应用样条插值提高GRAPES模式物理过程反馈精度

GRAPES (Global/Regional Assimilation and PrEdiction System) 模式动力框架中垂直方向变量的跳层设置采用Charney-Phillips分布，在整层上进行位温、水物质的计算，物理过程中在半层上对其进行处理。这样在GRAPES模式中，进入物理过程之前和物理过程计算完毕之后，都要采用线性插值进行整层和半层之间物理量的转换。由于线性插值精度欠佳，为提高上述反馈过程的精度，并保证水物质的正定性，该研究引入样条插值，并在水物质的插值过程中进行保单调处理，有效减小了位温场、水物质场的预报偏差，并提升了模式的综合预报性能。

Application of Spline Interpolation to Physical Process Feedback Accuracy Improvement of GRAPES Model

The variable distribution in the vertical direction of GRAPES model's dynamic core adopts Charney-Phillips method. Vertical velocity, potential temperature, water substance are calculated at the whole layer, horizontal velocity and dimensionless pressure are calculated at the half layer, but in physical process, all the variables are placed on the half layer. In order to satisfy the needs of the central difference calculations and better representation of the physical processes in the boundary layer, a nonuniform stratification is adopted, which is dense near the ground, and the higher the more sparse. Therefore, in GRAPES model, linear interpolation is needed to convert variables between whole and half layers before and after the physical process calculation.For the weather prediction model of various international centers, Lorenz layers are used in the physical part and all the variables are on the half layer. Most models also use Lorenz layers in the dynamic core, except for the Unified Model of the UK Meteorological Office, which chooses Charney-Philips layer for dynamic core and uses linear interpolation in dealing with the similar problem of interpolation between whole and half layers.Linear interpolation is relatively simple, but the accuracy is not high, and it will cause deviation especially for lower and higher layers. The cumulative deviation in the temperature and humidity fields will further impact the height and wind fields. In addition, the interpolation process of water substance is also required to ensure monotonic, but the traditional cubic spline interpolation, polynomial interpolation, cannot be guaranteed monotonic, which will bring negative water, instability and other issues.In order to solve the problems above, the traditional cubic spline interpolation method is introduced for potential temperature interpolation in GRAPES model. After some special handling of the boundary value based on the traditional one, a monotonic cubic spline interpolation method is established for water substance, by which the forecast error of potential temperature and humidity fields in the GRAPES model is effectively reduced. The feedback accuracy of physical process is improved, and the model comprehensive performance is also enhanced.