Using hybrid isentropic-sigma vertical coordinates in nonhydrostatic atmospheric modeling

Transcription

1 Using hybrid isentropic-sigma vertical coordinates in nonhydrostatic atmospheric modeling Michael D. Toy NCAR Earth System Laboratory/ Advanced Study Program Boulder, Colorado, USA 9th International SRNWP Workshop on Nonhydrostatic Modeling Bad Orb, Germany May 16, 2011 NCAR is sponsored by the National Science Foundation

2 Background z coordinates The Eulerian mesh height z x

3 Background Isentropic coordinates height The quasi-lagrangian mesh : - Lagrangian in vertical - Eulerian in horizontal - Formulated by Starr (1945) increasing! Material surfaces! materially conserved for adiabatic processes -! is zero - no cross-coordinate mass flux x

4 Outline System of equations 2D mountain wave simulation Semi-implicit time differencing for acoustic mode stability: --! vs. " coordinates 3D supercell thunderstorm simulation Summary Next steps

5 Nonhydrostatic system of equations in a generalized vertical coordinate (") Horizontal momentum Vertical momentum Mass continuity Thermodynamic energy Geopotential energy Dv Dt + f k! v = " 1 # $ p + 1 &p % m &% $ z + F % Dw Dt =! 1 "p m "#! g + F z " # $!m!t % & ' ( + ) ( *(mv) +!!( (m &() = 0!t + v #$" + &%!% = Q &!t + v #$" + &%!% = wg Diabatic heating Geopotential! " gz

6 Nonhydrostatic system of equations in a generalized vertical coordinate (") Generalized vertical velocity Material time derivative Mass variable (pseudo-density) &! " D! Dt D Dt! % " & ' "t + v #$ ( ) * m! " #z #$ + + &+ " "+

7 Let " be a hybrid vertical coordinate Hydrostatic models Bleck (1978) Konor and Arakawa (1997) hybrid coordinate Nonhydrostatic models Skamarock (1998) He (2002) Zängl (2007) Toy and Randall (2009)! " z # z $ S = 0 at surface (S) % z T # z S & = 1 at model top (T)

8 Downslope windstorm simulation Boulder, CO -- Jan Isentropes (colors+black lines) and model levels (bold red lines) at t = 70 min Height (km) x (km) 296!x =1000 m

9 Downslope windstorm simulation Boulder, CO -- Jan Isentropes (colors+black lines) and model levels (bold red lines) at t = 180 min Height (km) x (km)!x =1000 m

10 An adaptive grid Coordinate surface smoothing Arbitrary Lagrangian-Eulerian (ALE) method Details in Toy and Randall (2009) Isentropes 376 Model levels mass flux m &! ( ) 312 ( m &! ) " smoothing & ( ( ' ( ( ) # 4 z # 2 z ( $z) % $z k+1 ( $z) k+1/2 ( ) k

11 A comparison in the transport of a passive tracer HYBRID COORDINATE Isentropes SIGMA COORDINATE Isentropes z (km) z (km) Tracer concentration Tracer concentration 3-hour simulation

12 Semi-implicit time differencing:! vs. " coordinates For the numerical stability of vertically propagating acoustic waves Terms in red are responsible for acoustic modes and are treated implicitly, i.e., they involve n+1 time step! coordinates Horiz. momentum Vertical momentum Continuity Thermodynamic energy

13 Semi-implicit time differencing:! vs. " coordinates For the numerical stability of vertically propagating acoustic waves Terms in red are responsible for acoustic modes and are treated implicitly, i.e., they involve n+1 time step! coordinates " coordinates Horiz. momentum Vertical momentum Continuity Thermodynamic energy Geopotential energy

14 Supercell thunderstorm simulation Cloud-water mixing ratio at t = 30 min Hybrid-coordinate model *!-coordinate model * WRF model ** (Eulerian mass coordinate) Initial sounding from Weisman and Klemp (1982) with quartercircle shear at lower levels!x =2 km 40 levels g kg -1 * No rain production ** Autoconversion turned off

15 Supercell thunderstorm simulation Maximum updraft speed (m s -1 ) Hybrid coordinate! coordinate max(w) (m s -1 ) WRF model!!! Time (min)

16 Supercell thunderstorm simulation Hybridcoordinate model Isentropes!-coordinate model t = 30 min g kg -1

17 Supercell thunderstorm simulation Hybridcoordinate model Isentropes Model levels!-coordinate model t = 30 min g kg -1 Description of latent heating and handling of vertical coordinate in Toy (MWR, 2011) (in press)

18 Hybridcoordinate model Supercell thunderstorm simulation Cross-coordinate mass flux (kg m -2 s -1 ) Near-zero vertical mass flux!-coordinate model t = 30 min (kg m -2 s -1 )

19 Summary Fine-scale nonhydrostatic motion was simulated using a hybrid QL/Eulerian vertical coordinate model A reduction in the numerical error associated with vertical transport of a tracer was demonstrated The cross-coordinate vertical mass flux in the environmental air near a convective disturbance is significantly reduced with the hybrid coordinate Next Steps Add rain to the microphysics scheme Perform further testing to quantitatively determine the overall benefit of using the hybrid-coordinate over the conventional Eulerian coordinate NCAR is sponsored by the National Science Foundation