Representations of inverse covariances by differential operators

In the cost function of three- or four-dimensional variational data assimilation, each term is weighted by the inverse of its associated error covariance matrix and the background error covariance matrix is usually much larger than the other covariance matrices. Although the background error covariances are traditionally normalized and parameterized by simple smooth homogeneous correlation functions, the covariance matrices constructed from these correlation functions are often too large to be inverted or even manipulated. It is thus desirable to find direct representations of the inverses of background error correlations. This problem is studied in this paper. In particular, it is shown that the background term can be written into f dx|Dv(x)|^2, that is, a squared L2 norm of a vector differential operator D, called the D-operator, applied to the field of analysis increment v(x). For autoregressive correlation functions, the D-operators are of finite orders. For Gaussian correlation functions, the D-operators are of infinite order. For practical applications, the Gaussian D-operators must be truncated to finite orders. The truncation errors are found to be small even when the Gaussian D-operators are truncated to low orders. With a truncated D-operator, the background term can be easily constructed with neither inversion nor direct calculation of the covariance matrix. D-operators are also derived for non-Gaussian correlations and transformed into non-isotropic forms.     

面向室内WLAN定位的动态自适应模型

提出了一种面向无线局域网(wireless local area network,WLAN)位置指纹匹配定位的动态自适应模型,借助多个基站的实时数据为稳健室内定位提供更新的匹配数据库——radio map。基于基站与radio map采样点之间的空间关联性,将基站数据和radio map分别作为多层神经网络的输入和输出,动态更新radio map;利用多元数据异常探测技术检验基站数据捕获环境的时空变化;根据探测结果采用顾及室内布局的数值内插和再训练的方式更新模型,从而使其适应环境的时空变化。在室内动态环境中进行了多次验证试验。试验结果显示,在时变因素作用下,相比较传统方法,采用所提模型的定位方法的平均误差至少下降10%;在空间变化因素(以信标移动为例)作用下,其他方法平均定位误差大幅增加了至少165%,而采用所提模型方法的平均定位误差只增加了10%~20%,定位精度维持在3m左右(即原始精度)。结果证明采用了所提模型的定位系统能够自适应环境的时空变化而保持原有定位表现。不过,与传统位置指纹匹配定位方法相比,该模型带来了更多的计算负荷。     

A Re-examination of Density Effects in Eddy Covariance Measurements of CO2 Fluxes

Corrections of density effects resulting from air-parcel expansion/compression are important in interpreting eddy covariance fluxes of water vapor and CO2 when open-path systems are used. To account for these effects, mean vertical velocity and perturbation of the density of dry air are two critical parameters in treating those physical processes responsible for density variations. Based on various underlying assumptions, different studies have obtained different formulas for the mean vertical velocity and perturbation of the density of dry air, leading to a number of approaches to correct density effects. In this study, we re-examine physical processes related to different assumptions that are made to formulate the density effects. Specifically, we re-examine the assumptions of a zero dry air flux and a zero moist air flux in the surface layer, used for treating density variations, and their implications for correcting density effects. It is found that physical processes in relation to the assumption of a zero dry air flux account for the influence of dry air expansion/compression on density variations. Meanwhile, physical processes in relation to the assumption of a zero moist air flux account for the influence of moist air expansion/compression on density variations. In this study, we also re-examine mixing ratio issues. Our results indicate that the assumption of a zero dry air flux favors the use of the mixing ratio relative to dry air, while the assumption of a zero moist air flux favors the use of the mixing ratio relative to the total moist air. Additionally, we compare different formula for the mean vertical velocity, generated by air-parcel expansion/compression, and for density effect corrections using eddy covariance data measured over three boreal ecosystems.     

Three-year Variations of Water, Energy and CO$_2$ Fluxes of Cropland and Degraded Grassland Surfaces in a Semi-arid Area of Northeastern China

Based on 3 years （2003-05） of the eddy covariance （EC） observations on degraded grassland and cropland surfaces in a semi-arid area of Tongyu （44°25′N, 122°52′E, 184 m a.s.1.）, Northeast China, seasonal and annual variations of water, energy and CO2 fluxes have been investigated. The soil moisture in the thin soil layer （at 0.05, 0.10 and 0.20 m） clearly indicates the pronounced annual wet-dry cycle; the annual cycle is divided into the wet （growing season） and dry seasons （non-growing season）. During the growing season （from May to September）, the sensible and latent heat fluxes showed a linear dependence on the global solar radiation. However, in the non-growing season, the latent heat flux was always less than 50 W m^-2, while the available energy was dissipated as sensible, rather than latent heat flux. During the growing season in 2003-05, the daily average sensible and latent heat fluxes were larger on the cropland surface than on the degraded grassland surface. The cropland ecosystem absorbed more CO2 than the degraded grassland ecosystem in the growing season in 2003-05. The total evapotranspiration on the cropland was more than the total precipitation, while the total evapotranspiration on the degraded grassland was almost the same as the total annual precipitation in the growing season. The soil moisture had a good correlation with the rainfall in the growing season. Precipitation in the growing season is an important factor on the water and carbon budget in the semi-arid area.     

Evaporation of perennial semi‐arid woodland in southeastern Australia is adapted for irregular but common dry periods

Measurements of water vapour flux from semi‐arid perennial woodland (mallee) were made for 3 years using eddy covariance instrumentation. There have been no previous long‐term, detailed measures of water use in this ecosystem. Latent energy flux (LE) on a half hourly basis was the measure of the combined soil and plant evaporation, ‘evapotranspiration’ (E_LE) of the site. Aggregation over 3 years of the site measured rain (1136 mm) and the estimated evaporation (794 mm) suggests that 342 mm or 30% of rain had moved into or past the root zone of the vegetation. Above average rainfall during 2011 and the first quarter of 2012 (633 mm, 15 months) would likely have been the period during which significant groundwater recharge occurred. At times immediately after rainfall, E_LE rates were the same or exceeded estimates of potential E calculated from a suitably parameterized Penman–Monteith (E_PMo) equation. Apparent free water E from plant interception and soil evaporation was about 2.3 mm and lasted for 1.3 days following rainfall in summer, while in autumn, E was 5.1 mm that lasted over 5.4 days. The leaf area index (LAI) needed to adjust a wind function calibrated Penman equation (E_PMe) to match the E_LE values could be back calculated to generate seasonal change in LAI from 0.12 to 0.46 and compared well with normalized difference vegetation index; r = 0.38 and p = 0.0213* and LAI calculated from digital cover photography. The apparently conservative response of perennial vegetation evaporation to available water in these semi‐arid environments reinforces the conclusion that these ecosystems use this mechanism to survive the reasonably common dry periods. Plant response to soil water availability is primarily through gradual changes in leaf area. Copyright © 2015 John Wiley & Sons, Ltd.     

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。     

The equivalence of predictions from universal kriging and intrinsic random-function kriging

A proof is provided that the predictions obtained from kriging based on intrinsic random functions of orderk are identical to those obtained from anappropriate universal kriging model. This is a theoretical result based on known variability measures. It does not imply that people performing traditional universal kriging will get the same predictions as those using intrinsic random functions, because traditionally these methods differ in how variability is modeled. For intrinsic random functions, the same proof shows that predictions do not depend on the specific choice of the generalized covariance function. It is argued that the choice between these methods is really one of modeling and estimating the variability in the data.     

AR（P）参数估计协方差方法与其改进型方法的对比研究

定性分析协方差方法及其改进型在ＡＲ（Ｐ）参数估计中的应用，提供了一种估计参数的计算机上机流程图，比较了协方差方法及其改进型谱估计结果。     

Size Scaling of Cross Correlation Between Multiple Variables

Reservoir models have large uncertainty because of spatial variability and limited sample data. The ultimate aim is to use simultaneously all available data sources to reduce uncertainty and provide reliable reservoir models for resource assessment and flow simulation. Seismic impedance or some other attribute provides a key source of data for reservoir modeling. These seismic data are at a coarser scale than the hard well data and it not an exact measurement of facies proportions or porosity. A requirement for data integration is the cross-covariance between the well and seismic data.The size-scaling behavior of the cross correlation for different measurement scales was nvestigated. The size-scaling relationship is derived theoretically and validated by numerical studies (including an example with real data). The limit properties of the cross-correlation coefficient when the averaging volume becomes large is shown. After some averaging volume, the volume-dependent cross-correlation coefficient reaches a limit value. This plateau value is controlled mainly by the large-scale behavior of the cross and direct variograms.The cross correlation can increase or decrease with volume support depending on the relative importance of long- and short-scale covariance structures. If the direct and cross variograms are proportional, there is no change in the cross correlation as the averaging volume changes. Our study shows that the volume-dependent cross-correlation coefficient is sensitive to the shape of the cross variogram and differences between the direct variograms of the well data and seismic data.     

单轴压缩下岩石应变局部化的应变梯度塑性解

通过在屈服函数中引入材料内部长度建立应变梯度塑性增量本构关系,对岩石材料在单轴压缩条件下应变局部化的二维情况进行了研究。首先,建立了在Mises屈服准则下平面应变情况的岩石材料应变局部化带的带宽与其倾角的关系式,讨论了其带宽的分布范围和最大值与最小值形成的条件,给出岩石材料破坏Ⅰ, Ⅱ类变形的条件,并推出破坏的临界角度;其次,对岩石材料Ⅰ类变形进行了详细地分析,讨论了在不同泊松比 和 条件下材料应变局部化带的倾角的变化范围;最后,利用所得的结论同材料破坏的库仑准则进行对比研究,对内摩擦系数给予了合理的解释。