Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Conceptually-based shot noise modeling of streamflows at short time interval

A conceptual-stochastic approach to short time runoff data modelling is proposed, according to the aim of reproducing the hydrological aspects of the streamflow process and of preserving as much as possible the dynamics of the process itself. This latter task implies preservation of streamflow characteristics at higher scales of aggregation and, within a conceptual framework, involves compatibility with models proposed for the runoff process at those scales. At a daily time scale the watershed response to the effective rainfall is considered as deriving from the response of three linear reservoirs, respectively representing contributions to streamflows of large deep aquifers, with over-year response lag, of aquifers which run dry by the end of the dry season and of subsurface runoff. The surface runoff component is regarded as an uncorrelated point process. Considering the occurrences of effective rainfall events as generated by an independent Poisson process, the output of the linear system represents a conceptually-based multiple shot noise process. Model identification and parameter estimation are supported by information related to the aggregated runoff process, in agreement to the conceptual framework proposed, and this allows parameter parsimony, efficient estimation and effectiveness of the streamflow reproduction. Good performances emerged from the model application and testing made with reference to some daily runoff series from Italian basins.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

大地电磁二维对称各向异性介质的有限元数值模拟

假定垂直轴为二维对称各向异性介质主轴之一，构造走向与另一主轴方向成任一夹角，用伽勒金（Ｇａｌｅｒｋｉｎ）有限元法和矩形网格，优化地合成总体刚度矩阵，使二维各向异性介质的基本方程形成有限元代数方程组，求出各节点场值，并利用ＭＯＭ法求出辅助场，进而求出张量阻抗等响应函数．同时还对有关文献的计算模型进行了数值模拟检验     

成都粘土裂隙成因研究

根据成都粘土中裂隙特征与地质环境条件的分析，提出成都粘土中途中眩要裂隙类型的成因模式，上升剥蚀引起的垂向卸荷作用产生波状水平裂隙，冲沟切割引起的侧向卸荷作用，产生平行斜列隙裂。     

地震应力触发数值模拟的初步研究

本文基于有限元方法，初步建立了西南地区二维和三维数值模拟有限元模型，并针对川滇地区，重点建立了包括上地壳、下地壳、上地幔等的三维有限元模型。最后，讨论了地震产生的应力变化对整个西南地区的应力调整情况。结果表明：前一地震对后续地震有一定的触发作用。因此，强震活动有限元模型的建立对判定未来强震危险区有一定的作用。     

Resolution Sensitivity and Scaling of Large-Eddy Simulations of the Stable Boundary Layer

Large-eddy simulations (LES) of the continuously turbulent quasi-equilibrium stable boundary layer (SBL) are conducted with grid lengths in the range of 12.5 m to 2 m, in order to explore resolution sensitivity, and determine at what point grid convergence occurs. The structure of the mean potential temperature, winds, and turbulent fluxes varies significantly over this resolution range. The highest resolution simulations show a significant degree of convergence. The dimensionless momentum diffusivity asymptotes to a value of 0.06, corresponding to a limiting flux Richardson number of 0.15.Using the converged simulations, some scaling hypotheses underpinning first-order and second-order closure models are revisited. The effective Richardson number stability functions of the LES are compared with the forms often used in numerical weather prediction (NWP). The mixing implied by the LES is less than that used in NWP. The commonly used similarity profiles for heat and momentum fluxes, and the scalings for dissipation and pressure covariances are compared with the LES. This information could provide guidance for the next generation of SBL parametrization schemes.     

Large-Eddy Simulation of Turbulent Flow Over a Rough Surface

A family of wall models is proposed that exhibits moresatisfactory performance than previousmodels for the large-eddy simulation (LES) of the turbulentboundary layer over a rough surface.The time and horizontally averaged statistics such asmean vertical profiles of windvelocity, Reynolds stress, turbulent intensities, turbulentkinetic energy and alsospectra are compared with wind-tunnel experimental data.The purpose of the present study is to obtain simulatedturbulent flows that are comparable with wind-tunnelmeasurements for use as the wind environment for thenumerical prediction by LES of source dispersion in theneutral atmospheric boundary layer.     

Laboratory and Numerical Studies of the Convective Boundary Layer Capped by a Strong Inversion

The convective boundary layer (CBL) with a wide range of stability is simulated experimentally using a thermally stratified wind tunnel, and numerically by direct numerical simulation (DNS). The turbulence structures and flow characteristics of various CBL flows, capped by a strong temperature inversion and affected by surface shear, are investigated. The various vertical profiles of turbulence statistics similar to those from the observed CBL in the field are successfully simulated in both the wind-tunnel experiment and in DNS. The comparison of the wind-tunnel data and DNS results with those of atmospheric observations and water-tank studies shows the crucial dependence of the turbulence statistics in the upper part of the layer on the strength of the inversion layer, as well as the modification of the CBL turbulence regime by the surface shear.