Application Of A High-order Accuracy And Positive-definite Advection Scheme Into GRAPES Model

The advection process plays an essential role in fluid dynamics, and is generally knownas an important process in atmosphere dynamics. A good advection scheme is of greatsignificance in improving the performance of numerical weather prediction (NWP) models. InNWP models, prediction of scalar variables, such as water substances, always is paid specialattention on keeping their positive-definite characteristics. Also, good scalar advection schemeshould have ability in treating the large spatial variations or discontinuities existing in thedistribution of scalar variables. The appearance of overshoots and undershoots in the solutioncan destroy the original spatial features of scalar variables and mass conservation if a usualadvection scheme is of second-order or higher-order accuracy. On the other hand, highresolution NWP models require much higher accuracy advection scheme, and it becomes moreimportant in cloud-resolving models. This study applies a high-order accuracy andpositive-definite scheme into the GRAPES model. Main purpose of this study is to improvethe forecast skill of the GRAPES model, especially in heavy rainfall forecast during summer.At present, heavy rainfall forecast is still a big challenge in NWP society. The GRAPESmodel developed by CMA suffers such problem. For example, rainfall more than 100 mm/dayis difficult to predict, and the forecasted rain band appears narrower than the observation insummer months. Due to the large horizontal gradient of moisture field over Asian region insummer, it is expected to improve the rainfall forecast through improving the accuracy ofwater substance advection in the model. A new advection scheme named as the piecewiserational method(PRM)is applied here in placement of the original quasi-monotonesemi-Lagrangian scheme(QMSL) utilized in GRAPES model. As presented in Xiao et al.(2004),the PRM is developed based on piecewise rational function, and is of conservative, high-order accuracy, positive-definite and shape preserving characters. The PRM scheme hasbeen applied widely in computational fluid dynamics; it has rather good ability in solvingshock waves. The PRM is a finite-volume scheme which uses the average value of the gridvolumes rather than the grid point values. Due to the convexity preserving nature of therational function, oscillation-less solutions are easy to obtain by using PRM.In this study, comparison studies have been conducted between the PRM and QMSLadvection schemes through the forecast experiments. The 24 hour rainfall forecast has beenmade continuously for three months: June, July and August in 2005. The analysis field ofT213L31 is utilized as the initial values. Through detailed analysis, it is found that the PRMadvection scheme shows obvious advantages over the original QMSL in forecasting therainfall larger than 25 mm/day both for the rainfall amount and occurring location of heavyrainfall.