Hydraulic geometry model at small watershed outlets on the Loess Plateau of China.

Hydraulic geometry at watershed outlets plays an important role in determining parameters for hydrologic models, flood process evolution and disaster warning. Taking Qiaozi-West and Qiaozi-East watersheds in the hilly and gully loess region as study areas, we first simulated observed hydraulic data from 1987 to 2006 at the Qiaozi-West Watershed outlet using the power function, natural logarithmic function and second logarithmic function models, and then evaluated the performance of the three models using the determination coefficient (R2) and residual sum of squares (RSS), in order to determine the superior models for simulating hydraulic geometry relationships between discharge rate and mean flow velocity, flow width and mean flow depth. All the observed data from the Qiaozi-West Watershed were randomly separated into two groups, one group with 594 data pairs from 1987 to 2002 was used for model calibration, and the other group with 362 data pairs from 2003 to 2006 was used for model validation. The root mean square error (RMSE), model efficiency coefficient (E) and graph fitting were used to measure model validity. The model calibration and validation results indicated that the relationship between discharge rate and mean flow velocity and that between discharge rate and mean flow depth were best expressed by the natural logarithmic function model (RMSE values were 19.89% and 30.70% and E values were 0.59 and 0.84, respectively), while the discharge rate-flow width relationship was best simulated by the second order logarithmic function model (RMSE=3.84%, and E=0.87). Furthermore, observed data during year 1987-2006 with totally 1006 data pairs from the Qiaozi-East Watershed outlet were used to examine the universality of the determined hydraulic geometry models in similar watersheds. The results showed that the model of discharge rate-mean flow depth displayed a better performance compared with that in Qiaozi-West Watershed, while the other two models were less satisfactory. This study could provide a basic tool for flood monitoring and forecasting in small watersheds on the Loess Plateau.