An online model correction method based on an inverse problem: Part I—Model error estimation by iteration

Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.     

数值天气预报中的两类反问题及一种数值解法──理想试验

针对数值预报中产生误差的两个来源提出了数值预报中存在着两类反问题。并在一维的非线性平流扩散方程上，用共轭方程的解法对提出的两类反问题作出了理想场的数值试验。试验结果表明，这种解反问题的方法非常有效。它利用＂观测资料＂所包含的时间演变的信息确定出了方程的初值或方程中误差订正项的空间分布状况。而且无论对＂观测资料＂的超定还是欠定都能得出较有意义的结果。因而有很大的利用前景。     

模式误差动力特征：模式参数误差和物理过程描绘缺失误差

模式变最初始场误差和模式误差都是制约数值天气预报准确性提高的重要因素,传统数值预报和变分同化均忽略模式误差的影响.随着研究的深入,关于模式误差对数值预报影响的研究显得尤为重要.本文从非线性动力方程出发,推导出在模式存在参数误差和物理过程描绘缺失误差情况下的模式预报误差演变方程及短时间内误差平方均值近似表达式,并利用Li...     

Rapid scale-up of negative emissions technologies: social barriers and social implications

We describe a new approach that allows for systematic causal attribution of weather and climate-related events, in near-real time. The method is designed so as to facilitate its implementation at meteorological centers by relying on data and methods that are routinely available when numerically forecasting the weather. We thus show that causal attribution can be obtained as a by-product of data assimilation procedures run on a daily basis to update numerical weather prediction (NWP) models with new atmospheric observations; hence, the proposed methodology can take advantage of the powerful computational and observational capacity of weather forecasting centers. We explain the theoretical rationale of this approach and sketch the most prominent features of a “data assimilation–based detection and attribution” (DADA) procedure. The proposal is illustrated in the context of the classical three-variable Lorenz model with additional forcing. The paper concludes by raising several theoretical and practical questions that need to be addressed to make the proposal operational within NWP centers.     

登陆热带气旋降水预报研究回顾与展望

重点围绕登陆热带气旋（LTC）降水预报研究进行了回顾和总结,指出针对LTC降水有三类预报技术：动力模式、统计方法和动力-统计结合的预报方法。以数值天气预报（NWP）模式为代表的预报技术对LTC降水的预报能力仍然非常有限。改进NWP模式预报误差的途径主要有两条：一是发展NWP模式;二是发展动力-统计结合的方法。分析表明,动力-统计相似预报是一项很有潜力的技术;针对现有研究中的不足,开展LTC降水动力-统计相似预报研究,探索减小数值模式LTC降水预报误差的有效方法,将是一个充满希望的研究领域和方向。     

The Atmospheric Boundary Layer Over Baltic Sea Ice

A new parametrization for the surface energy balance of urban areas is presented. It is shown that this new method can represent some of the important urban phenomena, such as an urban heat island and the occurrence of a near-neutral nocturnal boundary layer with associated positive turbulent heat fluxes, unlike the traditional method for representing urban areas within operational numerical weather prediction (NWP) models. The basis of the new parametrization is simple and can be applied easily within an operational NWP model. Also, it has no additional computational expense compared to the traditional scheme and is hence applicable for operational forecasting requirements. The results show that the errors for London within the Met Office operational mesoscale model have been significantly reduced since the new scheme was introduced. The bias and root-mean-square (rms) errors have been approximately halved, with the rms error now similar to the model as a whole. The results also show that a seasonal cycle still exists in the model errors, but it is suggested that this may be caused by anthropogenic heat sources that are neglected in the urban scheme.The British Crowns right to retain a non-exclusive royalty-free license in and to any copyright is acknowledged.     

各种物理强迫激发的平均经圈环流特征及其对数值天气预报模式系统误差的贡献

本文证明7种强迫作用激发经圈环流的线性叠加性，分项考察了各种物理强迫激发经圈环流的特征，通过考察一个数值模式的模式大气和实际大气各种物理强迫激发经圈环流的差异，分析了模式系统误差的成因，这种建立在动力背景之上的模式误差分析方法，其物理意义明确，具有较为普遍的适用性。     

支持向量机与卡尔曼滤波集合的西太平洋副热带高压数值预报误差修正

基于T106数值预报产品资料,提出了支持向量机和卡尔曼滤波相结合的方法来进行夏季西太平洋副热带高压数值预报的误差修正与预报优化。首先采用支持向量机方法建立了西太平洋副热带高压面积指数的误差修正模型。基于支持向量机预报优化模型尽管有比较好的拟合精度和预报效果,但与实际副热带高压指数尚有一定的差异。究其原因,除预报对象(副热带高压)本身比较复杂、模型优化因子不够充分以及数值预报误差自身的随机性以外,优化模型的输入、输出基本上是一个静态映射结构,因此前一时刻的预测误差难以得到有效的反馈、调整和修正。为考虑前一时刻预报误差的反馈信息,动态跟踪副高的变化趋势,随后引入卡尔曼滤波方法建立支持向量机-卡尔曼滤波模型,对支持向量机模型的输出结果作进一步的调整和优化。试验结果表明,该方法模型的预报优化效果优于T106数值预报产品以及单纯的神经网络修正模型和卡尔曼滤波修正模型的优化效果,能够较为客观、有效地修正西太平洋副热带高压指数的数值预报误差,改进和优化西太平洋副热带高压的数值预报效果。该方法为副热带高压等复杂天气系统和要素场预报提供了一种新的思路,表现出较好的应用前景。     

Chen-Chao Koo and the Early Numerical Weather Prediction Experiments in China

Although the first successful numerical weather prediction(NWP)project led by Charney and von Neumann is widely known,little is known by the international community about the development of NWP during the 1950s in China.Here,a detailed historical perspective on the early NWP experiments in China is provided.The leadership in NWP of the late Professor Chen-Chao Koo,a protége of C.G.Rossby at the University of Stockholm during the late 1940s and a key leader of modern meteorology(particularly of atmospheric dynamics and physics)in China during the 1950s?70s,is highlighted.The unique contributions to NWP by Koo and his students,such as the ideas of formulating NWP as an“evolution”problem,in which the past data over multiple time steps are utilized,rather than an initial-value problem,and on the cybernetic aspects of atmospheric processes,i.e.,regarding the motion of the atmosphere at various time scales as an optimal control system,are also emphasized.     

资料同化中二维特征长度随模式分辨率变化的分析研究

特征长度是资料同化中的重要参量，决定了观测信息在空间的传递特征，而特征长度随模式水平分辨率增减而变化的特点与背景误差湍流功率谱分布特点密切相关。通过对不同来源实际资料计算获得的特征长度数据分析和对理想数据数值试验分析，结果表明随着模式分辨率的提高，特征长度会按照二次根的规律递减。特征长度的这种变化由背景误差湍流功率谱，特别是与次天气尺度（20～60波）到中尺度波（大于60波）的湍流功率谱斜率特征决定。当湍流功率谱斜率从-5/3变化到-4时，特征长度随模式分辨率变化的敏感性降低。作者估计出的温度场的实际背景误差湍流功率谱斜率在次天气尺度到中尺度大约在-2.8左右。对特征长度的估计除传统方法外，可以根据背景误差的湍流功率谱斜率特征来更方便地给出，该方法可作为传统方法的补充来匹配应用。     

A Model Output Machine Learning Method for Grid Temperature Forecasts in the Beijing Area

In this paper, the model output machine learning (MOML) method is proposed for simulating weather consultation, which can improve the forecast results of numerical weather prediction (NWP). During weather consultation, the forecasters obtain the final results by combining the observations with the NWP results and giving opinions based on their experience. It is obvious that using a suitable post-processing algorithm for simulating weather consultation is an interesting and important topic. MOML is a post-processing method based on machine learning, which matches NWP forecasts against observations through a regression function. By adopting different feature engineering of datasets and training periods, the observational and model data can be processed into the corresponding training set and test set. The MOML regression function uses an existing machine learning algorithm with the processed dataset to revise the output of NWP models combined with the observations, so as to improve the results of weather forecasts. To test the new approach for grid temperature forecasts, the 2-m surface air temperature in the Beijing area from the ECMWF model is used. MOML with different feature engineering is compared against the ECMWF model and modified model output statistics (MOS) method. MOML shows a better numerical performance than the ECMWF model and MOS, especially for winter. The results of MOML with a linear algorithm, running training period, and dataset using spatial interpolation ideas, are better than others when the forecast time is within a few days. The results of MOML with the Random Forest algorithm, year-round training period, and dataset containing surrounding gridpoint information, are better when the forecast time is longer.     

Adaptive observations for hurricane prediction

Summary This study proposes a method that can be used to provide guidelines to aircraft reconnaissance for hurricane observations. The method combines numerical weather prediction (NWP) model with a statistical approach to target adaptive observations over areas where the hurricane predictions are very sensitive to the initial analysis for the NWP-model. A single model experiment is performed using regular initial analysis, while 50 other ensemble runs are performed from randomly perturbed initial states. Under the perfect model assumption, the single model experiment serves as a true state. The method first computes the forecast error variances at a certain verification time, e.g. hour 48, and then locates the maximum centers of variances. After the locations of the maximum forecast error variances are known, various correlations of different variables between these maximum variance points and the perturbation fields at the target time, e.g. hour 12, are calculated to identify those locations at the target time, over where the observational errors might be responsible for the growth of forecast error variances at the verification time. Statistically, these correlation fields indicate where the most sensitive areas are at the target time, i.e. where the need for additional observations is suggested. Hurricane Fran of 1996 is used to test the proposed method. The reason for choosing this case is that, during the first 48 hour forecast, the track forecast from NWP-model was very close to the best track. Two additional experiments were designed to examine the method. One experiment updates predicted variables at the target time (12 h) over the areas, to where the proposed method indicates the forecast would be sensitive. The updating combines observations (or truth) with the first guess (predicted) fields. Another experiment also modifies predicted variables at the target time (12 h), but over the areas where the method indicates the forecast errors are less correlated to. The results show that the modification has greatly reduced the forecast error variances at the verification time (48 h) in the first experiment, however it has a very little impact on the variance fields at the forecast hour (48 h) in the second experiment. It is very clear from our experiments, that the proposed method is able to identify sensitive areas, where additional observations can help to reduce hurricane forecast errors from an NWP-model. Received July 19, 1999 Revised November 28, 1999     

一种基于进化策略的气象学反问题求解算法研究

数值天气预报准确性直接取决于好的预报模式和初始场。在预报业务中,依赖观测数据调整初始场和模式参数属气象上的反问题。通过对模式参数识别和初始场调整问题进行等价转化,提出了一种基于进化策略的气象学反问题求解算法。在一维扩散方程和Lorenz-96简单预报模式进行了两类理想数值试验,试验结果表明经过优化后的预报误差均控制在非常小的范围内且预报稳定,从而验证了方法的有效性。     

变分四维同化方法若干问题的数值试验

资料误差和模式误差都可能影响变分四维同化的结果,针对这一问题利用浅水方程模式进行了变分四维同化的数值模拟试验。试验分三种情况进行：（１）仅修正初始场,（２）仅修正模式;（３）二者同时修正。试验结果表明,当模式有误差时,传统的变分四维同化方法（仅修正初始场）可能将模式的误差混淆到初始场中去,尽管在同化期间可得到较好的拟合,但却不一定能保证同化后有好的预报。如果不修正初始场而修正模式,当模式误差不大时     

消除系统性观测误差的时空梯度信息同化方法研究

随着气象观测手段的进步,各种气象观测资料在数值预报模式中的应用不断发展.然而由于观测资料存在观测误差,尤其一些非常规资料存在系统性偏差,且难以对此类误差进行充分订正,使得观测资料在数值预报模式同化应用过程中的作用没有被充分发挥.文中提出一种消去此类误差的时间及空间梯度信息变分同化方法,其特点在于不需要知道系统性偏差的具体估计,而是用一个梯度信息算子对原变量进行变换从而隐性回避此类误差.通过浅水波模式四维变分同化理想试验结果表明,此同化方法完全消除平整性系统性偏差对同化结果的影响,本身数值较小的模式变量更能够获得好的同化效果,大数值变量则可通过估算来确定适用范围.由于最优解不唯一性质的存在,同化效果更多的吸收观测场的整体时空梯度分布趋势而非观测量值本身,这对具有较低可信度的观测资料是适用的.     

数值天气预报多要素深度学习融合订正方法

数值天气预报作为现代天气预报的主流技术方法,近年来不断朝着精细化方向发展,但预报误差至今仍无法避免.文中在CU-Net模型中引入稠密卷积模块形成数值预报要素偏差订正模型Dense-CUnet,在此基础上进一步融合多种气象要素和地形特征构建了Fuse-CUnet模型,开展不同模型的偏差订正试验和对比分析.以均方根误差(R...     

Assimilation of time-averaged observations in a quasi-geostrophic atmospheric jet model

The problem of reconstructing past climates from a sparse network of noisy time-averaged observations is considered with a novel ensemble Kalman filter approach. Results for a sparse network of 100 idealized observations for a quasi-geostrophic model of a jet interacting with a mountain reveal that, for a wide range of observation averaging times, analysis errors are reduced by about 50% relative to the control case without assimilation. Results are robust to changes to observational error, the number of observations, and an imperfect model. Specifically, analysis errors are reduced relative to the control case for observations having errors up to three times the climatological variance for a fixed 100-station network, and for networks consisting of ten or more stations when observational errors are fixed at one-third the climatological variance. In the limit of small numbers of observations, station location becomes critically important, motivating an optimally determined network. A network of fifteen optimally determined observations reduces analysis errors by 30% relative to the control, as compared to 50% for a randomly chosen network of 100 observations.     

Wind Speed and Altitude Dependent AMDAR Observational Error and Its Impacts on Data Assimilation and Forecasting

Aircraft Meteorological Data Relay (AMDAR) observations have been widely used in numerical weather prediction (NWP) because of its high spatiotemporal resolution. The observational error of AMDAR is influenced by aircraft flight altitude and atmospheric condition. In this study, the wind speed and altitude dependent observational error of AMDAR is estimated. The statistical results show that the temperature and the observational error in wind speeds slightly decrease as altitude increases, and the observational error in wind speed increases as wind speed increases. Pseudo single AMDAR observation assimilation tests demonstrate that the wind speed and altitude dependent observational error can provide more reasonable analysis increment. Furthermore, to assess the performance of wind speed and altitude dependent observational error on data assimilation and forecasting, two-month 3-hourly cycling data assimilation and forecast experiments based on the Weather Research and Forecasting Model (WRF) and its Data Assimilation system (WRFDA) are performed for the period during 1 September-31 October, 2017. The results of the two-month 3-hourly cycling experiments indicate that new observational error improves analysis and forecast of wind field and geo-potential height, and has slight improvements on temperature. The Fractions Skill Score (FSS) of the 6-h accumulated precipitation shows that new wind speed and altitude dependent observational error leads to better precipitation forecast skill than the default observational error in the WRFDA does.     

伴随模式同化系统在修正模式误差中的应用研究

资料误差和模式误差都是制约数值预报结果准确性提高的关键因素,传统四维资料同化都是假设模式完全正确仅对初始资料进行修正,忽略了模式误差本身造成的预报误差。伴随模式同化系统不仅具有修正资料误差的能力,也可应用于修正模式误差方面的研究。本文将卫星中心导风系统提供的GMS5卫星风场与非常规温度资料用于MM5伴随同化系统修正模式地形误差进行试验性研究表明,该方法能够反演出一个既与初始气象要素场相匹配,又与模式更协调的地形场,得到比一般包络地形更好的效果,改善模式对强降水中心及降水区域的预报;数值试验结果还揭示模式误差对模式预报造成一定的影响,用伴随方法对观测资料进行修正的同时也对模式误差进行修正的方法是可行的。     

雷达资料与中尺度数值预报的融合方法研究及其在临近预报中的应用

通过融合多普勒天气雷达资料与中尺度数值预报产品,发展了一种便于临近预报业务使用的方法。该方法首先通过相关分析计算当前相同时刻雷达估测降水与中尺度数值预报的反射率因子估测降水之间的位置偏差,导出一个位移偏差矢量场;然后,利用人机交互的方式对矢量场进行分区,并对各分区的矢量场进行平滑处理,计算出各分区的平均位移偏差矢量;最后,采用最小二乘法对各分区连续多次的平均位移偏差矢量进行线性拟合,得到各分区平均位移偏差矢量随时间的变化特征,订正未来时段相应区域的数值预报反射率因子估测降水的位置偏差。利用该方法对2012和2013年夏季发生在重庆西部、四川东部的3次强降水天气过程进行临近预报试验并对预报结果进行了检验,结果表明:对0~2 h的临近预报,融合预报效果总体上优于模式预报效果;另外,与雷达外推定量降水预报相比,0~1 h雷达外推预报效果优于融合预报效果,1~2 h融合预报效果优于雷达外推预报效果。