THE INVERSE PROBLEM OF KLEIN-GORDON EQUATION BOUNDARY VALUE PROBLEM AND ITS APPLICATION IN DATA ASSIMILATION

Since the solution of elliptic partial differential equations continuously depends on the boundary condition, the Euler equation derived from variational method cannot be solved without boundary condition. It is often difficult to provide the exact boundary condition in the practical use of variational method. However, in some application problems such as the remote sensing data assimilation, the values can be easily obtained in the inner region of the domain. In this paper, the boundary condition is tried to be retrieved by using part solutions in the inner area. Firstly, the variational problem of remote sensing data assimilation within a circular area is established. The Klein-Gordon elliptic equation is derived from the Euler method of variational problems with assumed boundary condition. Secondly, a computer-friendly Green function is constructed for the Dirichlet problem of two-dimensional Klein-Gordon equation, with the formal solution according to Green formula. Thirdly, boundary values are retrieved by solving the optimal problem which is constructed according to the best approximation between formal solutions and high-accuracy measurements in the interior of the domain. Finally, the assimilation problem is solved on substituting the retrieved boundary values into the Klein-Gordon equation. It is a type of inverse problem in mathematics. The advantage of this method lies in that it overcomes the inherent instability of the inverse problem of Fredholm integral equation and alleviates the error introduced by artificial boundary condition in data fusion using variational method in the past.     

云分析方法对浙江省一次强对流天气数值模拟的应用初探

基于云分析方法,利用WRF-ARW模式设计一套快速更新循环同化方案,对2019年3月21至22日发生在浙江省的一次强对流天气过程进行模拟研究。通过设计两组对比试验,对云分析同化雷达反射率效果进行诊断分析。在控制试验中,模拟降水落区和降水量与实况差别较大,而采用云分析方法同化雷达反射率（CA-DA）的模拟试验中,降水模拟效果相对较好,雨带明显东移,强度与实况接近。初步结果表明,利用云分析同化雷达反射率因子可以改进模式初始场的风、温度、水汽场以及水凝物等信息,进而缩短模式spin-up时间,提高降水落区及强度的预报。     

Theory for Reconstruction of an Unknown Number of Contaminant Sources using Probabilistic Inference

We address the inverse problem of source reconstruction for the difficult case of multiple sources when the number of sources is unknown a priori. The problem is solved using a Bayesian probabilistic inferential framework in which Bayesian probability theory is used to derive the posterior probability density function for the number of sources and for the parameters (e.g., location, emission rate, release time and duration) that characterize each source. A mapping (source–receptor relationship) that relates a multiple source distribution to the concentration measurements made by an array of detectors is formulated based on a forward-time Lagrangian stochastic model. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source–receptor relationship and realized in terms of a backward-time Lagrangian stochastic model, is described. An efficient computational algorithm based on a parallel tempered Metropolis-coupled reversible-jump Markov chain Monte Carlo (MCMC) method is formulated and implemented to draw samples from the posterior probability density function of the source parameters. This methodology allows the MCMC method to initiate jumps between the hypothesis spaces corresponding to different numbers of sources in the source distribution and, thereby, allows a sample from the full joint posterior distribution of the number of sources and the parameters for each source to be obtained. The proposed methodology for source reconstruction is tested using synthetic concentration data generated for cases involving two and three unknown sources.     

Model Uncertainty Representation for a Convection-Allowing Ensemble Prediction System Based on CNOP-P

Formulating model uncertainties for a convection-allowing ensemble prediction system(CAEPS) is a much more challenging problem compared to well-utilized approaches in synoptic weather forecasting. A new approach is proposed and tested through assuming that the model uncertainty should reasonably describe the fast nonlinear error growth of the convection-allowing model, due to the fast developing character and strong nonlinearity of convective events. The Conditional Nonlinear Optimal Perturbation related to Parameters(CNOP-P) is applied in this study. Also, an ensemble approach is adopted to solve the CNOP-P problem. By using five locally developed strong convective events that occurred in pre-rainy season of South China, the most sensitive parameters were detected based on CNOP-P, which resulted in the maximum variations in precipitation. A formulation of model uncertainty is designed by adding stochastic perturbations into these sensitive parameters. Through comparison ensemble experiments by using all the 13 heavy rainfall cases that occurred in the flood season of South China in 2017, the advantages of the CNOP-P-based method are examined and verified by comparing with the well-utilized stochastically perturbed physics tendencies(SPPT) scheme. The results indicate that the CNOP-P-based method has potential in improving the under-dispersive problem of the current CAEPS.     

有限元集中质量法在非饱和土壤水流中的应用

利用Ｇａｌｅｒｋｉｎ有限元集中质量法,讨论了非饱和土壤水流动的数值计算模型,用以模拟均质土壤,地下水埋藏很深且在不同的初始和边界条件下的水分运动。通过将第一类边界条件齐次化,而对于第二类非线性边界条件采用变分的办法将其直接转化为已知边界通量的计算,从而容易且较好地处理了带通量约束边界条件。对于入渗或蒸发问题,用通常的离散方法容易产生振荡非物理解。我们采用有限元集中质量法,将质量矩阵的非对角元集中到主对角元,避免了这种非物理解的产生。利用该方案统一地模拟如下情况：稳定入渗和蒸发、蒸发一段时间后达到风干率,以及波动入渗蒸发时土壤水势的变化状况。模拟表明,在已知有关土壤参数的情况下,该模型能较好地模拟非饱和流水势及含水量分布。     

The differential method for calculation of cloud motion vectors

The problem ofcloud data retrieval for the periods between the fixed terms ofobservations from geostationary satellites is solved using the differential methods for the optical flow. To solve the problem, the possibility of using different methods for computing cloud motion vectors is investigated. The estimates of the accuracy of computed vectors based on artificially generated test sequences are presented. The test results reveal that the accuracy of the optical flow calculation with the modt fied Brox’s method excels the other mentioned methods. The software is implemented for creating the smooth animation of cloud movement using the modified Brox’s method.     

一类时滞离散非线性系统的全维观测器设计

通过类Lyapunov方法,结合线性矩阵不等式(LMI)技术,给出了具有时滞的Lipschitz非线性离散系统全维观测器存在的充分条件.在此基础上,设计了具有扰动的时滞Lipschitz非线性离散系统的鲁棒观测器,提出了该鲁棒观测器存在的一个充分条件,并用具体例子说明了其可行性与有效性.     

THE STUDY OF RETRIEVAL THEORY AND METHODS FROM SATELLITE REMOTE SENSING FOR METEOROLOGICAL PARAMETERS OVER EASTERN ASIA-PARTI:ISPRM AND SRRM*

A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process.the full advantage of every prior information available must be taken.It is necessary to turn the ill-posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.     

THE STUDY OF RETRIEVAL THEORY AND METHODS FROM SATELLITE REMOTE SENSING FOR METEOROLOGICAL PARAMETERS OVER EASTERN ASIA-PARTI:ISPRM AND SRRM

A review of ten-year's practice in developing the improved simultaneous physical retrievalmethod(ISPRM)is given in the hope that some creative ideas can be drawn from it.Theimprovement upon the SPRM is associated with the under-determinedness of this ill-posed inverseproblem.In our experiment,the precondition is observed that prior information must beindependent of the satellite measurements.The well-posed retrieval theory has told us that theforward process is fundamental for the retrieval,and it is the bridge between the input of satelliteradiance and the output of retrievals.In order to obtain a better result from the forward process.the full advantage of every prior information available must be taken.It is necessary to turn the ill-posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayesalgorithm to find the optimal combination among the first guess,the theoretical analogueinformation and the satellite observations,the impact of the under-determinedness of this inverseproblem on the numerical solution is minimized.     

A Variational Method for Estimating Near-Surface Soil Moisture and Surface Heat Fluxes

A variational data assimilation method is proposed to estimate the near-surface soil moisture and surface sensible and latent heat fluxes.The method merges the five parts into a cost function,i.e.,the differences of wind,potential temperature,anti specific humidity gradient between observations and those computed by the profile method,the difference of latent heat fluxes calculated using the ECMWF land surface evaporation scheme and the profile method,and a weak constraint for surface energy balance.By using an optimal algorithm,the best solutions are found.The method is tested with the data collected at Feixi Station (31.41°N,117.08°E) supported by the China Heavy Rain Experiment and Study (HeRES) during 7-30 June 2001.The results show that estimated near-surface soil moistures can quickly respond to rainfall,and their temporal variation is consistent with that of measurements of average soil moisture over 15-cm top depth with a maximum error less than 0.03 m~3 m~(-3).The surface heat fluxes calculated by this method are consistent with those by the Bowen ratio method,but at the same time it can overcome the instability problem occurring in the Bowen ratio method when the latter is about-1.Meanwhile,the variational method is more accurate than the profile method in terms of satisfying the surface energy balance.The sensitivity tests also show that the variational method is the most stable one among the three methods.     

扩散系数反演及其差分格式研究

空气污染预报属于正问题，而从污染物浓度来求解扩散系数则属于反问题。正问题和反问题有着本质的不同，在解的定义和求解方法上也有很大的区别。从最优控制的角度定义了大气边界层中垂直扩散系数反演问题的解，用伴随模式方法得到目标函数的梯度并求解反问题。研究中发现，反演的结果与模式差分格式的选取有关，与测试源的设置也有直接的关系。在经过多次数值试验后，对于误差的来源进行了理论分析，发现了反演结果与差分格式及测试源之间的联系，得到了满意的反演结果，并为实验测定扩散系数提供了依据。     

NUMERICAL EXPERIMENTS ON MULTI-LEVEL STATISTICAL ESTIMATION OF DYNAMIC BALANCE CONSTRAINTS IN GRAPES-3DVAR

This paper further explores the estimating and expressing of dynamic balance constraints using statistical methods in GRAPES-3DVAR (Version GM). Unlike the single-level scheme which only considers the coupling between mass and wind at one level, the multi-level scheme considers the coupling between their vertical profiles and calculates the balanced mass field at each layer using the rotational wind at all model levels. A reformed ridge regression method is used in the new scheme to avoid the multicollinearity problem and reduce the noises caused by unbalanced mesoscale disturbances. The results of numerical experiments show that the new scheme can get more reasonable vertical mass field, reduce the magnitude of the adjustment by the initialization, and improve the potential temperature analysis performance. Furthermore, the results of forecast verification in January (winter) and July (summer) both confirm that the new scheme can significantly improve the temperature forecast accuracy and bring slight positive effects to the pressure and wind forecast.     

A CRPS-Based Spatial Technique for the Verification of Ensemble Precipitation Forecasts

Traditional precipitation skill scores are affected by the well-known“double penalty”problem caused by the slight spatial or temporal mismatches between forecasts and observations. The fuzzy (neighborhood) method has been proposed for deterministic simulations and shown some ability to solve this problem. The increasing resolution of ensemble forecasts of precipitation means that they now have similar problems as deterministic forecasts. We developed an ensemble precipitation verification skill score, i.e., the Spatial Continuous Ranked Probability Score (SCRPS), and used it to extend spatial verification from deterministic into ensemble forecasts. The SCRPS is a spatial technique based on the Continuous Ranked Probability Score (CRPS) and the fuzzy method. A fast binomial random variation generator was used to obtain random indexes based on the climatological mean observed frequency, which were then used in the reference score to calculate the skill score of the SCRPS. The verification results obtained using daily forecast products from the ECMWF ensemble forecasts and quantitative precipitation estimation products from the OPERA datasets during June-August 2018 shows that the spatial score is not affected by the number of ensemble forecast members and that a consistent assessment can be obtained. The score can reflect the performance of ensemble forecasts in modeling precipitation and thus can be widely used.     

An unsaturated soil water flow problem and its numerical simulation

1.IntroductionUnsaturatedsoilwaterflowisaflowwherewaterisnotfullofsoilhole,whichisanimportantformofflowinporousmedia.Predictionofanunsaturatedflowisprovidedwithsignificanceinmanybranchesofscienceandengineering.Theseincludeatmosphericscience,soilscien...     

集合卡尔曼滤波数据同化在一维波动方程中的应用

简要回顾了集合卡尔曼滤波(EnKF：Ensemble Kalman Filter)数据同化方法的发展历史,并介绍了EnKF数据同化方法的基本原理,利用一维非线性波动方程进行了数值试验。EnKF数据同化方法的实现过程简单可行。避免了EKF中协方差演变方程预报过程中出现的计算不准确和关于协方差矩阵的大量数据的存储问题,最主要的是EnKF可以有效控制模式变量估计误差方差的增长,改善预报效果。     

Solving the map overlay problem with a fuzzy approach

The map overlay problem occurs when mismatched gridded data need to be combined, the problem consists of determining which portion of grid cells in one grid relates to the partly overlapping cells of the target grid. This problem contains inherent uncertainty, but it is an important and necessary first step in analysing and combining data; any improvement in achieving a more accurate relation between the grids will positively impact the subsequent analysis and conclusions. Here, a novel approach using techniques from fuzzy control and artificial intelligence is presented to provide a new methodology. The method uses a fuzzy inference system to decide how data represented in one grid can be distributed over another grid using any additionally available knowledge, thus mimicking the higher reasoning that we as humans would use to consider the problem.     

A developing boundary layer over an evaporating surface

The problem of air flow over a sudden change in surface temperature and humidity has been solved using mixing-length theory. The method is similar to that used by P. A. Taylor (1970) with some modifications. The form of the mixing length suggested by Blackadar is used and this allows calculation farther downwind. A vapor diffusion equation is included in the set of conservation equations and a vapor buoyancy term is included in the stability length. The vapor buoyancy is found to enhance significantly the turbulent diffusion but to a lesser degree than does the thermal buoyancy.     

中尺度扰动不稳定的数值研究

利用一个二维Boussinesq流体的绝热无粘非静力数值模式,将中尺度不稳定问题作为一个初值问题进行数值研究.线性情况下数值试验的结果基本与采用特征值方法研究得到的结论一致.非线性情况的数值试验表明,其不稳定发生的范围可与线性情况不一致;非线性不稳定的增长率一般较线性不稳定的增长率要小;非线性作用会造成波型的陡凸,从而造成流函数正负环流的不对称和环流流线的密集;非线性情形下的流型有些与强对流系统的流型相像.     

基于MVAD技术的多普勒雷达径向速度退模糊方法的改进研究

对Gong（2003）提出的基于Modified VAD技术的多普勒雷达径向速度退模糊方法进行了改进。原方法从各高度上径向风速的方位梯度信息中估计水平风廓线的分布,在使用各高度参考风进行一次退模糊的基础上,进行连续性检验完成整个退模糊过程。使用参考风进行退模糊能在很大程度上提高退模糊的效率。但是由于中小尺度系统的扰动和复杂的采样覆盖的影响,一般很难获得比较准确的估计水平风速,这将对进一步的退模糊过程产生很大的影响。针对这个问题,在水平风估计过程增加了质量控制参数,使其能够更好地估计水平风。此外,还对原方法中的几项参数的选择进行了讨论和调整。通过对两个个例的退模糊试验,检验了改进后方法的效果。     

多因变量矩阵回归预报方法

本文针对一个因变量多元回归在气象预报应用中的不足和局限，引入多因变量多元回归，讨论了应用中的公共预报因子问题和因子筛选问题，并对多因变量回归与单因变量回归、场展开预报、逐步回归、逐段回归等方法进行了比较，探讨了其特点及应用效果。