Super-rotation (SR) independent ofhorizontal diffusion reproduced in a Venus
GCM
Norihiko Sugimoto1, Yukiko Fujisawa1, Nobumasa Komori1,Hiroki Kashimura2, Masahiro Takagi3, and Yoshihisa Matsuda4(1Keio Univ., 2Kobe Univ., 3Kyoto Sangyo Univ., 4Tokyo Gakugei Univ.)

Super-rotation independent of horizontal diffusion reproduced in a Venus GCM,
N. Sugimoto, Y. Fujisawa, N. Komori, H. Kashimura, M. Takagi, and Y. Matsuda,Earth, Planets and Space, (2023), Vol.75, 44, https://doi.org/10.1186/s40623-023-01806-7.

1. Why Venus?
EarthVenus

EarthRadius

6050 km

6378 km

Revolution

224 days

365 days

Rotation

243 days(1.8m/s)

1 day(460m/s)

1 solar day

117 days

1 dayComposition

CO2N2, O2

Albedo0.78

0.3

Surface pres.

92 bar1 bar

Solar heating

雲層Venus

Temperature✓ Very slow rotation✓ Dense CO2 atmosphere✓ Thick cloud layer (45～70km)

Pressure

Altitude

UVobservation

Mystery of the Venus’s atmosphere“Super rotation” (fast zonal flow)
V9 & V10

Altitude (km)100m/s !!
60 times fasterthan surface
rotation rate

✓ The atmosphere circles the planet
about 4 Earth days, much faster thanthe planet's sidereal day of 243 days.

Zonal flow

Schubert et al. (1980)

Venus spins in the opposite direction from Earth (retrograde, or backward, rotation)

Mechanism of the super rotation
1. Mean meridional circulation
MMC (Gierasch 1975)

2. Thermal tide
(Fels & Lindzen, 1986)
Solar moves(a)
Altitude 70 km
cloud layer
Altitude 50 km(b)dissipation by the friction

surfacewest✓ Vertical transport by MMC✓ Horizontal transport by eddies

east✓ Excitation by the solar heating✓ Dissipation by the friction

2. Venus GCMs studies

Qz(+) = Zonal solar heating (strong)
Q3D(+) = 3D solar heating (strong)
NC = Newtonian heating and cooling

Papers

Forcing

Resolution Results

YT2003Qz+

T10L50Super-rotation (SR); uniform at low latitude

YT2004a Qz+

T21L50SR

YT2004b Q3D+

T21L50SR; strong thermal forcing below the cloudYT2006

Q3D+

T21L52SR; strong thermal forcing below 55 km

Ho2007

Qz+, Qz~T21L56

SR; SR is not reproduced for Qz (3 cell)

TM2007

Qt

T10L60SR; equatorial jet

Lee2005

NC~T21L32

Weak SR; short relaxation time of NC

Lee2007

NC~T21L32

Weak SR; short relaxation time of NC

KW2008Qz

T21L60Multiple equilibrium state of U50 & U0 (weak SR)

KW2009

Q3D

T21L60Multiple equilibrium state of U50 & U0 (weak SR)

YT2009

Q3D+

T21L52

SR is not reproduced for realistic Qz

Leb2010

Q3D~T21L50

SR (with topo.); SR is not reproduced for Qz

Leb2016

Q3D~T42L50

SR (with rad.); equatorial jet

YT(Yamamoto & Takahashi), Ho(Hollingsworth et al.), TM(Takagi & Matsuda),
Lee(Lee et al.), KW(Kido & Wakata), Leb(Lebonnois et al.)Sugimoto+2019 GRL: Super rotation reproduced with small vertical viscosity✓ After 500 Earth years (Ey)： Fully developed SR is maintained for 𝜐𝑉 = 0.0015 m2/s
50 Ey

300 EyZonal flow (contour)

Eddy Kinetic Energy (color)

500 Ey500 Ey; from initial SR

Fast SR; 𝜐𝑉 ≤ 0.02 m2/s
Weak SR; 𝜐𝑉 ≥ 0.025 m2/s

(I) Motionless state(II) Super rotation
converge each other⇒ There is no multiple
equilibrium state• Yamamoto & Takahashi (2022): SR in their GCM depends on the horizontal diffusion
30 day; weak

1 day

5 day

0.25 day; strong

The second-order hyper diffusion (Laplacian squared); the same as AFES-Venus

Dependence on the horizontal diffusion in T21 (AFES-Venus)• Relaxation time for horizontal diffusion (∇^4) to the highest wavenumber

1/8 [Eday] 1/4
Mean zonal wind

Energy spectra

1/2

12

4

8-5/3

At least in low-resolution, SR depends on the strength of horizontal diffusion.

This study• Sensitivity check of SR• with several cases of the horizontal diffusion (Hd)• There are robust regions of SR• spectral analysis• with higher resolution• Including thermal tides (wo. Yamamoto & Takahashi 2022, Sugimoto+2019)• may need for larger horizontal diffusion

Experimental setting• AFES-Venus (Atmospheric GCM for the Earth Simulator for Venus)• Resolution: T42L60 (128×64×60) & T159L120 (480×240×120)• Initial state: idealized SR (but also SR is reproduced from motionless state)• Solar heating: Tomasko (1980), Qt / Qz (with/wo thermal tide)• Infrared radiation: Newtonian cooling based on Crisp (1986)• T42Qt: 8 cases of horizontal diffusion from 0.01 to 30 days.
• T159Qt: 12 cases of horizontal diffusion from 0.0001 to 1 day.

• T42Qz: 8 cases of horizontal diffusion from 0.01 to 30 days.
The second-order hyper diffusion (Laplacian squared) term with a diffusion coefficient; 𝝂, 𝝂∆𝟐 = 𝝂𝜵𝟒

Results (T42Qt); Zonal mean zonal flow in latitude-height(a) 0.01 day(b) 0.05 day(c) 0.1 day(d) 0.2 day(e) 0.5 day(f) 1 day(g) 5 day(d) 30 day

From 0.1 to 1 day, SR is almost robust: independent of the horizontal diffusion

Results (T42Qt): Spectral analysis
Dep. of Hd (@70km)

Dep. of z (0.5 day)From 0.1 to 1 day, it might be
OK at 70 km.
But accumulation in smallscales may appear at higher
altitude for 0.5 day.
Too strong horizontal diffusion(0.01 or 0.05 day) will causesome dissipation in large-scales.

Results (T42Qt): Horizontal section (U) at 70 km(a) 0.01 day(b) 0.05 day(c) 0.1 day(d) 0.2 day(e) 0.5 day(f) 1 day(g) 5 day(d) 30 day

0.1 day would be the best choiceResults (T159Qt): Zonal mean zonal wind in lat-z(a) 0.0001 day(d) 0.001 day(g) 0.01 day(j) 0.1 day(b) 0.0002 day(e) 0.002 day(h) 0.02 day(j) 0.5 day(c) 0.0005 day(f) 0.005 day(i) 0.05 day(k) 1 dayFrom 0.0005 to 0.1
day, SR is robust:
independent ofhorizontal diffusion

Results (T159Qt): Spectral analysis
Dep. of Hd (@70km)

Dep. of z (0.05day)

From 0.0005 to 0.1 day, itmight be OK at 70 km.
Black line of T42L60 (T42Qt)
is mostly overlapped to thegood cases of T159Qt.
Too strong horizontal diffusion(0.0001 or 0.0002 day) willcause some dissipation in largescales.

Results (T159Qt): Horizontal section (U) at 70 km(a) 0.0001 day(d) 0.001 day(g) 0.01 day(j) 0.1 day(b) 0.0002 day(e) 0.002 day(h) 0.02 day(j) 0.5 day(c) 0.0005 day(f) 0.005 day(i) 0.05 day(k) 1 day0.01 day in
Kashimura(2019) would
be good.

Discussion• The expressions of the horizontal diffusion (Hd);

Second terms are for zonallyuniform component to conserve
angular momentum.

4th order Hd: Since T159 is 4 times higher resolution of T42, Hd is 44~256 times stronger.
Then, T42 with 1 day is comparable to T159 with 0.004 day (both cases are verified).
In contrast, T159 with 0.02 day is comparable to T42 with 5 day (T42 case is not reliable).

Summary• We investigated how the super-rotation depends on the magnitude ofhorizontal hyper diffusion using a Venus GCM (AFES-Venus) with medium(T42L60) and high (T159L120) resolutions.
✓ In both the runs, we found a parameter range where the structure of fully
developed super-rotation is almost independent of the magnitude ofhorizontal diffusion.
✓ Spectral analysis shows that unrealistically strong super-rotation is developed
when medium-scale disturbances are dissipated by stronger horizontal
diffusion.
✓ On the other hand, artificially weak super-rotation is also realized because
spurious small-scale disturbances are accumulated when the horizontal
diffusion is too weak.
We should carefully check the magnitude of horizontal diffusion by the spectral
analysis and higher resolution runs before conducting Venus GCM simulations.

Recent progress• AFES-Venus (Atmospheric general circulation model For the Earth Simulator for Venus)✓ 3-D Primitive equation on sphere (hydro static balance) without moist processes✓ Resolution: T42L60 to T639L260 (Δx～20 km Δz～0.25 km)…
✓ Rayleigh friction: lowest and above 80 km (sponge layer except for zonal flow)✓ No topography and planetary boundary layer✓ Simplified Solar heating based on Tomasko et al. (1980)✓ Simplified Infrared radiative process by Newtonian cooling based on Crisp (1986)✓ Idealized initial super rotation with realistic temperature (static stability) distribution• 16 papers: Baroclinic instability (Sugimoto+2014, JGR & GRL), Polar vortex with coldcollar (Ando+2016, Ncom; 2017, JGR), Thermal tide (Takagi+2018, JGR; Suzuki+2022,JGR), Planetary scale streak structure (Kashimura+2019, Ncom), Super rotation(Sugimoto+2019, GRL), Static stability (Ando+2020, SciRep; 2022, JGR), Gravity wave
from thermal tide (Sugimoto+2021, Ncom), 4-day and 5-day waves (Takagi+2022, JGR),
Cloud physics (Ando+2020, 2021, JGR)…

Recent progress (cont.)*Local Ensemble Transform Kalman Filter#Observing System Simulation Experiment• ALEDAS-V (AFES LETKF* Data Assimilation System for Venus)✓ First data assimilation system for the Venus atmosphere• 9 papers: First check (Sugimoto+2017, SciRep), Vex UVI wind (Sugimoto+2019, GRL),OSSE# for cross-link radio occultation (Sugimoto+2020, JSCE, Fujisawa+2023, Icarus),
OSSE for Kelvin wave (Sugimoto+2021, 2022, Atmos.), First analysis of Akatsuki UVIwind (Fujisawa+2022, SciRep), OSSE for Akatsuki LIR temperature (Sugimoto+2022,GeoSciLett), Cold collar (Ando+2023, JGR)…

*Ｔ42Ｌ60の4年積分；最後の1年(360データ)分を平均した東西平均風(Qt)Results (T42qz) zonal mean zonal flow in lat-z(a) 0.01 day(b) 0.05 day(c) 0.1 day(d) 0.2 day(e) 0.5 day(f) 1 day(g) 5 day(d) 30 day

From 0.05 to 1 day SR is robust: independent of horizontal diffusion

*最後の一年平均

Results (T42qz) spectral analysis(a) Dep. of hd (@70km)(b) Dep. of z
(0.5 day)(c) Dep. of t(0.5 day)

*最終日のスナップショット：高波数の溜まりを確認

Results (T42qz) horizontal section at 70 km(a) 0.01 day(b) 0.05 day(c) 0.1 day(d) 0.2 day(e) 0.5 day(f) 1 day(g) 5 day(d) 30 day

0.1 would be the best choice