Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: ① the traditional rotation angles θ , φ ,ψ are substituted with a , b, c which are three re-spective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.     

TIN向规则格网DEM转换的新算法

由TIN生成规则格网DEM是基于TIN的离散点数据栅格化的重要一步,在基于一种数学原理的基础上运用逆向思维提出了TIN向规则格网DEM转换的新算法,不用传统的分块和建立索引,而是通过逐个遍历三角形来判断格网节点位于哪一个三角形中并实现格网节点的插值。通过编程实现、测试该算法,证明它具有非常高的插值效率。     

在空间抽象中线状目标间拓扑关系的等价转换

拓扑关系在抽象过程中的等价转换是维护多尺度空间关系一致性的基础。本文以空间拓扑关系组合推理所描述的线状目标之间的拓扑关系为例,采用成分抽象的等价转换方法,研究了线之间拓扑关系等价转换的原则,并绘出了相应的等价转换图。     

基于2维行程的栅格数据快速动态压缩算法

分析了常规2维行程压缩算法存在的不足,在此基础上提出了一种在遍历栅格数据过程中直接快速动态生成2维行程的栅格数据压缩算法.该算法以MD码代替行列号来扫描栅格数据,对于一个2×2的窗口由MD码反解行列号只需转换左上角格网单元,同时以动态线性表代替静态线性表.在提取栅格单元的过程中,直接检测对比格网单元的属性值,动态分配内存来建立2维行程编码.最后,大量实验表明,算法在运行效率和内存占有量方面均优于常规的2维行程压缩算法.     

TIN DEM线性内插不确定性的随机过程模型

基于随机过程模型导出了TIN DEM线性内插的随机过程模型,给出了不规则随机空间三角形的不确定性描述,讨论了TIN节点误差在线性内插中的传播问题。通过理论推导和实际算例,得到了TIN DEM线性内插点的点位方差和误差椭球半轴的解析表达式、线性内插精度最高点坐标的解析表达式,该结论与三角形的形状无关;对DEM线性外推导致精度急剧下降的必然性结论进行了理论证明;得到TIN线性内插的平均点位方差解析式,从理论上说明了本文结论的有效性。     

线性不等式约束平差模型的一种解算方法

不等式约束是实际测量中存在的一种约束,本文利用整标集法求解附线性不等式约束平差模型。首先了介绍带有不等式约束平差的最小二乘问题转化成凸二次规划问题,然后在Kuhn-Tucker条件下把二次规划问题转换成线性互补问题的基础上,利用整标集法来求出参数的最佳估值,最后通过一个数值算例来说明了该方法的可行性。     

线性综合模型用于崩滑体变形预报的研究

综合分析和比较了自回归模型和回归模型的特点,提出了采用线性综合模型来预报崩滑体变形的思想,以弥补自回归模型或回归模型预报的不足。实测资料的处理结果表明,综合线性模型具有特别的适用性。     

The separation of the influence of nutrients and climate on the varve time-series of baldeggersee, Switzerland

The varve data-set from a freeze-core taken in the deepest part of Baldeggersee was subjected to different multivariate statistical analyses in order to estimate the amount of variance in the varve thickness measures explicable by past climate and by the trophic state of the lake. A comparison of two different time-periods (1902 to1992 versus 1920 to 1980) revealed that the lake restoration programme since 1982 has had a significant impact on the formation of the seasonal layers. Results of the partitioning of the variance in the varve thickness measures showed that about two thirds of the variance are unexplained by a climate and trophic state model and that trophic state explains 6%, whereas climate accounts for about 28% of the variance before the effect of lake restoration had a strong impact on the varves. Among the climate parameters the amount of annual precipitation is a strong predictor for explaining the thickness of both dark layer and total couplet thickness, whereas summer precipitation is important for the thickness of the light layer.     

Assessing regression‐based statistical approaches for downscaling precipitation over North America

This paper assesses linear regression‐based methods in downscaling daily precipitation from the general circulation model (GCM) scale to a regional climate model (RCM) scale (45‐ and 15‐km grids) and down to a station scale across North America. Traditional downscaling experiments (linking reanalysis/dynamical model predictors to station precipitation) as well as nontraditional experiments such as predicting dynamic model precipitation from larger‐scale dynamic model predictors or downscaling dynamic model precipitation from predictors at the same scale are conducted. The latter experiments were performed to address predictability limit and scale issues. The results showed that the downscaling of daily precipitation occurrence was rarely successful at all scales, although results did constantly improve with the increased resolution of climate models. The explained variances for downscaled precipitation amounts at the station scales were low, and they became progressively better when using predictors from a higher‐resolution climate model, thus showing a clear advantage in using predictors from RCMs driven by reanalysis at its boundaries, instead of directly using reanalysis data. The low percentage of explained variances resulted in considerable underestimation of daily precipitation mean and standard deviation. Although downscaling GCM precipitation from GCM predictors (or RCM precipitation from RCM predictors) cannot really be considered downscaling, as there is no change in scale, the exercise yields interesting information as to the limit in predictive ability at the station scale. This was especially clear at the GCM scale, where the inability of downscaling GCM precipitation from GCM predictors demonstrates that GCM precipitation‐generating processes are largely at the subgrid scale (especially so for convective events), thus indicating that downscaling precipitation at the station scale from GCM scale is unlikely to be successful. Although results became better at the RCM scale, the results indicate that, overall, regression‐based approaches did not perform well in downscaling precipitation over North America. Copyright © 2013 John Wiley & Sons, Ltd.     

土层分层参数不确定时对二维工程场址地震动影响分析

工程场地地震安全性评价中计算二维复杂场地地震反应分析时,如采用一维等效线性化分析模型会带来较大的误差,而直接采用二维的非线性模型在技术上还存在一定的困难和不合理性。目前工程中多采用对一维分析结果进行二维修正的思想给出设计地震动及反应谱。然而在建立二维分析模型时,由于勘测条件的限制使模型建立出现很多不确定性。基于以往提出的二维复杂工程场址设计地震动的修正分析思想,建立了几种可能且工程认可的二维复杂场地模型,主要研究不同分层特征模型及土层剪切波速这一物理参数不确定时对设计地震动的影响,进一步考虑不同场地类别下,不同二维分层模型及土体物理参数对地震动的影响。根据分析结果提出了不同类别场地下,方便且合理建立二维复杂场地地震动分析模型的方法,为实际工程中模型的建立及参数的选取提供一些参考。