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
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摘要
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，1km~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（W100，100km~2）、吕二沟（W10，10km~2）、桥子东沟（W1-a，1km~2）和桥子西沟（W1-b，1km~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4.8mm h~(-1)和4.2mm 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4.8mm h~(-1)或4.2mm 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4.8mm h~(-1)的模拟结果优于采用稳定入渗率4.2mm 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-0.08–7.4mm，均值为0.35mm，相对误差变化范围为8%–~(-1)03%，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).85m~3s~(-1)和-63%，均值分别为-0.02m~3s~(-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0.99h和~(-1)09%，均值分别为-0.09h和~(-1)7%。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。
The hydrological processes of small watersheds are closely related to water resourcetheory, land surface ecology, and soil erosion. Severe soil and water loss in the loesshilly–gully region of the Loess Plateau has attracted much concern. Small watersheds arethe basic unit for soil and water conservation. Models of hydrologic processes for smallwatersheds could serve as an important aid for soil and water conservation, water resourceoptimization 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 asingle rainfall event was studied. In Qiaozi-West watershed (W1-b,1km~2), the modelestablishment, calibration and validation for watershed infiltration, runoff, and flow routingwere studied. In the watersheds of Luoyugou (W100,100km~2), Lvergou (W10,10km~2),Qiaozi-East (W1-a,1km~2) and Qiaozi-West (W1-b,1km~2), the Hydraulic Geometrytheory was introduced to study the measuring method of watershed runoff. Preliminaryconclusions of the study are summarized as follows:
(1) A method was developed for modifying NRCS-CN model. By introducing steadyinfiltration to the NRCS-CN model, the modified NRCS-CN (MCN) model was developed.The steady infiltration rates for the study watershed were determined as4.8mm h~(-1)byusing observed initial abstraction, and4.2mm h~(-1)by using calculated initial abstraction.Both of the MCN and NRCS-CN models were used to simulate watershed runoff processfor the study events. The results showed that the simulation of watershed infiltration andrunoff 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 of4.8mm h~(-1)was superior to thatusing4.2mm 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 wasdetermined by Back Calculation (BC) and Event Analysis (EA) methods. The initialabstraction ratios were determined as0.1and0.17by using BC and EA methods,respectively. Using three initial abstraction ratio values of0.1,0.17and0.2, runoffamounts for the study watershed were predicted by NRCS-CN model. Considering both oferror analyses and curve fitting results, the value of0.1was indicated as the appropriatevalue 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 outletswere fitted with the discharge rate, using both Hydraulic Geometry power function andlogarithmic function models for the Luoyugou (W100,100km~2), Lvergou (W10,10km~2),Qiaozi-East (W1-a,1km~2) and Qiaozi-West (W1-b,1km~2) watersheds. The coefficient ofdetermination (R~2) and model efficiency coefficient (E) were used to evaluate modelcalibration and validation results, respectively. The effect of watershed scale on the modelparameters was examined by using model calibration results from W100, W10and W1-awatersheds. It was found that the parameter k (flow velocity for unit discharge rate) in thepower function model was negatively correlated with watershed size, while parameter m(rate of change of flow velocity) had an opposite correlation with watershed size comparedwith parameter k. In the logarithmic function model, parameter e (rate of change of flowvelocity) had no significant correlation with watershed size, while parameter d (flowvelocity for unit discharge rate) was negatively correlated with watershed size, similar toparameter k The calibration results from the two paired watersheds (W1-a and W1-b) wereused for exploring the effect of watershed land use on the model parameters. Theparameter k in the power function model for W1-a watershed was significantly higher thanthat of W1-b watershed (P<0.001). The parameter m for the two paired watersheds showedno significant difference. The parameter e in the logarithmic function model for W1-bwatershed was higher than that of W1-a watershed, however the difference was notsignificant (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 totest the two function models. The results showed that both of the model functions yieldedacceptable results, nevertheless the power function model generally showed superiorperformance 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 as11slopes,which were connected by a channel. The runoff for each slope in the watershed wascalculated using NRCS-CN model based on watershed rainfall process input for the year1987–2006. A new conceptual method was developed and used to calculate flow routing ofthe runoff from each slope, to derive watershed hydrograph. The predictions for the threeimportant hydraulic variables: runoff, peak discharge rate and time to peak were examined.The absolute error for runoff depth prediction varied from-0.08to7.4mm, the mean was0.35mm; the relative error changed from8%to~(-1)03%, the mean was~(-1)%. The maximumabsolute and relative errors for peak discharge rate prediction were~(-1).85m~3s~(-1)and-63%,and the mean were-0.02m~3s~(-1)and10%, respectively. For the prediction of time to peak,the maximum absolute and relative errors were0.99h and~(-1)09%, and the mean were-0.09h and~(-1)7%. Moreover, the slopes of linear fitting for peak discharge rate and time to peakwere1.09and1.04(both close to1), with coefficients of determination (R~2) both close to1(0.99and0.97). For runoff prediction, the slope and R~2values for the linear fitting were0.83and0.78. The root mean square error (RMSE), model efficiency coefficient (E), andcoefficient of residual mass (CRM) were calculated for the simulations of each hydraulicvariable. It was shown that the simulation of peak discharge rate was best, followed by thatof time to peak, and runoff.
(5) A new method was suggested to accurately measure the discharge from thewatersheds by measuring the flow velocity and using the relationship between flowvelocity and discharge rate. The power function of flow velocity-discharge rate wasestablished by deriving the inverse function of Hydraulic Geometry power function, takingthe 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 fromthe measuring weirs of Luoyugou (W100), Lvergou (W10), Qiaozi-East (W1-a) andQiaozi-West (W1-b) watershed outlets. According to the calculation of coefficients ofdetermination (R~2), the model calibration of W100was best, followed by those of W1-a, W10and W1-b. Based on model efficiency coefficient (E) calculation results, thesimulation accuracy of W1-a watershed was highest, followed by those of W100, W10andW1-b. The study indicated that the derived power function could be used to determinedischarge rate at study watershed outlets. Therefore, a new method was developed formeasuring discharge rate given the measurement of the flow velocity instead of flow depth.
The results of the study contribute to better understanding watershed hydrologicalcycle, and could supply basic tools for the study of water resource optimization, soilerosion, and sediment transport for the small watersheds on the Loess Plateau.
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，1km~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（W100，100km~2）、吕二沟（W10，10km~2）、桥子东沟（W1-a，1km~2）和桥子西沟（W1-b，1km~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4.8mm h~(-1)和4.2mm 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4.8mm h~(-1)或4.2mm 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4.8mm h~(-1)的模拟结果优于采用稳定入渗率4.2mm 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-0.08–7.4mm，均值为0.35mm，相对误差变化范围为8%–~(-1)03%，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).85m~3s~(-1)和-63%，均值分别为-0.02m~3s~(-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0.99h和~(-1)09%，均值分别为-0.09h和~(-1)7%。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。
The hydrological processes of small watersheds are closely related to water resourcetheory, land surface ecology, and soil erosion. Severe soil and water loss in the loesshilly–gully region of the Loess Plateau has attracted much concern. Small watersheds arethe basic unit for soil and water conservation. Models of hydrologic processes for smallwatersheds could serve as an important aid for soil and water conservation, water resourceoptimization 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 asingle rainfall event was studied. In Qiaozi-West watershed (W1-b,1km~2), the modelestablishment, calibration and validation for watershed infiltration, runoff, and flow routingwere studied. In the watersheds of Luoyugou (W100,100km~2), Lvergou (W10,10km~2),Qiaozi-East (W1-a,1km~2) and Qiaozi-West (W1-b,1km~2), the Hydraulic Geometrytheory was introduced to study the measuring method of watershed runoff. Preliminaryconclusions of the study are summarized as follows:
(1) A method was developed for modifying NRCS-CN model. By introducing steadyinfiltration to the NRCS-CN model, the modified NRCS-CN (MCN) model was developed.The steady infiltration rates for the study watershed were determined as4.8mm h~(-1)byusing observed initial abstraction, and4.2mm h~(-1)by using calculated initial abstraction.Both of the MCN and NRCS-CN models were used to simulate watershed runoff processfor the study events. The results showed that the simulation of watershed infiltration andrunoff 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 of4.8mm h~(-1)was superior to thatusing4.2mm 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 wasdetermined by Back Calculation (BC) and Event Analysis (EA) methods. The initialabstraction ratios were determined as0.1and0.17by using BC and EA methods,respectively. Using three initial abstraction ratio values of0.1,0.17and0.2, runoffamounts for the study watershed were predicted by NRCS-CN model. Considering both oferror analyses and curve fitting results, the value of0.1was indicated as the appropriatevalue 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 outletswere fitted with the discharge rate, using both Hydraulic Geometry power function andlogarithmic function models for the Luoyugou (W100,100km~2), Lvergou (W10,10km~2),Qiaozi-East (W1-a,1km~2) and Qiaozi-West (W1-b,1km~2) watersheds. The coefficient ofdetermination (R~2) and model efficiency coefficient (E) were used to evaluate modelcalibration and validation results, respectively. The effect of watershed scale on the modelparameters was examined by using model calibration results from W100, W10and W1-awatersheds. It was found that the parameter k (flow velocity for unit discharge rate) in thepower function model was negatively correlated with watershed size, while parameter m(rate of change of flow velocity) had an opposite correlation with watershed size comparedwith parameter k. In the logarithmic function model, parameter e (rate of change of flowvelocity) had no significant correlation with watershed size, while parameter d (flowvelocity for unit discharge rate) was negatively correlated with watershed size, similar toparameter k The calibration results from the two paired watersheds (W1-a and W1-b) wereused for exploring the effect of watershed land use on the model parameters. Theparameter k in the power function model for W1-a watershed was significantly higher thanthat of W1-b watershed (P<0.001). The parameter m for the two paired watersheds showedno significant difference. The parameter e in the logarithmic function model for W1-bwatershed was higher than that of W1-a watershed, however the difference was notsignificant (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 totest the two function models. The results showed that both of the model functions yieldedacceptable results, nevertheless the power function model generally showed superiorperformance 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 as11slopes,which were connected by a channel. The runoff for each slope in the watershed wascalculated using NRCS-CN model based on watershed rainfall process input for the year1987–2006. A new conceptual method was developed and used to calculate flow routing ofthe runoff from each slope, to derive watershed hydrograph. The predictions for the threeimportant hydraulic variables: runoff, peak discharge rate and time to peak were examined.The absolute error for runoff depth prediction varied from-0.08to7.4mm, the mean was0.35mm; the relative error changed from8%to~(-1)03%, the mean was~(-1)%. The maximumabsolute and relative errors for peak discharge rate prediction were~(-1).85m~3s~(-1)and-63%,and the mean were-0.02m~3s~(-1)and10%, respectively. For the prediction of time to peak,the maximum absolute and relative errors were0.99h and~(-1)09%, and the mean were-0.09h and~(-1)7%. Moreover, the slopes of linear fitting for peak discharge rate and time to peakwere1.09and1.04(both close to1), with coefficients of determination (R~2) both close to1(0.99and0.97). For runoff prediction, the slope and R~2values for the linear fitting were0.83and0.78. The root mean square error (RMSE), model efficiency coefficient (E), andcoefficient of residual mass (CRM) were calculated for the simulations of each hydraulicvariable. It was shown that the simulation of peak discharge rate was best, followed by thatof time to peak, and runoff.
(5) A new method was suggested to accurately measure the discharge from thewatersheds by measuring the flow velocity and using the relationship between flowvelocity and discharge rate. The power function of flow velocity-discharge rate wasestablished by deriving the inverse function of Hydraulic Geometry power function, takingthe 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 fromthe measuring weirs of Luoyugou (W100), Lvergou (W10), Qiaozi-East (W1-a) andQiaozi-West (W1-b) watershed outlets. According to the calculation of coefficients ofdetermination (R~2), the model calibration of W100was best, followed by those of W1-a, W10and W1-b. Based on model efficiency coefficient (E) calculation results, thesimulation accuracy of W1-a watershed was highest, followed by those of W100, W10andW1-b. The study indicated that the derived power function could be used to determinedischarge rate at study watershed outlets. Therefore, a new method was developed formeasuring discharge rate given the measurement of the flow velocity instead of flow depth.
The results of the study contribute to better understanding watershed hydrologicalcycle, and could supply basic tools for the study of water resource optimization, soilerosion, and sediment transport for the small watersheds on the Loess Plateau.
引文
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