Simulating daily sediment transport using the Water Quality and Sediment Model (WQSED)

High erosion and sediment yield rates continue to pose a significant threat to the environment globally. Information on erosion and sediment rates is key for supporting effective and sustainable mitigation measures. Models that estimate sediment yield are vital in providing information about erosion and sediment yield rates, as empirical studies are prohibitive over large spatial and temporal scales. In this study, we simulate daily sediment transport using the WQSED model and assess the effectiveness of the tool in providing crucial estimations of sediment yield. The model structure links the Modified Universal Soil Loss Equation (MUSLE) to a simple sediment storage component. The model was applied to the Odzi River catchment in Zimbabwe and The Rio Tanama River catchment in Puerto Rico, where daily observations of sediment yield exceeding a decade were available for calibration and validation. In both catchments, we achieved a coefficient of efficiency and R2 and NSE of > 0.7 during model calibration and > 0.6 during model validation. The percentage bias remained below 45% for both calibration and validation periods. These results indicate that the WQSED model can be applied to provide estimates of sediment yield that are reliable for erosion, sediment yield and water quality management. An effective and relatively simple sediment yield model incorporating sediment storage is essential for catchment management in erosion-prone areas.


Introduction
Soil erosion and sedimentation are some of the world's acute environmental problems impacting food (Thompson et al. 2010) and water security (Le Roux & Waal, 2020).Erosion and sedimentation are significant social-ecological problems because of the loss of topsoil, biodiversity and the reduction in the sustainability of dams and other ecological infrastructure (Le Roux 2018).The threat of climate change is expected to worsen the problem of water erosion and sedimentation by changing the dynamics of catchment processes related to vegetation cover, soil moisture (Li and Fang 2016) and runoff."When climate change issues are superimposed upon the existing vulnerabilities, the effects and functioning (Le Roux 2018; Msadala and Basson 2017; Roux and Waal, 2020).The loss of reservoir storage capacity results in wide-ranging ecological, social and economic problems, such as a shortage of water for irrigation, domestic and industrial use, as well as a loss in reservoir floodattenuation capacity.Besides water quantity consequences, excessive sedimentation also affects water quality (Issaka and Ashraf 2017).In this regard, increased turbidity negatively impacts riverine communities through disruption of the filter-feeding mechanisms of some macro-invertebrates and reduction in suitable habitats (Akamagwuna et al. 2019;Bilotta and Brazier 2008).Other impacts on human society include increasing water treatment costs and other ecosystem services linked to a healthy ecosystem.
Globally, the urgent need to mitigate and adapt to the environmental effects of water erosion/sedimentation is widely recognised (Nearing et al. 2017).In order to respond to the erosion and sedimentation challenge, information about and understanding erosion drivers and processes is vital.Information on sediment loads' spatial and temporal distribution is critical and highly sought after for informing catchment management planning.Unfortunately, physical measurements of erosion or sedimentation at sufficiently representative sites are challenging to achieve in many countries because data collection methods are expensive and time-consuming (Alewell et al. 2019;Pandey et al. 2016).Therefore, modelling tools are widely used to provide additional information that can be used for catchment management (Pandey et al. 2016).Models also allow for the investigation of different scenarios of future change.However, model results depend on our ability to account for the variable natural processes that influence erosion and sediment transport loads, both spatially and temporally (Pandey et al. 2016).
The most popular erosion and sediment yield models were developed in the United States of America and Europe (Gao 2008).The Universal Soil Loss Equation (USLE) (Wischmeier and Smith 1978), as well as later versions of the Modified-USLE (Williams 1975) and Revised-USLE (Renard et al. 1997), have been applied worldwide (Alewell et al. 2019;Benavidez et al. 2018;Gacheri et al. 2023;Luo et al. 2016;Odongo et al. 2013;Sadeghi et al. 2013).Because they were developed for specific conditions, it often becomes necessary to modify them before application in areas outside of which they were developed (Sadeghi et al. 2013) and to add additional components to account for more processes and to improve their predictive ability.MUSLE has been included as part of comprehensive hydrology and water quality models such as the Soil and Water Assessment Tool (SWAT) (Arnold et al. 1998;Neitsch et al. 2005)  The initial model testing reported by Gwapedza et al. (2021) was conducted using a short record of daily observed data constituting a single summer rainfall season.Further model application using long-term daily data is necessary to evaluate the model performance in simulating erosion and sediment transport over a long period.This is important in Southern African countries where sediment yield threatens the long-term sustainability of reservoirs in terms of water quantity and quality (Le Roux 2018).The current study responds to this need by applying the WQSED model to two catchments with long-term daily observed data records.The aim is to evaluate the WQSED model and determine its robustness and applicability for daily long-term sediment simulations.Another important objective of this work is to provide a sensitivity and uncertainty analysis regarding the model application.Additionally, the WQSED model was developed for coupling with the Water Quality Systems Assessment Model (WQSAM) (Slaughter et al. 2017) to provide sediment inputs for water quality modelling.Evaluating the model's effectiveness is, therefore, key before coupling occurs.The WQSED model will be part of an interlinked suite of models (including the Pitman Model (Hughes 2013) and WQSAM) that form the Spatial and Time Series Information Modelling (SPATSIM) framework (Hughes and Forsyth 2006) and are commonly used for water resources management in Southern Africa.Therefore, WQSED is aligned for practical use within the region's water management framework (Gwapedza 2021).

Upper Odzi catchment
The Upper Odzi River Catchment is located near Mutare in the Eastern Highlands of Zimbabwe (Fig. 1).The catchment outlet is at a gauging station located at latitude − 18.92° and longitude 32.41°.The Upper Odzi River catchment is part of the larger Odzi River catchment that is also part of the larger Save catchment and water management area.The catchment area measures approximately 2 436 km 2 .The landscape is scattered with hill outcrops, resulting in a large variation in altitude ranging from 950 masl to 2 160 masl.The geology is dominated by granite bedrock and weathered sandy soils.The old granite basement is extensively weathered (in situ), and bare rock can only be seen on mountain peaks (Lidén et al. 2001).The soils covering the catchment are thick and of igneous origin.While red laterite clay soils are present in the catchment, coarse-grained sands and sandy loam soils Although the model was generally developed for application to catchments of sub-Saharan Africa, long-term historical daily observed data records were unavailable for most African catchments.Therefore, one catchment was selected from Zimbabwe (Southern Africa) and another from Puerto Rico (North America).

Rio Tanama catchment
The Rio Tanama River catchment is located in the northwestern part of Puerto Rico (Fig. 2).The catchment's outlet is at a gauging station located at latitudes 18.29° and longitude -66.78°, with an area of approximately 49 km − 2 .The altitude of the catchment ranges from a low of 200 to 800 mamsl.Geology is dominated by volcanic rocks and coastal alluvial plains (Monroe 1980).Erodible sandy clay soils dominate the catchment (Monroe 1980).The Rio Tanama catchment has a warm rainforest-type climate (Monroe 1980).Although significant rain occurs throughout the year, more rainfall is experienced from May to October.Vegetation is dominated by evergreen rainforest (> 70%), while the remaining vegetation is a mixture of shrubs and grassland.Dominant land use is an urban development in the form of settlements and transport networks.
dominate and are known to be highly erodible (Stocking and Elwell 1973).The climate is characterised by highly seasonal rainfall, generally cold and dry winters and hot and rainy summers.The rainy season usually commences in November and ends in March.Rainfall average ranges from 700 mm year − 1 -1 200 mm year − 1, and average runoff is 150 mm year − 1 -400 mm yr − 1 , with higher runoff recorded in the mountainous parts of the catchment.
Vegetation is comprised of natural forest, savannah grassland, and bushveld.Large-scale plantations of pines and gum trees are common, and these are a big source of sediment when the trees are harvested.A mixture of commercial and communal farming dominates the land use in the catchment.The main crop in the communal areas is maize, planted during the rainy season.Commercial farms grow tobacco during the rainy season and wheat in winter (Lidén et al. 2001).Swedish Meteorological and Hydrological Institute (SMHI) and was funded by the Swedish International Development Co-operation Agency (SIDA) through the Working Group for Tropical Ecology, Uppsala University (Karlsson and Rahmberg 1999).The Odzi data was collected over the high rainfall and runoff months, and sampling was discontinued during dry flow periods (see Fig. 3).
The flow and sediment data for the Rio Tanama catchment were downloaded from the United States Geological Survey (USGS; https://waterdata.usgs.gov/nwis/rt,last accessed 27 October 2020).The Rio Tanama flow and sediment discharge were collected consistently through high flow periods (see Fig. 4).

The WQSED model
The WQSED model applied in this study comprises the MUSLE (Williams and Berndt, 1977) coupled with a simple sediment storage module (Gwapedza et al. 2021).The

Flow and sediment data
The flow data for the Odzi catchment (Table 1) was measured by the Department of Water Development (DWD), Zimbabwe, now known as the Zimbabwe National Water Authority (ZINWA).The flow and sediment data for the Odzi were measured under the Streamflow and Sediment Gauging and Modelling project in Zimbabwe (GAMZ); Lidén et al. (2001) give details on the GAMZ sampling program.The project was undertaken by DWD together with the Maximum daily total flow (Q max ) (m 3 s − 1 ) 14 Sediment delivery power parameter (DPOW)* Where Sy is sediment yield (in tonnes ha − 1 ) on a storm basis for the entire catchment, R is the runoff factor and K, L, S, C, and P are the soil erodibility (in t ha h MJ − 1 mm − 1 ), slope length, slope steepness, crop management and soil erosion control practice factors, respectively.QD is total runoff depth in mm and qdp is peak runoff in mm h − 1 .Similar to the USLE, and a and b are location coefficients, whereas Area is the total catchment area in ha.The derivation of the physical characteristics defining K, L, S, C and P is detailed in the supplementary material of this article.
In applying the storage, the first step is to estimate the proportion of the daily MUSLE Sy that contributes directly to daily sediment delivery at the catchment outlet (Gwapedza or lost.The sediment storage module is driven by ratios of the daily total stream flow to maximum stream flow and the sediment storage ratio (a fraction raised to the QPOW power).Only total daily streamflow greater than the discharge threshold parameter result in any sediment released from storage.Therefore, this group of parameters is used to determine the timing of sediment delivery relative to the quantity of sediment generated by the MUSLE.
The overall model assessment involved splitting the available observed sediment data into two independent datasets; one set was used for calibration and the other for validation.The choice of periods used aimed to capture the range of flow variation in each calibration and validation dataset.
accuracy is highly dependent on the accuracy of the flow inputs and the WQSED model structure and parameters.

Calibration, validation
The WQSED model requires calibration of the input parameters shown in Table 2. Calibration is successful when simulated outputs reflect the temporal and spatial variation of the observed data.The model is typically run with an initial set of estimated parameters, after which manual parameter adjustment is performed to ensure the best fit between the observed and simulated data.D pow and D con (Table 2) are the parameters of a non-linear equation that estimates storm duration from daily streamflow volumes, from which the peak flow value in the erosivity part of the MUSLE is estimated.The maximum sediment storage and the initial storage fraction are calibrated to achieve a dynamic equilibrium in which stored sediment is not consistently accumulated  ).An analysis of parameter combinations and their respective model performance was conducted to quantify the sensitivity of the selected parameters.The main parameters of the MUSLE (LS, K, C and P) were not included in the sensitivity analysis because they are linear scaling factors and understanding the impacts of changes in their values is relatively trivial.In addition, these parameters are estimated through physical measurements or based on GIS coverages.Therefore, the MUSLE factors are generally determined by estimation rather than by calibration, although calibration may be performed if a sufficient justification for parameter adjustment is provided (see Gwapedza et al. 2021).

Model calibration and verification
Figures 6 and 7 show that the model simulations of sediment (tons day − 1 ) for the Odzi and Rio Tanama catchments captured the timing of the observed sediment data time series.While most intermediate and high peak events are well simulated, the model fails to capture some of the highest peak events.The statistical evaluations (Table 4) show that the model estimated the sediment yield relatively well compared to the observed data.The R 2 and NSE values were significantly higher than the 0.5 thresholds for satisfactory model performance prescribed in the literature.Nevertheless, the model simulations during the validation period have high PBIAS values.Table 5 provides the parameter values that were used in the final simulations.
Additional graphical assessments of the model outputs using X-Y scatter plots, and frequency curves are presented in Figs. 8 and 9, respectively.The scatter plots illustrate the effect of poor simulation of some of the highest observed peaks in the Rio Tanama catchment.Furthermore, the sediment cumulative frequency curves (Fig. 9) indicated that the highest peaks were generally under-stimulated, whereas very low sediment yield events were generally over-simulated in the Rio Tanama.The frequency curve for the validation period for the Odzi catchment shows that the model performed well, but the model's total sediment yield is oversimulated, as shown in Table 4.

Sensitivity assessment
The sensitivity analysis for the two catchments (Figs. 10 and 11) suggests that the parameter mid-range values are associated with better model performance.Only positive values of the combined statistic (NSE + 1-ABS(%Bias)/100), which has a maximum value of 2) are plotted on the graphs.A more detailed examination of the results confirms that the

Assessment of model performance
In this study, the coefficient of determination (R 2 ), the Nash-Sutcliffe coefficient of efficiency (NSE) (Nash and Sutcliffe 1970) and the percentage bias (PBIAS) are applied to assess the goodness of fit between observed and simulated data.Moriasi et al. (2007) highlight that the levels of acceptability based on the objective functions vary with the type of the variable being simulated.An NSE value of > 0.50 and a − 25% < PBIAS < 25% can be considered acceptable for streamflow, whereas a − 55% < PBIAS < 55% can be considered acceptable for sediment (Moriasi et al. 2007).

Parameter sensitivity and uncertainty
The One at a Time (OAT) (Pianosi et al. 2016) sensitivity approach was adopted in this study.In this approach, five calibration parameters were identified that had the potential to influence model outputs.The parameters include D con , SS max , QPOW, SPOW and DPOW.For each parameter, a maximum, minimum and medium range were assigned.Table 3 indicates the assigned ranges for each parameter, which were largely subjectively quantified after the initial calibration runs.
Using the three values in the range of each parameter, we generated 243 unique combinations of the five parameters.We ran the model using all the parameter ranges, capturing each run's NSE and PBIAS statistics.For each run, one parameter varies while all the others are kept fixed (Pianosi 1 3 and lower values give better results for the Odzi and Rio Tanama catchments, respectively.Parameter 3 is very insensitive for both catchments, while parameter 5 is not very sensitive within the range used.The patterns for parameter 4 (QPOW) are quite different for the two catchments, which may reflect the differences in the variability of the flow regimes (Figs. 3 and 4).

Sediment transport simulations
The WQSED simulations for the Odzi River catchment indicated that while the model managed to represent the timing of observed sediment yield sufficiently, it could not represent the highest peaks and tended to underestimate sediment at average and low flows.The observed data for the selected model's poor performance runs in the middle part of the x-axis (sum of run indices between 8 and 12) are associated with combinations of low-and high-range values across the five parameters.However, Figs. 10 and 11 also suggest that some parameter combinations that include values that are not 'medium' can also generate good overall results.When the lower ranges dominate (left side of the graphs), the combined statistic is generally more negative than when the higher ranges dominate (right side of the graphs).
The assessment of individual parameter sensitivity based on the OAT method is presented in Figs. 12 and 13 (refer to Table 3 for the meaning of the parameter numbers).The results for parameter 1 (D con ) suggest that the results are quite sensitive to the estimation of peak flow in the MUSLE, particularly for the Odzi (the lower range value gives a negative value for the combined performance index).The model is also sensitive to the maximum storage value (parameter 2), and the medium value used is not the best, while higher developing and low-income countries where agricultural practices are insufficient to protect soils (Pimentel and Burgess 2013).Therefore, agricultural practices that promote vegetation cover and the restoration of abandoned and existing agricultural land are vital for reducing accelerated erosion and sediment transport (Nearing et al. 2017).Some proposed mitigation strategies to reduce sediment yield include vegetation restoration and paving roads that connect to coffee farms (Korman et al. 2020).Previous studies in catchments neighbouring the Rio Tanama in Puerto Rico reported sediment yield rates ranging between 0.2 t ha − 1 year − 1 and 12 t ha − 1 year − 1 (Korman et al. 2020; Larsen and Webb 2009;Yuan et al. 2016) and the present study estimates fall within this range.Similarly, the observed and simulated sediment yields of the Odzi catchment are in the range of the 1-10 t ha − 1 year − 1 reported in a review by Vanmaercke et al. (2014) and in a global soil erosion assessment conducted by Borrelli et al. (2017).period (1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988) indicates that the average sediment yield is 7.08 t ha − 1 , which is 19% higher than the simulated average sediment yield of 5.95 t ha − 1 .The observed and simulated sediment yields are in the range of the 1-10 t ha − 1 year − 1 reported in a review by Vanmaercke et al. (2014) and a global soil erosion assessment conducted by Borrelli et al. (2017).The model results for the Rio Tanama (RT) catchment showed a simulated sediment yield rate of 3.4 t ha − 1 year − 1 .The Rio Tanama catchment exhibits a high sediment output, although this is much lower than for the larger Odzi catchment.
As in Southern Africa, Puerto Rico experiences high river sediment yields (Gellis et al. 2006), and poor coastal water quality associated with river sediment yield has been linked to the loss of coral reefs (Korman et al. 2020;Larsen and Webb 2009), which poses an urgent problem given that tourism comprises a significant component of that country's economy (Gellis et al. 2006).High erosion and sediment transport rates threaten agricultural systems, especially in These are partly associated with the relatively simple way peak discharges, required for the erosivity calculations in the MUSLE, are estimated from mean daily discharges.Another critical issue is that storage modules require calibration with observed data.Therefore, applying the model in ungauged catchments may be a very uncertain exercise, although parameter regionalisation options can be explored to combat this problem.
The WQSED was shown to consistently under-estimate the highest peak sediment yield events.While this effect may be partially attributed to the estimation of peak discharge (referred to above), a further possibility is that WQSED simulates rill and sheet erosion based on the MUSLE, whereas gully or bank erosion that has the potential to contribute large amounts of sediment is not explicitly considered.The storage module absorbs sediment during low to moderate-flow events and delivers sediment during high-flow events, a phenomenon consistent with the highly variable hydrology (in time and space) of most Southern African catchments (see Rowntree et al. 2016).Nevertheless, including a storage module significantly improved the The calibrated model yielded a good performance compared to established models previously applied in the catchments.The performance of WQSED for the Odzi catchment was similar to that of the HBV-SED.However, the WQSED has an advantage over other established models in that while it incorporates some necessary sediment storage and delivery functions, it remains relatively simple.The approach adopted in WQSED is supported by Griensven et al. (2013), who concluded that complicated models do not necessarily provide better results than simpler models.However, complex models may describe the catchment processes in greater detail.It is essential to highlight that observed flow inputs were used within the current evaluation of WQSED, as the model does not simulate flow independently, as is the case with SWAT and HBV-SED.As sediment yield simulations will always depend on the quality of the flow input data, the success of the WQSED application may be partly attributed to the use of observed flow data.However, consistent under-simulation of the highest observed peak sediment yields suggests that even using observed mean daily flow data, some uncertainties in the input data remain.A disparity in the sensitivity of the low and high parameter ranges for the storage parameters can possibly be attributed to the variations in discharge and area of the two catchments.The Rio Tanama is a small, highly erosive catchment, so the influence of internal catchment storage effects may be much smaller.It should also be acknowledged that the patterns of total sensitivity of the model results for these four parameters will be quite complex, and their individual effects will not be independent of the values of the other parameters.This issue has not been explored in detail in this study but was evident from the detailed outputs of the 243 model sensitivity runs.For example, the range of values used for the SS max parameter influences the optimum values of the three storage power parameters.Similarly, the discharge power parameter (DPOW) value will influence the optimum D con parameter as they both determine how much sediment is directly delivered without being delayed or attenuated through storage.model representation of peak and recession sediment loads and enhanced the model performance over a long-term simulation period.

Sensitivity assessment
The sensitivity analysis results (Figs. 10 and 11) suggest that parameters close to the medium values (based on calibration) are associated with better model performance, suggesting that the calibration exercise was largely successful.The sensitivity assessment results (Figs. 12 and 13) indicate that the model outputs are very sensitive to the D con parameter as it relates to estimates of storm duration, peak discharge and, therefore, the R factor in the MUSLE.Shorter durations associated with thunderstorms have higher peak intensity than longer-duration frontal rainfall and will inevitably generate more sediment yield.The results for both catchments indicate that the median values of D con give the best model estimates.However, the failure to simulate some of the higher sediment loads may be attributed to the simple way the model translates mean daily discharges into peak discharges across a wide range of different values.

Fig. 1
Fig. 1 Map showing the location of the Upper Odzi River catchment in Zimbabwe and the Agricultural Catchments Research Unit (ACRU) model (Schulze 1995).The Institute for Water Research (IWR), Rhodes University, linked the MUSLE with a simple storage and transport model (Gwapedza et al. 2021) as part of the development of the Water Quality and Sediment model (WQSED).The work mirrors the previous work by Picouet et al. (2001), where a simple storage model estimating sediment transport was developed specifically for the Upper Niger Basin and follows the global need to improve the accuracy and process representation of existing approaches (Mohapatra 2022).

Fig. 2
Fig. 2 A map of the Rio Tanama River catchment in Puerto Rico

Fig. 3
Fig. 3 Distribution of the average monthly runoff and sediment discharge recorded in the Odzi catchment over the selected period

Fig. 4
Fig. 4 Distribution of the average monthly runoff and sediment discharge recorded in the Rio Tanama catchment over the selected period

Fig. 5
Fig. 5 Conceptual structure of the erosion and sediment transport (WQSED) model

Fig. 6
Fig. 6 Observed and simulated sediment output for the Odzi catchment.The dotted brackets separate the calibration period from the validation period at the beginning of the time series

Fig. 7
Fig. 7 Observed and simulated sediment output for the Rio Tanama catchment.The dotted brackets separate the calibration period from the validation period

Fig. 8
Fig. 8 Scatterplots showing the calibration and validation periods of the sediment yield (SY) simulations (tons day − 1 ) for the Odzi and Rio Tanama catchments

Fig. 9
Fig. 9 Sediment frequency distribution graphs (Log Y-axis) of the erosion and sediment transport model (WQSED) simulations (red lines) versus observations (black lines) (tons day − 1 ) for the Odzi (left) and Rio Tanama catchments for the calibration and validation periods

Fig. 10 A
Fig. 10 A plot showing parameter values' performance based on a combined performance index for the Odzi catchment.A greater number of high performances are clustered around the middle range of the parameters.The horizontal axis represents the sum of the parameter

Fig. 11 A
Fig. 11 A plot showing parameter values' performance based on a combined performance index for the Rio Tanama catchment.A greater number of runs with high performance are clustered around the middle to high range of the parameters

Table 1
Summary of available flow and sediment data for selected

Table 3
Ranges of calibration parameters selected for the sensitivity

Table 4
Performance indicators for the Odzi and Rio Tanama catchments

Table 5
A list of estimated and calibrated parameters that were used for the Odzi and Rio Tanama catchments.The MUSLE factors (LS, K, C, P) shown in the table are mean catchment values