ECCE Summer School for Advanced Study in Climate and Environment 2006年7月30-8月12,北京 包含地下水位动态变化的陆面过程模型 及其应用 谢正辉，及其研究小组 中国科学院大气物理研究所 http://web.lasg.ac.cn/staff/xie/xie.htm

全球水循环框架 凝结 凝结 升华 降水 降水 冰雪 蒸散发 融雪 径流 水面蒸发 径流 土壤水 海洋蒸发 湖泊 下渗 海洋 地下水含水层 水平对流 凝结 凝结 升华 降水 降水 冰雪 蒸散发 融雪 径流 水面蒸发 径流 土壤水 海洋蒸发 湖泊 下渗 海洋 地下水含水层

全球水循环数量（单位：1000km3） 111 385

陆面过程 陆面过程是能够影响气候变化的发生在陆地表面土壤中控制陆地与大气之间动量、热量、及水分交换的那些过程；

陆面过程的简单介绍； 陆面模式研究前沿问题； 在陆面模型及气候模拟中引入地下水位的动 态变化的重要性； 地下水位动态表示模型； 地表径流机制； 地下基流机制； 模型耦合及模拟 结论与讨论

陆面过程 陆面过程是能够影响气候变化的发生在陆地表面土壤中控制陆地与大气之间动量、热量、及水分交换的那些过程； 这些过程受大气环流和气候的影响，反过来影响大气的运动，有不同的时空变化，由于人类活动改变地表的特性，使这些过程更为复杂； 如何准确描述气候模式中的大尺度陆面水文过程, 已经引起气候模式研究人员、水文学家和生态学家的关注。

陆面过程的主要方面 地面上的热力过程：发生在大气、植被和土壤表面的辐射过程（直接辐射、反射辐射和长波辐射）、土壤、植被、大气间的感热和潜热交换； 地面上的水文过程：大气降水、蒸发和植物蒸腾、凝结、地表径流以及冰雪融化和冻结； 地面上的动量交换：地面对风的摩擦和植被的阻挡； 地表与大气的物质交换：气体、气溶胶、烟尘向上输送和大气悬垂物的沉落； 地面以下土壤的热传导与气隙中的热输送； 地下的水文过程：大气降水、地面水的渗漏和深层水的上吸、植物根系的吸收、地下水流及土壤冻结和融化。

陆面模式的发展经历了三代 第一代从60年代末到70年代，用空气动力学总体输送公式和几个均匀的陆地表面参数简单地参数化土壤水的蒸发和地表径流，即水桶模式（Bucket）； 第二代，80年代以来，GCM中陆面参数化的一大进展是引入了植被生物物理过程，一系列不同详尽程度的陆面过程模式不断涌现，在本质上它们都属于计算土壤、植被与大气间交换方案（SVATS）； 第三代从90年代以后，植物生理学和生态学研究取得显著的进展以及卫星遥感技术的发展，考虑植物吸收CO2进行光合作用的生物化学模式引入陆面模式中，使植物能生长并响应气候的变化，即考虑碳循环作用的第三代陆面过程模式。

陆面过程模型中地下水位动态表示: Dai, Zeng, and Dickinson，1998, NCAR LSM, BATS, IAP94(Yongjiu Dai and Qingcun Zeng, 1997). CLM prototype, the initial CLM code. December 2001: to be released with the whole CCSM package officially. Liang and Xie (2001) developed a new parameterization to represent the Horton runoff mechanism in VIC-3L and combined it effectively with the original representation of the Dunne runoff mechanism(Xie et al., 2003). 谢正辉等, 1998, 中国科学. Liang, Xie, Huang,, 2003, Groundwater model (method 1)， Journal of Geophysical Research. Liang, Xie, 2003, Global Planetary Change. Yang and Xie, 2003, Groundwater model (method 2) , Progress in Natural Progress. 谢正辉等, 2004, 大气科学. Yeh et al 2005 JC,Maxwell et al 2005, JHM. Tian and Xie, et al, 2006, Science in China.

陆面模式研究前沿问题 水文过程研究需要深入； 生态过程机制（C,N循环）需要发展； 各种非均匀性问题； 雪盖、冻土和旱土、大面积水面作用的描述简单，冻土、雪盖占陆面面积都远大于1/4，沙漠区占1/4，水热耦合问题； 陆面模型参数移植与标定； 陆面数据同化问题； 与区域与全球气候模式的耦合； 各种应用问题。

地表地下水文及陆地覆盖变化引起气候的改变 气候与植被、地表水、地下水有重要的相互作用 气候变化引起区域水文生态过程的变化 地表地下水文及陆地覆盖变化引起气候的改变 气候与植被、地表水、地下水有重要的相互作用 北方干旱 南方洪涝 高原冰川退化 全球与区域尺度的气候变暖及频繁的人类活动，引起水文过程的变化；如我国北方干旱、南方洪涝、高原冰川退化； 河道断流干枯、地下水位下降，植被减少、土地沙化； 生态环境恶化的同时也使气候条件发生改变，极端灾害事件不断发生 ； 气候与地表水、地下水有重要的相互作用。 河道干枯 地下水位下降 植被减少 土地沙化 生态环境恶化

Changes in surface runoff, soil water and baseflow,groundwater table due to climate feed back to influence climate Current climate models neglect the dynamical variability of the groundwater table A surface runoff model, a groundwater model and a new surface runoff model are implemented in the Community Atmosphere Model

Climate, vegetation, and surface water and groundwater has important interactions, which play an important role in energy and water budgets of the land-atmosphere system, water resources management, ecological system, and water quality studies Interactions between Climate & groundwater(ICG) Effects of climate on groundwater(ECG).

Current climate models: No groundwater component No ICG & ECG Newly developed Climate model: Groundwater component+Surface runoff model+Base model+CAM Groundwater component (Liang et al.2003,JGR, Yang and Xie, 2003,Progress in Natural Science) New runoff mechanism (Liang & Xie, 2001, AWR) Subsurface runoff (Tian and Xie, 2006, Science in China)

Schematic representation of the numerical model 地下水位动态表示模型 q(t) z=0   Ground surface z=   Groundwater table (Moving boundary)   z=L   Bedrock Schematic representation of the numerical model

The governing hydrodynamic equation

infiltration boundary condition: where  is soil moisture, D() is the soil water diffusivity, K() is the unsaturated hydraulic conductivity, and q(t) is the infiltration or evaporation rate at the upper boundary.

For saturated zone: where (t) is the ground table to the surface, and L is the depth from surface to the bedrock

where： Initial condition Boundary Condition Moving Boundary condition

The moving boundary condition is where ne is effective porosity.

The mass balance equation:

Numerical scheme (1)Initializing (z,0) with (0). (2)Pre-estimate moisture profile  (z,t+t/2) through linear extrapolation from the old moisture distributions. Compute the coefficient matrix associated with the finite element method using moisture profile (z,t+t/2). (3)   Compute (z,t+t). (4)   Compute (t+t) based on (z,t+t). (5)   Repeat steps (2)-(5) until (t+t) converges for the next step.

Numerical schemes by two methods [0,L] is partitioned,moving boundary problem,Finite element, Mass lumped, direct method. [0, (t)], reducing the moving boundary problem into fixed boundary problem, Finite element, Mass lumped, Indirect method.

Method 1 Moving boundary problem FEM, Mass lumped, direct method Unsaturated zone Saturated zone L 谢正辉等, 2004, 大气科学, Liang, Xie, 2003, JGR Liang, Xie, 2003, Global Planetary Change

Method 2 The following coordinate transformation is used Reduce a moving boundary problem into the fixed boundary problem Yang and Xie, 2003, Progress in Natural Progress

A numerical model is based on mass lumped finite element method Unsaturated zone Saturated zone Moving boundary problem Fixed boundary problem

The Richards equation can be written as follows: Boundary condition: can be obtained:

The variational formulation is as follows: Divide [0,1] into n parts with n+1 nodes : i=1,……n+1, then where Linear function

It can be written as follows:

同时考虑地下水位、潜水面水分通量与储存的地下径流机制 主要是以潜水面上的Boussinesq方程为基础来建立地下径流机制 在该方程线性化解析解的基础上，发展了同时考虑潜水面水分通量与储存量的地下径流机制 田向军,谢正辉,张生雷,梁妙龄，基于Boussinesq-Storage同时考虑水分储存和入渗的地下径流机制，中国科学(D), 2006

The Dupuit-Boussinesq equation, describing the unconfined groundwater flow in a slope aquifer under a time-varying rate ,can be written as

The subsurface runoff is parameterized by the model with storage and recharge as

Where is subsurface runoff, is total storage of the aquifer

Where are the infinite number roots of

地表径流模型 超渗产流(Horton runoff) 蓄满产流(Dunne runoff) 土壤次网格空间变率 Input: 降水 Output: 地表径流 Liang and Xie, 2001, Advances in Water Resources Xie, Liang et al, 2003, AAS Su, Xie et al, 2003, Progress in Natural Progress

蓄满产流(shaded area) 和超渗产流(shed area with broken lines) 图表（over a studied area）

Runoff and drainage R=R1(y)+R2(y) i=i m[1-(1-A)1/b] f = f m[1-(1-C)]1/B] i m R2 f m Potential infiltration rate [L/T] Soil moisture capacity [L] y W P i 0 R1 R2 /t wp Wt W/t A C As 1 (a) 1 Fraction of studied area (b) Fraction of the area (1-As)

Saturation excess runoff R1(y) where i0 -- the point soil moisture capacity im -- maximum soil moisture capacity b -- shape parameter(soil moisture capacity) P --precipitation

Infiltration excess runoff R2(y) where fmm -- the average potential infiltration rate fm – the maximum potential infiltration rate B -- shape parameter(potential infiltration rate) P --precipitation ∆t--time step

NSRM 计算示意图 yes no R2 R1 R2 R1 P P As As W0 W0 1 1 Begin Precitation P P+i0<im i i0 +P i im im R2 i0 +P i0 R1 W Y R2 P Ssoil moisture Capacity Ssoil moisture Capacity R1 W Y i0 P W0 W0 As As 1 1 Fraction of Area Fraction of Area Solve Y Infiltration excess runoff R1 Saturation excess runoff R2 No Last time step ? Yes Stop

How to estimate fm From We get tf, then fmm

Example: Horton Infiltration Curve f(t) f0 f(t) = fc + (f0 - fc)e-kt Infiltration Rate (mm/h) W0 where f(t) ---- the infiltration capacity[L/T] f0 ---- the initial infiltration capacity[L/T] fc ---- the final capacity[L/T] k ---- an empirical constant[T-1] tf t Time (hour)

Infiltration Rate (mm/h) Example: Philip Infiltration Curve f(t) f0 Infiltration Rate (mm/h) W0 t tf where f(t) ---- the infiltration capacity[L/T] Kp---- the final capacity[L/T] Sp---- an empirical constant Time (hour)

CLM+ 地表径流 +地下水+基流 Land framework Groundwater Runoff and subsurface parameterization: the surface model (蓄满、超渗、土壤次网格课件变率) Subsurface parameterization：同时考虑潜水面水分通量与储存量

模型主要特征 10 soil layers for soil temperature and soil moisture+groundwater; A multi-layer parameterization of snow processes, with up to 5 layers; Liquid water + ice water; Runoff and subsurface parameterization: the surface model(蓄满、超渗、土壤次网格课件变率), Subsurface parameterization：同时考虑潜水面水分通量与储存量; Photosynthesis-conductance model; Mosaic treatment of subgrid fraction of energy and water balance; A global land cover and vegetation database derived from AVHRR data, and a global database of root vertical distribution; The full use of FORTRAN90 in the code.

Coupling of CLM and NDMs The new land surface model: CLM+NDMs Remark: Land surface model+NDM

E R P K2 K1 D2 D1 Qb z=-zn z=-z1 z=0 z=-z2 CLM Layers Multi-Layers

Comparison of daily observed groundwater table with the simulated groundwater table at the well Haizhou

Comparison of mean monthly observed groundwater table with the simulated groundwater table at the well Haizhou

Coupling of the three hydrological mechanisms with the Climate model CAM The new climate model: CAM+Groundwater component+Surface runoff model+Base model

(soil moisture,groundwater table) CLM 10 layer soil moisture CAM model CLM model Surface runoff model CLM groundwater model (soil moisture,groundwater table) New base runoff model CLM 10 layer soil moisture CLM model . . . Next step

Dynamic variation of groundwater table can be described as a moving boundary problem, which can be reduced to a fixed boundary problem through a coordinate transformation. With this method, the computational cost is decreased; The numerical simulations by the newly developed groundwater model coupled with CLM show that the land surface model can simulate dynamic variation of groundwater table; It has potential to explore interactions between land and atmosphere.

Thank You for your attention! 谢谢各位！ zxie@lasg.iap.ac.cn