Application of an Error Statistics Estimation Method to the PSAS Forecast Error Covariance Model

In atmospheric data assimilation systems, the forecast error covariance model is an important component. However, the paralneters required by a forecast error covariance model are difficult to obtain due to the absence of the truth. This study applies an error statistics estimation method to the Pfiysical-space Statistical Analysis System （PSAS） height-wind forecast error covariance model. This method consists of two components： the first component computes the error statistics by using the National Meteorological Center （NMC） method, which is a lagged-forecast difference approach, within the framework of the PSAS height-wind forecast error covariance model; the second obtains a calibration formula to rescale the error standard deviations provided by the NMC method. The calibration is against the error statistics estimated by using a maximum-likelihood estimation （MLE） with rawindsonde height observed-minus-forecast residuals. A complete set of formulas for estimating the error statistics and for the calibration is applied to a one-month-long dataset generated by a general circulation model of the Global Model and Assimilation Office （GMAO）, NASA. There is a clear constant relationship between the error statistics estimates of the NMC-method and MLE. The final product provides a full set of 6-hour error statistics required by the PSAS height-wind forecast error covariance model over the globe. The features of these error statistics are examined and discussed.

Analysis on the Reason of Local Heavy Rainstorm Forecast Error in the Subtropical High Control

[Objective] The research aimed to study the reason of local heavy rainstorm forecast error in the subtropical high control. [Method] Started from summarizing the reason of forecast error, by using the conventional ground observation data, the upper air sounding data, T639, T213 and European Center (ECMWF) numerical prediction product data, GFS precipitation forecast product of U.S. National Center for Environmental Prediction, the weather situation, physical quantity field in a heavy rainstorm process which happened in the north of Shaoyang at night on August 5, 2010 were fully analyzed. Based on the numerical analysis forecast product data, the reason of heavy rainstorm forecast error in the subtropical high was comprehensively analyzed by using the comparison and analysis method of forecast and actual situation. [Result] The forecasters didn’t deeply and carefully analyze the weather situation. On the surface, 500 hPa was controlled by the subtropical high, but there was the weak shear line in 700 and 850 hPa. Moreover, they neglected the influences of weak cold air and easterlies wave. The subtropical high quickly weakened, and the system adjustment was too quick. The wind field variations in 850, 700 and 500 hPa which were forecasted by ECMWF had the big error with the actual situation. It was by east about 2 longitudes than the actual situation. In summer forecast, they only considered the intensity and position variations of 500 hPa subtropical high, and neglected the situation variations in the middle, low levels and on the ground. It was the most key element which caused the rainstorm forecast error in the subtropical high. The forecast error of numerical forecast products on the height field situation variation was big. The precipitation forecasts of Japan FSAS, U.S. National Center for Environmental Prediction GFS, T639 and T213 were all small. The humidity field forecast value of T639 was small. In the rainstorm forecast, the local rainstorm forecast index and method weren’t used in the forecast practice. In the precipitation forecast process, they only paid attention to the score prediction of station and didn’t value the non-site prediction. Some important physical quantity factors weren’t carefully studied. [Conclusion] The research provided the reference basis for the forecast and early warning of local heavy rainstorm.

Partition of Forecast Error into Positional and Structural Components

Weather manifests in spatiotemporally coherent structures.Weather forecasts hence are affected by both positional and structural or amplitude errors.This has been long recognized by practicing forecasters(cf.,e.g.,Tropical Cyclone track and intensity errors).Despite the emergence in recent decades of various objective methods for the diagnosis of positional forecast errors,most routine verification or statistical post-processing methods implicitly assume that forecasts have no positional error.The Forecast Error Decomposition(FED)method proposed in this study uses the Field Alignment technique which aligns a gridded forecast with its verifying analysis field.The total error is then partitioned into three orthogonal components:(a)large scale positional,(b)large scale structural,and(c)small scale error variance.The use of FED is demonstrated over a month-long MSLP data set.As expected,positional errors are often characterized by dipole patterns related to the displacement of features,while structural errors appear with single extrema,indicative of magnitude problems.The most important result of this study is that over the test period,more than 50%of the total mean sea level pressure forecast error variance is associated with large scale positional error.The importance of positional error in forecasts of other variables and over different time periods remain to be explored.

The Relationship between Deterministic and Ensemble Mean Forecast Errors Revealed by Global and Local Attractor Radii

It has been demonstrated that ensemble mean forecasts, in the context of the sample mean, have higher forecasting skill than deterministic(or single) forecasts. However, few studies have focused on quantifying the relationship between their forecast errors, especially in individual prediction cases. Clarification of the characteristics of deterministic and ensemble mean forecasts from the perspective of attractors of dynamical systems has also rarely been involved. In this paper, two attractor statistics—namely, the global and local attractor radii(GAR and LAR, respectively)—are applied to reveal the relationship between deterministic and ensemble mean forecast errors. The practical forecast experiments are implemented in a perfect model scenario with the Lorenz96 model as the numerical results for verification. The sample mean errors of deterministic and ensemble mean forecasts can be expressed by GAR and LAR, respectively, and their ratio is found to approach2^(1/2) with lead time. Meanwhile, the LAR can provide the expected ratio of the ensemble mean and deterministic forecast errors in individual cases.

Possible Sources of Forecast Errors Generated by the Global/Regional Assimilation and Prediction System for Landfalling Tropical Cyclones.PartⅠ:Initial Uncertainties

This paper investigates the possible sources of errors associated with tropical cyclone （TC） tracks forecasted using the Global/Regional Assimilation and Prediction System （GRAPES）. The GRAPES forecasts were made for 16 landfaIling TCs in the western North Pacific basin during the 2008 and 2009 seasons, with a forecast length of 72 hours, and using the default initial conditions （＂initials＂, hereafter）, which are from the NCEP-FNL dataset, as well as ECMWF initials. The forecasts are compared with ECMWF forecasts. The results show that in most TCs, the GRAPES forecasts are improved when using the ECMWF initials compared with the default initials. Compared with the ECMWF initials, the default initials produce lower intensity TCs and a lower intensity subtropical high, but a higher intensity South Asia high and monsoon trough, as well as a higher temperature but lower specific humidity at the TC center. Replacement of the geopotential height and wind fields with the ECMWF initials in and around the TC center at the initial time was found to be the most efficient way to improve the forecasts. In addition, TCs that showed the greatest improvement in forecast accuracy usually had the largest initial uncertainties in TC intensity and were usually in the intensifying phase. The results demonstrate the importance of the initial intensity for TC track forecasts made using GRAPES, and indicate the model is better in describing the intensifying phase than the decaying phase of TCs. Finally, the limit of the improvement indicates that the model error associated with GRAPES forecasts may be the main cause of poor forecasts of landfalling TCs. Thus, further examinations of the model errors are required.

Day-Ahead Probabilistic Load Flow Analysis Considering Wind Power Forecast Error Correlation

Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration of wind speed and wind power output forecast error’s correlation, the probabilistic distributions of transmission line flows during tomorrow’s 96 time intervals are obtained using cumulants combined Gram-Charlier expansion method. The probability density function and cumulative distribution function of transmission lines on each time interval could provide scheduling planners with more accurate and comprehensive information. Simulation in IEEE 39-bus system demonstrates effectiveness of the proposed model and algorithm.

Risk analysis of dynamic control of reservoir limited water level by considering flood forecast error

Flood control forecast operation mode is one of the main ways for determining the upper bound of dynamic control of flood limited water level during flood season. The floodwater utilization rate can be effectively increased by using flood forecast information and flood control forecast operation mode. In this paper, Dahuofang Reservoir is selected as a case study. At first, the distribution pattern and the bound of forecast error which is a key source of risk are analyzed. Then, based on the definition of flood risk, the risk of dynamic control of reservoir flood limited water level within different flood forecast error bounds is studied. The results show that, the dynamic control of reservoir flood limited water level with flood forecast information can increase the floodwater utilization rate without increasing flood control risk effectively and it is feasible in practice.

Mixed Aleatory-epistemic Uncertainty Modeling of Wind Power Forecast Errors in Operation Reliability Evaluation of Power Systems

As the share of wind power in power systems continues to increase, the limited predictability of wind power generation brings serious potential risks to power system reliability. Previous research works have generally described the uncertainty of wind power forecast errors(WPFEs) based on normal distribution or other standard distribution models, which only characterize the aleatory uncertainty. In fact, epistemic uncertainty in WPFE modeling due to limited data and knowledge should also be addressed. This paper proposes a multi-source information fusion method(MSIFM) to quantify WPFEs when considering both aleatory and epistemic uncertainties. An extended focal element(EFE) selection method based on the adequacy of historical data is developed to consider the characteristics of WPFEs. Two supplementary expert information sources are modeled to improve the accuracy in the case of insufficient historical data. An operation reliability evaluation technique is also developed considering the proposed WPFE model. Finally,a double-layer Monte Carlo simulation method is introduced to generate a time-series output of the wind power. The effectiveness and accuracy of the proposed MSIFM are demonstrated through simulation results.

Large tropical cyclone track forecast errors of global numerical weather prediction models in western North Pacific basin

Although tropical cyclone(TC)track forecast errors(TFEs)of operational warning centres have substantially decreased in recent decades,there are still many cases with large TFEs.The International Grand Global Ensemble(TIGGE)data are used to study the possible reasons for the large TFE cases and to compare the performance of different numerical weather prediction(NWP)models.Forty-four TCs in the western North Pacific during the period 2007-2014 with TFEs(+24 to+120 h)larger than the 75 th percentile of the annual error distribution(with a total of 93 cases)are identified.Four categories of situations are found to be associated with large TFEs.These include the interaction of the outer structure of the TC with tropical weather systems,the intensity of the TC,the extension of the subtropical high(SH)and the interaction with the westerly trough.The crucial factor of each category attributed to the large TFE is discussed.Among the TIGGE model predictions,the models of the European Centre for Medium-Range Weather Forecasts and the UK Met Office generally have a smaller TFE.The performance of different models in different situations is discussed.

THE IMPACT OF NOAA SATELLITE SOUNDING DATA ON THE SYSTEMATIC FORECAST ERROR OF B-MODEL

This paper is to examine the impact of satellite data on the systematic error of operational B-model in China.Em- phasis is put on the study of the impact of satellite sounding data on forecasts of the sea level pressure field and 500 hPa height.The major findings are as follows. (1)The B-model usually underforecasts the strength of features in the sea level pressure(SLP)field,i.e.pressures are too low near high pressure systems and too high near low pressure systems. (2)The nature of the systematic errors found in the 500 hPa height forecasts is not as clear cut as that of the SLP forecasts,but most often the same type of pattern is seen,i.e.,the heights in troughs are not low enough and those in ridges are not high enough. (3)The use of satellite data in the B-model analysis/forecast system is found to have an impact upon the model's forecast of SLP and 500 hPa height.Systematic errors in the vicinity of surface lows/500 hPa troughs over the oceans are usually found to be significantly reduced.A less conclusive mix of positive and negative impacts was found for all other types of features.

SYSTEMATIC FORECAST ERROR IN U.S.NMC OPERATIONAL SPECTRAL MODEL

The distribution of monthly mean error of NMC model forecasts and its seasonal variation are investi- gated.The ratio of monthly mean error to standard deviation is used here to find out that the region where a correction of systematic error is needed and appropriate is mainly in low latitudes.The improvement,after the model's vertical resolution and some physical parameters were changed from April 1985,is investigated,and the NMC operational model forecasts have also compared with those of ECMWF.

Extended Range(10–30 Days) Heavy Rain Forecasting Study Based on a Nonlinear Cross-Prediction Error Model

Extended range （10-30 d） heavy rain forecasting is difficult but performs an important function in disaster prevention and mitigation. In this paper, a nonlinear cross prediction error （NCPE） algorithm that combines nonlinear dynamics and statistical methods is proposed. The method is based on phase space reconstruction of chaotic single-variable time series of precipitable water and is tested in 100 global cases of heavy rain. First, nonlinear relative dynamic error for local attractor pairs is calculated at different stages of the heavy rain process, after which the local change characteristics of the attractors are analyzed. Second, the eigen-peak is defined as a prediction indicator based on an error threshold of about 1.5, and is then used to analyze the forecasting validity period. The results reveal that the prediction indicator features regarded as eigenpeaks for heavy rain extreme weather are all reflected consistently, without failure, based on the NCPE model; the prediction validity periods for 1-2 d, 3-9 d and 10-30 d are 4, 22 and 74 cases, respectively, without false alarm or omission. The NCPE model developed allows accurate forecasting of heavy rain over an extended range of 10-30 d and has the potential to be used to explore the mechanisms involved in the development of heavy rain according to a segmentation scale. This novel method provides new insights into extended range forecasting and atmospheric predictability, and also allows the creation of multi-variable chaotic extreme weather prediction models based on high spatiotemporal resolution data.

ANALYSIS ON ABNORMAL TROPICAL CYCLONE TRACK FORECAST ERROR OF ECMWF-IFS IN THE WESTERN NORTH PACIFIC

By considering distance error and direction error, Tropical Cyclone(TC) track forecasts with abnormal forecast error(AFE) at lead time of 48 h by ECMWF-IFS are selected out from 2010 to 2013. Factors closely related to AFE cases are investigated. There are 7 factors which are closely related to AFE cases. The most common one is Landfall or Passing through big island(LP) which appears 21 times among all 55 AFE cases. But LP often coexists with other factors to cause AFE cases. The second in the list is Coexistence with other TC or cloud cluster(CO) which affects more than one third of all AFE cases. Besides those 7 factors, fault of TCtracker also results in some AFE cases. There are no simple indicators for forecasters to anticipate a possible AFE case in advance. It seems that forecasters still have to anticipate AFE cases by their experiences and with synthetic analysis on all available data. Some possible ways to improve AFE cases are discussed and proposed to forecasters. That includes relying on products from ensemble prediction system or guidance from other models, simple translation process and manual analysis of TC track by forecasters under some circumstances.

STUDY OF THE EFFECTS OF REDUCING SYSTEMATIC ERRORS ON MONTHLY REGIONAL CLIMATE DYNAMICAL FORECAST

A nested-model system is constructed by embedding the regional climate model RegCM3 into a general circulation model for monthly-scale regional climate forecast over East China. The systematic errors are formulated for the region on the basis of 10-yr (1991-2000) results of the nested-model system, and of the datasets of the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) and the temperature analysis of the National Meteorological Center (NMC), U.S.A., which are then used for correcting the original forecast by the system for the period 2001-2005. After the assessment of the original and corrected forecasts for monthly precipitation and surface air temperature, it is found that the corrected forecast is apparently better than the original, suggesting that the approach can be applied for improving monthly-scale regional climate dynamical forecast.

河南2023年麦收期连阴雨极端特征及预报偏差分析

基于多尺度观测资料、多种数值模式和主观预报产品,分析了2023年河南麦收关键期出现的连续降水天气过程的极端性特征,并对主客观预报进行检验评估。结果表明:5月20日至6月4日累计降水量距平百分率全省平均为170.3%,累计雨量有17个站达到历史同期排名第一;5月25日至6月4日出现长达11天的全省范围的连阴雨过程,历史排名第二。2023年5月2530日500 hPa平均场副高西伸脊点较气候态偏西33个经度以上,河南上空高度场较气候态高出160~200 gpm。中层气流变化导致降水系统移动方向发生变化,是豫西强降水漏报的主要原因;模式对台风和副高位置预报的偏差,是导致雨带向南偏差的直接原因,进而导致各数值模式暴雨以上量级降水评分偏低。豫西地形对风场影响的机理较为复杂,需对更多个例诊断分析,得到客观结论。

基于误差幅空特性分析的空间负荷预测误差评价方法

对空间负荷预测误差进行有效评价是客观认识预测结果,指导预测结果合理应用的前提。然而,现有空间负荷预测误差评价的研究存在对误差的空间分布不考虑或考虑不充分导致评价不准确的问题。为此,提出一种基于误差幅空特性分析的空间负荷预测误差评价方法。首先,从空间负荷预测误差幅值大小和空间分布对电网规划影响的角度出发,对误差的幅空特性进行详细分析;其次,利用运输问题的数学模型来表征正负误差的幅空抵消特性,使用各空间邻近度–幅值误差值曲线与x轴围成面积之和来表征剩余未抵消误差的幅空叠加特性;然后,分别通过伏格尔法和各梯形面积累加公式来计算正负误差的幅空抵消影响值和剩余未抵消误差的幅空叠加影响值,并在此基础上构建空间负荷预测误差评价指标;最后,基于误差对电网规划的实际影响给出对误差评价指标性能的检验方法。算例分析表明,与传统方法相比,该文所提误差评价方法从幅值和空间两个维度实现了对空间负荷预测误差更为全面的评估,与误差对电网规划影响的实际情况贴近度更高。

考虑光伏随机性的交直流混合配电网鲁棒机会约束安全域模型

为实现高比例光伏接入下交直流混合配电网的安全评估,构建了交直流混合配电网的鲁棒机会约束安全域模型。首先,提出一种基于区间划分的自适应带宽核密度估计方法,以获取光伏预测误差概率分布,构建光伏出力机会约束不确定集合;其次,采用功率与节点电压幅值比值为状态变量,在已有交流线性化潮流模型的基础上推导一种交直流混合配电网线性化潮流模型;然后,提出交直流混合配电网鲁棒机会约束安全域的概念和模型,结合列与约束生成算法和径向迭代搜索算法生成可观测的鲁棒机会约束安全域空间。最后,算例分析验证了所提模型能够在鲁棒机会约束安全域上准确、直观的反映光伏出力的随机性,进而为交直流混合配电网的准确安全评估提供支撑。

Improvement in Background Error Covariances Using Ensemble Forecasts for Assimilation of High-Resolution Satellite Data

Satellite data obtained over synoptic data-sparse regions such as an ocean contribute toward improving the quality of the initial state of limited-area models. Background error covariances are crucial to the proper distribution of satellite-observed information in variational data assimilation. In the NMC （National Meteorological Center） method, background error covariances are underestimated over data-sparse regions such as an ocean because of small differences between different forecast times. Thus, it is necessary to reconstruct and tune the background error covariances so as to maximize the usefulness of the satellite data for the initial state of limited-area models, especially over an ocean where there is a lack of conventional data. In this study, we attempted to estimate background error covariances so as to provide adequate error statistics for data-sparse regions by using ensemble forecasts of optimal perturbations using bred vectors. The background error covariances estimated by the ensemble method reduced the overestimation of error amplitude obtained by the NMC method. By employing an appropriate horizontal length scale to exclude spurious correlations, the ensemble method produced better results than the NMC method in the assimilation of retrieved satellite data. Because the ensemble method distributes observed information over a limited local area, it would be more useful in the analysis of high-resolution satellite data. Accordingly, the performance of forecast models can be improved over the area where the satellite data are assimilated.

计及误差信息的自适应超短期风速预测模型

为提升超短期风速预测精度,提出一种计及误差信息的自适应混合预测模型。应用自适应噪声的完备集合经验模态分解模型与鲸鱼优化的变分模态分解模型分别对风速样本数据与预测误差进行分解,同时计算各子序列的模糊熵以判断序列复杂程度。在此基础上,应用鲸鱼优化的长短期网络预测复杂程度较高的序列,差分自回归移动平均模型预测复杂程度较低的序列。最后,将初始风速预测结果和风速误差预测值相加得到基于误差修正的超短期风速预测值。结果表明,修正预测误差与考虑分解策略可有效提升点预测的性能,与基准模型相比,所提模型在多场景下均具备优良的预测精度。

基于Vine Copula的梯级水库短期发电调度风险估计

基于能准确描述高维变量相关关系的Vine Copula,考虑短期径流预报误差的空间相关性,构建了梯级水库短期发电调度风险估计模型,并将模型应用于长江上游溪洛渡、向家坝和三峡水库,分析了径流预报误差带来的单一水库、梯级水库短期发电调度风险。结果表明:基于C-vine Copula构建的联合分布能较好地描述屏山站、朱沱站、寸滩站和武隆站的日径流预报误差特性;随着水库可调节安全区间范围增大,单一水库发电量不足风险率、弃水风险率均越来越小,梯级水库发电量不足、弃水联合风险率和同现风险率越来越小,即水库调节库容越大,其承担的风险也就越小。