The Analysis on Variation of Horizontal De-correlation Length with Model Resolution in Data Assimilation System
资料同化中二维特征长度随模式分辨率变化的分析研究

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 descri