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Highlights • 7 temperature-based R s models were adopted to improve the Makkink model for ET 0 estimation in Northwest China. • The applicability of the 7 MK i models, original Makkink model, Jensen-Haise and Irmak model were evaluated on different time scales. • The 7 MK i models were more accurate than the 3 physical models. • The M5 model with temperature and relative humidity as input data has the best accuracy. Abstract Reference evapotranspiration (ET 0) is an important parameter for climatological and hydrological studies, as well as for agricultural water resources management. In this study, 7 temperature-based solar radiation models were adopted to improve the Makkink model for ET 0 estimation in Northwest China. The temperature-based models only require air temperature as input data, which can be easily monitored in most areas around the world. The applicability of the improved Makkink models (M1-M7), the original Makkink (MK) model, the Jensen-Haise (JH) model as well as the Irmak (IK) model were evaluated on different time scales using meteorological data obtained from 12 weather stations in Northwest China. The results showed that the 7 improved Makkink (MK i) models (R 2 ranged 0.71–0.86) were more accurate than the 3 physical models (R 2 ranged 0.64–0.76) for daily ET 0 estimation at the 4 sub-zones of Northwest China, and the M4, M5, M6 and M7 models were superior to the other models. The M5 model had the best estimation accuracy for daily ET 0 on daily scale, followed by M7 and M6, with the R 2 median of 0.83, 0.83 and 0.82, the RMSE median of 0.86, 0.88 and 0.89 mm/d, and the GPI median of 1.03, 0.90 and 0.87, respectively. On monthly scale, the 7 MK i models (with relative error almost less than 20%) were also better than the 3 physical models (with relative error usually more than 20%) at the 4 sub-zones. The M5 model also showed the best performance for monthly average daily ET 0 estimation, followed by M7 and M6, with the R 2 median of 1.00, 1.00 and 1.00, the RMSE median of 0.13, 0.16 and 0.19 mm/d, and the GPI median of 0.25, 0.05 and 0.02, respectively. Overall, the estimation accuracy of the Makkink model was much improved by using the temperature-based solar radiation models, and in Northwest China, M5 model which only requires temperature and relative humidity as input data is highly recommended to estimate ET 0 on both daily and monthly scales. [ABSTRACT FROM AUTHOR]

Summary Ephemeral gullies or rills are major sediment sources and the primary channel to convey runoff and sediments from hillslopes. Quantifying the detachment rate is important for understanding the erosion process of ephemeral gullies. This study suggests a method to estimate the detachment rate for use in WEPP model, using sediment distribution data along an eroding rill or ephemeral gully under controlled flume experiments, conducted at four slope gradients (8.74%, 17.62%, 26.78%, and 36.38%) and four flow rates (32, 64, 128 and 256 L min −1 ). The experimental soil materials were packed into the flume of 0.5 m wide, 0.6 m deep and 12 m long, to a thickness of 0.5 m at a bulk density of 1300 kg m −3 . Regulated water flow was introduced to soil surface at the upper end of flumes. The detachment rate was calculated from the spatial distribution data of sediment concentrations measured with sediment-laden water samples simultaneously taken along the gullies at one meter intervals. Results showed that the detachment rate was well fitted with downslope distance along the rill or ephemeral gully by an exponential equation. The regression parameters indicated that detachment rate decreases linearly with sediment load in the gully flow. The feedback relationship between sediment load and detachment rate in rill or ephemeral gullies could be adequately represented by the first-order coupling equation for loess soil under steep slopes and high flow rates. The detachment rates along the rills or ephemeral gullies were found to increase with slope gradient and flow rate and the detachment rate was positively related to unit stream power and the deficit between max sediment load and the local sediment load. [ABSTRACT FROM AUTHOR]

Highlights • Three data driven models with nine input combinations are proposed for estimation of E pan. • A national-scale assessment of data driven models along with SS and PenPan models are performed. • ELM model with complete input has the best accuracy. • Air temperature is the most sensitive parameter to data driven models. Abstract Evaporation is an essential component in hydrological processes, and accurate estimation of evaporation is of importance for sustainable management of water resources. This study conducted a national-scale assessment of different models for pan evaporation (E pan) estimation at 178 meteorological stations across different climatic zones of China, including the temperate continental zone (TCZ), temperate monsoon zone (TMZ), mountain plateau zone (MPZ) and subtropical monsoon zone (SMZ). Firstly, three data-driven models, including extreme learning machine (ELM), artificial neural networks optimized by particle swarm optimization (PSO-ANN) and genetic algorithm (GA-ANN), were trained with nine input combinations of climatic variables. The performance of the 27 proposed models along with the empirical Stephens and Stewart (SS) and physically-based PenPan models were investigated and compared using relative root mean square error (RRMSE), Nash-Sutcliffe coefficient (NS) and mean absolute error (MAE). The three statistical indicators were further normalized to global performance indicator (GPI), by which all the evaluated models can be easily ranked. The results showed that the data-driven models with complete inputs generally obtained more accurate E pan estimation, where the ELM model with full input data provided the best accuracy, with average RRMSE of 12.5%–15.2%, NS of 0.909–0.936 and MAE of 11.7–19.9 mm/m. Air temperature was found to be the most influential parameter to data-driven models, followed by sunshine duration , wind speed and relative humidity. The SS model provided slightly better results in MPZ and TCZ, and slightly less accurate results in SMZ and TMZ, compared with the data-driven models under the same input conditions. Overall, ELM was recommended as the best model for E pan estimation when all the selected climatic data are available, while temperature-based PSO-ANN is recommended in MPZ and SMZ and temperature-based GA-ANN is recommended in TCZ and TMZ when the other climatic data are missing. [ABSTRACT FROM AUTHOR]

Highlights • Applying the electrolyte tracer pulse method to measure shallow water flow velocity on hill-slope. • An equation for estimating flow velocity on the basis of the measurement distance was established. • The new equation could be used to simulate results from other experimental data sets. • The steady flow velocities and the distances when water flow reached stability were determined by the new equation. Abstract Understanding the velocity distribution of shallow water flow along hill-slope is of great significance in soil erosion studies. This study proposes a method to estimate the steady flow velocity and the distance when water flow reaches stability, using hill-slope flow velocity distribution data along a simulated rill measured by the electrolyte tracer pulse method. Laboratory experiments were performed using a flume of 12 m long, 0.1 m wide and 0.3 m height under five slope gradients (5°, 10°, 15°, 20° and 25°) and four flow discharges (2, 4, 8 and 16 L min−1). The electrolyte tracer pulse method was employed to measure the flow velocities at locations of 1, 2, 3, 4, 6, 8, 10 and 12 m from the inlet of the flowing water. The flow velocities measured by the dye tracer method served as a control. The results showed that the flow velocities measured by the electrolyte tracer pulse method initially accelerated and then reached a steady value. An equation for estimating flow velocity on the basis of the measurement distance was established. The flow velocities calculated by the equation agreed well with those measured by the electrolyte tracer pulse method. The determination (R2) and the Nash-Sutcliffe model efficiency (NSE) were greater than 0.800, except for a few cases. In addition, the equation established in this study was shown to successfully predict flow velocities measured in other studies. The steady flow velocities and the distances when water flow reached stability under different slope gradients and flow discharges were determined by this equation. When the differences between the measured flow velocity and the steady flow velocity were very small, that is, 5% and 10%, the steady distances ranged from 2.239 m to 4.772 m and from 2.843 m to 6.059 m, respectively. By comparing the steady flow velocities with the flow velocities measured by the dye tracer method, the results indicated that the steady flow velocities were 0.702–0.735 times that of the flow velocities measured by the dye tracer method at various slope gradients and flow discharges. A linear function existed between the two, and the regressed parameter k (i.e., 0.718) could be used as the correction factor between the two. In general, the equation established in this study can facilitate the prediction of the steady flow velocity. [ABSTRACT FROM AUTHOR]

Accurate estimation of sediment concentration is essential to establish physically-based erosion models. The objectives of this study were to evaluate the effects of flow discharge (Q), slope gradient (S), flow velocity (V), shear stress (τ), stream power (ω) and unit stream power (U) on sediment concentration. Laboratory experiments were conducted using a 10 × 0.1 m rill flume under four flow discharges (2, 4, 8 and 16 L min −1 ), and five slope gradients (5°, 10°, 15°, 20° and 25°). The results showed that the measured sediment concentration varied from 87.08 to 620.80 kg m −3 with a mean value of 343.13 kg m −3 . Sediment concentration increased as a power function with flow discharge and slope gradient, with R 2  = 0.975 and NSE = 0.945. The sediment concentration was more sensitive to slope gradient than to flow discharge. The sediment concentration was well predicted by unit stream power (R 2  = 0.937, NSE = 0.865), whereas less satisfactorily by flow velocity (R 2  = 0.470, NSE = 0.539) and stream power (R 2  = 0.773, NSE = 0.732). In addition, using the equations to simulate the measured sediment concentration of other studies, the result further indicated that slope gradient, flow discharge and unit stream power were good predictors of sediment concentration. In general, slope gradient, flow discharge and unit stream power seem to be the preferred predictors for estimating sediment concentration. [ABSTRACT FROM AUTHOR]

Abstract: Measurement of the velocity of shallow water flow on a hill slope is of great importance in soil erosion studies. Electrolyte tracers have been tried to estimate mean velocity of water flow with the velocity of the leading edge of the solute propagation multiplied with a somewhat arbitrary correction factor. In this study, an analytical solution of solute (tracer) transport was formulated to serve as the mathematical foundation for measuring shallow water flow velocity. To estimate the flow velocity, a procedure was advanced. In the procedures, the analytical solution is fitted with the measured propagation curve and given the ‘the least square’ estimation of velocity. A detailed mathematical description is outlined for this purpose. Experimental results are given to show the feasibility of the method, including the analytical solution and the estimation procedures. This study provides the theoretical foundation for measuring the velocity of shallow water flow and for studies of overland solute transport. [Copyright &y& Elsevier]