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。

The Analysis on Variation of Horizontal De-correlation Length with Model Resolution in Data Assimilation System

De-correlation length of background error covariance is one of the most important parameter in data assimilation system,it determines the spatial spread of observation information.The theoretic results show that de-correlation length defined in global domain with harmonic space and in regional domain with Bessel function space is equal,it is determined by all power spectra of background errors.The de-correlation length is shorter when the wave number is larger,or model resolution is higher,and the rate of variation is decided by the slope of global power spectra.The atmospheric energy power spectra obey the law of-3 in synoptic scale(420 wave numbers) and the law of-5/3 in mesoscale(larger than 60 wave numbers).This law is not changed with season and model domain,but the power spectra of background error in mesoscale is greater than power-5/3 due to model dissipation.The high dissipation tends to increase the slope and to deviate the power spectra of background errors away from atmospheric power spectra.By comparing and analyzing various sources of de-correlation length data provided by the published papers and background files from NWP models,the results show that de-correlation length and model resolution will basically obey the law of square-root of two when model resolution is less than 350 km.In an ideal numerical experiment,the power spectra of background errors within synoptic scale are set to be the same as Fig.6 of Rabier et al.(1998).From subsynoptic scale to mesoscale,the slope of horizontal autocorrelatoin spectra as a function of horizontal total wavenumber in a log-log graph is set varying from-5/3 to-4.The results also show that the decrease of de-correlation length is slower as model resolution increases,and the sensitivity of de-correlation length to model resolution is reduced.The slope of-2.8 is most fitting to real data for temperature.This paper provides one method to estimate de-correlation directly based on energy power spectra of background error,and is different to other estimation methods,such as innovation vector method,and NMC-method etc.The innovation method is based on density radio-sonde data in observation space,and the domain is within 30004000 km and the distance between stations is larger than 300 km.That means the innovation method can only provide power spectra within 1070 wave numbers.The NMC-method based on model space,and it can provide power spectra for all wave number resolved by model resolution.Both methods have no ability for high model resolution.The merit of this method in this paper is that it can directly use the power spectra derived from ideal or real background error with slope of-2.8 to estimate temperature de-correlation length,and this is also helpful when the model resolution is high.it does not need to recalculate background error covariance again with NMC-method.It can directly use old background field from NWP model after only tuning the de-correlation length using the relationship described above.