Kristin Bunte

Variation of rock fragment cover and size along semiarid hillslopes: a case-study from southeast Spain

Abstract The spatial variation of rock fragment cover (Rc) and rock fragment size (Rs) along semiarid hillslopes and transects in the Mediterranean is largely controlled by hillslope gradient. Total rock fragment cover (Rc>5 mm) often increases in a convex upward curve with hillslope gradient while the D50 of the surface rock fragments >5 mm increases linearly with hillslope gradient. On south-facing slopes, Rc>5 mm is slightly higher than on north-facing slopes. Lithology controls the size distribution of the stone pavement rather than its cover percentage. Spatial variation of rock fragment cover reflects spatial variation in past erosion and deposition rates. Hillslope sections that are steep, south-facing, or have been abandoned a long time ago have undergone intense interrill and rill erosion, and thus have high rock fragment covers. Tillage erosion leads to high rock fragment covers on convex hillslopes in intensively cultivated areas. Thus, using information on hillslope gradient, aspect, lithology and landuse, we have been able to describe the spatial variation of rock fragment cover and size along semiarid hillslopes in southeast Spain. Such information is crucial for understanding and modelling the spatial variation of the hydrological and erosion response of semiarid hillslopes under environmental change, especially in semiarid environments of the Mediterranean where vegetation cover is predicted to decrease due to climatic or landuse changes and rock fragments at the surface become the only soil surface stabilisers.

A Comparison of Coarse Bedload Transport Measured with Bedload Traps and Helley-Smith Samplers

Gravel bedload transport rates were measured at eight study sites in coarse-bedded Rocky Mountain streams using 4-6 bedload traps deployed across the stream width and a 76 by 76 mm opening Helley Smith sampler. Transport rates obtained from bedload traps increased steeply with flow which resulted in steep and well-defined transport rating curves with exponents of 8 to 16. Gravel transport rates measured by the Helley- Smith sampler started with much higher transport rates during low flows and increased less steeply, thus fitted bedload rating curves were less steep with exponents of 2 to 4. Transport rates measured with both samplers approached similar results near or above bankfull flow, but at 50 % of bankfull, transport rates from the bedload traps were 2-4 orders of magnitude lower than those obtained from the Helley-Smith sampler. The maximum bedload particle sizes also differed between the two samplers. They were smaller in the bedload traps than the Helley-Smith sampler at low flows, while at higher flows bedload traps collected larger particles than the Helley-Smith sampler. Differences in sampler opening size and sampling time contribute to the measured differences, but the biggest effect is likely attributable to the bedload traps being mounted on ground plates thus avoiding direct contact between the sampler and the bed and preventing involuntary particle pick up.

Detecting cumulative watershed effects: the statistical power of pairing

Abstract The statistical power for detecting change in water quality should be a primary consideration when designing monitoring studies. However, some of the standard approaches for estimating sample size result in a power of less than 50%, and doubling the pre- and post-treatment sample size are necessary to increase the power to 80%. The ability to detect change can be improved by including an additional explanatory variable such as paired watershed measurements. However, published guidelines have not explicitly quantified the benefits of including an explanatory variable or the specific conditions that favor a paired watershed design. This paper (1) presents a power analysis for the statistical model (analysis of covariance) commonly used in paired watershed studies; (2) discusses the conditions under which it is beneficial to include an explanatory variable; and (3) quantifies the benefits of the paired watershed design. The results show that it is beneficial to include an explanatory variable when its correlation to the water quality variable of concern is as low as about 0.3. The ability to detect change increases non-linearly as the correlation increases. Power curves quantify sample size requirements as a function of the correlation and intrinsic variability. In general, the temporal and spatial variability of many watershed-scale characteristics, such as annual sediment loads, makes it very difficult to detect changes within time spans that are useful for land managers or conducive to adaptive management.

Applicability of bed load transport models for mixed‐size sediments in steep streams considering macro‐roughness

In steep mountain streams, macro-roughness elements typically increase both flow energy dissipation and the threshold of motion compared to lower-gradient channels, reducing the part of the flow energy available for bed load transport. Bed load transport models typically take account of these effects either by reducing the acting bed shear stress or by increasing the critical parameters for particle entrainment. Here we evaluate bed load transport models for mixed-size sediments and models based on a median grain size using a large field data set of fractional bed load transport rates. We derive reference shear stresses and bed load transport relations based on both the total boundary shear stress and a reduced (or “effective”) shear stress that accounts for flow resistance due to macro-roughness. When reference shear stresses are derived from the total boundary shear stress, they are closely related to channel slope, but when they are derived from the effective shear stress, they are almost invariant with channel slope. The performance of bed load transport models is generally comparable when using the total shear stress and a channel slope-related reference shear stress, or when using the effective shear stress and a constant reference shear stress. However, dimensionless bed load transport relations are significantly steeper for the total stress approach, whereas they are similar to the commonly used fractional Wilcock and Crowe (WC) transport model for the effective stress approach. This similarity in the relations allows the WC model, developed for lower-gradient streams, to be used in combination with an effective shear stress approach, in steep mountain streams.

Maximum likelihood parameter estimation for fitting bedload rating curves

Fluvial sediment loads are frequently calculated with rating curves fit to measured sediment transport rates. Rating curves are often treated as statistical representations in which the fitted parameters have little or no physical meaning. Such models, however, may produce large errors when extrapolation is needed, and they provide no insight into the sediment transport process. It is shown that log-linear least squares, the usual method for fitting rating curves, does not generally produce physically meaningful parameter values. In addition, it cannot accommodate data that include zero-transport samples. Alternative fitting methods based nonlinear least squares and on maximum likelihood parameter estimation are described and evaluated. The maximum likelihood approach is shown to fit synthetic data better than linear or nonlinear least squares, and to perform well with data that include zero-transport samples. In contrast, nonlinear least squares methods produce large errors in the parameter estimates when zero-transport samples are present or when the variance structure of the data is incorrectly specified. Analyses with fractional bedload data from a mountain stream suggest that bedload transport rates are gamma distributed, that the arrivals of bedload particles in a sampler conform to a Poisson distribution, and that the variance of nonzero samples can be expressed as a power function of the mean. Preliminary physical interpretations of variations in the rating curve parameters fit to fractional bedload data with the maximum likelihood method are proposed, and their relation to some previous interpretations of rating curve parameters are briefly discussed.