Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Present methodological research on geographically weighted regression (GWR) focuses primarily on extensions of the basic GWR model, while ignoring well-established diagnostics tests commonly used in standard global regression analysis. This paper investigates multicollinearity issues surrounding the local GWR coefficients at a single location and the overall correlation between GWR coefficients associated with two different exogenous variables. Results indicate that the local regression coefficients are potentially collinear even if the underlying exogenous variables in the data generating process are uncorrelated. Based on these findings, applied GWR research should practice caution in substantively interpreting the spatial patterns of local GWR coefficients. An empirical disease-mapping example is used to motivate the GWR multicollinearity problem. Controlled experiments are performed to systematically explore coefficient dependency issues in GWR. These experiments specify global models that use eigenvectors from a spatial link matrix as exogenous variables.This study was supported by grant number 1 R1 CA95982-01, Geographic-Based Research in Cancer Control and Epidermiology, from the National Cancer Institute. The author thank the anonymous reviewers and the editor for their helpful comments.     

基于卫星观测的两例青藏高原低涡结构的初步分析

应用风云2C卫星云图和配有云顶亮温的MTSAT卫星红外云图,描述了两例青藏高原低涡形成、发展及消亡过程,云图清晰显示了高原低涡具有涡眼和暖心结构的特征,并利用水汽图分析揭示了缺乏水汽供应是导致这类低涡不能进一步发展并移出高原的重要原因.最后用1°×1°NCEP分析资料对高原低涡形成眼结构时的基本物理场进行了诊断计算.结果表明:低涡整体为上升气流,而涡眼区在近地层为下沉气流,上层为相对涡区较弱的上升气流;低层辐合,高层辐散.进而印证了动力学研究工作得出的高原低涡具有与热带气旋类低涡(TCLV, tropical cyclone-like vortices)类似的涡眼和暖心结构特征的结论.     

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications

It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.     

近代回归分析在交通调查分析建模中的应用

本文以出行发生量模型的建立为例,较为系统地讨论了近代回归分析中的自变量选择及回归诊断方法在交通调查分析建模中的应用。分析了在获取调查数据后,如何借助回归自变量选择方法来选择最佳自变量子集,以确定简捷的回归模型;文中应用回归诊断方法,讨论了修正回归模型、探测错误的调查数据的方法,从而为建立简捷、高精度的交通模型打下了基础。最后,作者提出了应用自变量选择及回归诊断方法建立出行发行量模型的一般步骤。     

1998/2000年ENSO冷事件过程诊断

通过对1998／2000年ENSO冷事件发展过程的诊断分析，揭示了这次事件爆发快、强度较大、结束时东太平洋海温变化突然，大气响应滞后等特点。通过与其它冷事件特征的比较，着重分析了冷事件爆发前期次表层海温及大气风场的演变特征，指出次表层冷水异常的发展和东移是本次冷事件爆发的基本条件，大气风场特征对冷事件的形成和加强起着关键作用，同时冷事件和爆发季节对事件的长度和强度有着非常重要的影响。     

Towards a comprehensive approach to parameter estimation in land surface parameterization schemes

In climate models, the land–atmosphere interactions are described numerically by land surface parameterization (LSP) schemes. The continuing improvement in realism in these schemes comes at the expense of the need to specify a large number of parameters that are either directly measured or estimated. Also, an emerging problem is whether the relationships used in LSPs are universal and globally applicable. One plausible approach to evaluate this is to first minimize uncertainty in model parameters by calibration. In this paper, we conduct a comprehensive analysis of some model diagnostics using a slightly modified version of the Simple Biosphere 3 model for a variety of biomes located mainly in the Amazon. First, the degree of influence of each individual parameter in simulating surface fluxes is identified. Next, we estimate parameters using a multi‐operator genetic algorithm applied in a multi‐objective context and evaluate simulations of energy and carbon fluxes against observations. Compared with the default parameter sets, these parameter estimates improve the partitioning of energy fluxes in forest and cropland sites and provide better simulations of daytime increases in assimilation of net carbon during the dry season at forest sites. Finally, a detailed assessment of the parameter estimation problem was performed by accounting for the decomposition of the mean squared error to the total model uncertainty. Analysis of the total prediction uncertainty reveals that the parameter adjustments significantly improve reproduction of the mean and variability of the flux time series at all sites and generally remove seasonality of the errors but do not improve dynamical properties. Our results demonstrate that error decomposition provides a meaningful and intuitive way to understand differences in model performance. To make further advancements in the knowledge of these models, we encourage the LSP community to adopt similar approaches in the future. Copyright © 2012 John Wiley & Sons, Ltd.     

Weibel Turbulence in Laboratory Experiments and GRB/SN Shocks

It has recently been realized that the Weibel instability plays a major role in the formation and dynamics of astrophysical shocks of gamma-ray bursts and supernovae. Thanks to technological advances in the recent years, experimental studies of the Weibel instability are now possible in laser-plasma interaction devices. We, thus, have a unique opportunity to model and study astrophysical conditions in laboratory experiments – a key goal of the Laboratory Astrophysics program. Here we briefly review the theory of strong non-magnetized collisionless GRB and SN shocks, emphasizing the crucial role of the Weibel instability and discuss the properties of radiation emitted by (isotropic) electrons moving through the Weibel-generated magnetic fields, which is referred to as the jitter radiation. We demonstrate that the jitter radiation field is anisotropic with respect to the direction of the Weibel current filaments and that its spectral and polarization characteristics are determined by microphysical plasma parameters. We stress that the spectral analysis can be used for accurate diagnostics of the plasma conditions in laboratory experiments and in astrophysical GRB and SN shocks.     

Density and temperature diagnostics of solar emission lines from NeV/MgV and SiVII/MgVII Ions

We present NeV/MgV and SiVII/MgVII theoretical line intensity ratios as a function of electron densityN _e and temperatureT _e . These are shown in the form of ratio-ratio diagrams, which should in principle allow bothN _e andT _e to be deduced for the emitting region of the solar plasma. We apply these diagnostics in the solar atmosphere, and discuss the available observations made from space. In most cases, however, we deduceN _e andT _e from the computed absolute line intensities in a spherically symmetric model atmosphere of the Sun. Possible future applications of this investigation to spectral data from the Coronal Diagnostic Spectrometer (CDS) on the Solar and Heliospheric Observatory (SOHO) are briefly discussed.     

Multicriteria sensitivity analysis as a diagnostic tool for understanding model behaviour and characterizing model uncertainty

Complex hydrological models are being increasingly used nowadays for many purposes such as studying the impact of climate and land‐use change on water resources. However, building a high‐fidelity model, particularly at large scales, remains a challenging task, due to complexities in model functioning and behaviour and uncertainties in model structure, parameterization, and data. Global sensitivity analysis (GSA), which characterizes how the variation in the model response is attributed to variations in its input factors (e.g., parameters and forcing data), provides an opportunity to enhance the development and application of these complex models. In this paper, we advocate using GSA as an integral part of the modelling process by discussing its capabilities as a tool for diagnosing model structure and detecting potential defects, identifying influential factors, characterizing uncertainty, and selecting calibration parameters. Accordingly, we conduct a comprehensive GSA of a complex land surface–hydrology model, Modélisation Environmentale–Surface et Hydrologie (MESH), which combines the Canadian land surface scheme with a hydrological routing component, WATROUTE. Various GSA experiments are carried out using a new technique, called Variogram Analysis of Response Surfaces, for alternative hydroclimatic conditions in Canada using multiple criteria, various model configurations, and a full set of model parameters. Results from this study reveal that, in addition to different hydroclimatic conditions and SA criteria, model configurations can also have a major impact on the assessment of sensitivity. GSA can identify aspects of the model internal functioning that are counter‐intuitive and thus help the modeller to diagnose possible model deficiencies and make recommendations for improving development and application of the model. As a specific outcome of this work, a list of the most influential parameters for the MESH model is developed. This list, along with some specific recommendations, is expected to assist the wide community of MESH and Canadian land surface scheme users, to enhance their modelling applications.