Study Of A Chaotic-Attractor-Theory Oriented Data Assimilation Method

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.