We applied the integrated sediment transport model to the Ammer catchment, located in southwestern Germany (Fig. 1). The River Ammer is a tributary to the River Neckar within the Rhine basin. It covers approximately 130 km2 and is dominated by agricultural land use that accounts for 67 % of the total area. The hydrogeology is dominated by the middle-Triassic Upper Muschelkalk limestone formation which forms the main karstified aquifer (Selle et al., 2013). In this catchment, annual precipitation is 700–800 mm. The Ammer River, approximately 12 km long, is the main stem, with a mean discharge of ∼1 m3 s-1. It has two major tributaries, the Kochhart and Käsbach streams. Two wastewater treatment plants (WWTPs), Gäu-Ammer and Hailfingen, also contribute flow and suspended sediments to the Ammer River. During dry weather conditions, the discharge of WWTP Gäu-Ammer is 0.10–0.12 m3 s-1, and the effluent turbidity is approximately 3 NTUs (nephelometric turbidity units). The WWTP in Hailfingen is comparatively small, with flow rates of 0.012–0.015 m3 s-1, and its turbidity is in the same range as that of the WWTP Gäu-Ammer.

With the exception of a small stripe at the northeastern boundary of the study domain, highlighted by the forest land use in Fig. 1, the topography of the catchment is only slightly hilly (with mean slope of 4.2∘), which agrees with the bed rock being a carbonate platform, partially overlain by upper Triassic mudstones and loess. Soils are dominated by luvisols on loess with mostly high probability of deep infiltration and low risk of soil erosion, according to the state geological survey of the state of Baden-Württemberg (LGRB, http://maps.lgrb-bw.de, last access: 21 June 2018).

Based on the digital elevation model (DEM) of the Ammer catchment, we delineated 14 subcatchments using the watershed delineation tool of the Better Assessment Science Integrating point & Nonpoint Sources (BASINS) model (see Fig. 1). Table 1 shows the proportions of different land-use types and the areas of each subcatchment.

Hourly precipitation and air-temperature data are the driving forces of the hydrological model. We use hourly precipitation data of the weather station Herrenberg, operated by the German weather service DWD (CDC, 2017), whereas air temperatures are taken from the weather station Bondorf of the agrometeorological service Baden-Württemberg (BwAm, 2016). The generation and transport of sediments behave differently for different land uses and topography. We use the digital elevation model with 10 m resolution and land-use map of the state topographic service of Baden-Württemberg and Federal Agency for Cartography and Geodesy (BKG, 2009; LGRB, 2011; UBA, 2009). The river-hydraulics model requires bathymetric profiles of the River Ammer and its main tributaries. We use 230 profiles at 100 m spacing, obtained from the environmental protection agency of Baden-Württemberg (LUBW, 2010).

Only one gauging station is installed in the main channel of the Ammer River at the outlet of the studied catchment in Pfäffingen (red triangle in Fig. 1); here, hourly discharge and turbidity measurements are available, which we used for model calibration and validation. The water levels and turbidity data were measured by online probes (UIT GmbH, Dresden, Germany). The hydrograph was converted to discharge time series by rating curves, whereas the suspended sediment concentrations are derived from continuous turbidity measurements (Rügner et al., 2013). The linear relationship between suspended-sediment concentrations and turbidity with a conversion factor of 2.02 (mg L-1 NTU-1) has been reported to be robust in the Ammer River (Rügner et al., 2013, 2014).

The simulation period covers the years 2013–2016. In this time, the maximum discharge reflected an event with a 2–10-year return period according to the long-time statistics of the gauging station (LUBW, http://www.hvz.baden-wuerttemberg.de/, last access: 21 June 2018).

The integrated sediment-transport model consists of a catchment-scale hydrological model, a river-hydraulics model, a catchment sediment-generating model and a river sediment-transport model (Fig. 2). The catchment-scale hydrological model is used to estimate river discharge along the entire stream. The river-hydraulics model uses the discharge of the hydrological model and the river bathymetry to compute the river stage, cross-sectional area, velocity, and bottom shear stress, which are needed for the river-transport model. In this study we use HEC–RAS in quasi-steady-state mode. The catchment sediment-generating model is used for simulating particle accumulation in urban areas during dry weather periods, particle wash-off during storms, and erosion from rural areas during rain periods. The river sediment-transport model is used to simulate in-stream processes (advection, dispersion, and deposition, as well as bank and bed erosion). Wastewater treatment plants are treated as point inputs with constant discharge and sediment concentration during dry weather periods. Under low-flow conditions, when no soil erosion and urban particle wash-off occur and the suspended sediment concentrations in the streams are relatively small, we use a constant concentration to represent the sediment input under these conditions. Based on our prior knowledge of the Ammer catchment, soil erosion is very limited (the information supporting this statement will be discussed in Sect. 4.2), and thus a well-known approach and a simplified method are used to simulate particles from urban and rural areas, respectively. Mobilization of particles from different sources depends on different processes; e.g., input of urban particles depends on the build-up and wash-off processes and rural particles rely on soil erosion, whereas bed and bank erosion are substantially affected by river hydraulics. Considering these processes enables us to diagnose the importance of different sediment sources well.

The catchment-scale hydrological model is based on the HBV model (Hydrologiska Byråns Vattenbalansavdelning) (Lindström et al., 1997). However, we have added a quick recharge component and an urban surface runoff component to explain the special behavior of discharge in the Ammer catchment (see Sect. 2.1). The main Ammer springs are fed by groundwater from the karstified middle-Triassic Muschelkalk formation. The measured hydrograph indicates a rapid increase of base flow in sporadic events. We explain this behavior with a model that contains three storages of water in the subsurface: soil moisture in the top soils, a subsurface storage in the deeper unsaturated zone, and groundwater in the karstic aquifer. In our conceptual model, we assume water storage in the deep unsaturated zone, which spills over when a threshold value is reached, causing quick groundwater recharge to occur that then leads to a rapid increase of base flow. An urban surface runoff component is used to obtain surface runoff depths in urban areas in order to simulate particle wash-off from urban land surface. Details of the hydrological model are given in Appendix A. The temporal resolution of the hydrological model is 1 h. We use the catchment-scale hydrological model to simulate discharge contributions from the 14 subcatchments shown in Fig. 1 (detailed information see Sect. 2.1).

In order to better understand in-stream processes, we feed the discharge data of the hydrological model into the river-hydraulics model HEC–RAS (Brunner, 2016), which solves the one-dimensional Saint Venant equations. The HEC–RAS model simulates hourly quasi-steady flow using the hourly discharge of the 14 subcatchments simulated by the hydrological model as change-of-discharge input. The locations where the discharge from 14 subcatchments enters into the main channel are set to the corresponding cross sections. The upstream boundary condition was set to time series of flow and the downstream one to normal depth. We have 258 measured cross sections and we used the built-in interpolation algorithm in HEC-RAS to obtain the additional cross sections, which results in totally 385 cross sections for the entire river network. The distances between computed cross sections range from 10 to 100 m depending on the changes of river bathymetry. The model requires river profiles in cross sections along the river channel and yields the water-filled cross-sectional area, the water depth, flow velocity, and shear stress, among other factors, as model output, which are needed in the river sediment-transport model. The detailed settings of HEC–RAS can be found in the Supplement.

The land use is classified into urban and rural areas as well as forested areas. Impervious surfaces such as roads and roofs are regarded as urban areas, while rural areas consist of pervious surfaces such as gardens, parks, and agricultural land. The sediment-generating processes are different for the two types of land use. Sediment generation in forested areas is considered to be negligible. The sediment-generating model is used to obtain hourly sediments of urban and rural particles from the 14 subcatchments.

We consider two types of sediment: suspended sediment in the aqueous phase (mobile component) and bed sediment (immobile component). Figure 3 shows a schematic of the river sediment-transport model, which considers advection, dispersion, deposition, bank erosion, bed erosion, and lateral input of suspended sediments. We use this model to calculate the average concentration of the mobile component and the mass of the immobile component for every computation cell (formed by two cross sections) every hour.

Mobile component. We use a finite-volume discretization for suspended-sediment transport for the main channel, considering storage in the aqueous phase, advection, dispersion, bed and bank erosion, deposition, and lateral inputs (tributaries and WWTPs): ∂cwV∂t=-∂cwQ∂xΔx+AD∂2cw∂x2Δx+rbed+rbankΔx-rdV+∑clatiQlati, in which cw (mg L-1) is suspended-sediment concentration; V (m3) is the cell volume; Δx (m) is the cell length; Q (m3 s-1) and A (m2) are the flow rate and cross sectional area; D (m2 s-1) is the dispersion coefficient; clati (mg L-1) and Qlati (m3 s-1) represent the suspended-sediment concentration and flow rate of the ith lateral inflow; rd (mg L-1 s-1), rbank (g m-1 s-1), and rbed (g m-1 s-1) indicate the deposition, bed-erosion, and bank-erosion rates, respectively. For the advective term, we use upstream weighting, whereas the second derivative of concentration appearing in the dispersion term is evaluated by standard finite differences.

This model component requires the sediment concentrations in the lateral inputs (tributaries and WWTPs) as well as in the Ammer spring as boundary conditions. The lateral inputs are computed by the sediment-generating model. For the sediment input by the Ammer spring, we consider the turbidity of ∼3 NTU measured under base-flow conditions. Rügner et al. (2013) showed that the karst springs in the Ammer catchment contribute to turbidity, which is in agreement with many previous studies showing that karst systems can contribute suspended sediments (Bouchaoua et al., 2002; Meus et al., 2013). Thus, the turbidity under base-flow conditions is potentially generated by subsurface flow through the karst matrix. The karstic sediment flux was calculated by subsurface flow rates and constant suspended sediment concentrations.

For the estimation of parameters, we used the well-known Nash–Sutcliffe efficiency (NSE) as model performance criterion: NSE=1-∑i=1nOi-Mi2∑i=1nOi-O‾2, in which Oi and Mi are the ith observed and modeled values, O‾ is the mean of all observed values. An NSE value approaching unity indicates good agreement between model and data, whereas NSE values smaller than zero imply that the model performs worse than taking the mean of all observations. We obtained the best set of parameters by systematically scanning the parameter space.

The hydrological model was applied to 14 subcatchments. Each subcatchment has three types of land use: agricultural areas, forest, and urban areas. We used daily average discharge data of 2013–2014 and 2015–2016 for calibration and validation, respectively. We generated 1000 realizations of the 14 parameters by Latin hypercube sampling (LHS) and calculated the corresponding NSE value for each parameter set. If NSE was ≥ 0.55, the parameter set was regarded acceptable. In the same way, we used the accepted parameter sets for validation. Subsequently we calculated the 90 % confidence intervals and the NSE value for high flows (flow rate greater than the mean discharge) using the accepted parameter sets. Finally, we identified the best-fit parameter values.

For the calibration and validation of the sediment-generating and the river sediment-transport models, we performed a literature survey to identify a reference range of each parameter. We performed a manual calibration of the corresponding parameters within the given range, fitting the modeled and measured suspended sediment concentrations at the river gauge. Subsequently, we used the identified parameter set as base values in a local sensitivity analysis, the details of which are given in Table S1 of the Supplement. Within the given parameter variations, the manually calibrated parameter sets were confirmed as optimal. The parameters of the sediment-generating model and the river sediment-transport models are listed in Tables 2 and 3, respectively.

The best-fit parameter set of the hydrological model resulted in NSE values of 0.63 and 0.59 for calibration and validation, respectively. Figure 4 shows the measured and simulated hydrographs for the calibration and validation periods with 90 % confidence intervals. It can be seen that the discharge was reproduced quite well, both in the general trend and the dynamics. The measured discharge data almost all fall within the 90 % confidence interval of the simulation. The NSE value for high flows (greater than the mean discharge, 1 m3 s-1) of the simulation period is 0.43, implying an acceptable fit of high flows. There are few events that cannot be reproduced by the model. These events occurred in the summer months and probably resulted from thunderstorms, which are very local and may be missed by precipitation measurements, so that the resulting flow peaks could not be predicted by the hydrological model.

Figure 5 depicts measured suspended-sediment concentrations and the simulation results of the sediment-transport model during the calibration (year 2014) and validation (year 2016) periods. The corresponding NSE values are 0.46 and 0.32, respectively, which indicates an acceptable fit, albeit not as good as for the hydrograph. The integrated sediment transport model can capture the dynamics of the suspended sediment concentrations. In particular, the model captures the concentration peaks well. However, two events, one in the calibration and the other in the validation period, were not well fitted. These are events which were also not captured by the hydrological model, occurring in the summer months and due to thunderstorms.

After calibration and validation, the model results can be used to analyze the importance of different sediment sources. Figure 6 displays the modeled annual suspended-sediment loads from catchment and in-stream processes for the entire Ammer River network. The annual suspended-sediment load at the gauge ranges between 410 and 550 t yr-1. Equation (13) describes the overall mass balance of sediments in the entire catchment: Loadgauge=Loadurban+Loadrural+LoadkarstCatchment+Loadbde+Loadbke-Loaddep-ΔSStream, in which Loadgauge (t yr-1) indicates the suspended-sediment load at the river gauge. Loadurban (t yr-1), Loadrural (t yr-1), and Loadkarst (t yr-1) denote the suspended-sediment loads from urban areas generated by surface runoff and WWTP effluent, rural areas generated by soil erosion, and the karst system carried by subsurface flow, respectively. These three terms represent the catchment processes. Loadbde (t yr-1), Loadbke (t yr-1), Loaddep (t yr-1), and ΔS (t yr-1) are the suspended-sediment loads from bed erosion, bank erosion, deposition, and the change of sediment storage in the entire river channel, respectively. These four terms represent the in-stream processes.

In the Ammer catchment, urban particles (266–337 t yr-1) and the sediment input from the karst system (106–160 t yr-1) dominate the annual suspended sediment load, accounting for 59.1 and 24.9 %, respectively. Bed erosion, bank erosion, and rural sediment contribute much less, namely 6.2, 6.3, and 3.5 % of the total annual load, respectively. The contribution of rural runoff sediment in the Ammer catchment was very small, which may appear to be surprising at first. We have collected several independent lines of evidence that support these findings and included them in the Supplement:

The suspended sediments of the Ammer River are strongly contaminated by polycyclic aromatic hydrocarbons and other persistent organic pollutants (Schwientek et al., 2013b). Table S2 and Eqs. (S1)–(S7) of the Supplement present an end-member-mixing analysis indicating a fraction of rural particles amounting to only 3 %.

The state geological survey of the state of Baden-Württemberg has developed a soil-erosion risk map shown Fig. S1, putting most of Ammer catchment into the class of lowest soil-erosion risk. This is so because the surface runoff from agricultural areas is small due to a comparably flat topography. The same agency associates most of the catchment with deep infiltration as the main discharge mechanism.

Schwientek et al. (2013a) found a lacking connection between soils and streams in the Ammer catchment. The catchment has a large water storage capacity due to the karst and the slopes of this catchment are mild. During the simulation period, the precipitation intensity was not large enough to exceed the maximum infiltration rates or to reach storage capacity of the subsurface. Compared with literature values of maximum infiltration rates (10–20 and 5–10 mm h-1 for loamy soil and clay loamy soil, respectively; http://www.fao.org/docrep/S8684E/s8684e0a.htm, last access: 21 June 2018), only a few events exceed 10 mm h-1 of the precipitation intensity during the simulation period. Thus, hardly any surface runoff occurred in the rural area, so that sediment generation and transport from rural areas to the river channel were small.

The comparably flat topography can be explained by the geological formation. The Muschelkalk limestone is a carbonate platform that is partially overlain by mudstones of the upper Triassic. Along the Ammer main stem, there is only a small stretch where the river is incised somewhat deeper into the limestone rock. The river lost its former headwater catchment in the early Pleistocene to river Nagold so that the currently existing small river has a too-wide valley given its discharge.

As discussed above, we used a simplified approach to simulate the average sediment delivery from rural areas in our study because the contribution of rural areas to sediment delivery was so small. In particular, we did not distinguish between different crop types and seasons and estimated the average sediment load that reaches the streams instead. In other catchments, where the rural contributions to the sediment load are considerably higher, the description of soil erosion processes would require more differentiations.

To identify seasonal variations of suspended sediment loads originating from different processes, we used the model results of 2014–2016 to analyze the monthly mean suspended sediment loads from the urban areas, rural areas, the karst system, bed erosion, bank erosion, and deposition (Fig. 7). More suspended-sediment loads from urban areas and at the gauge can be observed in June and July (summer months). In summer months events with high rain intensity are more common than in winter months, which results in higher discharge peaks, more sediments generated in urban areas, and higher suspended-sediment loads at the gauge. Monthly suspended-sediment loads at the gauge have similar dynamics as the monthly urban particle contributions. The suspended-sediment load from the karst system is higher in winter months because the subsurface flow in the Ammer catchment is higher in winter months. Rural particles contribute to the overall particle flux only during a few months because annual precipitation and rainfall intensity were relatively small, so that surface runoff generated from rural areas was also low.

In the model simulation period, the seasonal patterns of bed erosion and bank erosion are obvious. High bed erosion and bank erosion occur from June to August due to increased bed shear occurring during big events. The area above the line of Loadgauge indicates net deposition, which shows small variations with a slight increase in July and August. The slight increase in summer is due to increased suspended-sediment concentrations during summer months. Comparing monthly mean bed erosion and deposition shows that bed erosion was greater than deposition in July, which indicates that accumulated bed sediment can be partly eroded in July.

Figure 8 shows the relationship between hourly mean discharge and the simulated hourly suspended sediment loads from the catchment, bed erosion, and bank erosion. The hourly suspended-sediment load from the catchment monotonically increases with increasing hourly mean discharge by a power-law relationship (Fig. 8a), which is consistent with the particle wash-off rate being a power-law function of discharge. Bed erosion requires that the bed shear stress exceeds a critical value, so that bed erosion is almost 0 when hourly mean flow is smaller than 1.5 m3 s-1, namely 1.5 times mean discharge (Fig. 8b). For discharge larger than this threshold (1.5 m3 s-1), bed erosion increases approximately linearly with discharge. The simulated hourly bed-erosion loads for a given flow rate vary substantially because bed erosion is not only influenced by the shear stress, which directly depends on discharge, but also on the bed sediment storage, which depends on previous deposition and erosion events. Bank erosion occurs when the hourly mean flow rate is larger than 2.5 m3 s-1, i.e., 2.5 times mean discharge (Fig. 8c). The relationship between bank-erosion-related loads and discharge is more unique than that of bed-erosion loads because we assume an infinite source for bank erosion.

Figure 9 shows the suspended sediment loads from in-stream (bed erosion and bank erosion) and catchment processes (input from the karst system, urban areas, and rural areas) under different flow regimes. The fractions of suspended-sediment contributions from different processes change with flow regimes. The contributions of in-stream processes are negligible in the flow regime of discharge smaller than 5 m3 s-1. With the discharge increasing, the contributions of in-stream processes increase. The in-stream processes play significant roles in high-flow regimes, which contribute 23 and 34 % of total suspended sediment loads under flow regimes of 10≤Q (m3 s-1) < 15 and Q (m3 s-1) ≥15, respectively. The relative contribution of the karst system is high in the low-flow regime (Q < 5, in m3 s-1, while it can be neglected under high-flow regimes (Q > 10, in m3 s-1). With the increase in flow rates, the contribution of urban particles becomes dominant in terms of catchment processes, especially when discharge is larger than 10 m3 s-1.

From above observations, we can see that the sources of suspended sediments differ under different flow conditions in the following way (Table 4):

The annual mean rates of bed erosion and deposition (mass per unit length per year) along the main channel can be used to identify hotspots of bed erosion and net sediment trapping (Fig. 10). The rates of deposition and bed erosion vary substantially along the main stem, ranging from essentially zero to a maximum of 8.6 and 8.0 kg m yr-1, respectively. Bed erosion is higher in the river segment close to the gauge because the flow rate is higher due to the contributions of the tributaries. Bed erosion is rather low in the river segments within 5–6.5, 7–8, 8.5–9, and 10–11 km to the gauge, where the channel slope is very mild. The river sections with the steepest channel slope typically do not show the highest bed erosion because there is not enough sediment available for erosion, which is caused by insufficient deposition. Figure 10 also shows that when the channel slope is very mild, the deposition rate is very high, while the bed erosion rate is nearly zero. These are sections where net sediment trapping (blue dash–dotted line) was observed. With increasing channel slope, bed erosion rates increase and deposition rates decrease. In a small range of channel slopes, deposition rates equal to erosion rates, resulting in a local steady state. If the channel slope continues to increase, the erosion rate will be higher than the deposition rate, which results in net sediment erosion if the sediment storage in the channel is large enough (red dash–dotted line, very few in Fig. 10). Where the channel slope is very steep, both sediment deposition and erosion rates are very small.

Figure 11 shows monthly means of the bed erosion rates along the Ammer main stem, computed for the simulated years 2014 to 2016. Bed erosion is stronger in the summer months, especially in July, which is consistent with the monthly load of suspended sediments discussed in Sect. 4.2. The hot moments of bed erosion are the extreme events caused by summer thunderstorms. The downstream river segments close to the gauge show higher bed erosion rates than the sections further upstream because flow rates and thus bed shear stresses are higher even with identical channel slope.