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水文循环模拟中下垫面参数化方法综述

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1. 广州地理研究所广东省地理空间信息技术与应用公共实验室,广州 510070

2. 中国科学院地理科学与资源研究所中国科学院陆地水循环及地表过程重点实验室,北京 100101

3. 北京师范大学水科学研究院,北京 100875

4. 安徽理工大学地球与环境学院,淮南 232001

5. 波兰亚当密茨凯维支大学自然地理与环境规划学院,波兹南 61-608

A review of underlying surface parametrization methods in hydrologic models

ZHAOLingling¹^,², LIUChangming²^,³, WUXiaoxiao⁴^,, LIULihong⁴, WANGZhonggen², LeszekSOBKOWIAK⁵

1. Guangdong Open Laboratory of Geospatial Information Technology and Application, Guangzhou Institute of Geography, Guangdong Academy of Sciences, Guangzhou 510070, China

2. Key Laboratory ofWater Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China

3. College of Water Sciences, Beijing Normal University, Beijing 100875, China

4. Department of Earch and Entironment, Anhui University of Science & Technology, Huainan 232001, Anhui, China

5. Institute of Physical Geography and Environmental Planning, Adam Mickiewicz University, Poznan 61-608, Poland

通讯作者:吴潇潇(1992-), 女, 安徽砀山人, 硕士, 研究方向为水文学与水资源。E-mail:zyywxx0910@163.com
收稿日期:2015-11-8
修回日期:2016-03-28
网络出版日期:2016-07-25
版权声明:2016《地理学报》编辑部本文是开放获取期刊文献，在以下情况下可以自由使用：学术研究、学术交流、科研教学等，但不允许用于商业目的.
基金资助:

国家自然科学基金项目(41501046)

广东省水利科技创新项目(2014-14, 2016-14)

广东省自然科学基金项目(2015A030310234)

广东省科学院优秀青年科技人才基金项目(rcjj201303)

广东省科学院平台环境与能力建设专项资金项目(2016GDASPT-0210, 2016GDASPT-0301)

The Scientific Platform and Innovation Capability Construction Program of GDAS, No.2016GDASPT-0210,No.2016GDASPT-0301

展开

摘要
针对水文循环模拟中地形、土地利用覆被等流域下垫面参数化方法众多,且模拟效果相差较大的现状。本文首先根据水文循环模拟中产汇流原理,对常用水文循环模拟中产汇流模拟方法进行汇总和分类;在此基础上,对产流模拟中的降水径流相关系数法、蓄满产流和超渗产流等及汇流模拟中的等流时线、单位线、圣维南方程、马斯京根法等主要模拟方法中地形、土地利用覆被和土壤类型参数化方法进行分析和讨论;根据其中流域地形、土地利用覆被和土壤类型参数化方法对机理过程的描述程度,将其分为无明确表示类、率定型参数类、确定型参数类、物理过程表达类;进而阐明不同参数化方法中流域地形、土地利用覆被和土壤类型对水文循环模拟结果的响应和贡献。最后回归模型本质,阐述水文循环模拟中流域下垫面参数化方法中存在经验关系对复杂机理简单表述的合理性和物理机理过程描述的欠缺性问题,并预估未来水文循环模拟中下垫面参数化方法朝着简洁实用化和复杂机理化两个方向发展。

关键词：水文循环模拟;流域地形;土地利用覆被;流域特征;参数化方法
Abstract
In this paper, firstly, in accordance with the principles of the hydrologic cycle simulation, methods commonly used in the runoff yield simulation were analyzed. On this basis, the rainfall-runoff coefficient of correlation, the storage-full runoff and the runoff yield under excess infiltration applied in the runoff simulations, as well as the methods of isochronic hydrograph, unit hydrograph, the Saint-Venant equations, the Muskingum method applied in the flow concentration simulations, and also parametrization methods of topography, land cover, land use and soil type applied in major simulation methods were analyzed and discussed. In addition, the degree of description of the simulation process mechanism by these parametrization methods of watershed topography, land cover, land use and soil types was discussed and the parametrization methods were divided into different categories, namely: the not clearly expressed category, the rating parameters category, the deterministic parameters category and the expressed by physical processes category. Furthermore, the influence of the applied in different parametrization methods topography, land cover, land use and soil types on the hydrologic cycle simulation results was clarified. Finally, returning to the hydrologic models nature, major drawbacks of the simplified description of complex rational and physical mechanisms existing in the underlying surface parametrization methods in hydrologic models were outlined, and also two directions in the future development of those methods in the hydrologic cycle simulations were discussed.

Keywords：hydrologic cycle simulation;watershed topography;land use;land cover;soil type;watershed characteristics;parametrization

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赵玲玲, 刘昌明, 吴潇潇, 刘丽红, 王中根, 苏磊. 水文循环模拟中下垫面参数化方法综述[J]. , 2016, 71(7): 1094-1104 https://doi.org/10.11821/dlxb201607001
ZHAO Lingling, LIU Changming, WU Xiaoxiao, LIU Lihong, WANG Zhonggen, Leszek SOBKOWIAK. A review of underlying surface parametrization methods in hydrologic models[J]. 地理学报, 2016, 71(7): 1094-1104 https://doi.org/10.11821/dlxb201607001

1 引言

自然界水循环系统是一个多环节的庞大动态系统,水循环基础研究从最初降水、蒸发、截留、下渗、径流等单一过程实验观测开始^[1]。20世纪50年代中期,开始将流域水循环作为完整的系统来研究,随后提出了“流域水文模型”概念,综合研究流域水循环的多过程及其相互作用。流域水循环模拟是应用物理数学及水文学知识,将流域概化成系统,根据输入条件（降雨、流域的蒸散发能力、下垫面等）对流域水文过程进行模拟,进而求出输出结果（流域出口断面的流量过程等）^[2]。水循环模拟是水资源评价、配置、管理和决策的基础,在防洪减灾、水土流失、水资源开发利用、水环境保护、水生态系统修复、道路及城市规划、人类活动的流域响应等方面都需要水文模型的支持^[3-6]。
流域的地形、土地利用覆被和土壤与降水的截留、下渗、蒸发等水文要素密切相关,直接影响产汇流过程和流域出口断面的流量过程,因此下垫面在水文循环模拟中尤其重要^[7]。水文循环模拟中下垫面参数化方法众多,例如,SWAT模型在计算产流时常采用SCS曲线数法,将冠层截留、地表蓄水及产前下渗集成到初损中,不单独计算冠层的降雨截留等;SWMM、HIMS、WEP等模型用Green & Ampt法或Horton法计算下渗后仍要考虑植物截留、洼地填洼等造成的降雨损失;在汇流方面所采用的方法也不尽相同,三水源新安江模型、斯坦福IV、HSPE、HIMS等模型常采用单位线法计算坡面产流,TOPMODEL及DTVGM常采用线性水库法计算坡面产流;河道流量演常采用以圣维南方程组为理论基础的运动波、动力波、扩散波及马斯京根法,不同的汇流方法对下垫面的表述方法与程度也不尽相同;本文通过对水文循环模拟中下垫面参数化方法进行总结分析,探讨地形、土地利用覆被和土壤参数化方法中存在的问题及其未来发展趋势。

2 水文循环物理过程机理及数学表达方法

水流运动遵从连续性方程和能量守恒方程,连续性方程通常在水文循环模拟中称为水量平衡方程。由于水流所处介质和特性的不同呈现不同的形式：土壤水由于其在土壤中的非饱和特性符合土壤水运动的理查兹方程;坡面汇流和河道汇流符合有持续净雨输入源的水动力方程,而无旁支输入的河道汇流则符合圣维南方程;地下水由于其饱和、流动缓慢符合地下水控制方程;由于实际情况复杂和实测资料短缺,动力方程假设条件、初始和边界条件难以满足;在水文循环模拟中,通常用简化方程或经验公式代替动力方程。在产流模拟中土壤水运动的Richards方程通常只考虑垂向的下渗,基于动力方程的下渗理论虽然提供了揭示下渗规律和分析影响因素的工具,基于上述原因通常由经验下渗公式代替,如Kostiakov公式、霍顿公式、菲利普公式、Holtan公式、Smith公式、Simth-Parlange公式等;而在水文循环模拟的坡面汇流方面,坡面汇流的动力模型简化主要有基于线性叠加原理的等流时线、单位线过程线、汇流曲线、瞬时过程线等,河道汇流的动力波方程通过对水流惯性项和河道附加比降的忽略简化为扩散波和运动波方程,而在求解过程中和水文学方法相结合的特征河长法和马斯京根法等;地下水汇流的运动方程通常简化为线型水库和非线性水库方法。

2.1 土壤水运动的Richards方程

1931年理查兹通过实验证明非饱和土壤水运动符合达西定律,即非饱和水流的渗流速度与总土水势梯度成正比,且与土壤中空隙通道的几何性质有关。即：

\begin{matrix} v = - K (θ) \frac{? φ}{? x} \end{matrix}

（1）
与土壤水运动的连续方程：

\begin{matrix} - \frac{? θ}{? t} = \frac{? v_{x}}{? x} + \frac{? v_{y}}{? y} + \frac{? v_{z}}{? z} \end{matrix}

（2）
得到三维理查兹方程：

\begin{matrix} \frac{? θ}{? t} = \frac{?}{? x} (K (θ) \frac{? φ}{? x}) + \frac{?}{? y} (K (θ) \frac{? φ}{? y}) + \frac{?}{? z} (K (θ) \frac{? φ}{? z}) \end{matrix}

（3）
通常在水文循环模拟中仅考虑垂直方向的非饱和水流运动,则简化为垂向一维理查兹方程：

\begin{matrix} \frac{? θ}{? t} = \frac{?}{? z} (K (θ) \frac{? φ}{? z}) \end{matrix}

（4）
该方程是水文循环过程中下渗和土壤蒸发机理讨论的基本依据。

2.2 汇流动力方程

天然河道里的洪水波运动属于非恒定流。其水力要素随时间空间变化。1871年法国的Barre de Saint-Venant提出了非恒定流的基本方程组,当无旁侧入流时其形式如下：

\begin{matrix} \frac{? A}{? t} + \frac{? Q}{? L} = 0 \end{matrix}

（5）

\begin{matrix} - \frac{? Z}{? L} = S_{f} + \frac{1}{g} \times \frac{? v}{? t} + \frac{v}{g} \times \frac{? v}{? L} \end{matrix}

（6）
式中：A为过水断面（m²）;Q为过水断面流量（m³/s）;L为沿河道的距离（m）;Z为水位（m）;v为断面流速（m/s）;S_f为摩阻比降。

2.3 地下水运动的控制方程

地下水运动的连续方程：

\begin{matrix} \frac{?}{? t} [ρ_{w} n ? x ? y ? z] = - [\frac{? (ρ_{w} v_{x})}{? x} + \frac{? (ρ_{w} v_{y})}{? y} + \frac{? (ρ_{w} v_{z})}{? z}] ? x ? y ? z \end{matrix}

（7）
能量守恒方程：

\begin{matrix} \{\begin{matrix} v_{x} = - K_{sx} \frac{? φ}{? x} \\ v_{y} = - K_{sy} \frac{? φ}{? y} \\ v_{z} = - K_{sz} \frac{? φ}{? z} \end{matrix} \end{matrix}

（8）
式中：ν_x、ν_y、ν_z分别为X、Y、Z方向上的地下水流速;K_sx、K_sy、K_sz分别为3个方向上的饱和渗透系数。

3 水文循环模拟中常用产汇流模拟方法

水文循环模拟中产流模拟方法主要有：蓄满产流、超渗产流、混合产流和降雨径流相关关系等方法^[8-9]（表1）。
Tab. 1
表1
表1常用水文模型产流方法汇总
Tab. 1The classification of runoff yield methods in hydrological model

产流类型	产流计算方法	常用模型
降水径流相关关系	SCS、非线性产流方法	DTVGM^[10-12]、HIMS^[13-14]、SWMM^[15]、SWAT^[16-17]、HEC-HMS^[18]
蓄满产流	土壤蓄水容量曲线	新安江^[19]、VIC^[20-21]、EasyDHM^[22-23]
蓄满产流	地形指数	TOPMEDEL^[24-25]、TOPKAPI^[26]
超渗产流	土壤下渗能力曲线	陕北模型^[19]、水箱模型^[32]、EasyDHM、TOPMEDEL、VIC
超渗产流	Green-Ampt	SWAT、WEP、HIMS、SWMM、PRMS^[32]、HEC-HMS
动力方程法	Richards方程	VIC、WEP^[28]、VIP^[29]、MIKE SHE^[30-31]

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水文循环模拟中汇流模拟包括坡面汇流计算及河道洪水演算（表2）。河道汇流模拟方法主要有：圣维南方程组、运动波方程、动力波方程、扩散波方程、惯性波方程、水库调洪演算法、马斯京根法（Muskingum）、Muskingum-Cunge法、变量存储系数法等^[33]。在大、中型流域,研究地表径流汇流时,常忽略坡面汇流阶段,只考虑河道演算,但在小流域汇流中不能忽略坡面汇流,坡面汇流模拟方法主要有：等流时线、单位线法、线性水库方程、非线性水库方程、运动波方程^[34]。
模型的应用目的和模型的时间尺度有关,通常洪水预报要求小时尺度甚至分钟;而水资源管理要求日或者月尺度;气候变化等的环境评价月尺度即可满足要求。由于不同时间尺度对产汇流过程描述的刻画细致程度要求不同,所以,即使同一模型不同时间尺度在产汇流过程模拟中选取的方法差异较大,进而模型对数据的需求程度也不同。
Tab. 2
表2
表2常用水文模型汇流方法汇总
Tab. 2The classification of confluence methods in hydrological model

汇流过程	汇流计算方法	模型
坡面汇流	单位线法	新安江模型、SWMIV、HSPF、HEC-1、TOPMODEL、VIC-3L、HIMS、SWAT
	等流时线法	新安江模型、HIMS
	线性水库方程	新安江模型、TOPMODEL、DTVGM
	非线性水库方程	SWMM、TOPKAPI
河道汇流	运动波方程	HEC-1、TOPKAPI、DTVGM、WEP-L^[36]、EasyDHM
	动力波方程	SHE、VIC-3L^[35]、PRWS、WEP-L
	马斯京根法	新安江模型、HBV、HEC-1、SWAT、HIMS、EasyDHM
	变量存储系数法	SWAT、EasyDHM

新窗口打开

4 产流模拟中土地利用覆被与地形参数化方法

4.1 植物截留与填洼

4.1.1 植被截留在水文过程模拟中,截留主要受自然特性、植被覆盖类型及密度、季节、降水特性等因素的影响。在实际应用中通常采用经验模型,如Horton模型（1919）、LKP模型（1949）、Meriam模型（1960）等。Horton提出了用于不同植物的一系列经验方程,应用比较广泛的经验公式（表3）,参数S_v、C采用经验值。
Tab. 3
表3
表3产流原理公式汇总
Tab. 3The summary of runoff formation methods

产流方法		主要原理	主要公式	参数	确定方法	备注
植被截留		Horton经验公式	$\begin{matrix} I_{n} = S_{v} + C P_{c} \end{matrix}$ ^[32]	S_v、C	经验值	I_n为截留损失;S_v为林冠遮蔽区植被的蓄水能力;P_c为植被覆盖处降雨
洼地填洼		流域上填洼量的大小与洼地的分布和降雨量有关	$\begin{matrix} V = a exp (- bs) \end{matrix}$ $\begin{matrix} V = (I - f) \exp (- kPe) \end{matrix}$ ^[37-39]	s、k	由实测资料及公式计算获得	V为洼地容积;s为洼地蓄量;I为雨强;f为下渗率;Pe为净雨量;a、b、k为常数
降雨径流相关关系法	SCS曲线数方法	是在实测资料的基础上经过统计分析并总结而得到的经验关系	$\begin{matrix} Q_{surf} = \frac{(R_{day} - I_{a})^{2}}{(R_{day} - I_{a} + S)} \end{matrix} \begin{matrix} S = 25.4 (\frac{1000}{CN} - 10) \end{matrix}$ ^[40-41]	CN	查表获得	Q_surf为日地表径流;R_day为日降水量;I_a为初损量;S为截留量;CN为流域综合参数
降雨径流相关关系法	非线性时变增益产流方法	降雨径流的系统关系是非线性的,其重要的贡献是产流过程中土壤湿度（即土壤含水量）不同所引起的产流量变化	$\begin{matrix} R (t) = G (t) X (t) \end{matrix}$ $\begin{matrix} G (t) = g_{1} + g_{2} API (t) \end{matrix}$ ^[12,42]	N值	经验值	R（t）为有效净雨;X（t）为降雨;G（t）为系统增益,与流域土湿有较理想的线性近似关系;g₁、g₂分别为产流模型参数;N为效力参数
蓄满产流	流域需水容量曲线法	流域蓄水容量曲线是将流域内各地点包气带的蓄水容量,按从小到大顺序排列得到的一条蓄水容量与相应面积关系的统计曲线	$\begin{matrix} α = 1 - {(1 - \frac{W M^{'}}{WMM})}^{b} \end{matrix}$ $\begin{matrix} WM = \frac{WMM}{1 + b} \end{matrix}$ ^[44]	WM、b	由公式计算获得	WM′为各地点包气带蓄水容量值,WMM为其中的最大值;α为流域面积的相对值;WM为全流域平均的蓄水容量;b为常数
	地形指数	壤中流始终处于稳定状态,单宽集水面积由α_i表示,饱和地下水的水力坡度由地表局部坡度tanβ_i表示	$\begin{matrix} Q_{b} = A T_{0} \exp (- λ^{}) \exp (- \overset{?}{z} / S_{zm}) \end{matrix} \begin{matrix} λ^{} = \frac{1}{A} \int_{A} \ln (\frac{α_{i}}{\tan β_{i}}) dA \end{matrix}$ ^[24-25]	A、 $\begin{matrix} \overset{?}{z} \end{matrix}$ 、T₀、S_zm	由实测资料及公式计算获得	Q_b为壤中流;T₀为饱和导水率;A为流域面积; $\begin{matrix} \overset{?}{z} \end{matrix}$ 为流域平均地表水面深度;S_zm为非饱和区最大蓄水深度
	Richards方程	Richards在1931年研究流体通过多孔介质中毛细管传导作用时推导得到	$\begin{matrix} \frac{? θ}{? t} = \frac{?}{? x} [K_{x} (θ) \frac{? ?}{? x}] \\ + \frac{?}{? y} [K_{y} (θ) \frac{? ?}{? y}] \\ + \frac{?}{? z} [K_{z} (θ) \frac{? ?}{? z}] \end{matrix}$ ^[45-46]	K	由公式计算获得	θ为含水量;t为时间;K为渗透系数;φ为非饱和土壤的总土水势;x、y、z分别表示坐标轴方向
超渗产流	下渗曲线法	判别降雨是否产流的标准是雨强是否超过下渗能力,因此,用实测的雨强过程扣除下渗过程,就可得净雨过程,即产流量过程	$\begin{matrix} F_{P} (t) = a + bt - a e^{- βt} \end{matrix}$ $\begin{matrix} a = \frac{1}{β} (f_{0} - f_{c}), b = f_{c} \end{matrix}$ ^[8]	β、f₀、f_c	实测获得	F_p（t）为t时刻累积下渗水量;β为系数;f₀为起始下渗率;f_c为稳定下渗率
	初损后损法	下渗曲线法的一种简化方法,它把实际的下渗过程简化为初损和后损两个阶段	$\begin{matrix} P_{et} = \{\begin{matrix} 0 ? ? \sum P_{i} < I_{a} \\ P_{t} - f_{c} \sum P_{i} > I_{a}, P_{t} > f_{c} \\ 0 ? \sum P_{i} > I_{a}, P_{t} < f_{c} \end{matrix} \end{matrix}$ ^[47-48]	I_a、f_c	由实测资料及公式计算获得	P_et为净雨量;P_t为t~t+Δt时段面平均雨量;I_a为降雨初损量;f_c为流域最大潜在的降雨损失率
	盈亏常数法	认为初损量是随着时间和降雨的发展而变化的变量,在长期不降雨后,初损量会逐渐恢复至初值	$\begin{matrix} I_{at} = I_{a} - P_{t} + V_{t} \end{matrix}$ ^[47-48]	I_a、f_c、v_c	由实测资料及公式计算获得	I_at为t时刻的初损量;I_a为最初的初损量;P_t为t时刻的降雨量;V_t为t时刻的初损恢复量
	Green&Ampt(物理概念公式)	假定入渗过程中湿润锋面始终为一个干湿截然分开的界面,湿润锋前为初始含水量,湿润锋面处存在一个固定不变的吸力	$\begin{matrix} f_{t} = K [\frac{1 + (φ - θ_{t}) S_{t}}{F_{t}}] \end{matrix}$ ^[49]	K、S_t、 $\begin{matrix} θ_{t} \end{matrix}$ 、 $\begin{matrix} φ \end{matrix}$	可以通过具体实验测定,也可以采用参考值	f_t为t时段的降雨损失;K为饱和水力传导度;F_t为体积土壤缺水量;S_t为t时刻的累积降雨损失; $\begin{matrix} (φ - θ_{t}) \end{matrix}$ 为湿润土厚度
	Horton(经验公式)	认为下渗率不仅是时间的函数,还应该跟土壤含水量的状态有关。土壤含水量大,则下渗能力低,渗透率增加	$\begin{matrix} f_{p} = f_{c} + (f_{0} - f_{c}) e^{- kt} \end{matrix}$ ^[50-51]	K、f_c	经验值、具体实验测定	f_p为下渗容量;f₀为初始下渗容量;f_c为稳定下渗率;k为经验参数;t为入渗历时
	Kostiakov(经验公式)	认为在下渗过程中,下渗容量f_p与累积下渗量F_p成反比;α为比例常数	$\begin{matrix} f_{p} = \sqrt[]{\frac{α}{2}} t^{- \frac{1}{3}} \end{matrix}$ ^{[8-9, 32]}	α	经验值	f_p为下渗容量;α为经验参数;t为入渗历时
	Philip (经验公式)	认为在下渗过程中,（f_p-f_c）与（F_p-f_ct）成反比;α为比例常数	$\begin{matrix} f_{p} = \sqrt[]{\frac{α}{2}} t^{- \frac{1}{2}} + f_{c} \end{matrix}$ ^[52]	α、f_c	经验值、具体实验测定	f_p为下渗容量;f_c为稳定下渗率;α为经验参数;t为入渗历时
	Hotan (经验公式)	基于蓄量概念的下渗经验公式	$\begin{matrix} f_{p} = GI \times α \times S A^{1.4} + f_{c} \end{matrix}$ ^{[8-9, 32]}	α、f_c	根据土壤类型及作物情况确定	f_p为下渗容量;SA为表层土壤缺水量;GI为作物生长指数;α为地面孔隙率指数;t为入渗历时
	Smith (经验公式)	认为下渗率受限于降雨强度,然后土壤表面的水压力水头开始趋于零,而t_p时刻开始出现径流	$\begin{matrix} f_{p} = f_{\infty} + A (t - t_{0})^{- α} \end{matrix}$ ^{[8-9, 32]}	A、t₀、α	经验值	f_p为下渗容量;f_∞为理论上等于饱和水力传导度;A、t₀、α分别为与土壤类型、初始土壤含水量和雨强有关的参数
	Smith-Parlange (经验公式)	可用来计算积水后的积水时间和下渗容量	$\begin{matrix} \int_{0}^{t_{p}} idi = \frac{B (θ_{i})}{i_{p} - K_{s}} \approx \frac{\frac{s^{2}}{2}}{i_{p} - K_{s}} \end{matrix}$ ^[53]	i_p、s	根据土壤性质或是下渗试验获得	i_p为积水时的雨强;s为菲利普定义的吸收度;K_s为饱和水力饱和度

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4.1.2 洼地填洼在平原及坡水区,由于地面洼陷较多,填洼量较大,洼地填洼在很大程度上改变流域响应,Ullah等^[37-38]于1979年提出了洼地容积V（cm³）与地表坡度s之间的关系（表3）;根据洼地特征,Linsley^[39]于1975年推导出洼地储蓄容量V与洼地蓄量S之间的关系（表3）,可看出在产流过程模拟中,地形的不同对洼地填洼的影响较大。

4.2 降雨径流相关关系法

4.2.1 SCS曲线数法 SCS曲线数法是在实测资料的基础上经过统计分析并总结而得到的经验关系,在计算地表径流时,SCS曲线数法将冠层截留、地表蓄水及产前下渗集成到初损中,因此当计算地表径流时,不必单独计算冠层的降雨截留等^[40]。SCS曲线数法计算地表径流的经验公式及截留量的计算公式如表3所示。土地利用覆被对产流过程的影响主要是通过CN值反映,CN值越大说明流域的截留量越小,地表径流产流量越大。SCS模型的开发者给出了一套详细的CN值查询表,但是由查表得到的CN值计算的产流量误差太大,在实际应用中CN值的确定仍然是SCS曲线数方法应用的瓶颈^[41]。
4.2.2 非线性时变增益产流方法水文非线性系统的时变增益模型（TVGM）是夏军提出的一种简便有效的水文非线性系统方法,总结流域产流的主要公式（表3）^[42]。DTVGM月模型可采用Bagrov模型的效力参数N值,对流域土地利用类型进行分类赋值^[43]。

4.3 蓄满产流

4.3.1 流域蓄水容量曲线法流域的产流过程在空间上是不均匀的,在全流域蓄满前存在部分地区蓄满而产流,一般可由流域蓄满容量曲线表征土壤缺水量空间分布的不均匀性,流域蓄水容量曲线公式见表3。在水循环模拟中常输入的参数有流域平均蓄水容量WM、流域蓄水容量分布曲线指数b,WM值与流域干旱情况有关,常数b则反映流域蓄水容量的不均匀性^[44],流域蓄水容量曲线法对流域地形、土地利用覆被及土壤对产流的影响没有明确表述,但参数b隐含地表示了下垫面的影响。
4.3.2 地形指数 Beven等^[24-25]提出的地形指数模型（TOPMODEL）,主要是利用地形指数ln(α/tanβ)来反映流域水文现象,通过流域含水量来确定源面积的大小,含水量由地貌指数确定。地形指数和含水量的关系根据稳态理论进行推导,即假定流域的地下水位动态变化可以由单位面积均匀壤中流控制,用局部坡面角近似表示侧向地下径流通量,流域内地貌指数值相等两点具有水文相似性。

4.4 超渗产流方法

4.4.1 下渗曲线法流域的下渗规律用下渗曲线来表示（表3）,采用下渗曲线法进行产流计算时,为了提高计算精度,降低降雨强度时空分布的不均匀性对产流的影响,降雨时段长度不宜大,常以分钟计,流域也应按雨量站分布状况划分为较小的单元区域进行产流计算。但流域下渗能力曲线的确定需要很多径流资料或实地试验才能获得,在实际应用中往往难以实现。
应用中对下渗能力曲线通常采用初损后损法和盈亏常数法进行简化,初损后损法是下渗曲线法的一种简化方法,它把实际的下渗过程简化为初损和后损两个阶段。产流以前的总损失水量称为初损,以流域平均水深表示;后损主要是流域产流以后的下渗损失,以平均下渗率f_c表示。Skaggs等^[27]给出了不同土壤类型f_c的参考值,在缺少数据的条件时,可以根据此参考值初步设定流域的下渗率;盈亏常数法与初损后损法类似,但其与初损后损法不同的是,盈亏常数法认为初损量是随着时间和降雨的发展而变化的变量,在长期不降雨后,初损量会逐渐恢复至初值,因此,除了初损量I_a和后续下渗率f_c两个参数外,还需要给定恢复速率v_c。
4.4.2 下渗公式下渗公式主要分为物理概念公式和经验下渗公式两类,常见的物理概念公式有Green&Ampt;经验下渗公式应用较多的有Horton、Kostiakov、Philip、Hotan、Smith、Smith-Parlange（表3）,采用经验下渗公式计算产流时,确定参数常采用经验值。
综上,水文循环模拟在产流过程的植被截留中考虑土地利用覆被对水循环的影响,在填洼过程中考虑地形对水循环的影响,而在主要的产流方法中,降雨径流相关关系主要通过试验得到的经验关系或者半定量的关系来刻画下垫面的影响,在蓄满产流方法中主要通过率定型的经验参数考虑地形和土地利用的影响;而超渗产流法通常在下渗曲线中通过下渗公式中的经验参数对下垫面中的土壤进行描述,地形和土地利用覆被则是隐含影响因素,并没有直接表述。

5 汇流模拟中流域下垫面参数化方法

5.1 坡面汇流模拟

经验性地表汇流模拟以线性叠加理论为基础,主要的方法有等时流线法、单位线（包括时段单位线、瞬时单位线、地貌单位线）及线性水库等简化的方法^[54]。
5.1.1 等流时线法等流时线法则是将汇流的物理过程简化,能够较好的应用到分布式水文模型中,等流时线法的原理及主要公式如表4所示。汇流速度确定是等流时线法的关键,通常根据流域已有实测资料和经验给定,所以该方法对流域下垫面的作用无明确表述,暗含在等流时线的经验参数中。
Tab. 4
表4
表4汇流原理及公式汇总
Tab. 4The summary of flow concetration methods

汇流方法			主要原理	主要公式	参数	确定方法	备注
坡面汇流	等流时线		假定流域中存在着等流时线,认为在同一条等流时线上的水滴将同时流到出口断面,采用汇流速度得出了等流时线的分布	$\begin{matrix} Q_{t} = \frac{1}{Δt} \overset{k_{2}}{\sum_{j = k_{1}}} r_{d, j} Δ A_{t - j + 1} \end{matrix}$ ^[54]	c	多以洪峰附近的流速值为主要依据确定汇流速度c值	Q_t为t时段末的出流量;r_d为时段净雨量;ΔA_i为第i块等流时面积;Δt为单位时段长;t为流量时序;k₁、k₂分别为累积界限
	单位线	时段单位线	将流域看作一个系统,假定系统是线性的、时不变的,即净雨产生的径流可由线性运算出来	$\begin{matrix} Q_{d, t} = \overset{k_{2}}{\sum_{j = k_{1}}} r_{d, j} q_{t - j + 1} \end{matrix}$ ^[54]	r_d、q	分析法、试错法、最小二乘法、图解法等	Q_d为流域出口断面时段末直接径流流量;r_d为时段净雨量;q为单位线时段末流量
		瞬时单位线(J.E.Nash)	一个单位的瞬时入流通过串联的n个等效线性水库的调蓄,其出流就是IUH	$\begin{matrix} u (t) = \frac{1}{KΓ (N)} {(\frac{t}{K})}^{N - 1} e^{- t / K} \end{matrix}$ ^[55-56]	N、K	用矩阵法求参数,也可根据地形信息求N值,然后用最优化方法求K值	N为串联线性水库个数;K为线性水库内水流传播时间
		地貌瞬时单位线	假定瞬时注入流域分布均匀的净雨量是由多个水质点组成的,又假定各水质点间成弱相关性,因此求流域瞬时单位线就是水质点滞留时间概率密度函数	$\begin{matrix} Q (t) = I_{0} * f_{B} (t), t > 0 \end{matrix}$ $\begin{matrix} f_{B} (t) = \frac{d F_{B} (t)}{d (t)} \\ = \sum^{} f_{x_{1}} \times f_{x_{2}} \times ? \times f_{x_{k}} (t) p (s) \end{matrix}$ ^[57-58]	流速	由公式计算获得	I₀为净雨量;f_xi为滞留时间T_xi的概率密度函数;p(s)为路径概率; $\begin{matrix} * \end{matrix}$ 为卷积相乘
		SCS模型单位线	SCS模型单位线的净雨时段是变化的,故不能给出各时段的无因次单位线纵坐标值,因此,在转绘此无因次单位线时必须十分准确	$\begin{matrix} q_{p} = \frac{0.208 FR}{t_{p}}, t_{p} = \frac{2}{3} t_{c} \\ t_{c} = \frac{5}{3} L, L = \frac{l^{0.8} {(S + 25.4)}^{0.7}}{7069 y^{0.5}} \end{matrix} \begin{matrix} D = 0.133 t_{c} \end{matrix}$ ^[41]	$\begin{matrix} q_{p} \end{matrix}$ 、L、D	根据公式获得	$\begin{matrix} q_{p} \end{matrix}$ 为单位线洪峰流量;L为洪峰滞时;D为单位线时段长
	线性水库方程		流量水量平衡方程式和蓄量方程式	$\begin{matrix} K \frac{dQ}{dt} + Q = I \end{matrix}$ ^[62-63]	K	水文分析法	K为蓄量常数(平均流域汇流时间)
	非线性水库方程		流量水量平衡方程式和蓄量方程式	$\begin{matrix} nk Q^{n - 1} \frac{dQ}{dt} + Q = I \end{matrix}$ ^[62-63]	n、k	水文分析法	n、k为常数
河道流量演算	圣维南方程组		由连续方程和动量方程组成,其基本定律为质量守恒定律和动量守恒定律	$\begin{matrix} \frac{? A}{? t} + \frac{? Q}{? x} = 0 \end{matrix}$ $\begin{matrix} - \frac{? Z}{? x} = S_{f} + \frac{1}{g} \frac{? υ}{? t} + \frac{υ}{g} \frac{? υ}{? x} \end{matrix}$ ^{[32, 62]}	n、C、K	通过查表获得	x为沿河道距离;Z为水位;υ为断面平均流速;n为曼宁糙率系数;C为谢才系数;K为流量模数
	简化动力方程式	运动波方程	以圣维南方程组为理论基础,忽略动量方程中的惯性项和附加比项	$\begin{matrix} \frac{? Q}{? t} + c_{k} \frac{? Q}{? x} = 0, c_{k} = ηυ \end{matrix}$ ^59]	η	根据实测资料按照公式获得	η为波速系数
		扩散波方程	以圣维南方程组为理论基础,忽略动量方程中的惯性项	$\begin{matrix} \frac{? Q}{? t} + c \frac{? Q}{? x} = μ \frac{?^{2} Q}{? x^{2}} \end{matrix}$ ^[60-61]	C、η	根据实测资料按公式获得	c为波速;η为扩散系数
		动力波方程	动量方程中的每项均不可忽略	$\begin{matrix} \frac{? A}{? t} + \frac{? Q}{? x} = 0 \end{matrix}$ ^[60-61] $\begin{matrix} υ \frac{? υ}{? x} + \frac{? υ}{? t} + g \frac{? y}{? x} = g (i_{0} - \frac{υ^{2}}{C^{2} R}) \end{matrix}$	n、C、K	通过查表获得	n为曼宁糙率系数;C为谢才系数;K为流量模数
	经验关系代替动力方程式	水库调洪演算法	水量平衡方程和槽蓄方程	$\begin{matrix} V_{2} + \frac{Δt}{2} Q_{2} \\ = \frac{Δt}{2} (I_{1} + I_{2}) + V_{1} - \frac{Δt}{2} Q_{1} \end{matrix}$ ^[63]	I、Q、V	图解法、试错法	I为入流量;Q为出流量;V为河段槽蓄量
		Muskingum法	水量平衡方程和槽蓄方程	$\begin{matrix} Q_{2} = C_{0} I_{2} + C_{1} I_{1} + C_{2} Q_{1} \end{matrix}$ $\begin{matrix} C_{0} = \frac{0.5 Δt - KX}{0.5 Δt + K (1 - X)} \end{matrix}$ ^[64] $\begin{matrix} C_{1} = \frac{0.5 Δt + KX}{0.5 Δt + K (1 - X)} \end{matrix} \begin{matrix} C_{2} = \frac{- 0.5 Δt + K (1 - X)}{0.5 Δt + K (1 - X)} \end{matrix}$	K、X	可用河段的水力学和地形特征表示参数;也可用最小二乘法、图解法、矩阵法等确定参数	K为蓄量常数;X为常数,有各种解释,其范围和它的解释是相互依赖的
		Muskingum-Cunge法	Muskingum-Cunge法是对Muskingum的改进,最大的区别在于参数K、x的确定,Muskingum-Cunge法的参数是由水流资料确定的	$\begin{matrix} Q_{2} = C_{0} I_{1} + C_{1} I_{2} + C_{2} Q_{1} + C_{3} Q_{lat} \end{matrix}$ C₀、C₁、C₂、公式同上 $\begin{matrix} C_{3} = \frac{Δt}{0.5 Δt + K (1 - X)} \end{matrix}$ $\begin{matrix} K = \frac{Δx}{c} \end{matrix} \begin{matrix} X = \frac{1}{2} (1 - \frac{Q}{cΔxB S_{0}}) \end{matrix}$ ^[65-66]	K、X	由实测水流资料确定的	c为波速;Q_lat为旁侧入流;B为水面宽度;S_o是河床坡度
		变量存储系数法	对马斯京根法的改进,考虑到河段的洪水波传播时间与河段长度和坡度有关,不同河段K值应该不同	$\begin{matrix} K = \frac{L}{V_{c}}, V_{c} = \frac{5 V}{3}, V = \frac{R^{\frac{2}{3}} \sqrt[]{i}}{n} \end{matrix}$	x、n、R	通过查表、公式计算获得	x为常数;n为曼宁系数;R为水力半径

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5.1.2 单位线单位线是一种经验的模拟方法,将流域看作一个整体,不考虑净雨与下垫面的不均匀性,符合倍比性及叠加性条件（表4）。由Nash^[55-56]根据串联线性水库概念,利用流域的空间特性对单位线法进行改进,提出了瞬时单位线的概念,但Nash瞬时单位线在参数确定仍具有一定的经验性,并不能完全根据流域下垫面信息确定单位线。1979年,Rodriguez-IturbeI^[57],提出了地貌瞬时单位线（GIUH）的概念,利用概率论法将流域下垫面信息与单位线联系起来,随后Gupta等^[58]对其进行了扩展,提出由地形、地貌参数及水力参数表达的地貌单位线公式。采用地貌瞬时单位线来确定汇流过程是解决无资料地区汇流模拟的有效途径。Nash瞬时单位线和地貌单位线在方法上对产流中流域地形地貌的影响有基于物理机理的刻画,但仍是基于流域是一个整体的假设,因此,不能对汇流过程实现空间描述和模拟,无法处理较大流域中降水不均匀的情况。

5.2 河道流量演算

河道流量演算是以由水流连续方程和能量守恒方程组成圣维南方程组为理论基础。圣维南方程组是基于物理机理的河道汇流方程,对河道坡降、糙率均有考虑,同时方程组属于一阶双曲型拟线性偏微分方程组,利用数值解法可以求解,但是求解过程比较复杂,且不一定得到好的效果。
5.2.1 简化动量方程式对圣维南方程组的动力方程式进行简化,忽略其中的不同项可得到不同形式的洪水波（运动波、动力波、扩散波、惯性波等）。目前比较常用的有运动波、动力波、扩散波,忽略动力方程中的惯性项和附加比所描述的洪水波是运动波;扩散波忽略动量方程中的惯性项;动力波动量方程中的每一项^[59-60]。与其他方法相比采用运动波法计算汇流所需要的地貌信息较少,应用相对简单,因此,运动波在坡面汇流和分布式水文模型汇流计算中比较广泛^[61]。运用圣维南方程组及简化动量方程式计算汇流时对地形信息的要求主要是实测的河道断面资料。
5.2.2 其他经验关系代替动力方程式此类算法将圣维南方程组中的连续性方程简化为河段水量平衡方程:

\begin{matrix} \frac{I_{1} + I_{2}}{Δt} - \frac{Q_{1} + Q_{2}}{Δt} = V_{2} - V_{1} \end{matrix}

（9）
式中：I₁、I₂为时段初、末的入流量;Q₁、Q₂为时段初、末的出流量;和V₁、V₂为时段初、末的河段槽蓄量;Δt为时段。
动力方程简化为河段的水量槽蓄方程,用I、Q、V之间的某种近似关系代替,通过河段的入流过程演算出流过程,不同的近似关系得到不同的演算方法,常用的演算方法有水库调洪演算法^[62-63]、马斯京根法（Muskingum）^[64]、Muskingum-Cunge^[65-66]法及变量存储系数法（表4）。Muskingum在具体应用时首先要确定参数K和X。K是河段平均传播时间,其值依赖于河段长度和波速。参数X表示入流和出流对蓄量的相对影响,X取值范围为[0~1]。K、X的确定存在一定的经验性。Muskingum-Cunge法是由Cunge在Muskingum法的基础上提出的,与Muskingum法最大的区别是参数K、X的确定,Muskingum-Cunge法参数K、X可以根据时间步长、河床坡度及洪水波速等直接计算（表4）。Muskingum-Cunge法能够在一定程度上反映流域地貌和河网结构的空间特性对汇流过程的影响。
地形地貌对汇流过程影响较大,也是研究最多的影响因子。对小流域而言,地表覆被等下垫面特征会通过糙率等水力学特性影响径流过程,目前的研究还多侧重于有实测资料地区,或通过建立经验关系实现。
在水文循环模拟计算河道流量演算时,需要对坡地及河道进行适当的概化或简化,部分或全部的忽略坡面或河道水力特性的空间变化,而采用统一的参数对其进行调试,这在很大程度上限制了方法本身对汇流过程的空间描述能力和精度。

6 流域水文循环模拟中产汇流参数化方法分类

根据流域水文循环模拟中对地形和土地利用覆被参数化方法对产汇流中机理过程的描述程度将其分为4类,即：对地形和土地利用覆被在产汇流中的作用无明确表示的无明确表述类、用经验参数表示地形和土地利用覆被在产汇流中的作用,但经验参数根据实测资料率定的率定型参数类、根据地形和土地利用覆被与产汇流过程经验关系通过查表或简单计算得到表示参数值的确定型参数类、根据地形和土地利用覆被与产汇流过程物理关系的参数化方案归为物理过程表达类。按照产汇流模拟中流域下垫面中流域地形、土地利用覆被和土壤类型参数化对其物理机理描述程度将其分类如表5和表6所示。
Tab. 5
表5
表5常用产流参数化方法分类表
Tab. 5The classification of parameterization in runoff yield process

产流方法		类别
降雨径流相关关系法	SCS曲线数方法	确定型参数类
降雨径流相关关系法	非线性时变增益产流方法	确定型参数类
蓄满产流	土壤需水容量曲线法	率定型参数类
	地形指数	确定型参数类
	Richards方程	物理概念型
超渗产流	下渗曲线法	无明确表达类
	初损后损法	无明确表达类
	盈亏常数法	率定型参数类
	Green&Ampt(物理概念公式)	物理概念型
	Horton(经验公式)	率定型参数类
	Kostiakov(经验公式)	率定型参数类
	Philip(经验公式)	率定型参数类
	Hotan(经验公式)	率定型参数类
	Smith(经验公式)	率定型参数类
	Smith-Parlange(经验公式)	率定型参数类

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Tab. 6
表6
表6常用汇流参数化方法分类表
Tab. 6The classification of flow concentration methods

汇流方法			类别
坡面汇流	等流时线		率定型参数类
	单位线	时段单位线	无明确表达类
		瞬时单位线(J.E.Nash)	率定型参数类
		地貌瞬时单位线	物理概念型
		SCS模型单位线	确定型参数类
	线性水库方程		率定型参数类
	非线性水库方程		率定型参数类
河道流量演算	圣维南方程组		物理概念型
	简化动力方程	运动波方程	确定型参数类
		扩散波方程	确定型参数类
		动力波方程	确定型参数类
	其他经验关系代替动力方程	水库调洪演算法	率定型参数类
		Muskingum法	率定型参数类
		Muskingum-Cunge法	率定型参数类
		变量存储系数法	率定型参数类

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7 讨论和未来发展趋势预估

在常用的流域水循环模拟中,对流域下垫面中地形、土地利用覆被和土壤类型在产汇流中的物理机理描述程度多为经验参数类,而经验参数多以率定方式来确定,确定型参数类一般是根据参数表或者经验关系来确定;物理过程表达类虽然有确定的物理方程来表示其响应关系,且随着计算技术的发展,复杂方程的求解问题变得简单,但复杂方程增加了模型待确定参数,往往缺乏观测资料支撑。
模型是对客观现实过程的一种模拟或者抽象,流域水文循环模拟是对自然界中复杂水循环过程的一种抽象。模型的建立一类用于对水文循环自然规律的研究和探索,这类模型通过各类实验和数学方程逼近现实过程,对自然界水循环机理过程进行较为准确的刻画,随着物理数学技术的进步,这类模型也更为复杂,机理刻画更为准确,例如SHE模型;而另一类模型为了解决某一现实问题而构建,通常对模拟精度影响不大的过程加以简化,以最简单的计算,最小的数据需求,达到实际应用精度为原则,随着机理认识的深入,这类模型通常会更加简洁实用,例如TVGM。
而水文循环模拟中流域下垫面参数化方法的发展趋势与水文模型的发展趋势一致,一类用简洁方法描述主要规律达到实用需求,例如系统模型;另一类为尽可能详尽刻画现实过程探讨其物理机理,例如VIC模型。上文中无明确表达类、率定型参数类及部分确定型参数类属于前一类,该类参数化方法力求用简化的经验关系表示下垫面在流域水循环中的作用,通常采用实测数据来率定该关系,但采用率定的关系表述,能否反映流域下垫面的作用及该关系是否反映该复杂机理的简单规律有待进一步的讨论和验证;物理表达类和部分确定型参数类属于第二类,该类参数化方法具有或者部分具有物理机理,但这类方法较少,未来研究有较大探索空间。

8 讨论

水文循环模拟中下垫面参数化方法众多,本文从以下几个方面对流域水文循环模拟中下垫面参数化方法进行综述。
（1）首先对流域水文循环模拟常用方法中的产汇流模拟方法进行分类,然后对常用流域水文循环模拟中产汇流方法的流域地形、土地利用覆被和土壤类型各类参数化方法进行回顾,探讨其对下垫面在流域水文循环模拟中的作用描述的方法和机理刻画程度。
（2）将产汇流过程中下垫面参数化方法对其物理机理的表述程度分为无明确表达,率定型参数、确定型参数和物理表达4类。当前常用的参数化方法对流域下垫面中地形、土地利用覆被和土壤类型在产汇流中的物理机理描述程度最多的为率定型参数类,其次是确定型参数类,且一般是根据参数表或者经验关系来确定;而物理过程表达类虽然有确定的物理方程来表示其响应关系,但是由于其定解条件缺少数据支持,在应用中难以实现。
（3）回归模型本质,在应用需求和机理研究的驱动下,参数化方法一方面用简洁方法描述主要规律达到实用需求而朝着简单实用方向发展,另一方面尽可能详尽刻画降水径流物理机制和流域特征而朝着复杂机理化方向发展。
The authors have declared that no competing interests exist.

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被引期刊影响因子

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[9]	Bao Weimin, Zhang Jianyun. HydrologicForecasting.Beijing: China Water Power Press, 2008. [本文引用: 1] [包为民, 张建云. 水文预报. 北京:中国水利水电出版社, 2008.] [本文引用: 1]
[10]	Xia Jun, Wang Gangsheng, Ye Aizhong, et al.A distributed monthly water balance model for analyzing impacts of land cover change on flow regimes. Pedosphere, 2005, 15(6): 761-767.https://doi.org/10.1002/jpln.200424108 URL摘要 The Miyun Reservoir is the most important water source for Beijing Municipality, the capital of China with a population of more than 12 million. In recent decades, the inflow to the reservoir has shown a decreasing trend, which has seriously threatened water use in Beijing. In order to analyze the influents of land use and cover change (LUCC) upon inflow to Miyun Reservoir, terrain and land use information from remote sensing were utilized with a revised evapotranspiration estimation formula; a water loss model under conditions of human impacts was introduced; and a distributed monthly water balance model was established and applied to the Chaobai River Basin controlled by the Miyun Reservoir. The model simulation suggested that not only the impact of land cover change on evapotranspiration, but also the extra water loss caused by human activities, such as the water and soil conservation development projects should be considered. Although these development projects were of great benefit to human and ecological protection, they could reallocate water resources in time and space, and in a sense thereby influence the stream flow.
[11]	Xia Jun, Wang Gangsheng, Tan Ge, et al.Development of distributed time-variant gain model for nonlinear hydrological systems. Science in China: Series D, 2005, 48(6): 713-723.https://doi.org/10.1360/03yd0183 URL摘要 In this paper, a rainfall-runoff modeling system is developed based on a nonlinear Volterra functional series and a hydrological conceptual modeling approach. Two models, i.e. the time-variant gain model (TVGM) and the distributed time-variant gain model (DTVGM) that are built on the platform of Digital Elevation Model (DEM), Remote Sensing (RS) and Unit Hydrological Process were proposed. The developed DTVGM model was applied to two cases in the Heihe River Basin that is located in the arid and semiarid region of northwestern China and the Chaobai River basin located in the semihumid region of northern China. The results indicate that, in addition to the classic dynamic differential approach to describe nonlinear processes in hydrological systems, it is possible to study such complex processes through the proposed systematic approach to identify prominent hydrological relations. The DTVGM, coupling the advantages of both nonlinear and distributed hydrological models, can simulate variant hydrological processes under different environment conditions. Satisfactory results were obtained in forecasting the time-space variations of hydrological processes and the relationships between land use/cover change and surface runoff variation.
[12]	Xia Jun.Theory and Method of Nonlinear Hydrological System. Wuhan: Wuhan University Academic Library, 2002. [夏军. 水文非线性系统理论与方法. 武汉: 武汉大学出版社, 2002.]
[13]	Liu Changming, Wang Zhonggen, ZhengHongxing, et al. Development and application of HIMS system and its custom model. Science in China Series E: Technology Science, 2008, 38(3): 350-360.URL摘要水循环既是水文科学的基本理论，又是进行水资源科学评价、合理利用和有效保护的基础．从水资源研究的需要出发，广泛参考国内外有关水文建模的经验，立足自主开发，建立了一种具有多种功能的水文水资源模拟系统（HydroInformatic Modeling System，简称：HIMS）．该系统已取得多项国家版权局的软件著作权．结合国家“973”项目对黄河的研究，进行了具体的研发和应用，已取得实用性的成果，并且与澳大利亚联邦科工组织（csmo）合作，利用澳大利亚的331个流域50多年来逐日降雨径流观测数据进行验证，取得良好的效果．研究表明HIMS系统具有比较广泛的适应性，能够针对不同的水文水资源问题进行模拟，并具备定制模型与二次开发的应用前景． [刘昌明, 王中根, 郑红星, 等. HIMS系统及其定制模型的开发与应用 . 中国科学E辑: 技术科学, 2008, 38(3): 350-360.]URL摘要水循环既是水文科学的基本理论，又是进行水资源科学评价、合理利用和有效保护的基础．从水资源研究的需要出发，广泛参考国内外有关水文建模的经验，立足自主开发，建立了一种具有多种功能的水文水资源模拟系统（HydroInformatic Modeling System，简称：HIMS）．该系统已取得多项国家版权局的软件著作权．结合国家“973”项目对黄河的研究，进行了具体的研发和应用，已取得实用性的成果，并且与澳大利亚联邦科工组织（csmo）合作，利用澳大利亚的331个流域50多年来逐日降雨径流观测数据进行验证，取得良好的效果．研究表明HIMS系统具有比较广泛的适应性，能够针对不同的水文水资源问题进行模拟，并具备定制模型与二次开发的应用前景．
[14]	Li Jun, Liu Changming, Wang Zhonggen, et al.Two universal runoff yield models: SCS vs. LCM. Acta Geographica Sinica, 2014, 69(7): 926-932.https://doi.org/10.11821/dlxb201407005 URL Magsci摘要产流计算是水文模拟的关键环节之一。在一定的空间尺度上,产流是一个十分复杂的非线性过程。目前在不同水文模型中,产流计算并不唯一。本文通过对比同时期提出的LCM模型与SCS模型,基于理论及数值分析发现:(1)SCS模型在其比例相等假设下,是LCM模型的一种简单线性化表示。LCM模型更加反映流域宏观产流的非线性。 (2)LCM模型参数与SCS模型参数存在严格的数学关系。LCM模型参数的确定可以利用SCS模型参数研究成果。(3)LCM模型参数很容易通过野外实验进行测定,而SCS模型参数很难实测,也可通过LCM模型参数为SCS模型参数确定提供依据。(4)SCS模型揭示了流域产流期内总降雨损失与总降雨量存在倒数线性关系,而LCM模型通过泰勒展开发现具有同样规律。 [李军, 刘昌明, 王中根, 等. 现行普适降水入渗产流模型的比较研究: SCS与LCM . 地理学报, 2014, 69(7): 926-932.]https://doi.org/10.11821/dlxb201407005 URL Magsci摘要产流计算是水文模拟的关键环节之一。在一定的空间尺度上,产流是一个十分复杂的非线性过程。目前在不同水文模型中,产流计算并不唯一。本文通过对比同时期提出的LCM模型与SCS模型,基于理论及数值分析发现:(1)SCS模型在其比例相等假设下,是LCM模型的一种简单线性化表示。LCM模型更加反映流域宏观产流的非线性。 (2)LCM模型参数与SCS模型参数存在严格的数学关系。LCM模型参数的确定可以利用SCS模型参数研究成果。(3)LCM模型参数很容易通过野外实验进行测定,而SCS模型参数很难实测,也可通过LCM模型参数为SCS模型参数确定提供依据。(4)SCS模型揭示了流域产流期内总降雨损失与总降雨量存在倒数线性关系,而LCM模型通过泰勒展开发现具有同样规律。
[15]	Huber W C.Storm Water Management Model User's Manual (V 5.0). US: Environmental Protection Agency, 2008.URL摘要 This chapter discusses how SWMM models the objects and operational parameters that constitute a stormwater drainage system. Details about how this information is entered into the program are presented in later chapters. An overview is also given on the
[16]	Neitsch S L, Arnold J G, Kiniry J R, et al.Soil and Water Assessment Tool Theoretical Documentation (Version 2009). Texas Water Resources Institute, 2011.https://doi.org/10.1016/j.csl.2009.04.006 URL摘要 There are many speech and language processing problems which require cascaded classification tasks. While model adaptation has been shown to be useful in isolated speech and language processing tasks, it is not clear what constitutes system adaptation for such complex systems. This paper studies the following questions: In cases where a sequence of classification tasks is employed, how important is to adapt the earlier or latter systems? Is the performance improvement obtained in the earlier stages via adaptation carried on to later stages in cases where the later stages perform adaptation using similar data and/or methods? In this study, as part of a larger scale multiparty meeting understanding system, we analyze various methods for adapting dialog act segmentation and tagging models trained on conversational telephone speech (CTS) to meeting style conversations. We investigate the effect of using adapted and unadapted models for dialog act segmentation with those of tagging, showing the effect of model adaptation for cascaded classification tasks. Our results indicate that we can achieve significantly better dialog act segmentation and tagging by adapting the out-of-domain models, especially when the amount of in-domain data is limited. Experimental results show that it is more effective to adapt the models in the latter classification tasks, in our case dialog act tagging, when dealing with a sequence of cascaded classification tasks.
[17]	Arnold J G.Williams J R. Srinivasan R, et al.Large area hydrological modeling and assessment (Part 1): Model development. Journal of the American Water Resources Association, 1998, 34(1): 73-89.
[18]	Feldman A D.HEC models for water resources system simulation: Theory and experience. Advance in Hydroscience, 1981, 12: 297-423.https://doi.org/10.1016/B978-0-12-021812-7.50010-9 URL
[19]	Zhao Renjun.Regional Hydrological Simulation: Xin'anjiang Model and Shanbei Model. Beijing: China Water Power Press, 1984. [赵人俊. 流域水文模拟: 新安江模型和陕北模型. 北京: 中国水利水电出版社, 1984.]
[20]	Liang Xu, Lettenmaier D P, Wood E F.A simple hydrologically based model of land surface water and energy fluxes for general circulation models. Journal of Geophysical Research, 1994, 99(7): 14415-14428.https://doi.org/10.1029/94JD00483 URL摘要 A generalization of the single soil layer variable infiltration capacity (VIC) land surface hydrological model previously implemented in the Geophysical Fluid Dynamics Laboratory general circulation model (GCM) is described. The new model is comprised of a two-layer characterization of the soil column, and uses an aerodynamic representation of the latent and sensible heat fluxes at the land surface. The infiltration algorithm for the upper layer is essentially the same as for the single layer VIC model, while the lower layer drainage formulation is of the form previously implemented in the Max-Planck-Institut GCM. The model partitions the area of interest (e.g., grid cell) into multiple land surface cover types; for each land cover type the fraction of roots in the upper and lower zone is specified. Evapotranspiration consists of three components: canopy evaporation, evaporation from bare soils, and transpiration, which is represented using a canopy and architectural resistance formulation. Once the latent heat flux has been computed, the surface energy balance is iterated to solve for the land surface temperature at each time step. The model was tested using long-term hydrologic and climatological data for Kings Creek, Kansas to estimate and validate the hydrological parameters, and surface flux data from three First International Satellite Land Surface Climatology Project Field Experiment intensive field campaigns in the summer-fall of 1987 to validate the surface energy fluxes.
[21]	Liang Xu, Wood E F, Lettenmaier D P.Surface soil moisture parameterization of the VIC-2L model: Evaluation and modification. Global and Planetary Change, 1996, 13(1): 195-206.
[22]	Lei Xiaohui, Liao Weihong, Jiang Yunzhong, et al.Distributed hydrological model EasyDHM I: Theory. Journal of Hydraulic Engineering, 2010, 41(7): 786-794.URL摘要介绍了自主开发的分布式水文模型EasyDHM的空间单元离散方式、主要理论模块以及相应的模型软件系统MWEasyDHM。EasyDHM的空间离散采用通用子流域划分算法，很大程度上扩展了分布式水文模型的通用性。同时，它支持多种产汇流算法，还支持用户对主要产汇流参数的敏感性分析和参数优化，以优化模型模拟效果。 [雷晓辉, 廖卫红, 蒋云钟, 等. 分布式水文模型EasyDHM (I): 理论方法 . 水利学报, 2010, 41(7): 786-794.]URL摘要介绍了自主开发的分布式水文模型EasyDHM的空间单元离散方式、主要理论模块以及相应的模型软件系统MWEasyDHM。EasyDHM的空间离散采用通用子流域划分算法，很大程度上扩展了分布式水文模型的通用性。同时，它支持多种产汇流算法，还支持用户对主要产汇流参数的敏感性分析和参数优化，以优化模型模拟效果。
[23]	Lei Xiaohui, Jiang Yunzhong, Wang Hao, et al.Distributed hydrological model EasyDHM II: Application. Journal of Hydraulic Engineering, 2010, 41(8): 893-899. [雷晓辉, 蒋云钟, 王浩, 等. 分布式水文模型EasyDHM (II): 应用方法 . 水利学报, 2010, 41(8): 893-899.]
[24]	Beven K J, Kirkby M J, Schofield N, et al.Testing a physically based flood-forecasting model (Topmodel) for three UK catchments. Journal of Hydrology, 1984, 69: 119-14.https://doi.org/10.1016/0022-1694(84)90159-8 URL [本文引用: 1]摘要 A previously developed model has been tested on three catchments: Crimple Beck (8 km ) near Harrogate, Hodge Beck (36 km ) on the North York Moors and the Wye headwater (10.5 km ) in central Wales. The model was originally validated on subcatchments within Crimple Beck. For this study forecasts were made over a period of one year, based only on rainfall and evaporation data. The model parameters were derived from a defined program of field measurements over a period of 2-4 weeks, and no formal optimization procedures were carried out before comparing forecasts with the measured stream discharge record. As a result of the comparisons, the model is seen as a useful approach for ungauged catchments of up to 500 km in humid-temperature climates.
[25]	Beven K, Lamb R, Quinn P, et al.Topmodel: Computer Models of Watershed Hydrology. USA: Water Resources Publications, 1995: 627-668.URL [本文引用: 1]摘要 This book contains 29 chapters. Introductory remarks on watershed modelling, model calibration and reliability estimation are presented in chapters 1-3. Chapters 4-13 describe civil engineering applications of watershed hydrology models (HEC-1 flood hydrograph package, RORB, Tank model, Xinanjiang model, UBC watershed model, the Precipitation-Runoff Modeling System (PRMS), the National Weather ...
[26]	Liu Z, Todini E.Towards a comprehensive physically-based rainfall-runoff model. Hydrology and Earth System Sciences Discussions, 2002, 6(5): 859-881.https://doi.org/10.5194/hess-6-859-2002 URL摘要 This paper introduces TOPKAPI (TOPographic Kinematic APproximation and Integration), a new physically-based distributed rainfall-runoff model deriving from the integration in space of the kinematic wave model. The TOPKAPI approach transforms the rainfall-runoff and runoff routing processes into three 鈥榮tructurally-similar鈥 non-linear reservoir differential equations describing different hydrological and hydraulic processes. The geometry of the catchment is described by a lattice of cells over which the equations are integrated to lead to a cascade of non-linear reservoirs. The parameter values of the TOPKAPI model are shown to be scale independent and obtainable from digital elevation maps, soil maps and vegetation or land use maps in terms of slope, soil permeability, roughness and topology. It can be shown, under simplifying assumptions, that the non-linear reservoirs aggregate into three reservoir cascades at the basin scale representing the soil, the surface and the drainage network, following the topographic and geomorphologic elements of the catchment, with parameter values which can be estimated directly from the small scale ones. The main advantage of this approach lies in its capability of being applied at increasing spatial scales without losing model and parameter physical interpretation. The model is foreseen to be suitable for land-use and climate change impact assessment; for extreme flood analysis, given the possibility of its extension to ungauged catchments; and last but not least as a promising tool for use with General Circulation Models (GCMs). To demonstrate the quality of the comprehensive distributed/lumped TOPKAPI approach, this paper presents a case study application to the Upper Reno river basin with an area of 1051 kmbased on a DEM grid scale of 200 m. In addition, a real-world case of applying the TOPKAPI model to the Arno river basin, with an area of 8135 kmand using a DEM grid scale of 1000 m, for the development of the real-time flood forecasting system of the Arno river will be described. The TOPKAPI model results demonstrate good agreement between observed and simulated responses in the two catchments, which encourages further developments of the model.
[27]	Skaags R W, Khaleel R.Infiltration, hydrologic modeling of small watersheds. American Society of Agricultural Engineers, St. Joseph, MI, USA, 1982.URL [本文引用: 1]
[28]	Jia Yangwen, Ni Guangheng, Kawahara Y, et al.Development of WEP model and its application to an urban watershed. Hydrological Process, 2001, 15: 2175-2194.https://doi.org/10.1002/hyp.275 URL摘要 A distributed hydrological model, water and energy transfer processes (WEP) model, is developed to simulate spatially variable water and energy processes in watersheds with complex land covers. In the model, state variables include depression storage on land surfaces and canopies, soil moisture content, land surface temperature, groundwater tables and water stages in rivers, etc. The subgrid heterogeneity of land use is also taken into consideration by using the mosaic method. For hydrological processes, evapotranspiration is computed by the Penman-Monteith equation, infiltration excess during heavy rains is simulated by a generalized Green-Ampt model, whereas saturation excess during the remaining periods is obtained by doing balance analysis in unsaturated soil layers. A two-dimensional simulation of multilayered aquifers is performed for groundwater flow. Flow routing is conducted by using the kinematic wave method in a one-dimensional scheme. For energy processes, short-wave radiation is based on observation or deduced from sunshine duration, long-wave radiation is calculated according to temperatures, latent and sensible fluxes are computed by the aerodynamic method and surface temperature is solved by the force-restore method. In addition, anthropogenic components, e.g. water supply, groundwater lift, sewerage drainage and energy consumption, etc. are also taken into account. The model is applied to the Ebi River watershed (27 km2) with a grid size of 50 m and a time step of 1 h. The model is verified through comparisons of simulated river discharges, groundwater levels and land surface temperatures with the observed values. A comparison between water balance at present (1993) and that in the future (2035) is also conducted. It is found that the hydrological cycle in the future can be improved through the implementation of infiltration trenches for the storm water from urban canopies.
[29]	Mo Xingguo, Liu Suxia.Simulating the water balance of the Wuding River Basin in the Loess Plateau with a distribution eco-hydrological model. Acta Geographica Sinica, 2004, 59(3): 341-348.https://doi.org/10.3321/j.issn:0375-5444.2004.03.003 URL Magsci摘要利用黄土高原无定河流域1982～1991年的水文气象、土地利用、土壤质地、数字高程和NOAA-AVHRR遥感信息,建立基于土壤-植被-大气传输机理的分布式生态水文模型,模拟流域水量平衡的时空分布.研究结果发现,该流域的年平均植被指数(NDVI)的年际变化不明显,但NDVI最大值的年际变化显著.该流域年累计NDVI与降水年总量关系不明显,说明该流域植被的生长并不完全受控于降水总量.模拟的实际蒸散量用无定河及其岔巴沟子流域实测降水与实测径流的差值进行验证,误差小于5%.整个流域模拟时段的平均降水量为372±53 mm yr-1,实际蒸散量为334±33 mm yr-1,其中蒸腾为130±21 mm yr-1,有明显的年际波动.地表径流的年际变化相对较小.蒸散发的季节变化特征与降雨基本一致,即7、8、9月雨季高,其他月份低.降水量和实际蒸散量呈现显著的空间分异性,表现出由东南(高NDVI)向西北(低NDVI)递减的梯度差异.地表径流的空间分异亦沿东南-西北梯度变化,但高值分散在中部.以岔巴沟子流域1991年的地表覆被度为基准,发现在全流域都覆盖上某一种植被的情况下,蒸腾和土壤蒸发的变化非常明显,地表径流和实际总蒸散的变化并不显著.只有在全流域都变成荒漠情景下,实际总蒸散才显示出较明显变化(17%),表明在西北干旱半干旱区,土地利用/覆被变化对水量平衡的影响非常复杂. [莫兴国, 刘苏峡. 无定河流域水量平衡变化的模拟 . 地理学报, 2004, 59(3): 341-348.]https://doi.org/10.3321/j.issn:0375-5444.2004.03.003 URL Magsci摘要利用黄土高原无定河流域1982～1991年的水文气象、土地利用、土壤质地、数字高程和NOAA-AVHRR遥感信息,建立基于土壤-植被-大气传输机理的分布式生态水文模型,模拟流域水量平衡的时空分布.研究结果发现,该流域的年平均植被指数(NDVI)的年际变化不明显,但NDVI最大值的年际变化显著.该流域年累计NDVI与降水年总量关系不明显,说明该流域植被的生长并不完全受控于降水总量.模拟的实际蒸散量用无定河及其岔巴沟子流域实测降水与实测径流的差值进行验证,误差小于5%.整个流域模拟时段的平均降水量为372±53 mm yr-1,实际蒸散量为334±33 mm yr-1,其中蒸腾为130±21 mm yr-1,有明显的年际波动.地表径流的年际变化相对较小.蒸散发的季节变化特征与降雨基本一致,即7、8、9月雨季高,其他月份低.降水量和实际蒸散量呈现显著的空间分异性,表现出由东南(高NDVI)向西北(低NDVI)递减的梯度差异.地表径流的空间分异亦沿东南-西北梯度变化,但高值分散在中部.以岔巴沟子流域1991年的地表覆被度为基准,发现在全流域都覆盖上某一种植被的情况下,蒸腾和土壤蒸发的变化非常明显,地表径流和实际总蒸散的变化并不显著.只有在全流域都变成荒漠情景下,实际总蒸散才显示出较明显变化(17%),表明在西北干旱半干旱区,土地利用/覆被变化对水量平衡的影响非常复杂.
[30]	Abbott M B, Bathhurst J C, Cunge J A, et al.An introduction to the European Hydrological System-Systeme Hydrologique European, SHE; 1. History and philosophy of a phasically based distributed modeling system. Journal of Hydrology, 1986, 87(1): 45-59.
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[32]	Xu Zongxue. Hydrological Model.Beijing: Science Press, 2009. [徐宗学. 水文模型. 北京:科学出版社, 2009.]
[33]	Zhang Wenhua, Guo Shenglian.The Theory and Method of Rainfall-Runoff. Wuhan: Hubei Science and Technology Press, 2007. [本文引用: 1] [张文华, 郭生练. 流域降雨径流理论与方法. 武汉: 湖北科学技术出版社, 2007.] [本文引用: 1]
[34]	Li Li.Study on flood routing of distributed hydrologic models [D]. Nanjing: Hohai University, 2007. [本文引用: 1] [李丽. 分布式水文模型的汇流演算研究[D] . 南京: 河海大学, 2007.] [本文引用: 1]
[35]	Yuan Fei, Xie Zhenghui, Liu Qian, et al.An application of the VIC-3L land surface model and remote sensing data in simulating streamflow for the Hanjiang River basin. Canadian Journal of Remote Sensing, 2004, 30(5): 680-690.https://doi.org/10.5589/m04-032 URL摘要 Not Available
[36]	JiaYangwen, Wang Hao, Zhou Zuhaoet al. Development of the WEP-L distributed hydrological model and dynamic assessment of water resources in the Yellow River Basin. Journal of Hydrology, 2006, 331(3): 606-629.https://doi.org/10.1016/j.jhydrol.2006.06.006 URL摘要 Dynamic assessment of water resources becomes desirable to reflect water resources variations in the basins under strong human impacts. A physically based distributed hydrological model, WEP-L, which couples simulations of natural hydrological processes and water use processes, is developed for the purpose. Concepts of special water resources (i.e., surface water resources and groundwater resources) and general water resources (i.e., the special water resources plus the precipitation directly utilized by ecosystem) are proposed, and an approach for dynamic assessment of water resources is suggested. Basin subdivision, classification of land covers, and deduction of water use spatial/temporal distributions in the Yellow River basin are carried out with the aid of remote sensing (RS) data and geographic information system (GIS) techniques. The basin is subdivided into 8485 sub-watersheds and 38,720 contour bands, and the WEP-L model is verified by comparing simulated and observed discharges at main gage stations. Lastly, continuous simulations of 45 years (1956-2000) in variable time steps (from 1 h to 1 day) are performed for various land cover and water use conditions, and water resources assessment results under present condition of land cover and water use are compared with those under historical condition of land cover and water use. The study results reveal that: (1) the surface water resources reduced, but the groundwater resources non-overlapped with the surface water resources increased under the impact of human activities in the Yellow River basin; and (2) the special water resources reduced, but the general water resources increased accompanied with increase of the precipitation directly utilized by ecosystem in the basin.
[37]	Ullah W, Dickinson W T.Quantitative description of depression storage using a digital surface model: I. Determination of depression storage. Journal of Hydrology, 1979, 42(1/2): 63-75.https://doi.org/10.1016/0022-1694(79)90006-4 URL [本文引用: 1]摘要 Depression storage is a dominating storage element which accounts for most of the retention on a watershed surface. Because of practical difficulties in making direct measurement of the dimensions of individual depressions, the values of depression storage have either been assumed or indirectly estimated. The physical properties of a surface in terms of depression storage depend upon the surface configuration which can be modelled with a set of elevation values given as a function of horizontal coordinates. These values constitute a digital surface model. A photogrammetric technique has been used to develop digital surface models for fifteen sample plots, of about 160 cm 脳 200 cm size, having similar physiographic conditions. A simple digital technique has been developed and used to determine the geometric properties of individual depressions of all sample plots. The method scans the digital surface model and identifies characteristic points of depressions such as low points, pour points, etc. The information obtained in the process is used to compute the geometric properties of depressions, depth, surface area and volume.
[38]	Ullah W, Dickinson W T.Quantitative description of depression storage using a digital surface model: II. Characteristics of surface depressions. Journal of Hydrology. 1979, 42(1/2): 77-90.https://doi.org/10.1016/0022-1694(79)90007-6 URL [本文引用: 1]摘要 Results of a subsequent analysis of data of volume, depth and surface area of individual depressions are presented. The spatial distribution of depressions is found to be both random and direction oriented. Depression storage volume decreases with the slope of the plot due to a reduction in both the number of depressions and the dimensions of individual depressions. The three geometric properties depth, surface area and volume are also related to each other. The geometric properties of the depressions exhibit a frequency distribution of somewhat similar characteristicity. The observed frequency distribution can be satisfactorily described by the Weibull distribution.
[39]	Linsley R K, Kohler M A, Paulhus J L, et al.Hydrology For Engineers. New York: McGraw- Hill Book Company, 1975. [本文引用: 1]
[40]	Soil Conservation Service.National Engineering Hand-book. Section 4: Hydrology. USDA, Springfield, VA, 1993.URL [本文引用: 1]摘要 CiteSeerX - Scientific documents that cite the following paper: Section 4 in National Engineering Handbook
[41]	Mishra S K, Singh V P.Soil Conservation Service Curve Number (SCS-CN) Methodology. Netherlands: Kluwer Academic Publishers, 2003.https://doi.org/10.1061/(ASCE)HE.1943-5584.0000694 URL [本文引用: 1]摘要 The Soil Conservation Service (SCS) curve number (CN) method is one of the most popular methods for computing the runoff volume from a rainstorm. It is popular because it is simple, easy to understand and apply, and stable, and accounts for most of the runoff producing watershed characteristics, such as soil type, land use, hydrologic condition, and antecedent moisture condition. The SCS-CN method was originally developed for its use on small agricultural watersheds and has since been extended and applied to rural, forest and urban watersheds. Since the inception of the method, it has been applied to a wide range of environments. In recent years, the method has received much attention in the hydrologic literature. The SCS-CN method was first published in 1956 in Section-4 of the National Engineering Handbook of Soil Conservation Service (now called the Natural Resources Conservation Service), U. S. Department of Agriculture. The publication has since been revised several times. However, the contents of the methodology have been nonetheless more or less the same. Being an agency methodology, the method has not passed through the process of a peer review and is, in general, accepted in the form it exists. Despite several limitations of the method and even questionable credibility at times, it has been in continuous use for the simple reason that it works fairly well at the field level.
[42]	Xia Jun.A system approach to real time hydrological forecasts in watersheds. Water International, 2002, 27(1): 87-97. [本文引用: 1]
[43]	Wang Gangsheng.Theory and method of distributed time-variant gain model [D]. Beijing: Institute of Geographic Sciences and Natural Resources Research, CAS, 2005. [本文引用: 1] [王纲胜. 分布式时变增益水文模型理论与方法研究[D] . 北京: 中国科学院地理科学与资源研究所, 2005.] [本文引用: 1]
[44]	Zhao Renjun, Zhuang Yiling.Regional pattern of rainfall-runoff relationship. Journal of East China Technical University of Water Resources Engineering, 1963(S2): 53-68.URL [本文引用: 1]摘要正一次降雨量与其所产生的径流量之間的关系,也就是水文預报与水文計算中的“扣損失”問題,是水文中一个重要的基本的問題。现在,在有实測水文資料的流域中,借助于統計相关的方法,可以在实用上解决这个問題,但所得的精度还不够高。而在缺乏实測資料的流域中,則还沒有妥善的解决办法。我們认为,要进一步解决这个問題,一方面应当深入揭露出降雨产生径流的现象,使降雨径流关系建立在明确的成因基础上;另一方面,应当找出这种关系与其有关参数在地区上的分布规律,使得对缺乏实測資料的地区也可以进行計算。本文所研究的地区是浙江省与湖南省的山丘区,可以代表一般湿潤山丘区的情况。 [赵人俊, 庄一鸰. 降雨径流关系的区域规律. 华东水利学院学报, 1963(S2): 53-68.]URL [本文引用: 1]摘要正一次降雨量与其所产生的径流量之間的关系,也就是水文預报与水文計算中的“扣損失”問題,是水文中一个重要的基本的問題。现在,在有实測水文資料的流域中,借助于統計相关的方法,可以在实用上解决这个問題,但所得的精度还不够高。而在缺乏实測資料的流域中,則还沒有妥善的解决办法。我們认为,要进一步解决这个問題,一方面应当深入揭露出降雨产生径流的现象,使降雨径流关系建立在明确的成因基础上;另一方面,应当找出这种关系与其有关参数在地区上的分布规律,使得对缺乏实測資料的地区也可以进行計算。本文所研究的地区是浙江省与湖南省的山丘区,可以代表一般湿潤山丘区的情况。
[45]	Richards L A.Capillary conduction of liquids through porous mediums. Journal of Applied Physics, 1931, 1(5): 318-333.https://doi.org/10.1063/1.1745010 URL摘要 The flow of liquids in unsaturated porous mediums follows the ordinary laws of hydrodynamics, the motion being produced by gravity and the pressure gradient force acting in the liquid. By making use of Darcey's law, that flow is proportional to the forces producing flow, the equation K63 2 ψ+63K·63ψ+g68K/68z=61ρ s A68ψ/68t may be derived for the capillary conduction of liquids in porous mediums. It is possible experimentally to determine the capillary potential ψ=∫dp/ρ, the capillary conductivity K, which is defined by the flow equation q=K(g6171ψ), and the capillary capacity A, which is the rate of change of the liquid content of the medium with respect to ψ. These variables are analogous, respectively, to the temperature, thermal conductivity, and thermal capacity in the case of heat flow. Data are presented and application of the equations is made for the capillary conduction of water through soil and clay but the mathematical formulations and the experimental methods developed may be used to express capillary flow for other liquids and mediums. The possible existance of a hysteresis effect between the capillary potential and moisture content of a porous medium is considered.
[46]	Lei Zhidong.Soil-water Dynamics. Beijing: Tsinghua University Press, 1988. [雷志栋. 土壤水动力学. 北京: 清华大学出版社, 1988.]
[47]	USACE. HEC-HMS Hydrologic Modeling System User′s Manual. Hydrologic Engineering Center, Davis, CA, 2001.
[48]	USACE. HEC-HMS Hydrologic Modeling System Technical Reference Manual, Hydrologic Engineering Center, Davis, CA, 2000.URL摘要 The Hydrologic Modeling System (HEC-HMS) is new-generation software for precipitation-runoff simulation that will supersede the Hydrologic Engineering Centefs HEC-l program. Technical capabilities and operational features of HEC HMS are described, with emphasis on technical capabilities that differ from those in HEC-l.
[49]	Green W H, Ampt G A.Studies on soil physics (Part 1): The flow of air and water through soils. The Journal of Agricultural Science, 1911, 4: 1-24.https://doi.org/10.1515/ijnsns-2015-0060 URL摘要 In this paper, the numerical solutions for groundwater flow in unsaturated layered soil using the Richards equation are presented. A linearisation process for the nonlinear Richards equation to deal with groundwater flow in unsaturated layered soil is derived. To solve one-dimensional flow in the unsaturated zone of layered soil profiles, flux conservation and the continuity of pressure potential at the interface between two consecutive layers are considered in the numerical model. In addition, a novel method, named the dynamical Jacobian-inverse free method, incorporated with a two-side equilibration algorithm for solving ill-conditioned systems with extreme contrasts in hydraulic conductivity is proposed. The validity of the model is established in numerous test problems by comparing the numerical results with the analytical solutions. The results show that the proposed method can improve convergence and numerical stability for solving groundwater flow in unsaturated layered soil with extreme contrasts in hydraulic conductivity.
[50]	Horton R E.Surface runoff phenomena. Horton Hydrology Laboratory, 1935.URL
[51]	Horton R E.An approach towards a physical interpretation of infiltration-capacity. Soil Science Society of America Journal, 1940, 5: 399-417.
[52]	Philip J R.An infiltration equation with physical significance. Soil Science, 1954, 77(2): 153-157.https://doi.org/10.1097/00010694-195402000-00009 URL摘要 An abstract is unavailable. This article is available as a PDF only.
[53]	Smith R E.Parameter-efficient hydrologic infiltration model. Water Resources Research, 1978, 14(3): 533-538.https://doi.org/10.1029/WR014i003p00533 URL摘要 By adopting two extreme assumptions concerning the behavior of unsaturated soil hydraulic conductivity K near saturation, we derived a two-branched model for ponding time and infiltration rate decay for arbitrary rainfall rates. One assumption was that K varies slowly near saturation and leads to an expression for ponding time and infiltration decay. For initially ponded conditions, ponding time is zero, and with rainfall rate r →∞, the familiar Green and Ampt (1911) expression results. The other, rather opposite assumption was that K varies rapidly, e.g., exponentially, near saturation. This model also holds for both rainfall and ponded surface conditions, and for ponded conditions the expression is identical to that of Parlange (1971). Each model uses only two parameters, saturated soil conductivity Kand a parameter that is roughly related to sorptivity and responds nearly linearly to variations in initial saturation. Both parameters are physically related to measurable soil properties. Methods are presented to estimate parameters of either model from infiltrometer tests. The two models are compared with a precise numerical solution of the unsaturated soil water diffusion equations for three soils that represent a range of soil behaviors near saturation. Our results show that either assumption would be an excellent model for most hydrologic purposes, and the relative goodness of fit of each model is generally consistent with the appropriate behavior of K(θ→θ).
[54]	Zhan Daojiang, Ye Shouze. EngineeringHydrology.Beijing: China Water Power Press, 2000. [本文引用: 1] [詹道江, 叶守泽. 工程水文学. 北京: 中国水利水电出版社, 2000.] [本文引用: 1]
[55]	Nash J E.The form of the instantaneous unit hydrograph. Hydrologic Science B, 1957, 45(3): 114-121.URL [本文引用: 1]摘要 SUMMARY An equation is derived for the instantaneous unit hydrograph by assuming that the operation performed by the catchment on the effective rainfall is analogous to that performed by routing through a series of linear reservoirs. A method by which the<< best
[56]	Nash J E.A unit hydrograph study with particular reference to British catchments. Proceedings of the Institution of Civil Engineers B, 1960, 17(3): 249-282.https://doi.org/10.1680/iicep.1960.11649 URL [本文引用: 1]摘要 Paper No. 6433 AUNITHYDROGRAPHSTUDY,WITHPARTICULAR REFERENCE TO BRITISH CATCHMENTS bY James Edward Nash, M.E., A.M.I.C.E.I. Principal Scientific Officer, Hydraulics Research Station, Departmentof Scientific and Industrial Research FordiscussionatanOrdinaryMeeting on Tuesday, 6 December, 1960, at 5.30 p.m., and for subsequent written discussion SYNOPSIS The moments of the instantaneous unit hydrograph are correlated with the topographical characteristics for a large number of British catchments, and a general equation for the instantaneous unit hydrograph chosen. The use of the correlation to predict the hydrograph for catchments where sufficient data on rainfall and streamflow are not available is explained, and examples given...
[57]	Rodriguez-Iturbe I, Valdes J B.The geomorphological structure of hydrologic response. Water Resources Research, 1979, 15(6): 1409-1420. [本文引用: 1]
[58]	Gupta V K, Waymire E, Wang C T.A representation of an instantaneous unit hydrograph from geomorphology. Water Resources Research, 1980, 16(5): 855-862.https://doi.org/10.1029/WR016i005p00855 URL [本文引用: 1]摘要 The channel network and the overland flow regions in a river basin satisfy Horton's empirical geo-morphologic laws when ordered according to the Strahler ordering scheme. This setting is presently employed in a kinetic theoretic framework for obtaining an explicit mathematical representation for the instantaneous unit hydrograph (iuh) at the basin outlet. Two examples are developed which lead to explicit formulae for the iuh. These examples are formally analogous to the solutions that would result if a basin is represented in terms of linear reservoirs and channels, respectively, in series and in parallel. However, this analogy is only formal, and it does not carry through physically. All but one of the parameters appearing in the iuh formulae are obtained in terms of Horton's bifurcation ratio, stream length ratio, and stream area ratio. The one unknown parameter is obtained through specifying the basin mean lag time independently. Three basins from Illinois are selected to check the theoretical results with the observed direct surface runoff hydrographs. The theory provided excellent agreement for two basins with areas of the order of 1100 mi 2 (1770 km 2 ) but underestimates the peak flow for the smaller basin with 300-mi 2 (483-km 2 ) area. This relative lack of agreement for the smaller basin may be used to question the validity of the linearity assumption in the rainfall runoff transformation which is embedded in the above development.
[59]	Govindaraju R S.Approximate analytical solutions for overland flows. Water Resources Research, 1990, 26(12): 2903-2912.https://doi.org/10.1029/WR026i012p02903 URL [本文引用: 1]摘要 Following the study of Govindaraju et al. (1988), approximate analytical solutions are presented to the diffusion and kinematic wave models subject to space and time-varying rainfall. An approximation in the form of the first term of an infinite sine series has been considered. This converts the partial differential equation to an ordinary differential equation, and analytical solutions for both rising and recession phases of the hydrograph can be developed. Time variation in rainfall is found to play a key role. Comparisons with full Saint-Venant solutions, the kinematic wave approximation and experimental results are presented for validating the proposed solution methodology. The one-term analytical solution is shown to perform well in some cases of physical interest. It is concluded that the analytical solution is useful for estimating runoff from steep overland flow sections.
[60]	Singh V P.Accuracy of kinematic wave and diffusion wave approximations for space-independent flows. Hydrological Processes, 1994, 8(1): 45-62.URL [本文引用: 1]
[61]	Orlandini S.On the storm flow response of upland alpine catchments. Hydrological Processes, 1999, 13: 549-562.https://doi.org/10.1002/(SICI)1099-1085(199903)13:43.0.CO;2-S URL [本文引用: 1]摘要 Detailed measurements of near-surface soil hydraulic conductivity, Ks, across the Bracciasco catchment (Central Italian Alps) are incorporated into a distributed, digital elevation model-based hydrological model to evaluate the effect of soil heterogeneity on catchment storm flow response. Surface and subsurface storm flow components are simulated for different distributions of Ks, including that obtained directly from measurements, that obtained by averaging measured data and others obtained on the basis of a simple functional parameter model. The reproduction of the catchment storm flow responses obtained using distributions of Ks based on measurements is satisfactory although an adjustment of such distributions is suggested to reproduce the hydrograph peaks owing to rapid surface runoff concentration and to improve the description of recession limbs at the same time. Numerical experiments indicate that the simulated storm flow response of the study catchment is substantially insensitive to near-surface soil heterogeneity in as far as the predominant mechanism of channel storm flow generation is subsurface flow. However, Ks is found to play an important role in the generation of overland flow during intense rainfall and, under these circumstances, monitoring of near-surface heterogeneity may be important to provide accurate descriptions of both surface and subsurface storm flow components.
[62]	Rui Xiaofang. Physical Hydrology.Beijing: China Water Power Press, 2004. [本文引用: 1] [芮孝芳. 水文学原理. 北京: 中国水利水电出版社, 2004.] [本文引用: 1]
[63]	Zhang S, Cordery L, Sharma A.Application of an improved linear storage routing model for the estimation of large floods. Journal of Hydrology, 2002, 258: 58-68.https://doi.org/10.1016/S0022-1694(01)00540-6 URL [本文引用: 1]摘要 A runoff routing model, which incorporates a linear routing structure and attempts to provide a physically realistic distribution of storage effects, has recently been developed. The model with its physically realistic storage effects has been shown to provide consistently good reproduction of observed large floods without the need for parameter fitting or calibration. Storage distribution is determined from a volume law that accounts for the distribution of river channel storage in natural catchments. The model is briefly described, but the emphasis is on demonstrating its ability to reproduce large observed floods and design floods in China and Australia. The model results are compared with those from two commonly used non-linear storage routing models using several measures of performance. The probable maximum floods (PMFs) estimated based on all three models are also compared. The linear model using the proposed volume law is recommended for estimation of design floods because it has been shown to represent the observed geomorphological processes more realistically than other models, and because it reproduces observed large floods at least as well as the other models considered in this study.
[64]	McCarthy G T. The unit hydrograph and flood routing. Conference of the North Atlantic Division of US Corps of Engineers, 1938.URL [本文引用: 1]
[65]	Bajracharya K.Accuracy criteria for linearised diffusion wave flood routing. Journal of Hydrology, 1997, 195: 200-217.https://doi.org/10.1016/S0022-1694(96)03235-0 URL [本文引用: 1]摘要 The spatial step size for the second-order accurate Muskingum-Cunge (M-C) method is determined by the spatial weighting factor. Both the spatial weighting factor and the time step must be selected judiciously to obtain accurate solutions. In this study, accuracy criteria for the linearised diffusion routing problem are discussed. Starting from the truncation error analysis of the general finite-difference scheme used to solve the kinematic wave equation (of which the M-C method is a special case), conditions necessary to obtain second-, third- and fourth-order accurate solutions to the linearised diffusion routing equation are derived. For given diffusion coefficient and celerity, the spatial step of the fourth-order scheme is fixed, whereas third- and second-order solutions are available for independently selected spatial steps. In order to achieve optimal solutions to the second-order accurate scheme, the truncation error criteria are combined with a condition derived from the concept of column holdup. This combination is shown to produce results as good as those from the third-and fourth-order accurate schemes. The simplest explicit method is shown to give satisfactory results for flood data from the River Wye (UK).
[66]	Cunge J A.On the subject of a flood propagation computation method (Muskingum Method). Journal of Hydraulic Research, 1969, 7(2): 205-230.URL [本文引用: 1]摘要 CiteSeerX - Scientific documents that cite the following paper: On the subject of flood propagation method (Muskingum method

水文循环模拟中下垫面参数化方法综述

本站小编 Free考研考试/2021-12-29

A review of underlying surface parametrization methods in hydrologic models

1 引言

2 水文循环物理过程机理及数学表达方法

2.1 土壤水运动的Richards方程

2.2 汇流动力方程

2.3 地下水运动的控制方程

3 水文循环模拟中常用产汇流模拟方法

4 产流模拟中土地利用覆被与地形参数化方法

4.1 植物截留与填洼

4.2 降雨径流相关关系法

4.3 蓄满产流

4.4 超渗产流方法

5 汇流模拟中流域下垫面参数化方法

5.1 坡面汇流模拟

5.2 河道流量演算

6 流域水文循环模拟中产汇流参数化方法分类

7 讨论和未来发展趋势预估

8 讨论

参考文献原文顺序
文献年度倒序
文中引用次数倒序
被引期刊影响因子

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水文循环模拟中下垫面参数化方法综述

本站小编 Free考研考试/2021-12-29

A review of underlying surface parametrization methods in hydrologic models

1 引言

2 水文循环物理过程机理及数学表达方法

2.1 土壤水运动的Richards方程

2.2 汇流动力方程

2.3 地下水运动的控制方程

3 水文循环模拟中常用产汇流模拟方法

4 产流模拟中土地利用覆被与地形参数化方法

4.1 植物截留与填洼

4.2 降雨径流相关关系法

4.3 蓄满产流

4.4 超渗产流方法

5 汇流模拟中流域下垫面参数化方法

5.1 坡面汇流模拟

5.2 河道流量演算

6 流域水文循环模拟中产汇流参数化方法分类

7 讨论和未来发展趋势预估

8 讨论

参考文献文献选项 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

相关话题/水文 过程 经验 计算 系统

参考文献原文顺序
文献年度倒序
文中引用次数倒序
被引期刊影响因子

相关话题/水文过程经验计算系统