A network model for prediction and diagnosis of sediment dynamics at the watershed scale

Authors

  • Sopan Patil,

    Corresponding author
    1. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA
    2. Now at National Health and Environmental Effects Research Laboratory, U.S. Environmental Protection Agency, Corvallis, Oregon, USA
      Corresponding author: S. Patil, National Health and Environmental Effects Research Laboratory, U.S. Environmental Protection Agency, Corvallis, OR 97333, USA. (sopan.patil@gmail.com)
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  • Murugesu Sivapalan,

    1. Department of Geography, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
    2. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
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  • Marwan A. Hassan,

    1. Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada
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  • Sheng Ye,

    1. Department of Geography, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
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  • Ciaran J. Harman,

    1. Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, Maryland, USA
    2. Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona, USA
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  • Xiangyu Xu

    1. Department of Hydraulic Engineering, Tsinghua University, Beijing, China
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Corresponding author: S. Patil, National Health and Environmental Effects Research Laboratory, U.S. Environmental Protection Agency, Corvallis, OR 97333, USA. (sopan.patil@gmail.com)

Abstract

[1] We present a semi-distributed model that simulates suspended sediment export from a watershed in two stages: (1) delivery of sediments from hillslope and bank erosion into the river channel, and (2) propagation of the channel sediments through the river network toward the watershed outlet. The model conceptualizes a watershed as the collection of reaches, or representative elementary watersheds (REW), that are connected to each other through the river network, and each REW comprises a lumped representation of a hillslope and channel component. The flow of water along the stream network is modeled through coupled mass and momentum balance equations applied in all REWs and sediment transport within each REW is simulated through the sediment balance equations. Every reach receives sediment inputs from upstream REWs (if present) and from the erosion of adjacent hillslopes, banks and channel bed. We tested this model using 12 years (1982–1993) of high temporal resolution data from Goodwin Creek, a 21.3 km2 watershed in Mississippi, USA. The model yields good estimates of sediment export patterns at the watershed outlet, with Pearson correlation coefficient (R value) of 0.85, 0.87, and 0.95 at daily, monthly, and annual resolution, respectively. Furthermore, the model shows that the dynamics of sediment transport are controlled to a large extent by the differences in the behavior of coarse and fine sediment particles, temporary channel storage, and the spatial variability in climatic forcing. These processes have a bearing on the patterns of sediment delivery with increasing scale.

1. Introduction

[2] Characterization of fluvial sediment dynamics at the watershed scale requires an understanding of the connectivity between sediment generation within the landscape and its eventual transport within the river channel network [Ferro and Porto, 2000; Verstraeten et al., 2007; Medeiros et al., 2010]. The processes that control sediment delivery at any given point in a river are largely determined by its location within the network hierarchy and the geomorphic properties of the surrounding landscape [Asselman, 1999; Vericat and Batalla, 2006]. For instance, in lower order streams, the supply of sediments from local hillslope erosion plays a major role in the temporal dynamics of sediment export. On the other hand, sediment dynamics in higher order streams are additionally controlled by the fluvial supply of sediments from upstream reaches and bank erosion. A challenging task, however, is to translate this general process understanding into predictive models of sediment transport. Smith et al. [2011]outline three main difficulties faced by modelers at the watershed scale: (1) erosion and deposition of sediments is highly variable in space and time, since bulk of the sediment transport happens during highly localized short-term events; (2) the primary mechanisms (erosion, deposition, and transport) are nonlinear with respect to the controlling water flux; and (3) there is high uncertainty in the quantity and duration of sediment storage in the intermediate zones between sources and sinks. This inherent complexity in sediment dynamics has led to the development of diverse approaches in sediment transport modeling [Merritt et al., 2003; Aksoy and Kavvas, 2005].

[3] Network based models of fluvial sediment transport can be broadly classified into two categories: coarse scale models and fine scale models (in both space and time). Coarse scale models operate at monthly to annual temporal resolution and provide estimates of sediment export over the span of decades to centuries [Benda and Dunne, 1997; Asselman, 1999; Hancock et al., 2010]. These models also tend to be implemented at a low spatial resolution (1 km2 grid or larger), which makes them appealing for sediment modeling at large river basins. Prosser et al. [2001] developed the Sediment River Network Model (SEDNET) that operates at an annual time step. In SEDNET, the suspended sediment supply from the landscape is modeled using the Universal Soil Loss Equation (USLE) [Wischmeier and Smith, 1965], whereas sediment output from the channel is simulated based on the sediment transport capacity of streamflow [Prosser and Rustomji, 2000]. Pelletier [2012]developed a coarse grid-based model for estimating long-term suspended sediment discharge from large river basins. This model uses an empirical equation containing slope, soil texture, mean monthly rainfall, and mean monthly leaf area index to calculate sediment detachment from the landscape, and a Rouse number based transport criterion to route the detached sediment toward the basin outlet. While coarse scale models are ideal for testing the long-term erosion/deposition scenarios and landscape evolution patterns in large watersheds (>1000 km2), they are not designed for prediction of the localized and sporadic sediment transport events which typically occur at sub-daily (or even sub-hourly) temporal resolution.

[4] In contrast to the coarse scale models, fine scale models operate at daily or finer time step and are suitable for simulation of the short-term events. Few examples of the fine scale models are: ANSWERS [Beasley et al., 1980], KINEROS [Smith, 1981], WEPP [Nearing et al., 1989], EUROSEM [Morgan et al., 1998], AGNPS [Young et al., 1989], and SHETRAN [Ewen et al., 2000]. In fine scale models, the sediment generation and transport processes on the landscape are typically linked with the runoff generation processes of hydrologic models. For instance, the SHETRAN model [Ewen et al., 2000] simulates soil erosion on the landscape with equations for rainfall and shear detachment that are coupled with the SHE hydrologic model [Abbott et al., 1986]. The AGNPS model uses a modified form of the USLE equation for hillslope erosion that is coupled with the SCS-curve number hydrologic model [Young et al., 1989]. For the network component, many fine scale models use equations based on the sediment transport capacity of streamflow to simulate deposition and re-entrainment of sediments in the stream channel [Morgan et al., 1998; Viney and Sivapalan, 1999]. Additional process components such as bank erosion and collapse, bed load movement, rill and gully erosion, landslides, etc. can be selectively included or excluded in these models [Bathurst et al., 2006]. Unfortunately, the application of spatially distributed models at sub-daily temporal resolution has typically been restricted to single-event scale predictions in small watersheds (drainage areas of few hectares) [Smith et al., 2011]. The primary reason for this restriction has been the high computational expenditure involved in providing continuous simulations over a large area for an extended period of time [Srinivasan and Engel, 1994; Elliott et al., 2012]. An important consequence of this restriction is the hindrance to diagnostic evaluation of the fine time-scale processes that tend to evolve over the span of multiple sediment events and exhibit a high degree of spatial heterogeneity. As such, there is a need for a simple yet physically based network model for fluvial sediment transport that: (1) operates at the temporal resolution that matches the fine scale models (sub-daily); (2) characterizes sediment dynamics at a larger spatial scale than the current fine scale models (>10 km2), with a potential to be applicable at the spatial scale of coarse models (>1000 km2); and (3) provides continuous time simulations over a longer period (multiple years) with reasonable computational expenditure.

[5] In this study, we develop a semi-distributed model that seeks to capture the essential elements of fluvially driven sediment movement from individual hillslopes to the watershed scale. The model conceptualizes a watershed as a collection of reaches associated with representative elementary watersheds (REW) that are connected to each other through the hierarchical river network. We have tested this model using a high temporal resolution (15 min) data from the Goodwin Creek Experimental Watershed (drainage area of 21.3 km2) in Mississippi, USA. While previous high resolution sediment modeling efforts at this watershed have mostly focused on single event-scale predictions [Johnson et al., 2000; Rojas et al., 2008], the model presented here performs continuous time simulation of stream discharge and sediment load at 15 min resolution for 12 years (1982–1993). We also provide a validation of the model performance using observed data from five different locations within the Goodwin Creek watershed. The purpose of this paper is to demonstrate that: (1) a semi-distributed model containing a simple yet physically based representation of the sediment generation and transport processes can provide reasonable continuous time prediction of sediment dynamics at watershed scales, and (2) this model is an effective tool to investigate how sediment delivery patterns vary at different locations within a watershed's stream network, and what factors control the spatial heterogeneity of fluvial sediment export.

2. Model Description

[6] The modeling framework used in this study combines a dynamic network hydrology model with a network sediment transport model. In this section, we provide a detailed description and the corresponding equations of both these models.

2.1. Network Hydrology Model

[7] The network hydrology model is based on the Representative Elementary Watershed (REW) theory and builds on the balance equations for mass and momentum for a hierarchical river network [Reggiani et al., 2001]. In the REW approach, a watershed is divided into a number of reaches (REWs), which are considered as the smallest functional unit of the model. Each REW consists of two components: a hillslope region and a channel region (Figure 1). Tian [2006] developed a numerical model called THREW (TsingHua Representative Elementary Watershed) that solves the set of ordinary differential equations of coupled mass and momentum balance at the REW scale. Different versions of the THREW model have been used in recent studies on hydrologic partitioning [Li and Sivapalan, 2011] and nutrient transport [Ye et al., 2012].

Figure 1.

Schematic representation of the coupled network hydrology and sediment transport models: (a) discretization of the watershed into several REWs, (b) a single REW containing the hillslope (landscape element) and stream channel component, and (c) sediment exchange processes occurring within the stream channel.

2.1.1. Hillslope Component

[8] Following Ye et al. [2012], we use a simple lumped bucket model to represent the hillslope hydrologic response at each individual REW i:

display math
display math
display math
display math

where Shillslopei is water storage in the hillslope [L], Pi is the rainfall intensity [L T−1], Rhillslopei is the runoff generated from the hillslope [L T−1], and ETi is the rate of actual evapotranspiration (L T−1). Rhillslopei consists of the summation of surface and subsurface runoff components (equation (1b)). Surface runoff can occur through either infiltration-excess or saturation-excess mechanism. We model the infiltration-excess mechanism using the phi-index method [Menabde and Sivapalan, 2001], where Rsurfacei = Piicap if Pi > icap, and Rsurfacei = 0 if Pi < icap. icap is the soil infiltration capacity [L T−1] (obtained through calibration). Saturation-excess runoff occurs only whenShillslopei is filled to its capacity Scap (obtained through calibration), in which case, Rsurfacei = Pi. Subsurface runoff Rsubsurfacei is calculated using equation (1c), where τhis the response time-scale that determines the rate of decline in subsurface runoff (obtained through calibration).Equation (1d) provides the formula for actual evapotranspiration, where PETi is the potential evapotranspiration [L T−1] that is calculated from the 15 min resolution air temperature data using the Hamon equation [Hamon, 1963].

2.1.2. Channel Component

[9] The water balance equation for river reach i, associated with REW i, with inflows from the hillslope and upstream nodes (if present), is as follows:

display math

where SMCi (=AMCi × Li; AMCiis the cross-sectional area of the flow andLi is the length of local reach) is water storage in reach i, Qhillslopei (=Rhillslopei × Ahillslopei; Ahillslopei is the area of adjoining hillslope) is the water flow that enters the channel network directly from REW i, Qupj (=vj × AMCj; vj is the velocity at upstream end, for reach j, and AMCjis cross-sectional area of thejth upstream reach) are the inflows from upstream nodes (in a bifurcating network we assume there are at most two upstream reaches). Qouti (=vi × AMCi; where vi is the velocity at local reach i) is the outflow from reach i.

[10] The cross-sectional area of the flowAMCi at any time step is estimated by dividing the water storage (SMCi) by the channel reach length (Li), while the velocity viis estimated through recourse to a reach scale momentum balance equation (i.e., Saint-Venant momentum balance equation) [Reggiani et al., 2001]. Following Ye et al. [2012], we use a simplified version of the Saint-Venant equation to obtain channel velocity as follows:

display math

where, for a REW i, Rhi is the hydraulic radius, Pri is the average wetted perimeter, ni is the channel roughness coefficient, i.e., Manning's n (obtained from a previously reported value in the literature; see Section 3.2), sin γi is the mean channel slope, and hi is the mean water depth in the channel. In equation (3), when reach j is upstream of reach i, the sign in front of the middle term is positive, and it is negative when reach j is downstream of reach i.

2.2. Network Sediment Transport Model

[11] The sediment transport model simulates the export of sediments from a river basin in two stages: (1) delivery of the sediments from hillslope and bank erosion into the river channel, and (2) propagation of the sediments in the channel through the river network toward watershed outlet. This model simulates the transport of two types of sediment: sand (coarse sediment) and mud (fine sediment that consists of silt and clay). The model does not simulate bed load sediment transport, and assumes that all sediment moves within the stream channel only in suspension. The model further assumes that the supply of mud sediment to the river network comes primarily from hillslope erosion, with some contributions from bed and bank erosion; whereas the supply of sand sediment to the river network comes mostly from bank erosion (and bed erosion to some extent). A rationale for this assumption in our case-study watershed is provided inSection 5. The following sub-sections provide a detailed description of the different components of the sediment transport model.

2.2.1. Sediment Generation on the Hillslope

[12] Sediment generation from each REW is modeled as a shear stress induced response to the surface runoff. In each REW, soil erosion occurs on a hillslope when the shear stress generated by surface runoff exceeds the critical shear stress of the soil on hillslope. The formula for hillslope erosion can be written as:

display math

And,

display math

where, τi (N/m2) is the mean shear stress generated by the average depth of surface runoff Rsurfacei, sin θi is the mean slope of REW i, ρw is the density of water (1000 kg/m3) and g is the gravitational acceleration (9.81 m/s2). The hillslope sediment load yhi is directly proportional to the difference between the mean shear stress τi and the critical hillslope shear stress τchi (obtained through calibration). Ch (s/m) is a proportionality constant that is obtained through calibration. Sediment load is generated from the hillslope only when τi > τchi. The model assumes that there is no temporary storage of sediment on the hillslope, and thus, all of the sediment eroded from each REW is delivered directly to the stream channels.

2.2.2. Channel Sediment Balance

[13] The channel component of the sediment transport model divides a channel into three parts: water column (suspended sediment), the active bed layer and the river bank (Figure 1c). The continuity equation of sediment transport in the water column can be expressed as:

display math

where, SAi is the sediment stored in the water column at local channel i, ynk is the sediment delivered from upstream nodes, yhi is the sediment input from the hillslope at local reach i, yni is the sediment transported out of local reach i, eni is the erosion of sediment (sand and mud) from active layer at local reach i, ebi is the bank erosion at local reach i, and sni is the deposition of sediment to the active layer at local reach i. The mass balance for sediment in the active layer can be expressed as:

display math
display math
display math

in which, SBi is the sediment storage in the active layer of channel reach i. For simplicity, we assume in the model that bank erosion occurs only when the sediment storage in active layer is completely depleted.

2.2.3. In-Channel Sediment Processes

[14] Deposition (settling) and erosion are the two in-channel sediment processes that are simulated by the model. We first outline the deposition and erosion equations for the sand sediment, followed by those for the mud sediment.

2.2.3.1. Deposition of Sand

[15] Following Abad et al. [2008], the deposition rate of sand is expressed as:

display math

where, vss is the sediment settling velocity (m/s), Cssis the depth-averaged suspended sediment concentration in the water column (kg/m3), and ZR is the Rouse number. Equations for these three properties are provided below:

display math
display math
display math

where d is the grain size of sand particle, v is the kinematic viscosity of water at 20°C (=1.0036 × 10−6 m2/s), and R is the dimensionless sediment submerged specific gravity. Ideally, d should be the median grain size of the bed sediment. However, this information was not available for our study catchment; therefore, we assumed a value of d = 0.35 mm. SA and Sw in equation (6c) are the sediment storage and the water storage in the water column respectively, k is the dimensionless von Karman's constant (=0.4), and u* is the shear velocity. R in equation (6b) is defined as:

display math

where ρs and ρw are respectively the mass density of sediment and water. The shear velocity u* in equation (6d) is defined as:

display math

INT in equation (6a) stands for ‘integral’, which is an integration of the suspended sediment concentration profile in the water column. Abad and García [2006] have presented the following numerical approximation for INT:

display math

where the coefficients are: C0 = 1.1038, C1 = 2.6626, C2 = 5.6497, C3 = 0.3822, C4 = −0.6174, C5 = 0.1315, C6 = −0.0091. These coefficients were obtained through regression analysis of the above numerical approximation (equation (6g)) with the analytical solution of INT (see Abad and García [2006] for details).

2.2.3.2. Erosion of Sand

[16] The erosion rate for sand is expressed as [Garcia and Parker, 1991]:

display math

where, A is a constant (=1.3 × 10−7), and Zu is expressed as:

display math

Rep is the dimensionless sediment Reynolds number, and (α1, α2) = (1, 0.6) for Rep > 2.36 and (α1, α2) = (0.586, 1.23) for Rep < 2.36.

2.2.3.3. Erosion and Deposition of Mud

[17] The erosion or deposition of mud sediment at any given time depends on the value of actual shear stress relative to the critical shear stress. Actual shear stress in the channel is calculated as follows:

display math

Critical shear stress in the channel is expressed as [Mitchener and Torfs, 1996]:

display math

where, ρb is the bulk density of mud (=ρs ⋅ (1 − np)). np is the sediment porosity in channel, which is obtained through calibration.

[18] If τbi > τci, the erosion and deposition rates are as follows:

display math
display math

where, e0 = 0.2 × 10−3 (kg/m2/s).

[19] If τbi < τci, the erosion and deposition rates are as follows:

display math
display math

where Css is the suspended sediment concentration, and ws is the settling velocity. The formula for calculating ws depends on the value of Css relative to the zone concentration limits C1 and C2 [Hwang, 1989] (C1 = 0.15 and C2 = bw/(2mw − 1)0.5).

[20] If CssC1,

display math

If C1 < CssC2,

display math

If C2 < Css,

display math

where aw is the velocity scaling coefficient (=0.08), nw is the flocculation settling exponent (=1.65), bw is the hindered settling coefficient (=3.5), mw is the hindered settling exponent (=1.88).

3. Methods

3.1. Study Site and Data

[21] The THREW hydrology and sediment transport model was tested at the Goodwin Creek Experimental Watershed (GCEW), a 21.3 km2 watershed located in the bluff hills region of the Yazoo river basin in north central Mississippi, USA (Figure 2). GCEW is a highly instrumented watershed monitored by the U.S. Department of Agriculture's (USDA) Agricultural Research Service (ARS). This watershed was selected as a case-study because it has multiple years of continuous record for streamflow and suspended sediment load at a very high temporal resolution (15 min interval) and at multiple locations along the stream network. The topographic elevation within GCEW ranges from 68 m to 128 m above mean sea level. The terrain of GCEW consists of broad ridges that are overlaid with loess deposits and relatively narrow valleys that are filled with alluvial deposits derived from post-European settlement erosion. About 50% of the watershed has a slope less than 0.02, whereas 15% of the watershed has a slope greater than 0.03. Channel slope ranges from 0.002 to 0.02, with an average slope of 0.004; and the channel depth ranges from 0.8 to 3.1 m, with the average depth of 1.9 m. The dominant soil material is silt loam that is easily eroded in the absence of vegetation cover [King et al., 1999]. Land use patterns in GCEW range from timbered areas to row crops. About 13 percent of the watershed area is used for agriculture and the rest is idle pasture and forested land [Kuhnle et al., 1996]. Average annual precipitation in this region is 1400 mm, while the average annual air temperature is about 17°C. Runoff events that can trigger intense erosion are commonly caused by severe thunderstorms in late winter or spring [Molnár and Ramírez, 1998].

Figure 2.

Map of the Goodwin Creek Experimental Watershed (GCEW), including the stream network, 11 REWs, elevation above m.s.l., and the locations of main stem and tributary streamgages.

[22] A study by Blackmarr [1995]has described two main influences on the development of present channel morphology in Goodwin Creek. First, deforestation and agricultural use that followed the European settlement (ca. 1830 onwards) led to the erosion of hillslopes and rapid sedimentation in the valley. This prompted several reclamation efforts by the landowners (between 1840 and 1930) through construction of drainage ditches and stream channelization. Second, large flood control structures were built on major rivers in the lower Mississippi valley during mid-20th century. More importantly, these structures were located upstream of the confluence between large rivers and tributaries such as Goodwin Creek, and caused significant reduction in the flood stages of the larger receiving streams. Goodwin Creek responded to these combined changes (channelization efforts + low flood stage in the larger receiving stream) by rapid incision, which led to the development of steep, narrow channels with easily erodible bank slopes.

[23] For simulation and testing of the THREW model, we used the data for precipitation, streamflow, and sediment load within GCEW from 12 years spanning from 1982 to 1993. The temporal resolution of this data is 15 min. The catchment was divided into 11 REWs (Figure 2). Numerous rain gauge stations are present within and near GCEW. As such, precipitation and air temperature data from the rain gauges located closest to each REW were used as the spatially distributed climatic forcing. To analyze the performance of the THREW model, we used data from multiple streamgage locations within the watershed. There are 14 long-term streamflow and sediment gauging stations located within GCEW. Of these, we found two stations on the main stem of Goodwin Creek that perfectly coincide with our REW outlet points. The first main stem location is at the watershed outlet (which is also the outlet of REW 1; contributing drainage area = 21.3 km2), while the second is at the outlet of REW 6 (contributing drainage area = 8.8 km2). There are three additional tributary streamgages that are located entirely within first order REWs (see Figure 2), but their locations do not coincide well with the corresponding REW outlet. These stations are located within REW 3, 5, and 7 (contributing drainage area = 1.2, 1.6, and 3.6 km2 respectively). Due to the mismatch in gauge and REW outlet locations, we did not expect a good match between observed and simulated data at these three REWs (in comparison to the main stem gauge locations). Nonetheless, the tributary gauges provide vital information regarding the hydrologic and sediment processes occurring at smaller scales.

3.2. Estimation of Model Parameters

[24] The THREW hydrology and sediment transport model contains seven free calibration parameters, viz., icap, Scap, τh, τch, Ch, np, and n. Of these seven parameters, five parameters (icap, Scap, τh, τch, Ch) relate to the flow and sediment generation processes at a hillslope, whereas the remaining two (np, n) relate to the in-channel processes. We did not implement an automated parameter optimization procedure due to the high computational expenditure required for iterative simulation runs. Nonetheless, each parameter was either adjusted manually within a pre-determined parameter range (through trial and error) or was estimated from a previously reported value in the literature. Comparison of the observed and simulated data at watershed outlet was used to determine the acceptability of parameter values. It is important to note that once adjusted and finalized, the same parameter value was used for the hillslopes and channels within all 11 REWs. Below, we explain how these seven parameters were estimated for the simulation at GCEW.

[25] Due to the combined effect of high rainfall intensity and low soil infiltration capacity (icap), a large proportion of the runoff in GCEW is generated through infiltration-excess mechanism [Sharma, 2000]. However, this mechanism appears to exhibit a strong seasonality in GCEW. Figure 3shows the 15-min resolution precipitation, streamflow and sediment load data at the watershed outlet for the calendar year 1991. The watershed is hydrologically more responsive to the intense precipitation events during the winter and spring seasons than during the summer and fall seasons. For all the high intensity precipitation events in summer and fall (day 150 to 300), virtually no runoff and sediment response was observed. Likely causes include the presence of seasonal vegetation (grass and shrubs) and/or development of large soil cracks during the summer months that temporarily increase the infiltration capacity of soils. Therefore, for winter and spring seasons (November to May), we adjusted the value oficapbetween 2–20 mm/h (which is roughly the range for clay to silt-dominated soils [Sharma, 2000]), and found that a value of 8 mm/h provided an appropriate amount of hydrologic response. For the summer and fall seasons (June to October), we chose an arbitrarily high icap value (400 mm/h) that exceeds the observed maximum precipitation intensity (of 120 mm/h) within our period of record. The hillslope bucket capacity Scapwas adjusted between 100–500 mm, and the value of 300 mm was found to be appropriate. We varied the value for subsurface flow response time-scaleτh between 2–10 h, and finalized at 5 h.

Figure 3.

Observed patterns of the measured data at GCEW outlet for calendar year 1991: (a) precipitation, (b) stream discharge, and (c) sediment load.

[26] Parameters τch and Ch control the timing and magnitude of the sediment generated from the hillslope. Unfortunately, we did not have access to any direct hillslope sediment measurements while adjusting these parameters, and had to test their indirect influence on the sediment export at the watershed outlet. τch is the critical hillslope shear stress that determines whether a given surface runoff event has the ability to mobilize sediment from the hillslope to the channel. We found that a low value of τch resulted in the generation of too many sediment events (that were not observed), whereas a high τch value suppressed too many sediment events. We adjusted the value of τch from 0.1–0.5 N/m2, and found the value of 0.3 N/m2 to be most appropriate. Parameter Ch is the proportionality constant that relates the excess shear stress (above critical value τch) to the actual amount of sediment that moves from hillslope to the channel, thereby potentially controlling the magnitude of a sediment export event. A low value of Ch causes too little sediment to be mobilized from the hillslope, whereas a high Ch value leads to excessive sediment being dumped into the channel. We adjusted the value of Ch from 0.001–0.01 s/m and finalized at 0.003 s/m.

[27] Parameters n and npcontrol the in-channel hydrologic and sediment transport processes.n is Manning's roughness coefficient. Langendoen [2000] has reported n = 0.03 for the channel bed in GCEW. We found this value to be adequate for our model. np is the sediment porosity in stream channel, and controls the bulk density and critical shear stress of mud sediment in the channel active layer. We adjusted np from 0.1–0.5, and found the value of 0.2 to be most appropriate. While this porosity is much lower than the values reported in literature (Langendoen [2000] used 0.4), higher porosity values resulted in excessive sediment export during our test runs. We think that the mixture of sand and mud in the channel might be causing an increase in the overall bulk density of channel sediment.

4. Results

4.1. Analysis of Model Performance Using GCEW Data

[28] We first analyze the performance of the THREW model at the two main stem Goodwin Creek stations (outlets of REW 1 and 6; see Figure 2). Figure 4 shows the relationship between observed and simulated sediment loads at the two REW outlets for daily, monthly, and annual time steps. These daily, monthly, and annual values are a temporal aggregation of the 15 min resolution data. The model performed better at REW 1 than at REW 6. At REW 1, the Pearson correlation coefficients (R value) were 0.85 (daily), 0.87 (monthly), and 0.95 (annual). In comparison, the R values at REW 6 were 0.76 (daily), 0.78 (monthly), and 0.80 (annual). The R values for the 15 min resolution data (not shown) were much lower at both locations (R = 0.43 and 0.28 for REW 1 and 6, respectively), suggesting that the model performance drops off appreciably at the very short time scales.

Figure 4.

Observed versus simulated sediment loads at the outlet of (a, b, c) REW 1 and (d, e, f) REW 6 for daily, monthly, and annual temporal resolution. Solid black line is the 1:1 line.

[29] To show the detailed model simulations at fine time scales, we focused on two specific calendar years within the simulation period, 1989 and 1991. These two years were chosen for illustration since they have different temporal patterns of sediment load response. The frequency of high intensity flow and sediment export events was higher in 1991 than in 1989. Consequently, the annual sediment load at the watershed outlet in 1991 was almost twice the amount in 1989. Figures 5 and 6 show the observed and predicted time series of streamflow and sediment load at the outlet of REW 1 and REW 6, respectively. At both locations, the model performed well in capturing the overall temporal patterns of streamflow and sediment dynamics over a period of multiple events, especially during the winter and spring seasons. To assess the event scale prediction, we focused on a 10 day period during the year 1991, in which two separate flow events occurred. Figure 7 shows the time series of streamflow and sediment load for that 10 day period at the watershed outlet (REW 1). For both events, there was a slight mismatch in the timing of streamflow and sediment load at the 15 min resolution, but the overall dynamics of the events were appropriately captured by the model. Figure 8shows the load-discharge relationships for these two events separately. The arrows indicate the general direction of the hysteresis loop. Although hysteresis is present in the simulated load-discharge relationships, the patterns are distinctly different from the observed load-discharge relationships. Nonetheless, the direction of hysteresis loop (clockwise) was same for the observed and simulated data. Thus, due to the fine temporal resolution of the model, differences between observed and simulated values appear to be more pronounced at the scale of individual events. Similar patterns of model behavior were observed at the event scale in REW 6 (results not shown).

Figure 5.

Temporal patterns of the observed versus simulated stream discharge and sediment load at GCEW outlet (REW 1) for calendar years 1989 and 1991.

Figure 6.

Temporal patterns of the observed versus simulated stream discharge and sediment load at the outlet of REW 6 for calendar years 1989 and 1991.

Figure 7.

Temporal patterns of the observed versus simulated stream discharge and sediment load at GCEW outlet (REW 1) for a 10 day period (event scale) in calendar year 1991.

Figure 8.

Observed and simulated load-discharge relationships for the two separate sediment transport events shown inFigure 7. Black arrows show the general direction of the hysteresis loop.

[30] Figure 9shows the observed and simulated cumulative sediment loads during the span of years 1989 and 1991 in REW 1 and 6. The sediment model under-predicted the annual sediment output in REW 1 during both years (−13.4% for 1989 and −23.5% for 1991). In REW 6, the sediment model slightly over-predicted the annual sediment output in 1989 (+7.8%), but under-predicted in 1991 (−21.6%). A visual comparison of the two years shows that, at both locations (REW 1 and 6), the match between observed and simulated cumulative sediment export patterns is better in 1989 than in 1991 (Figure 9). Interestingly, the larger cumulative errors in 1991 were caused by bad prediction of just one or two sediment export events over the entire year.

Figure 9.

Observed versus simulated patterns of the cumulative sediment load at the outlets of (a, b) REW 1 and (c, d) REW 6 for calendar years 1989 and 1991.

[31] We next analyze the performance of the THREW model at three of the first order catchments, REWs 3, 5, and 7. Figure 10 shows the relationship between observed and simulated sediment loads at the outlets of these three REWs for daily, monthly, and annual time steps. The model performance at tributaries was poorer than at main stem locations, partly due to the mismatch in gauge and REW outlet locations. Performance at daily and monthly time steps was similar at the two smaller REWs (REW 3 area = 1.2 km2; REW 5 area = 1.6 km2), with R values ranging from 0.43 to 0.58. However, the difference between REW 3 and 5 was significant at the annual time step (R = 0.26 and 0.62 respectively). Simulated data at REW 7 (area = 3.6 km2) showed a better correlation with the observed data, and the R values (0.79 to 0.83) were on par with those from the main stem gauge locations. Nonetheless, the model under-predicted annual loads in 10 out of the 11 years at REW 7. The correlations between the observed and simulated sediment loads at 15-min temporal resolution were relatively low, with R = 0.15, 0.10, and 0.31 for REW 3, 5, and 7, respectively.

Figure 10.

Observed versus simulated sediment loads at the outlet of (a, b, c) REW 3, (d, e, f) REW 5 and (g, h, i) REW 7 for daily, monthly, and annual temporal resolution. Solid black line is the 1:1 line.

4.2. Analysis of Sediment Dynamics Across Multiple Scales

[32] The semi-distributed configuration of the THREW model enables comparison of how sediment processes are simulated at different parts of the watershed and across multiple observation scales. To analyze the temporal patterns of sediment dynamics from different parts of the watershed, we chose the outlets of two first order catchments, REW 3 (contributing area: 1.25 km2) and REW 9 (contributing area: 2.16 km2), as well as the watershed outlet, REW1 (contributing area: 21.3 km2). These two first order REWs were selected because they are located far from each other, and should have a completely different influence on the sediment dynamics at the watershed outlet. Specifically, since REW 3 is located closer to the watershed outlet, the sediment generated from REW 3 is more likely to reach REW 1 faster than that from REW 9 (see Figure 2). Figure 11 shows the simulated cumulative sediment loads (area normalized) at each of the three REWs for the years 1989 and 1991. For the year 1989 (Figure 11a), the magnitude as well as the timing of major sediment events were different at each REW. For instance, when a major sediment event occurred at day 63 in REW 9, no significant load increase was observed at REW 1 and 3. Also, the load per unit contributing area during 1989 was in a similar range of magnitude at all the three REWs. Conversely, for the year 1991 (Figure 11b), although the magnitude of sediment loads was different at each REW, the timing of most major sediment events was well-synchronized throughout the year. The load per unit contributing area during 1991 was significantly greater at the second order reach (REW 1) than at the first order reaches (REW 3 and 9).

Figure 11.

Simulated cumulative sediment load at the outlets of REW 1, REW 3, and REW 9 for calendar years 1989 and 1991.

[33] The simulated temporal patterns of sediment transport were distinctly different for sand and mud. Figure 12 shows the dynamics of sand and mud loads separately at the watershed outlet (REW 1) for the years 1989 and 1991. At the GCEW outlet, the frequency of mud events was significantly higher and appeared to be controlled by the temporal patterns of the hydrologic dynamics. On the other hand, the sediment events when significant quantities of sand particles are transported out of the watershed were infrequent. During the events where high sand loads were observed, the magnitude of sand output was significantly greater than the magnitude of mud output (see Figure 12). Interestingly, the patterns of sand and mud load were different in small first order REWs than at the watershed outlet. Figure 13 shows the sand and mud load patterns separately at the outlet of REW 3 for the years 1989 and 1991. While the frequency of sand and mud events was similar at REW 3, the magnitude of mud loads was an order of magnitude higher than that of the sand loads. A similar pattern was also observed at the outlet of REW 9 (result not shown). Figure 14 shows the simulated cumulative sand loads at the outlet of REWs 1, 3, and 9 for the years 1989 and 1991. The major sand load events, which were observed in Figure 12, are distinctly observable in the signal of REW 1 for both the years. These major events, however, were not observed in the first order reaches of REW 3 and 9. Contrary to the cumulative total sediment load (Figure 11), the cumulative load per unit contributing area for sand alone was an order of magnitude higher at the outlet of REW 1 (second order) than at the outlet of REW 3 and 9 (first order; see Figure 14).

Figure 12.

Simulated temporal patterns of sand load and mud load at GCEW outlet (REW 1) for calendar years 1989 and 1991.

Figure 13.

Simulated temporal patterns of sand load and mud load at the outlet of REW 3 for calendar years 1989 and 1991.

Figure 14.

Simulated cumulative sand load at the outlets of REW 1, REW 3, and REW 9 for calendar years 1989 and 1991.

5. Discussion

[34] By providing continuous time simulations in a semi-distributed configuration, the THREW model presented in this paper explicitly accounts for the local, non-local, and in-channel processes that influence the sediment export patterns. The model also accounts for the differences in the movement patterns of fine (mud) and coarse (sand) sediments. Results show that the outflow of fine sediment at the watershed outlet is more sensitive to streamflow patterns (compared to coarse sediment; seeFigure 12). This is physically intuitive, since less energy would be expended to move fine particles along the stream network compared to coarse particles [Molnár and Ramírez, 1998; Prosser et al., 2001]. The disparity in sand and mud sediment dynamics also appears to be governed by their individual sources. We assumed in the model that the supply of sand was primarily provided by bank erosion, whereas the mud supply came mostly from hillslope erosion (see Section 2.2). This assumption is consistent with the study by Kuhnle et al. [1996], where they found that in the short term the supply of sand in Goodwin Creek comes predominantly from the near-channel sources because hillslope overland flow is generally insufficient to entrain sand. The modeled export of sand particles from first order reaches was an order of magnitude lower than that of the mud particles (Figure 13). Thus, the contribution from hillslope tends to be the dominant sediment source in smaller reaches and is a critical component that connects fine sediment transport to the flow dynamics [Harvey, 1991].

[35] Spatial heterogeneity of the sediment supply sources is another important factor that controls sediment dynamics along the stream network and necessitates a distributed modeling approach. While some parts of the watershed might have a propensity to be dominant contributors, the spatial distribution of sediment contribution can also change from year to year due to the variability of climatic forcing [Prosser et al., 2001]. As seen in Figure 11, the sediment load per unit contributing area from REW 9 (with respect to the watershed outlet at REW 1) was significantly higher in 1989 than in 1991. Moreover, the dominant sediment outflow events in a first order reach might not necessarily occur simultaneously at a higher order reach (Figure 11). This suggests that the temporary storage of sediment in stream channels can be an important controller of sediment supply at higher stream order channels [Ferro and Porto, 2000; Smith et al., 2011]. Temporary channel storage appears to have an even more significant influence for the transport of coarser material like sand (Figures 12 and 13), since high magnitude sand export events were not common in the first order REWs. This suggests that sand particles tend to accumulate in the channels of intermediate stream reaches, and get flushed out only during the sporadic high flow events when enough energy is available to transport them. Figure 15 shows the relationship between simulated annual sediment load at GCEW outlet and the percentage contribution of sand in the annual load for all 12 years in the study period (1982–1993). This relationship shows that the proportion of sediment exported as sand is consistently high in the years when the total sediment export is high. High sediment output in a given year indicates that more energy was available during that year (in the form of high stream discharge) to flush out sediments from the watershed, thereby increasing the sand contribution.

Figure 15.

Relationship between simulated annual sediment load at GCEW outlet and the percentage contribution of sand in that annual load for all 12 calendar years (1982–1993).

[36] Good estimates of the overall sediment dynamics suggest that the level of model complexity applied in this study might be sufficient for simulation at GCEW. Moreover, the model performance improves as the outputs are aggregated over longer time steps, which indicates that, even if individual sediment events are not matched well, the longer term sediment dynamics are being appropriately simulated by the model. Nonetheless, we made several assumptions/simplifications in the model which may have contributed to the errors and uncertainties in simulation performance, especially at an individual event resolution. The first major simplification that we made was to use the same parameter values at all 11 REWs, which ignores the spatial variability in soil/land-use patterns within the watershed. A direct consequence of using spatially constant model parameters is that the sediment supply might be over-estimated in some parts of the watershed and/or under-estimated in other parts. This could also be part of the reason for poorer model performance at the three first order REWs (in comparison to the main stem gauges; seeFigures 4 and 10). Spatially variable parameters can be better implemented in a grid-based modeling approach where an individual pixel is typically assigned a single soil/land-use type [Kuhnle et al., 1996; Pelletier, 2012]. For the semi-distributed approach used in THREW model, the fundamental units (REWs) in GCEW were large enough to accommodate multiple soil/land-use categories within the same unit. One approach to explicitly incorporate spatially variable parameters would be to identify the dominant soil/land-use type in each REW and then introduce a free calibration parameter that can be used to estimate the critical hillslope shear stressτchi in equation (4b)from a measured soil property (e.g., roughness). However, it is not clear whether the relationship between measured soil properties and critical hillslope shear stresses can be sufficiently constrained through calibration procedures. Also unknown would be the amount of error introduced by aggregating multiple soil/land-use classes into a single value.

[37] Another simplification in our model was the use of phi-index method [Menabde and Sivapalan, 2001] to simulate infiltration-excess mechanism in the hillslope hydrology component. The phi-index method assumes a constant soil infiltration capacity and does not explicitly account for the antecedent moisture conditions when calculating the infiltration-excess runoff. Other methods, such as the Green-Ampt Mein-Larson (GAML) equation [Mein and Larson, 1973] or the Philip's equation [Philip, 1957], provide a more dynamic approach for simulating infiltration-excess runoff. Nonetheless, our results show a good match between the observed and predicted streamflow (Figures 5, 6, and 7), which suggests that the use of a simple phi-index method might be sufficient for representing the hydrology at GCEW. A likely reason for this could be that the typical rainfall intensity at GCEW is much higher than the soil infiltration capacityicap, which makes any error associated with using constant icapvalue to be small compared to the amount of surface runoff generated. Moreover, the dynamic methods for estimating infiltration-excess runoff can be readily incorporated in our modeling framework if the phi-index method is found to be insufficient at a given watershed. Sediment generation at the hillslope was simplified as a shear stress induced response to surface runoff. This approach does not provide explicit treatment to the different sediment generation processes (e.g., rain splash, rill erosion, gully erosion) that might be occurring simultaneously during a single sediment event.

[38] For the in-channel processes, we assumed that bank erosion occurs only after the sediment in the channel's active layer is depleted. This implies that bank erosion can occur in the model only if a sufficiently large hydrologic event occurs (when excess energy is available for erosion) or if the supply of sediment from upland sources is significantly depleted prior to a normal hydrologic event. One approach to relaxing this assumption would be to incorporate an explicit bank erosion model within our framework so that the erosion of bank and channel active layer can occur simultaneously in the simulations. While fine resolution models of bank erosion/collapse have been developed at the scale of individual stream reaches [Langendoen, 2000; Simon et al., 2000], the highly localized and detailed geotechnical information required to constrain these models is typically not available across the entire river network. The model also assumes that the channel features such as the cross-section geometry, longitudinal slope, length, and sinuosity remain unchanged throughout the simulation period. This simplification ignores the long-term processes of channel evolution that can be observed through changes in the longitudinal profile, channel migration, and cross-section changes due to bank collapse. Another simplification related to in-channel processes is that we use the same channel roughness value (Manning'sn) in all REWs. Manning's n is used in our model is to calculate the stream velocity vi (equation (3)), which influences if (and when) erosion/deposition of channel sediments will occur. Accounting for the spatial variability in Manning's ncan potentially lead to an improved characterization of the temporary sediment storage hot spots within the river network. The THREW model also ignores the sediment processes related to overbank flow dynamics and assumes that sediment export occurs solely through lateral accretion from hillslopes and within-channel transport. While this assumption might have to be relaxed for model application in other watersheds, it is appropriate at GCEW since overbank flow is a very rare occurrence in this watershed due to the deeply incised structure of its stream channels (created by the factors described inSection 3.1).

[39] Computational expenditure, especially in terms of the simulation run-time, has been a long-standing issue in sediment transport modeling [Srinivasan and Engel, 1994; Merritt et al., 2003]. For prediction at a fine temporal resolution, Elliott et al. [2012]suggested that the high computational expenditure is the primary cause that limits the applicability of grid-based sediment transport models to single event-scale simulations. In this regard, the semi-distributed approach of THREW model provides some improvement by performing continuous time simulations within a reasonable time-frame. A single run of THREW model simulated 12 years of sediment and water dynamics within GCEW (21.3 km2), at 15-min resolution (∼420,000 time steps), in about 20 min on a standard laptop computer. On the other hand, grid-based sediment transport models, such as CAESER [Coulthard and Wiel, 2006; Hancock et al., 2010], SHETRAN [Bathurst et al., 2006; Elliott et al., 2012], and CASC2D-SED [Johnson et al., 2000; Rojas et al., 2008], have been shown to require substantially greater run-time. However, the computational speed achieved here is still not fast enough to enable a comprehensive sensitivity analysis of the model parameters using the Monte-Carlo approach. Moreover, despite these improvements, we suspect that computational expenditure would still be a problem if THREW model is to be applied at watersheds with drainage areas significantly larger than GCEW (>100 km2).

6. Summary and Conclusions

[40] In this study, we developed a coupled network hydrology and sediment transport model that seeks to capture the essential elements of fluvially driven sediment delivery from a hillslope to the watershed scale. The model was tested using the high temporal resolution (15 min) data from Goodwin Creek, a 21.3 km2watershed in Mississippi, USA. Our results demonstrate that a semi-distributed model containing simple, yet physically based, representation of sediment generation and transport processes can provide good predictions of sediment dynamics at the watershed scale. Model simulations at GCEW showed that distinct differences exist in the transport behavior of coarse (sand) and fine (mud) sediment particles, which influence the sediment delivery patterns at different locations along the stream network. Temporary storage of sand in stream channels appeared to be more important in the large second order reaches than in the small first order reaches. The temporary channel storage of sand creates conditions where an infrequent large flow event, caused by intense precipitation, flushes out large quantities of sand from the watershed. In contrast, the transport of mud sediment from hillslopes to the watershed outlet appeared to be more synchronized with the hydrologic flow patterns. The relative proportion of sand and mud transport was also sensitive to the total amount of sediment exported annually. Spatial variability of climatic forcing is another important factor that potentially increases the heterogeneity of sediment supply within the watershed. Intense local precipitation events in certain parts of the watershed can temporarily increase their sediment contribution. As seen in our results (Figure 9), the proportion of sediment contribution from different parts of the watershed tends to vary from year to year. The effects of heterogeneous inputs will most likely have a greater influence as the spatial scale of interest increases beyond that of a small watershed. The stream network hierarchy greatly influenced the differences between first and second order reaches, in terms of sediment transport behavior. This influence will most likely amplify as we move toward the larger scales of third or higher order reaches.

[41] The modeling approach presented here provides some improvement on the computational limitations typically faced by fully distributed grid-based models, and provides for faster simulation run-times. Low computational expenditure (without any loss in temporal resolution) makes such a model suitable for simulating sediment dynamics over larger watersheds. The semi-distributed nature of the model further allows for the diagnosis of process patterns and interactions across multiple scales. Importantly, the model captures differences in the behavior of fine and coarse sediments, and can therefore provide insight on the complex, scale-dependent interactions between sediment generation, temporary channel storage, and the spatially variable climatic forcing.

Acknowledgments

[42] Work on this paper commenced during the Summer Institute organized at the University of British Columbia (UBC) during June–August 2010 as part of the NSF-funded Hydrologic Synthesis project, “Water Cycle Dynamics in a Changing Environment: Advancing Hydrologic Science through Synthesis” (NSF grant EAR-0636043, M. Sivapalan, PI). We acknowledge the support and advice of numerous participants at the Summer Institute (students and faculty mentors). We would also like to thank Alexander Densmore (editor), John Pitlick (associate editor), Peter Wilcock, and the two anonymous reviewers for providing insightful comments that have greatly improved this paper.

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