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。     

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.     

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.     

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。     

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。     

可用于陆面过程模型的地形指数水文模型中简化参数化方案的研究

在全球气候系统模型中,陆面水文过程对提高模拟精度有显著作用.土壤水分空间非均匀分布对于蒸发和径流的计算以及能量在潜热和感热之间的分配具有重要的影响,但现有的多数陆面过程模式未能考虑土壤水分水平非均匀性的影响.地形指数模型以其较好的物理基础、参数少、计算量小,且能考虑地形变化对土壤水分非均匀分布影响等优点,使其有潜力模拟陆面过程中水分过程分布非均匀二维特性.目前地形指数水文模型已被推荐应用于陆面过程模式(Land surface models,LSMs)中以改进对陆面水文过程的模拟能力.在地形指数模型中,数据的空间分辨率、河道的起始临界值、非饱和区域的分区和空间各点的坡度等因子不同的确定,都能对模拟结果产生重要影响,对它们如何合理地给定,既不降低模型精度,又能省时、省资源是十分重要的.本研究通过大量的敏感性模拟试验,较系统地探讨上述参数不同的确定方案对流域水量平衡模拟结果的影响.主要结论有:(1)将流域按地形指数值大小分为16块与仅区分饱和区与非饱和区或仅区分饱和区、较湿润区和较干区3块模拟结果相差不大,因此将地形指数模型应用于陆面模式时仅区分饱和区与非饱和区或区分饱和区、较湿润区和较干区3块这种简化方案也许是一种可行的选择;(2)不考虑坡度会扭曲水量平衡各要素的计算,用一个平均坡度替代实际坡度的办法就会有比较接近了实际坡度的结果.因此,LSM模型中一维均匀的网格做法应该改进,但太细致的坡度取法也许没必要.以上结论可为今后发展用于陆面模式的大尺度水文模型提供依据.     

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.     

基于概念模型的麦田土壤水分动态模拟研究

农田土壤水分模拟是农业用水管理的重要依据。以根区土体水量平衡方程为依据,考虑根区下界面水分通量,构建了农田土壤水分变化模拟模型,该模型由作物蒸散量模型、根区下界面水分通量模型以及水量平衡方程等组成。采用山西水利职业技术学院试验基地2007年和2008年2个年度冬小麦试验资料,确定了模型参数。结果表明,土壤储水量模拟计算值与实测值有较好的一致性,其相关系数达到0.9555;F检验结果达到极显著水平,所建立的麦田土壤水分动态模型可用于作物蒸散量、根区下界面水分通量和田间土壤水分的模拟计算;计算精度平均达到3%～11%。表明该模型可较好地描述农田士壤水分转化过程。     

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.     

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。     

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.     

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape. Part I: Theory and Integral Formulae

The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments.Classic integral formulas and their variants are used to formulate solutions for the coupled problems.In the absence of data holes,the total solution is the sum of two integral solutions.One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components(velocity potential and streamfunction) can be constructed by applying Green’s function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain.The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain.By setting either the velocity potential(or streamfunction) component to zero,the other component of the externally induced solution can be expressed by the imaginary(or real) part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution.The streamfunction(or velocity potential) for the externally induced solution can also be expressed by the boundary integral of a double-layer(or singlelayer) density function.In the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions.     

Analytic solutions to long's model: A comparison of nonhydrostatic and hydrostatic cases

Summary In this paper, analytic solutions of the nonhydrostatic and hydrostatic forms of Long's model were obtained under two different sets of vertical boundary conditions: The first uses a sumusoidal obstacle at the lower boundary and a rigid-lid top for the upper boundary. The second set applies an isolated obstacle of the Witch of Agnesi type at the lower boundary, while still using a rigid lid at the top. Following the solution evaluations, comparisons between the nonhydrostatic and hydrostatic solutions were processed in order to describe several influences introduced by using the hydrostatic assumption in this model.Through comparisons we have found that, in the case of a sinusoidal lower boundary condition, the hydrostatic solution is obtained as the zero mode of the nonhydrostatic solution. The influence of the hydrostatic assumption on the model solution is trivial in this case. When an isolated lower boundary condition is applied, however, the solutions illustrate dramatic differences, showing the significance of the effect of hydrostatic assumption on this model's solutions. These effects vary considerably with the model parameters as well. The comparison results also reveal that the realization of the hydrostatic assumption in this model's solutions is accomplished through the vertical boundary conditions used in the model evaluations.With 5 Figures