Firstly, the annual variation of sandstorm and strong sandstorm weather process in China from 2000 to 2012 is analyzed according to the"Sand-Dust Weather Yearbook" (2012). Secondly, based on the ERA-Interim Reanalysis from ECMWF and MISR data from the Terra satellite, we investigate the correlation between different dust weather process and land meteorological elements. Finally, the temporal and spatial distribution features of the aerosol optical depth (AOD) in the Taklamakan Desert is studied. And we compare the Taklamakan Desert AOD with nationwide AOD. The results show that: (1) the frequency of sandstorm and strong sandstorm has shown a downward trend and the occurrence of sandstorm decreases more in recent years. (2) In the Taklamakan Desert, the number of sandstorm is positively correlated with the surface temperature, meanwhile, negatively related to the surface relative humidity. (3) In all seasons, the average of AOD in Taklamakan Desert is higher than that of the whole country, and there are obvious differences among the four seasons.
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An experimental Ensemble Data Assimilation (YH‐EDA) system has been built with 10 ensemble members based on the operational YH4DVAR system. The system can provide flow‐dependent background‐error variances, which are superior to the operational ones both in structure and magnitude. However, the finite ensemble size implies a detrimental sampling noise for the variances estimation. To solve this problem, a spectral filtering technique is implemented to formulate a low‐passing filter. Taking into account the typical horizontal length scales of noise and signal, the filter can eliminate the sampling noise while extracting the signal of interest. In the ensemble variance filtering experimentations of the 9th typhoon “Jebi” in 2013, our results show that the 10‐members' filtered variances exhibit better performance than 30‐members's estimation. The successful implementation of the spectral filtering reduces the requirement of large ensemble size of Ensemble Data Assimilation system, which indicates that spectral filtering has become an important and necessary technology in EDA operational implementation.
In gradient computations of the variational data assimilation (VDA) by the adjoint method, in order to overcome a lot of shortcomings such as low accuracy, difficult implementation, and great complexity, etc., a novel data assimilation method is proposed based on the dual-number theory. The important advantages are that the coding of adjoint models and reverse integrations are not necessary any more, and the values of cost functional and its corresponding gradient vectors can be attained simultaneously only by one forward computation in dual-number space. Furthermore, the accuracy of gradient can be close to the computer machine precision without other error sources. The paper is organised as follows. Firstly, the dual-number theory and algorithm rules are introduced. Then, the issues of gradient analysis and computation in VDA are transformed into the processes of calculating the cost functional numerically in dual-number space, and the gradient vectors can be obtained at the same time in an easy, efficient and accurate way. Secondly, the new algorithm for data assimilation in nonlinear physical systems is developed by combining accurate gradient information from the dual-number method with classical optimization algorithm. Thirdly, numerical experiments on sensitivity analysis for an ENSO nonlinear air-sea coupled oscillator are implemented, and the results are presented to demonstrate the important advantages of the dual-number method in the calculation of derivative information. Finally, numerical simulations for data assimilation are carried out respectively for the typical Lorenz 63 chaotic systems, the specific humidity evolving equation with physical “on-off” process at a single grid point, and a parabolic partial differential equation. Some conclusions can be drawn from the numerical experiments. The newly proposed method may be suited to many kinds of optimization problems with ordinary or partial differential equations as constraints, such as data assimilation, parameter estimation, inverse problems, sensitivity analysis etc. Results show that the new method can reconstruct the initial conditions or parameters of a nonlinear dynamical system very conveniently and accurately. Its another advantage is being very easy to implement with a high accuracy in gradient computation, so it is robust in the process of numerical optimization. The estimated initial states or parameters are convergent to real value in the cost of no more computations, when there are noises in the observations. But many tests are still needed to demonstrate the validity and advantages of the new data assimilation method, especially in more complex and realistic numerical prediction models of atmosphere and ocean.
A large amount of sampling noise which exists in the ensemble-based background error variance need be reduced effectively before being applied to operational data assimilation system.Unlike the typical Gaussian white noise,the sampling noise is scaled and space-dependent,thus making its energy level on some scales much larger than the average. Although previous denoising methods such as spectral filtering or wavelet thresholding have been successfully used for denoising Gaussian white noise,they are no longer applicable for dealing with this kind of sampling noise.One can use a different threshold for each scale,but it will bring a big error especially on larger scales.Another modified method is to use a global multiplicative factor,α, to adjust the filtering strength based on the optimization of trade-off between removal of the noise and averaging of the useful signal.However,tuning α is not so easy,especially in real operational numerical weather prediction context.It motivates us to develop a new nearly cost-free filter whose threshold can be automatically calculated.#br#According to the characteristics of sampling noise in background error variance,a heterogeneous filtering method similar to wavelet threshold technology is employed.The threshold,TA,determined by iterative algorithm is used to estimate the truncated remainder whose norm is smaller than TA.The standard deviation of truncated remainder term is regard as first guess of sampling noise.Non-Guassian term of sampling noise,whose coefficient modulus is above TA,is regarded as a small probability event.In order to incorporate such a coefficient into the domain of[-T,T],a semi-empirical formula is used to calculate and approach the ideal threshold.#br#According to the characteristics of sampling noise in background error variance,a heterogeneous filtering method similar to wavelet threshold technology is employed.The threshold,TA,determined by iterative algorithm is used to estimate the truncated remainder whose norm is smaller than TA.The standard deviation of truncated remainder term is regard as first guess of sampling noise.Non-Guassian term of sampling noise,whose coefficient modulus is above TA,is regarded as a small probability event.In order to incorporate such a coefficient into the domain of[-T,T],a semi-empirical formula is used to calculate and approach the ideal threshold.#br#A new nearly cost-free filter is proposed to reduce the scale and space-dependent sampling noise in ensemble-based background error variance.It is able to remove most of the sampling noises,while extracting the signal of interest. Compared with those of primal wavelet filter and spectral filter,the performance and efficiency of proposed method are improved in 1D framework and real data assimilation system experiments.Further work should focus on the sphere wavelets,which is appropriate for analysing and reconstructing the signals on the sphere in global spectral models.
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