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黄土高原丘陵沟壑区不同尺度小流域次降雨水文过程 模型研究
周淑梅
Subtype博士
Thesis Advisor雷廷武
2013-05
Degree Grantor中国科学院研究生院
Place of Conferral北京
Keyword流域 入渗 降雨–径流过程 水力几何 黄土高原
Abstract

小流域地表水文过程与水资源理论、地表生态、土壤侵蚀密切相关。黄土高原丘
陵沟壑区水土资源流失备受关注。小流域是水土保持综合治理的基本单元,研究小流
域水文过程模型为流域水土保持、水资源优化配置和洪水预报等提供辅助工具。
本论文以黄土丘陵沟壑区为研究区,研究建立不同尺度小流域次降雨水文过程模
型。在桥子西沟小流域(W1-b,1 km 2 ),重点研究小流域降雨入渗、产流、汇流过
程模型的构建、率定及验证;在罗玉沟(W100,100 km 2 )、吕二沟(W10,10 km 2 )、
桥子东沟(W1-a,1 km 2 )和桥子西沟(W1-b,1 km 2 )流域,应用水力几何理论研
究多尺度流域产流过程测量方法。论文主要得出以下初步结论:
(1)提出了修正 NRCS-CN 模型的方法,引入流域稳定入渗修正 NRCS-CN 模
型,得到 MCN 模型。根据桥子西沟小流域降雨–径流过程观测数据,采用初损量观
测值和计算值,计算得到流域稳定入渗率分别为 4.8 mm h -1 和 4.2 mm h -1 。根据计算
得到的流域稳定入渗率,应用 MCN 和 NRCS-CN 模型估算流域径流过程。结果表明,
稳定入渗率取值 4.8 mm h -1 或 4.2 mm h -1 时,MCN 模型模拟流域入渗、径流的效果均
优于 NRCS-CN 模型,对较大的入渗、径流事件更为明显;MCN 模型采用稳定入渗
率 4.8 mm h -1 的模拟结果优于采用稳定入渗率 4.2 mm h -1 的模拟结果。
(2)根据桥子西沟流域降雨–径流过程水文数据及流域 DEM、土壤和土地利用
等空间数据,分别采用反算法(Back Calculation,BC)和事件分析法(Event Analysis,
EA)计算 NRCS-CN 模型初损率。反算法和事件分析法确定初损率分别为 0.1 和 0.17。
初损率分别取 0.1、0.17 和 0.2 时应用 NRCS-CN 模型预报流域产流量。误差分析和图
形拟合评价结果表明,桥子西沟流域 NRCS-CN 模型初损率适宜取值为 0.1。
(3)采用水力几何关系幂函数模型和对数函数模型拟合罗玉沟(W100)、吕二
沟(W10)、桥子东沟(W1-a)和桥子西沟(W1-b)四个流域出口量水堰流量―流速
关系。应用确定性系数(R 2 )和模型效率系数(E)分别评价模型拟合效果及验证效
果。通过分析 W100、W10 和 W1-a 三个流域模拟结果探查流域尺度对两种模型参数
取值的影响。结果表明幂函数参数 k(单位流量流速)与流域尺度呈负相关关系,参数 m(流速变化率)随流域尺度的变化趋势与参数 k 相反。对数函数参数 e(流速变
化率)与流域尺度相关性不显著,参数 d(单位流量流速)与流域尺度呈负相关关系;
通过分析 W1-a 和 W1-b 两个流域模拟结果研究流域土地利用方式对两种模型参数取
值的影响。结果表明 W1-a 流域幂函数参数 k 显著大于 W1-b 参数 k(P<0.001),两流
域参数 m 无显著差异。W1-b 流域对数函数参数 e 比 W1-a 参数 e 偏大,但无显著差
异(P<0.05)。W1-a 流域对数函数参数 d 显著大于 W1-b 参数 d(P<0.05)。分别采用
不同研究流域观测数据验证两种函数模型,验证结果均可以接受,在流速取值更为广
泛的条件下,幂函数模型模拟效果优于对数函数模型。
(4)应用 GIS 工具将桥子西沟流域划分成 11 个坡面,通过一条沟道连接。以流
域 1987–2006 年降雨过程数据为输入,应用 NRCS-CN 模型计算流域坡面产流过程。
采用自行设计的概念模型法对各坡面产流进行汇流演算,得到流域出口径流过程。通
过考察径流深、洪峰流量和洪峰出现时间三个水文变量评价模型效果。径流深预测的
绝对误差变化范围为-0.08–7.4 mm,均值为 0.35 mm,相对误差变化范围为8%–-103%,
均值为-1%。洪峰流量预测的绝对和相对误差最大值分别为-1.85 m 3 s -1 和-63%,均值
分别为-0.02 m 3 s -1 和 10%;洪峰出现时间预测的绝对和相对误差最大值分别为 0.99 h
和-109%,均值分别为-0.09 h 和-17%。此外,洪峰流量和洪峰出现时间模拟结果的线
性拟合斜率分别为 1.09 和 1.04。模型的确定性系数(R 2 )分别为 0.99 和 0.97。径流
模拟结果的线性拟合斜率和确定性系数分别为 0.83 和 0.78。计算得到了各水文变量
拟合的均方根误差(RMSE)、模型效率系数(E)和整群剩余系数(CRM),结果表
明模型对洪峰流量模拟效果最好,其次是洪峰出现时间和径流深。
(5)提出一种通过测量流速根据流速-流量关系确定流量的新方法。通过求解水
力几何(Hydraulic Geometry)关系幂函数反函数,建立以流速为自变量、流量为因
变量的流速–流量幂函数模型。将模型应用于罗玉沟(W100)、吕二沟(W10)、桥子
东沟(W1-a)和桥子西沟(W1-b)四个流域出口量水堰流速–流量关系模拟。根据模
型确定性系数(R 2 ),幂函数模型拟合优度依次为 W100、W1-a、W10 和 W1-b。根
据模型效率系数(E),幂函数模型模拟效率依次为 W1-a、W100、W10 和 W1-b。模
型验证结果表明,水力几何关系幂函数反函数模型能够用于测量流域流量,建立了一
种通过测量流域出口流速而非水深确定流量的新方法。
本论文研究结果有助于理解黄土高原小流域水文循环过程,为研究流域水资源优
化配置、土壤侵蚀和泥沙运移等提供辅助工具。
关键词:流域;入渗;降雨–径流过程;水力几何;黄土高原

Other Abstract

The hydrological processes of small watersheds are closely related to water resource
theory, land surface ecology, and soil erosion. Severe soil and water loss in the loess
hilly–gully region of the Loess Plateau has attracted much concern. Small watersheds are
the basic unit for soil and water conservation. Models of hydrologic processes for small
watersheds could serve as an important aid for soil and water conservation, water resource
optimization and flood prediction.
In this study, by taking the hilly-gully regions of the Loess Plateau as the study area,
the establishment of hydrological process models for different-scale watersheds during a
single rainfall event was studied. In Qiaozi-West watershed (W1-b, 1 km 2 ), the model
establishment, calibration and validation for watershed infiltration, runoff, and flow routing
were studied. In the watersheds of Luoyugou (W100, 100 km 2 ), Lvergou (W10, 10 km 2 ),
Qiaozi-East (W1-a, 1 km 2 ) and Qiaozi-West (W1-b, 1 km 2 ), the Hydraulic Geometry
theory was introduced to study the measuring method of watershed runoff. Preliminary
conclusions of the study are summarized as follows:
(1) A method was developed for modifying NRCS-CN model. By introducing steady
infiltration to the NRCS-CN model, the modified NRCS-CN (MCN) model was developed.
The steady infiltration rates for the study watershed were determined as 4.8 mm h -1 by
using observed initial abstraction, and 4.2 mm h -1  by using calculated initial abstraction.
Both of the MCN and NRCS-CN models were used to simulate watershed runoff process
for the study events. The results showed that the simulation of watershed infiltration and
runoff by the MCN model was better than that of NRCS-CN model by using either  calibrated steady infiltration rate, especially in simulating larger infiltration, runoff events;
the infiltration simulation using steady infiltration rate of 4.8 mm h -1 was superior to that
using 4.2 mm h -1 for MCN model.
(2) Based on Qiaozi-West watershed rainfall-runoff process data, watershed DEM,
soil and land use digital maps, the initial abstraction ratio of the NRCS-CN model was
determined by Back Calculation (BC) and Event Analysis (EA) methods. The initial
abstraction ratios were determined as 0.1 and 0.17 by using BC and EA methods,
respectively. Using three initial abstraction ratio values of 0.1, 0.17 and 0.2, runoff
amounts for the study watershed were predicted by NRCS-CN model. Considering both of
error analyses and curve fitting results, the value of 0.1 was indicated as the appropriate
value of the initial abstraction ratio for the NRCS-CN model in Qiaozi-West watershed.
(3) The observed flow velocity data from the measuring weirs at watershed outlets
were fitted with the discharge rate, using both Hydraulic Geometry power function and
logarithmic function models for the Luoyugou (W100, 100 km 2 ), Lvergou (W10, 10 km 2 ),
Qiaozi-East (W1-a, 1 km 2 ) and Qiaozi-West (W1-b, 1 km 2 ) watersheds. The coefficient of
determination (R 2 ) and model efficiency coefficient (E) were used to evaluate model
calibration and validation results, respectively. The effect of watershed scale on the model
parameters was examined by using model calibration results from W100, W10 and W1-a
watersheds. It was found that the parameter k (flow velocity for unit discharge rate) in the
power function model was negatively correlated with watershed size, while parameter m
(rate of change of flow velocity) had an opposite correlation with watershed size compared
with parameter k. In the logarithmic function model, parameter e (rate of change of flow
velocity) had no significant correlation with watershed size, while parameter d (flow
velocity for unit discharge rate) was negatively correlated with watershed size, similar to
parameter k The calibration results from the two paired watersheds (W1-a and W1-b) were
used for exploring the effect of watershed land use on the model parameters. The
parameter k in the power function model for W1-a watershed was significantly higher than
that of W1-b watershed (P<0.001). The parameter m for the two paired watersheds showed
no significant difference. The parameter e in the logarithmic function model for W1-b
watershed was higher than that of W1-a watershed, however the difference was not
significant (P<0.05). The parameter d for W1-a watershed was significantly higher than  that of W1-b watershed (P<0.05). Another data set from the study watersheds was used to
test the two function models. The results showed that both of the model functions yielded
acceptable results, nevertheless the power function model generally showed superior
performance to the logarithmic function model for the wide value range of flow velocity.
(4) By using GIS tools, the Qiaozi-West (W1-b) watershed was dissected as 11 slopes,
which were connected by a channel. The runoff for each slope in the watershed was
calculated using NRCS-CN model based on watershed rainfall process input for the year
1987–2006. A new conceptual method was developed and used to calculate flow routing of
the runoff from each slope, to derive watershed hydrograph. The predictions for the three
important hydraulic variables: runoff, peak discharge rate and time to peak were examined.
The absolute error for runoff depth prediction varied from -0.08 to 7.4 mm, the mean was
0.35 mm; the relative error changed from 8% to -103%, the mean was -1%. The maximum
absolute and relative errors for peak discharge rate prediction were -1.85 m 3 s -1 and -63%,
and the mean were -0.02 m 3 s -1 and 10%, respectively. For the prediction of time to peak,
the maximum absolute and relative errors were 0.99 h and -109%, and the mean were -0.09
h and -17%. Moreover, the slopes of linear fitting for peak discharge rate and time to peak
were 1.09 and 1.04 (both close to 1), with coefficients of determination (R 2 ) both close to 1
(0.99 and 0.97). For runoff prediction, the slope and R 2 values for the linear fitting were
0.83 and 0.78. The root mean square error (RMSE), model efficiency coefficient (E), and
coefficient of residual mass (CRM) were calculated for the simulations of each hydraulic
variable. It was shown that the simulation of peak discharge rate was best, followed by that
of time to peak, and runoff.
(5) A new method was suggested to accurately measure the discharge from the
watersheds by measuring the flow velocity and using the relationship between flow
velocity and discharge rate. The power function of flow velocity-discharge rate was
established by deriving the inverse function of Hydraulic Geometry power function, taking
the discharge rate as the dependent variable with flow velocity as the independent variable.
The inverse power function model was tested by the flow velocity-discharge rate data from
the measuring weirs of Luoyugou (W100), Lvergou (W10), Qiaozi-East (W1-a) and
Qiaozi-West (W1-b) watershed outlets. According to the calculation of coefficients of
determination (R 2 ), the model calibration of W100 was best, followed by those of W1-a,  W10 and W1-b. Based on model efficiency coefficient (E) calculation results, the
simulation accuracy of W1-a watershed was highest, followed by those of W100, W10 and
W1-b. The study indicated that the derived power function could be used to determine
discharge rate at study watershed outlets. Therefore, a new method was developed for
measuring discharge rate given the measurement of the flow velocity instead of flow depth.
The results of the study contribute to better understanding watershed hydrological
cycle, and could supply basic tools for the study of water resource optimization, soil
erosion, and sediment transport for the small watersheds on the Loess Plateau.
Key words: watershed; infiltration; rainfall–runoff process; Hydraulic Geometry;
Loess Plateau

Language中文
Document Type学位论文
Identifierhttp://ir.iswc.ac.cn/handle/361005/8979
Collection水保所知识产出(1956---)
Recommended Citation
GB/T 7714
周淑梅. 黄土高原丘陵沟壑区不同尺度小流域次降雨水文过程 模型研究[D]. 北京. 中国科学院研究生院,2013.
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