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.     

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.     

地图数字化位置误差的协方差函数

针对数字化地图的精度 ,利用平稳随机过程的理论来估计位置数据的不确定性 ,提出了一套计算方法 ,主要内容包括运用平稳随机过程的各态历经性 ,对任意点坐标的X、Y按距离拟合求定其协方差 ,其特点是应用了统计估计原理 ,使得到的结果更为合理和简便。     

Correcting method of eddy covariance fluxes over non-flat surfaces and its application in ChinaFLUX

Although Eddy Covariance (EC) technique is one of the best methods for estimating the energy and mass exchanges between underlying surface and atmosphere in micrometeorology, errors and uncertainties still exist without necessary corrections. In this paper, we will focus on the effect of coordinate system on the eddy fluxes. Based on the data observed over four sites (one farmland site, one grassland site and two forest sites), the effects of three coordinate system transforming methods (Double Rotation-DR, Triple Rotation-TR and Planar Fit-PF)on the turbulent fluxes are analyzed. It shows that (i) the corrected fluxes are more or less than the uncorrected fluxes, which is related mainly to the sloping degree of surface, wind speed and wind direction; and (ii) pitch angle has a sinusoidal dependence on wind direction, especially in the regular sloping terrain; and (iii) PF method is something like the simplification of TR or DR,and there are not obvious distinctions in correction in sloping grassland and flat farmland, but PF method is not suitable for uneven and irregular forest sites.     

Establishment of apparent quantum yield and maximum ecosystem assimilation on Tibetan Plateau alpine meadow ecosystem

The alpine meadow is widely distributed on the Tibetan Plateau with an area of about 1.2×106kn2. Damxung County, located in the hinterland of the Tibetan Plateau, is the place covered with this typical vegetation. An open-path eddy covariance system was set up in Damxung rangeland station to measure the carbon flux of alpine meadow from July to October,2003. The continuous carbon flux data were used to analyze the relationship between net ecosystem carbon dioxide exchange (NEE) and photosynthetically active radiation (PAR), as well as the seasonal patterns of apparent quantum yield (α) and maximum ecosystem assimilation (Pmax).Results showed that the daytime NEE fitted fairly well with the PAR in a rectangular hyperbola function, with α declining in the order of peak growth period (0.0244 μmolCO2 · μmol-1pAR) ＞early growth period ＞ seed maturing period ＞ withering period (0.0098 μmolCO2 · μmol-1pAR).The Pmax did not change greatly during the first three periods, with an average of 0.433mgCO2· m-2· s-1, i.e. 9.829 μmolCO2· m-2· s-1. However, during the withering period, Pmax was only 0.35 mgCO2 · m-2 · s-1, i.e. 7.945 μmolCO2 · m-2 · s-1. Compared with other grassland ecosystems, the α of the Tibetan Plateau alpine meadow ecosystem was much lower.     

A new approach to estimate canopy evaporation and canopy interception capacity from evapotranspiration and sap flow measurements during and following wetting

Canopy interception and its evaporation into the atmosphere during irrigation or a rainfall event are important in irrigation scheduling, but are challenging to estimate using conventional methods. This study introduces a new approach to estimate the canopy interception from measurements of actual total evapotranspiration (ET) using eddy covariance and estimation of the transpiration from measurements of sap flow. The measurements were conducted over a small‐scale sprinkler‐irrigated cotton field before, during and after sprinkler irrigation. Evaporation and sap flow dynamics during irrigation show that the total ET during irrigation increased significantly because of the evaporation of free intercepted water while transpiration was suppressed almost completely. The difference between actual ET and transpiration (sap flow) during and immediately following irrigation (post irrigation) represents the total canopy evaporation while the canopy interception capacity was calculated as the difference between actual ET and transpiration (sap flow) during drying (post irrigation) following cessation of the irrigation. The canopy evaporation of cotton canopy was calculated as 0.8 mm, and the interception capacity was estimated to be 0.31 mm of water. The measurement uncertainty in both the non‐dimensional ET and non‐dimensional sap flow was shown to be very low. Copyright © 2015 John Wiley & Sons, Ltd.     

基于方差递推法的Kalman滤波在钟差预报中的应用

卫星导航系统中星载原子钟的钟差预报对于导航、定位及授时具有重要的作用。为了提高卫星钟差预报的精度,设计了一种两步确定卫星钟噪声协方差矩阵的Kalman滤波钟差预报模型。该方法首先基于Hadamard总方差确定卫星钟噪声协方差矩阵的初值,然后,使用方差递推法得到滤波过程中卫星钟的噪声协方差矩阵。使用GPS系统的星载铷钟数据进行短期预报,并与常用的二次多项式模型、灰色模型进行对比,结果表明:本文中提出的方法可以实现高精度的卫星钟差预报且预报效果优于两种常用模型,同时,该方法能够在一定程度上弥补预报误差随预报时间增加而不断变大的不足。     

变分同化框架通过背景误差协方差构建动力平衡约束的研究进展

通过背景误差协方差构建动力平衡约束是变分同化框架设计的重要环节。它不仅帮助实现变量间的协同分析,提高观测使用效率,还能改善变分极小化问题的性状。本文在系统梳理通过背景误差协方差引入动力平衡约束的方式、流程的基础上,对求解目前全球和有限区域变分同化系统普遍采用的准地转平衡和静力平衡约束的共性问题和存在的不足作了归纳总结。分析了求解准地转平衡约束的三类方案:动力平衡方程方案、统计方案和动力-统计相结合方案的优缺点。对照比较了不同垂直离散方案下求解静力平衡约束时遇到的欠定问题的表现以及解决途径。最后,展望了基于背景误差协方差构建动力平衡约束在赤道等特殊地区、高分辨率同化系统、以及集合-变分混合同化系统发展中面临的挑战和机遇。     

配置法在局部大地水准面精化中的实例研究

从最小二乘配置方法的基本原理出发,以我国某地区范围内1km分辨率的大地水准面高模型数据为例,根据实用公式计算了试验区大地水准面高的协方差值后,采用多项式函数模型和高斯函数模型分别拟合了该地区大地水准面高的局部协方差函数,并对试验区内18个检核点做了推估计算。根据推估值(Nfit)与实测值(NGPSL)的比较分析表明,虽然多项式协方差函数模型略优于高斯协方差函数模型,但它们都能以厘米级的精度拟合局部大地水准面,这表明了配置法用于精化厘米级大地水准面的有效性。     

国产磁通门磁力仪稳定性分析

国产磁通门磁力仪(GM-3磁通门磁力仪)在全国各地磁台站推广应用,两年来,该仪器在武汉地震台工作比较稳定。本文对该仪器的基线值进行了多层线性回归分析。结果表明仪器性能比较稳定。