利用WRF3D-Var同化多普勒雷达反演风场试验研究

为了将C波段雷达风场资料更好地应用于数值预报模式中,利用两步变分法反演多普勒雷达风场资料,并处理成标准的常规探空资料,以WRF模式及其三维变分同化系统为平台,针对2013年6月19日发生在天水的一次强暴雨过程进行同化雷达反演风的试验研究.试验结果表明:同化雷达反演风场后,对降水预报的改进能维持12h,尤其同化雷达反演风场后3~9h效果非常显著;0~3h作用不是很明显;9~12h预报具有一定的正作用.另外,循环同化比同化一次效果好,但并不是同化次数越多越好.因此,同化C波段雷达反演风场后,对降水预报具有一定的正作用.     

伴随数据同化方法及其在地幔对流中的应用

伴随数据同化方法是一个基于梯度法的反演技巧,尤其适用于对非线性问题的反演。最近几年里,该方法在地球物理问题中的应用取得了长足发展。文中试图从理论推导到其在地幔对流中的应用对该方法进行系统阐述,并附例图加以说明。伴随数据同化方法的基础是扰动理论,将模型输出与观测值的差别归因于模型输入中存在的误差,而该输入误差可以通过输出误差的最小二乘对输入条件的一阶倒数(梯度)来表示,这个联系就称作伴随算子。非线性问题的反演需要用到多次迭代;对输入误差的预估程度会直接影响计算和结果收敛的速度。作为描述当前地幔结构最有力证据的地震层析成像技术的不断进步,不论是在区域还是全球尺度上,都为地幔对流的反演提供了一个出发点。通过进一步同化或者比较相关的地质学证据特别是地表动力沉降观测,地幔对流反演可以克服目前仍然存在的地幔动力学各参数的不确定性的影响,从而进一步揭示壳幔系统的动力学机制。讨论的一个实际的例子是如何使用该方法反推出Farallon板块于晚白垩世时期在北美板块下的平俯冲过程以及该研究所导致的地球物理学及地质学意义。     

Impact of additional surface observation network on short range weather forecast during summer monsoon 2008 over Indian subcontinent

The three dimensional variational data assimilation scheme (3D-Var) is employed in the recently developed Weather Research and Forecasting (WRF) model. Assimilation experiments have been conducted to assess the impact of Indian Space Research Organisation’s (ISRO) Automatic Weather Stations (AWS) surface observations (temperature and moisture) on the short range forecast over the Indian region. In this study, two experiments, CNT (without AWS observations) and EXP (with AWS observations) were made for 24-h forecast starting daily at 0000 UTC during July 2008. The impact of assimilation of AWS surface observations were assessed in comparison to the CNT experiment. The spatial distribution of the improvement parameter for temperature, relative humidity and wind speed from one month assimilation experiments demonstrated that for 24-h forecast, AWS observations provide valuable information. Assimilation of AWS observed temperature and relative humidity improved the analysis as well as 24-h forecast. The rainfall prediction has been improved due to the assimilation of AWS data, with the largest improvement seen over the Western Ghat and eastern India.     

Adjoint retrieval of prognostic land surface model variables for an NWP model: Assimilation of ground surface temperature

Based on a 2-layer land surface model, a rather general variational data assimilation framework for estimating model state variables is developed. The method minimizes the error of surface soil temperature predictions subject to constraints imposed by the prediction model. Retrieval experiments for soil prognostic variables are performed and the results verified against model simulated data as well as real observations for the Oklahoma Atmospheric Surface layer Instrumentation System (OASIS). The optimization scheme is robust with respect to a wide range of initial guess errors in surface soil temperature (as large as 30 K) and deep soil moisture (within the range between wilting point and saturation). When assimilating OASIS data, the scheme can reduce the initial guess error by more than 90%, while for Observing Simulation System Experiments (OSSEs), the initial guess error is usually reduced by over four orders of magnitude. Using synthetic data, the robustness of the retrieval scheme as related to information content of the data and the physical meaning of the adjoint variables and their use in sensitivity studies are investigated. Through sensitivity analysis, it is confirmed that the vegetation coverage and growth condition determine whether or not the optimally estimated initial soil moisture condition leads to an optimal estimation of the surface fluxes. This reconciles two recent studies. With the real data experiments, it is shown that observations during the daytime period are the most effective for the retrieval. Longer assimilation windows result in more accurate initial condition retrieval, underlining the importance of information quantity, especially for schemes assimilating noisy observations.     

二维平面非恒定流数学模型的遥感水位数据同化

为了在水流计算中定量化利用遥感水位数据,基于偏微分方程最优化控制理论建立了变分模型来融合二维平面非恒定流的数学模型和数据。根据遥感数据空间信息密集的特点,提出遥感水位数据同化的新算法。采用人工合成数据考察了面域遥感数据对于定常参数和时变两类参数的反演效果。试验结果表明,遥感数据提供的空间分布式信息有利于空间分布式参数的反演识别,而且通过引入考虑水面空间变化信息的附加项,可以改善观测信息的同化,更好地辨识时变参数(流量过程)。以Moselle河的RADARSAT卫星遥感水位数据检验了模型的实用性。     

Sur l'assimilation variationnelle de données par un modèle d'écosystème marin de type NPZ

A variational data assimilation method is applied to a simplified marine ecosystem model of NPZ (Nutrient Phytoplankton Zooplankton) type, which implies five parameters. The method allows us to optimise these parameters by an iterative process of minimisation of a cost function which quantifies the quadratic discrepancy between observations and simulation results. The first part of this note describes how to obtain the adjoint model of the NPZ model allowing us to compute the gradient of the cost function relative to the parameters. Two experiments of artificial data assimilation then show the efficiency of this method, but also its limitations because of non-linearities and sensitivity problems of the model relative to the parameters. To cite this article: Y. Leredde et al., C. R. Geoscience 337 (2005).     

一个基于模拟退火法的陆面数据同化算法

陆面数据同化系统是近年来兴起的新领域。我们发展了一个实验型的陆面数据同化方案,它使用一种启发式优化算法——模拟退火法极小化目标泛函。与变分法和Kalman滤波方法比较,这一算法具有独立于目标泛函的优点,可处理模型和观测算子的非线性和不连续性。使用GAME—Tibet实验中的土壤水分观测值进行单点数值实验,成功地将土壤水分观测同化到陆面过程模型SiB2中。结果表明,与不进行同化相比,土壤水分的估计值有较大改善。     

Ensemble filter methods with perturbed observations applied to nonlinear problems

The ensemble Kalman filter (EnKF) has been shown repeatedly to be an effective method for data assimilation in large-scale problems, including those in petroleum engineering. Data assimilation for multiphase flow in porous media is particularly difficult, however, because the relationships between model variables (e.g., permeability and porosity) and observations (e.g., water cut and gas–oil ratio) are highly nonlinear. Because of the linear approximation in the update step and the use of a limited number of realizations in an ensemble, the EnKF has a tendency to systematically underestimate the variance of the model variables. Various approaches have been suggested to reduce the magnitude of this problem, including the application of ensemble filter methods that do not require perturbations to the observed data. On the other hand, iterative least-squares data assimilation methods with perturbations of the observations have been shown to be fairly robust to nonlinearity in the data relationship. In this paper, we present EnKF with perturbed observations as a square root filter in an enlarged state space. By imposing second-order-exact sampling of the observation errors and independence constraints to eliminate the cross-covariance with predicted observation perturbations, we show that it is possible in linear problems to obtain results from EnKF with observation perturbations that are equivalent to ensemble square-root filter results. Results from a standard EnKF, EnKF with second-order-exact sampling of measurement errors that satisfy independence constraints (EnKF (SIC)), and an ensemble square-root filter (ETKF) are compared on various test problems with varying degrees of nonlinearity and dimensions. The first test problem is a simple one-variable quadratic model in which the nonlinearity of the observation operator is varied over a wide range by adjusting the magnitude of the coefficient of the quadratic term. The second problem has increased observation and model dimensions to test the EnKF (SIC) algorithm. The third test problem is a two-dimensional, two-phase reservoir flow problem in which permeability and porosity of every grid cell (5,000 model parameters) are unknown. The EnKF (SIC) and the mean-preserving ETKF (SRF) give similar results when applied to linear problems, and both are better than the standard EnKF. Although the ensemble methods are expected to handle the forecast step well in nonlinear problems, the estimates of the mean and the variance from the analysis step for all variants of ensemble filters are also surprisingly good, with little difference between ensemble methods when applied to nonlinear problems.     

A numerical study on rapid intensification of Hurricane Charley (2004) near landfall

The rapid intensification of Hurricane Charley (2004) near landfall is studied using the fifth-generation Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) Mesoscale Model (MM5) and its adjoint system for both vortex initialization and forecasts. A significant improvement in both track and intensity forecasts is achieved after an ill-defined storm vortex, derived from large-scale analysis, in the initial condition is replaced by the vortex generated by a four-dimensional data variational (4D-Var) hurricane initialization scheme. Results from numerical experiments suggest that both the inclusion of the upper-level trough and the use of high horizontal resolution (6 km) are important for numerical simulations to capture the observed rapid intensification as well as the size reduction during the rapid intensification of Hurricane Charley. The approach of the upper-level trough significantly enhanced the upper-level divergence and vertical motion within simulated hurricanes. Small-scale features that are not resolvable at 18 km resolution are important to the rapid intensification and shrinking of Hurricane Charley (2004). Numerical results from this study further confirm that the theoretical relationship between the intensification and shrinking of tropical cyclones based on the angular momentum conservation and the cyclostrophic approximation can be applied to the azimuthal mean flows.     

The variational technique of data assimilation using adjoint equations in a shallow water model

The variational technique of data assimilation using adjoint equations has been illustrated using a nonlinear oceanographic shallow water model. The technique consists of minimizing a cost function representing the misfit between the model and the data subject to the model equations acting as constraints. The problem has been transformed into an unconstrained one by the use of Lagrange multipliers. Particular emphasis has been laid on finite difference formulation of the algorithm. Several numerical experiments have been conducted using simulated data obtained from a control run of the model. Implications of this technique for assimilating asynoptic satellite altimeter data into ocean models have been discussed.     

Impact of satellite soundings on the simulation of heavy rainfall associated with tropical depressions

The present study is carried out to examine the impact of temperature and humidity profiles from moderate resolution imaging spectroradiometer (MODIS) or/and atmospheric infrared sounder (AIRS) on the numerical simulation of heavy rainfall events over the India. The Pennsylvania State University–National Centre for Atmospheric Research fifth-generation mesoscale model (MM5) and its three-dimensional variational (3D-Var) assimilation technique is used for the numerical simulations. The heavy rainfall events occurred during October 26–29, 2005, and October 27–30, 2006, were chosen for the numerical simulations. The results showed that there were large differences observed in the initial meteorological fields from control experiment (CNT; without satellite data) and assimilation experiments (MODIS (assimilating MODIS data), AIRS; (assimilating AIRS data); BOTH (assimilating MODIS and AIRS data together)). The assimilation of satellite data (MODIS, AIRS, and BOTH) improved the predicted thermal and moisture structure of the atmosphere when compared to CNT. Among the experiments, the predicted track of tropical depressions from MODIS was closer to the observed track. Assimilation of MODIS data also showed positive impact on the spatial distribution and intensity of predicted rainfall associated with the depressions. The statistical skill scores obtained for different experiments showed that assimilation of satellite data (MODIS, AIRS, and BOTH) improved the rainfall prediction skill when compared to CNT. Root mean square error in quantitative rainfall prediction is less in the experiment which assimilated MODIS data when compared to other experiments.     

评估集合卡曼滤波反演土壤湿度廓线的性能

集合卡曼滤波由于易于使用而被广泛地应用到陆面数据同化研究中,它是建立在模型为线性、误差为正态分布的假设上,而实际土壤湿度方程是高度非线性的,并且当土壤过干或过湿时会发生样本偏斜.为了全面评估它在同化表层土壤湿度观测来反演土壤湿度廓线的性能,特引入不需要上述假设的采样重要性重采样粒子滤波,比较非线性和偏斜性对同化算法的影响.结果显示:不管是小样本还是大样本,集合卡曼滤波都能快速、准确地逼近样本均值,而粒子滤波只有在大样本时才能缓慢地趋近;此外,集合卡曼滤波的粒子边缘概率密度及其偏度和峰度与粒子滤波完全不同,前者粒子虽不完全满足正态分布,但始终为单峰状态,而后者粒子随同化推进经历了单峰到双峰再到单峰的变化.     

A multiresolution ensemble Kalman filter using the wavelet decomposition

We present a method of using classical wavelet-based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena involve the interaction of features at multiple scales. Blending of observational and model error across scales can result in large forecast inaccuracies since large errors at one scale are interpreted as inexact data at all scales due to the misrepresentation of observational error. Our method uses a partitioning of the range of the observation operator into separate observation scales. This naturally induces a transformation of the observation covariance and we put forward several algorithms to efficiently compute the transformed covariance. Another advantage of our multiresolution ensemble Kalman filter is that scales can be weighted independently to adjust each scale’s affect on the forecast. To demonstrate feasibility, we present applications to a one-dimensional Kuramoto-Sivashinsky (K–S) model with scale-dependent observation noise and an application involving the forecasting of solar photospheric flux. The solar flux application uses the Air Force Data Assimilative Photospheric Transport (ADAPT) model which has model and observation error exhibiting strong scale dependence. Results using our multiresolution ensemble Kalman filter show significant improvement in solar forecast error compared to traditional ensemble Kalman filtering.     

考虑预报偏差的迭代式集合卡尔曼滤波在地下水水流数据同化中的应用

集合卡尔曼滤波（Ensemble Kalman Filter,EnKF）方法已广泛应用于地下水水流和污染物运移模拟相关问题的求解。但前人研究多建立在同化系统预报模型是准确的基础上,忽视了模型概化的不确定性。当模型概化不准确时,将导致预报偏差,可能带来错误的系统估计。因此,文章提出考虑模型预报偏差的迭代式集合卡尔曼滤波（Bias aware Ensemble Kalman Filter with Confirming Option,Bias-CEnKF）方法。以地下水水流数据同化为例,研究模型概化存在不确定条件下,边界条件、初始条件、源汇项概化不准确时新方法的有效性。结果表明,当预报模型概化不准确时,使用标准EnKF方法进行数据同化,可能会导致滤波发散,造成同化失败。Bias-CEnKF方法不仅保留了较好的同化性能,同时减小了参数、变量、偏差项非线性关系带来的不一致性。针对文章中4种情景,Bias-CEnKF同化获得的含水层渗透系数场以及水头场均接近真实场,且预报结果可靠。本研究进一步提升了模型概化不确定时EnKF方法的适用性,为实际野外复杂条件下地下水水流数据同化问题提供了可靠的方法。     

Data Assimilation (4D-VAR) for Shallow-Water Flow: The Case of the Chicoutimi River

This is a web presentation of the work presented at the 10th Annual Conference of the CFD Society of Canada, “CFD 2002”, at the University of Windsor on June 9-11, 2002. This discussion paper presents the four-dimensional variational data assimilation (4D-VAR) technique as a tool to forecast floods. This discussion will be limited to hydrological forecast. We assume that the weather, here a large rainstorm, had already been forecasted by the meteorological services. In the 4D-VAR technique, we need to minimize, in the sense of Lagrange, a cost function which measures the difference between the forecast and the observations. The physical equations acts as a set of constraints. Here, the model is the shallow-water equations modified to include sediment transport. The minimum was found by using the steepest descent algorithm. This is made possible because the gradient of the cost function can be calculated analytically by using the adjoint equations of the model. To illustrate the 4D-VAR technique, the bypass of a simple theoretical dam as well as the more complex overflowing of the Chicoutimi River at the Chute-Garneau dam (during the 1996 flood) are investigated.     

Development of extended WRF variational data assimilation system (WRFDA) for WRF non-hydrostatic mesoscale model

The paper intends to present the development of the extended weather research forecasting data assimilation (WRFDA) system in the framework of the non-hydrostatic mesoscale model core of weather research forecasting system (WRF-NMM), as an imperative aspect of numerical modeling studies. Though originally the WRFDA provides improved initial conditions for advanced research WRF, we have successfully developed a unified WRFDA utility that can be used by the WRF-NMM core, as well. After critical evaluation, it has been strategized to develop a code to merge WRFDA framework and WRF-NMM output. In this paper, we have provided a few selected implementations and initial results through single observation test, and background error statistics like eigenvalues, eigenvector and length scale among others, which showcase the successful development of extended WRFDA code for WRF-NMM model. Furthermore, the extended WRFDA system is applied for the forecast of three severe cyclonic storms: Nargis (27 April–3 May 2008), Aila (23–26 May 2009) and Jal (4–8 November 2010) formed over the Bay of Bengal. Model results are compared and contrasted within the analysis fields and later on with high-resolution model forecasts. The mean initial position error is reduced by 33% with WRFDA as compared to GFS analysis. The vector displacement errors in track forecast are reduced by 33, 31, 30 and 20% to 24, 48, 72 and 96 hr forecasts respectively, in data assimilation experiments as compared to control run. The model diagnostics indicates successful implementation of WRFDA within the WRF-NMM system.     

Development of Artificial Intelligence Technology in Weather Forecast

Numerical weather prediction, which is the major basis of current weather forecast, has some shortcomings, such as the understanding of the law of atmospheric motion, the assimilation and application of observation data, the expression of model physics, etc., leading to the forecast error of weather. The rapid development of artificial intelligence technology in recent years provides a new possibility for the advancement and innovation of weather forecast. In this paper, the background of the development of artificial intelligence, the current situation of the application of artificial intelligence technology to weather forecast and the future development trend are mainly described to account for this possibility. After that, the idea for development of weather forecast technology based on the integration of artificial intelligence and numerical forecast is put forward. Particularly, this study stresses that, in order to advance the AI algorithm of weather forecast in the future, it is requested to focus on the nonlinear and chaotic characteristics of atmospheric motion leading to the uncertainty of forecast. Starting from the essence of mathematics and physics, we need to realize the hybrid modeling of mathematics and physics, not only to establish the framework of input-output mapping, but also to provide solutions to the bottleneck problems of weather forecast.     

Application of the representer method for parameter estimation in numerical reservoir models

A data assimilation method was applied to estimate poorly known parameters (permeabilities) in a numerical reservoir model. Most variational methods for data assimilation are based on the assumption that the model is perfect except for the poorly known parameters. The representer method allows also for model errors, i.e. for uncertainties in the state variables (pressures and saturations). The method is based on minimizing a cost functional, assuming all the errors and parameters to be multivariate Gaussian random variables with given mean and covariances. The uncertain parameters and variables are expanded into a finite sum of basis functions called representers, and the gradients of the cost functional are obtained with an adjoint method. This approach gives an optimal parametrization in the sense that the final result is equal to the solution of the full inverse problem. The method was tested on a simple one-dimensional model to simulate two-phase (oil-water) flow through a heterogeneous reservoir. The results show that the method is able to provide an acceptable estimate of the permeability field. We used pressure measurements from a small number of observation wells in between the injection and production wells, but the representer method could be used equally well to assimilate data from other sources. The method appears to be a promising data assimilation tool for applications in reservoir engineering.     

Numerical simulation of cyclonic storms FANOOS, NARGIS with assimilation of conventional and satellite observations using 3-DVAR

In this work, the impact of assimilation of conventional and satellite data is studied on the prediction of two cyclonic storms in the Bay of Bengal using the three-dimensional variational data assimilation (3D-VAR) technique. The FANOOS cyclone (December 6?C10, 2005) and the very severe cyclone NARGIS (April 28?CMay 2, 2008) were simulated with a double-nested weather research and forecasting (WRF-ARW) model at a horizontal resolution of 9?km. Three numerical experiments were performed using the WRF model. The back ground error covariance matrix for 3DVAR over the Indian region was generated by running the model for a 30-day period in November 2007. In the control run (CTL), the National Centers for Environmental Prediction (NCEP) global forecast system analysis at 0.5° resolution was used for the initial and boundary conditions. In the second experiment called the VARCON, the conventional surface and upper air observations were used for assimilation. In the third experiment (VARQSCAT), the ocean surface wind vectors from quick scatterometer (QSCAT) were used for assimilation. The CTL and VARCON experiments have produced higher intensity in terms of sea level pressure, winds and vorticity fields but with higher track errors. Assimilation of conventional observations has meager positive impact on the intensity and has led to negative impact on simulated storm tracks. The QSCAT vector winds have given positive impact on the simulations of intensity and track positions of the two storms, the impact is found to be relatively higher for the moderate intense cyclone FANOOS as compared to very severe cyclone NARGIS.     

Kalman滤波在气象数据同化中的发展与应用

气象学领域各种观测(特别是遥感遥测等非常规观测)数据的大量增多和数值天气预报模式的不断进步,推动气象数据同化技术不断发展。回顾了Kalman滤波在气象数据同化中的引入和几个发展阶段;介绍了Kalman滤波(尤其是简化Kalman滤波和总体Kalman滤波)在气象数据同化中的重要地位和应用进展。