黄土高原小流域出口断面水力几何模型

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

流域出口断面水力几何关系能够为流域水文模型参数获取、洪水过程演变及灾害预警提供辅助工具。以黄土高原丘陵沟壑区桥子西沟和桥子东沟2水土流失对比流域为研究对象,首先采用幂函数、自然对数函数和二阶对数函数模型分别拟合桥子西沟流域1987—2006年出口断面水文观测数据,应用模型决定系数(R2)和模拟残差平方和(RSS)评价3种模型拟合结果,优选平均流速-流量、水面宽-流量与平均水深-流量的水力几何模型。然后将桥子西沟流域观测数据随机分为2部分:1987—2002年共594组数据用于率定优选模型,2003—2006年共362组数据用于验证。采用均方根误差(RMSE)、模型效率系数(E)以及图形拟合等手段评价各优选模型的有效性。桥子西沟流域模型率定及验证结果表明:平均流速-流量和平均水深-流量关系适用于自然对数函数表达(RMSE值为19.89%和30.70%,E值为0.59和0.84),而水面宽-流量关系则适用于二阶对数函数表达(RMSE=3.84%,E=0.87)。进一步应用桥子东沟流域1987—2006年出口断面共1 006组观测数据验证各优选水力几何模型在相似流域的适用性,结果表明:平均水深-流量关系拟合效果优于桥子西沟流域,而平均流速-流量和水面宽-流量关系拟合优度稍逊于桥子西沟流域。该研究为黄土高原地区小流域洪水监测与预报提供基础。

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.