An adaptive hybrid EnKF-OI scheme for efficient state-parameter estimation of reactive contaminant transport models

Reactive contaminant transport models are used by hydrologists to simulate and study the migration and fate of industrial waste in subsurface aquifers. Accurate transport modeling of such waste requires clear understanding of the system’s parameters, such as sorption and biodegradation. In this study, we present an efficient sequential data assimilation scheme that computes accurate estimates of aquifer contamination and spatially variable sorption coefficients. This assimilation scheme is based on a hybrid formulation of the ensemble Kalman filter (EnKF) and optimal interpolation (OI) in which solute concentration measurements are assimilated via a recursive dual estimation of sorption coefficients and contaminant state variables. This hybrid EnKF-OI scheme is used to mitigate background covariance limitations due to ensemble under-sampling and neglected model errors. Numerical experiments are conducted with a two-dimensional synthetic aquifer in which cobalt-60, a radioactive contaminant, is leached in a saturated heterogeneous clayey sandstone zone. Assimilation experiments are investigated under different settings and sources of model and observational errors. Simulation results demonstrate that the proposed hybrid EnKF-OI scheme successfully recovers both the contaminant and the sorption rate and reduces their uncertainties. Sensitivity analyses also suggest that the adaptive hybrid scheme remains effective with small ensembles, allowing to reduce the ensemble size by up to 80% with respect to the standard EnKF scheme.     

Short-term optimal operation of water systems using ensemble forecasts

Short-term water system operation can be realized using Model Predictive Control (MPC). MPC is a method for operational management of complex dynamic systems. Applied to open water systems, MPC provides integrated, optimal, and proactive management, when forecasts are available. Notwithstanding these properties, if forecast uncertainty is not properly taken into account, the system performance can critically deteriorate.Ensemble forecast is a way to represent short-term forecast uncertainty. An ensemble forecast is a set of possible future trajectories of a meteorological or hydrological system. The growing ensemble forecasts’ availability and accuracy raises the question on how to use them for operational management.The theoretical innovation presented here is the use of ensemble forecasts for optimal operation. Specifically, we introduce a tree based approach. We called the new method Tree-Based Model Predictive Control (TB-MPC). In TB-MPC, a tree is used to set up a Multistage Stochastic Programming, which finds a different optimal strategy for each branch and enhances the adaptivity to forecast uncertainty. Adaptivity reduces the sensitivity to wrong forecasts and improves the operational performance.TB-MPC is applied to the operational management of Salto Grande reservoir, located at the border between Argentina and Uruguay, and compared to other methods.     

基于集合预报产品的降尺度降水预报试验

利用降水距平百分率的降尺度预报方法和1951-2008 NCEP资料及我国降水资料,建立了降水距平百分率的预报模型,基于T106L19模式的月动力延伸集合预报结果,进行了2007-2009年3 a的预报试验和效果检验.结果表明,基于集合预报产品的统计降尺度方法对降水距平百分率的预报技巧高于模式降水的预报技巧;500 hPa月平均高度场的预报技巧直接影响到降水距平百分率的预报技巧,平均环流的预报技巧越高,降水距平百分率的预报技巧越高;无论集合成员数为多少,集合预报的结果都明显优于控制预报,随着集合成员数的增多,预报技巧呈增大的趋势;我国降水具有显著的季节性和区域性,以江淮地区的降水距平百分率预报技巧最高,华南地区的预报技巧其次.     

Application and Verification of Joint Probability Method in Potential Forecast for Severe Convective Weather in Anhui Province

In consideration of large uncertainties in severe convective weather forecast, ensemble forecasting is a dynamic method developed to quantitatively estimate forecast uncertainty. Based on ensemble output, joint probability is a post-processing method to delineate key areas where weather event may actually occur by taking account of the uncertainty of several important physical parameters. An investigation of the environments of little rainfall convection and strong rainfall convection from April to September (warm season) during 2009-2015 was presented using daily disastrous weather data, precipitation data of 80 stations in Anhui province and NCEP Final Analysis (FNL) data. Through ingredients-based forecasting methodology and statistical analysis,four convective parameters characterizing two types of convection were obtained, respectively, which were used to establish joint probability forecasting together with their corresponding thresholds. Using the ECMWF ensemble forecast and observations from April to September during 2016-2017, systematic verification mainly based on ROC and case study of different weather processes were conducted. The results demonstrate that joint probability method is capable of discriminating little rainfall convection and non-convection with comparable performance for different lead times, which is more favorable to identifying the occurrence of strong rainfall convection. The joint probability of little rainfall convection is a good indication for the occurrence of regional or local convection, but may produce some false alarms. The joint probability of strong rainfall convection is good at indicating regional concentrated short-term heavy precipitation as well as local heavy rainfall. There are also individual missing reports in this method, and in practice, 10% can be roughly used as joint probability threshold to achieve relative high TS score. Overall, ensemble-based joint probability method can provide practical short-term probabilistic guidance for severe convective weather.     

Improved initial sampling for the ensemble Kalman filter

In this paper, we discuss several possible approaches to improving the performance of the ensemble Kalman filter (EnKF) through improved sampling of the initial ensemble. Each of the approaches addresses a different limitation of the standard method. All methods, however, attempt to make the results from a small ensemble as reliable as possible. The validity and usefulness of each method for creating the initial ensemble is based on three criteria: (1) does the sampling result in unbiased Monte Carlo estimates for nonlinear flow problems, (2) does the sampling reduce the variability of estimates compared to ensembles of realizations from the prior, and (3) does the sampling improve the performance of the EnKF? In general, we conclude that the use of dominant eigenvectors ensures the orthogonality of the generated realizations, but results in biased forecasts of the fractional flow of water. We show that the addition of high frequencies from remaining eigenvectors can be used to remove the bias without affecting the orthogonality of the realizations, but the method did not perform significantly better than standard Monte Carlo sampling. It was possible to identify an appropriate importance weighting to reduce the variance in estimates of the fractional flow of water, but it does not appear to be possible to use the importance weighted realizations in standard EnKF when the data relationship is nonlinear. The biggest improvement came from use of the pseudo-data with corrections to the variance of the actual observations.     

Multiscale ensemble filtering for reservoir engineering applications

Reservoir management requires periodic updates of the simulation models using the production data available over time. Traditionally, validation of reservoir models with production data is done using a history matching process. Uncertainties in the data, as well as in the model, lead to a nonunique history matching inverse problem. It has been shown that the ensemble Kalman filter (EnKF) is an adequate method for predicting the dynamics of the reservoir. The EnKF is a sequential Monte-Carlo approach that uses an ensemble of reservoir models. For realistic, large-scale applications, the ensemble size needs to be kept small due to computational inefficiency. Consequently, the error space is not well covered (poor cross-correlation matrix approximations) and the updated parameter field becomes scattered and loses important geological features (for example, the contact between high- and low-permeability values). The prior geological knowledge present in the initial time is not found anymore in the final updated parameter. We propose a new approach to overcome some of the EnKF limitations. This paper shows the specifications and results of the ensemble multiscale filter (EnMSF) for automatic history matching. EnMSF replaces, at each update time, the prior sample covariance with a multiscale tree. The global dependence is preserved via the parent–child relation in the tree (nodes at the adjacent scales). After constructing the tree, the Kalman update is performed. The properties of the EnMSF are presented here with a 2D, two-phase (oil and water) small twin experiment, and the results are compared to the EnKF. The advantages of using EnMSF are localization in space and scale, adaptability to prior information, and efficiency in case many measurements are available. These advantages make the EnMSF a practical tool for many data assimilation problems.     

双分辨率集合卡尔曼滤波同化方案及模拟试验

高分辨率中尺度模式集合卡尔曼滤波实际应用的困难是集合预报会耗费大量的时间。而双分辨率集合卡尔曼滤波是由一组低分辨率样本提供同化所需的背景误差协方差矩阵,这种方法可以减少集合预报的时间。为了检验其有效性,文中利用模拟资料,与标准高分辨率集合卡尔曼滤波方法比较。结果表明：在第一个同化时次,两者对500 hPa水平风场和扰动位温场的分析增量场均与真实增量场的高低值中心位置一致,且结构与真实增量场接近,前者（高分辨率集合卡尔曼滤波）的增量值比后者（双分辨率集合卡尔曼滤波）的增量值更接近真实情况;在连续的预报-同化循环试验中,随着同化次数的增加,两种方法分析变量的均方根误差总体上都是下降的,均表现了很好的同化能力,但后者与前者相比仍存在一定的差距;在相同的运行环境下,后者的运行时间仅是前者的1/6。     

基于幅频分离的气候时间序列预测试验

从气候波动的瞬时频率与瞬时振幅出发,结合最小二乘支持向量机技术,提出了基于幅频分离技术的气候时间序列预测方法,并对南京地区降水距平进行了30候的预测试验。结果表明,幅频分离预测法能够对所有模态的振幅和高频模态的瞬时频率进行较好的预测,而预测的瞬时频率累积误差会对模态分量的预测距平相关性产生敏感影响,该新方法能够显著提高气候序列高频模态的预测效果。对于气候序列的低频模态分量,集合经验模态分解的边界效应会对瞬时频率的求解产生较大误差,使得序列边界区的幅角计算不准确,导致对低频模态的最终预测效果不理想。对气候序列的高频分量采用幅频分离并进行最小二乘支持向量机预测,而对其低频分量仅采用最小二乘支持向量机进行直接预测,可同时提高高、低频分量的预测效果,并最终提高整个气候序列的预测准确性。该分频预测方法可以使南京降水预测的30候距平相关保持在0.4以上。     

Quantifying uncertainty in changes in extreme event frequency in response to doubled CO2 using a large ensemble of GCM simulations

We discuss equilibrium changes in daily extreme surface air temperature and precipitation events in response to doubled atmospheric CO₂, simulated in an ensemble of 53 versions of HadSM3, consisting of the HadAM3 atmospheric general circulation model (GCM) coupled to a mixed layer ocean. By virtue of its size and design, the ensemble, which samples uncertainty arising from the parameterisation of atmospheric physical processes and the effects of natural variability, provides a first opportunity to quantify the robustness of predictions of changes in extremes obtained from GCM simulations. Changes in extremes are quantified by calculating the frequency of exceedance of a fixed threshold in the 2 × CO₂ simulation relative to the 1 × CO₂ simulation. The ensemble-mean value of this relative frequency provides a best estimate of the expected change while the range of values across the ensemble provides a measure of the associated uncertainty. For example, when the extreme threshold is defined as the 99th percentile of the 1 × CO₂ distribution, the global-mean ensemble-mean relative frequency of extremely warm days is found to be 20 in January, and 28 in July, implying that events occurring on one day per hundred under present day conditions would typically occur on 20–30 days per hundred under 2 × CO₂ conditons. However the ensemble range in the relative frequency is of similar magnitude to the ensemble-mean value, indicating considerable uncertainty in the magnitude of the increase. The relative frequencies in response to doubled CO₂ become smaller as the threshold used to define the extreme event is reduced. For one variable (July maximum daily temperature) we investigate this simulated variation with threshold, showing that it can be quite well reproduced by assuming the response to doubling CO₂ to be characterised simply as a uniform shift of a Gaussian distribution. Nevertheless, doubling CO₂ does lead to changes in the shape of the daily distributions for both temperature and precipitation, but the effect of these changes on the relative frequency of extreme events is generally larger for precipitation. For example, around one-fifth of the globe exhibits ensemble-mean decreases in time-averaged precipitation accompanied by increases in the frequency of extremely wet days. The ensemble range of changes in precipitation extremes (relative to the ensemble mean of the changes) is typically larger than for temperature extremes, indicating greater uncertainty in the precipitation changes. In the global average, extremely wet days are predicted to become twice as common under 2 × CO₂ conditions. We also consider changes in extreme seasons, finding that simulated increases in the frequency of extremely warm or wet seasons under 2 × CO₂ are almost everywhere greater than the corresponding increase in daily extremes. The smaller increases in the frequency of daily extremes is explained by the influence of day-to-day weather variability which inflates the variance of daily distributions compared to their seasonal counterparts.     

风暴尺度集合预报中的混合初始扰动方法及其在北京2012年“7.21”暴雨预报中的应用

风暴尺度集合预报系统（Storm-Scale Ensemble Forecast system,简称SSEFs）中集合成员之间发散度不足一直都是研究的难点。本文尝试了将Barnes空间滤波融入到集合转换卡尔曼滤波（ETKF）更新预报系统中的混合初值扰动法。该方案将ETKF方法的小尺度信息与来自于侧边界条件扰动的大尺度信息相结合,缓解了扰动在侧边界不匹配的问题。通过2012年北京“7.21”暴雨并使用邻位方法对比分析了不同初值扰动方案在不同时间尺度与空间尺度上的特征,在此基础上进一步探讨了构造混合初始扰动法的可行性。结果表明:ETKF试验所构造的初始扰动无法与侧边界条件扰动相匹配,混合后的初始扰动可以有效缓解SSEFs中由于初始扰动与侧边界扰动不匹配产生的虚假波动,其中大尺度信息保留较多的混合试验（ETKF80）和动力降尺度方案（Down）在减少虚假波动方面的效果最优;从集合离散度来看,在前期暖区降水阶段ETKF的离散度在小尺度上最大,随着锋面降水的开始,Down的离散度逐渐超过ETKF,而使用各滤波波段构造的混合试验同时具备ETKF与Down二者的特征。选择合理的滤波波段可以获得最为合理的离散度表现（ETKF180）,说明仅考虑侧边界匹配（Down和ETKF80）并不能获得最合理的集合离散度,应综合考虑其他因素。从降水概率预报结果来看,选取合适的滤波波段所构造的混合扰动试验同样获得了较好的效果。