基于吸引子理论的同化方法研究
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摘要
本文在前人提出的基于大气吸引子理论的同化(CDA)思想的基础上,利用奇异值分解(SVD)方法,提出了一个新的同化方法4DSVD,给出了详细同化方案,并且用标准Fortran90语言编写完成了模块化的4DSVD同化系统。首先利用简单的Lorenz-28变量模式进行了理想数值试验,对4DSVD与4DVAR两种方法进行了对比分析。其次,通过简单三维试验研究了观测误差、模式误差和样本误差对4DSVD分析误差的影响。同时初步研究了样本的选取方法和样本容量与4DSVD分析结果的关系,讨论了基向量个数对4DSVD分析结果的影响。并在此基础上,利用中尺度气象模式WRF及观测系统模拟数值试验对4DSVD的同化性能进行了检验,进一步验证了简单数值试验所得到的结果。
其次,利用大气初始场信息随时间衰减的性质,提出了带时间权重的同化方法TW4DSVD,讨论了时间权重的物理意义;比较了线性和指数两种不同权重函数形式对同化效果的影响;利用中尺度气象模式WRF做了一系列观测系统模拟试验,对TW4DSVD的同化性能进行了初步检验。
最后,考虑到日益增多的各种非常规观测资料,通过改进TW4DSVD提出了适用于观测算子未知或观测算子误差很大情况下的同化方法NOO4DSVD。并利用模拟的卫星辐射资料进行了理想数值试验,对NOO4DSVD进行了初步检验,并对NOO4DSVD与TW4DSVD两种方法进行了比较。
总结全文,得到以下主要结果与结论:
(1)与4DVAR相比,4DSVD可以用相对较少的计算量获得和4DVAR基本相同的分析场,在观测量较多的情况下分析结果4DSVD与4DVAR相当,在观测量较少的情况下分析结果4DSVD可能优于4DVAR;由此可见,4DVAR的分析结果对观测量的多少十分敏感,4DSVD反之。对于4DSVD,并不是基向量个数越多越好,而存在最优的基向量个数,并且对于实际情况最优的基向量个数远远小于模式自由度。最优基向量个数不仅仅由吸引子相空间的维数决定,还与观测误差,观测量等其他因素有关。4DSVD能够用完整模式动力作为约束,保证分析场与模式动力相平衡,但这需要更多试验进一步验证。4DSVD分析误差的主要误差源是截断误差、样本误差、观测代表性误差、观测误差和模式误差。截断误差产生的分析误差随着基向量个数的增多而减小;观测代表性误差、观测误差和模式误差引起的分析误差随着基向量个数的增多而增大。同时样本选取方法和样本容量对分析误差有重要影响。基于以上分析研究,本文认为采用历史模式结果作为样本源可以大大节约计算时间,间隔一定时间取样可以最大限度的保证样本间的独立性,还可以减少所需要的样本容量。分析误差随着样本容量的增加而减少,但是当样本容量达到一定的量时,分析结果不会再随着样本的增加而有明显变化。对于实际的中尺度大气模式和模拟的传统观测资料同化,几百个样本就可以满足需要了。
(2)在4DSVD中对不同时刻的观测引入不同的时间权重系数是合理的。与4DSVD相比,TW4DSVD的优点是它拓展了同化分析时刻,可以将同化时间窗内的任意时刻作为分析时刻。试验验证了权重系数与同化时刻时间间隔的关系满足指数衰减的函数形式,与理论结果一致。权重函数中参数的物理意义是权重衰减到1/e的时间,存在最优权重衰减e折时间。模拟观测系统试验表明TW4DSVD在实际的模式和模拟的探空观测情况下,同化效果比较理想。
(3)NOO4DSVD和TW4DSVD一样具有同化卫星辐射资料的能力,可以得到较好的温度和湿度廓线,但是对其他要素,NOO4DSVD同化能力优于TW4DSVD。NOO4DSVD的分析误差对观测误差的大小相对比较敏感,而观测误差对TW4DSVD的分析结果影响相对较小。对于温度,NOO4DSVD的分析误差在有些层比TW4DSVD的分析误差小,有些层比TW4DSVD的分析误差大。对于湿度,NOO4DSVD的分析结果要明显优于TW4DSVD的分析结果。
Based on Chaotic-Attractor theory,Qiu and Chou proposed a new data assimilation method called CDA in 2006.A new four-dimensional data assimilation scheme(4DSVD) for CDA is given using Singular Value Decomposition(SVD)in this thesis.The codes of the 4DSVD are completed using standard Fortran 90 language.We also compare the performances of the 4DSVD and four-dimension variational assimilation(4DVAR) through simple experiments using Lorenz 28-variable model.The impacts of the observation error,sampling error,truncation error and model error on the analysis error are analyzed.In another chapter,the relationship between the analysis error and both sampling strategy and sample content of 3-Dimensional assimilation using 4DSVD is researched.The relationship between the truncation number of the base vector and the analysis error is discussed.The observation system simulated experiments(OSSE)are designed with the Weather Research and Forecasting(WRF)Modeling System to test the performance of the 4DSVD using the realistic model and observations.
The results illustrate that the accuracy of the analysis state of the 4DSVD is similar to that of the 4DVAR;however,the required computational time of the 4DSVD is much less than that of the 4DVAR,and the 4DSVD also avoids having to estimate the background error covariance matrix.There exist an optimal base vector number.The optimal base vector number is much smaller than the degree of the model freedom.The main sources of the analysis error are observation error,model error,truncation error and sampling error.The larger the observation error is,the larger the analysis error is.The larger the model error is,the larger the analysis error is.The sample strategy and sample content have importran influence on the analysis error.The more the samples there are, the smaller the analysis error is.A better sample strategy can improve the analysis,and it can also save a lot of computation time.The historical model outputs are a good source of samples.For OSSE,about 500 samples are enough for the 4DSVD to get good analysis fields.
The information of the intial conditions for atmospheric model is damping with time and the damping effects are given by exponential function.Considering this feature of the atmosphere,a time weighted 4DSVD(TW4DSVD)is proposed.Some simple OSSEs using WRF model are designed to test the performance of the TW4DSVD and to determine the function of the weight with the time.OSSEs are designed to test the performance of the TW4DSVD to assimilate observations of radiosonde temperature and u-and v-wind components.
The performance of the TW4DSVD is better than that of the 4DSVD.And the weight coefficients of different time are given by exponential function which is better than the linear function.The optimal damping coefficient may the determined by the time length that the information of the initial condition dampes to 1/e.The TW4DSVD has the ability to assimilate observations of radiosonde to obtain the good analysis for the model.
The observation variables are not always the same with the atmospheric variables. To assimilate these observations,the traditional data assimilation methods,such as 4DVAR,need the observation operator which provides the link between the model variables and the observations.Some times,the observation operator of some obervations is not known accurately.To assimilate these observations whose observation operator is not known or is difficult to determine accurately,a new data assimilation method called NOO4DSVD is proposed.To test the performance of the NOO4DSVD and compare it with the TW4DSVD,some experiments which assimilate the radiance data of HIRS on NOAA-15 are designed.
The larger the observation error is,the larger the analysis error for the NOO4DSVD is.The analysis error of the temperature of NOO4DSVD is smaller than that of the TW4DSVD at some levels,but at other levels,the analysis error of the temperature for NOO4DSVD is larger than that of TW4DSVD.The analysis error of the humidity profiles of the NOO4DSVD is much smaller than that of the TW4DSVD.These results imply that the NOO4DSVD has the ability to assimilate the obervations whose observation operator is unknown to get good analysis.
其次,利用大气初始场信息随时间衰减的性质,提出了带时间权重的同化方法TW4DSVD,讨论了时间权重的物理意义;比较了线性和指数两种不同权重函数形式对同化效果的影响;利用中尺度气象模式WRF做了一系列观测系统模拟试验,对TW4DSVD的同化性能进行了初步检验。
最后,考虑到日益增多的各种非常规观测资料,通过改进TW4DSVD提出了适用于观测算子未知或观测算子误差很大情况下的同化方法NOO4DSVD。并利用模拟的卫星辐射资料进行了理想数值试验,对NOO4DSVD进行了初步检验,并对NOO4DSVD与TW4DSVD两种方法进行了比较。
总结全文,得到以下主要结果与结论:
(1)与4DVAR相比,4DSVD可以用相对较少的计算量获得和4DVAR基本相同的分析场,在观测量较多的情况下分析结果4DSVD与4DVAR相当,在观测量较少的情况下分析结果4DSVD可能优于4DVAR;由此可见,4DVAR的分析结果对观测量的多少十分敏感,4DSVD反之。对于4DSVD,并不是基向量个数越多越好,而存在最优的基向量个数,并且对于实际情况最优的基向量个数远远小于模式自由度。最优基向量个数不仅仅由吸引子相空间的维数决定,还与观测误差,观测量等其他因素有关。4DSVD能够用完整模式动力作为约束,保证分析场与模式动力相平衡,但这需要更多试验进一步验证。4DSVD分析误差的主要误差源是截断误差、样本误差、观测代表性误差、观测误差和模式误差。截断误差产生的分析误差随着基向量个数的增多而减小;观测代表性误差、观测误差和模式误差引起的分析误差随着基向量个数的增多而增大。同时样本选取方法和样本容量对分析误差有重要影响。基于以上分析研究,本文认为采用历史模式结果作为样本源可以大大节约计算时间,间隔一定时间取样可以最大限度的保证样本间的独立性,还可以减少所需要的样本容量。分析误差随着样本容量的增加而减少,但是当样本容量达到一定的量时,分析结果不会再随着样本的增加而有明显变化。对于实际的中尺度大气模式和模拟的传统观测资料同化,几百个样本就可以满足需要了。
(2)在4DSVD中对不同时刻的观测引入不同的时间权重系数是合理的。与4DSVD相比,TW4DSVD的优点是它拓展了同化分析时刻,可以将同化时间窗内的任意时刻作为分析时刻。试验验证了权重系数与同化时刻时间间隔的关系满足指数衰减的函数形式,与理论结果一致。权重函数中参数的物理意义是权重衰减到1/e的时间,存在最优权重衰减e折时间。模拟观测系统试验表明TW4DSVD在实际的模式和模拟的探空观测情况下,同化效果比较理想。
(3)NOO4DSVD和TW4DSVD一样具有同化卫星辐射资料的能力,可以得到较好的温度和湿度廓线,但是对其他要素,NOO4DSVD同化能力优于TW4DSVD。NOO4DSVD的分析误差对观测误差的大小相对比较敏感,而观测误差对TW4DSVD的分析结果影响相对较小。对于温度,NOO4DSVD的分析误差在有些层比TW4DSVD的分析误差小,有些层比TW4DSVD的分析误差大。对于湿度,NOO4DSVD的分析结果要明显优于TW4DSVD的分析结果。
Based on Chaotic-Attractor theory,Qiu and Chou proposed a new data assimilation method called CDA in 2006.A new four-dimensional data assimilation scheme(4DSVD) for CDA is given using Singular Value Decomposition(SVD)in this thesis.The codes of the 4DSVD are completed using standard Fortran 90 language.We also compare the performances of the 4DSVD and four-dimension variational assimilation(4DVAR) through simple experiments using Lorenz 28-variable model.The impacts of the observation error,sampling error,truncation error and model error on the analysis error are analyzed.In another chapter,the relationship between the analysis error and both sampling strategy and sample content of 3-Dimensional assimilation using 4DSVD is researched.The relationship between the truncation number of the base vector and the analysis error is discussed.The observation system simulated experiments(OSSE)are designed with the Weather Research and Forecasting(WRF)Modeling System to test the performance of the 4DSVD using the realistic model and observations.
The results illustrate that the accuracy of the analysis state of the 4DSVD is similar to that of the 4DVAR;however,the required computational time of the 4DSVD is much less than that of the 4DVAR,and the 4DSVD also avoids having to estimate the background error covariance matrix.There exist an optimal base vector number.The optimal base vector number is much smaller than the degree of the model freedom.The main sources of the analysis error are observation error,model error,truncation error and sampling error.The larger the observation error is,the larger the analysis error is.The larger the model error is,the larger the analysis error is.The sample strategy and sample content have importran influence on the analysis error.The more the samples there are, the smaller the analysis error is.A better sample strategy can improve the analysis,and it can also save a lot of computation time.The historical model outputs are a good source of samples.For OSSE,about 500 samples are enough for the 4DSVD to get good analysis fields.
The information of the intial conditions for atmospheric model is damping with time and the damping effects are given by exponential function.Considering this feature of the atmosphere,a time weighted 4DSVD(TW4DSVD)is proposed.Some simple OSSEs using WRF model are designed to test the performance of the TW4DSVD and to determine the function of the weight with the time.OSSEs are designed to test the performance of the TW4DSVD to assimilate observations of radiosonde temperature and u-and v-wind components.
The performance of the TW4DSVD is better than that of the 4DSVD.And the weight coefficients of different time are given by exponential function which is better than the linear function.The optimal damping coefficient may the determined by the time length that the information of the initial condition dampes to 1/e.The TW4DSVD has the ability to assimilate observations of radiosonde to obtain the good analysis for the model.
The observation variables are not always the same with the atmospheric variables. To assimilate these observations,the traditional data assimilation methods,such as 4DVAR,need the observation operator which provides the link between the model variables and the observations.Some times,the observation operator of some obervations is not known accurately.To assimilate these observations whose observation operator is not known or is difficult to determine accurately,a new data assimilation method called NOO4DSVD is proposed.To test the performance of the NOO4DSVD and compare it with the TW4DSVD,some experiments which assimilate the radiance data of HIRS on NOAA-15 are designed.
The larger the observation error is,the larger the analysis error for the NOO4DSVD is.The analysis error of the temperature of NOO4DSVD is smaller than that of the TW4DSVD at some levels,but at other levels,the analysis error of the temperature for NOO4DSVD is larger than that of TW4DSVD.The analysis error of the humidity profiles of the NOO4DSVD is much smaller than that of the TW4DSVD.These results imply that the NOO4DSVD has the ability to assimilate the obervations whose observation operator is unknown to get good analysis.
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