Tributary streams flow from the headwaters directly to the main stem in the valley axis and represent an important general stream type with high surface areas to volume and high streambed exchanges along much of their length. These characteristics strongly influence water quantity and quality in tributary streams, as well as the underlying groundwater and, eventually, the main stem. Tributary streams can be described as consisting of upland, central, and distal reaches, each with temporal trends in streambed exchanges unique to their spatial position along the tributary stream. In this work, thermal tracing and hydraulic monitoring reported in earlier works have been analyzed to compare surface-water/groundwater streambed exchange patterns along Fish Creek Wyoming (US), a well-studied tributary stream in a humid watershed. Results of this analysis demonstrate that composite thermal/hydraulic techniques successfully differentiated reach-specific streambed exchanges to distinguish upland, central, and distal reaches along Fish Creek above the Snake River. The upland and central reaches streambed exchanges were primarily vertical and horizontal streambed exchanges normal to general streamflow, while the distal reach streambed exchanges were lower in magnitude and more longitudinal in the same direction as streamflow. Heat-based streambed hydraulic conductivities were highest (and isotropic) for the upland reach and lowest (and strongly anisotropic) for the distal reach, in accordance with general downstream sediment fining approaching a main stem. These distinct reach patterns should show general transfer value, since general tributary streambed exchange patterns are expected to be influenced by proximity to headwaters in the upland reach, by buffering within alluvial fill in the central reach, and by proximity to the main stem in the distal reach.
 Tributary streams are rarely defined in hydrologic research, with a definition simply assumed even within the most comprehensive geomorphology volumes such as Leopold et al. . A typical general dictionary definition is “a tributary (or affluent) stream is one that flows directly into a main stem (or parent) river or lake,” and though sparse, this is a reasonable definition. As a more spatially inclusive definition, a tributary stream may be defined as a stream that flows from a headwater source directly into the main stem stream (or a lake) in the axis of the valley. By this definition, a tributary stream may or may not have a headwater stream flowing into its upper reach and may or may not have secondary streams flowing into its length before it reaches the main steam, indicating that “a stream flowing directly into the main stem” is the necessary and sufficient definition of a tributary stream, though both headwater streams and secondary streams coming into the tributary stream are highly likely in humid watersheds. The present work deals with this general case, not addressing the topographic end-member tributary streams represented by backwater streams sluggishly flowing toward a main stem in a swamp or oxbow valley or headwater streams discharging directly to a main stem flowing through a canyon.
 Relative to the main stem, tributary streams generally have high surface area to volume ratios demonstrated by factors such as rapid stream temperature changes and having high streambed exchange rates due to seasonal renewal of higher hydraulic conductivies and dynamic hydraulic gradients in response to changing groundwater elevations between the headwaters and the main stem. These properties combine to strongly influence water quantity and quality in the tributary stream, as well as the underlying groundwater and eventually the main stem. Surface-water/groundwater streambed exchanges (abbreviated here on as “streambed exchanges”) along tributary streams are expected to be different in general for streams in humid, semiarid, and arid watersheds, though the present work only addresses tributary streams flowing through humid watersheds as the least challenging to investigate initially. This work analyzes and interprets a series of U.S. Geological Survey (USGS) reports on an extensively studied stream in western Wyoming, as an excellent example, to quantitatively identify specific reach types using trends in seasonal streambed exchange patterns along this tributary stream flowing through a humid watershed.
2. Research on Streambed Exchange Patterns
 A trio of researchers may be considered pioneers in investigating the complexity of flow between surface-water and underlying sediments. Toth  recognized that flow paths simultaneously exist on several scales; Vaux  mapped out detailed spatial-scale streambed exchange patterns, while Winter et al.  documented large spatial-scale fluxes near surface-water bodies in general. From their insights, streambed exchanges are recognized as influenced by sediment hydraulic conductivity and hydraulic gradient mechanisms in the following manner. Universally heterogeneity in streambed hydraulic conductivities leads to streambed exchanges in all three orientations, plan view [e.g., Conant, 2004], cross section, and longitudinal to stream [e.g., Becker et al., 2004; Essaid et al., 2006]. For significant hydraulic gradients, Su et al.  portrayed the influence of variable hydraulic conductivities on the complexity of streambed flow patterns, and Cox et al.  showed the impacts of gradual downstream changes in both hydraulic gradients and hydraulic conductivities on cross-section streambed exchange patterns. On a larger spatial scale, combined seasonal variability in near-stream and regional groundwater flow patterns combined with reach-specific streambed geomorphology has been shown to result in both spatial and temporal variability in streambed exchanges along tributary streams [e.g., Niswonger and Prudic, 2003; Stonestrom et al., 2007]. After Vaux  published his pioneering descriptions of longitudinal streambed exchanges on the scale of centimeters to tens of centimeters, his research was followed by Bencala and others beginning in the 1980s [e.g., Bencala and Walters, 1983; Harvey and Wagner, 2000]. For small streambed hydraulic gradients, topographic relief in the stream and in streambed surface topography induces sufficient gradients to create streambed exchanges [e.g., Cardenas et al., 2004; Cardenas and Wilson, 2006, Naranjo et al., 2012]. Studies to describe complexity in longitudinal streambed flowpaths are ongoing [e.g., Gooseff et al., 2006; Lautz and Siegel, 2006; Cardenas and Wilson, 2007; Fanelli and Lautz, 2008; Cardenas, 2009; Boano et al., 2010; Shope et al., 2012]. Results of this extensive research demonstrate that streambed exchanges are temporally and spatially complex, controlled by heterogeneity in streambed conductivity, topographically driven hydraulic gradients, and a mixture of local and regional groundwater flow patterns. This suggests that streambed exchange patterns are both dynamic and potentially “reach-distinctive” along tributary streams, since the upland reach is more influenced by headwaters' impacts on controlling factors, the distal reach is more influenced by main stem's impacts on controlling factors, and the central reach is more buffered from these influences than adjoining reaches along tributary streams. The objective of the present work is to analyze long-term data collected for Fish Creek as reported in USGS reports [Wheeler and Eddy-Miller, 2005; Eddy-Miller et al., 2009; Eddy-Miller and Wheeler, 2010; Eddy-Miller et al., 2010], with the goal of isolating seasonal, reach-specific patterns of streambed exchanges along Fish Creek flowing from the headwaters down near the confluence with the Snake River, and to identify reach-specific streambed exchange patterns for potential transfer value to tributary streams in humid watersheds in general.
3. Setting, Methods, and Procedure
 As shown in Figure 1, Fish Creek is a 25 km long tributary stream of the Snake River located in Jackson Hole (valley), with a drainage area is 183 km2 at the USGS streamflow-gaging station Fish Creek at Wilson, Wyoming. Depth to bedrock deepens rapidly away from the Tetons, which are lifted up several thousand feet north and west of Fish Creek [Nolan et al., 1998]. Several intermittent and perennial tributaries from the west flow directly off the steep headwaters or through incised canyons into Fish Creek, as is common for tributary streams in the region [Nolan and Miller, 1995]. Flows in Fish Creek are correlated to groundwater level changes influenced by natural recharge, recharge from local flood irrigation, injection of tertiary treated sewage, and recharge from infiltration through the streambed of ditches, tributaries such as Lake Creek. The climate near Fish Creek is humid to semiarid in nature, with cold winters and cool, often wet summers, and snowfall typically begins to accumulate in the valley in November with occasional melting during the winter, with the bulk of the snowpack on the valley floor usually melts in one event during late March to early May, evidenced by a rapid rise in the alluvial water table. Snowmelt from the headwaters occurs over a longer period of time from May to July, and irrigation begins in late April to early May and continues until September, depending on the year's climate and agricultural needs, contributing shallow groundwater to Fish Creek.
 A composite thermal/hydraulic technique was employed for a more comprehensive analysis of both streambed fluxes and heat-based estimates of hydraulic conductivities unavailable without tandem hydraulic monitoring. Thermal techniques afford increased qualitative and quantitative success in estimating streambed exchanges, including, for example, the work of Constantz et al. , Constantz , Constantz and Stonestrom , Constantz et al. , Constantz et al. , Cardenas et al. , Cardenas and Wilson [2006, 2007], Conant , Schmidt et al. , Rosenberry et al. , Anibus et al. , Barlow and Coupe [2009, 2011], and Rau et al. . The present analysis stemmed from Ronan et al.  in which detailed initial reports of fluxes within streambed cross sections normal to the mean direction of streamflow using heat tracing, as summarized graphically in Constantz [2008, Figure 9]. Work by Conant [2004, Figures 8 and 10] provides depictions of plan views and cross sections of conductivity-induced flux variability that have been broadly insightful to the hydrologic community. Work by Bense and Kooi  demonstrates that streambed heterogeneity induces seepage variability, which in turn is reflected in the patterns of shallow streambed temperatures over time. The present analysis also relied on Essaid et al. [2006, Figure 3] in which preferential discharge through a stream at the location where a clay layer was breached on one side of the streambed, and Essaid et al.  in which seasonal variability in streambed exchanges were most pronounced in high hydraulic conductivity zones in the streambed. Brookfield et al.  examined the use of a fully integrated 3-D model in the near-stream environment with thermal tracing, though available data from USGS reports cited above were insufficient to permit this comprehensive approach.
3.3. Analysis Procedure
 Synthesis and interpretation of multiple studies using thermal tracing, hydraulic techniques, and stable isotopes [Wheeler and Eddy-Miller, 2005; Eddy-Miller et al., 2009; Eddy-Miller and Wheeler, 2010; Eddy-Miller et al., 2010] were used in the present study to aid in separating out a trio of distinct reaches within the tributary stream length of Fish Creek. The streambeds at Teton Village (TV) cross section in the upland reach, Resor's Bridge (RB) cross section in the central reach, and Wilson (W) cross section in the distal reach were each instrumented with five piezometers to continuously monitor stream and groundwater temperature and water levels during 2004–2006. With completion of the composite thermal/hydraulic data collection, a two-dimensional (2-D) groundwater-flow and heat-transport simulations were then used to quantitatively interpret measured temperature and hydraulic-head distributions. Stage, water level, and temperature data were used to calibrate cross-section data, and VS2DH [Healy and Ronan, 1996; Hsieh et al., 2000; Healy, 2008] simulation models of 2-D streambed flow into or out of the stream at the three cross-section locations were analyzed from results reported in Eddy-Miller et al. . Model simulation results were used to estimate aquifer properties, such as the effective hydraulic conductivity of the streambed, and to estimate lateral and vertical streambed exchanges across the boundaries, and subsequently in the present work, these results were analyzed to characterize reach-specific spatial and temporal streambed exchanges along Fish Creek.
4. Results and Discussion
4.1. Streambed Exchange Patterns at Each Reach
4.1.1. Upland Reach
 For the TV cross section, Figure 2a depicts streambed exchanges across the center of the streambed, showing that water exchanges were primarily upward into the stream channel as the stream began flowing in the spring. This is supported by positive differences in hydraulic gradient as well as measured negligible diurnal fluctuations in streambed temperature at depth indicating groundwater discharge up into the upland reach. For June and July, inspection of Figure 2a indicates that groundwater was significantly cooler than stream water in June and July, representing a pulse of recharge from headwaters snowmelt on the nearby headwater flanks to the north and west in a rapid fashion similar to rapid percolation in less humid watersheds, e.g., Constantz and Thomas . In Figure 3a, simulation results indicate negligible shallow lateral flow into the sides of the streambed, and inflow across the right-bottom (western) boundary was generally greater and cooler than inflow from the east, due to cooler headwaters recharge compared with groundwater inflow from the eastern side from irrigation water in central reach ditches and fields. By the end of September, creek flow and regional groundwater levels had decreased due to lack of snowmelt and irrigation (Figure 3a, 30 September 2006). Hydraulic disconnect is often an important feature in stream exchanges with groundwater [Brunner et al., 2009; Desilets et al., 2008], which briefly occurs in the upland reach during early fall just prior to ephemeral conditions. Simulation results indicate generally cooler conditions during the warm season than downstream reaches even though the general climatic patterns, riparian vegetation size, and density were similar during the study period. This probably indicates a greater percentage of discharge from snowmelt-derived headwaters recharge and surface runoff into Fish Creek in the upland reach, in accordance with the observation of less evaporative fractionation of stable isotopes in the upland reach [Eddy-Miller and Wheeler, 2010].
4.1.2. Central Reach
 For the RB cross section, streambed exchanges in the central reach were influenced by a combination of infiltration of valley-floor snowmelt in early spring, snowmelt recharge from the mountain range to the west in early summer, and recharge to the east from irrigation. Vertical streambed exchanges of headwaters recharge to the stream occurred mainly in June and July, as indicated by the positive head differences and the relatively steady cool temperatures in the center of the streambed (RB-2 in Figure 2b, and Figure 3b 12 June 2006). The streambed exchanges were minimal during late August to early September, suggesting little groundwater recharge (Figure 3b, 23 August 2006), and based on measurements at the RB cross section, the central reach became a losing reach during the fall and winter as groundwater levels declined (Figure 3b, 19 October 2005). Lateral streambed exchanges fluctuating through the year were superimposed on these more seasonal trends on larger spatial scales in the watershed; for example, temperatures on the west bank (RB-5, Figure 2b) show a dip in temperature similar to that observed below the center of the streambed (RB-3) during June and July, suggesting inflow of headwaters recharge from the Teton range on the west that is not evident on the eastern bank (RB-1), which also illustrated by the relatively high lateral streambed exchanges from the west predicted by simulations (12 June 2006, Figure 3b). In contrast, an earlier dip in temperatures can be observed on the eastern (RB-1) and western bank (RB-5) during April and early May (Figure 2b), which was more pronounced on the east than the west, and not evident below the center of the channel (RB-3), with the timing of this pulse of colder recharge, suggesting the origin was valley floor snowmelt. During the dry season, a lateral east to west flow component develops at this site (see hydraulic gradient shown in Figure 2b, and boundary flows in Figure 3b, 19 October 2005). The direction of lateral flow across the right-hand (western) boundary changed, suggesting that local shallow groundwater flow patterns reverse during the year as the influence headwaters recharge on the west decreases and the influence of irrigation and the Snake River to the east increases through the summer and fall. Wider ranges in stable isotopic fractions in the central reach relative to the upland reach suggests that in addition to the headwaters recharge pulse on the west side of the creek in the central (during June and July), there was more influence of shallow riparian water sources at this central location [Eddy-Miller and Wheeler, 2010].
4.1.3. Distal Reach
 For the W cross section, unlike upstream, there was no evidence of headwater snowmelt recharge in the temperature distributions (W-1, W-3, and W-5 in Figure 2c) during June and July. Review of the W cross section results indicated that smaller head differences lead to smaller streambed exchanges than in the upland and central reaches, and highly variable streambed exchange patterns likely due to a greater sensitivity to stream and streambed topography changes with very low vertical hydraulic gradient in the distal reach. Streambed exchanges appear more apparent from the northern side of the stream than from the southern side, and the lateral flow direction fluctuates seasonally on the south (Figure 3c; 27 June 2005, 21 April 2006, and 16 August 2006). The temperature distribution on the northern bank (W-1, Figure 2c) showed a pattern that is similar to the seasonal stream temperature with a time lag. This may be an indication of longitudinal downstream shallow groundwater flow across the meander in Fish Creek upstream of the W cross section in the distal reach, similar to the longitudinal downstream flow patterns in the models of Cardenas  and Boano et al. . In agreement, stable isotope analysis in the distal reach revealed more evaporative fractionation compared with the upland and central reach sites, suggesting greater in-stream and shallow groundwater evaporation [Eddy-Miller and Wheeler, 2010]. Streambed exchange was nearly always from the groundwater to the stream, with the only exception related to an ice jam that raised the stage of the creek causing a pulse of cold stream water to infiltrate into the streambed and banks (Figure 3c, 10 December 2005). The streambed exchange distribution showed that most of the groundwater flowing into the stream came across the bottom boundary, with the exception of 27 June 2005 (Figure 3c) when a relatively cold pulse of water was flowing in through the northern boundary. In contrast to the upland and central reach sites, the spring temperature distributions in the distal reach (Figure 2c and 21 April 2006; Figure 3c) showed warmer water in the center of the streambed (W-3), relative to the laterally inflowing water (W-1 and W-3), and given the smaller hydraulic gradients in the streambed at the W cross section, the warmer water in the distal reach may be an indication of dominant longitudinal downstream flow, i.e., most of the streambed flow was normal to the cross section shown in Figure 3c, supported by lower vertical heat transport during longitudinal streambed flow [Constantz, 2008].
4.2. Comparisons of Exchange Patterns Between Reaches
 As displayed in Figure 3, late April streambed was warmer for the distal than the upland reach due to both solar heating with downstream travel and lack of colder headwaters recharge present downstream, while in June, the distal reach streambed was warmer due to streambed localized longitudinal flow. Westside headwaters recharge in the upland reach was colder than the eastside, indicating continuous recharge from the west, which is apparent for the central reach when comparing June with August thermal patterns. In the distal reach, smaller vertical streambed exchanges and warmer streambeds are in agreement with significant longitudinal flow in the distal reach, and the warming of the distal reach by shallow groundwater is seen by comparing December with April. Comparisons of heat-based hydraulic conductivities derived from simulations provide a sense of downstream trends in streambed conductance along Fish Creek. The uplands streambed at the TV cross section had isotropic hydraulic conductivity of 1 × 10−4 m/s for both the horizontal and vertical directions, due to reworking of the stream channel. Streambed hydraulic conductivity (K) developed increasing anisotropy from the central to the distal-reach cross sections as follows. The central reach at the RB cross section had horizontal (h) and vertical (v) heat-based K values of Kh = 5 × 10−5 m/s and Kv = 1 × 10−5 m/s, and the distal reach at the W cross section had horizontal and vertical K values of Kh = 1 × 10−4 m/s and Kv = 5 × 10−6 m/s. Decreased streamflow velocities approaching the main stem, resulting in Stoke's law settling of finer material, which may have caused this trend in downstream lowering of vertical K values, and fining is expected regardless of the wetness of the watershed, see Stonestrom et al. [2007, Figure 3 p. 87]. Seasonal trends in Figure 3 are apparent as well, with the later seasonal values trending toward losing conditions in the lower left portion of the graph, coincident with the largest diurnal variations in streambed temperatures plotted in Figure 2 as heat was convectively transported downward during percolation in response to the reversal in hydraulic gradient. Generally, negligible hydraulic gradients in the distal reach results in horizontal flow in the streambed, such that heat flow was primarily limited to diffusive heat conduction in the vertical directions (Figure 2c).
 In Figure 4, vertical streambed exchanges based on simulation results measured streambed temperatures versus measured vertical hydraulic gradients are plotted in the thalweg of each cross sections representing the upland, central, and distal reaches. There is a general pattern of both greater vertical streambed exchanges and hydraulic conductivies in the upland and central reach compared with the distal reach as the tributary stream transitioned from significant elevation gradients beneath the headwater to a nearly flat water at the distal reach above the main stem. Due to Darcy relations of the slopes, three linear fits represent a quantitative measure of vertical streambed conductivities in the middle of the channel progressively downstream for the three reaches. Simulation results for vertical K values are 1 × 10−4 m/s, 1 × 10−5 m/s, and 5 × 10−6 m/s for the upland, central, and distal cross sections, respectively, and linear-fit coefficients vertical K values are 4.5 × 10−5 m/s, 2.1 × 10−5 m/s, and 7.4 × 10−6 m/s for the upland, central, and distal reaches, respectively. Though qualitative agreement is apparent, the discrepancies in absolute agreement (specifically at TV) probably stems from reliance only on lower boundary to derive linear-fit coefficient values in Figure 4. Even with this limitation, this final analysis provides a reasonably quantitative and coherent graphical picture of streambed exchanges and hydraulic conductivities trends for Fish Creek that may qualitatively apply in general to tributary streams in humid watersheds.
5. Summary and Conclusions
 Data available in several USGS reports describing watershed characteristics and streambed exchanges along the Fish Creek proved to be a valuable suite of quantitative information for formulating an analysis of reach-specific streambed exchanges patterns to delineate each reach type in the following manner. Dynamic patterns in uplands reach streambed exchanges were strongly influenced by headwaters recharge and large fluctuations in the water table initiated from from the east with significant irrigated agriculture; though for tributary streams in humid watersheds with more modest headwaters and negligible ditches and/or irrigation, the upland exchange pattern would be expected to be less dynamic. For Fish Creek, the immediate presence of the headwaters and ample irrigation to the east created strongly gaining conditions, except in the driest period into fall when headwater reserves and irrigation were greatly reduced, resulting in a rapid drop in the groundwater elevation and, eventually, strongly losing conditions. Streambed exchanges in the central reach were buffered from the headwater's variability, with the central reach receiving a range of groundwater inputs both from headwaters further west and extensive valley fill on either bank. The central reach streambed exchanges showed lateral inflow of valley fill snowmelt during spring, following by upward discharge of snowmelt-derived groundwater during summer, and during the rest of the year, the central reach was either neutral or losing stream water, and the direction of lateral streambed exchanges were highly variable in both the central and distal reaches and sensitive to local hydrologic conditions. In both the upland and central reaches, regional groundwater flow appeared to be superimposed on localized groundwater flowpaths as a compound influence on streambed exchanges, whereas the distal reach's streambed exchanges were dominated by localized flowpaths that were sensitive to seasonal variations that can reverse lateral flow directions in the streambed. The distal reach had the longest surface water travel time from the headwaters above the upland reach, while receiving groundwater discharge in very short-range travel paths from immediately upstream of the cross section and from the surrounding shallow water table. The distal reach showed little indication of headwaters recharge during summer, with streamflows being maintained by streamflow in the upper part of the tributary stream and within the distal reach. The longitudinal streambed flows were due to very low hydraulic gradients as a result of the nearby main stem, which should be expected for distal reaches in tributary stream in humid watersheds. In sum, the graphic trends expressed in Figure 4 may be common for many tributary streams in humid watersheds, though muted in the presence of headwaters of modest elevation.
 For the future, an appreciation of approximate reach boundaries between upland, central, and distal reaches should afford the opportunity to confine measurements within specific reaches to more accurately characterize intrareach hydraulic properties and hydrologic processes, including net gains and losses within each reach. Finally, an understanding of where and when to expect streambed exchanges has significance beyond water supply and quality to a broad array of environmental issues, including fishery habitats in tributary streams.
 Fish Creek landowners provided property access. The Teton Conservation District, Teton County, Wyoming Water Science Center, and National Research Program, USGS, provided funds. D. A. Stonestrom (USGS) provided detailed interpretations of unpublished isotope data, and Grant Ferguson and two anonymous reviewers provided substantial colleague reviews.