600 km2) alpine watershed in the southern Rocky Mountains of Colorado to help understand mechanisms of streamflow generation. We observed linear increases of concentrations of chemical constituents in streamflow as accumulated drainage area increased along the main channel of Saguache Creek. We tested two conceptual models of streamflow generation against our stream chemistry observations. One model is essentially two-dimensional and treats streamflow generation at the large watershed scale as the aggregation of runoff responses from individual hillslopes, primarily surface and shallow subsurface flow paths. Alternatively, a fully three-dimensional conceptual model treats streamflow generation as being controlled by a distribution of large-scale groundwater flow paths as well as surface and shallow subsurface flow paths. The structure and magnitude of groundwater contributions in streamflow as a function of increasing scale provided a key distinction between these two conceptual models. End-member mixing analysis and measurements of hydraulic head gradients in streambeds were used to quantify basin-scale groundwater contributions to streamflow with increasing spatial scale in the Saguache Creek watershed. Our data show that groundwater contributions are important in streamflow generation at all scales and, more importantly, that groundwater contributions to streamflow do increase with increasing watershed scale. These results favor the three-dimensional conceptual model in which long groundwater flow paths provide a streamflow generation process at large scales that is not operative at smaller scales. This finding indicates that large watersheds may be more than simply the aggregation of hillslopes and small catchments.
 The characterization of streamflow generation processes in hillslopes and small catchments less than 100 km2 has been well documented in the hydrological literature (see Beven  for reviews). Yet few of these studies attempt to scale their results to larger watersheds. In addition, the characterization of streamflow generation processes in watersheds larger than 1000 km2 remains uncertain, in part because of logistical difficulties imposed by the larger watershed size [Rodgers et al., 2005]. All these factors create a complicated problem for watershed hydrologists, especially since there is an increasing urgency to understand streamflow generation processes at larger watershed scales [Naiman et al., 2001; Peterson et al., 2005]. One approach toward solving this problem is to aggregate the runoff responses from individual hillslopes and effectively upscale that aggregated response to the larger watershed. The logic behind this approach is that process understanding at smaller scales is much more complete than it is at larger scales. The problem with this approach is that hillslope processes tend to be highly complex and heterogeneous and upscaling these processes will result in models that are also highly complex at the watershed scale [McDonnell, 2003; Sivapalan, 2003; Uhlenbrook, 2006]. This approach also ignores possible processes that are unique to the larger scale and may not be operative at smaller scales. An alternative approach is to identify features or processes that connect hillslope-scale runoff processes to the streamflow response of the larger watershed, in other words, to seek common threads between hillslope and watershed processes [Sivapalan, 2003; Beighley et al., 2005]. Such features or processes may provide the important link that allows us to bridge the gap in understanding between small-scale complexity and large-scale simplicity [Dooge, 1997; McDonnell et al., 2007; Spence, 2007].
 The second approach is particularly appealing. It allows watershed hydrologists to investigate the scalability of a specific feature or process without first deriving a conceptual model of runoff generation at the smaller hillslope scale. This is beneficial for two reasons: it accelerates current progress in process understanding, and in the long term, it promotes the development of new theories regarding hydrological processes at the large watershed scale. In fact, according to Sivapalan [2003, pp. 1039–1040], “much faster progress can be achieved, in terms of linking conceptualizations across the scales, if the hillslope and network responses can be described physically, but in terms of travel time distributions, to match the usual physical meaning of the unit hydrograph for the watershed as a travel time distribution.”
 Studies have, in fact, investigated the relationship between catchment area and residence times [McGlynn et al., 2003; McGuire et al., 2005; Hrachowitz et al., 2010]. These studies, however, indicate that there may not be a correlation between catchment area and residence times. In fact, the recent findings of Hrachowitz et al.  suggest that the controls on mean travel times did not change with increasing scale and that travel times converged on a median value with increasing scale. However, these studies are almost exclusively based on applications of the stable isotope convolution integral method [Małoszewski and Zuber, 1982]. This method is essentially a linear model, while catchment responses tend to be highly nonlinear and can contain multiple storage elements interacting with one another at very different timescales. These concepts were recently examined in the work of Botter et al. . Our concern is that the output residence times from the convolution integral model do not vary significantly from the temporal span of the input function, and this may skew apparent ages of streamflow toward younger ages [Stewart et al., 2010] (refer to McGuire and McDonnell  for direct comparisons). On the basis of these concerns, we chose to test the concepts using a different approach.
 In this paper, we follow the suggestion of Sivapalan  and investigate the processes that control the structuring of streamflow chemistry across multiple scales and, in particular, with increasing scale in a large watershed (defined here as a drainage area larger than 1000 km2). Several studies have documented structured trends in stream chemistry that become apparent as basin scale increases [Wolock et al., 1997; Shaman et al., 2004; Temnerud and Bishop, 2005; Uchida et al., 2005]. Since this behavior seems to be a common occurrence, streamflow chemistry may be particularly useful in linking process understanding across multiple scales. In the following paragraphs, we develop two conceptual models that could explain the structured trends in streamflow chemistry. It is important to note that these conceptualizations are essentially end-members in the range of conceptual models for streamflow generation; in reality, most streamflow generation processes probably fall somewhere between these two end-members.
 We use the results of Wolock et al. , Shaman et al. , Temnerud and Bishop , and Uchida et al.  to define and illustrate a 2-D conceptual model of streamflow generation processes at the large watershed scale. Shaman et al.  and Wolock et al.  found that low-flow stream chemistry in the Neversink River watershed located in southern New York was quite spatially variable in subbasins of less than 8 km2 and that above this basin threshold, stream chemistry became scale invariant. Shaman et al.  attributed this behavior to the integration of contributions from shallow subsurface macropores and bedrock fractures and by the effective damping of the chemical signature by mixing processes with water stored in the riparian soil matrix. Uchida et al.  also found that low-flow stream chemistry was quite spatiotemporally variable in very small subbasins and hillslopes (areas <0.1 km2) in Japan. This variability was thought to be controlled by spotty contributions of subsurface water from the bedrock to the soil water and to the stream itself. They concluded, however, that the chemical signatures from these hillslopes were damped by mixing in the stream and not in the riparian zone since streams in their study were not always bounded by laterally extensive riparian areas. Temnerud and Bishop  observed similar behavior in two Swedish boreal catchments but found that stream chemistry became stable beyond a critical basin size of 15 km2. The common theme among these studies is that concentrations of chemical constituents in streamflow approached an asymptotic concentration or converged on a median concentration as basin scale increased. This is an important characteristic of the 2-D conceptual model and provides the framework for the network-mixing conceptual model.
 Since the authors of the studies described above did not find evidence that contributions from basin-scale groundwater were spatially continuous or significant components of streamflow chemistry, any structure in stream chemistry that became apparent with scale was thought to be controlled by mixing processes within the stream network and/or mixing in the riparian zone [Shaman et al., 2004; Uchida et al., 2005]. These findings fit within the conceptual framework of “hillslope aggregation” described in the work of Sivapalan , and we term this behavior the “network-mixing conceptual model.” This is essentially a 2-D conceptual model with limited storage, and runoff is generated primarily by surface and shallow subsurface flow paths along hillslopes (Figure 1a). As a consequence, network mixing will produce a rapid runoff response (Figure 1b) and short travel times when the basin is subjected to a tracer pulse (Figure 1c). In this conceptual model, inputs from surface and shallow subsurface flow paths become increasingly mixed as scale increases, and this leads to the convergence of streamflow chemistry toward asymptotic concentrations of chemical constituents in streamflow (Figure 1d).
 Alternatively, we can use the topography-driven flow concepts originated by Tóth [1963, 1995, 1999] and results from the work of Kirchner et al. [2000, 2001], Lindgren et al. , and Cardenas  to illustrate and define a 3-D conceptual model for streamflow generation at the large watershed scale. In this conceptual model, streamflow will be generated by runoff from surface and shallow subsurface flow paths at the hillslope scales and also by basin-scale groundwater flow paths whose lengths may increase significantly as the scale of the basin increases. The basin-scale groundwater conceptualization is based upon the topography-driven flow model proposed by József Tóth, in which local, intermediate, and regional groundwater flow paths develop in basins as a consequence of the distribution of topographic features and energy gradients [Tóth, 1963, 1995]. These flow paths have different distributions of residence times associated with them, and consequently the amounts of solutes, water age, and heat that they transport to surface drainages are controlled by varying residence time in the subsurface [Tóth, 1999; Kirchner, 2003; Cardenas, 2007]. For example, low-order streams might receive groundwater contributions that have sampled primarily shorter flow paths, and the residence time distribution of the groundwater discharged to the stream will be dominantly young. On the other hand, high-order streams might receive groundwater discharge originating from flow paths of a variety of lengths and tortuosities, and the residence time distribution discharged to the stream will have a tail of much older age. The influence of hydrogeologic setting on geochemical cycling has been documented at very small scales [Devito et al., 2000]; however, unfortunately, very little is known about the role of basin-scale groundwater contributions in streamflow generation from large watersheds. From a Tóthian flow perspective, it seems logical to infer that contributions to streamflow from longer basin-scale groundwater flow paths will become more important as watershed scale increases.
 The 3-D catchment-mixing conceptual model is shown in Figure 1e. The salient difference between this conceptual model and the network-mixing model is that there is much more storage and much more variability in flow path length. The runoff response from this model will be lagged or damped in comparison to that of the network-mixing model (Figure 1f), and the travel time distribution will be very different (Figure 1g). The increased storage and variability in flow path lengths and tortuosities will result in longer residence times in the subsurface. Components of this long residence time groundwater that are discharged to the stream will create tailing in the travel time distribution for the watershed. This behavior has been reported in the work of Kirchner et al. , Lindgren et al. , and Cardenas . Longer residence times also enhance rock-water interactions [Lasaga, 1984]; therefore, basin-scale groundwater that has a long residence time will be more geochemically evolved than runoff flowing along short flow paths. Since these groundwater components have evolved or evolving geochemical signatures [Kirchner, 2003], concentrations of chemical constituents in streamflow should likewise increase with increasing scale (Figure 1h) and should not asymptotically approach some median concentration.
 In this paper, we use end-member mixing analysis (EMMA) on 4 years of stream chemistry and stable isotope data to quantify the components of streamflow generation in the Saguache Creek watershed, a large (approximately 1600 km2) mountainous watershed located in the San Juan Mountains of southwestern Colorado (38°5′14″N and 106°8′29″W). We analyzed the chemistry and stable isotopic composition of streamflow from nested headwater and tributary subwatersheds and at increments in accumulated drainage area working longitudinally down the main channel of Saguache Creek. This nested approach allowed us to monitor streamflow generation processes in scales ranging from 56 to 1400 km2. We also measured vertical hydraulic gradients in minipiezometers installed in streambeds distributed throughout the watershed to quantify the spatial patterns of groundwater discharge to streamflow. The EMMA results and measurements of vertical hydraulic gradient were used to test the two proposed conceptual models. Since contributions from basin-scale groundwater are so critical in distinguishing between these two conceptual models, we were interested in answering the following questions. What is the role of groundwater in streamflow generation in the Saguache Creek watershed, and do groundwater contributions in streamflow become structured with increasing scale? If we see evidence of structured contributions of groundwater in streamflow, then our data set would support the 3-D catchment-mixing conceptual model. On the other hand, evidence of insignificant groundwater contributions in streamflow and/or evidence of asymptotic behavior in streamflow chemistry with increasing scale would support the network-mixing conceptual model.
2. Watershed Climate, Hydrology, and Geology
 The Saguache Creek watershed is located in the San Juan Mountains of southern Colorado (Figure 2). The elevations in the watershed range from 2352 to 4237 m above sea level (asl). Temperatures are strongly correlated with elevation in the watershed. The average daily growing season temperature (May–September) ranges from 8.3°C to 16.3°C at elevations ranging from 3490 and 2350 m, respectively. Temperatures can drop below −40°C in the watershed during the winter. The watershed is drained by a perennial stream, Saguache Creek, which flows into the northern San Luis Valley. There is one continuous stream gauging station in the watershed, and it is located at an elevation of 2448 m asl. The station is operated by the Colorado Division of Water Resources (DWR), and it has an extensive data history (1914 to present). The overall average daily streamflow in Saguache Creek from 1927 to 2010 is 1.78 m3 s−1 (9.98 × 10−3 cm d−1). The minimum average daily streamflow on record is 0.20 m3 s−1 (1.12 × 10−3 cm d−1), and the maximum average daily streamflow on record is 19.2 m3 s−1 (108 × 10−3 cm d−1). These streamflow data are very comparable to other tributary streams of the Upper Rio Grande (URG), where the URG is defined as that portion of the Rio Grande located upstream of the border between Colorado and New Mexico.
 The total meteoric water input to the watershed was calculated from existing precipitation records and data from our own measurements of precipitation (rainfall plus snow water equivalents calculated from snow depths). At elevations lower than 2700 m in the watershed, snow water equivalent (SWE) accounts for 70% of the average annual meteoric input, and rainfall comprises the remainder. In comparison, SWE accounts for approximately 90% of the average annual meteoric input at elevations higher than 2700 m. The overall average annual rainfall recorded at the Saguache Creek DWR weather station is 21.2 cm, the record minimum annual rainfall is 10.8 cm, and the record maximum annual rainfall is 41.2 cm. Approximately 75% of the annual rainfall occurs during the months of June–October; however, June and October are typically dry months receiving less than 7% each. May and October are both transitional months, where rainfall and snowfall are both encountered. The Saguache Creek watershed contains one Natural Resources Conservation Service Snow Telemetry (SNOTEL) site at Cochetopa Pass with a limited history of only 5 years. However, more extensive data sets are available from the Porphyry Creek SNOTEL site located to the north of the watershed and the Slumgullion Pass SNOTEL site located to the southwest of the watershed. Both sites are located within 20 km of the Saguache Creek watershed, but the Slumgullion site may actually be more representative of the high-elevation headwaters of the Saguache Creek watershed. The average maximum SWE for the Slumgullion SNOTEL site is 39.9 cm, with a historical range of 20.6–57.7 cm. Snowpacks typically begin to accumulate on 14 October (water year day 14) and are, on average, depleted by 30 May (water year day 232). These data yield average annual snowpack persistence of approximately 7 months.
 The geology of the Saguache Creek watershed is dominated by felsic volcanic tuffs from the San Juan Volcanic Field (see Taf units in Figure 3) that overlie intermediate composition precaldera lavas and breccias (see Tpl units in Figure 3) from the Conejos and Rawley formations [Steven and Lipman, 1976; Bachmann et al., 2002; Lipman and McIntosh, 2008]. A portion of the massive volcanic rim of the La Garita Caldera [Mason et al., 2004] is located in the headwaters of the watershed, and the presence of the caldera wall in the headwaters has likely played some role in the readjustment, development, and connectivity of groundwater flow paths in the watershed (see black dotted line in Figure 3). Rock glaciers and expansive talus-covered regions are present in the steep headwater subwatersheds (see Ql and Qd units in Figure 3). Headwater streams are intermittently bounded by narrow riparian corridors and narrow floodplains except where alpine meadows, which allow wider floodplain development, are present. In the low-elevation reaches of Saguache Creek, the stream is bounded by a relatively narrow riparian corridor; however, in most cases, the floodplain is wider (Figure 3). The floodplain is itself bounded by cliffs of volcanic bedrock in much of the downstream reach, and this land is used for grazing and nonirrigated hay fields. The riparian corridors and floodplains of the lower reaches of Saguache Creek are developed in gravels and alluvium of the Pinedale and Bull Lake glaciations (see Qg units in Figure 3).
 We classified soils in the field using soil pits because the soils in the watershed had not been classified beyond the soil association level. These classifications indicated that the thin, high-elevation soils have little or no organic development, loamy AE horizons, and relatively weakly developed B horizons. The soils typically contain fragments of biotite, quartz, and sodium- and calcium-rich feldspars and often overlie highly fractured bedrock (Figure 4a). Hillslope and low-elevation soils often contain a shallow, laterally extensive layer of platy, felsic volcanic rocks, which most likely promotes rapid infiltration and throughflow (Figure 4b). Saprolite was encountered in both high-elevation and low-elevation soil pits at depths ranging from 16 to 25 cm and persistent to depths greater than 40 cm. Similar saprolite layers were also encountered within that same range of depth in the soil profiles of study sites in the Front Range of Colorado discussed by Huber et al. . This layer serves as a translatory unit during snowmelt events that saturates from above and then slowly transmits water to the underlying fractured bedrock. Consequently, this layer may be an important control on deep percolation and recharge to bedrock aquifers within the mountain block [Wilson and Guan, 2004].
3.1. Collection of Geochemical and Stable Isotopic Data
 In addition to monitoring streamflow, every effort was made to identify and monitor all the geochemically unique sources of water that may potentially become components of streamflow in the watershed. Frisbee  provides a detailed description of the criteria used in end-member selection (see http://www.ees.nmt.edu/alumni/thesis.php). Streamflow samples were collected monthly during the ice-free season from 2005 to 2009 in nested headwater subwatersheds and longitudinally down the main channel of Saguache Creek. The results from six of those sampling sites will be presented in this paper (Figure 2). Samples were analyzed for pH, electrical conductivity, total dissolved solids, and temperature while in the field. Field acidification was not performed on water samples since the samples were analyzed quickly after collection for chloride (Cl−), calcium (Ca2+), and sodium (Na+) using ion-selective electrodes (ISE). Over 700 water samples were collected during this study, and approximately 20% of the total samples were also subjected to a full general chemistry analysis of all basic cations and anions. We created regressions between the concentrations measured by ion-selective electrodes and those concentrations measured using inductively coupled plasma–mass spectrometry to assess the uncertainty of the ISEs. All water samples were analyzed using the same analytical methods (the analytical methods and variability of duplicates are listed in Table 1). The geochemical evolution of waters in the Saguache Creek watershed is shown in Figure 5.
Table 1. Analytical Methods and Variability of Duplicatesa
In total, over 700 samples were collected during this study. All 700 samples were analyzed for and , and 140 samples were subjected to full geochemical analysis. The charge imbalance for the 140 samples was acceptable and ranged from −0.93% to 3.54%. USEPA, U.S. Environmental Protection Agency.
 Rainfall and fresh snowfall represent beginning points in the geochemical evolution of water in the watershed. In general, rainfall and fresh snowfall were both chemically dilute and exhibited little chemical variation with elevation. Rainfall was collected during the months of April–September 2007 and 2008 from 11 precipitation collectors installed at elevations ranging from 2530 to 3220 m asl. Fresh early season snow (October–February) and fresh late season snow (March through late May) were collected during snow-sampling trips from 2006 through early 2009. Samples of snow from remnant snowpacks (often encountered in May) were collected during the snowmelt seasons of 2006–2009. Bulk and modified bulk snowfall collectors were constructed by modifying the designs presented by Earman et al.  and Frisbee et al. [2010a]. These collectors were installed in October 2007 at remote, high-elevation sites in the watershed prior to the onset of snowpack accumulation during October 2007 [Frisbee et al., 2010a].
 Surface and subsurface runoff represent intermediate stages in the geochemical evolution of water in the watershed. Surface runoff from late season snowpacks and from rainfall were lumped into one end-member because the geochemical composition of surface runoff from remnant snowpacks was not distinctly different than surface runoff collected during rainfall events and the majority of surface runoff was generated during the snowmelt season (surface runoff during the summer rainfall season was not frequently observed). Surface runoff samples were obtained by grab samples made during late April to May for snowmelt runoff and from May to October for runoff from rain events.
 When rainfall, snowfall, or runoff from these sources infiltrated the soil, further geochemical evolution was achieved. Geochemical transformations were quite rapid in the soil, and lengthy residence times were not always needed to obtain significant geochemical evolution in the soil [Davis, 1964; Kennedy, 1970; Campbell et al., 1995; Frisbee et al., 2010a]. We monitored soil water using soil cores and modified passive capillary samplers (M-PCAPS) to constrain the geochemistry of the shallow subsurface runoff component. M-PCAPS were installed at remote, high-elevation locations in the watershed to obtain samples of infiltrating meltwater during snowmelt and infiltrating rainwater during summer precipitation [Frisbee et al., 2010a, 2010b]. Soil cores were collected near the M-PCAPS, and soil water was distilled from these cores for stable isotopic analysis.
 Inputs of rainfall, snowfall, snowmelt, or subsurface runoff that percolate into the underlying fractured bedrock may ultimately recharge the bedrock aquifer. Geochemical transformations in the saturated bedrock are controlled by flow velocities, residence times, rates of kinetic weathering of minerals, and supply of weatherable material in the bedrock [Goldich, 1938]. As a consequence, water from the bedrock aquifer should thus represent an approximate end point in chemical evolution within a watershed [Lasaga, 1984; Bricker and Jones, 1995]. In order to obtain waters samples representative of longer residence times, springs and wells were sampled in the watershed. Seventeen perennial springs were sampled from 2005 to 2009, spanning an elevation range from 2500 to 3400 m asl. Wells are sparse in the watershed, and consequently, only six wells were sampled. Most are located below an elevation of 2600 m asl. However, two wells were located in the backcountry at elevations of 2900 and 3100 m asl. All wells appear to terminate in the local bedrock, with well depths ranging from 25 to 50 m below ground surface. The depth to groundwater is often shallow at low-elevation wells, with depths ranging from a few meters to approximately 10 m below ground surface.
 Minipiezometers were installed in 11 streams in order to sample the chemical and stable isotopic composition of groundwater discharging to the stream through the streambed and to measure the latter's vertical hydraulic gradient [Baxter et al., 2003; Cey et al., 1998; Pretty et al., 2006]. Our minipiezometers were constructed from 1.5 m lengths of CPVC pipe with a 20.3 cm ported interval and were installed at depths ranging from 0.80 to ∼1.10 m into the streambed according to the methodology presented by Baxter et al. . Minipiezometers were pumped and allowed to refill prior to sampling. Samples were retrieved on a monthly basis from installation in June 2008 to removal in October 2008.
3.2. End-Member Mixing Analysis
 End-member mixing analysis reduces data sets of streamflow chemistry so that chemical constituents and end-members are identified that explain the greatest amount of variability in the chemical data set. No a priori information about the end-member population is needed. This is a well-established methodology that has been used to identify sources of water responsible for runoff generation in hillslopes, small catchments, and larger watersheds spanning a range of geographic, geologic, climatic, and environmental conditions [Christophersen and Hooper, 1992; Hooper, 2003; Liu et al., 2004, 2008]. Diagnostic tools of mixing were first applied to identify conservative tracers and determine the dimension of the mixing subspace. A principal component analysis was performed on the conservative tracers of the end-member matrix. Eigenvectors were extracted from the correlation matrix of conservative tracers, and these eigenvectors were used to reproject both streamflow samples and end-member samples into a mixing subspace [Liu et al., 2008]. Residuals calculated from the reprojected streamflow chemistry and original chemistry data set were used to ascertain the appropriateness of the tracers. Random distributions (p > 0.05 and R2 < 0.2) in the plot of residuals versus actual chemical concentration of chemical constituent indicated a well-posed model, while structure in the plot indicated a poorly constrained model [Hooper, 2003; Liu et al., 2008]. The relative root-mean-square error (RRMSE) was also used to ascertain model “fit.” In a well-posed model, the RRMSE typically decreased from the 1-D (two end-members) mixing subspace to higher-dimensional subspaces (e.g., from 1-D to 2-D subspace). The orthogonal projections of the streamflow samples and end-members were then used to calculate the geometric mixing proportions of each end-member. The reprojected concentrations of each individual constituent were then plotted against actual concentrations to ascertain how well the model recreated stream chemistry (a well-posed model produces R2 > 0.70). In order to enhance the accuracy of the EMMA simulations with respect to groundwater, we only included springs and wells that were located in close proximity to the individual stream sampling sites in each simulation. We did not use an average value for groundwater in any of the EMMA simulations because the geochemical and stable isotopic composition of groundwater evolves with scale, and it cannot be assumed that there is only one true or average groundwater signature that contributes to streamflow.
3.3. Measurement of Streamflow
 Discharge was measured at each stream site on a monthly basis during the ice-free seasons from 2005 to 2009. Stream discharge was measured primarily using the velocity-area method; however, the salt dilution method was used in small, shallow streams and during the late summer and fall when streamflow was lowest [U.S. Geological Survey, 1977]. In addition, both methods were employed at individual sites contemporaneously to assess the error between the two methods. The regression between the two measurements of discharge indicated that there was close agreement between the two methods (slope of regression was 0.95, and R2 was 0.98). The uncertainty in streamflow measurement, EQ, was calculated using the root-mean-square approach described by Sauer and Meyer :
where Ed is the standard error attributable to depth measurement errors, Et is the standard error attributable to velocity pulsation, Ei is the instrument error associated with the velocity meter, Es is the standard error due to error in the vertical velocity distribution over an entire cross section, Eh is the standard error due to horizontal angles due to oblique flow, and Ev is the standard error due to the horizontal distribution of depth and velocity between verticals. This error, EQ, is expressed as a percentage, and it ranged from 5.4% to 6.9% for the discharge measurements presented in this paper.
3.4. Quantification of Solute Loads
 Solute loads (kg d−1) at each sampling site were calculated by multiplying the stream discharge (converted into units of L d−1) by the concentration of the chemical constituent of interest (converted into units of kg L−1). We calculated increments in solute load between successive stream sampling sites by subtracting the solute load of the upstream site from the solute load of the downstream site. These increments were then compared to the solute loads input to the stream by tributary flow occurring between the successive stream sites. If the increment in solute load between successive sites was larger than the tributary inputs, then tributary inputs of solute alone could not account for increases in solute load between successive sites. Cumulative uncertainties in solute load calculations were determined using the root-mean-square error propagation approach described by Harmel et al. :
where EQ is the cumulative error attributable to error in streamflow measurement, Esc is the standard error attributable to sample collection methodology, Essp is the standard error attributable to sample storage and preservation, Eaic is the analytical error associated with instrument calibration, and Eaid is the analytical error associated with instrument repeatability (duplicate error). The total potential error in solute load calculation is also expressed as a percentage and ranged from 6.7% to 8.0% for sodium and 9.9% to 10.9% for calcium.
4.1. Trends of Streamflow Chemistry in Saguache Creek
 Our hydrochemical data set reveals that concentrations of chemical constituents in streamflow increase somewhat linearly with increasing accumulated watershed area (Figure 6). This is especially true for the samples collected during the later portion of the season (August–October). The samples collected during the snowmelt season (May–July) often show increased variability at all scales. Although we did not collect monthly samples extending up the headwater streams during every sampling trip for logistical reasons, it is apparent that the linear trends in stream chemistry originate in the headwater streams having drainage areas of 80.8 and 89.0 km2 (Figure 7). This is in stark contrast to the asymptotic trends observed by Wolock et al. , Shaman et al. , Temnerud and Bishop , and Uchida et al. .
 The geochemical evolution of postinfiltration water in the Saguache Creek watershed appears to be controlled first by relatively rapid geochemical transformations in the soil [Frisbee et al., 2010a] and then by much slower geochemical transformations in the bedrock aquifer [Frisbee, 2010]. Results from a weathering study in the watershed indicate that the chemical weathering of bedrock minerals, namely, sodium- and calcium-rich feldspars, potassium feldspar, biotite, quartz, and hornblende, is the primary source of solute release to groundwater, streamflow, and spring flow [Frisbee, 2010]. The chemical weathering of bedrock is a kinetically controlled process, and the release of solutes from bedrock because of weathering is directly related to the residence time of the water in the bedrock. From a Tóthian flow perspective, we envision a suite of flow path lengths and tortuosities in the watershed, with water discharging from each flow path having a distinct geochemical signature and residence time distribution. Shaman et al.  argue that although there is some flow path heterogeneity in natural systems, there is, nevertheless, open exchange and mixing between deeper, older groundwaters and shallower, younger surficial waters. This mixing effectively masks or damps the signature of older groundwaters, and instead, integrated chemical signatures emerge as scale increases. However, we argue that if components of groundwater characterized by increasingly longer residence times are being discharged to the stream, then the stream water should continue to become geochemically enriched even if the long residence time groundwater mixes with younger waters in the hyporheic zone or with waters flowing along shallower flow paths (Figures 1e and 1h).
4.2. End-Member Contributions in Headwater Subwatersheds
 The Saguache Creek watershed has three headwater subwatersheds: North Fork (SCNF), Middle Fork (SCMF), and South Fork (SCSF) of Saguache Creek (Figure 2), with areas of 55.7, 89.0, and 80.8 km2, respectively. The chemistry of North Fork is very different from nearby Middle Fork or South Fork and tends to disrupt the linear trends in stream chemistry beginning in the headwaters (see gray ovals in Figure 6). The primary reason for the anomalous stream chemistry in North Fork is that stream water is diverted from across the watershed divide for irrigation supplementation in the Saguache Creek watershed. The diverted water ultimately flows into North Fork, and as a consequence, streamflow chemistry in North Fork does not display the same variability of Middle Fork and South Fork headwater streams originating within the surficial boundary of the watershed divide. The streamflow separations for North Fork will not be presented in this paper. The Middle Fork drains a high-elevation subwatershed with a maximum elevation of 4237 m asl, and the South Fork drains a high-elevation subwatershed with a maximum elevation of 3900 m asl. The South Fork headwater subwatershed is geologically similar to Middle Fork.
 Stream samples from the Middle Fork and South Fork headwater subwatersheds could be plotted in 2-D mixing subspaces requiring three end-members. To conserve space, data from the regression lines created between the residuals from reprojected stream chemistry and actual stream chemistry for all stream sampling sites are compiled in Table 2. The U-space projections and separated streamflows for Middle Fork and South Fork are shown in Figures 8a, 8b, 8c, and 8d, respectively.
Table 2. Data From the Correlations Between Residuals of Reprojected Spring Chemistry and Original Spring Chemistry for Each Sampling Sitea
EC (μS cm−1)
Ca2+ (mg L−1)
Na+ (mg L−1)
Cl− (mg L−1)
R2 is the coefficient of determination, the p value is the observed significance level at which the null hypothesis will be accepted or rejected (in this case the null hypothesis test is designed to reject end-members that do not contribute significantly to streamflow water quantity, and the p value limits are p > 0.05), and D is the dimension of the mixing subspace where the end-members to be retained are equal to D + 1.
The degrees of freedom are low for SCHR because of limited sampling. EC, electrical conductivity.
 The steep topography and related climatology of these subwatersheds is conducive to small-scale runoff processes such as overland flow and shallow subsurface flow, especially during snowmelt and during intense thunderstorm activity. In fact, the EMMA results indicated that late season snow and rainfall were strong end-members for both headwater subwatersheds (Figures 8a and 8c). The late season snow and rainfall end-members are both relatively dilute and chemically distinct from soil water and groundwater (Figure 5). In order for these dilute chemical signatures to constitute a significant component of streamflow, geochemical transformations during the runoff process must be minimal. These results suggest that rapid runoff processes are important components of streamflow generation in the headwater subwatersheds (Figures 8b and 8d).
 The groundwater components represented by the water samples from the minipiezometers were selected as the third end-member for each headwater stream. The chemistries of all the minipiezometer water samples plotted very close to the chemistry of the water from Stone Cellar well (Figures 8a and 8c). Streamflow generation in South Fork and Middle Fork was controlled mostly by event contributions from rainfall and late season snow in 2007 and early 2008 and primarily by groundwater and late season snow in late 2008 (Figures 8a and 8c). Overall, groundwater accounts for 14%–44% of streamflow generation during the peak of the snowmelt freshet, and it accounts for 19%–78% of streamflow generation during the remainder of the year (Figures 8b and 8d). In this paper, we define the snowmelt freshet as the streamflow occurring from April through July, with a peak pulse occurring typically in June or July. The strength of the groundwater end-member during the peak of snowmelt is surprising given the large volume of event water that these small, high-elevation subwatersheds convey during the snowmelt season. This indicates that groundwater flow paths are well developed in the headwater subwatersheds in drainage areas smaller than 100 km2.
4.3. End-Member Contributions in Saguache Creek
 Saguache Creek was sampled longitudinally downstream from the confluence of the headwater streams (SCHW) to the sampling site near the outlet on the Hill Ranch (SCHR, Figure 2). Saguache Creek is a gaining stream at and upstream of SCHR but changes to a losing stream downstream of SCHR because of groundwater pumping for irrigation in the northern San Luis Valley and diversions from the stream for the town of Saguache, Colorado. Minipiezometers were installed at all locations with the exception of the site located at the confluence of the headwater streams. The minipiezometers at SCHW were repeatedly vandalized or stolen; therefore, no minipiezometer data are available at this site. The SCHW, SCCR, SC1, SC2, and SCHR sampling sites represent accumulated watershed areas of 359, 538, 692, 1083, and 1409 km2, respectively.
 Rainfall, soil water, and groundwater were selected as the three end-members for sampling sites SCHW and SCCR, which are located in the upper reach of the main channel of Saguache Creek (Figure 8e). In the lower reach of Saguache Creek, rainfall, late season snow, and groundwater were selected as the three end-members at sampling sites SC1, SC2, and SCHR (Figures 8g, 8i, and 8k). The strength of the rainfall end-member indicates that rapid runoff must contribute to streamflow at these sampling sites. Field observations indicated that surface runoff in these portions of the watershed occurs primarily during the peak of snowmelt when the floodplain becomes saturated. However, surface runoff was also infrequently observed during very intense summer thunderstorms. The intense summer thunderstorm activity combined with the typically rocky soil cover and relatively short, sparse vegetative cover on the slopes of the lower reaches of Saguache Creek is sufficient to generate surface runoff [Beven, 2002]. Rainfall was a stronger end-member in SCHW and SCCR and accounted for 8%–48% of streamflow generation (Figure 8f). Rainfall was a relatively minor contributor to streamflow in SC1, SC2, and SCHR and accounted for 6%–37% of streamflow generation (Figures 8h, 8j, and 8l). The appearance of rainfall as a minor component of streamflow generation in Saguache Creek indicates that fast runoff processes do occur in this region of the watershed, although they are not dominant.
 It is unlikely that the strength of the late season snow end-member at SC1, SC2, and SCHR is due to local rapid runoff generation (Figures 8g, 8i, and 8k). Snowpacks are relatively thin in the lower reaches of Saguache Creek, these snowpacks melt early in the snowmelt season, and snowmelt runoff is not temporally persistent. Instead, the strength of the late season snow end-member is presumably derived from the integration of snowmelt runoff from the tributary and headwater subwatersheds into the main channel of Saguache Creek. The late season snow end-member becomes important at SC1, remains important at SC2, and is also important at the final sampling site SCHR (Figures 8h, 8j, and 8l). Within this span, Saguache Creek receives flow from confluences with Hodding Creek, Sheep Creek, Middle Creek, and Ford Creek. This suggests that channel routing and connectivity between the main channel of Saguache Creek and its tributaries are important in the overall runoff response from Saguache Creek during very large events and during the recession following these events.
 The in-stream integration of tributary solute loads could potentially increase the solute load of the main channel of Saguache Creek in a structured fashion similar to that proposed by the network-mixing conceptual model [Uchida et al., 2005]. One way to test the dependence of the trends in stream chemistry on the integration of tributary contributions is to calculate the increment in solute load in Saguache Creek between successive sampling sites and compare those loads to the calculated solute loads from each of the tributary subwatersheds. For example, if the increment in solute load between SC1 and SC2 would simply be equal to the solute load inputs from Sheep Creek and Hodding Creek, then this would indicate that in-stream integration processes are responsible for the observed structure in stream chemistry. Table 3 provides the results of these mass balance calculations. The first column contains the sampling location (reference Figure 2). The second column has the Na+ and Ca2+ loads at each sampling location in kg d−1 and at each tributary input. Tributary inputs are listed in Table 3 between the sampling sites that they may influence. The third column has the difference in Na+ and Ca2+ between successive sampling locations. There are no tributary inputs between SCCR and SC1. The input labeled “tributary input 1” is the combined tributary input from Sheep Creek and Hodding Creek that occurs between SC1 and SC2, and the input labeled “tributary input 2” is the combined tributary input from Middle Creek and Ford Creek that occurs between SC2 and SCHR. It is apparent from Table 3 that increments in stream chemistry do not equal the sum of the solute additions from the tributaries. It is also apparent that the increments in solute load are larger than the tributary solute loads plus estimated standard error. Instead, a considerable amount of solute is missing on the basis of this calculation. The most plausible source of this missing solute is groundwater discharge. These findings suggest that while in-stream integration of tributary runoff may be an important process in the overall runoff response from Saguache Creek, it does not explain the structured linear increases in stream chemistry as accumulated drainage area increases.
Table 3. Data Showing the Increments in Na+ and Ca2+ Between Stream Sampling Locations
Na+ Load (kg d−1)
ΔNa+ Load (kg d−1)
384.1 ± 25.7
407.8 ± 27.3
SC1 − SCCR
Tributary input 1
44.1 ± 3.52
516.5 ± 34.6
SC2 − SC1; (SC2 − SC1) > input 1
Tributary input 2
55.6 ± 4.4
584.1 ± 39.1
SCHR − SC2; (SCHR − SC2) > input 2
Ca2+ Load (kg d−1)
ΔCa2+ Load (kg d−1)
1091.8 ± 108.1
1121.5 ± 111.0
SC1 − SCCR
Tributary input 1
112.3 ± 12.1
1370.3 ± 135.7
SC2 − SC1; (SC2 − SC1) > input 1
Tributary input 2
193.5 ± 20.9
1572.5 ± 155.7
SCHR − SC2; (SCHR − SC2) > input 2
 Groundwater was a strong end-member at all sampling sites in Saguache Creek. Groundwater accounts for 6%–12% of streamflow generation at SCCR during the snowmelt freshet and 31%–56% of streamflow during the remainder of the year (Figure 8f). More extensive sampling histories are available at SC1 and SC2, and the groundwater component in streamflow at these sites remains relatively consistent, accounting for 15%–26% of streamflow generation during the snowmelt freshet and as much as 48%–64% of streamflow during the remainder of the year (Figures 8h and 8j). This range also seems reasonable for the final sampling site, SCHR, which represents the largest accumulated drainage area in our study. Although the sampling history is limited, groundwater accounted for 26%–61% of streamflow generation at this site (Figure 8l).
4.4. Structure of Groundwater Contributions and Vertical Hydraulic Gradients
 In order to determine if structure was present in groundwater contributions to streamflow, we plotted individual monthly groundwater contributions against drainage area (Figure 9). During September, the groundwater contributions are very structured and show two distinct trends: (1) groundwater contributions increase with increasing scale in drainage areas greater than 100 km2, and (2) groundwater contributions decrease with increasing scale in headwater drainage areas less than 100 km2. For the headwater drainages, groundwater contributions are quite large, illustrating the importance of groundwater at small scales. The physical processes responsible for the variations in groundwater contributions at small drainage scales are not known at this time but are being investigated further using environmental tracers and hydrogeologic modeling efforts. More importantly, we do not observe asymptotic behavior in Figure 9a. Therefore, these findings provide support for the 3-D catchment-mixing conceptual model.
 The trends in groundwater contributions during August 2008 suggest that groundwater contributions are becoming structured with increasing scale but not to the same extent as observed during September (Figure 9b). During early August, the recession of the snowmelt pulse was still working through the stream network. This snowmelt input coupled with inputs from rainfall probably accounts for the variability observed in Figure 9b. This effect is very strong near the confluence of the headwater streams (see SCHW at ∼350 km2 in Figure 9b). Otherwise, we do observe some structure in groundwater contributions beyond the confluence of the headwater streams at approximately 500 km2.
 Vertical hydraulic gradients were positive in all minipiezometers during the period of observation (approximately 4 months during 2008). Although the minipiezometers provide only point sources of data, this behavior indicates that the contributions from groundwater were relatively consistent during the period of observation. Vertical hydraulic gradients were also plotted against drainage area to investigate the role of groundwater contributions with increasing scale during August and September 2008 (Figure 10). During September, it is apparent that vertical hydraulic gradients do increase with increasing scale beyond 350 km2 (Figure 10a). Data were limited during August 2008 because of vandalism, and a relationship with increasing scale cannot be accurately inferred (Figure 10b). When considered together, the data presented in Figures 9a and 10a provide strong support for the 3-D catchment-mixing conceptual model.
4.5. Geologic Impacts to Basin-Scale Groundwater Flow Path Development
 Small headwater drainages less than 100 km2 exhibit variability in the groundwater component of streamflow, but drainages greater than 350 km2 show structured increases in the groundwater component of streamflow with increasing scale (Figure 9a). An accumulated drainage area of approximately 350 km2 seems to be significant and suggests that the basin-scale groundwater flow field may not be continuous in the Saguache Creek watershed. In fact, this drainage area coincides with the geographical location of the La Garita caldera wall (Figures 2 and 3) [Lipman, 1997]. As a consequence, groundwater flow paths in the headwater subwatersheds might penetrate more deeply than they would in the absence of this barrier, and/or the groundwater flow fields of the headwater subwatersheds might be disconnected from the groundwater flow paths in the high-order, low-elevation regions of the watershed. These structures and their effect on groundwater flow patterns at the large watershed scale are poorly understood. However, recent work indicates that the contrast in permeabilities between these structures and surrounding subsurface media and/or the orientation of these structures with respect to the groundwater flow direction may have significant effects on percolation and groundwater flow patterns [Caine and Tomusiak, 2003].
 The influence of the La Garita caldera wall on groundwater flow path development is one possible explanation for the two trends discussed above. If, for example, the subsurface is a homogeneous medium and contributions from Tóthian groundwater flow fields are the only sources of water and solutes to streamflow, then we would expect to see a relatively smooth increase in streamflow chemistry with increasing watershed scale [Cardenas, 2007]. However, natural media are almost never homogeneous. As a consequence, geologic features in other watersheds may disrupt the development and connectivity of basin-scale flow fields, and this, in turn, may mask trends in streamflow chemistry and age distributions if the geologic history of the watershed is not considered.
 We designed our study to test two conceptual models of streamflow generation at large watershed scales. Plots of chemical constituents in streamflow revealed linear increases in concentrations of various constituents with increasing accumulated drainage area. We used end-member mixing analyses (EMMA) and measurements of vertical hydraulic gradients (VHG) in streambeds to quantify the role of deep, large-scale groundwater in streamflow generation. EMMA results indicated that groundwater contributions increase with increasing scale from accumulated drainage areas greater than approximately 350 km2. This was supported by measurements of VHG, which indicated that VHG increased with increasing scale from accumulated drainage areas greater than 350 km2. When considered together, these findings support the 3-D catchment-mixing conceptual model over the network-mixing conceptual model.
 What are the implications of these findings? These results indicate that large-scale, long residence time groundwater contributions are important controls on streamflow generation and trends in streamflow chemistry with increasing scale in the Saguache Creek watershed. However, from a Tóthian perspective, components of long residence time, geochemically evolved groundwater associated with larger-scale flow systems will not necessarily be observed at the hillslope and/or small headwater catchment scale. Instead, streamflow chemistry at hillslope and smaller catchment scales may be controlled by water sources having limited geochemical evolution indicative of faster runoff processes and even perhaps local groundwater flow. In comparison, the groundwater system appears to be well developed at all scales in the Saguache Creek watershed, and as scale increases, it appears that components of older, more geochemically evolved waters are discharging to the stream. This provides a dominant control on the evolution of streamflow chemistry and provides one explanation why asymptotic trends in streamflow chemistry were observed at much smaller scales in previous studies and not within the Saguache Creek watershed.
 The structure of groundwater contributions in streamflow also has important implications for our perception of apparent ages in streamflow. Contributions to streamflow range from direct inputs during meteoric events to very old contributions from longer, tortuous basin-scale groundwater flow paths. These old, persistent contributions from groundwater are likely responsible for the tailing observed in residence time distributions in watersheds. For example, the 3-D catchment-mixing conceptual model that we propose in this paper may provide an explanation for the fractal scaling of residence times reported in the work of Kirchner et al. [2000, 2001]. Previous modeling efforts have indicated that the topography-driven flow field concepts proposed by Tóth  can generate fractal behavior in residence time distributions [Cardenas, 2007]. In fact, Lindgren et al.  proposed that in watersheds where residence time distributions are fractal, most of the solute mass in streamflow must be contributed by groundwater flow paths as opposed to rapid runoff processes. We assert that in the Saguache Creek watershed, groundwater contributions are the framework for the geochemical signal observed in streamflow across multiple scales and that hillslope-scale runoff processes superimpose noise on that signal. Our findings in the Saguache Creek watershed cast doubt on the hillslope aggregation concepts for scaling runoff processes to larger watershed scales. When viewed from a Tóthian flow perspective, large watersheds are more than simply the aggregation of hillslope runoff responses.
 Funding for this research was provided by the Sustainability of Semi-arid Hydrology and Riparian Areas (SAHRA) Science and Technology Center of the National Science Foundation (NSF agreement EAR-9876800). Funding was also provided by the New Mexico Water Resources Research Institute in the form of a student water research grant. We thank the Saguache Field Office of BLM/USFS for logistical support with field installations in the Saguache Creek watershed. We thank Emily Engle, Ginny Bracht, Andrew Fargo, Jesus Gomez, Andre Ritchie, Frank Hack, Shasta Marrero, Matt Baillie, Jane Overton, Siona Curtis-Briley, and Sam Siemens for field assistance. We also thank Bonnie Frey, Frederick Partey, and Dustin Baca at the New Mexico Bureau of Geology and Mineral Resources Chemical Laboratory and Gabe Graf and Matt Earthman in the New Mexico Tech Stable Isotope Laboratory. Certain aspects of this study would not have been accomplished without the cooperation of local ranching families, and we are very grateful for the support provided by the Curtis, Gilbert, Hill, Nielsen, and Williams families. The comments and suggestions from Hoshin V. Gupta and three anonymous reviewers greatly improved this paper.