ANALYSIS OF SPHERICAL FUNCTION SPECTRAL STRUCTURE OF THE NORTHERN HEMISPHERE 500 HPA MONTHLY MEAN HEIGHT*

Study is undertaken of spherical function spectral structures of long-term mean and anomaly patterns of the Northern Hemisphere 500 hPa monthly mean geopotential height together with the seasonal and interannual variations investigated.Results show that they are marked by low dimensions and low orders,and the mean and anomaly fields can be described in terms of 20 and 50 spherical function components,respectively.     

An erosion criterion for gravel-bed rivers

A theoretically-based erosion criterion is developed for gravel-bed rivers which incorporates the effect of both grain geometry and turbulent velocity fluctuations. It is derived from a balance of instantaneous drag, lift, and gravity forces operating on individual grains and is calculated for spherical grains arranged in three distinct geometries. To accommodate the temporal variation in bed shear stress, the model includes a stochastic element based on the characteristics of turbulence derived from the flume evidence of McQuivey (1973a, b). In terms of the Shields parameter, results show reasonable agreement with the range of observations quoted from the field and with the experimental data of Fenton and Abbott (1977). Finally, the argument is generalized to cover applications in the wider context of field conditions including a range of grain sizes and flow conditions.     

Efficiency of kriging estimation for square, triangular, and hexagonal grids

Although several researchers have pointed out some advantages and disadvantages of various soil sampling designs in the presence of spatial autocorrelation, a more detailed study is presented herein which examines the geometrical relationship of three sampling designs, namely the square, the equilateral triangle, and the regular hexagon. Both advantages and disadvantages exist in the use of these designs with respect to estimation of the semivariogram and their effect on the mean square error or variance of error. This research could be used to design optimal sampling strategies; it is based on the theory of regionalized variables, in which the intrinsic hypothesis is satisfied. Among alternative designs, an equilateral triangle design gives the most reliable estimate of the semivariogram. It also gives the minimum maximum mean square error of point estimation of the concentration over the other two designs for the same number of measurements when the nugget effect is small relative to the variance. If the nugget effect is large (.90 ² or more), and the linear sampling density is >0.85r where r is the range, the hexagonal design is best. This study computes and compares the maximum mean square error for each of these designs.     

A test of granulometric control of desert dune geometry

I. G. Wilson's hypothesis of coarse-tail grain-size control of dune spacing was derived from three dunefields in the Sahara and, although it was supplemented by measurements of spacing from other parts of the world, the grain-size data come only from North Africa. In this paper the hypothesis is tested in the Australian dunefields. Australian dunes do not form separate categories on a P₂₀/s (twentieth percentile/spacing) plot and, when placed on Wilson's diagram, the Australian data form a continuum between dunes and draas. Ripples maintain their identity, suggesting that the average saltation length of sand controls ripple wavelength while dunes and Wilson's draas are formed by secondary flow of some kind. In Australia the spread of data on the P₂₀/s diagram indicates that grain-size is not the prime control on s. Data from Australia and the Sahara indicate that direct linear relationships between s and h (dune spacing and height means respectively for blocks of dunes) occur but they have different slopes in different areas. These differences possibly reflect variations in vegetation and substrate as well as differences in wind regime. The separation of dunes from draas in the Sahara reflects the greater role of grain-size in an area where coarse grains frequently occur in dune crests. The relative paucity of coarse grains in Australian dune crests may reflect the fine-grained alluvium from which the dunes are derived. These differences may be ascribed to differing topography in Australia and the Sahara.     

Modelling of mantle postglacial relaxation in axisymmetric geometry with a composite rheology and a glacial load interpolated by adjusted spherical harmonics analysis

Although studies on glacial isostatic adjustment usually assume a purely linear rheology, we have previously shown that mantle relaxation after the melting of Laurentide ice sheet is better described by a composite rheology including a non-linear term. This modelling is, however, based on axially symmetric geometry and glacial forcing derived from ICE-3G and suffers from a certain amount of arbitrariness in the definition of the ice load. In this work we apply adjusted spherical harmonics analysis to interpolate the ice thicknesses of ICE-3G and ICE-1 glaciological models. This filters out the non-axisymmetric components of the ice load by considering only the zonal terms in the spherical harmonics expansion. The resulting load function is used in finite-element simulation of postglacial rebound to compare composite versus purely linear rheology. Our results confirm that composite rheology can explain relative sea level (RSL) data in North America significantly better than a purely linear rheology. The performance of composite rheology suggests that in future investigations, it may be better to use this more physically realistic creep law for modelling mantle deformation induced by glacial forcing.     

Comparison of resection–intersection algorithms and projection geometries in radiostereometry

Three resection–intersection algorithms were applied to simulated projections and clinical data from radiostereometric patients. On simulated data, the more advanced bundle-adjustment-based algorithms outperformed the classical Selvik algorithm, even if the error reductions were small for some parameters. On clinical data, the results were inconclusive.The two different projection geometries had a much larger influence on the error size and distribution. For the biplanar configuration, the position and motion errors were small and almost isotropic. For the uniplanar configuration, the position errors were comparably high and anisotropic, but still resulted in a high accuracy for some motion parameters at the expense of others.The simplified resection–intersection algorithm by Selvik may still be considered a good and robust algorithm for radiostereometry. More studies will have to be performed to find out how the theoretical advantages of the bundle methods can be utilized in clinical radiostereometry.     

EFFECTIVE DISCHARGE CALCULATION GUIDE

1 mTRonvcnox: moareS Aun CoxcmSAJluvial rivers have the pOtenhal to adjust their shaPe and dimensions to all flows that tranSPOrtsediment, but Inglis (l94l) suggested that, for rivers that are in regime, a single steady flow could beidenhfied which would Produce the same bankfll dimensions as the natural sequence of events. Hereferrd to this now as the dondnan discharge.Wolman and Mller (l960) idenhfied that the flow doing most bed material transPort over a period ofyears may be taken tO…     

土壤大孔隙流研究中分形几何的应用进展

土壤中普遍存在的大孔隙使水及溶质快速穿过土壤，污染地下水，确定土壤大孔隙流性质需要大量的野外和室内实验。本文在对分形几何概念进行简要阐述的基础上，介绍了分形几何在土壤大孔隙流研究中所取得的成果，结果表明应用分形几何确定土壤大孔隙流性质是一种省时、省力和具有广泛代表性的方法，最后对分形几何在土壤在大孔隙流研究中应用前景作了展望。     

实际预报可预报性的时空依赖性分析

本文利用国家气象中心1990年1月1日至1992年2月29日的1～5 d、500 hPa高度场业务预报结果研究了不同球谐函数谱分量和经验正交函数(EOF)谱分量的可预报性。对球谐函数谱分量的研究表明可预报性并不是随着空间尺度的增加呈现单调的递减关系，主要表现为在总波数n等于5附近具有最大可预报性。可预报性主要依赖于总波数n，经卷大圆上的波数和纬向圆周上的波数对可预报性具有完全相同的重要意义。对EOF谱分量的分析表明，随着EOF指数(即序号数)的增大，可预报性依次减小。从EOF和球谐函数的关系发现前几个EOF分量正是对应着最可预报的球谐函数分量。进一步分析表明，最可预报的分量对应大气运动的慢变流型。这些结果对如何使用数值预报产品以及如何进行延伸预报具有重要意义。     

自转微椭、非均匀地球的潮汐变形

鉴于当前国际上关于自转微椭、非均匀地球（ＳＲＥＨＩ）的固体潮汐响应的结果之间存在明显分歧，特别是Ｌｏｖｅ数ｋ及重力潮汐因子δ对纬度的依赖情况截然不同，本文借助于摄动法与张量正则分量的广义球谐展开建立起来的侧向非均匀、自转微椭、粘弹地球的潮汐模拟理论，计算了ＳＲＥＨＩ地球的潮汐形变及相应的引力位变化．结果表明，描述径向位移的Ｌｏｖｅ数的纬度依赖部分系数ｈ＿＋与球对称部分ｈ＿０＋δｈ＿０之比不大于１．０‰；对Ｏ＿１波为０．２７‰；对Ｍ＿２波为０．１９‰；对Ｍ＿３波为０．４９‰；对Ｍ＿４波为０．８８‰．描述地球引力位变化的Ｌｏｖｅ数的纬度依赖部分系数ｋ＿＋与球对称部分ｋ＿０＋δｋ＿０之比小于３．０‰；对Ｏ＿１波为２．６７‰；对Ｍ＿２波为１．８９‰；对Ｍ＿３波为２．２４‰；对Ｍ＿４波为２．７０‰．