The Impact of Verification Area Design on Tropical Cyclone Targeted Observations Based on the CNOP Method

This study investigated the impact of different verification-area designs on the sensitive areas identified using the conditional nonlinear optimal perturbation (CNOP) method for tropical cyclone targeted observations.The sensitive areas identified using the first singular vector (FSV) method,which is the linear approximation of CNOP,were also investigated for comparison.By analyzing the validity of the sensitive areas,the proper design of a verification area was developed.Tropical cyclone Rananim,which occurred in August 2004 in the northwest Pacific Ocean,was studied.Two sets of verification areas were designed;one changed position,and the other changed both size and position.The CNOP and its identified sensitive areas were found to be less sensitive to small variations of the verification areas than those of the FSV and its sensitive areas.With larger variations of the verification area,the CNOP and the FSV as well as their identified sensitive areas changed substantially.In terms of reducing forecast errors in the verification area,the CNOP-identified sensitive areas were more beneficial than those identified using FSV.The design of the verification area is important for cyclone prediction.The verification area should be designed with a proper size according to the possible locations of the cyclone obtained from the ensemble forecast results.In addition,the development trend of the cyclone analyzed from its dynamic mechanisms was another reference.When the general position of the verification area was determined,a small variation in size or position had little influence on the results of CNOP.     

The Impact of Horizontal Resolution on the CNOP and on Its Identified Sensitive Areas for Tropical Cyclone Predictions

In this study,the impacts of horizontal resolution on the conditional nonlinear optimal perturbation (CNOP) and on its identified sensitive areas were investigated for tropical cyclone predictions.Three resolutions,30 km,60 km,and 120 km,were studied for three tropical cyclones,TC Mindulle (2004),TC Meari (2004),and TC Matsa (2005).Results show that CNOP may present different structures with different resolutions,and the major parts of CNOP become increasingly localized with increased horizontal resolution.CNOP produces spiral and baroclinic structures,which partially account for its rapid amplification.The differences in CNOP structures result in different sensitive areas,but there are common areas for the CNOP-identified sensitive areas at various resolutions,and the size of the common areas is different from case to case.Generally,the forecasts benefit more from the reduction of the initial errors in the sensitive areas identified using higher resolutions than those using lower resolutions.However,the largest improvement of the forecast can be obtained at the resolution that is not the highest for some cases.In addition,the sensitive areas identified at lower resolutions are also helpful for improving the forecast with a finer resolution,but the sensitive areas identified at the same resolution as the forecast would be the most beneficial.     

A New Approach to Data Assimilation

A significant attempt to design a timesaving and efficient four-dimensional variational data assimilation (4DVar) has been made in this paper, and a new approach to data assimilation, which is noted as 'three-dimensional variational data assimilation of mapped observation (3DVM)' is proposed, based on the new concept of mapped observation and the new idea of backward 4DVar. Like the available 4DVar, 3DVM produces an optimal initial condition (IC) that is consistent with the prediction model due to the inclusion of model constraints and best fits the observations in the assimilation window through the model solution trajectory. Different from the 4DVar, the IC derived from 3DVM is located at the end of the assimilation window rather than at the beginning conventionally. This change greatly reduces the computing cost for the new approach, which is almost the same as that of the three-dimensional variational data assimilation (3DVar). Especially, such a change is able to improve assimilation accuracy because it does not need the tangential linear and adjoint approximations to calculate the gradient of cost function. Therefore, in numerical test, the new approach produces better IC than 4DVar does for 72-h simulation of TY9914 (Dan), by assimilating the three-dimensional fields of temperature and wind retrieved from the Advanced Microwave Sounding Unit-A (AMSU-A) observations. Meanwhile, it takes only 1/7 of the computing cost that the 4DVar requires for the same initialization with the same retrieved data.     

INTELLIGENT ALGORITHMS FOR SOLVING CNOP AND THEIR APPLICATIONS IN ENSO PREDICTABILITY AND TROPICAL CYCLONE ADAPTIVE OBSERVATIONS

Some intelligent algorithms (IAs) proposed by us, including swarm IAs and single individual IAs, have been applied to the Zebiak-Cane (ZC) model to solve conditional nonlinear optimal perturbation (CNOP) for studying El Ni?o – Southern Oscillation (ENSO) predictability. Compared to the adjoint-based method (the ADJ-method), which is referred to as a benchmark, these IAs can achieve approximate CNOP results in terms of magnitudes and patterns. Using IAs to solve CNOP can avoid the use of an adjoint model and widen the application of CNOP in numerical climate and weather modeling. Of the proposed swarm IAs, PCA-based particle swarm optimization (PPSO) obtains CNOPs with the best patterns and the best stability. Of the proposed single individual IAs, continuous tabu search algorithm with sine maps and staged strategy (CTS-SS) has the highest efficiency. In this paper, we compare the validity, stability and efficiency of parallel PPSO and CTS-SS using these two IAs to solve CNOP in the ZC model for studying ENSO predictability. The experimental results show that CTS-SS outperforms parallel PPSO except with respect to stability. At the same time, we are also concerned with whether these two IAs can effectively solve CNOP when applied to more complicated models. Taking the sensitive areas identification of tropical cyclone adaptive observations as an example and using the fifth-generation mesoscale model (MM5), we design some experiments. The experimental results demonstrate that each of these two IAs can effectively solve CNOP and that parallel PPSO has a higher efficiency than CTS-SS. We also provide some suggestions on how to choose a suitable IA to solve CNOP for different models.     

Comparison of nonlinear local Lyapunov vectors with bred vectors,random perturbations and ensemble transform Kalman filter strategies in a barotropic model

The breeding method has been widely used to generate ensemble perturbations in ensemble forecasting due to its simple concept and low computational cost. This method produces the fastest growing perturbation modes to catch the growing components in analysis errors. However, the bred vectors(BVs) are evolved on the same dynamical flow, which may increase the dependence of perturbations. In contrast, the nonlinear local Lyapunov vector(NLLV) scheme generates flow-dependent perturbations as in the breeding method, but regularly conducts the Gram–Schmidt reorthonormalization processes on the perturbations. The resulting NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more components in analysis errors than the BVs.In this paper, the NLLVs are employed to generate initial ensemble perturbations in a barotropic quasi-geostrophic model.The performances of the ensemble forecasts of the NLLV method are systematically compared to those of the random perturbation(RP) technique, and the BV method, as well as its improved version—the ensemble transform Kalman filter(ETKF)method. The results demonstrate that the RP technique has the worst performance in ensemble forecasts, which indicates the importance of a flow-dependent initialization scheme. The ensemble perturbation subspaces of the NLLV and ETKF methods are preliminarily shown to catch similar components of analysis errors, which exceed that of the BVs. However, the NLLV scheme demonstrates slightly higher ensemble forecast skill than the ETKF scheme. In addition, the NLLV scheme involves a significantly simpler algorithm and less computation time than the ETKF method, and both demonstrate better ensemble forecast skill than the BV scheme.     

Reducing the Prediction Uncertainties of High-Impact Weather and Climate Events:An Overview of Studies at LASG

This paper summarizes recent progress at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences in studies on targeted observations, data assimilation, and ensemble prediction, which are three effective strategies to reduce the prediction uncertainties and improve the forecast skill of weather and climate events. Considering the limitations of traditional targeted observation approaches, LASG researchers have developed a conditional nonlinear optimal perturbation-based targeted observation strategy to optimize the design of the observing network. This strategy has been employed to identify sensitive areas for targeted observations of the El Ni?o–Southern Oscillation, Indian Ocean dipole, and tropical cyclones, and has been demonstrated to be effective in improving the forecast skill of these events. To assimilate the targeted observations into the initial state of a numerical model, a dimension-reducedprojection-based four-dimensional variational data assimilation(DRP-4DVar) approach has been proposed and is used operationally to supply accurate initial conditions in numerical forecasts. The performance of DRP-4DVar is good, and its computational cost is much lower than the standard 4DVar approach. Besides, ensemble prediction,which is a practical approach to generate probabilistic forecasts of the future state of a particular system, can be used to reduce the prediction uncertainties of single forecasts by taking the ensemble mean of forecast members. In this field, LASG researchers have proposed an ensemble forecast method that uses nonlinear local Lyapunov vectors(NLLVs) to yield ensemble initial perturbations. Its application in simple models has shown that NLLVs are more useful than bred vectors and singular vectors in improving the skill of the ensemble forecast. Therefore, NLLVs represent a candidate for possible development as an ensemble method in operational forecasts. Despite the considerable efforts made towards developing these methods to reduce prediction uncertainties, much challenging but highly important work remains in terms of improving the methods to further increase the skill in forecasting such weather and climate events.     

The Roles of Spatial Locations and Patterns of Initial Errors in the Uncertainties of Tropical Cyclone Forecasts

In this study,a series of sensitivity experiments were performed for two tropical cyclones (TCs),TC Longwang (2005) and TC Sinlaku (2008),to explore the roles of locations and patterns of initial errors in uncertainties of TC forecasts.Specifically,three types of initial errors were generated and three types of sensitive areas were determined using conditional nonlinear optimal perturbation (CNOP),first singular vector (FSV),and composite singular vector (CSV) methods.Additionally,random initial errors in randomly selected areas were considered.Based on these four types of initial errors and areas,we designed and performed 16 experiments to investigate the impacts of locations and patterns of initial errors on the nonlinear developments of the errors,and to determine which type of initial errors and areas has the greatest impact on TC forecasts.Overall,results from the experiments indicate the following:(1) The impact of random errors introduced into the sensitive areas was greater than that of errors themselves fixed in the randomly selected areas.From the perspective of statistical analysis,and by comparison,the impact of random errors introduced into the CNOP target area was greatest.(2) The initial errors with CNOP,CSV,or FSV patterns were likely to grow faster than random errors.(3) The initial errors with CNOP patterns in the CNOP target areas had the greatest impacts on the final verification forecasts.     

Statistics of the Z–R Relationship for Strong Convective Weather over the Yangtze–Huaihe River Basin and Its Application to Radar Reflectivity Data Assimilation for a Heavy Rain Event

The relationship between the radar reflectivity factor(Z) and the rainfall rate(R) is recalculated based on radar observations from 10 Doppler radars and hourly rainfall measurements at 6529 automatic weather stations over the Yangtze–Huaihe River basin. The data were collected by the National 973 Project from June to July 2013 for severe convective weather events. The Z–R relationship is combined with an empirical qr–R relationship to obtain a new Z–qr relationship, which is then used to correct the observational operator for radar reflectivity in the three-dimensional variational(3 DVar) data assimilation system of the Weather Research and Forecasting(WRF) model to improve the analysis and prediction of severe convective weather over the Yangtze–Huaihe River basin. The performance of the corrected reflectivity operator used in the WRF 3 DVar data assimilation system is tested with a heavy rain event that occurred over Jiangsu and Anhui provinces and the surrounding regions on 23 June 2013. It is noted that the observations for this event are not included in the calculation of the Z–R relationship. Three experiments are conducted with the WRF model and its 3 DVar system, including a control run without the assimilation of reflectivity data and two assimilation experiments with the original and corrected reflectivity operators. The experimental results show that the assimilation of radar reflectivity data has a positive impact on the rainfall forecast within a few hours with either the original or corrected reflectivity operators, but the corrected reflectivity operator achieves a better performance on the rainfall forecast than the original operator. The corrected reflectivity operator extends the effective time of radar data assimilation for the prediction of strong reflectivity. The physical variables analyzed with the corrected reflectivity operator present more reasonable mesoscale structures than those obtained with the original reflectivity operator. This suggests that the new statistical Z–R relationship is more suitable for predicting severe convective weather over the Yangtze–Huaihe River basin than the Z–R relationships currently in use.     

What Kind of Initial Errors Cause the Severest Prediction Uncertainty of El Nino in Zebiak-Cane Model

With the Zebiak-Cane （ZC） model, the initial error that has the largest effect on ENSO prediction is explored by conditional nonlinear optimal perturbation （CNOP）. The results demonstrate that CNOP-type errors cause the largest prediction error of ENSO in the ZC model. By analyzing the behavior of CNOPtype errors, we find that for the normal states and the relatively weak E1 Nifio events in the ZC model, the predictions tend to yield false alarms due to the uncertainties caused by CNOP. For the relatively strong E1 Nino events, the ZC model largely underestimates their intensities. Also, our results suggest that the error growth of E1 Nifio in the ZC model depends on the phases of both the annual cycle and ENSO. The condition during northern spring and summer is most favorable for the error growth. The ENSO prediction bestriding these two seasons may be the most difficult. A linear singular vector （LSV） approach is also used to estimate the error growth of ENSO, but it underestimates the prediction uncertainties of ENSO in the ZC model. This result indicates that the different initial errors cause different amplitudes of prediction errors though they have same magnitudes. CNOP yields the severest prediction uncertainty. That is to say, the prediction skill of ENSO is closely related to the types of initial error. This finding illustrates a theoretical basis of data assimilation. It is expected that a data assimilation method can filter the initial errors related to CNOP and improve the ENSO forecast skill.     

Observation System Experiments for Typhoon Nida (2004) Using the CNOP Method and DOTSTAR Data

This study investigated the influence of dropwindsonde observations on typhoon forecasts. The study also evaluated the feasibility of the conditional nonlinear optimal perturbation (CNOP) method as a basis for sensitivity analysis of such forecasts. This sensitivity analysis could furnish guidance in the selection of targeted observations. The study was performed by conducting observation system experiments (OSEs). This research used the fifth-generation Mesoscale Model (MM5), the Weather Research and Forecasting (WRF) model, and dropsonde observations of Typhoon Nida at 1200 UTC 17 May 2004. The dropsondes were collected under the operational Dropsonde Observations for Typhoon Surveillance near the Taiwan Region (DOTSTAR) program. In this research, five kinds of experiments were designed and conducted:(1) no observations were assimilated; (2) all observations were assimilated;(3) observations in the sensitive area revealed by the CNOP method were assimilated;(4) the same as in (3), but for the region revealed by the first singular vector (FSV) method;and (5) observations within a randomly selected area were assimilated. The OSEs showed that (1) the DOTSTAR data had a positive impact on the forecast of Nida’s track;(2) dropsondes in the sensitive areas identified by the MM5 CNOP and FSV remained effective for improving the track forecast for Nida on the WRF platform;and (3) the greatest improvement in the track forecast resulted from the CNOP-based (third) simulation, which indicated that the CNOP method would be useful in decision making about dropsonde deployments.     

Impacts of Multigrid NLS-4DVar-based Doppler Radar Observation Assimilation on Numerical Simulations of Landfalling Typhoon Haikui (2012)

We applied the multigrid nonlinear least-squares four-dimensional variational assimilation(MG-NLS4DVar) method in data assimilation and prediction experiments for Typhoon Haikui(2012) using the Weather Research and Forecasting(WRF) model. Observation data included radial velocity(V_r) and reflectivity(Z) data from a single Doppler radar, quality controlled prior to assimilation. Typhoon prediction results were evaluated and compared between the NLS-4DVar and MG-NLS4DVar methods. Compared with a forecast that began with NCEP analysis data, our radar data assimilation results were clearly improved in terms of structure, intensity, track, and precipitation prediction for Typhoon Haikui(2012). The results showed that the assimilation accuracy of the NLS-4DVar method was similar to that of the MG-NLS4DVar method,but that the latter was more efficient. The assimilation of V_r alone and Z alone each improved predictions of typhoon intensity, track, and precipitation; however, the impacts of V_r data were significantly greater that those of Z data.Assimilation window-length sensitivity experiments showed that a 6-h assimilation window with 30-min assimilation intervals produced slightly better results than either a 3-h assimilation window with 15-min assimilation intervals or a 1-h assimilation window with 6-min assimilation intervals.     

An Economical Approach to Four-dimensional Variational Data Assimilation

Four-dimensional variational data assimilation (4DVar) is one of the most promising methods to provide optimal analysis for numerical weather prediction (NWP). Five national NWP centers in the world have successfully applied 4DVar methods in their global NWPs, thanks to the increment method and adjoint technique. However, the application of 4DVar is still limited by the computer resources available at many NWP centers and research institutes. It is essential, therefore, to further reduce the computational cost of 4DVar. Here, an economical approach to implement 4DVar is proposed, using the technique of dimension-reduced projection (DRP), which is called ``DRP-4DVar." The proposed approach is based on dimension reduction using an ensemble of historical samples to define a subspace. It directly obtains an optimal solution in the reduced space by fitting observations with historical time series generated by the model to form consistent forecast states, and therefore does not require implementation of the adjoint of tangent linear approximation. To evaluate the performance of the DRP-4DVar on assimilating different types of mesoscale observations, some observing system simulation experiments are conducted using MM5 and a comparison is made between adjoint-based 4DVar and DRP-4DVar using a 6-hour assimilation window.     

GRAPES Hybrid-3DVar对台风苏迪罗的数值试验

为了把反映天气形势变化的背景误差协方差引入到变分分析系统中来提高分析质量,本文在GRAPES区域三维变分框架的基础上通过扩展控制变量方法实现动态与静态背景误差协方差耦合,建立混合三维变分分析系统（GRAPES Hybrid-3DVar）。通过控制变量扰动产生的集合样本进行单点观测分析试验验证Hybrid-3DVar及其局地化方案的合理性,并针对台风苏迪罗进行实际观测资料同化和数值预报试验,结果表明:用集合样本描述的背景误差协方差是随着天气流型变化的,动力场和质量场的离散度在台风中心处最大,因而混合同化的分析增量包含更多细微结构和中小尺度信息;其分析和24 h内预报要素质量优于3DVar,24 h内降水强度和落区预报也更准确,混合同化分析改善了3DVar分析的降水空报问题;同时混合同化分析的24 h内台风路径预报也最接近实况,台风强度预报在48 h之内都比3DVar更接近观测。     

基于扰动模式的四维变分资料同化系统框架的设计完善和数值试验

为了建立一个应用于区域数值预报的四维变分资料同化（4DVar）系统,在近期开发的扰动预报模式GRAPES_PF基础上,开发完善增量四维变分同化系统框架。该框架中暂不包含物理过程（长短波辐射、边界层过程、对流参数化和云微物理等）。对比业务使用的GRAPES 3DVar系统,增加了温度控制变量。将无量纲Exner气压与流函数的线性风压平衡方程直接在地形追随垂直坐标面上求解,且通过广义共轭余差法（GCR）求解扰动亥姆霍兹（Helmholtz）伴随方程。利用人造“探空”资料对2015年10月台风“彩虹”进行了理想数值试验。试验结果表明,所开发的扰动四维变分同化框架得到了预期的结果,即同化更多资料并反复受到模式约束的四维变分同化系统能有效改善初值质量,进而改善区域数值预报。建立的区域四维变分同化框架合理可行,为进一步发展包含完整物理过程的区域四维变分同化系统奠定了研究基础。      

GRAPES全球四维变分同化系统极小化算法预调节

在进行多次外循环更新的增量分析框架下,前一次极小化迭代过程中产生的信息可提供给下一次极小化做预调节。该文在GRAPES全球四维变分同化系统中对极小化算法——L-BFGS算法实施了这种预调节,通过全观测的个例试验和批量试验进行评估,发现进行预调节后L-BFGS算法的收敛效率得到明显提高,而且在1个月的循环试验中表现十分稳定。该工作可以帮助GRAPES全球四维变分同化系统有效减少极小化的迭代次数,有利于满足业务化运行的时效要求。另外,间隔6 h和间隔24 h的两次4DVar分析对应的海森矩阵变化不大,因此,前一时刻极小化过程产生的信息提供给后一时刻的极小化进行预调节也有一定效果。     

The Structure of Background-error Covariance in a Four-dimensional Variational Data Assimilation System: Single-point Experiment

A four dimensional variational data assimilation (4DVar) based on a dimension-reduced projection (DRP-4DVar) has been developed as a hybrid of the 4DVar and Ensemble Kalman filter (EnKF) concepts. Its good flow-dependent features are demonstrated in single-point experiments through comparisons with adjoint-based 4DVar and three-dimensional variational data (3DVar) assimilations using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5). The results reveal that DRP-4DVar can reasonably generate a background error covariance matrix (simply B-matrix) during the assimilation window from an initial estimation using a number of initial condition dependent historical forecast samples. In contrast, flow-dependence in the B-matrix of MM5 4DVar is barely detectable. It is argued that use of diagonal estimation in the B-matrix of the MM5 4DVar method at the initial time leads to this failure. The experiments also show that the increments produced by DRP-4DVar are anisotropic and no longer symmetric with respect to observation location due to the effects of the weather trends captured in its B-matrix. This differs from the MM5 3DVar which does not consider the influence of heterogeneous forcing on the correlation structure of the B-matrix, a condition that is realistic for many situations. Thus, the MM5 3DVar assimilation could only present an isotropic and homogeneous structure in its increments.     

基于历史样本投影的四维变分陆面数据同化方法及其初步应用

法面临着计算量上的挑战。本研究将一种历史样本投影的四维变分同化方法(Historical-Sample-Projection4DVar,简写为HSP-4DVar)应用于陆面数据同化,建立起CoLM陆面模型的HSP-4DVar系统。相比其他四维变分同化方法,HSP-4DVar的分析值是显式求解,不需要编写和使用伴随模式,从而大大节省了计算量,是一种易于实现的同化方案。通过同化56个月的土壤湿度观测数据表明,新的陆面同化系统不仅省时,而且能够有效吸取观测信息,使得同化后的均方根误差显著降低,各层土壤湿度模拟都有所改善,陆表1000mm层的改善最为明显。     

Doppler Radar Data Assimilation with a Local SVD-En3DVar Method

An observation localization scheme is introduced into an ensemble-based three-dimensional variational (3DVar) assimilation method based on the singular value decomposition technique (SVD-En3DVar) to improve assimilation skill. A point-by-point analysis technique is adopted in which the weight of each observation decreases with increasing distance between the analysis point and the observation point. A set of numerical experiments, in which simulated Doppler radar data are assimilated into the Weather Research and Forecasting (WRF) model, is designed to test the scheme. The results are compared with those obtained using the original global and local patch schemes in SVD-En3DVar, neither of which includes this type of observation localization. The observation localization scheme not only eliminates spurious analysis increments in areas of missing data, but also avoids the discontinuous analysis fields that arise from the local patch scheme. The new scheme provides better analysis fields and a more reasonable short-range rainfall forecast than the original schemes. Additional forecast experiments that assimilate real data from 10 radars indicate that the short-term precipitation forecast skill can be improved by assimilating radar data and the observation localization scheme provides a better forecast than the other two schemes.     

Sensitivity of the DRP-4DVar Performance to Perturbation Samples Obtained by Two Different Methods

The dimension-reduced projection four-dimensional variational data assimilation (DRP-4DVar) approach utilizes the ensemble of historical forecasts to estimate the background error covariance (BEC) and directly obtains the analysis in the ensemble space.As a result,the quality of ensemble members significantly affects the DRP-4DVar performance.The historical-forecast-based initial perturbation samples are flow-dependent and can describe the error-growth pattern of the atmospheric model and the balanced relat...