Corresponding author: A. M. Helton, Department of Biology, Duke University, Box 90338, Durham, NC 27708, USA. (firstname.lastname@example.org)
 Biogeochemical cycling within river ecosystems is strongly influenced by geomorphic and hydrologic dynamics. To scale point observations of temperature and dissolved oxygen (DO) to a hydrologically complex and dynamic three-dimensional river-floodplain-aquifer system, we integrated empirical models of temperature and biotic oxygen utilization with a recently published hydrogeomorphic model. The hydrogeomorphic model simulates channel flow, floodplain inundation, and surface-subsurface water exchange on the 16 km2 Nyack Floodplain, Middle Fork Flathead River, Montana, USA. Model results were compared to observed data sets of DO to test the hypothesis that complexity in spatiotemporal patterns of biogeochemistry emerges from a comparatively simple representation of biogeochemical processes operating within a multidimensional hydrologic system. The model explained 58% of the variance in 820 DO measurements that spanned the study site longitudinally, laterally, vertically, and across river discharge conditions and seasons. We also used model results to illustrate spatial and temporal trends of temperature and DO dynamics within the shallow alluvial aquifer, which is an extensive hyporheic zone because subsurface alluvial flow paths are recharged primarily by channel water. Our results underscore the importance of geomorphic, hydrologic, and temperature dynamics in driving river ecosystem processes, and they demonstrate how a realistic representation of a river's physical template, combined with simple biogeochemical models, can explain complex patterns of solute availability.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Predictable one-dimensional patterns of solute concentrations occur along subsurface hydrologic flow paths at the scale of centimeters to meters as each solute is consumed and produced by biogeochemical processes [Baker et al., 2000; Hedin et al., 1998; Vidon and Hill, 2004, Zarnetske et al., 2011]. As individual hydrologic flow paths diverge and converge within the surface and subsurface of larger river systems, different combinations of solutes are brought together, creating a three-dimensional landscape that encompasses a wide range of biogeochemical possibilities [Fisher et al., 2004; McClain et al., 2003]. Projecting our understanding of small-scale biogeochemical patterns to predict large-scale floodplain behavior requires a quantitative approach to integrating physico-chemical changes commonly observed along individual flow paths into complex hydrogeomporphic networks. Developing methods to scale observed one-dimensional biogeochemical patterns to three-dimensional river-floodplain-aquifer systems is fundamental for understanding the complex spatiotemporal patterns of biogeochemical cycling across fluvial landscapes.
 Rivers systems include hydrologically interdependent compartments: surface channel(s), the subsurface alluvial aquifer including the hyporheic zone, and the floodplain surface including riparian ponds, wetlands, and areas periodically inundated during high flow [Stanford and Ward, 1993]. Hydrologic flow drives the exchange of dissolved and particulate materials among river compartments, where these transported materials may be retained and transformed by various physical and biological processes [Baker et al., 2000; Dahm et al., 1998; Fisher et al., 1998]. For example, when the ratio of subsurface to surface flow is high, microbial processes within hyporheic zones can account for the majority of whole ecosystem processes [Fellows et al., 2001], and hyporheic water discharged back to the channel can influence surface water chemistry [Dent et al., 2001] and temperature [Arrigoni et al., 2008]. Thus, hydrologic dynamics of a river ecosystem control both the magnitude and rate of solute exchange among different river compartments, and the contact time between solutes and microbial communities within those compartments.
 Traditional methods that focus on understanding hydrologic connections between river compartments are inadequate for describing hydrologic fluxes at the fluvial landscape-scale (e.g., 10 s of meters to kilometers) and therefore the effects of hydrologic dynamics on biogeochemical fluxes and processes at the landscape scale [Bencala et al., 2011]. Widely applied tracer techniques capture hydrologic exchanges that are short in time and space (hours to several days; centimeters to meters) [Poole et al., 2008], and regional analysis of river gauges capture only the net (not the gross) hydrologic exchange between the river channel and other compartments over spatiotemporally coarser scales. Existing groundwater flow simulation models (e.g., MODFLOW) [McDonald and Harbaugh, 2003] are designed to simulate subsurface water movement and lack the ability to simulate dynamic patterns of inundation across complex, low-relief landscapes, like floodplains [Jones et al., 2008]. Thus, such models lack the ability to describe spatiotemporal variability in surface water hydraulic head that drives hydrologic exchange [Poole et al., 2006].
 Here, we used a recently published three-dimensional hydrogeomorphic model of a river-floodplain-aquifer system, the 16 km2 Nyack Floodplain of the Middle Fork Flathead River [Helton et al., 2012]. We linked the hydrogeomorphic model to empirical models of temperature and biotic oxygen utilization to simulate temperature and oxygen dynamics across the study site. The hydrogeomorphic model parameterization included analysis of a high resolution elevation data set to delineate geomorphic controls on inundation dynamics [Jones et al., 2008] and thus represents detailed spatiotemporal variation in floodplain inundation, which drives additional hydrologic exchange between surface- and aquifer water.
 Our objective was to determine if a relatively simple, one-dimensional flow path biogeochemical model, when integrated within a sufficiently realistic three-dimensional hydrologic model, could explain complex spatial and temporal patterns in dissolved oxygen (DO) dynamics across the expansive shallow alluvial aquifer. Patterns in model output were compared to large observed data sets in both space (longitudinal, lateral, and vertical patterns within the floodplain) and time (across discharge conditions and seasonal variability) to determine whether spatiotemporal complexity in observed DO and temperature dynamics emerges from simple biogeochemical dynamics operating within the relatively complex hydrologic system of this Rocky Mountain alluvial river.
2. Study Site
 The study site is a 16 km2 montane floodplain (Figure 1) on the gravel- and cobble-bedded Middle Fork of the Flathead River, located in northwest Montana, USA. The river is unregulated and most of the 2300 km2 upstream catchment is in federally protected wilderness or Glacier National Park, including the hillslopes adjacent to the floodplain. Hay production and some logging have occurred on the floodplain over the last 100 years and a railroad traverses the western portion of the floodplain, but the river is wholly unregulated and generally lacks man-made structures (e.g., dikes and levees) that would influence patterns of floodwater inundation.
 The hydrology and geomorphology of the study site are well characterized [Helton et al., 2012; Poole et al., 2002, 2004, 2006]. The floodplain is constrained laterally by bedrock valley walls and bounded upstream and downstream by canyon segments with bedrock river beds. The annual flow regime of the fifth-order river is dominated by snowmelt, with a mean discharge of 80 m3 s−1 and mean peak discharge of 600 m3 s−1 (discounting the extraordinary peak discharge of nearly 4000 m3 s−1 that occurred in 1964) [Poole et al., 2004]. Annual spring floods inundate large areas of the non-channel floodplain surface [Helton et al., 2012].
 Complex channel morphology and coarse, well-sorted sediments on the floodplain facilitate high rates of surface-subsurface water exchange with an extensive alluvial aquifer that is greater than 25 m thick near the upstream end of the floodplain and decreases to approximately 5 m thick near the downstream end of the floodplain. The aquifer spans the width of the floodplain (up to 1.5 km), and is constrained by an underlying aquiclude of clay deposits and bedrock [Stanford et al., 1994].
 Within this study site, we consider the alluvial aquifer as an expansive hyporheic zone, because subsurface flow through the alluvium is recharged predominantly from the river channel [Poole et al., 2006]. The main channel of the river loses approximately 30% of its base flow to the underlying alluvial aquifer as it passes over the upstream 1/3 of the floodplain's length [Stanford et al., 2005]. Water that recharges the alluvial aquifer flows down-valley in the subsurface, then later discharges back to the surface, either into the main channel or into spring channels. Spring channels subsequently flow along or across the floodplain until they rejoin a main river channel before the water flows off the floodplain, into the downstream canyon.
3. Model Description
 We linked empirical temperature and oxygen models with a mechanistic hydrogeomorphic model of the Nyack study site [Helton et al., 2012]. Temperature and oxygen models were derived from comparisons between data sets of observed temperature and DO patterns with previous simulations of hydrologic residence time. We then integrated the empirical temperature and oxygen models into the existing hydrogeomorphic model of surface and subsurface water storage, flux, and exchange within the Nyack study site.
3.1. Hydrogeomorphic Model
 We used results from a hydrogeomorphic model applied by Helton et al.  and originally developed by Walton et al.  . The model is a finite volume, or “link and node,” model in which the floodplain is divided into discrete patches, represented by nodes in a three-dimensional irregular lattice network (Figure 2). One-dimensional flows are calculated along links between adjacent nodes in all three spatial dimensions. Thus, the model represents (1) horizontal surface water flow and floodplain inundation, (2) horizontal and vertical subsurface flow, and (3) vertical exchange between surface and subsurface waters.
 The method used to delineate model patches was developed for low-relief landscapes and analyzes patterns of potential surface water connectivity across the floodplain to delineate patch boundaries [Jones et al., 2008], based on a digital elevation model (DEM) derived from light detection and ranging (LiDAR) data (±10 cm vertical accuracy, 1 m2 grid cell size). The patch boundaries represent hydrologic divides, which are the most significant topographic obstacles to surface water connectivity and inundation across the floodplain. A vertically stacked column of underlying subsurface patches was delineated for each surface patch (Figure 3). The subsurface layers include soil, ‘shallow’ alluvial aquifer, and ‘deep’ alluvial aquifer. Thicknesses of each layer within each patch were determined based on empirical relationships derived from well logs collected throughout the study site.
Helton et al.  performed a model simulation for the period from 1 November 1996 to 31 December 2000. Consecutively, these years encompassed one relatively high, one relatively low, and two intermediate snowmelt-driven hydrographs, thus representing the inter-annual range of hydrologic conditions expected at the study site.
3.2. Simulated Hydrologic Residence Time
 To parameterize the temperature and dissolved oxygen models (see below), we used estimates of hydrologic residence time from the river channel through the aquifer to each well where temperature and DO were measured. These estimates were derived from a particle tracking postprocessor, developed and implemented by Helton et al. , that routes particles through the model domain (the link-and-node lattice representing the channel-floodplain-aquifer hydrosystem) based on model output. The particle tracker simulates the release of conservative tracer particles at a user-specified time and model node, assuming particles move along links at the same velocity as water. Thus, conservative tracer particle releases track the movement of water molecules through the study site, calculating the location of each particle within the modeled network over time. When a particle reaches a model node, the particle is routed along a random outflow link from the node, where the likelihood of entering each outflow link is proportional to the volume of water flowing through the outflow link.
Helton et al.  conducted nine simulated instantaneous particle releases within the model; three during base flow, three during rising limbs, and three during falling limbs of annual hydrographs. We calculated the travel time of each particle from its time of instantaneous release at the upstream end of the simulated floodplain to its arrival at each node. The average of these travel times for all the particles arriving at a given node was considered the mean hydrologic residence time of water arriving at that node. This mean residence time is an overall average of the hydrologic residence time distributions experienced by the nine parcels of simulated water labeled by the nine particle releases. The mean simulated residence times used for this analysis were the average over the entire simulation, and thus were constant for each model node across season and discharge conditions.
 This measure of hydrologic residence time is likely an overestimate of the actual residence time at any given location because particles are forced to travel along modeled links between model nodes, even where links are not perpendicular to isopleths of groundwater head. Thus, mean hydrologic residence time is a measure of relative, not absolute, water residence time. However, our estimates of residence time span a similar range to prior simulations based on the MODFLOW groundwater model and MODPATH particle tracking software, which estimated groundwater flow paths with residence times up to 1.5 years [Diehl, 2004].
3.3. Temperature Model
 The relationship between simulated mean hydrologic residence time and observed temperature in corresponding wells was used to develop an empirical model that simulates spatial and temporal patterns of temperature across the study site. We obtained temperature records from 40 wells and surface water sites spanning the floodplain laterally, longitudinally, and vertically (Figure 1a). The data set consisted of 1) hourly temperature logger data for one to two years (data collected from 23 July 2002 to 22 November 2004 and from 3 July 2008 to 15 October 2009) for each of 12 wells and three surface water sites, 2) hourly temperature logger data for less than a year (2 to 11 months; data collected from 22 September 2002 to 16 July 2004) for each of 20 wells, and 3) manual monthly temperature measurements for 5 additional wells from 1 May 2008 to 15 October 2009. Data records exceeding one year were used for temperature model development (n = 20), and data records less than one year were used to evaluate the temperature model (n = 20).
 Monitoring wells consisted of two- or three-inch schedule 40 PVC slotted over the depth of the well, installed to depths of 5 to 8 m (see Diehl  for well installation details). Wells were instrumented with either VEMCO™ Minilog data loggers or Solinst Leveloggers® to record hourly temperature. Loggers were installed at multiple depth intervals on smaller diameter PVC inserted into the wells, and baffles were attached to the PVC inserts between loggers to isolate well water at different depths. Manual temperature measurements were recorded with a YSI 85 (Yellow Springs Instruments, Inc.) in conjunction with DO measurements (see Section 3.4, below).
 We aggregated the hourly temperature records to daily means and analyzed the model development data according to Arrigoni et al. . Specifically, we fit a cosine wave to the observed annual cycle of temperature for each sampling location by minimizing the root mean squared error for the following equation [Arrigoni et al., 2008] (Figure 4):
where Td is the observed mean daily water temperature (°C) for a given day of the year (d), M is the mean annual temperature in °C, R is the annual temperature range (or wave amplitude) in °C, and PL is the local phase (day of year when the peak temperature at the sampling location occurred) and c is 2π/365, a constant to convert day of the year to radians, such that the calculated cosine wave has a period of one year. Since PL is cyclical over a 365 day period, we constrained PL to range between 1 and 365 when fitting parameters. The phase shift, or change in timing of peak temperature from the river to a given location within the aquifer, can be defined as the difference between the local phase at a given location (PL) minus the annual temperature phase in the river (P). Note that temperature is not a conservative hydrologic tracer. The phase shift is positively related to hydrologic transport time, but a heat transport model that includes conduction with sediments would be necessary to provide a direct estimate of hydrologic transport time from temperature signals [Anderson, 2005].
 We used the relationships between the mean simulated residence time and characteristics of the corresponding observed annual temperature cycles (R and PL) (Figure 5) to estimate average daily temperature for each model node for each day of the year. First, we used the mean simulated hydrologic residence time for each node to estimate R and PL for that node based on empirical power law relationships (Figure 5). Then, we calculated the average daily temperatures for each node from its R and PL (equation (1)), thus populating every node of the model with daily average temperature estimates during the period of simulation. Thus, we used an empirical extrapolation to estimate the spatial distribution of temperature for each day of the year across the study system.
3.4. Dissolved Oxygen Model
 The model uses a mass balance approach to simulate DO concentration for each node within the floodplain subsurface, based on advection to and from adjacent cells and microbial uptake:
where DOt is the mass of dissolved oxygen at time t in a given model node, Δt is the time step of the model, is the sum of advective transport of DO into the model node (mg h−1), is the sum of advective transport of DO out of the model node (mg h−1), uDO,t is biological uptake, [DO]t is DO concentration (mg L−1), and Vt is water stored within a given model node. The rate of water flux between nodes (Q ; L h−1) and water storage within nodes (Vt; L) is derived from the hydrogeomorphic model, described above.
 For subsurface model nodes, DO uptake (uDO,t) is simulated at a given time and DO concentration with a temperature-dependent Michaelis-Menten uptake function:
where [DO] is concentration of dissolved oxygen (mg L−1), umax is the maximum uptake rate of DO (mg L−1 h−1), and Ks is the half-saturation concentration of DO (mg L−1). Maximum uptake was observed to be linearly related to water temperature, so a simple empirical relationship was used to simulate umax:
where a and b are the slope and intercept of the linear regression of observed data and T is water temperature (°C).
 We parameterized and evaluated the DO model with a large (n = 850) data set of DO concentration measurements that spanned the Nyack study site longitudinally, laterally, and vertically (Figure 1b), and across seasonal variability and river discharge (Table 1). Data included measured DO concentration from 2003, 2004, 2008, and 2009 collected during 28 sampling events. Between 7 and 21 wells and 2 and 5 main stem surface water sites were sampled during each sampling event. Wells were typically sampled at two discrete depths: near the water table and at least 2 m below the water table, providing observed data corresponding to both our shallow and deep modeled aquifer layers.
Table 1. Simulated and Observed Dates for Dissolved Oxygen Model Evaluationa
For each range of simulated dates, average modeled DO concentration was calculated for each model node. These average concentrations were compared to measured DO concentrations from observed dates for model nodes that correspond spatially to sampled wells.
Pairs of simulated and observed dates were grouped according to season (winter, summer, spring, and fall) and river discharge condition (base flow and peak, rising, and receding (“falling”) flood flows).
24–30 Oct 1998
15–16 Oct 2009
21–22 Nov 1998
7–10 Nov 2003
10–14 Sep 1999
10–11 Sep 2008
23–25 Sep 1999
16–17 Sep 2009
25–30 Sep 1999
26–30 Oct 2004
25–30 Sep 1999
25 Sep–23 Oct 2008
19–22 May 1999
25–30 May 2004
25–29 May 1999
28 May–1 Jun 2009
14–15 Jun 1999
13–14 Jun 2008
21–23 Jun 1999
26–27 Jun 2008
20–25 Apr 1999
20–21 Apr 2009
20–25 Apr 1999
5–12 Apr 2004
12–15 May 1999
1–2 May 2008
23–29 Aug 1999
11–12 Aug 2008
23 Aug–1 Sep 1999
17–20 Aug 2009
28 Aug–1 Sep 1999
28 Aug 2008
14 Jun 1999
18 Jun 2009
16 Jul 1999
1 Jul 2009
17–19 Jul 1999
15–16 Jul 2008
2–5 Jul 1999
2–8 Jul 2008
25–26 Jul 1999
15–16 Jul 2009
10–11 Aug 1999
30 Jul 2008
13–20 Aug 1999
25 Jul–4 Aug 2004
11–14 Jan 1999
14–15 Jan 2009
2–4 Dec 1998
3–4 Dec 2008
15–24 Feb 1999
18–23 Feb 2004
20–21 Mar 1999
26–28 Mar 2009
8–10 Mar 1999
4–14 Mar 2009
 Wells were sampled using a modified straddle packer design to sample at discrete depth intervals. Immediately prior to collecting each DO measurement, wells were pumped with a hand-operated diaphragm pump until water ran clear for the entire depth of the well. We then inserted tubing that was slotted at the bottom and baffled with foam packers to isolate one-meter intervals for a discrete depth sample into the well. A 12V electric submersible pump (Whale Submersible 881, Whale Systems Specialists) was then inserted into the tubing, and the isolated well segment was purged again until DO measurements in the pump effluent stabilized. Measurements were collected using a YSI 55 dissolved oxygen probe (Yellow Springs Instruments, Inc.) in 2003 and 2004 (data reported by Reid ), and with a YSI 85 dissolved oxygen probe in 2008 and 2009.
 The monitoring data set was divided into parameterization data and evaluation data. Evaluation data included 820 DO concentration measurements taken across the floodplain and seasons. The parameterization data set (n = 30) was selected from one surface water and four well locations sampled on six dates. The wells were installed along a paleochannel, which is a preserved cobble-boulder bed of a historic river channel that fills over time with finer sediments creating preferential flow paths in the floodplain subsurface [Poole et al., 1997]. Paleochannel features were identified with Ground Penetrating Radar at the well locations [Hawkins, 2003], and historical aerial photographs confirm that the Middle Fork of the Flathead River flowed through this section of the floodplain [Whited et al., 2007].
 We fit DO uptake parameters for each of six sampling dates by finding the umax and Ks parameters that minimized the root mean squared error between predicted DO concentrations and observed DO concentrations from the parameterization data set (Figure 6). We estimated the hydrologic residence time corresponding to each well location based on output from the particle tracking model. Our simulated residence times are relative and not absolute residence times, so biological parameters developed here should not be extrapolated to other systems. We used the average Ks value across the six dates (4.5 mg L−1) and the relationship between umax and water temperature (Figure 7a) for floodplain-scale simulations. The model uses this observed relationship between umax and temperature to simulate umax within each model node over time (Figure 7b).
 The model requires DO concentrations in surface water as input. Therefore, for surface model nodes, we estimated DO concentrations based on the linear empirical relationship between point measurements of DO concentration and temperature taken in the main stem of the Middle Fork Flathead River at the study site (Figure 8).
4. Model Simulation and Evaluation
 We simulated daily DO and temperature dynamics for one year, which corresponded to the intermediate flow year from the previously run hydrologic simulations, 1 November 1998 to 31 October 1999. We ran the model for one simulation year prior to 1 November 1998 to assure that initial conditions were unlikely to affect model output.
 To verify the accuracy of our temperature model, we compared predicted daily average temperatures to daily average temperatures derived from 20 temperature records that spanned 2 to 11 months in 2002, 2003, 2004, 2008, and 2009 (see section 3.3 above for data description; well locations shown in Figure 1a). Since we did not have temperature records for the hydrologic simulation year, we compared observed values to predicted values on the same day of the year.
 We evaluated the DO model by comparing model output to observed data from 2003, 2004, 2008, and 2009 (see section 3.4 above for data description; well locations shown in Figure 1b). Since we did not have observed data for the simulation year, we compared simulated values to observed values collected in the same month of the year and with a similar river discharge (Table 1). River discharges for observed dates were within 5% of river discharge for simulated dates. We categorized each simulated versus observed comparison by season and river discharge condition (Table 1). Seasons included winter, summer, spring, and fall. Discharge conditions included base flow, peak flow, the rising limb of the flood spate before peak flow (“rising”), and the falling limb of the flood spate after peak flow (“falling”).
 Observed water temperature ranged from 0.5 to 16.0°C in surface waters and 0.1 to 15.5°C within the aquifer, varying longitudinally, laterally and vertically, and across different river discharge conditions and seasons. The temperature model fit the observed temperature data from 20 sampling locations well (r21:1 = 0.66; RMSE = 1.27°C; Figure 9). The slope of the linear regression for simulated versus observed values was less than one (Figure 9), and model residuals (predicted minus observed temperature) were negatively correlated to observed temperature (r2 = 0.31; p < 0.001), suggesting the model modestly under-predicts temperature at high temperatures and over-predicts temperature at low temperatures.
 Observed DO concentration ranged from 8.44 to 13.1 mg L−1 in surface water and from 0.14 to 12.8 mg L−1 within the aquifer, varying longitudinally, laterally and vertically, and across different river discharge conditions and seasons. The DO model explained substantial variation in the whole data set (r21:1 = 0.58; Figure 10) and among seasons (Table 2). The DO model fit varied across seasons and flow conditions, with model explained variance (r21:1) ranging from 32% for spring peak flows to 71% for winter base flow conditions (Table 2 and Figure 11). Model residuals (predicted minus observed DO concentration) were unrelated to observed DO for the full data set (p > 0.05). Among seasons, model residuals were negatively correlated to observed DO during spring peak flow (r2 = 0.31; p < 0.001), summer base (r2 = 0.32; p < 0.001), and summer falling (r2 = 0.24; p < 0.001). Residuals were unrelated to observed DO for fall and winter base flows and spring rising flows (p > 0.05). Simple linear regressions between predicted and observed values always yielded a slope less than one, independent of season or discharge conditions (Table 2).
Table 2. Simulated Versus Observed Statistics for Dissolved Oxygen Modela
[DO] (mg L−1)
RMSE (mg L−1)
Abbreviations are as follows: n, number of observations; [DO], average observed DO concentration ±Std. Dev.; r1:12, coefficient of determination calculated for 1:1 model lines (shown in Figures 10 and 11); RMSE, root mean square error; NRMSE, normalized root mean square error (, where Xobs,max and Xobs,min are the maximum and minimum observed DO concentrations, respectively); and SLR, simple linear regression. Last column shows simple linear regression equations and r2 for simulated versus observed values. All SLRs were significant at p < 0.001. See Table 1 for a description of model comparison data sets.
Full data set
5.6 ± 3.0
y = 0.83x + 0.19; r2 = 0.67
7.2 ± 3.3
y = 0.88x + 1.05; r2 = 0.73
7.2 ± 2.6
y = 0.87x + 0.71; r2 = 0.66
6.0 ± 2.6
y = 0.65x + 1.54; r2 = 0.58
5.3 ± 2.6
y = 0.72x + 0.51; r2 = 0.67
4.5 ± 2.5
y = 0.62x + 0.54; r2 = 0.57
4.7 ± 3.0
y = 0.74x + 0.09; r2 = 0.61
6.1. Scaling Understanding of Flow Path Oxygen Dynamics
 The simple models of temperature and DO uptake integrated with the relatively complex three dimensional hydrogeomorphic model explained a substantial amount of variation in measured DO concentrations across the study site and through time (Figures 10 and 11 and Table 2). These results illustrate the importance of understanding the hydrogeomorphic dynamics of a river to simulate spatiotemporal patterns of ecosystem processes. The relationship between simulated and observed DO was strong across among seasons and river discharge conditions (Figure 11), indicating that the drivers of oxygen dynamics simulated by the model (advection, uptake, and temperature) are generally applicable across a wide array of conditions that vary with space and time within the Nyack Floodplain aquifer.
 The slope of the relationship between simulated and observed DO concentrations was always less than one, and the model typically under-predicted DO concentrations (Figure 11 and Table 2). This suggests that the model over-predicts DO uptake, or that there is some additional source of DO along subsurface flow paths. The model may over-predict DO uptake because of limitation by carbon or other nutrients to microbial respiration [e.g., Zarnetske et al., 2011]. The model also does not account for some potential sources of DO, including exchange between saturated sediments and overlying unsaturated sediments or the atmosphere [Smith et al., 2011], and DO inputs from plant roots to the subsurface [Colmer, 2003; Reddy et al., 1989]. Recent research by Smith et al.  suggests that diffusion may be an important DO source for some areas in the Nyack aquifer.
 Observations of declines in DO along one-dimensional hyporheic flow paths are common [Findlay et al., 1993, 2003; Fernald et al., 2006; Holmes et al., 1994], but these studies typically occur in small streams and along flow paths of only a few meters. Scaling this observed pattern to DO dynamics along multiple, interactive flow paths (that can be hundreds of meters long) requires quantifying hydrologic advection of DO across time and space, as we have attempted to do here. The results of our effort show the potential to scale understanding of short flow path scale dynamics across much larger, complex, three-dimensional river-floodplain-aquifer systems with relatively simple biogeochemical models, when hydrologic advection is adequately represented.
6.2. Simulating Temperature Dynamics
 Previous research shows that heat (as measured by temperature) can be used as a groundwater tracer [reviewed by Anderson, 2005] and that temperature range decreases and phase shift (or difference in surface and subsurface peak temperatures) increases with subsurface flow path length in extensive hyporheic zones [Poole et al., 2008]. A strong correlation between the annual temperature cycle and mean simulated hydrologic residence times (Figure 5) indicates that our simulated hydrologic residence time is an accurate representation of the relative hydrologic residence times within the Nyack study site. The relationship between annual temperature cycles (local phase and range) and simulated hydrologic residence times correspond qualitatively to patterns observed by Arrigoni et al.  for diel temperature cycles: as hydrologic residence time increases, the range of water temperature decreases (the temperature signal is “buffered”) and the local phase, or day of year to peak temperature at a given location, is delayed (the temperature signal is “lagged”) relative to surface water.
 The strong relationship between characteristics of the temperature signal and simulated hydrologic residence times allowed us to reasonably extrapolate average daily temperature dynamics across the Nyack study site (Figure 9). Although the empirical model explained substantial variation in the observed data set, the model tended to over-predict temperatures at low temperatures and under-predict temperatures at high temperatures. Relatively shallow aquifers can be affected by surface temperatures [Taniguchi, 1993; Vogt et al., 2012], so Nyack subsurface water may experience additional warming during summer months and cooling during winter months. Alternatively, and perhaps more likely considering the large volume of the aquifer and high rates of flow through the aquifer [Helton et al., 2012], the model represents the annual cycle of daily mean temperature as a cosine wave, a somewhat inaccurate simplifying assumption (e.g., Figure 4a) that may yield modest errors especially at peak and trough annual temperatures. In fact, one reason that this approach works well within the Nyack study site is the high hydrologic connectivity between nodes and the dominance of advective processes. Thus, a model like this might not be expected to work as well in systems where hydraulic conductivity is lower and a more mechanistic approach that accounts for non-advective influences of heat transfer would be necessary.
6.3. Spatial and Temporal Patterns in Fluvial Landscapes
 Hydrologically driven transport of solutes is fundamental for understanding and predicting important times and locations of biogeochemical processes (e.g., “hot moments and hot spots” [sensu McClain et al., 2003]) that may drive whole-system rates of ecosystem processes. Ecohydrologic models for terrestrial hillslopes simulate hydrologically explicit biogeochemical dynamics, even predicting important times and locations of biogeochemical processes within hillslopes [Band et al., 2001]. Our modeling framework for river-floodplain-aquifer systems is analogous to ecohydrologic models for terrestrial systems (reviewed by Boyer et al. ; Kulkarni et al. ). Our model results illustrate spatial and temporal patterns of temperature and oxygen dynamics within the alluvial aquifer of the Nyack Floodplain (Figure 12).
 Patterns of temperature (Figure 12, left) produced by the model illustrate the heterogeneity within the alluvial aquifer that results from complex multidimensional hydrologic dynamics. During wintertime (e.g., January, Figure 12), temperature tends to increase with distance from the river channel because river surface water (and hence near-channel aquifer water recently recharged from the river) is cooler than aquifer water farther from the channel that was recharged during warmer spring and summer months. The inverse of this pattern occurs during summer months (e.g., July, Figure 12), when river surface water is warmer than aquifer water that was recharged during colder fall and winter months. Spring and autumn (e.g., April and October, Figure 12) show less dramatic spatial patterns in temperature, since river water recharging the aquifer is similar in temperature to aquifer water. Thus, seasonal patterns alternate spatially between steep increases and decreases in, and relatively homogenous cool and warm aquifer temperatures.
 Spatiotemporal trends in simulated DO concentrations illustrate the influence of hydrologic dynamics on biogeochemical patterns (Figure 12, right). Dissolved oxygen concentrations within the alluvial aquifer range from near saturation to near zero during all seasons. Because DO concentrations decrease with residence time (as DO is taken up by biota), near channel DO is typically higher than DO concentrations farther from the channel. The steepest gradients of DO concentrations occur in the winter (e.g., January, Figure 12), when the river channel water recharging the aquifer is coldest relative to the warmer aquifer water. As river channel water temperature increases through the spring and summer, DO concentrations become more homogenous within the aquifer (e.g., changes in DO spatial gradient from January to July, Figure 12). During warmer months, higher temperatures cause lower saturated DO concentrations in water entering the aquifer and higher rates of biological uptake, hence lower near channel DO concentration within the aquifer and more homogenous patterns of DO across the aquifer (July, Figure 12). Thus, seasonal patterns shift spatially from steep spatial DO gradients that set up during the winter to shallower DO gradients, with overall lower DO concentrations, as the summer progresses.
 Although winter and summer months show general spatial trends from near-channel to the floodplain fringes, high variability in temperature and DO concentrations exists within the near channel alluvial aquifer. Localized areas of low DO concentrations, or high temperature relative to river water temperature in the winter (January, Figure 12) and low temperature relative to river water temperature in the summer (July, Figure 12), correspond to areas of upwelling, or aquifer discharge to the river channel. Alternating spatial patterns of recently recharged (“new”) aquifer water and discharging (“old”) aquifer water create a spatial mosaic of temperature and dissolved oxygen that is more complex near the river channel.
 Model simulation results show how complex hydrologic dynamics create a shifting habitat mosaic [sensu Stanford et al., 2005] of temperature and dissolved oxygen within the alluvial aquifer that likely influences a wide array of aquatic organisms and ecosystem processes [Malard and Hervant, 1999]. We can use the simulation model results to understand or develop hypotheses and predictions about spatial and temporal patterns of various ecological and biogeochemical phenomena.
 Localized areas of cool aquifer water discharging to the river channel during summer months creates important spawning and rearing habitats for cold-water fishes [e.g., Eberle and Stanford, 2010] and invertebrates [Anderson, 2008]. At the Nyack Floodplain, spatial patterns within the aquifer apparently influence local abundances of the many aquatic invertebrates that occur within the aquifer. Benthic species reside mostly within a few meters below and lateral to the river channel, but a wide variety of insects (mostly Plecoptera) and crustaceans occupy the entire aquifer, with insect larvae migrating from the aquifer to the channel to emerge as flying adults [Stanford et al., 1994, 2005]. Abundances per species are consistently lower in areas of the aquifer where DO concentrations approach hypoxia [Reid, 2007]. Thus, the model may inform research that seeks to answer questions about the influence of environmental conditions on aquatic biota or to better understand the distribution and abundance of benthic species.
 Microbially mediated ecosystem processes occurring within the aquifer may also be linked to spatiotemporal patterns of temperature and dissolved oxygen. Microbial respiration drives declines in DO along subsurface flow paths [e.g., Hedin et al., 1998]. Various aerobic and anaerobic microbial processes are likely correlated with patterns of dissolved oxygen. Low areas of DO concentrations may indicate important times and locations for denitrification, methanogenesis, or other anaerobic processes, whereas near channel areas of high DO concentrations may indicate high rates of aerobic processes, like nitrification.
 Because of highly variable DO concentrations near the channel (Figure 12), complex biogeochemical patterns may emerge as different suites of solutes are brought into contact with one another. For example, when flow paths of varying residence times converge (e.g., near channel localized areas of discharging aquifer water with low DO intersect recharging aquifer water with high DO), “hot spots and moments” of aerobic processes that use anaerobic end products may occur, such as the consumption of methane by methane oxidizing microbes. Thus, simulated spatiotemporal patterns of temperature and dissolved oxygen provide predictions about when and where biogeochemical processes are likely to occur within the aquifer, which provide a tool for linking point measurements of these processes to their overall influence across multidimensional fluvial landscapes.
 The coupled hydrogeomorphic-temperature-dissolved oxygen simulation model explained substantial variance in temperature and DO observations made across seasonal variability in discharge for the alluvial aquifer of the Nyack Floodplain. Our results illustrate how one-dimensional flow path biogeochemical dynamics can be reasonably scaled to a larger three-dimensional river-floodplain system by integrating a simple biogeochemical model with a detailed floodplain temperature and hydrogeomorphic model. This research provides an approach for scaling spatially and temporally dynamic biogeochemical processes from flow paths to fluvial landscapes, particularly large gravel bedded river systems. It shows that spatiotemporal complexity in biogeochemical patterns, including “hotspots and hot moments,” may emerge from relatively simple biogeochemical dynamics operating within a complex, three-dimensional hydrologic system, and thus highlights the importance of understanding the hydrogeomorphic template of a system that drives the hydrologic flux and storage of biogeochemical constituents. These coupled models provide the first step toward a mechanistic prediction of the times and locations that may have disproportionate influence on biogeochemical processes within expansive three dimensional fluvial landscapes.
 This research was supported by the National Research Initiative of the USDA Cooperative State Research, Education and Extension Service (2005-35102-16288), by the Gordon and Betty Moore Foundation, and by an EPA Star Fellowship for AMH. EPA has not officially endorsed this publication, and the views expressed herein may not reflect the views of the EPA. This manuscript was improved by comments from two anonymous reviewers.