二阶精度半隐式半拉格朗日轨迹计算和时间积分方案在GRAPES区域模式中的应用

摘要

The Stable Extrapolation Two-Time-Level Scheme (SETTLS)has been implemented in the GRAPES regional model to determine the trajectory and nonlinear terms.To make the scheme stable,selecting a relatively warm reference temperature is necessary.The first-order decentered averaging of the linear terms of the previous version of the GRAPES relaxes the restric-tion of a relatively warm reference temperature but its large weight results in a significant damping for the low-wavenumber modes.Therefore,a second-order accuracy decentering of the linear terms and warmer reference temperature are applied in the GRAPES model.The results from the ideal experiments show that the new semi-implicit semi-Lagrangian scheme is stable and leads to much less damping than the original time integration scheme.%将两时间层稳定外插方案（Stable Extrapolation Two-Time-Level Scheme，SETTLS）引入GRAPES区域模式，并将其用于上游点和非线性项的时间外插计算。对线性项采用二阶精度的非中央权重时间平均，并取等温参考大气的温度大于实际大气平均温度，以保证半隐式积分方案的稳定性。原GRAPES时间积分方案对线性项做一阶非中央权重时间平均，对参考大气的选择并无限制，而为保证稳定性，须取较大的非中央权重系数，但非中央权重系数会对低波数波动产生较强的衰减作用。理想试验结果表明，相比原GRAPES半隐式半拉格朗日（SISL）时间积分方案，新SISL 时间积分方案计算稳定且对波动的衰减作用较弱。