A modified atmospheric non-hydrostatic model on low aspect ratio grids

Abstract

A B S T R A C TIt is popular to use a horizontal explicit and a vertical implicit (HE-VI) scheme in the compressible nonhydrostatic (NH) model. However, when the aspect ratio becomes small, a small time-interval is required in HE-VI, because the Courant-Fredrich-Lewy (CFL) criterion is determined by the horizontal grid spacing. Furthermore, simulations from HE-VI can depart from the forwardÁbackward (FB) scheme in NH even when the time interval is less than the CFL criterion allowed. Hence, a modified non-hydrostatic (MNH) model is proposed, in which the left-hand side of the continuity equation is multiplied by a parameter d (45d516, in this study). When the linearized MNH is solved by FB (can be other schemes), the eigenvalue shows that MNH can suppress the frequency of acoustic waves very effectively but does not have a significant impact on the gravity waves. Hence, MNH enables to use a longer time step than that allowed in the original NH. When the aspect ratio is small, MNH solved by FB can be more accurate and efficient than the NH solved by HE-VI. Therefore, MNH can be very useful to study cloud, Large Eddy Simulation (LES), turbulence, flow over complex terrains, etc., which require fine resolution in both horizontal and vertical directions.

NTU/PU model simulations and observed flow over mountains

“…The algorithm is stable and does not generate computational modes as shown in Hsu and Sun (2001) and Sun (2011). In addition, using a time-splitting scheme and parallel computing (Hsu et al 2006;Shieh et al 2006Shieh et al , 2011, we also modify the 3D divergence equation as discussed in Sun et al (2012 to suppress unwanted high-frequency sound waves while not damping internal gravity waves in order to increase the time step according to the CFL criterion.…”

“…The semi-implicit scheme developed by Sun (2011) is applied to solve the terms involved in the various wave phenomena, and the advection scheme in Sun (1993) is used to solve the advection terms. Comparisons between the filtered acoustic waves by using the implicit vertical scheme and the modified 3D divergence equation applied in the NTU/PU model was discussed in Sun et al (2012. In addition to its basic dynamic framework, the model takes into account many physical processes, such as land/ocean processes, cloud microphysics, atmospheric turbulence, etc., that are also included in the Purdue Regional Climate Model (Sun et al 2008).…”

Backward Integration of Diffusion Equation

“…Hence, an assigned value of TKE is used here. It is noted that the TKE was explicitly calculated in many atmospheric models, including Purdue Regional Climate Model (Sun and Chern, 1993;Sun et al, 2009;Min and Sun, 2015) and NTU-Purdue Model Sun, 2001, Sun and, and CRESS model (Tsuboki and Sakakibara, 2007;Sun et al, 2012Sun et al, , 2013c, etc.…”

Bernoulli equation and flow over a mountain

“…The detailed equations, physics, parameterizations, and numerical schemes of the model can be found in Hsu and Sun (2001), Sun and Hsu (2005), and Sun (2013). Following Sun et al (2012Sun et al ( , 2013c, we also partially filter the highfrequency acoustic waves to permit a larger time interval while solving for internal gravity waves, since the model uses a time-splitting technique.…”