Verification of an operational ocean circulation-surface wave coupled forecasting system for the China's seas

An operational ocean circulation-surface wave coupled forecasting system for the seas off China and adjacent areas(OCFS-C) is developed based on parallelized circulation and wave models. It has been in operation since November 1, 2007. In this paper we comprehensively present the simulation and verification of the system, whose distinguishing feature is that the wave-induced mixing is coupled in the circulation model. In particular, with nested technique the resolution in the China's seas has been updated to(1/24)° from the global model with(1/2)°resolution. Besides, daily remote sensing sea surface temperature(SST) data have been assimilated into the model to generate a hot restart field for OCFS-C. Moreover, inter-comparisons between forecasting and independent observational data are performed to evaluate the effectiveness of OCFS-C in upper-ocean quantities predictions, including SST, mixed layer depth(MLD) and subsurface temperature. Except in conventional statistical metrics, non-dimensional skill scores(SS) is also used to evaluate forecast skill. Observations from buoys and Argo profiles are used for lead time and real time validations, which give a large SS value(more than 0.90). Besides, prediction skill for the seasonal variation of SST is confirmed. Comparisons of subsurface temperatures with Argo profiles data indicate that OCFS-C has low skill in predicting subsurface temperatures between 100 m and 150 m. Nevertheless, inter-comparisons of MLD reveal that the MLD from model is shallower than that from Argo profiles by about 12 m, i.e., OCFS-C is successful and steady in MLD predictions. Validation of 1-d, 2-d and 3-d forecasting SST shows that our operational ocean circulation-surface wave coupled forecasting model has reasonable accuracy in the upper ocean.     

The impact of ocean data assimilation on seasonal predictions based on the National Climate Center climate system model

An ensemble optimal interpolation (EnOI) data assimilation method is applied in the BCC_CSM1.1 to investigate the impact of ocean data assimilations on seasonal forecasts in an idealized twin experiment framework. Pseudo-observations of sea surface temperature (SST), sea surface height (SSH), sea surface salinity (SSS), temperature and salinity (T/S) profiles were first generated in a free model run. Then, a series of sensitivity tests initialized with predefined bias were conducted for a one-year period; this involved a free run (CTR) and seven assimilation runs. These tests allowed us to check the analysis field accuracy against the “truth”. As expected, data assimilation improved all investigated quantities; the joint assimilation of all variables gave more improved results than assimilating them separately. One-year predictions initialized from the seven runs and CTR were then conducted and compared. The forecasts initialized from joint assimilation of surface data produced comparable SST root mean square errors to that from assimilation of T/S profiles, but the assimilation of T/S profiles is crucial to reduce subsurface deficiencies. The ocean surface currents in the tropics were better predicted when initial conditions produced by assimilating T/S profiles, while surface data assimilation became more important at higher latitudes, particularly near the western boundary currents. The predictions of ocean heat content and mixed layer depth are significantly improved initialized from the joint assimilation of all the variables. Finally, a central Pacific El Ni?o was well predicted from the joint assimilation of surface data, indicating the importance of joint assimilation of SST, SSH, and SSS for ENSO predictions.     

利用热带太平洋TAO浮标阵列评估全球高分辨率浪-潮-流耦合模式同化结果

In order to evaluate the assimilation results from a global high resolution ocean model, the buoy observations from tropical atmosphere ocean(TAO) during August 2014 to July 2015 are employed. The horizontal resolution of wave-tide-circulation coupled ocean model developed by The First Institute of Oceanography(FIOCOM model) is 0.1°×0.1°, and ensemble adjustment Kalman filter is used to assimilate the sea surface temperature(SST), sea level anomaly(SLA) and Argo temperature/salinity profiles. The simulation results with and without data assimilation are examined. First, the overall statistic errors of model results are analyzed. The scatter diagrams of model simulations versus observations and corresponding error probability density distribution show that the errors of all the observed variables, including the temperature, isotherm depth of 20°C(D20), salinity and two horizontal component of velocity are reduced to some extent with a maximum improvement of 54% after assimilation. Second, time-averaged variables are used to investigate the horizontal and vertical structures of the model results. Owing to the data assimilation, the biases of the time-averaged distribution are reduced more than70% for the temperature and D20 especially in the eastern Pacific. The obvious improvement of D20 which represents the upper mixed layer depth indicates that the structure of the temperature after the data assimilation becomes more close to the reality and the vertical structure of the upper ocean becomes more reasonable. At last,the physical processes of time series are compared with observations. The time evolution processes of all variables after the data assimilation are more consistent with the observations. The temperature bias and RMSE of D20 are reduced by 76% and 56% respectively with the data assimilation. More events during this period are also reproduced after the data assimilation. Under the condition of strong 2014/2016 El Ni?o, the Equatorial Undercurrent(EUC) from the TAO is gradually increased during August to November in 2014, and followed by a decreasing process. Since the improvement of the structure in the upper ocean, these events of the EUC can be clearly found in the assimilation results. In conclusion, the data assimilation in this global high resolution model has successfully reduced the model biases and improved the structures of the upper ocean, and the physical processes in reality can be well produced.     

集合调整卡尔曼滤波方法在M2分潮数值模拟中的水深估计研究

数据同化利用观测信息对模型状态场调整的同时也可以对数值模型中的不确定参数进行估计,从而改进数值模型,提高数值模拟的精度。本文基于集合调整卡尔曼滤波方法,采用广义坐标系统的美国普林斯顿大学海洋模式的外模式开展了渤海和部分黄海海域M₂分潮模拟中的水深估计研究。理想数据同化试验结果表明,集合调整卡尔曼滤波方法能很好地降低模式模拟的水位误差并反演出“真实”的水深参数。而在NAO.99Jb和验潮站数据的实际数据同化试验中,与验潮站数据相比较,水深参数估计后,模式模拟的M₂分潮振幅与迟角误差分别降低了40.27%和49.19%。     

Combining Argo profiles with a general circulation model in the North Atlantic. Part 2: Realistic transports and improved hydrography,between spring 2002 and spring 2003

A set of Argo profiles collected in the North Atlantic between May 2002 and April 2003 is combined with a low-resolution general circulation model (GCM) using the adjoint method. Fitting the real hydrographic observations leads to vast improvements in the model circulation, including the sea surface height and the meridional heat transport. We find striking differences in basin-scale transports compared with previous assimilation experiments that use the same GCM and a similar spatial resolution. Based on forward modeling studies, it is argued that these differences are due to different assimilation experiment durations. Over 1 year, the hydrography interpolated with the GCM from Argo profiles better represents the contemporary structures than does a long-term averaged climatology. The GCM dynamics are robust enough to distinguish between contemporary hydrography and climatological hydrography.     

A singular evolutive extended Kalman filter to assimilate ocean color data in a coupled physical–biochemical model of the North Atlantic ocean

Within the European DIADEM project, a data assimilation system for coupled ocean circulation and marine ecosystem models has been implemented for the North Atlantic and the Nordic Seas. One objective of this project is to demonstrate the relevance of sophisticated methods to assimilate satellite data such as altimetry, surface temperature and ocean color, into realistic ocean models. In this paper, the singular evolutive extended Kalman (SEEK) filter, which is an advanced assimilation scheme where three-dimensional, multivariate error statistics are taken into account, is used to assimilate ocean color data into the biological component of the coupled system. The marine ecosystem model, derived from the FDM model [J. Mar. Res. 48 (1990) 591], includes 11 nitrogen and carbon compartments and describes the synthesis of organic matter in the euphotic zone, its consumption by animals of upper trophic levels, and the recycling of detritic material in the deep ocean. The circulation model coupled to the ecosystem is the Miami isopycnic coordinate ocean model (MICOM), which covers the Atlantic and the Arctic Oceans with an enhanced resolution in the North Atlantic basin. The model is forced with realistic ECMWF ocean/atmosphere fluxes, which permits to resolve the seasonal variability of the circulation and mixed layer properties. In the twin assimimation experiments reported here, the predictions of the coupled model are corrected every 10 days using pseudo-measurements of surface phytoplankton as a substitute to chlorophyll concentrations measured from space. The diagnostics of these experiments indicate that the assimilation is feasible with a reduced-order Kalman filter of small rank (of order 10) as long as a sufficiently good identification of the error structure is available. In addition, the control of non-observed quantities such as zooplankton and nitrate concentrations is made possible, owing to the multivariate nature of the analysis scheme. However, a too severe truncation of the error sub-space downgrades the propagation of surface information below the mixed layer. The reduction of the actual state vector to the surface layers is therefore investigated to improve the estimation process in the perspective of sea-viewing wide field-of-view sensor (SeaWiFS) data assimilation experiments.     

Improving Ocean State by Assimilating SARAL/AltiKa Derived Sea Level and Other Satellite-Derived Data in MITGCM

Assimilation of satellite-derived surface datasets has been explored in the study. Three types of surface data, namely sea level anomaly, sea surface temperature and sea surface salinity, have been used in various data assimilation experiments. The emphasis has been on the extra benefit arising out of the additional sea level assimilation and hence there are two parallel runs, in one of which sea level assimilation has been withheld. The model used is a state-of-the art ocean general circulation model (OGCM) and the assimilation method is the widely used singular evolutive extended Kalman filter (SEEK). Evaluation of the assimilation skill has been carried out by comparing the simulated depth of the 20°C isotherm with the same quantity measured by buoys and Argo floats. Simulated subsurface temperature and salinity profiles have also been compared with the same profiles measured by Argo floats. Finally, surface currents in the assimilation runs have been compared with currents measured by several off-equatorial buoys. Addition of sea level has been found to substantially improve the quality of simulation. An important feature that has been effectively simulated by the addition of sea level in the assimilation scheme is the near-surface temperature inversion (2-3°C) in the northern Bay of Bengal.     

基于拉格朗日方法的南海自动剖面浮标轨迹模拟系统*

南海自动剖面浮标轨迹模拟系统包括高分辨率模式流场、拉格朗日追踪模型和垂向浮标运动参数化方案等三个核心部分。该系统可在南海范围内模拟两类自动剖面浮标: 传统自动剖面浮标(停滞深度为1000m, 最大下潜深度为2000m)和新型深海自动剖面浮标(停滞深度为距海底500m)。通过对南海现有的6个传统浮标的模拟, 该系统可以预测其100d内的漂流轨迹。通过与真实浮标轨迹数据的对比, 验证了该模拟系统的准确性。此外, 根据该系统, 我们初步探讨了深海自动剖面浮标阵列(时空分辨率为2°×2°×30d)在南海内区布放方案的可行性。该模拟系统的建立和完善将有助于对现有传统剖面浮标布放策略进行优化, 并对未来深海剖面浮标在南海的推广应用提供初步的理论依据。     

Impact of SARAL/AltiKa-Derived Sea Level Anomaly in a Data Assimilative Ocean Prediction System for the Indian Ocean

The impact of SARAL/AltiKa derived sea level anomaly (SLA) has been studied by assimilating it along with Jason-2 and Cryosat-2 SLA in the Princeton Ocean model (POM) using ensemble optimal interpolation (EnOI) technique. For isolating the extra benefit brought by SARAKL/Altika, a parallel run with assimilation of only Jason-2 and Cryosat-2 SLA has also been conducted. The importance of SARAL SLA in a data assimilative ocean prediction system has been evaluated with special emphasis on the improvement in thermocline depth, depth of the 20° isotherm, subsurface temperature and currents. Comparison with RAMA buoy has shown a positive impact of up to 13% for 20°C isotherm and up to 17% for thermocline depth after assimilating SARAL SLA. An overall improvement in temperature profile is also observed when compared with analogous profiles from RAMA buoys and Argo floats. Improvement in zonal currents away from the equator has also been noticed.     

基于一维扩散方程反演温度垂直扩散系数的变分方法

Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.     

Combining Argo profiles with a general circulation model in the North Atlantic. Part 1: Estimation of hydrographic and circulation anomalies from synthetic profiles,over a year

Argo is a global array of profiling floats that provides temperature (T) and salinity (S) profiles from 2000 m to the surface every ten days with a nominal spatial resolution of 3°. Here we present idealized experiments where the adjoint method is used to synthesize simulated sets of Argo profiles with a general circulation model, over a one-year period, in the North Atlantic. Using a number of drifting profilers consistent with Argo deployment objectives, the simulated array permits one to identify large-scale anomalies in the hydrography and circulation, despite the presence of a simulated eddy noise of large amplitude. Model dynamics provide an objective means to distinguish eddy noise from large-scale oceanic variability, and to infer the absolute velocity field (including abyssal velocities and sea surface height) from sets of Argo profiles of T and S. In particular, our idealized experiments suggest that volume and heat transports can be efficiently constrained by sets of Argo profiles. Increasing the number of Argo floats seems to be an adequate strategy to further reduce errors in circulation estimates.     

海洋资料同化对气候季节-年际预测技巧及初始场的影响试验

集合卡尔曼滤波(Ensemble Kalman filter, EnKF)是一种国内外广泛使用的海洋资料同化方案, 用集合成员的状态集合表征模式的背景误差协方差, 结合观测误差协方差, 计算卡尔曼增益矩阵, 有效地将观测信息添加到模式初始场中。由于季节、年际预测很大程度上受到初始场的影响, 因此资料同化可以提高模式的预测性能。本文在NUIST-CFS1.0预测系统逐日SST nudging的初始化方案上, 利用EnKF在每个月末将全场(full field)海表温度(sea surface temperature, SST)、温盐廓线(in-situ temperature and salinity profiles, T-S profiles)以及卫星观测海平面高度异常(sea level anomalies, SLA)观测资料同化到模式初始场中, 对比分析了无海洋资料同化以及加入同化后初始场的区别、加入海洋资料同化后模式提前1~24个月预测性能的差异以及对于厄尔尼诺-南方涛动(El Niño-southern oscillation, ENSO)预测技巧的影响。结果表明, 加入海洋资料同化能有效地改进初始场, 并且呈现随深度增加初始场改进越显著的特征。加入同化后, 对全球SST、次表层海水温度的平均预测技巧均有一定的提高, 也表现出随深度增加预测技巧改进越明显的特征。但加入海洋资料同化后, 模式对ENSO的预测技巧有所下降, 可能是由于模式误差的存在, 使得同化后的预测初始场从接近观测的状态又逐渐恢复到与模式动力相匹配的状态, 加剧了赤道太平洋冷舌偏西、中东部偏暖的气候平均态漂移。     

Improvement of short-termforecasting in the northwest Pacific through assimilating Argo data into initial fields

The impact of assimilating Argo data into an initial field on the short-term forecasting accuracy of temper- ature and salinity is quantitatively estimated by using a forecasting system of the western North Pacific, on the base of the Princeton ocean model with a generalized coordinate system （POMgcs）. This system uses a sequential multigrid three-dimensional variational （3DVAR） analysis scheme to assimilate observation da- ta. Two numerical experiments were conducted with and without Argo temperature and salinity profile data besides conventional temperature and salinity profile data and sea surface height anomaly （SSHa） and sea surface temperature （SST） in the process of assimilating data into the initial fields. The forecast errors are estimated by using independent temperature and salinity profiles during the forecasting period, including the vertical distributions of the horizontally averaged root mean square errors （H-RMSEs） and the horizontal distributions of the vertically averaged mean errors （MEs） and the temporal variation of spatially averaged root mean square errors （S-RMSEs）. Comparison between the two experiments shows that the assimila- tion of Argo data significantly improves the forecast accuracy, with 24% reduction of H-RMSE maximum for the temperature, and the salinity forecasts are improved more obviously, averagely dropping of 50% for H-RMSEs in depth shallower than 300 m. Such improvement is caused by relatively uniform sampling of both temperature and salinity from the Argo drifters in time and space.     

Corrections to ocean surface forcing in the California Current System using 4D variational data assimilation

The option for surface forcing correction, recently developed in the 4D-variational (4DVAR) data assimilation systems of the Regional Ocean Model System (ROMS), is presented. Assimilation of remotely-sensed (satellite sea surface height anomaly and sea surface temperature) and in situ (from mechanical and expendable bathythermographs, Argo floats and CTD profiles) oceanic observations has been applied in a realistic, high resolution configuration of the California Current System (CCS) to sequentially correct model initial conditions and surface forcing, using the Incremental Strong constraint version of ROMS-4DVAR (ROMS-IS4DVAR). Results from both twin and real data experiments are presented where it is demonstrated that ROMS-IS4DVAR always reduces the difference between the model and the observations that are assimilated. However, without corrections to the surface forcing, the assimilation of surface data can degrade the temperature structure at depth. When using surface forcing adjustment in ROMS-IS4DVAR the system does not degrade the temperature structure at depth, because differences between the model and surface observations can be reduced through corrections to surface forcing rather than to temperature at depth. However, corrections to surface forcing can generate abnormal spatial and temporal variability in the structure of the wind stress or surface heat flux fields if not properly constrained. This behavior can be partially controlled via the choice of decorrelation length scales that are assumed for the forcing errors. Abnormal forcing corrections may also arise due to the effects of model error which are not accounted for in IS4DVAR. In particular, data assimilation tends to weaken the alongshore wind stress in an attempt to reduce the rate of coastal upwelling, which seems to be too strong due to other sources of error. However, corrections to wind stress and surface heat flux improve systematically the ocean state analyses. Trends in the correction of surface heat fluxes indicate that, given the ocean model used and its potential limitations, the heat flux data from the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) used to impose surface conditions in the model are generally too low except in spring-summer, in the upwelling region, where they are too high. Comparisons with independent data provide confidence in the resulting forecast ocean circulation on timescales ～14 days, with less than 1.5 °C, 0.3 psu, and 9 cm RMS error in temperature, salinity and sea surface height anomaly, respectively, compared to observations.     

中国Argo计划:Argo观测和资料应用进展

文章回顾了中国Argo计划已经取得的成果,主要包括中国Argo观测网的建设、浮标技术、数据质量控制及共享等。同时,讨论了Argo数据产品的开发以及数据在海洋、气象和大气研究中的应用,特别是在热带气旋（台风）、海洋环流、中尺度涡、湍流、海水热盐储量与输送、大洋水团,以及海洋、天气/气候业务化预测预报中的应用。最后,文章阐述了中国Argo海洋观测网长期维护和持续发展所面临的挑战和机遇,我们应在印度洋增加浮标数量,同时建立南海Argo区域海洋观测网,促进Argo资料在东南亚和印度洋沿岸国家的应用。     

Twenty years of ocean observations with China Argo

The international Argo program, a global observational array of nearly 4 000 autonomous profiling floats initiated in the late 1990s, which measures the water temperature and salinity of the upper 2 000 m of the global ocean, has revolutionized oceanography. It has been recognized one of the most successful ocean observation systems in the world. Today, the proposed decade action “OneArgo” for building an integrated global, full-depth, and multidisciplinary ocean observing array for beyond 2020 ...     

南海及邻近海域大气-海浪-海洋耦合精细化数值预报系统研制

本文主要介绍了南海及邻近海域大气-海浪-海洋耦合精细化数值预报系统的研制概况。预报区域为99°E~135°E,15°S~45°N,包括渤海、黄海、东海和南海及其周边海域。为了给耦合预报模式提供较准确的预报初始场,在预报开始之前,分别进行了海浪模式和海洋模式的前24小时同化后报模拟。海浪模式和海洋模式都采用了集合调整Kalman滤波同化方法,海浪模式同化了Jason-2有效波高数据;海洋模式同化了SST数据、MADT数据和ARGO剖面数据。为了改进海洋温度和盐度的模拟,我们在海洋模式的垂向混合方案中引入波致混合和内波致混合的作用。预报系统的运行主要包括两个阶段,首先海浪模式和海洋模式进行了2014年1月至2015年10月底的同化后报模拟,强迫场源自欧洲气象中心的六小时的再分析数据产品。然后耦合预报系统将同化后报模拟的结果作为初始场进行了14个月的耦合预报。预报产品包括大气产品（气温、风速风向、气压等）、海浪产品（有效波高和波向等）、海流产品（温度、盐度和海流等）。一系列观测资料的检验比较表明该大气-海浪-海洋耦合精细化数值预报系统的预报结果较为可靠,可以为南海及周边海洋资源开发和安全保障提供数据和信息产品服务。     

基于ROMS模式的南海SST与SSH四维变分同化研究

卫星遥感观测获得了大量高分辨率的海面实时信息,包括海面温度（SST）和海面高度（SSH）等,同化进入数值模式可有效提升模拟精度。本文基于ROMS模式与四维变分同化方法（4DVAR）,使用AVHRR SST和AVISO SSH数据,开展了南海区域同化实验。为检验同化的效果,分别利用HYCOM再分析资料和Argo温盐实测数据分析了同化结果的海面高度、流场及温盐剖面的精度。对比结果表明,SST和SSH的同化能够改善ROMS的模拟结果:同化后海面高度场能够更为准确地捕捉海洋的中尺度特征,与HYCOM海面高度再分析资料相比,平均绝对偏差和均方根误差分别为0.054 m和0.066 m;与HYCOM 10 m层流场相比,东向与北向流速平均绝对偏差分别为0.12 m/s和0.11 m/s,相比未同化均提升约0.01 m/s;温盐同化结果与Argo温盐实测具有较高的一致性,温度和盐度平均绝对偏差为0.45℃、0.077,均方根误差为0.91℃、0.11,单个的温盐廓线对比说明,同化结果与HYCOM再分析资料精度相当。     

Impact of Ocean Mean Dynamic Topography on Satellite Data Assimilation

The response of an eddy-permitting ocean model to changes imposed by the use of different mean dynamic topographies (MDT) is analyzed in a multivariate assimilation context, allowing the evaluation of this impact, not only on the surface circulation, but also on the interior ocean representation. The assimilation scheme is a reduced-order sequential Kalman filter (SEEK). In a first set of experiments, high resolution sea surface temperature, along-track sea surface height and sea surface salinity from climatology are assimilated into a 1/3° resolution North and Tropical Atlantic version of the HYCOM model. In a second experiment, in situ profile data are assimilated in addition to the surface measurements.

The first set of experiments illustrates that important differences in the representation of the horizontal model circulation pattern are related to differences in the MDT used. The objective of assimilation is to improve the representation of the 3D ocean state. However, the imperfect representation of the mean dynamic topography appears to be an important limiting factor with regard to the degree of realism obtained in the simulated flow.

Vertical temperature and salinity profiles are key observations to drive a general circulation ocean model toward a more realistic state. The second set of experiments shows that assimilating them in addition to sea surface measurements is a far from trivial exercise. A specific difficulty is due to inconsistencies between the dynamic topography diagnosed from in situ observations and that diagnosed from sea surface height. These two fields obtained from different data sources do not contain exactly the same information. In order to overcome this difficulty, a strategy is proposed and validated.     

Impact of Ocean Mean Dynamic Topography on Satellite Data Assimilation

The response of an eddy-permitting ocean model to changes imposed by the use of different mean dynamic topographies (MDT) is analyzed in a multivariate assimilation context, allowing the evaluation of this impact, not only on the surface circulation, but also on the interior ocean representation. The assimilation scheme is a reduced-order sequential Kalman filter (SEEK). In a first set of experiments, high resolution sea surface temperature, along-track sea surface height and sea surface salinity from climatology are assimilated into a 1/3° resolution North and Tropical Atlantic version of the HYCOM model. In a second experiment, in situ profile data are assimilated in addition to the surface measurements.

The first set of experiments illustrates that important differences in the representation of the horizontal model circulation pattern are related to differences in the MDT used. The objective of assimilation is to improve the representation of the 3D ocean state. However, the imperfect representation of the mean dynamic topography appears to be an important limiting factor with regard to the degree of realism obtained in the simulated flow.

Vertical temperature and salinity profiles are key observations to drive a general circulation ocean model toward a more realistic state. The second set of experiments shows that assimilating them in addition to sea surface measurements is a far from trivial exercise. A specific difficulty is due to inconsistencies between the dynamic topography diagnosed from in situ observations and that diagnosed from sea surface height. These two fields obtained from different data sources do not contain exactly the same information. In order to overcome this difficulty, a strategy is proposed and validated.