Study To The Key Technologies Of 4D-Var And Parallel Computing

Because of the importance of initial fields to the numerical weather prediction (NWP) and the difficulty of them being precisely determined, the advanced data assimilation techniques have become one of the most pivotal technologies to improve the quality of NWP. This thesis concentrates on the goal to resolve the key technologies to establish an operational four-dimensional variational assimilation (4D-Var) system. With the comprehensive utilization of various knowledge from meteorology, computational mathematics and computer application technology, this thesis researches the key algorithms and the parallel computing techniques which are crucial to improve assimilation effect and computing efficiency, and an experimental multi-resolutional 4D-Var system YH4DVAR based on incremental formulation is implemented. The main contents and innovations are as follows:(1) The basic principle and implementation technologies of 4D-Var are systematically investigated and the algorithms of it are theoretically deduced and analyzed as well. Against the defects of large computing cost and the information loss of medium and small scales in the inner loop optimization, a multi-resolutional and multi-incremental implementation of 4D-Var is proposed. The multi-incremental method can speed up the convergence of inner loop optimization iteration, reduce the computation cost and maintain the meteoric information of various scales. Therefore, we can obtain the incremental analysis with higher resolution and the analysis fields with more accuracy. Aimed at the simplification of which vertical and horizontal background error covariances are computed separately in the procedure of control variable transformation, a new control variable transformation operator is constructed based on the spherical wavelet transformation. The dependence between horizontal and vertical covariances is managed in the wavelet scale.(2) The statistical methods of background error covariances are investigated. The traditional NMC methods only estimate the background error theoretically or statically, so a NMC method based on the collective forecast is proposed, which can estimate the background error statistics flow-dependently. Against the defects while estimating the background error statistics with spectral method, a new method for simulating the global background error covariances is proposed basing on the spherical wavelet. It is proved theoretically and experimentally that the background error covariances model based on the spherical wavelet can get the local vertical matrix which depends on various scales and positions in the geographic space, which is quite important to improve the quality of global mesoscale forecast.(3) Considering the situation that the non-Gaussian observation error makes the cost function non-quadratic, a variational quality control algorithm based on the multi-resolutional iteration is proposed, in which the variation principle is applied to the quality control of observations. The quality control of observations and the procedure of 4D-Var are implemented integratedly and the observation term of cost function is modified in the iteration. The non-Gaussian property of obvious errors is also taken into consideration. The variational quality control can improve the utilization of various data. The observations, which are refused in the latest iteration, can be estimated and used again in the next iteration if they are consistent with the observations around. Therefore, they can affect the analysis fields all the same. It is indicated from the experiment results that the utilization of observations and quality of data assimilation make a significant improvement by the variational quality control.(4) The principle and implementation methods of massive optimal algorithms are investigated. In order to speed up the convergence of optimization iteration in the 4D-Var, based on the analysis of the conjugate gradient method and the LBFGS method, a new preconditioned LBFGS method is proposed, which uses the linear conjugate gradient method to perform the preconditioning. The new method builds upon the preconditioning and hybrid iteration step theories and takes the locality of cost function into consideration as well. Compared to the traditional LBFGS method, the new method has a sooner convergence. Numerical experiments show that the performance improvement is even more dramatic when the cost function is not strictly quadric. Therefore, the new method is quite adaptive to the 4D-Var of which the cost function is usually not strictly quadric because of the complex processing.(5) Against the computational bottlenecks of 4D-Var system, the massive scalable parallel algorithm for the spectral model with high resolution and variation framework is investigated. Considering the properties of the two space computation (grid space and spectrum space) algorithms and the two transformation (Fourier transformation and Legendre transformation) algorithms, a two-dimensional irregular domain decomposition algorithm is proposed, which eliminates the load imbalance and the low communication efficiency problems appearing in the one-dimensional data partition mode. Considering the computational properties of 4D-Var, an observation hybrid data partition algorithm is proposed according to the observation types, which effectively solves the load imbalance while calculating the observation space resulting from the randomly-distributed observations. This thesis parallelizes the spectrum model and 4D-Var framework according to the two-dimensional data partition and three-dimensional data transform. The forecasting experiment with real analysis fields indicates that it can dramatically satisfy the real-time requirements of the operational forecast, since the five days' forecast can be done in fifteen minutes by spectrum model with 512 processes.(6) The design and implementation of 4D-Var system is investigated. As 4D-Var system has the features of multitasking, complex data flow and huge computation, the computing flow is carefully designed and the operational time sequence is set up for the 4D-Var system based on the multi-resolutional multi-incremental algorithm. Considering the analysis effect and computational bottleneck, an experimental 4D-Var system YH4DVAR is implemented to which many new technologies above are applied, including background error covariance model based on the spherical wavelet, variational quality control, control variables transformation based on the wavelet, LBFGS algorithm with iteration preconditioning and the parallel computing of spectrum model with high resolution and the variational data assimilation framework. Being experimentally deployed in one of the PLA weather forecasting center, YH4DVAR can assimilate the observations within 12-hour assimilation window and get the analysis fields consistent with the model. YH4DVAR can achieve wonderful forecasting quality when it is combined with the model.