通过介绍几种标定C波段偏振雷达差分反射率因子ZDR和水平反射率因子ZH系统误差常用方法的原理,利用两部相同型号的可移式C波段双线偏振雷达(POLC)在云南、安徽等地的观测数据,对这些方法进行了检验和对比分析。结果表明,ZDR的标定方法中...通过介绍几种标定C波段偏振雷达差分反射率因子ZDR和水平反射率因子ZH系统误差常用方法的原理,利用两部相同型号的可移式C波段双线偏振雷达(POLC)在云南、安徽等地的观测数据,对这些方法进行了检验和对比分析。结果表明,ZDR的标定方法中,太阳法由于偏振雷达水平与垂直方向两个接收机在较弱的信号下很难保持一致性,目前实际应用比较困难;垂直指向法要求雷达天线必须达到90°仰角,机械上有所制约;仰角法要求探测到非常均匀的雨区,在时间与空间上极难满足;地物引起的ZDR变化,在统计上无任何规律可循,因此,地物法也基本上可以排除应用于实际;干雪的ZDR并不完全等于0 dB,并且需要知道0℃层的高度,0℃层以上满足信噪比(signal to noise ratio,SNR)条件的数据较少,并且水凝物相态难以确定为干雪,因而干雪法有着一定的局限性;微雨滴法理论清晰、结论可信,不需要专门的扫描方式,能够从正常的体扫观测中得到大量的满足SNR、ZH等阈值条件的数据,提供较为准确的ZDR系统误差估计,因此,微雨滴法是一种利用气象目标进行ZDR系统误差估计较好的方法。进一步分析ZH标定的自约束法的结果表明,自约束法能够大致地验证偏振雷达ZH标定是否正确,但是,其用于ZH标定时,对偏振参量数据质量要求较高,并且约束关系的系数也有待进一步验证。展开更多
The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM ), Galerkin method with weak form (GM / WF ), Pe...The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM ), Galerkin method with weak form (GM / WF ), Petrov-Galerkin method ( PGM), weighted residual method (WRY ), and least squares method or process ( LSM or LSP ) to construct finite element approximations in time. A correspondence is established between these integral forms and the elements of the calculus of variations: 1) to determine which methods of approximation yield unconditionally stable (variationally consistent integral forms, VC ) computational processes for which types of operators and, 2) to establish which integral forms do not yield unconditionally stable computations (variationally inconsistent integral forms, VIC ). It is shown that variationally consistent time integral forms in hpk framework yield computational processes for ODEs in time that are unconditionally stable, provide a mechanism of higher order global differentiability approximations as well as higher degree local approximations in time, provide control over approximation error when used as a time marching process and can indeed yield time accurate solutions of the evolution. Numerical studies are presented using standard model problems from the literature and the results are compared with Wilson’s θ method as well as Newmark method to demonstrate highly meritorious features of the proposed methodology.展开更多
文摘通过介绍几种标定C波段偏振雷达差分反射率因子ZDR和水平反射率因子ZH系统误差常用方法的原理,利用两部相同型号的可移式C波段双线偏振雷达(POLC)在云南、安徽等地的观测数据,对这些方法进行了检验和对比分析。结果表明,ZDR的标定方法中,太阳法由于偏振雷达水平与垂直方向两个接收机在较弱的信号下很难保持一致性,目前实际应用比较困难;垂直指向法要求雷达天线必须达到90°仰角,机械上有所制约;仰角法要求探测到非常均匀的雨区,在时间与空间上极难满足;地物引起的ZDR变化,在统计上无任何规律可循,因此,地物法也基本上可以排除应用于实际;干雪的ZDR并不完全等于0 dB,并且需要知道0℃层的高度,0℃层以上满足信噪比(signal to noise ratio,SNR)条件的数据较少,并且水凝物相态难以确定为干雪,因而干雪法有着一定的局限性;微雨滴法理论清晰、结论可信,不需要专门的扫描方式,能够从正常的体扫观测中得到大量的满足SNR、ZH等阈值条件的数据,提供较为准确的ZDR系统误差估计,因此,微雨滴法是一种利用气象目标进行ZDR系统误差估计较好的方法。进一步分析ZH标定的自约束法的结果表明,自约束法能够大致地验证偏振雷达ZH标定是否正确,但是,其用于ZH标定时,对偏振参量数据质量要求较高,并且约束关系的系数也有待进一步验证。
文摘The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM ), Galerkin method with weak form (GM / WF ), Petrov-Galerkin method ( PGM), weighted residual method (WRY ), and least squares method or process ( LSM or LSP ) to construct finite element approximations in time. A correspondence is established between these integral forms and the elements of the calculus of variations: 1) to determine which methods of approximation yield unconditionally stable (variationally consistent integral forms, VC ) computational processes for which types of operators and, 2) to establish which integral forms do not yield unconditionally stable computations (variationally inconsistent integral forms, VIC ). It is shown that variationally consistent time integral forms in hpk framework yield computational processes for ODEs in time that are unconditionally stable, provide a mechanism of higher order global differentiability approximations as well as higher degree local approximations in time, provide control over approximation error when used as a time marching process and can indeed yield time accurate solutions of the evolution. Numerical studies are presented using standard model problems from the literature and the results are compared with Wilson’s θ method as well as Newmark method to demonstrate highly meritorious features of the proposed methodology.
