水文循环模拟中下垫面参数化方法综述

doi:10.11821/dlxb201607001

Abstract

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.

Key words: hydrologic cycle simulation, watershed topography, land use, land cover, soil type, watershed characteristics, parametrization

Lingling ZHAO, Changming LIU, Xiaoxiao WU, Lihong LIU, Zhonggen WANG, SOBKOWIAK Leszek. A review of underlying surface parametrization methods in hydrologic models[J].Acta Geographica Sinica, 2016, 71(7): 1094-1104.

Figures/Tables 6

Tab. 1

Tab. 2

Tab. 3

The 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	$I n = S v + C P c$ ^[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	$V = a exp (- bs)$ $V = (I - f) exp (- kPe)$ ^[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	$Q surf = (R day - I a) 2 (R day - I a + S) S = 25.4 1000 CN - 10$ ^[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	$R (t) = G (t) X (t)$ $G (t) = g 1 + g 2 API (t)$ ^[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	$α = 1 - 1 - W M' WMM b$ $WM = WMM 1 + b$ ^[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	$Q b = A T 0 exp (- λ ) exp (- z ? / S zm) λ = 1 A ∫ A ln α i tan β i dA$ ^[24-25]	A、 $z ?$ 、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; $z ?$ 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	$? θ ? t = ? ? x [K x (θ) ? ? ? x] + ? ? y K y (θ) ? ? ? y + ? ? z K z (θ) ? ? ? z$ ^[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	$F P (t) = a + bt - a e - βt$ $a = 1 β (f 0 - f c), b = f c$ ^[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	$P et = 0 ? ? ∑ P i < I a P t - f c ∑ P i > I a, P t > f c 0 ? ∑ P i > I a, P t < f c$ ^[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	$I at = I a - P t + V t$ ^[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	$f t = K 1 + (φ - θ t) S t F t$ ^[49]	K、S_t、 $θ t$ 、 $φ$	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; $(φ - θ t)$ 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	$f p = f c + (f 0 - f c) e - kt$ ^[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	$f p = α 2 t - 13$ ^{[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	$f p = α 2 t - 12 + f c$ ^[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	$f p = GI × α × S A 1.4 + f c$ ^{[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	$f p = f ∞ + A (t - t 0) - α$ ^{[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	$∫ 0 t p idi = B (θ i) i p - K s ≈ s 2 2 i p - K s$ ^[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

Tab. 3

Tab. 4

The 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	$Q t = 1 Δt ∑ j = k 1 k 2 r d, j Δ A t - j + 1$ ^[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	$Q d, t = ∑ j = k 1 k 2 r d, j q t - j + 1$ ^[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	$u (t) = 1 KΓ (N) (t K) N - 1 e - t / K$ ^[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	$Q (t) = I 0 * f B (t), t > 0$ $f B (t) = d F B (t) d (t) = ∑ f x 1 × f x 2 × ? × f x k (t) p (s)$ ^[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; $*$ 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	$q p = 0.208 FR t p, t p = 23 t c t c = 53 L, L = l 0.8 (S + 25.4) 0.7 7069 y 0.5 D = 0.133 t c$ ^[41]	$q p$ 、L、D	根据公式获得	$q p$ 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	$K dQ dt + Q = I$ ^[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	$nk Q n - 1 dQ dt + Q = I$ ^[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	$? A ? t + ? Q ? x = 0$ $- ? Z ? x = S f + 1 g ? υ ? t + υ g ? υ ? x$ ^{[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	$? Q ? t + c k ? Q ? x = 0, c k = ηυ$ ^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	$? Q ? t + c ? Q ? x = μ ? 2 Q ? x 2$ ^[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	$? A ? t + ? Q ? x = 0$ ^[60-61] $υ ? υ ? x + ? υ ? t + g ? y ? x = g (i 0 - υ 2 C 2 R)$	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	$V 2 + Δt 2 Q 2 = Δt 2 (I 1 + I 2) + V 1 - Δt 2 Q 1$ ^[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	$Q 2 = C 0 I 2 + C 1 I 1 + C 2 Q 1$ $C 0 = 0.5 Δt - KX 0.5 Δt + K 1 - X)$ ^[64] $C 1 = 0.5 Δt + KX 0.5 Δt + K 1 - X) C 2 = - 0.5 Δt + K 1 - X) 0.5 Δt + K 1 - X)$	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	$Q 2 = C 0 I 1 + C 1 I 2 + C 2 Q 1 + C 3 Q lat$ C₀、C₁、C₂、公式同上 $C 3 = Δt 0.5 Δt + K 1 - X)$ $K = Δx c X = 121 - Q cΔxB S 0)$ ^[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	$K = L V c, V c = 5 V 3, V = R 23 i n$	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

Tab. 4

Tab. 5

Tab. 6

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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]

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

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

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

A review of underlying surface parametrization methods in hydrologic models

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