WRF is a mesoscale model fully compressible and non-hydrostatic (optional: hydrostatic for calculation) and the order truncation error is a major source of uncertainty during the model calculation. So reducing this error we always approach higher-order accuracy methods. In WRF-ARW there are the methods: RK2 and RK3 available but not RK4 which has higher accuracy.
Dear Jaydeep Singh
WRF relies on a three-stage, third-order Runge-Kutta scheme to advance in time the “slow processes”. The forward-backward and trapezoidal schemes are used to integrate the fast processes (the effective order of the method is second, regardless if we use a third or a fourth order Runge Kutta scheme). Considering this fact, it is not practical to use a higher order and more expensive RK4 for the slow processes (it will lead anyway to the overall second order time integration scheme).
In fact, in order to maintain a consistent order for time integration of low and high frequencies, we should use a two stage, second order method (RK-2). The entire problem is therefore related to investigation of the effective order of the time splitting applied in WRF.
I have attached a paper which further clarifies the problem of time integration in atmospheric models. According to the Authors, it is evident that the issue of time integration methods for atmospheric models is still open.
In addition to my first answer, I would like to include some references. The splitting algorithm used for the time stepping in WRF is described in a very well-known paper by Wicker and Skamarock: Time-Splitting Methods for Elastic Models Using Forward Time Schemes (MWR vol. 130, page 2088) discussing all the options considered in the model including the order of approximation for the space derivatives.
Please consult the following quote (page 2089):
“Runge–Kutta time integration schemes of second or higher order can be constructed from basic Taylor series. Gear (1971, 34–35) shows that second-order RK schemes have one free parameter and third-order schemes have two free parameters. Hundsdorfer et al. (1995) discusses the relative merits of different RK schemes of the same formal order in time. To facilitate the incorporation of the splitting, the following third- order RK time integration algorithm using the flux differencing (2) is used as the basis for our time-split method“
>End quote
The reasons for selecting the third order scheme are explicitly discussed in Hundsdorfer et al. (1995).
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