Application of Cascade Interpolation to GRAPES Model

For the numerical weather predicting model (NWM) based on semi-Lagrange scheme, it is not economical to apply the conventional point-by-point approach based on Cartesian product of one-dimensional Lagrange interpolation polynomials to evaluate up-stream variables at each integration time step. It takes O(N³) operations to calculate each point. The bigger the N value is, the more accurate the calculation may become. However, it involves too much calculation. When the method of a Cascade of one-dimensional interpolation of the entire data is employed, it requires only O(N) operations. The so-called Cascade method is a highly efficient means of carrying out the grid-to-grid interpolations required by a high-order semi-Lagrangian model. It goes like follows: The intersection points between the regular Eularian and curvilinear Lagrangian meshes form hybrid coordinate lines, and some variables of the intermediate points and the target point of the Lagrangian mesh can be interpolated by using one-dimensional curvilinear Lagrange interpolation method. First, the values of all intermediate points are interpolated. Then, the values of the target points are interpolated from the evaluated intermediate values step by step.The interpolation of the target points is not isolated because the adjoining target point uses shared some intermediate points. Some intermediate results can be repeatedly utilized so that it reduces the amount of computation in interpolation process.GRAPES (Global/Regional Assimilation and Prediction System) is a new generation of numerical weather prediction system of China developed by Research Center for Numerical Meteorological Prediction of CAMS (Chinese Academy of Meteorological Sciences) of CMA (China Meteorological Administration). It is designed based on the scheme using two time-level semi-Implicit time integration and semi-Lagrangian backward trajectories. It is also a fully compressible, non-hydrostatic grid model using latitude and longitude, as well as terrain-following height vertical coordinate. The model variables are staggered in two-dimension horizontal space in the form of an Arakawa-C grid. According to the designing principles of softw are engineering, GRAPES is a standardized, modularized, and coding infrastructure system. As far as the big numerical predicting models are concerned, the parallel computing becomes a necessary feature of them. The parallel computation of GRAPES is realized by means of decomposing zone in latitude and longitude directions. In order to parallelize Cascade interpolation code conveniently, the independent variables like distance on the curves need to be calculated in individual subsections instead of those from the start point.When the Cascade interpolation is applied in GRAPES model, predicting models are tested based on different horizontal grid resolutions such as those of 50km (720×360) and 100km (360×180). There are 31 vertical levels altogether.The timing of interpolating upstream points is monitored on the IBM-1600 cluster in CMA.The results of tests show that Cascade interpolation can significantly reduce computer running time by about 30%, compared with the conventional Cartesian interpolation, without affecting the accuracy of predicting models.