冬季大尺度流型与夏季中国降水量

对近45年（1951—1995年）前期冬季北半球500 hPa高度距平场和夏季中国降水量进行旋转奇异值分解（RSVD）,研究了耦合相关空间分布的区域特性,同时分析了相关型的时间演变。结果表明,旋转奇异值分解有效地揭示了前期冬季北半球500 hPa大尺度流型与夏季中国降水耦合相关型的区域分布特征,并且物理意义明确。利用Galerkin有限元集中质量法,讨论了非饱和土壤水流动的数值计算模型,用以模拟均质土壤,地下水埋藏很深且在不同的初始和边界条件下的水分运动。通过将第一类边界条件齐次化,而对于第二类非线性边界条件采用变分的办法将其直接转化为已知边界通量的计算,从而容易且较好地处理了带通量约束边界条件。对于入渗或蒸发问题,用通常的在分析比较不同地区降水化学特性时,如果列出各种离子的具体数值,既显得繁琐又不容易得出结论。现提出一种简便方法,即先概括出几种最重要的降水化学特性,分别以字母代表,再把这些特性分成几个等级以数字表示,就能很直观方便地比较这些地区的降水化学特性。还利用权威观测资料,以上述方法具体比较了世界主要酸雨地区的降水化学特性。       

三类陆面模式模拟土壤湿度廓线的对比研究

针对不同陆面模式对土壤湿度方程求解方法以及对土壤分层结构的差异, 本文选取了三类陆面模式（CLM, CABLE和ECMWF陆面模式）作比较研究。为了避免不同模式参数化方案引起的上边界误差, 上边界采用固定蒸发率、 入渗率和固定表层土壤湿度三类边界条件。土壤分层采用101层（细网格）和11层（粗网格）两种, 并考虑土壤性质沿深度变化。结果表明： 当土壤性质均匀时, 求解的差别主要在第三类边界条件下CLM 求出的水分入渗速度比其它两种快; 改用粗网格后由于土壤深层厚度加大无法与细网格得出的土壤湿度廓线相重合。当土壤性质非均匀时, 模拟结果间差别加大, 只有ECMWF模式模拟的土壤湿度廓线是严格连续的。对于模式和上边界的不同组合, 粗、 细网格模拟结果间均方根偏差不一致。一般而言, CABLE模拟的偏差除第一类条件较小外, 其它都是最大的。第二三类边界条件引起的偏差较大, 第一类最小。上述结果提示我们, 在比较不同陆面模式以及用观测资料来检验模拟结果时应充分考虑土壤分层及土壤性质非均匀性的可能影响。     

非饱和土壤水流方程的极值原理

讨论了非饱和土壤水流问题及其数值计算方案的极值原理,在理论上证明了连续问题及其数值格式均满足极值原理,即在一定的条件下,预报变量的最大值和最小值只能在边界上达到,从而描述了特定的物理性质.这些问题在讨论入渗、蒸发问题的研究中是重要的.     

陆面模型Noah-MP的不同参数化方案在沙漠区域的适用性研究

为研究陆面模型Noah-MP在沙漠下垫面的最优参数化方案组合,本文利用中国气象局塔克拉玛干沙漠气象野外科学试验基地观测数据,根据沙漠环境特征进行不同参数化方案组合的三组模拟实验,利用观测数据对10 cm土壤温湿度、感热、潜热通量模拟值对比分析得出最优组合。研究表明:第三组对10 cm的土壤温度模拟效果最好,主要原因是Chen97感热交换系数和全网格二流近似(gap=0)辐射传输方案比较符合沙漠的环境特征。三组试验对土壤湿度模拟效果差,其主要原因是沙漠的土壤信息未能体现在模式中,第二组选择CLM方案对土壤类型影响蒸发方面有一定考虑,其模拟结果相对较好。对于感热通量,第一、二组模拟值在波峰存在高估,尤其是第二组模拟值在降水后出现了明显低估情况,第三组模拟效果最好,主要得益于选择了感热交换系数Chen97方案,能够较为真实的刻画Ch变化特征。潜热通量在四个特征量中模拟效果最差,主要原因是沙漠土壤水分极低,观测降水和实际进入土壤的水量有差异,另外没有植被和植物根系,模式无法准确计算土壤蒸发和植被蒸散。根据统计分析和泰勒图可知,第三组能够更好地还原沙漠区域的陆面过程。     

基于陆面模式Noah-MP的不同参数化方案在半干旱区的适用性

针对陆面模式Noah-MP对兰州大学半干旱气候与环境观测站（SACOL）2009年8月地表热通量模拟值偏差大的问题,通过分析相关物理过程和模拟试验来探究偏差的来源,并确定合适的参数化方案:采用Chen97方案计算感热输送系数可以改善感热通量的模拟;采用Jarvis气孔阻抗方案能增大植被蒸腾,改进模式对潜热通量的模拟效果,同时也使热通量在感热和潜热间的分配比例合理;采用LP92方案可减小土壤蒸发阻抗并有利于土壤蒸发,使得模式对潜热通量的模拟效果变好。不同参数化方案的组合试验表明:同时采用2组或3组新的参数化方案组合可以进一步减小模拟的地表感热和潜热通量的均方根误差,但是土壤湿度和温度的模拟效果并没有同步改善。     

一个区域气候模式水文过程的改进及年尺度模拟研究

本文将更符合物理过程实际的考虑入渗非均匀和降水非均匀的水文模型VXM并入区域气候模式RegCM3模式,利用此区域水文气候模式分别对1988、1990、1991年3个不同气候年的水文气候进行了模拟.模拟结果表明,模式对入渗非均匀和降水非均匀的响应在年尺度上是敏感的:模式能成功模拟年平均降水及降水的年内变化,较好地再现了降水分布和大小;并入VXM模型后模式对南方径流的模拟能力得到较大的提高,模拟的年平均及年内变化与实际较为一致.结果还表明,径流机制的改进有助于改善降水模拟能力,并引起蒸发、温度等气候要素相应的变化;并入VXM模型后对模拟结果的影响更主要体现在夏季.     

降水气候强迫下非均匀地表区域平均径流的一种参数化方案

将任一中尺度区域的平均瞬间径流率考虑为区域平均降水量和地表土壤层水分渗透垦的余项.根据降水量在地理空间上分布的实测资料拟合其空间概率密度函数(PDF),并结合土壤入渗物理过程的数学描述及其经验公式,精确估计出地表土壤渗透率及其空间分布,由此建立区域地表径流率的统计-动力学估计方案.换言之,区域内地表产流率可视为区域平均降水量与区域平均的土壤下渗量之差值,而区域内土壤的平均下渗量又町分为非饱和区和饱和区两部分的下渗量来分别计算.就陆面水分循环的物理过程而言,地表入渗现象是在一定的下垫面特性基础上,由一定的水分供应源而形成的.根据大气降水向地表层输送水分的物理过程,在满足植被表层覆盖需水(截流水)和地表层土壤人渗水基础上,多余的降水量才会形成地表径流.凶此,推求地表产流率的主要关键在于地表土壤层需水量.为此奉文根据土壤水分通量方程推导出水分入渗公式.又从描述土壤水分和降水的空间PDF出发,推导出非均匀土壤含水量及降水气候强迫所形成的次网格尺度区域平均径流率计算公式.利用长江三角洲地区1996年降水量和土壤特性等实测资料建立区域平均地表径流率的估计公式,并对其影响凶素进行敏感性试验.结果表明,该方法与用Mosaic方法计算的区域径流率(或产流率)结果十分接近.由此可见,该文提出的降水气候强迫下非均匀地表区域平均径流的这种统计-动力参数化方案,具有相当的可靠性与可行性.     

海冰非均匀条件下大气环流模式和海洋环流模式耦合的实现

通过采用一种较好地考虑了海气通量交换对下垫面特征非线性依赖的通量计算方案,利用较成熟的逐日通量距平耦合方案实现了次网格尺度海冰非均匀条件下一个全球大气环流模式和一个全球海洋环流模式在高纬地区的耦合,并完成了一个50年的长期积分。模拟结果表明,通量计算方案中水道的作用是合理的,耦合模式能较好地模拟出北半球高纬海冰的主要地理分布特征,但夏季北冰洋内部靠近欧亚大陆部分边缘海区海冰密集度偏大。     

CLM3.5模式对青藏高原玛曲站陆面过程的数值模拟研究

利用通用陆面过程模式(CLM3.5)和青藏高原玛曲站2010年6月-2011年2月的观测资料进行了9个月的单点数值模拟试验。通过比较辐射通量、能量通量、土壤温度及土壤含水量的模拟值和观测值,结果表明,CLM3.5模式能较成功地模拟玛曲地区的陆面能量与水分特征。该模式对夏季向上短波辐射的模拟较好,冬季整体偏小。向上长波辐射的模拟整体较好,但模拟值稍偏大。净辐射的模拟整体较好,模拟值与观测值的相关系数为0.99,偏差为-1.28 W.m-2。感热通量的模拟较差,整体显著偏高。潜热通量的模拟较好,随季节变化特征明显。土壤热通量的模拟夏季较好,冬季土壤冻结及消融期的偏差较大,主要原因与冬季模拟的积雪偏少有关。土壤温度的模拟夏季较好、冬季较差,6层土壤温度模拟值与观测值的相关系数均在0.98以上,平均偏差为-1.80℃。模式较好地模拟出了冬季土壤冻结后存留的未冻水,冻结后土壤含水量的模拟较该模式以前的版本有了很大的改善,6层土壤含水量模拟值与观测值的平均相关系数为0.94,平均偏差为-0.015m3.m-3。     

卫星遥感结合数值模式估算金塔绿洲非均匀地表能量通量

针对遥感在面上计算的特点,将模式模拟的气象要素区域分布替代以往使用的单点观测值作为遥感估算蒸散发模型的初始场,引入到SEBS(Surface Energy Balance System)模型中,利用EOS/MODIS遥感资料对金塔绿洲非均匀下垫面地表能量通量进行了估算。对比估算结果与实测值表明,引入数值模拟结果后,绿洲地表感热通量的估算误差平均减小了5.8%,潜热通量的误差平均减小了5.5%,说明数值模拟结果的引入比较成功。通过分析地表通量的区域分布特征表明,数值模拟结果的引入在一定程度上更加细致地刻画了荒漠绿洲能量平衡的分布特征,在戈壁荒漠地区,潜热通量非常小,而绿洲集中的地区及水库附近出现了潜热通量的极大值。     

An unsaturated soil water flow problem and its numerical simulation

1.IntroductionUnsaturatedsoilwaterflowisaflowwherewaterisnotfullofsoilhole,whichisanimportantformofflowinporousmedia.Predictionofanunsaturatedflowisprovidedwithsignificanceinmanybranchesofscienceandengineering.Theseincludeatmosphericscience,soilscien...     

Optimization of Upstream Profiles in Modelled Flow Over Complex Terrain

This paper describes an adjoint method for data assimilation intoupstream boundary conditions of numerical modelsusing optimal control theory. Mathematical formalisms are given along with the numerical implementation of the schemein a column model of the atmospheric boundary layer. The optimized mean and turbulence profiles are used as an upstream solutionin a model of turbulent flow in complex terrain. To contrast thiswith other methods, two solutions for flow over an isolatedhill are calculated, one with an optimized upstream solution andone with a simple surface-layer formulation for the upstream solution.These two solutions are compared to observations and analytical theory. The adjoint optimization method is shown to producesolutions of flow in complex terrain that are substantively differentat the two solutions, with the optimized solution giving more accurate results.     

陆面过程模式中地下水位的参数化及初步应用

田间研究表明地表水和地下水有重要的相互作用,它与土壤含水量密切相关.土壤含水量不仅在陆气相互作用系统水和能量平衡中,而且在干旱、洪水预报、水资源管理、生态系统研究中起十分重要的作用.因此,研究地表水和地下水的相互作用,建立陆面模式中地下水位的动态表示,对于气候与水资源研究具有重要意义.将地下水位的动态表示问题归结为饱和与非饱和流问题,发展了其数值计算方案,建立了地下水位的动态表示,并与陆面过程模型耦合,建立了陆气相互作用中地下水位的动态表示,并进行了数值模拟研究.     

一类偶数阶Sturm-Liouvile四点边值问题多个正解的存在性

讨论了一类偶数阶四点边值问题正解的存在性,借助Leggett-Williams不动点定理和不等式技巧,得到了该边值问题至少存在三个和任意奇数个正解的充分条件.     

On no-slip boundary conditions for the incompressible Navier-Stokes equations

Two local implementations of no-slip boundary conditions are investigated for both the vorticity—streamfunction and momentum—pressure formulations of the time-dependent planar incompressible Navier-Stokes equations, as applied to barotropic ocean circulation modelling. The objective is to determine the extent to which the local accuracy and numerical consistency of these conditions affects the global solution. The effects of a non-local implementation of no-slip conditions for the vorticity—streamfunction equations are also studied. In all cases, boundary condition effects are measured by comparing time-averaged dynamics of turbulent solutions of numerical models based on the two formulations.In the model interior, the energy and enstrophy conserving Arakawa Jacobian is used for the vorticity—streamfunction equations while an extension of the energy and potential enstrophy conserving Arakawa and Lamb finite difference scheme is used for the momentum-pressure equations.Numerical experiments performed with a non-linear model similar to Bryan's barotropic ocean reveal no significant differences between the time-averaged solutions obtained with either of the two formulations, with each using either of the two local boundary conditions. A simple one-dimensional analogue of the vorticity—streamfunction equations is solved algebraically to explain the experimental results. A similar analogue suggests that an apparent inconsistency in the no-slip boundary conditions within the Cox stratified, primitive equation, ocean circulation model should not affect the accuracy or convergence of the global solution.     

地形对边界层影响的有限元数值模式

本文在定常和中性层结条件下应用有限元法初步建立了一个能够处理二线复杂地形上边界层问题的数值模式.模式使八节点抛物型等参元,有限元方程组用“波前法”求解.应用模式计算了几种典型地形上的近地层流动.模拟出了风速、气压、湍流动量通量以及湍流交换系数等气象要素的主要分布特征,并将计算结果与有关的观测事实做了比较.     

THE INVERSE PROBLEM OF KLEIN-GORDON EQUATION BOUNDARY VALUE PROBLEM AND ITS APPLICATION IN DATA ASSIMILATION

Since the solution of elliptic partial differential equations continuously depends on the boundary condition, the Euler equation derived from variational method cannot be solved without boundary condition. It is often difficult to provide the exact boundary condition in the practical use of variational method. However, in some application problems such as the remote sensing data assimilation, the values can be easily obtained in the inner region of the domain. In this paper, the boundary condition is tried to be retrieved by using part solutions in the inner area. Firstly, the variational problem of remote sensing data assimilation within a circular area is established. The Klein-Gordon elliptic equation is derived from the Euler method of variational problems with assumed boundary condition. Secondly, a computer-friendly Green function is constructed for the Dirichlet problem of two-dimensional Klein-Gordon equation, with the formal solution according to Green formula. Thirdly, boundary values are retrieved by solving the optimal problem which is constructed according to the best approximation between formal solutions and high-accuracy measurements in the interior of the domain. Finally, the assimilation problem is solved on substituting the retrieved boundary values into the Klein-Gordon equation. It is a type of inverse problem in mathematics. The advantage of this method lies in that it overcomes the inherent instability of the inverse problem of Fredholm integral equation and alleviates the error introduced by artificial boundary condition in data fusion using variational method in the past.     

Ｅ网格变量分布下差分格式的性质

本文用线性化的浅水波方程系统地分析、讨论了Ｅ网格变量分布下差分计算的性质；指出了目前有关讨论Ｅ网格差分性质在方法上存在的问题；给出了一种解决Ｅ网格中两个Ｃ网格分离的方法；提出了一种Ｅ网格用于海洋计算时，海洋侧边界条件的处理方法。初步的数值试验证明了这些方法对抑制Ｅ网格中的计算躁声是有效的。     

On the inertial motion of a homogeneous ocean

An investigation of properties of the solutions of the steady state inviscid barotropic vorticity equation in a rectangular basin was performed for various functional relationships between potential vorticity and the streamfunction. All computed solutions which have slow interior flow and satisfy Arnol'd-Blumen condition are qualitatively similar to Fofonoff's inertial gyre. A new class of solutions with a small vortex near the boundary current is described. Such solutions are not stable under finite amplitude perturbations and instability is manifested in the drift of the vortex. It is shown that the vortex is robust and decays only after collision with the boundary or under the influence of very large perturbations. We also show that the inertial boundary current may be much wider than in Fofonoff's model due to the appearance of a countercurrent on its seaward side.     

Finite-amplitude, neutral baroclinic eddies and mean flows in an internally heated rotating fluid: 1. Numerical simulations and quasi-geostrophic ‘free modes’

A series of numerical simulations of steady wave flows in a rotating fluid annulus, subject to internal heating and various thermal boundary conditions, is examined to characterise their structures, energetics and potential vorticity transport properties. The last of these characteristics, together with more conventional scaling considerations, indicate the possibility of applying quasi-geostrophic theory to the interior flow in a formulation similar to the inviscid, adiabatic models of Kuo and White.The analytical model of White, describing finite amplitude, neutral baroclinic eddies and mean flows as illustrations of the Charney-Drazin non-acceleration theorem, is then extended to include uniform diabatic heating and the effects of different forms of lateral shear in the background mean zonal flow. Like the solutions discussed by White, those obtained in the present paper consist of steady, internal jet, mean zonal flows, and baroclinic and barotropic Rossby wave components, all having the same three-dimensional wavenumber. Provided the diabatic heating is proportional to the stratification of the background flow, measured by the square of the Brunt-Vaisälä frequency N, the potential vorticity equation remains homogeneous. All the solutions are then characterised by zero net transfer of potential vorticity despite the possibility of non-zero eddy fluxes of heat or momentum and non-trivial Lorenz energy cycles.A series of particular three-component solutions (which, like some of the solutions discussed by White, do not obey conventional lateral boundary conditions) is examined as possible theoretical analogues of the steady waves observed in the numerical simulations of the laboratory flows, and is found to agree encouragingly well in the spatial variations of their mean flows, eddy stream function (pressure) and eddy fluxes of heat and momentum. Potential vorticity fluxes in the numerical simulations are relatively small (though crucially non-zero), supporting the possible analogy with the analytical model and exposing some limitations of the latter in not accounting for weak dissipation and forcing processes present in the laboratory flows.Further implications of the results are discussed, including possible analogies between the laboratory experiments and certain features in planetary atmospheres and oceans.