Adjusting the sediment delivery ratio (SDR)

The moderately explained spatial variability proved the limitations of the modelling framework (Tab. 15).

Irrespective of quantitative differences between the alternative model results, the high correlation coeffi-cients demonstrated that, especially for topography, data and algorithm choices would not help to lessen this unexplained variability. An exception is the empirical approximation of the USLE L factor (Lemp) which proved to be superior to both alternative approaches. Nonetheless, strong correlations also showed that empirical, catchment-based models can efficiently cope with topographic uncertainty by including simple regression models. According to the correlation analyses (Tab. 17), a hydrological catchment property was included in the SDR model (Eqs. 11–12).

The adjusted SDR values for non-alpine catchments were between 2.5 and 6.8%. The inverse correlation to catchment area (rS=-0.24) was stronger than for the original SDR (Fig. 11). The explained variability increased significantly even though one gauge was included which was excluded before. The average deviation for the Lemp-based SY estimates decreased from +30% (Tab. 15) to -3%. This lay within the degree of uncertainty due to the interpolation methods for SS data. For large-scale applications, qfast can be replaced by Pr. Results similarly improved for SYFSD. The r² value rose significantly even with the inclusion of three gauges not previously con-sidered (r²=0.64) and average deviation was also -3%.

The remaining unexplained variability and the model residuals have to be seen in the model scope which did not include the numerous anthropogenic activities, long-term deposition and other discharge-dependent sediment sources. In accordance with findings of Wu et al. (2005), the inherent limitations of the empirical modelling framework may not allow for much more accuracy.

Fig. 11: Adjusted SDR and modelled SDR for non-alpine catchments (SDR modelled with Lemp as USLE L factor and SYgraph)

The hydrological catchment property used for model improvement can be considered as proxy for catchment-wide hydraulic connectivity. Precipitation and surface runoff are not only driving forces of soil mobilization but also of sediment transport. With this adjustment, catchments receiving more precipitation or having more surface runoff are not only prone to more soil loss but to a higher proportion of sediment leaving the catch-ment as well. However, we are aware that the need for the hydrological adjustcatch-ment also refers to our estima-tion of the USLE R factor, despite the successful verificaestima-tion of the modelled soil erosion. This concerns the interpolation of long-term average precipitation as well as the suitability of the linear empirical equations to estimate the R factor from long-term annual precipitation.

3.7 Conclusions

We have demonstrated that established empirical approaches for soil erosion and sediment delivery, in com-bination with Europe-wide available input data, can sufficiently explain the spatial pattern of long-term aver-age yields of the erosion-related (critical) fractions of total suspended solid yields in hilly and mountainous catchments in southern Germany. To achieve a better explained variability of sediment yields in the study area, it was necessary to include a hydrological catchment property in the SDR approach. We expect that this modelling framework can also be applied in other European regions. Land use, flow distance (drainage densi-ty), hydrology (precipitation), and topography are commonly available for river catchments and thus suitable to estimate catchment-wide sediment delivery ratios in large-scale studies. However, within such modelling framework, multiple algorithms and DEM are available for derivation of topographic parameters and creation of validation data. Each alternative has a significant quantitative influence on topographic parameters, model estimates and validation data, respectively.

Our findings revealed that among these choices, DEM resolution had the largest impact on modelled soil ero-sion and sediment yields, with scale effects on slope angles and drainage density being most important. Model estimates were also strongly related to the choice of the slope algorithm with results differing by 30% between the neighbourhood and the maximum slope method. This value was close to the average deviation of 25%

between both approaches to obtain critical fractions of total yields for model validation.

We also found that the estimation of critical yields affected the prediction of the inter-annual variability of sediment yields. Unlike the spatial variability, the mathematically-founded FSD approach gave better results than the alternative graphical approach. However, our aggregated hydrological parameters only moderately explained the inter-annual variability. Although we used power equations instead of formerly proposed linear regression models, extremely high sediment yields were still clearly underestimated. More detailed input data are needed to improve predictions for flood years.

The inherent limitations of the empirical modelling framework, and coarse data resolution, may impede de-termination of which alternative algorithm is superior. The range of relationships between model outcomes and validation data has to be seen as methodical uncertainty. Nonetheless, high correlation coefficients of long-term averages and annual critical suspended solid yields in most cases showed that the tested algorithms and DEM resolutions alone have only minor impacts on the explained variability of critical yields.

The erosion estimates were consistent with other studies. However, the calculated critical SDR were uncorre-lated to our and other modelled SDR. Correlation analyses between critical SDR and catchment properties

revealed that empirical SDR models should consider hydrology (surface runoff, precipitation). Consequently, including our estimated surface runoff significantly improved the model evaluation.

Although this study discussed the consequences of method choices for an USLE context in a complex region, the identified principles are also relevant for other modelling frameworks and regions. First, the estimation of total and subsequently critical sediment yields will affect any model calibration and validation. However, our observed similarity is limited to different interpolation approaches and may not be valid for different meas-urement methods and sampling frequencies. Second, the qualitative similarity of even complex topographic parameters suggests that catchment-based models can use regression models for any region to handle topo-graphic uncertainty. Third, calibrating erosion models to total suspended solids overestimates the contribu-tion of soil erosion. We recommend using critical yields instead and applied two approaches to estimate such critical sediment yields from daily monitoring data. In general, the results were consistent and methodical modifications were of minor relevance. However, the data-sparing and easy-to-use FSD approach agreed less to the spatial pattern of modelled long-term sediment yields but described the inter-annual variability of critical yields much more reasonably than the alternative graphical-statistical approach.

From our findings, we propose three topics for future studies. First, an improved estimation of the USLE R factor would make the SDR adjustment more reliable. Second, some ambiguous results and gauge-specific problems suggest that both approaches to derive erosion-related fractions from suspended-solids data should be further scrutinized. Third, the very high sediment yields of flood years have to be better captured.

4 Modelling the inter-annual variability of sediment