A semi-implicit semi-Lagrangian time integration schemes with a predictor and a corrector and their applications in CMA-GFS
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摘要: CMA-GFS采用的是传统的二时间层半隐式半拉格朗日时间积分方案（SISL）。拉格朗日平流速度和非线性项需要采用时间外插进行计算，在急流轴附近等梯度大值区会造成计算不稳定，甚至积分中断现象。文中通过构造预估-校正半隐式半拉格朗日时间积分方案（SISL/P-C），以减少时间外插的影响；半隐式系数由原来的0.72减小到0.55，构造准二阶精度的时间积分方案。理想试验和实际资料试验证明新方案可以改善CMA-GFS的精确度、稳定性和质量守恒。0.25°水平分辨率下积分时间步长可以由300 s 增大到450 s，模式总体计算效率提高20%。
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关键词:
- 预估-校正法 /
- 二时间层半隐式半拉格朗日方案 /
- CMA-GFS
Abstract: A classical two-time level semi-implicit semi-Lagrange scheme (SISL) is used in CMA-GFS. Lagrange advection velocity and nonlinear terms are calculated by temporal extrapolation, which can cause computational instability and even integration interruption in large gradient areas such as the areas of jet. A SISL/P-C (predictor-corrector) algorithm is developed in CMA-GFS to reduce the impact of temporal extrapolation and construct a quasi-second order precision time discretization scheme by reducing the semi-implicit coefficients from 0.72 to 0.55. Results of idealized and real-data experiments show that this new scheme can effectively improve forecast accuracy, stability and conservation. The integration time step can be increased from 300 s to 450 s at 0.25° horizontal resolution, and the model calculation efficiency can be increased by 20%.-
Key words:
- Predictor-Corrector /
- Two-time-level SISL /
- CMA-GFS
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图 1 Rossby-Haurhawtz波试验积分15 d后700 hPa高度场 （a. 对照试验，b. SISL/P-C试验；单位：gpm）
Figure 1. 700 hPa height in the Rossby-Haurhawtz wave experiment after 15 d of integration （a. control，b. SISL/P-C；unit：gpm）
图 2 Rossby-Haurhawtz波试验 （40°S—40°N，10°—110°E） 积分15 d后700 hPa高度场 （黑色：初始值， 红色：对照试验，绿色：SISL/P-C ）
Figure 2. 700 hPa height in the Rossby-Haurhawtz wave experiment （40°S—40°N，10°—110°E） after 15 d of integration （black：initial value，red：control，green：SISL/P-C）
图 3 地形激发的罗斯贝波传播15 d 后700 hPa高度场 （a1、a2：对照试验，b1、b2. SISL/P-C；a1、b1. 1200 s，a2、b2. 600 s；单位：gpm）
Figure 3. 700 hPa height in the mountain-induced Rossby wave experiment after 15 d of integration （a1，a2. control，b1，b2. SISL/P-C； a1，b1. 1200 s，a2，b2. 600 s；unit：gpm）
图 4 地形激发的罗斯贝波传播15 d 后700 hPa （EQ—70°N，80°—160°E） 高度场 （实线：600 s，虚线：1200 s；黑色：对照试验，红色：SISL/P-C；单位：gpm）
Figure 4. 700 hPa height （EQ—70°N，80° —160°E） in the mountain-induced Rossby wave experiment after 15 d of integration （solid：600 s，dashed：1200 s； black：control， red：SISL/P-C； unit：gpm）
图 5 地形激发的罗斯贝波传播0—15 d 平均地面气压变化 （黑色：对照试验，红色：SISL/P-C；实线：600 s，虚线：1200 s；单位：hPa）
Figure 5. Averaged surface pressure changes over 0—15 d in the mountain-induced Rossby wave experiment （black：control，red：SISL/P-C；solid line：600 s，dashed line：1200 s；unit：hPa）
图 6 斜压波试验模式积分9天850 hPa上的温度场 （单位：K）（a.对照试验，b. SISL/P-C；单位：K）
Figure 6. 850 hPa temperature in the baroclinic wave experiment after 9 d of integration （a. control， b. SISL/P-C；unit：K）
图 7 斜压波试验模式积分9天850 hPa （30—70°N，120°E —120°W） 温度场 （a. 对照试验，b. SISL/P-C；黑色：600 s，蓝色：1200 s，红色：1800 s；单位：K）
Figure 7. 850 hPa temperature （30°—70°N，120°E—120°W） in the baroclinic wave experiment after 9 d of integration （a. control，b. SISL/ P-C；black：600 s，blue：1200 s，red：1800 s；unit：K）
图 8 2018年7月12日12时 （世界时） 起报72 h预报的500 hPa高度场 （黑色线：SISL/P-C，红色线：对照试验；实线：300 s，虚线：450 s；单位：gpm）
Figure 8. 500 hPa height after 72 h of integration starting from 12：00 UTC 12 July 2018 （solid：300 s，dash：450 s；black：SISL/P-C，red：control；unit：gpm）
图 9 2018年7月平均5 d 预报500 hPa高度场距平相关系数 （a） 和偏差 （b）
Figure 9. Anomaly correlations （a） and biases （b） of averaged 5 d 500 hPa height field in July 2018
图 10 SISL/P-C预报试验的综合评分卡 （a. 300 s，b. 450 s）
Figure 10. Comprehensive scoring cards for prediction experiment of SISL/P-C （a. 300 s，b. 450 s）
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