Dynamics of streamflow permanence in a headwater network: Insights from catchment-scale model simulations

Abstract

The hillslope and channel dynamics that govern streamflow permanence in headwater systems have important implications for ecosystem functioning and downstream water quality. Recent advancements in process-based, semi-distributed hydrologic models that build upon empirical studies of streamflow permanence in well-monitored headwater catchments show promise for characterizing the dynamics of streamflow permanence in headwater systems. However, few process-based models consider the continuum of hillslope-stream network connectivity as a control on streamflow permanence in headwater systems. The objective of this study was to expand a process-based, catchment-scale hydrologic model to better understand the spatiotemporal dynamics of headwater streamflow permanence and to identify controls of streamflow expansion and contraction in a headwater network. Further, we aimed to develop an approach that enhanced the fidelity of model simulations, yet required little additional data, with the intent that the model might be later transferred to catchments with limited long-term and spatially explicit measurements. This approach facilitated network-scale estimates of the controls of streamflow expansion and contraction, albeit with higher degrees of uncertainty in individual reaches due to data constraints. Our model simulated that streamflow permanence was highly dynamic in first-order reaches with steep slopes and variable contributing areas. The simulated stream network length ranged from nearly 98±2% of the geomorphic channel extent during wet periods to nearly 50±10% during dry periods. The model identified a discharge threshold of approximately 1 mm d−1, above which the rate of streamflow expansion decreases by nearly an order of magnitude, indicating a lack of sensitivity of streamflow expansion to hydrologic forcing during high-flow periods. Overall, we demonstrate that process-based, catchment-scale models offer important insights on the controls of streamflow permanence, despite uncertainties and limitations of the model. We encourage researchers to increase data collection efforts and develop benchmarks to better evaluate such models.

1. Introduction

Streamflow permanence–defined as the frequency, magnitude, duration, and timing of surface streamflow presence–in headwater streams impacts ecosystem function and downstream water quality (Wohl, 2017). Headwater streams account for approximately 53% of total river network length in the United States (Nadeau and Rains, 2007), providing services such as runoff storage, nutrient retention, and regional biodiversity (Boulton, 2014, Datry et al., 2018, Colvin et al., 2019). These networks expand and contract as a function of interacting hydrologic forcings, hillslope-stream network connectivity, and structural watershed properties (Bracken et al., 2013, Wohl, 2017, Ward et al., 2018, Durighetto and Botter, 2022). Importantly, streamflow permanence dictates habitat suitability for a variety of freshwater taxa, such as benthic macroinvertebrates (Clarke et al., 2010; Karaouzas et al., 2019) and fish (Davey and Kelly, 2007), which exhibit varying tolerances for stream channel wetting and drying.

Characterization of streamflow permanence in headwater systems remains elusive despite the recognized services such systems provide for the entire river network (Koundouri et al., 2017, Colvin et al., 2019, Ruiz et al., 2021). This is largely attributed to scarce data on and mapping of headwater systems (Poff et al., 2006), which has led to their limited federal protection under the Clean Water Act (CWA; e.g., Creed et al., 2017). Quantification of the watershed-scale function of headwater systems is one way to enhance their protection (Johnson et al., 2010), and this approach would benefit from the improved understanding of streamflow permanence dynamics at the catchment scale.

The presence or absence of streamflow in headwater streams results from multi-scale, multi-dimensional hydrologic processes (Hammond et al., 2021, Shanafield et al., 2021, Botter et al., 2021). Empirical studies focused on understanding streamflow permanence have made significant strides in elucidating the mechanisms of streamflow expansion and contraction (see review in Senatore et al., 2021). These include the use of biological and physical indicators as surrogate measures of hydroperiod classification (e.g., perennial, intermittent, ephemeral; see review in Fritz et al., 2020), repeated mapping of the flowing extent of the stream network (e.g., Godsey and Kirchner, 2014, Whiting and Godsey, 2016, Jensen et al., 2017, Shaw et al., 2017, Zimmer and McGlynn, 2017, Lovill et al., 2018, Meerveld et al., 2019, Durighetto et al., 2020, Senatore et al., 2021), and implementation of highly instrumented networks of flow-state sensors (Goulsbra et al., 2014, Zimmer and McGlynn, 2017, Jensen et al., 2019, Kaplan et al., 2020, Botter et al., 2021) to understand streamflow expansion and contraction (Prancevic and Kirchner, 2019). Flow-state sensors measure the presence or absence of surface water and, when strategically placed within riffles, can infer the presence or absence of streamflow (i.e., flowing or not flowing; Fritz et al., 2006). Furthermore, extensive literature has leveraged long-term discharge measurements to derive hydrologic metrics that have been used to classify streamflow duration throughout the United States and Europe (see review in Christensen et al., 2022). Such field-based methods from highly instrumented and studied catchments are the most reliable measures of the extent of surface streamflow within headwater systems (Jensen et al., 2018), which, in essence, is the response variable of connectivity from upstream surface and subsurface pathways (e.g., Godsey and Kirchner, 2014). Statistical and analytical models built from measured data have also been used to classify flow permanence and the extent of perennial, intermittent, and ephemeral streams (Svec et al., 2005, Russell et al., 2015, Villines et al., 2015, Jensen et al., 2018, Jaeger et al., 2019, Botter and Durighetto, 2020, Durighetto and Botter, 2022, Durighetto et al., 2022). Despite the reliability of these empirical methods to classify streamflow permanence, they face challenges pertaining to data acquisition, transferability, and projection of dynamics beyond the measured data (Godsey and Kirchner, 2014, Ward et al., 2018). For example, mapping the flowing extent of the stream network is infeasible over large areas, and repeated field surveys are often time prohibitive.

Recent advancements in process-based hydrologic models show promise for characterizing streamflow permanence in headwater systems and overcoming the logistical limitations of empirical classification methods (Williamson et al., 2015, Ward et al., 2018, Ward et al., 2020). Process-based models simulate fluxes and storage of water over spatiotemporal scales that are often difficult to measure in the field – thus facilitating investigation of dynamics and controls of hydrologic processes at scales that otherwise would not be possible, albeit with some degree of uncertainty (Clark et al., 2015b). Ward et al. (2018) recently developed a reduced-complexity, process-based modeling framework that considers in-stream continuity and net upwelling and downwelling processes to simulate high resolution dynamics of streamflow expansion and contraction longitudinally along the stream network. Williamson et al. (2015) used a regional TOPMODEL approach (Beven and Kirkby, 1979) and the saturation deficit (representing soil-water storage within catchment hillslopes) to predict landscape units with surface streamflow present. Findings from both studies demonstrate the efficacy of using process-based models to estimate streamflow permanence, the spatial and temporal trends of streamflow expansion and contraction, and controls of hydrologic connectivity within headwater networks.

These studies resulted in new methods to simulate headwater stream network extent; however, to our knowledge, few studies consider hillslope-stream network connectivity within a process-based hydrologic modeling context. For example, several studies treat lateral inflow as an area-weighted fraction of the outflow from the catchment (Godsey and Kirchner, 2014, Ward et al., 2018, Prancevic and Kirchner, 2019), which does not consider the within-hillslope and hillslope-stream network connectivity that affects variability of streamflow permanence in first- and second-order reaches (Bracken et al., 2013, Shanafield et al., 2021). Furthermore, models that simulate hillslope hydrologic connectivity, such as dynamic TOPMODEL (Beven and Freer, 2001) and the Visualizing Ecosystems for Land Management Assessment (VELMA) model (Abdelnour et al., 2011), do not include subroutines to simulate longitudinal hydrologic connectivity or streamflow permanence.

The improved simulation of the dynamics of streamflow permanence currently is limited by a number of uncertainties. Namely, verifying model fidelity is a well-known challenge with process-based hydrologic models because continuous channel monitoring, in both space and time, is rare and often requires increased data collection to reduce uncertainty of simulations (Stadnyk et al., 2013). Furthermore, such high-resolution models are often over-parameterized and computationally burdensome. Using hydrologic response units (HRUs) to group landscape components behaving in a hydrologically similar manner and calculating transport at the reach scale (i.e., on the order of tens to hundreds of meters) may reduce required input data and model run times, while retaining important information regarding reach-scale streamflow permanence. Further, leveraging data collected on moderately and highly instrumented headwater networks is a viable, yet unharnessed approach to reduce equifinality of streamflow permanence simulations.

The objective of this study was to develop a process-based, catchment-scale hydrologic model to investigate the spatiotemporal dynamics of headwater streamflow permanence and identify controls of headwater streamflow expansion and contraction. We apply the model to a headwater catchment on the central Appalachian Plateau in Kentucky, United States (USA), a site with adequate data to simulate streamflow permanence, yet less spatial and temporal hydrological monitoring and instrumentation than long-term catchment study sites (e.g., Goulsbra et al., 2014, Senatore et al., 2021). Therefore, we provide a framework from which to upscale simulated streamflow permanence to larger watersheds and regions throughout the United States that typically have limited available data in headwaters. Our model also explicitly considers within-hillslope connectivity (similar to Williamson et al., 2015), hillslope-stream network connectivity, and interactions between the surface stream and subsurface permeable zone (similar to Ward et al., 2018). We investigate the spatiotemporal dynamics and controls of headwater streamflow permanence with maps showing the variability of surface streamflow and timeseries of the flowing stream length within the catchment. Our approach characterizes headwater streamflow permanence using a process-based hydrologic model at the reach and catchment spatial-scale (as opposed to upwelling and downwelling of individual features at sub-meter spatial scales), which may assist with quantifying the function of headwater streams within larger watersheds (Creed et al., 2017).

2. Study Site and Materials

2.1. Study site

The Falling Rock catchment (0.96-km²) is a moderately well-monitored headwater system in the University of Kentucky’s Robinson Forest, located on the central Appalachian Plateau of Kentucky, U.S.A. (Fig. 1). The system is used as a control basin for silviculture management experiments and has been relatively undisturbed since the early 1900s, when timber was last harvested in the catchment (Overstreet, 1984). Land use in Falling Rock is almost entirely second-growth forest, with an overstory consisting of primarily hardwood trees (e.g., oak (Quercus sp.), hickory (Carya sp.), yellow poplar (Liriodendron tulipifera), American beech (Fagus grandifolia); Moriarty and McComb, 1985, Phillippi and Boebinger, 1986). Climate is classified as temperate-humid, with mean annual rainfall equal to 1121 mm (Sena et al., 2021). Minimum and maximum temperature ranges between −5 °C and 8 °C in the winter and 17 °C and 31 °C in the summer. Elevation ranges between 294 m and 459 m above sea level (NAVD 88; Fig. 1b and d). The study period spanned from approximately December 1, 2003 until September 30, 2006. Robinson Forest received 1,490 mm of precipitation in 2004, 1002 mm in 2005, and 1156 mm in 2006. Thus, this study spans a relatively wet year, a relatively dry year, and a year with approximately average precipitation.

Fig. 1.

Primary input data used to simulate discharge and streamflow permanence in the Falling Rock catchment (0.96-km²). (a) Relevant instrumentation, soil type, and the location of flow-state sensors (FC1-FC4) on reaches identified as perennial, intermittent, and ephemeral by Cherry (2006) in Falling Rock. (b) Hillshade map created with a 1.5-m digital elevation model (DEM). (c) Lithology in Falling Rock (Kentucky Geological Survey, 1998) and geomorphic stream channel used to simulate discharge and streamflow permanence. (d) Location and elevation of Falling Rock within the HUC 12 Buckhorn Creek Watershed (KYAPED, 2014). € Location of Falling Rock within the Central Appalachian Region of Kentucky, USA.

The depth of the soil above bedrock is estimated to be less than 1.0 m surrounding streams and to range between 0.7 m and 2.2 m on hillslopes (Fritz et al., 2008; Fig. 1a). Soils are shallow and well drained (Sloan et al., 1983, Williamson et al., 2015), with saturated hydraulic conductivities estimated to range between 0.02 and 0.50 m hr⁻¹. Catchment lithology consists primarily of sandstone, shale, and siltstone (Fig. 1c; Kentucky Geological Survey, 1998). Surface streamflow responds rapidly to precipitation, which is largely attributed to the presence of subsurface macropore pathways, shallow depths to confining bedrock, and steep hillslopes (Williamson et al., 2015). Consequently, little overland runoff has been observed on hillslopes in this region (Mahoney et al., 2021). The topography of Falling Rock is classified by steep, dissected hillslopes, and a dendritic drainage network. Stream slopes span nearly an order of magnitude (Table S1), with flattest slopes in higher-order reaches and steepest slopes in first-order reaches.

2.2. Materials used to simulate streamflow permanence

Falling Rock was chosen for this study because of its relative abundance of data dating from 1971, a substantial collection compared to catchments with limited or no hydrologic instrumentation in the region. The ecology and geomorphology of perennial, intermittent, and ephemeral reaches have been described and modeled in Falling Rock via a number of field and modeling investigations. Cherry (2006) mapped the extent of perennial and non-perennial reaches within the catchment (Fig. 1c) using methods developed by Fritz et al. (2006). Several studies have classified flow duration and perennial, intermittent, and ephemeral extent of streams within Falling Rock using models (Svec et al., 2005, Villines et al., 2015, Williamson et al., 2015). Fritz et al. (2008) surveyed physical and biological indicators of streamflow permanence, including stream morphology, sediment properties, habitat and bioassessments, discharge, and water quality. Johnson et al. (2010) used a similar dataset to investigate the downstream effects of headwater stream disturbance.

Locally collected environmental datasets were used to either parameterize or evaluate our model. Beginning in 1971, precipitation and air temperature were measured with weighted buckets, strip charts, and thermometers until being replaced with tipping buckets and electronic data loggers in 2005 (Sena et al., 2021). Weather stations were installed at the ridge and bottom of Falling Rock and approximately 2.5 km to the southwest (“Camp Weather Station”) of the watershed outlet (see Fig. 1c). Potential evapotranspiration rates were estimated using temperature data, an estimate of daylight length, and the Hamon (1961) formula, which was previously implemented to simulate PET in Falling Rock by Williamson et al. (2015). Further, Williamson and Barton (2020) corroborated findings from Lu et al. (2005) using the Hamon Formula, further supporting its use herein. We used data primarily collected from Camp Weather Station to drive the model due to gaps in data at the weather stations located within Falling Rock during the study period. Catchment morphologic properties were quantified using a 1.5-m digital elevation model (DEM, Fig. 1d and Table S1; KYAPED, 2014), morphometry data collected by Fritz et al. (2008), and regional regression analysis of stream bathymetry (Vesely et al., 2008).

Discharge has been monitored at the catchment outlet using a V-notched weir since 1971 (Sena et al., 2020). Flow state was recorded in four reaches (see Fig. 1a), identified by Cherry (2006) as perennial (FC1), intermittent (FC2), and ephemeral (FC3, FC4) between late 2003 and late 2006 using ecological indicators and an Onset Hobo flow-state sensor, Onset submersible case, and an encased cable (Fritz et al., 2006). Care was taken to position the flow-state sensor in the thalweg of stream reaches in erosional (riffle or run) habitats representative of the reach, with the logger contacts set within slotted stilling wells at the streambed surface. Several interruptions to data collection occurred due to sensor maintenance or malfunction, which contributes to uncertainty of the stream dynamics observed and simulated in Falling Rock. Therefore, it was necessary to additionally evaluate our model using qualitative estimates of hydroperiod from field maps and surveys as well as biological assessments (Cherry, 2006, Fritz et al., 2006), which inherently manifest from system dynamics. Available flow-state and discharge data used to validate the model are shown in Fig. S1. Additional flow-state data were collected in the catchment between 2011 and 2012 (Williamson et al., 2015), but were not used herein since little variability of flow state was observed in Falling Rock during this period (most sensors reported wet conditions) and given computational constraints of running the model for approximately 10 years.

Falling Rock was chosen for study over other highly instrumented headwater networks (e.g., Goulsbra et al., 2014, Ward et al., 2020) for several reasons. Although not extensively published or instrumented like other headwater catchments and watersheds throughout the western United States and Europe (e.g., Goulsbra et al., 2014, Senatore et al., 2021), the catchment has flow data on small perennial, intermittent, and ephemeral streams dating back to the 1970s, including continuous discharge gage data, flow-state data at multiple locations, as well as maps and surveys of the extent of perennial, intermittent, and ephemeral streams. Streamflow permanence descriptions in this catchment have been related to ecological niches, providing an additional means of model validation (Fritz et al., 2013). Falling Rock is therefore one of the most instrumented and studied watersheds in the central Appalachian ecoregion of the United States (Sena et al., 2021), and few studies to our knowledge contain the necessary data to simulate models to investigate streamflow permanence in this region (Williamson et al., 2015). This paucity of headwater modeling studies in central Appalachia gives credence to choosing Falling Rock as the study site, given (1) the importance of Appalachian headwaters for structuring habitats and biodiversity (Price et al., 2012, Drayer and Richter, 2016) and (2) the enhanced vulnerability that such systems face due to widespread land use change from strip mining and timber harvest as well as climate change (Zégre et al., 2013, Witt et al., 2016, Williamson and Barton, 2020). Furthermore, Falling Rock is nested within a larger headwater network that contains streamflow permanence data and discharge data. In this regard, we considered the study catchment to be an ideal testbed to develop a process-based hydrologic model that requires relatively low data inputs yet can be leveraged to simulate streamflow permanence by focusing on model fidelity at the reach scale. Further, application of the model to Falling Rock will facilitate future comparisons of streamflow expansion and contraction in catchments with variable structural watershed configurations and limited long-term, high spatial- and temporal-resolution streamflow permanence measurements.

3. Methods

3.1. Model formulation

We utilize dynamic TOPMODEL to simulate hydrologic fluxes and connectivity from hillslopes to the stream network (see reviews of dynamic TOPMODEL in Beven and Freer, 2001, Beven, 2011, Metcalfe et al., 2015). Dynamic TOPMODEL is a process-based hydrologic model that simulates hillslope hydrology using the variable upslope contributing area approach, building upon its widely applied predecessor, TOPMODEL (Beven and Kirkby, 1979), by incorporating an additional parameter, $s{d}_{\mathit{max}}$, to represent disconnectivity of upland hillslope units during periods of extensive drying and abandoning the original assumption of a quasi-steady water table (Metcalfe et al., 2015). Dynamic TOPMODEL solves a time-varying mass balance to simulate the change in subsurface and lateral flow between Hydrologic Response Units (HRUs) as:

$$\frac{\partial s}{\partial t}=\frac{\partial q}{\partial x}-r$$ (1)

where, $s$ is the subsurface storage deficit, $q$ is the downslope flow per unit plan area, and $r$ is the recharge from the unsaturated zone.

Lateral flow over the surface and through the subsurface is assumed in this study to follow the catchment topography, which likely holds true in systems with relatively steep slopes and shallow soil depths (Beven, 1997), albeit with some degree of uncertainty. Lateral connectivity to the stream network can be conceptualized using a weighted flow matrix, which maintains the structural contiguity of the hillslope by representing the proportion of flow from one landscape unit that flows into downstream landscape units, as discussed in Beven and Freer, 2001, Metcalfe et al., 2015. This matrix is defined as:

$$W=\left(\begin{array}{ccc}{p}_{11}& \dots & p_{1n}\\ ⋮& p_{ij}& ⋮\\ p_{n1}& \dots & p_{nn}\end{array}\right)$$ (2)

where each element of the matrix represents a landscape unit assumed to behave in a hydrologically similar manner (i.e., an HRU) and $\mathrm{i}$ represents the HRU which contributes flow to receiving HRU $\mathrm{j}$. The sum across columns is equal to unity, which represents the total flow from HRU $\mathrm{i}$ that is redistributed downstream, such that ${\sum }_{j=1}^n{p}_{ij}=1$, and $p_{ij}$ is the fraction of flow out of HRU $i$ that redistributes to HRU $j$ (or alternatively stream reach $j$). The fraction of flow that is redistributed from one HRU to another represents the structural connectivity of an HRU to a receiving landscape unit. $p_{ii}$ thus represents the fraction of cells (with a given HRU designation) that flow downstream to a cell with the same HRU designation as the upstream cell. In this regard, a portion of HRU flux will be redistributed to the same HRU, which reflects the downslope transfer of water through the HRU until reaching the boundary with another HRU or the stream network. In catchments where flow follows topography, it is assumed that the fraction of flow redistributed to a downstream HRU is equal to the areal fraction of landscape units directly downstream of the HRU; this is expected to hold true in the study catchment but is one limitation of the approach used herein. Elements along the diagonal of the matrix represent landscape units that flow into downstream landscape units with the same HRU designation. It is expected that weighting matrices will shift over geomorphic (decadal) timescales but will be constant at yearly timescales (Wainwright et al., 2011). The matrix may be parameterized using a flow direction raster, as discussed in Section 3.3.

Water is passed from upstream to downstream HRUs using a kinematic wave routing approach (Metcalfe et al., 2015), until flow from upland HRUs exfiltrates into the stream network. Inflow to a reach for a specific timestep is equal to the sum of flow entering the reach from upstream hillslope HRUs, which considers the unique upstream contiguity of the hillslope, as well as flow entering from upstream reaches as:

$$Q_{{total}_{i,j}=}{Q}_{{lat}_{i,j}}+Q_{{up}_{i,j}}$$ (3)

where $Q_{{total}_{i,j}}$ is the total amount of flow in a unique reach $j$ during a specific time step $i,Q_{{lat}_{i,j}}$ is the total amount of flow entering the reach from uniquely connected HRUs, as defined by Eq. (2), and $Q_{{up}_{i,j}}$ is the flow entering reach $j$ from an upstream reach during a time step. In this regard, at the most upstream end of the stream network, $Q_{up}$ is expected to be nil because there are no upstream reaches. Flow is then routed to downstream reaches, as described in section 3.2.

While dynamic TOPMODEL is well-recognized to adequately simulate hydrologic fluxes on hillslopes, the instream routing component is not currently equipped to simulate streamflow permanence in headwater reaches, and we have modified the model to include this feature. We conceptualize surface streamflow permanence by building off of findings from both field-based and modeling studies from Godsey and Kirchner, 2014, Ward et al., 2018, Prancevic and Kirchner, 2019, and Durighetto and Botter (2022) (Fig. 2; adapted from Beven and Freer, 2001, Ward et al., 2018). Wherever the total discharge supplied from upstream sources (i.e., upstream reaches and lateral hillslopes) is greater than the subsurface transport capacity of the permeable zone coincident with the geomorphic stream channel, surface flow is possible. This is written as a binary probability as:

$${P\left(F\right)}_{i,j}=\left\{\begin{array}{c}1,Q_{{total}_{i,j}}>Q_{{sub,c}_{,j}}\\ 0,Q_{{total}_{i,j}}\le Q_{{sub,c}_{,j}}\end{array}\right.$$ (4)

where $i$ and $j$ represent a unique temporal and spatial step, respectively, $P\left(F\right)$ represents the probability of streamflow presence within a reach (equal to 1 if surface streamflow is present, 0 if surface streamflow is absent), $Q_{total}$ is the total discharge in a reach contributed from the hillslope and upstream reaches, and $Q_{sub,c}$ is the subsurface capacity of the permeable sediment and bedrock surrounding the geomorphic stream channel in a particular reach. $Q_{sub,c}$ is conceptualized to be a reach-dependent structural watershed property that represents the total amount of subsurface flow that the reach can carry prior to streamflow emerging at the surface. In this regard, the model implicitly accounts for upwelling/downwelling, assuming that if the amount of flow in a reach during a time step is less than the $Q_{{sub,c}_{,j}}$ threshold, then downwelling occurs, otherwise upwelling will occur in the reach. We expand upon this assumption in Section 3.2.

Fig. 2.

Conceptualization of streamflow permanence at the reach scale used to simulate catchment-scale discharge and flow presence/absence (adapted from Beven and Freer, 2001, Ward et al., 2018). $Q_{lat}$ is the total streamflow entering a reach from the hillslope. $Q_{up}$ is streamflow entering a reach from upstream. $Q_{sub,c}$ is the subsurface capacity of the reach’s permeable zone. K is the hydraulic conductivity of the permeable zone. d is the depth of the permeable zone confined between the surface and the impermeable bedrock layer. S is the slope of the reach representing the hydraulic gradient. ${\mathrm{Q}}_{\mathrm{d}\mathrm{o}\mathrm{w}\mathrm{n}}$ is the total flow from the permeable zone, hillslope, and surface stream (if applicable) that is routed downstream. HRU represents hydrologic response units.

The subsurface capacity of the permeable zone is conceptualized using the Darcy equation similar to several recent field-based studies (e.g., Godsey and Kirchner, 2014, Prancevic and Kirchner, 2019) as:

$$Q_{sub,cj}=T_j{S}_j$$ (5)

and

$$T_j=a_j{K}_j$$ (6)

where $j$ is the reach, $T$ is the subsurface transmissivity [L³ T⁻¹], $S$ is the slope of the hydraulic gradient of the reach, assumed to be equal to its slope [L L⁻¹], $a$ is the cross-sectional area of the permeable zone [L²], and $K$ is the hydraulic conductivity of the permeable zone [L T⁻¹].

The total flowing length of the surface stream network during a timestep, $L_{{tot}_i}$, is thus the sum of the total number of reaches within the catchment which are predicted to have surface streamflow multiplied by the length of the active reaches, as:

$$L_{{tot}_i}={\sum }_{j=1}^m{P\left(F\right)}_{i,j}\cdot L_j$$ (7)

where $L_j$ is the length of stream reach $j$ and $m$ is the total number of reaches in the catchment.

The underlying assumptions utilized to formulate these equations have largely been informed by empirical data previously collected by others and analytical models applied in headwater catchments where streamflow permanence was monitored or simulated at relatively high temporal resolutions (e.g., Goulsbra et al., 2014, Ward et al., 2016, Prancevic and Kirchner, 2019, Durighetto et al., 2022).

3.2. Model Application

This version of dynamic TOPMODEL parameterizes several surface and subsurface storage zones to represent transport of water between an HRU and downstream landscape units (Beven and Freer, 2001). These include the root zone, unsaturated zone, saturated zone, and an excess storage zone to represent overland flow (Fig. 2). During instances of prolonged drying, it is assumed that upstream HRUs may be disconnected from downstream HRUs or the stream network when storage in the saturated zone is less than the ${sd}_{max}$ parameter. A kinematic wave approximation is then used to estimate the flux of water exiting the saturated zone of the HRU as total base flow (Metcalfe et al., 2015). Overland flow is routed to downstream landscape units similarly to base flow, with the possibility to reinfiltrate if the capacity of the downstream subsurface store is not filled (i.e., the saturation deficit is greater than zero). At the end of the simulation, a water balance check is conducted to ensure that the hydrologic outputs match inputs (Metcalfe et al., 2015). An overview of dynamic TOPMODEL, its implementation, and its limitations are given in the SI, with more in-depth information found in Beven and Freer, 2001, Metcalfe et al., 2015.

We modified the source code of dynamic TOPMODEL to explicitly define connectivity from hillslopes to individual reaches, route flow from individual reaches to the outlet of the catchment and simulate whether surface streamflow was present or absent in each reach. Discharge is routed to the catchment outlet by first defining Strahler order within each reach, and sequentially routing flow from first-order reaches to sequentially higher-order reaches using either a network-width approach (Beven, 2011) or a finite difference kinematic wave approach (e.g., Ward et al., 2018), depending on the user’s specification. Within each reach, total discharge is uniquely calculated as the sum of discharge from upstream reaches and lateral inflow from the hillslope. The model compares the total discharge in an individual reach to the estimated subsurface capacity of the reach to simulate the presence or absence of surface streamflow, as shown in Eq. (4). Surface streamflow presence/absence is estimated for each reach within Falling Rock for each timestep, which is discussed below.

We do not separate total flow into subsurface and surface flow in the instream routing subroutine. Instead, flow through the permeable zone is lumped with surface flow, and thus upwelling/downwelling is implicitly simulated as part of Eq. (4) and via the instream routing algorithm implemented herein. While this is one limitation and source of uncertainty of our approach, Ward et al. (2018) suggests that downstream flow in the surface stream is expected to be highly variable while flow through the subsurface permeable zone is controlled by the subsurface capacity of the reach. Thus, subsurface flow is expected to be relatively constant in time (but variable in space due to differences in reach morphology and saturated conductivity). This simplification improved the computational efficiency of the instream routing subroutine, thus allowing for more robust parameter uncertainty analysis.

3.3. Model Parameterization

We parameterized properties of the geomorphic stream network with several datasets. The geomorphic stream channel – defined here as the visibly identifiable network formed by channelized erosion and deposition (Godsey and Kirchner, 2014) – was digitized with a 1.5-m digital elevation model and an area-threshold approach within TauDEM (Tarboton, 2005). We iteratively chose area thresholds such that the geomorphic stream network created with TauDEM closely matched the extent of perennial, intermittent, and ephemeral streams identified during field reconnaissance by Cherry, 2006, Fritz et al., 2013. The geomorphic stream channel consisted of 3,154-m of first- and second-order reaches (70% of the total length, Table S1).

We used the dynatopmodel package in R to parameterize the hillslope component of dynamic TOPMODEL (Metcalfe et al., 2015). We calculated contiguous topographic wetness indices (TWI; Beven and Kirkby, 1979) from a 1.5-m DEM and combined these with landscape soil characteristics (SSURGO; U.S. Department of Agriculture - Natural Resource Conservation Service, 2012) to generate 20 HRUs within Falling Rock (Fig. S2). We iteratively adjusted the number of times each layer was discretized, thus changing the number of HRUs generated, to ensure prominent landscape features were captured and to minimize the number of HRUs generated to optimize model run times. We additionally determined the total within-HRU sum of squares to estimate the variability of TWI and soil of each HRU. Beyond 20 HRUs, little variability of the landscape was captured by the discretization (Fig. S3). Average HRU area was 0.05 km².

We routed water through the stream network using the network-width approach, similar to the implementation of dynamic TOPMODEL specified in Metcalfe et al. (2015). We estimated slope and transmissivity of each reach to parameterize the subsurface transport capacity. To simplify computational complexity and limit the number of additional parameters added to the model, we initially assumed a constant subsurface transmissivity $T$ within all reaches, which was later calibrated. While hydraulic conductivity and cross-sectional area of the permeable zone are likely to vary within reaches at the catchment scale, the constant T assumption should hold in systems where subsurface flow capacity varies as a linear function of reach slope (Prancevic and Kirchner, 2019, Shanafield et al., 2021). We emphasize that this assumption results in a fundamentally reduced-complexity simulation of stream network dynamics, similar to the approach of Ward et al. (2018), which may hinder the model’s capacity to predict instream disconnectivity and system fragmentation. While this assumption is one limitation of our approach, as transmissivity likely varies from reach to reach, our intention was to parameterize the subsurface using at least a reduced-complexity approach rather than disregarding it completely. Given the previous data collection efforts in Falling Rock, it would have been possible to calibrate a unique $T$ for each stream order in this catchment, however this would have added four new parameters to the model instead of one. We initially parameterized the model with parsimony in mind rather than complexity, which led to the choice of using a single $T$ to simulate subsurface transmissivity. Future studies may parameterize subsurface capacity of the permeable zone explicitly after conducting field campaigns to measure saturated hydraulic conductivity and depth to bedrock within each reach. The presence/absence of surface streamflow was predicted in each reach using Eq. (4) for each time step after total flow and the subsurface capacity had been determined.

Parameter ranges for the dynamic TOPMODEL and instream routing model are recorded in Table 1. We derived ranges for several parameters in Table 1 from previous application of dynamic TOPMODEL in headwater catchments (Beven and Freer, 2001, Metcalfe et al., 2015). These parameters described the overland flow velocity, initial root zone storage, channel routing velocity, lateral saturated transmissivity, maximum effective deficit of the saturated zone, and unsaturated zone time delay. Manning’s n values were chosen to represent the range from bedrock and heavily forested channels.

Table 1.

Parameter ranges to simulate catchment-scale discharge and surface streamflow presence/absence in reaches. Except for T, all parameters pertain to the dynamic TOPMODEL subroutine and were calibrated using a particle swarm optimization algorithm. $T$ is calibrated during the second phase of model evaluation to estimate the subsurface flow capacity of reaches and thus surface streamflow presence/absence. Optimal values found during model calibration are listed in the final column.

Symbol	Description	Units	Parameter Range
			Minimum	Maximum	Optimum
v.of	Overland flow velocity	m hr−1	10	150	141
srz.max	Maximum root zone storage	m	0.01	0.75	0.44
srz.0	Initial root zone storage	unitless	0.5	1	0.96
v.chan	Channel routing velocity	m hr−1	500	7000	4707
ln(T0)	Lateral saturated transmissivity	m2 hr−1	3	16	16
sd	Maximum effective deficit of saturated zone	m	0.2	0.8	0.63
td	Unsaturated zone time delay	m hr−1	0.01	100	99
n	Manning’s n	unitless	0.01	0.15	0.10
m 1	Exponential decline in conductivity soil type 1	m	5.01E-05	6.10E-02	1.5E-03
m 2	Exponential decline in conductivity soil type 2	m	5.01E-05	6.10E-02	4.22E-04
m 3	Exponential decline in conductivity soil type 3	m	5.01E-05	6.10E-02	4.38E-03
T	Transmissivity of permeable zone throughout the network	m3 hr−1	0.005	10	1.06

We used three parameters to simulate the exponential decline of conductivity in Falling Rock corresponding to the three soil types identified by the U.S. Department of Agriculture (USDA) soil survey (see Fig. 1). We extended the lower range of the m parameters defined in this study to better capture the behavior of the rapidly draining soils present in the catchment (Williamson et al., 2015). Previous studies have varied m between 0 and 0.1 (Beven, 1997), suggesting that the range used herein is physically plausible. We note that the addition of the surface streamflow presence/absence subroutine only added one parameter to the model, $T$, which represented network-wide transmissivity. The range of potential $T$ values was derived by determining the range of potential hydraulic conductivities (0.02–0.51 m hr−1), depths to bedrock (0.1–2.2 m), and width of the valley bottom (2.0–10.0 m) surrounding stream reaches from the USDA soil survey and field reconnaissance (U.S. Department of Agriculture - Natural Resource Conservation Service., 2012, Fritz et al., 2008). Additional information on model formulation, application, and parameterization is included in the SI.

Our objective during model formulation, application, and parameterization was to discretize the model to simulate catchment-scale discharge and surface streamflow presence/absence to investigate trends in streamflow permanence over a three-year study period. To fulfill this objective while maintaining computational efficiency, we ran the model at two-hour time steps at the reach scale (mean length equaled 137-m). While upwelling/downwelling of streamflow between the surface and subsurface flow is likely to occur at sub-meter spatial resolutions and sub-second temporal resolutions, for example due to turbulent bursting (Ward et al., 2016), using this fine-scale temporal resolution for model parameterization would be computationally prohibitive for long-term assessment of streamflow permanence within the stream network and would preclude model evaluation and uncertainty analysis. Thus, we did not adopt this highly resolved approach. Our approach facilitated evaluation of the probability that each reach contained surface streamflow during the three-year study period, the discharge within reaches, and the total stream network with surface streamflow for each time step of the study period, at the cost of potentially being unable to capture sub-reach scale disconnectivity and system fragmentation. Because this approach does not focus on simulated exfiltration, upwelling, or downwelling at a sub-meter spatial resolution, our simulations are instead representative of streamflow permanence processes at reach and longer spatial scales, similar to the approach of Ward et al. (2018). We discretized our model to balance the assumptions of local-scale runoff generation with the ability to apply the model at a catchment scale.

3.4. Model Calibration and Evaluation

Model calibration was carried out using discharge data at the outlet of the watershed to verify model accuracy (Clark et al., 2015a), and flow-state sensor data collected in four reaches (one perennial, one intermittent, and two ephemeral reaches) coupled with maps and surveys of the extent of perennial, intermittent, and ephemeral reaches throughout the network to assess model fidelity (Clark et al., 2015b, Holmes et al., 2020). Additional data in ephemeral tributaries would be required to more comprehensively evaluate the ability of the model to represent stream network dynamics. However, our objective with model calibration was to develop a model that could give reasonable flow estimates at the reach and catchment-scale, while simultaneously using adequate data to balance model fidelity and complexity, keeping in mind our research questions.

We used a two-stage calibration approach to evaluate discharge and flow permanence predictions in Falling Rock (Fig. 3). The two-stage approach assisted in verifying both model accuracy at the watershed outlet and model fidelity in lower-order reaches (e.g., Clark et al., 2015b, Holmes et al., 2020). In the first stage of evaluation, our objective function was to maximize the Kling-Gupta Efficiency (KGE) score of the natural logarithm of two-hour discharge simulations at the catchment outlet. We used the natural logarithm of discharge to better capture variability of low-flow periods during calibration given that such periods are critical for many ecosystem services in the central Appalachian Plateau (e.g., Price et al., 2012, Drayer and Richter, 2016) and stream drying during low-flow periods helped define the hydroperiod of a stream reach (Shanafield et al., 2021). Realizations with KGE score greater than 0.3 were considered behavioral, which represents the midpoint between the KGE calculated by the mean of the discharge time series (KGE = −0.41) and a KGE score where the simulation matches the observed data perfectly (KGE = 1; Knoben et al., 2019). We chose a relatively low benchmark in stage one to better understand how variable hydrologic states, as predicted with different model realizations, impacted the prediction of streamflow permanence within Falling Rock. Estimates of reach-scale discharge are used as inputs to stage two of model evaluation.

Fig. 3.

Two-stage model evaluation to simulate discharge and streamflow permanence at the catchment scale. (a) Stage one: outlet discharge optimization and reach-scale discharge prediction. (b) Stage two: optimization and prediction of reach-scale flow permanence. P is precipitation, PET is potential evapotranspiration, DEM is digital elevation model, LULC is land use and land cover, KGE is Kling-Gupta Efficiency, ${\mathrm{Q}}_{\mathrm{o}\mathrm{b}\mathrm{s}}$ is the observed streamflow, ${\mathrm{Q}}_{\mathrm{s}\mathrm{i}\mathrm{m}}$ is the simulated streamflow, ${\mathrm{Q}}_{\mathrm{s}\mathrm{u}\mathrm{b},\mathrm{c}}$ is the subsurface capacity of the permeable zone, and ${\mathrm{Q}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ is the total flow into a reach from the upstream and the hillslope. FC1-FC4 represent flow-state sensors, as shown in Fig. 1.

In the second stage of evaluation, we calibrated the network-wide transmissivity parameter, $T$, by minimizing the overall error between observed and predicted flow state at the four sites where flow-state data were collected with sensors for each behavioral parameter set from stage one, which included one reach classified as perennial, one reach classified as intermittent, and two reaches classified as ephemeral (FC1-FC4; Fig. 1; Fig. S1b). We did not classify model realizations as non-behavioral in the second stage of evaluation since we were unable to find existing lower benchmarks to assess performance of streamflow presence/absence and because the available data in Falling Rock only facilitated evaluation of our model in two ephemeral reaches. Stage two produced reach-scale estimates of surface streamflow presence/absence for each timestep and for each behavioral parameter set identified in stage one of calibration, which we then visually compared to maps and surveys of the perennial, intermittent, and ephemeral extent of stream networks derived from field reconnaissance for additional verification (Cherry, 2006). We then calculated the average flowing length of the network for each time step across behavioral parameterizations to account for potential uncertainty propagated from stage one of evaluation and uncertainty of subsurface transmissivity. While these data may not be adequate to evaluate small-scale exfiltration, upwelling, and downwelling processes, we found these data facilitated the investigation of streamflow permanence in the catchment at the reach scale – the scale at which our questions are relevant. Additional information on model evaluation is included in the SI.

4. Results and Discussion

4.1. Model Evaluation

4.1.1. Simulated discharge evaluation

Comparison of simulated and observed discharge at the watershed outlet indicated that the model predicted discharge relatively well throughout the study period. Model evaluation identified 454 parameter sets as behavioral, with the optimal parameterization having a KGE value of 0.78 (Fig. 4a and b; see optimal parameter values in Table 1). The p-factor and r-factor of the 95 percent parameter uncertainty (PPU) were 0.67 and 0.47, respectively, suggesting adequate model performance. Dotty plots (see Fig. S4) for the dynamic TOPMODEL parameters shown in Table 1 indicated that simulated discharge was sensitive to the exponential decline in conductivity and maximum root zone storage parameters, which is consistent with findings from previous TOPMODEL and dynamic TOPMODEL studies (Beven, 1997, Beven and Freer, 2001, Metcalfe et al., 2015).

Fig. 4.

Simulations of discharge and percent of the stream network with surface streamflow from the modified dynamic TOPMODEL. (a) Deficit between observed discharge and the optimal discharge simulation. (b) Simulated and observed discharge at the catchment outlet. The black line shows the optimal discharge simulation (Kling-Gupta Efficiency [KGE] = 0.78), the teal line shows the simulation that optimized flow state at reach FC4 (KGE = 0.45), the red line shows the observed discharge at the outlet, and the grey bars show the 95 percent prediction uncertainty. Note: axis limits in (a) and (b) are set between 0- and 20-mm day⁻¹ such that the graph better depicts low-flow dynamics. (c) Timeseries of the percent of the stream network predicted to have streamflow (total stream network length = 4.52 km). The black line represents the average percent of the stream network predicted to have streamflow across all behavioral parameter sets from stage one (n = 454). The grey bars show the standard deviation (STDEV) of the percent of the network with surface streamflow across behavioral parameterizations. Five events that correspond to approximately the 1st, 25th, 50th, 75th, and 98th exceedance percentiles of the flow-duration curve are highlighted. Maps of the flowing network extent during these events are shown in Fig. 6.

Visual inspection of the simulated time series (Fig. 4a) indicated that the model tended to underpredict base flow during late winter/early spring and failed to capture several large storm events during summer months. We offer several potential explanations for both occurrences. First, our model is calibrated using the natural logarithm of simulated and observed discharge to better predict recession periods, which places greater weight on low-flow periods. Second, the implementation of dynamic TOPMODEL in R does not currently consider infiltration excess overland flow (Metcalfe et al., 2015), which may be important during high-intensity storm events. Third, convective thunderstorms with spatially variable precipitation rates are common during summer months in Kentucky (Naylor and Kennedy, 2021). Thus, the weather station located 2.5 km to the southwest may not have accurately captured the total precipitation in Falling Rock during several events. Providing additional rainfall data and calibrating the model to both low- and high-flow periods may resolve some of these deficiencies. However, we emphasize the importance of optimizing low flow given recent findings that streamflow expansion and contraction is most variable during low- and moderate-flow conditions (Ward et al., 2018). Additionally, given that our modeling objective is to simulate surface flow presence/absence, we prioritized model performance during low-flow periods.

4.1.2. Flow permanence evaluation

We compared simulated and observed flow state in four reaches with variable Strahler order, which assisted with improving model fidelity of flow permanence simulations (see Fig. 5). Simulated flow state in reaches FC1-FC3 was predicted with greater than 95% accuracy over the study period (Fig. 5a – c) for all parameterizations. The performance of the model had little variability in reaches FC1-FC3 despite changes in the calibrated transmissivity parameter and variable model realizations. We attribute this to the relative stability of flow state observed throughout the study period in these reaches (flow-state sensors indicated that FC1-FC3 were generally wet during this period; see Fig. S1) and note that the FC3 sensor was only active during the wet year, which we acknowledge is suboptimal for simulating dynamic expansion and contraction at the reach scale. However, the performance statistics also underscore the model’s capacity to accurately predict the presence or absence of surface streamflow in reaches with Strahler orders greater than 1 that show the beginning of channelized streamflow (see Table 2 and Fig. S5).

Fig. 5.

Percentage of the observed flow state correctly predicted by the modified dynamic TOPMODEL versus Kling-Gupta Efficiency (KGE) of streamflow predicted at the catchment outlet for all behavioral parameter sets (n = 454) identified during stage one of calibration. The magnitude of the calibrated transmissivity parameter used to estimate the subsurface flow capacity of reaches for each behavioral realization is shown (in color) as a third dimension. (a) Percentage of the observed flow state correctly predicted at FC1, the most downstream flow-state sensor which was classified to flow perennially by Cherry (2006). (b) Percentage of the observed flow state correctly predicted at FC2, located on an intermittent reach. (c) Percentage of the observed flow state correctly predicted at FC3, located on an ephemeral reach. (d) Percentage of the observed flow state correctly predicted at FC4, the most upstream flow-state sensor which was classified to flow ephemerally. (e) Histogram and density plot of calibrated transmissivity values. The red circle shows the realization with optimal simulation of flow state in FC4. The green circle shows the optimal KGE for simulated discharge at the catchment outlet. The magenta circle shows a realization where both flow state and discharge at the catchment outlet are adequately simulated (e.g., Ebel and Loague, 2006, Holmes et al., 2020).

Table 2.

Reach-scale morphology, subsurface flow capacity, and likelihood of streamflow presence within Falling Rock. Flow-state sensors were placed in four reaches, as recorded in the last column and shown in Fig. 1. Reach ID 3802 is the most downstream reach.

Reach no.	Strahler Order	Slope (m m−1)	Upstream Area (m2)	Qsub,c (m3 hr−1)	Likelihood Streamflow Present	Flow-state sensor designation
1	4	0.03	954,609	0.0287	100
2	4	0.02	916,783	0.0255	100
3	4	0.02	898,584	0.026	100	FC1
4	4	0.03	785,984	0.0276	100
5	3	0.04	482,728	0.0394	100
6	3	0.05	300,299	0.0547	100
7	3	0.04	263,696	0.0416	100
8	3	0.03	219,253	0.0362	100	FC2
9	3	0.05	220,585	0.0518	100
10	3	0.06	117,539	0.0647	100
11	2	0.06	174,347	0.0614	100
12	2	0.14	52,007	0.1444	86.5
13	2	0.16	69,432	0.1727	98.1
14	2	0.14	57,838	0.152	85.8	FC3
15	2	0.08	92,160	0.0884	100
16	2	0.16	90,109	0.1708	98.5
17	1	0.32	15,737	0.3434	31.1
18	1	0.36	9,921	0.3851	1.9
19	1	0.36	21,300	0.3784	21.6
20	1	0.45	25,755	0.475	65.7
21	1	0.2	71,803	0.2084	43.9
22	1	0.18	54,620	0.1883	56.6
23	1	0.35	21,383	0.3697	2.1
24	1	0.4	10,251	0.4228	26
25	1	0.43	15,732	0.4508	22.8	FC4
26	1	0.46	21,102	0.4862	0
27	1	0.42	20,006	0.4448	37.2
28	1	0.23	18,446	0.2439	46.8
29	1	0.36	10,148	0.3782	32.4
30	1	0.42	22,004	0.4422	31.6
31	1	0.4	20,894	0.4223	71.4
32	1	0.22	77,674	0.2297	52.4
33	1	0.23	59,307	0.2434	10.2

Conversely, we observed a trade-off between the model’s ability to predict flow state in the most distal reach, FC4, and the ability to predict discharge at the catchment outlet (Fig. 5d). Specifically, the model realization that predicted FC4′s flow state optimally (87% of the study period) had a KGE value of 0.45, while the realization with the optimum KGE (KGE = 0.78) at the catchment outlet predicted FC4′s flow state correctly 69% of the study period. This finding underscores recent sentiment noting the difficulty of validating model performance of semi-distributed, process-based hydrologic models with singular discharge measurements at the catchment outlet – and emphasizes that increased data are necessary to verify model fidelity as in this approach (Ebel and Loague, 2006, Ebel et al., 2008, Holmes et al., 2020). We found that lower predicted transmissivity values in FC4 coincided with high discharge KGE values (Fig. 5d and e). Mean calibrated transmissivity across all behavioral parameterizations was equal to 1.06 m3 hr−1, which agrees with potential transmissivity values estimated from measured saturated hydraulic conductivity and soil depth (U.S. Department of Agriculture - Natural Resource Conservation Service, 2012) and estimated reach width (Vesely et al., 2008), and likely is representative of the average system transmissivity throughout the headwater network. The calibrated transmissivity values likely represent the potential range of transmissivities found in reaches throughout Falling Rock. Despite the model’s variability in predicting FC4′s flow state, flow state was predicted correctly on average 74% of the study period across all behavioral parameterizations in FC4, which confirms the model’s relatively strong performance even in this distal reach.

While the second stage of model calibration did not quantifiably reduce equifinality (Beven, 2006), the pareto front showing the trade-off between model performance of simulated discharge and simulated flow state in Fig. 5d assisted with identification of parameterizations that best represented internal states of the system (Ebel et al., 2008, Gupta et al., 2009, Holmes et al., 2020). We were unable to find any existing benchmarks within the literature to classify simulations as behavioral for flow state (other than noting that a prediction of 50% would be no better than chance). Model results indicated that the minimum percentage flow state was correctly predicted in first-order and higher-order reaches was 64% and 82%, respectively, across all parameterizations. We suggest that these numbers may serve as lower benchmarks of model performance for future modeling efforts in the Central Appalachian Plateau (Seibert et al., 2018). Given the importance of understanding headwater streamflow permanence with respect to the federal protection of waterways (Creed et al., 2017, Wohl, 2017), the vast number of metrics that have been used to assess streamflow permanence (e.g., Gallart et al., 2012, Fritz et al., 2020, Hammond et al., 2021), and the feasibility of utilizing models to simulate such processes as shown here and in previous studies (Williamson et al., 2015, Jensen et al., 2018, Ward et al., 2018, Botter and Durighetto, 2020, Durighetto and Botter, 2022), we encourage researchers to further investigate benchmarks to evaluate simulations of streamflow permanence.

The model evaluation also gives insight into the hydrological processes and controls of streamflow permanence in Falling Rock. Our model simulations imply that variability of the subsurface transport capacity within reaches ($Q_{sub,c}$, see Eq. (5) is controlled primarily by the slope of individual reaches and less by the subsurface transmissivity ($T$, see Eq. (6). This finding was perhaps surprising given that width, depth, and saturated hydraulic conductivity of the permeable zone were presumed to change throughout the system and thus affect subsurface flow capacity. Ultimately, this result is related to our assumption of a constant subsurface transmissivity used for the stream network, which is corroborated by Svec et al. (2005), who found that stream slope explained the majority of variability when predicting flow duration in eastern Kentucky streams. Recent literature suggests that transmissivity is proportional to upstream contributing area (Prancevic and Kirchner, 2019, Shanafield et al., 2021) as $T\alpha A^{-\gamma }$, where $\gamma$ is an exponent varying between −0.6 and 13.8, determined in mountain ranges located throughout the United States, and A is the upstream contributing area. In catchments where $\gamma$ approaches zero, transmissivity becomes relatively constant, such that the subsurface capacity of the permeable zone throughout the network is a linear function of slope. Our relatively successful use of a constant simulated transmissivity parameter throughout the stream network suggests that $T$ varies relatively weakly with upstream contributing area in Falling Rock, as evidenced by the consistent model performance in higher-order reaches (though with variable model performance in FC4). This result also suggests that the $\gamma$ for Falling Rock falls towards the lower-end of $\gamma$ values throughout the United States and corroborates findings from Prancevic and Kirchner (2019) that transmissivity can generally be predicted as a function of geomorphic catchment properties. However, field reconnaissance could verify this finding and values of $T$ in the catchment.

The two-stage calibration approach did indeed improve our confidence in model fidelity; however, uncertainty is present to different degrees in reaches where no streamflow permanence data were collected. Namely, our assessment of streamflow dynamics is constrained in other first-order reaches given the lack of streamflow permanence data collected in such reaches. It was therefore necessary to supplement these data with maps and surveys of hydroperiods derived from field studies as well as assessment of hydroperiod using biological assessments, as described below in section 4.2 (Cherry, 2006, Fritz et al., 2013). Data scarcity is a common and perpetual issue in catchment-scale hydrologic models and this study further highlights that long-term data collection is crucial to better-understanding and simulating headwater streamflow permanence. Our approach does, however, show promise for transferability to other catchments, by potentially using alternative validation approaches to verify model fidelity.

4.2. Simulated spatiotemporal dynamics of streamflow expansion and contraction

The simulated active stream network length varied between 50% ± 4% and 98% ± 2% ($\mu =74\mathrm{\%}$) of the geomorphic stream channel throughout the study period (see Fig. 4c). To derive the simulated active stream network length, we averaged the simulated wetted channel length across all behavioral parameterizations from stage two of model calibration, thus accounting for parameter uncertainty propagated from stage one of calibration. Visual inspection of the simulated time series of the percent of the stream network predicted to have streamflow (Fig. 4c) indicated that periods with the lowest flowing stream network length coincided with low-flow periods in the late summer and fall, which is generally the period with the least amount of precipitation in Robinson Forest (Sena et al., 2021).

The percentage of stream network with simulated surface flow appears to approach an asymptotic limit during low-flow periods approximately equal to 50% of the geomorphic stream network length, as observed around October 6, 2005 (Fig. 4b and c; Fig. 6a). This is likely related to increased residuum, lower slope, and increased base flow surrounding higher-order reaches maintaining surface streamflow annually whereas steeper slopes in low-order reaches promote rapid transmission of flow downstream (see Table 2; Shaw et al., 2017, Antonelli et al., 2020). We anticipated that a stepwise decline in simulated surface streamflow length may occur beyond the approximately 50% minimum predicted by the model given sufficient drying of the system, especially if flow from fracture conduits is interrupted. Specifically, for third-order streams to dry in this system, the total volumetric flow rate must be less than a simulated value of approximately 0.06 m3 hr−1 within reaches (Table 2; Fig. S5), which our model did not simulate during the study period. This flow was observed, however, for nearly 1.4% of the period between 2000 and 2015 outside of the study period, suggesting not only that predicting low-flow dynamics over longer periods may improve the model’s capability to simulate surface streamflow contraction, but that longer-duration simulations may be key to characterizing the true end-member conditions and likelihood of stream channel drying.

Figure 6.

Maps of flowing stream length for discharges of variable exceedance probabilities. Events correspond with those identified in Fig. 4. Maps are derived from a single behavioral parameterization with KGE > 0.7 and percentage of the flow state correctly predicted greater than 75% of the study period. The color of the boxes surrounding the captions for each event represent the event’s magnitude. The flow duration curve at the catchment outlet with events called out is plotted in the middle of the bottom half of the figure.

The model outputs were used to map simulated streamflow expansion and contraction dynamics as hydrologic conditions varied in the catchment (Fig. 6). Five events corresponded to approximately the 1st, 25th, 50th, 75th, and 98th exceedance percentiles of simulated discharge and the associated percentage of the network with simulated surface streamflow (Fig. 4 and Fig. 6, respectively). Simulated streamflow expansion and contraction maps are derived from one behavioral parameterization of the system where the percent of the study period with flow state correctly predicted was greater than 75% and the KGE of discharge was greater than 0.7 (magenta circle in Fig. 5d; Fig. 6). The maps suggest that first- and, to a lesser degree, second-order reaches generally are surficially inactive during the lowest flow regimes (>98% and 75% exceedance discharges), but become variably connected via surface streamflow during higher flow regimes. For example, we found that the 50% exceedance discharge corresponds with a simulated flowing stream network length equal to approximately 68% of the geomorphic stream network (3.49 km). We found that 61% and 100% of first- and second-order streams were predicted to be connected to downstream reaches during this event, respectively. The ability of the model to map simulated streamflow permanence is important given recent emphasis on procuring data to quantify the frequency and duration of flow in temporary streams (Jensen et al., 2017, Creed et al., 2017).

Large variability of simulated streamflow permanence in first-order reaches reflects the importance of representing hillslope-stream network connectivity in the structure of the model. We calculated the average percentage of the study period when simulated surface flow was present within each reach in Falling Rock across all behavioral parameterizations from stage one (Fig. 7a). Higher-order stream reaches were predicted to be connected between 85 and 100% of the study period. First-order streams had the largest variability in simulated streamflow permanence, and individual reaches were predicted to have surface streamflow between less than 1% and 71% of the study period. We attribute the variability of modeled surface streamflow to the range of slopes within first-order streams, upstream contributing area of reaches, the soil type of hillslopes upstream of reaches, and the proximity of hillslopes to the stream network (e.g., Bracken et al., 2013, Fritz et al., 2018, Leibowitz et al., 2018, Mahoney et al., 2020). The importance of hillslope-stream network connectivity is demonstrated in reach 27 and 31, which had similar slope and upstream contributing area, but were predicted to have surface streamflow for 37% and 71% of the study period, respectively (Table 2; Fig. S5).

Figure 7.

(a) Likelihood of streamflow presence (%) within reaches calculated as the percentage of the study period with streamflow present in a reach. (b) Intermittent stream network in Falling Rock identified by the National Hydrography Dataset Plus High Resolution (US Geological Survey 2018). (c) Perennial, intermittent, and ephemeral stream extent identified by Cherry (2006).

Model outputs indicate that first-order streams are important contributors to total simulated discharge at the catchment outlet. The optimal parameterization resulted in 39% of simulated discharge emanating from first-order streams in Falling Rock. Previous studies have indicated that quick flow contributes nearly 44% of total discharge in Falling Rock (Coltharp and Springer, 1980), which corroborates our results given that quick flow is generally expected to occur when ephemeral reaches are active. The model exemplifies one method to quantify the watershed-scale function of headwater systems, which in turn may assist with enhancement of headwater protection in future years (Johnson et al., 2010). Furthermore, this result underscores the importance of hydrologically effective restoration practices of disturbed lands, including the Forestry Reclamation Approach (Williamson and Barton, 2020), and may be one reason why water quality can be disproportionately affected by disturbance of these small streams (Fritz et al., 2010).

We compared the probability of simulated surface streamflow within individual reaches (Fig. 7a; Table 2) to the National Hydrography Dataset (NHD) Plus High Resolution map, which is a coarser (and vastly larger) mapping effort than ours (Fig. 7b; U.S. Geological Survey, 2018). The NHD Plus map overlapped with 27% of the geomorphic stream network from TauDEM. Model outputs indicated that nearly 100% of the network coincident with the NHD segment flowed perennially, but that an additional 1,215 m of stream length (26% of the geomorphic channel) was predicted to flow for 98% of the study period yet was not depicted by NHD. NHD Plus classified the mapped stream (Fig. 7b) as being entirely intermittent.

We additionally compared simulated streamflow permanence results to localized hydroperiod classification from Cherry (2006) (Fig. 7c), which further validated model results. Our model indicated that reaches identified as perennial by Cherry (2006) were simulated to have surface flow for 100% of the study period. Reaches identified as intermittent were simulated to have surface flow between 100% and 56.6% of the study period. Reaches identified as ephemeral were simulated to have surface flow between 86.5% and 1.0% of the study period. While the mapped results from Cherry (2006) generally agree with our model outputs, our results tended to indicate slightly wetter conditions than the classification from Cherry (2006). Likely this can be attributed to mapping during a singular instance versus the three-year study period which spanned a relatively wet, relatively dry, and an average year with respect to annual precipitation (Sena et al., 2021). Regardless, our model results support recent sentiment to improve inventories and understanding of perennial, intermittent, and ephemeral streams in headwater networks (Fritz et al., 2013, Creed et al., 2017, Leibowitz et al., 2018, Shanafield et al., 2021).

4.3. Simulated controls of streamflow permanence

We plotted average simulated stream length across behavioral parameterizations versus the optimum simulated discharge and fit power functions to the data to evaluate the rate at which the network expands and contracts (Fig. 8). Recent literature suggests that the rate of stream network expansion can be measured with reference to discharge at the catchment outlet using a power function (linear in log-log space; Godsey and Kirchner, 2014, Shaw et al., 2017, Whiting and Godsey, 2016, Prancevic and Kirchner, 2019, Antonelli et al., 2020) equal to $L\propto q^{\beta }$, where $L$ is the length of the flowing stream network (km), $q$ is the discharge (mm day⁻¹), and $\mathrm{\beta }$ is an exponent representing the rate at which the stream network expands as a function of discharge at the watershed outlet.

Figure 8.

Average flowing stream length versus optimal discharge simulated at the catchment outlet. Two regression lines are fit to the data which represent time steps when discharge is either below (R² = 0.93) or above (R² = 0.47) approximately 1 mm day⁻¹. The approximately 1 mm day⁻¹ threshold represents the discharge exceeded nearly 15% of the study period and was found to optimize the R² of the regression equations shown in the figure. Exponents of the regression equations correspond to β parameters representing the rate of stream expansion/contraction (e.g., Prancevic & Kirchner, 2019).

Visual inspection of model results indicated that two distinct patterns of stream wetting and drying occur within Falling Rock depending on the hydrologic regime of the system (Fig. 8). We developed two regression equations to represent the rate of simulated streamflow expansion and contraction and optimized a threshold discharge, $q_t=1$ mm d⁻¹ to maximize the R² of the two power functions (R² = 0.93 and R² = 0.47, respectively) as:

$$L=\left\{\begin{array}{c}4.33\cdot q^{0.17},q<q_t\\ 4.12\cdot q^{0.02},q\ge q_t\end{array}\right.$$ (8)

This result indicates that simulated surface streamflow expands relatively quickly during low-flow conditions until the threshold of 1 mm d⁻¹ is reached, at which point the rate of streamflow expansion decreases by approximately one order of magnitude. The active extent of the stream network is predicted to increase by approximately 2.3 km as discharge increases from 0.01 mm d⁻¹ to 1 mm d⁻¹, but only increase by 0.5 km when discharge increases from 1 mm day⁻¹ to 100 mm day⁻¹. This result is supported both experimentally and theoretically by several studies that also found a plateau in the rate of stream expansion above a threshold discharge (Ward et al., 2018, Jensen et al., 2019, Durighetto and Botter, 2022). We note that we used a static realization of the geomorphic stream network to represent the domain of stream expansion and contraction within Falling Rock. Thus, channel evolution and channel head migration are not accounted for within the model structure. This means that while overland runoff is accounted for with dynamic TOPMODEL (Metcalfe et al., 2015), the instream subroutine does not simulate instances when channelized flow occurs upstream of the geomorphic stream channel. Future iterations of the model might incorporate sediment transport subroutines that simulate channel head migration to realize a fully dynamic stream network.

Our results indicate that a combination of structural and functional watershed properties control simulated surface streamflow permanence and stream expansion/contraction during low-flow periods, while functional (hydrologic) influence of stream expansion decreases during high-flow periods. One potential reason for this is that as the water table rises during low-flow periods due to increased precipitation and lateral inflow, the subsurface capacity in higher-order streams with low slope and large upstream contributing area is initially filled, sustaining surface streamflow. Generally, little variability of streamflow permanence was simulated in streams with Strahler order greater than 2 (Fig. 7a, Table 2), suggesting that increasing upstream connectivity of hillslopes and upstream reaches stabilizes streamflow permanence (Ward et al., 2018, Jensen et al., 2019, Prancevic and Kirchner, 2019, Durighetto and Botter, 2022). Perennial reaches tended to coincide with upstream contributing areas of at least 9.2 ha.

On the other hand, significantly more variability in predicted streamflow permanence was simulated in reaches with low Strahler order, low upstream contributing area, and high slope (Fig. 7a, Table 2), which we attribute to a relatively increased subsurface flow capacity and variable connectivity of heterogeneous upstream HRUs. These results suggest that during low-flow periods, a combination of functional processes (e.g., water storage, precipitation, evapotranspiration) and the unique structural properties within a reach (e.g., watershed configuration, subsurface flow capacity) control the simulated presence/absence of streamflow within Falling Rock. We largely attribute the lack of sensitivity of the stream network expansion to hydrologic forcings during high-flow periods to the subsurface already being at or above its transport capacity. Specifically, at a simulated outlet discharge of 1 mm d⁻¹, nearly 85% of the geomorphic stream network was predicted to contain surface flow, indicating that the subsurface is already at capacity, and thus limiting further expansion of the simulated active stream length.

This result is corroborated by a recent study conducted by Ward et al. (2018), who found that the flowing length of the stream network was limited despite catchment outlet discharge varying nearly three orders of magnitude during wet conditions. Notably, Ward et al. (2018) found that the degree of stream network expansion and connectivity greatly decreased for outlet discharges greater than approximately 28.8 m³ hr⁻¹ (reported as 8 L s⁻¹) in a 96-ha catchment within the H.J. Andrews Experimental Forest in the western Cascade Mountains of Oregon, USA. Our results suggest that a similar threshold exists in Falling Rock at a simulated discharge of 1 mm d⁻¹, which corresponds to a volumetric flow rate of 39.6 m³ hr⁻¹ at the 96-ha catchment outlet. We found this result rather surprising given that our studies were conducted in different physiographic regions at opposite ends of the conterminous United States. While further investigation could confirm if such thresholds hold true in other headwater catchments, this perhaps is one piece of evidence supporting the claim from Godsey and Kirchner (2014) that despite varying geology, topography, and climate, stream expansion and contraction are phenomena that may be generalizable across systems. Additionally, this corroborates early findings from Strahler (1957) suggesting that similar-order stream networks behave in a hydrologically similar manner.

The model outputs suggested that expansion of the simulated active stream length in Falling Rock falls between systems identified as “stable” and “rapidly expanding” in recent literature, as represented by the power-function exponent (β) equal to 0.17 during low-flow periods. (e.g., Godsey and Kirchner, 2014, Whiting and Godsey, 2016, Jensen et al., 2017, Shaw et al., 2017, Prancevic and Kirchner, 2019). Prancevic and Kirchner (2019) summarized β parameters calculated via repeated field mappings of the flowing extent of the stream network and found that β varied between 0.04 and 0.59 (μ = 0.19) throughout headwater systems in the United States. Comparatively, during low-flow periods, Falling Rock was simulated to wet up slightly less quickly than the mean β identified by Prancevic and Kirchner (2019), indicating that the system is predicted to not be particularly flashy or stable compared to other systems. This is consistent with the relatively rapid drainage of sandy soils withing Falling Rock, with sustained surface streamflow attributed to the presence of subsoils with increased fractions of silt and clay.

During high-flow periods, the simulated stream network in Falling Rock expands slower than all other catchments discussed by Prancevic and Kirchner (2019), as represented by the power-function exponent (β) equal to 0.02 during high-flow periods. Our finding that variable rates of expansion and contraction exist within the network is consistent with results from several recent studies (e.g., Ward et al., 2018, Jensen et al., 2019, Durighetto and Botter, 2022) but has been discussed less frequently in studies that determine the rate of expansion via field surveys (e.g., Godsey and Kirchner, 2014, Whiting and Godsey, 2016, Jensen et al., 2017, Shaw et al., 2017). It is likely that the shift to a lower-magnitude β (or an overall nonlinear relationship between L-q) is typical in most systems given that theoretically there is an upper limit to the amount of discharge that can exist within the geomorphic stream channel during a given hydrologic event. However, this phenomenon is likely reported less frequently because measurement of flowing stream length is logistically constrained during high-flow periods (which often only exist over short time scales and are infeasible to map from ground observations for watersheds the size of Falling Rock or larger). These constraints can be overcome by using aerial imagery to characterize stream length at regular intervals (e.g., Hooshyar et al., 2015) or by applying extensive networks of flow-state sensors which extend well into ephemeral reaches (e.g., Jensen et al., 2019, Durighetto and Botter, 2022). We note that the static realization of the geomorphic stream network to represent the domain of stream expansion and contraction within Falling Rock is a necessary structural constraint of the model, and this relation may be further explored by explicitly considering channel evolution and channel head migration in the model structure.

We should note that while the power law function fits the L-q data well below the 1 mm d⁻¹ threshold, the fit of the power law above the threshold is less adequate. One particular issue with the application of a power function to represent L-q data above the 1 mm d⁻¹ threshold is that the function is monotonically increasing, which indicates that at large flows the stream length continues to grow towards infinity – albeit at a slow rate. We posit, however, that there is an upper limit to streamflow expansion in the study catchment given that, by definition, once the geomorphic channel is completely wetted up, the network can expand no further (noting that we conceptualize overland runoff from hillslopes separately from channelized flow). In this context, the ability of the power law function to describe the L-q relationship begins to break down at higher flow regimes. We should note that we used the power law equation to model the L-q relationship to compare β coefficients representing stream expansion rates among Falling Rock and the extensive literature using power laws to represent L-q dynamics (Roberts and Klingeman, 1972, Godsey and Kirchner, 2014, Shaw, 2016, Whiting and Godsey, 2016, Jensen et al., 2017, Prancevic and Kirchner, 2019, Antonelli et al., 2020). Further, we applied the power law for both the low- and high-flow regimes because we wanted to emphasize the change in L-q expansion rates above the 1 mm d⁻¹ threshold discharge value. Recent studies have suggested the use of sigmoid-type functions to better represent this L-q relationship (e.g., Durighetto and Botter, 2022), and we fitted a four-parameter Weibull function to the L-q data from Falling Rock with R² = 0.97, which corroborates this notion (see Fig. S6).

4.4. Model limitations and opportunities

Streamflow expansion and contraction are inherently complex processes resulting from fine-scale, multi-dimensional fluxes (Godsey and Kirchner, 2014, Ward et al., 2016, Ward et al., 2018). While we emphasize the efficacy of the catchment-scale, process-based modeling approach, it is often epistemologically and computationally challenging to discretize models at physically realistic spatial or temporal scales. For example, increasing the temporal discretization of our model from a two-hour timestep to a 15-minute timestep increased the computational time by approximately eight-fold, and calibrating the model once resulted in nearly 15 gigabytes of data. We recognize that high-spatiotemporal resolution simulations that capture fine-scale processes such as upwelling/downwelling, flow through alluvial deposits, exfiltration from springs, and sub-reach scale disconnectivity are particularly important for identification of the directionality of streamflow expansion (e.g., bottom-up, top-down, or converging; Goulsbra et al., 2014, Peirce and Lindsay, 2015, Shanafield et al., 2021) and within-reach variability of flow state. For example, minute-scale measurements/simulations might be required to fully capture rapid stream expansion in flashy systems (Goulsbra et al., 2014, Jensen et al., 2019), or ephemeral reach dynamics, and upwelling/downwelling fluxes between the surface and subsurface. Yet our model simulated low-flow dynamics and streamflow permanence relatively well using on average 0.05 km2 HRUs (Fig. S3) and approximately 130-m stream reaches at a two-hour time step, underscoring that investigating various components of streamflow permanence and runoff generation might require variable spatially and temporally scaled models. However, we should state this model is reliant upon findings from relatively well instrumented hillslope and sub-meter streamflow permanence studies to inform the necessary assumptions required to run the model (for example as discussed by Godsey and Kirchner, 2014, Goulsbra et al., 2014, and Peirce and Lindsay, 2015). Future streamflow expansion and contraction simulations would benefit from explicitly defined timescales, hydrologic processes, and model objectives relative to trade-offs in model accuracy, fidelity, and complexity (Clark et al., 2015b, Golden et al., 2017).

We aimed to develop a modular framework to simulate headwater streamflow permanence that might eventually be upscaled regionally throughout the United States and are currently testing this framework’s applicability in catchments with variable geologic and morphologic properties. A key model development opportunity is to improve flow routing in regions with modified or complex subsurface flow, e.g., in tile or ditch drained networks or karst systems (e.g., Ford et al., 2019, Husic et al., 2019, Evenson et al., 2021). Additionally, the hydrologic dynamics of small surface storage systems, e.g., geographically isolated wetlands or non-floodplain wetlands (see perspectives for modeling these systems in Evenson et al., 2015, Golden et al., 2017, Jones et al., 2019), which are important for the proper functioning of hydrological and ecological systems globally (Cohen et al., 2016, Creed et al., 2017, Evenson et al., 2018), need to be integrated into the model.

Discharge data for first- and second-order systems is scarce (Poff et al., 2006, Nadeau and Rains, 2007) and likely will remain scarce as the U.S. Geological Survey shift focus of hydrologic monitoring to population centers to support infrastructure rather than to headwaters (Hodgkins et al., 2019; U.S. Geological Survey, 2020, Golden et al., 2021). We integrated field reconnaissance, discharge measurements, and flow-state monitoring in perennial, intermittent, and ephemeral reaches to verify our model’s streamflow expansion and contraction dynamics. However, only two of the 12 ephemeral flow reaches identified by Cherry (2006) had flow-state sensors, and thus equifinality and parameter uncertainty indeed are present in the model. The use of supplementary validation data, such as additional flow sensor measurements and ecological descriptions, may improve the fidelity of streamflow permanence simulations (Seibert and McDonnell, 2002, Ebel and Loague, 2006, Clark et al., 2015b). For example, remotely sensed data (Svec et al., 2005, Vanderhoof et al., 2017, Wu and Lane, 2017), field surveys (e.g., Prancevic and Kirchner, 2019), physiochemical and biological indicators (Fritz et al., 2008, Johnson et al., 2010), stable isotope tracing (Stadnyk et al., 2013, Brooks et al., 2018, Holmes et al., 2020), and estimates of transmissivity via topographic catchment properties (e.g., Prancevic and Kirchner, 2019, Shanafield et al., 2021) have elucidated the dynamics of hydrologic connectivity and streamflow permanence in recent years and could be integrated as soft data verifying model behavior. The procurement and application of such data could be prioritized for future research in coming years and will be especially important for upscaling this model to larger watersheds and regions of the United States with invariably less data than Falling Rock.

5. Conclusions

We developed a process-based, catchment-scale hydrologic model to investigate the dynamics of surface streamflow permanence and the controls of streamflow expansion and contraction in headwater reaches. The framework considered explicit hillslope-stream network connectivity using a modified dynamic TOPMODEL approach and estimated the subsurface transport capacity of reaches to simulate the presence or absence of surface streamflow. We applied the model to a moderately well-monitored catchment in the central Appalachian Plateau of eastern Kentucky, USA. We found that:

1. The model simulated discharge at the catchment outlet and streamflow presence/absence within perennial, intermittent, and ephemeral reaches relatively well, albeit with some uncertainty. Considering hillslope-stream network connectivity in the model was particularly important for classifying streamflow in first-order reaches, where streamflow permanence was most variable in the study catchment.

2. Model outputs helped to create maps representing surface streamflow extents within the headwater network and to quantify first-order reach contributions to total discharge at the catchment outlet. Model outputs indicate that nearly 39% of total discharge is contributed by ephemeral reaches. When comparing model-generated maps of streamflow permanence probabilities to current headwater stream inventories in the United States, we predicted that 1,215 m of stream length (26% of the headwater network) was flowing for at least 98% of the three-year study period. Yet this part of the stream network was not mapped by national inventories. This finding underscores the need for improved stream mapping across the United States.

3. Our model outputs suggested that the interaction of a rising water table, upstream hydrologic connectivity, and structural properties defining a reach’s subsurface capacity control streamflow permanence during low-flow conditions, but that simulated sensitivity of stream network expansion to hydrologic forcing diminishes during high-flow periods. Recent experimental and modeling studies in headwater systems corroborate this finding despite being geographically dissimilar, suggesting that headwater expansion and contraction may have similar controls across systems.

4. Flow-state data (interpreted as the presence or absence of surface streamflow) assisted with model verification. However, continuous data to verify streamflow permanence in headwater systems is typically scarce (Poff et al., 2006), and it was necessary to supplement our model verification with field maps and surveys of the extent of perennial, intermittent, and ephemeral streams. Prioritizing the procurement and application of data to classify headwater streamflow will enable researchers to quantify the function of headwaters within the context of larger watershed systems. This advancement has the potential to enhance the protection of headwater systems in coming years.