GRAPES模式中高精度正定保形物质平流方案的研究Ⅱ：连续实际预报试验

针对半隐式半拉格朗日数值预报模式GRAPES,研究发展了与之相适合的高精度正定保形的物质平流方案--分段有理函数法(PRM,Piecewise Rational Method).文中在进行理想试验验证该方案简单、实用、易于编程对于空间变化幅度大的物理量具有较高的平流计算能力且在GRAPES模式中具有可行性的基础上,对2005年7月连续1个月的24小时降水进行实际预报试验.通过细致的个例分析、月平均比较以及TS评分计算,PRM方案实际预报结果与GRAPES模式中原来采用的水物质平流方案预报的主要雨带的分布、走向相一致,但对大雨以上量级的降水预报具有明显优势,对网格尺度的降水的影响比较敏感,进一步验证了高精度正定保形方案对实际降水预报的改进效果,表明该方案对于改进GRAPES模式大到暴雨预报能力具有较大的潜力.PRM平流方案较GRAPES原来采用的准单调正定保形的平流方案能够更加合理地计算水物质场的输送,尤其是能够很好地反映出梅雨季东亚大气下层水汽水平梯度大以及沿梅雨锋水汽的小尺度变率较大的特点描写.     

PRM标量平流方案在GRAPES全球预报系统中的应用

如何更好地模拟水物质的分布,对于数值天气预报效果的改进,特别是对于更好地模拟降水过程,具有重要的意义。半拉格朗日模式中的标量平流计算要求做到高精度、守恒、正定和保形,但GRAPES_GFS (Global-Regional Assimilation and PrEdiction System, Global Forecast System) 中采用的QMSL(Quasi-Monotone Semi-Lagrangian)平流方案在水汽的强梯度、不连续区域计算精度较低,且不能做到严格守恒。本研究借鉴计算流体力学领域的研究进展,将一个基于分段有理函数的物质平流方案PRM(Piecewise Rational Method)引入GRAPES_GFS中,按照通量形式求解水汽方程,并对极区进行了混合等技术处理。通过一系列理想试验对两种平流方案进行了对比,证明了PRM方案精度较高,特别是在水汽梯度大的区域优势明显,频散、耗散误差较小,守恒、保形性也要好于QMSL方案。通过对GRAPES_GFS中批量预报试验效果的检验,验证了PRM方案可以有效地改进模式对水物质分布的模拟,提高了降水的预报效果,对模式综合预报性能的提升也有明显作用。     

大气环流模式降水的模拟对水汽方程差分方案的敏感性试验

分别采用3种应用比较广泛的水汽方程差分方案:多维正定平流传输方案(MPDATA)、通量修正传输方案(FCT)和两步保形平流方案(TSPAS),对大气物理所9层大气环流模式(IAP 9L AGCM)的降水模拟作敏感性试验,分析比较3种方案下模式降水气候平均场的差异,从而揭示模式降水对水汽方程差分方案的敏感性.试验结果显示,不同的水汽方程差分方案对大气环流模式降水的气候模拟有较大影响,并由此从3种差分方案中为IAP 9L AGCM寻找出一种较好的水汽计算方案.     

水汽输送的算法精度与模式暴雨预报能力的对比分析

利用中尺度模式ＭＭ４，研究了中尺度模式的暴雨模拟对于不同不汽输送方案的敏感性。采用５种平流差分格式来计算水汽的水平输送，用该模式对３次暴雨过程作了数值试验。并把不同方案的降水模拟结果与实况进行了对比。结果表明，中尺度模式的暴雨模拟对水汽输送方案十分敏感，正定高精度的Ｐｒａｔｈｅｒ格式的模拟结果最接近实况。     

模式低空急流结构与水汽输送精度的数值试验

本文所使用的中尺度模式ＭＭ４改进了水汽平流的计算精度，引入了Ｐｒａｔｈｅｒ和Ｂｏｔｔ两种高精度正定闰流差分格式。首先探讨了仅考虑模式平流过程的情况下不同平流差分格式的误差特征对模式结果的可能影响。结果显示：ＭＭ４中原有的水汽平流差分格式在水汽梯度较大处产生水汽负值，而引入搞精度格式能正确模拟水汽为分布的特征，对不同精度的水汽平流分格式作了数值试验，不同格式下模式的低突急流结构有较明显差别，水汽输送     

水汽平流计算精度对暴雨模拟的影响与实例分析

利用改进了水汽平流精度的中尺度模式ＭＭ４模拟了一次江淮暴雨。通过对不同平流格式所模拟的水汽场的对比,并辅以动力热力机制分析,阐述了不同水汽平流格式造成不同的中－α、中－β尺度降水的原因。结果表明,将高精度、正定的水汽平流格式引入ＭＭ４模式有助于提高模式的模拟能力。     

包含正定水汽输送算法改进的MM4中尺度模式与暴雨实例数值试验

暴雨预报是一个既重要又十分困难的问题。水汽条件是产生暴雨的关键，水汽的平流输送在模式的水汽方程中占有重要地位，模式对暴雨的预报能力必然涉及到水汽输送的计算精度问题；本文以著名的中尺度模式ＭＭ４为基础，理论测试和分析为依据，以引入新的正定高精度水汽输送算法作为消除模式水汽负值和改进中尺度模式预报能力的途径，研制了取名为改进的ＭＭ４中尺度模式，该模式除仍保留原ＭＭ４模式的所有功能外，增加了５种水汽输送算法的改进与选择，这５种算法是：１）Ｂ网格二阶守恒中心差（原ＭＭ４平流格式），２）上游差分，３）Ｂｏｔ（２阶），４）Ｂｏｔ（４阶），５）Ｐｒａｔｈｅｒ格式。多个暴雨、台风个例试验表明模式预报能力对水汽输送算法精度有显著的依赖性，采用高精度的水汽输送算法水汽保证正值并提高了模式对暴雨区、降水结构、雨团活动的预报能力。改进水汽输送算法的精度是提高中尺度模式对暴雨预报能力的重要途径。     

中尺度模式MM4对高精度水汽输送#C$算法的敏感性试验

水汽输送的算法精度对中尺度模式的预报能力起有重要作用。本文在MM4的基础上用高精度的平流格式改进模式的水汽输送格式，使改进后的模式包含了对多种高精度的水汽输送格式的选择，如Prather格式和Bott格式。这些格式都是正定的，在理想风场的数值实验中几乎无数值耗散，无计算频散。我们在B网格中央差格式（原MM4中的格式）、Upstream格式和 Prather格式等模式选择项下，对1982年6月的一次梅雨期暴雨过程进行了数值对比实验。结果表明:1）模式的预报能力对水汽输送格式的精度较敏感， 2）高精度的水汽输送格式（Prather格式） 提高了模式对暴雨区、降水场结构、雨团活动的预报能力，较真实地模拟出了尺度较小的降水系统的活动。 高精度的水汽输送算法有助于提高中尺度模式的预报精度。     

通量和平流形式预报方程的数值预报试验

本文利用1982年5月8日和1979年6月28日两个实例,进行了四种方案的48小时数值预报试验,比较了它们的预报质量及彼此间的差异。四种方案是:经典通量、通量修正、经典平流和平流修正。试验表明,在有地形的数值预报模式中,采用平流形式的预报方程组比采用通量形式的为好,既可有较高的计算精度,又可节省计算时间。     

高阶正定守恒的中心约束多矩有限体积平流模式

采用新的均匀三点中心约束多矩有限体积方法（3-point Multi-moment Constrained finite-Volume scheme for Uniform Points with Center Constraints, MCV3_UPCC）,发展了一个三阶正定守恒的平流模式。三点多矩有限体积方法在单网格内定义等距的3个自由度,采用多矩约束条件并通过控制方程获得时间演变方程。新的三点中心约束多矩方法能在单网格内采用等距的3个点值及中心一阶、二阶导数作为约束条件进行空间4次多项式数值重构,获得3个自由度的时间演变方程;所构建的新数值方案具有三阶精度,边界通量连续性保证了其数值严格守恒。为了抑制该方法的非物理数值振荡,引入了边界保型限制器技术,它能够把数值解控制在既定物理场最小值（最小值为0时则保持数值正定）与最大值之间。数值试验表明新发展的三阶平流模式具有良好的计算精度,能够严格保持数值解的正定性和守恒性,同其他高精度平流模式相当,在实际大气模式水汽等平流输送应用中具备良好的发展潜力。      

Numerical analysis and case experiment for forecasting capability by using high accuracy moisture advectional algorithm

Summary The paper concerns the sensitivity of the regional mesoscale model (MM4) to a moisture transport algorithm with different accuracies, and the effective improvement of the capability to simulate meso-scale synoptical event by using the revised version of the algorithm. The two advective schemes of second-order moment conservational Prather scheme (PRS hereinafter) and the polynomial-fitted fourth-order Bott scheme and the upstream scheme (UPS) are introduced into the MM4 to calculate moisture transport in order to provide other types of the algorithm with different accuracies for choice in addition to the original B grid second-order central scheme. Of the three schemes, the first two ensure the positive definite character with high accuracy (almost no numerical disspation and computational dispersion); and the last one also keeps the positive definite feature, but possesses stronger capability of numerical dissipation. Case studies have been undertaken of several rainstorm and typhoon events by virtue of the different-accuracy moisture transport algorithm, other things being the same. Results reveal great differences between them. An significant improvement is found in determining meso-scale synoptic system structure, rain cluster activity, rainstorm belt and its center, severity and its persistence, and the false alarm of or failure to report subrainstorm center when the PRS scheme is employed. Obviously, these differences and improvement are only due to moisture re-distribution for different schemes of moisture transport and the related variation of latent heat. The paper investigates the influences of different numerical schemes. The high accuracy and positive solution PRS application which produces a significant improvement in the model result, demonstrating the sensitivity of the model to moisture distribution in the model represents an important measure to improve the simulation by means of revising the numerically calculating method.With 11 Figures     

Application of a Shape-Preserving Advection Scheme to the Moisture Equation in an E-grid Regional Forecast Model

This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preserving positive definite advection scheme in the moisture equation of the LASG-REM (LASG regional E-grid eta-coordinate forecast model). By trial-forecasting six local heavy raincases, the efficiency of the shape-preserving advection scheme in practical application has been examined. The LASG-REM with the shape-preserving advection scheme has a good forecasting ability for local precipitation.     

包含正定水汽高精度算法的MM5模式的暴雨实例试验

本文首先对非静力中尺度模式ＭＭ５的水汽输送方案作了半理想试验。结果显示,ＭＭ５原有的水汽平 流输送算法在水汽梯度较大的地方产生水汽负值,影响模式的模拟结果和模式的稳定性,对此,本文把一个正定的水汽输送算法Ｐｒａｔｈｅｒ算法引入ＭＭ５,并用实例作了数值试验,检验了模式的模拟能力,结果表明,对ＭＭ５的改进是敏感的有效的,Ｐｒａｔｈｅｒ格式增强了模式暴雨落区,暴雨中心的模拟能力。     

修正的质量通量积云对流方案及其模拟试验研究Ⅰ:方案介绍及对1991年洪涝过程的模拟

文中在综合比较各类积云对流参数化方案优缺点的基础上 ,主要参考陈伯民等修正的ECMWF质量通量积云参数化方案 ,对其进行简化和修改 ,发展了一个质量通量积云对流参数化方案 ,文中表示为 MFS(Mass Flux Scheme)。MFS是一种综合型的方案 ,既考虑了大尺度水汽辐合的重要性 ,又考虑了积云中的上升运动、下沉运动、环境中的补偿下沉运动 ,以及卷入、卷出和蒸发等 ,用总体云模式来描述积云与环境的相互作用 ,同时考虑了深对流和浅对流。将 MFS植入 NCAR区域气候模式 Reg CM2中 ,对 1 991年 5～ 7月江淮地区特大降水过程的夏季风气候特征和变化进行了模拟 ,并与 NCAR Reg CM2选用 Kuo方案 ,在同样初、边值条件和其它物理过程选择下的模拟结果进行了对比分析。分析结果表明 ,植入 MFS后的模式能够模拟这次极端的降水气候事件。在某些方面 ,如地表气温 ,降水的模拟上 ,植入 MFS后的模式的模拟结果要比原模式的结果更合理     

MODIFIED MASS FLUX CUMULUS CONVECTIVE PARAMETERIZATION SCHEME AND ITS SIMULATION EXPERIMENT—PART Ⅰ:MASS FLUX SCHEME AND ITS SIMULATION OF THE 1991 FLOOD EVENT*

Based on the existing cumulus convective parameterization schemes,a mass flux scheme (MFS) for cumulus convective parameterization has been successfully developed by reference to the work of Chen et al. (1996).The MFS is a comprehensive scheme.In MFS,not only the importance of the large-scale moisture convergence is taken into account,but also it includes the cumulus updrafts and downdrafts,cumulus-induced subsidence in the environmental air.entrainment,detrainment and evaporation.The interaction between the cumulus and the environment is described by using a one-dimensional bulk model.At the same time the scheme includes the penetrative and shallow convections.The MFS has been successfully incorporated into the regional climate model RegCM2 developed by NCAR.The new model has been applied to simulate summer monsoon characteristics and their variations of heavy rainfall process in the Changjiang-Huaihe River Basins for three months from May to July 1991.The results show that the new model can successfully simulate this rainfall prolonged process.By comparising the model outputs of RegCM2.using the Kuo scheme and the MFS.it is found that the MFS is better in simulating the surface temperature,rainfall position and amount,and rainfall duration.     

尺度自适应大气边界层参数化改进及其对一次海雾的数值模拟研究

大气边界层湍流运动是地球大气运动最重要的能量输送过程之一。当数值模式分辨率接近活跃含能湍涡长度尺度时，湍流运动被部分解析，被称为“灰色区域”，传统的边界层方案不适合此时模式湍流问题的描述。为了提高模式边界层方案在包括“灰色区域”的不同网格尺度上的描述能力，适应不同分辨率模式的需要，在雷诺平均湍流理论基础上，修正Mellor-Yamada-Nakanishi-Niino (MYNN)方案湍流长度尺度参数和非局地湍流的参数表达，改进湿度和温度在“灰色区域”的湍流输送参数化及对网格尺度的自适应能力。利用改进的MYNN尺度自适应方案，分别采用3 km和1 km、1.5 km和0.5 km分辨率单向嵌套网格WRF中尺度模式，对2014年2月26日的一次黄海海雾过程进行模拟试验，检验不同分辨率下改进后的MYNN大气边界层参数化方案的合理性和对海雾的模拟效果。尺度自适应MYNN大气边界层参数化方案在千米级网格尺度上获得稳定、合理的湍流垂直输送计算结果。参照雾区卫星云图，不同分辨率模式低层云水混合比模拟结果具有稳定表现，模拟的雾区分布和温度、湿度等物理量结构都较好地再现了再分析“观测事实”，初步表明该参数化方案有较高的网格尺度自适应能力。      

MODIFIED MASS FLUX CUMULUS CONVECTIVE PARAMETERIZATION SCHEME AND ITS SIMULATION EXPERIMENT—PART Ⅰ:MASS FLUX SCHEME AND ITS SIMULATION OF THE 1991 FLOOD EVENT

Based on the existing cumulus convective parameterization schemes,a mass flux scheme(MFS)for cumulus convective parameterization has been successfully developed by reference to thework of Chen et al.(1996).The MFS is a comprehensive scheme.In MFS,not only theimportance of the large-scale moisture convergence is taken into account,but also it includes thecumulus updrafts and downdrafts,cumulus-induced subsidence in the environmental air.entrainment,detrainment and evaporation.The interaction between the cumulus and theenvironment is described by using a one-dimensional bulk model.At the same time the schemeincludes the penetrative and shallow convections.The MFS has been successfully incorporated into the regional climate model RegCM2developed by NCAR.The new model has been applied to simulate summer monsoon characteristicsand their variations of heavy rainfall process in the Changjiang-Huaihe River Basins for threemonths from May to July 1991.The results show that the new model can successfully simulate thisrainfall prolonged process.By comparising the model outputs of RegCM2.using the Kuo schemeand the MFS.it is found that the MFS is better in simulating the surface temperature,rainfallposition and amount,and rainfall duration.     

The numerical scheme development of a simplified frozen soil model

In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.     

一种改进的对流凝结加热方案

众所周知,积云尺度和大尺度运动的水平和时间尺度相差甚远,因此,在较大尺度的网格点上应借助于参数化方法来描述积云尺度的运动。比如,假定对流凝结加热与潮湿空气的辐合量有关(郭晓岚1965,1974),或者假定与涡度或垂直速度成正比(李崇银1984),并且依赖确定的加热参数的垂直分布廓线。我们用李崇银(1984)的参数化方案对台风发展的数值模拟表明,加热强度参数和垂直分布廓线对模拟结果非常敏感。因此,有必要寻求其他途径或参数化方法。