ORBIT-SPIN COUPLING AND MARTIAN EARLY-SEASON GLOBALSCALE DUST STORMS: CHALLENGES AND OPPORTUNITIES
J. H. Shirley , TORQUEFX, Simi Valley, CA, USA, J. M. Battalio, Department of Geology and Geophysics,
Yale University, New Haven, CT, USA, D. M. Kass, Jet Propulsion Laboratory, Pasadena CA, USA, A.
Kleinböhl, Jet Propulsion Laboratory, Pasadena CA, USA, N. G. Heavens, Space Science Institute, Boulder,
CO, USA, S. Piqueux, Jet Propulsion Laboratory, Pasadena CA, USA, S. Suzuki, Jet Propulsion Laboratory,
Pasadena CA, USA, D, J. McCleese, Synoptic Sciences, Pasadena, CA, USA, J. T. Schofield, Jet Propulsion
Laboratory (retired), Pasadena CA, USA.
Introduction: The seven known Martian earlyseason global dust storms (GDS) of the historic record have at least two things in common: In addition
to their early inception dates (Ls<235°), all seven
occurred during intervals when Martian orbit-spin
coupling torques were rapidly changing (Fig. 1).

of Ls=201° (versus an observed date of Ls=208°).
Orbit-spin coupling accelerations (Shirley, 2017)
were included within the dynamical core of the
MarsWRF MGCM for that study. Century-long
model runs performed in this configuration replicated
the historic record of Mars years with and without
GDS with a hindcast success rate of nearly 80%
(Shirley, Newman et al., 2019). The temporal alignment between MGCM simulations and historic GDS
observations is significantly improved by the addition of orbit-spin coupling accelerations (Mischna &
Shirley, 2017; Shirley, Newman et al., 2019).
Orbit-spin coupling: A novel form of coupling
between the orbital and rotational motions of extended bodies is given by:
CTA = - c (  ωα)  r
Here CTA stands for “coupling term acceleration”, L is the orbital angular momentum of a solar
system extended body with respect to an inertial
frame, ωα is the angular velocity of the planetary
rotation, and r is a position vector identifying some
specific location on or within the extended body. The
leading term (-c) is a coupling efficiency coefficient,
which is analogous to the coefficient of friction employed in mechanical problems. The specified acceleration field takes the form of a reversing torque,
with complex time variability, and with axis lying in
the equatorial plane of the affected body (Fig. 2).

Fig. 1. The second time derivative of Mars’ orbital angular momentum, a proxy for the rate of
change of orbit-spin coupling torques, for Mars years
with early-season GDS (1877, 1909, 1977, 1982,
1994, 2001, 2018). After Fig. 8 of Shirley et al.
(2020). Dotted symbols indicate solar irradiance.
Numerical modeling investigations have had limited success in simulating early-season GDS. One
notable success is found in the study by Newman et
al. (2019), where a GDS was correctly simulated in
the 1982 model year, with a modeled inception date

Fig. 2. CTA (surface) acceleration vectors, comprising a torque (here, on the Earth) about the axis
indicated (see http://arxiv.org/abs/2112.02186).

The reader may visualize the planet rotating beneath, or within, the acceleration field of Fig. 2.
When the forcing function ( ) changes sign, the surface vectors of Fig. 2 will shrink and disappear,
thereafter re-emerging with reversed directions.
While the coupling efficiency parameter c may appear arbitrary, the results of the investigations performed to date indicate that nature does indeed prefer
and employ a non-zero value of c in this connection.
c helps to quantify the fraction of the orbital momentum that may participate in the excitation of dissipative geophysical variability (Shirley, 2017).
Somewhat misleadingly, in Mischna & Shirley
(2017), the accelerations were characterized as a
small effect, since the coupling is, from a planetary
dynamical perspective, a weak one. Simulations performed in the same study revealed a modulation of
Martian global wind speeds by factors of up to
~20%. This cannot accurately be described as a small
effect!
The prior numerical modeling efforts by Mischna
& Shirley (2017) and Newman et al. (2019) were
barely able to scratch the surface, as these were hampered by limited funding and other issues. Important
metrics, such as the time variability of atmospheric
momentum and energy, were neglected. The spatial
grid sizes employed were (at 5° x 5°) too coarse to
allow investigation of smaller scale phenomena.
Thus, multiple opportunities now exist to rapidly
advance our understanding through new modeling.
Here we highlight two insights gained after the prior
modeling studies were completed, and pose a new
question pertaining to the triggering processes of
early-season GDS (Fig. 1).
Frictional damping of an intensified
meridional overturning circulation (MOC): Intermittent intensification of Hadley-type meridional
circulation cells was recognized as a key consequence of CTA forcing of the large-scale circulation
in Mischna & Shirley (2017). The intensification
may be characterized as a “diagnostic observable.”
We ask: What is the time required to go from the
spun-up, or loaded, atmospheric state, to an unloaded, unforced condition, under the assumption of a
rapid disappearance of the driving accelerations?
Calculations addressing the relaxation time of an
intensified Hadley-type circulation are presented in
Shirley et al. (2020). Figure 3 illustrates the source
data (a) and the system diagram (b) for the calculation. Figure 3a illustrates the difference between a
forced simulation and a control simulation; here the
brown colors represent the intensification of a zonally averaged clockwise MOC, as simulated by
MarsWRF, averaged over an interval of 20° of Ls,
prior to the inception of the 1982 GDS. The cartoon
of Fig. 3b represents the same mean zonal circulation. We modeled the retardation of this circulation
by surface friction forces as a function of time. Space
limitations prevent a complete description of the

model; however, the following high-level attributes
are of interest. The linear velocity of the forced circulation near the surface exceeds than that of the
control simulation by ~3.6 m s-1, and the sequestered
energy associated with the intensified MOC is ~7 x
1017 J. Employing diurnally averaged values for surface wind stresses of 0.001 Nm-2, from Mischna &
Shirley (2017), we obtained a damping time of 5.1
sols. A number of caveats are listed in Shirley et al.
(2020); we nonetheless consider that a frictional
damping time of O(10) sols is reasonable.

Fig. 3. (a) Zonal mean meridional stream function
differences plot (forced – control) for the MY 15
simulation of Mischna & Shirley (2017). The scale
gives units of 109 kg s-1. Clockwise motions are represented in brown shades. The boxed area corresponds in latitude to the overturning cell sketched in
(b). Topography was ignored for the calculations.
Characterizing the spin-down phase: The
above scenario corresponds to periods when the forcing is greatly diminished, but in which momentum
has previously been cumulatively added to the largescale circulation. This corresponds to zero-crossings
of the dL/dt waveform, and to extrema of the second
derivative (Fig. 1). A rapid re-equilibration of the
atmospheric wind and pressure fields may occur during such episodes. Atmospheric vorticity may be
enhanced. Further, the extreme topographic relief of

the Martian surface may be expected to channel the
resulting large-scale flows. Mars exhibits a number
of preferred storm tracks. Flushing storms observed
within the storm tracks frequently have durations of
O(10) sols. Lastly, in addition, we recognize that the
above frictional damping timescale corresponds reasonably well to the observed duration of the 2018
“triggering” regional storm (Shirley, Kleinböhl, et
al., 2019), as illustrated here in Fig. 4.

(2020). The historic record (1877-present), together
with solar system dynamical considerations, allows
the identification of future “torque episodes.” Objective rules for the identification of torque episodes are
listed in Tables 6 and 9 of Shirley et al. (2020). Figure 5 illustrates torque episodes identified within the
timespan of MY 38.

Fig. 5. Dynamical waveforms and identified
torque episodes for Mars Year 38. The black dotted
line illustrates the d2L/dt2 waveform for MY 25, a
GDS year (2001). The dL/dt waveform has been
scaled by a factor of 10-8 for plotting. The yellow bar
indicates an early-season torque episode, while purple identifies a post-solstice torque episode.

Fig. 4. MCS atmospheric dust extinction, within
the Acidalia corridor, during the 2018 “triggering”
regional storm (after Shirley, Kleinböhl, et al., 2019).
Pre-storm conditions are shown on 29 May, while the
decay phase of the regional storm is well advanced
by 9 June. Dust layer peak altitudes increased from
~35 to ~60 km in this episode.
MCS observations confirm the existence of a
strongly enhanced regional-scale Hadley circulation
during the earliest days of the 2018 GDS (Shirley,
Kleinböhl, et al., 2019; Fig. 4). Whether or not these
observations may be explained by an atmospheric
spin-down and re-equilibration process is an open
question of considerable interest.
Challenges and opportunities: Will an earlyseason global-scale dust storm occur in 2025?
Advance forecasts, addressing the likelihood of future GDS in MY 35-40, are provided in Shirley et al.

Figure 5 shows a close correspondence between
the d2L/dt2 waveforms for 2025-26 and 2001, an
early-season GDS year (MY 25). The early-season
torque episode of Fig. 5 begins on 24 October 2025
(Ls=160°). Shirley et al. (2020) conclude that this
represents the highest likelihood interval for a future
GDS between now and MY 40. MY 38 is likewise
in-family with the three GDS years plotted in the
lower panel of Fig. 1 (1909, 1977, 2001). All three
of these GDS originated in Mars’ southern hemisphere, in the vicinity of Hellas and/or Noachis. Priority should be given to observing campaigns that
can comprehensively characterize atmospheric phenomena during this future torque episode.
We have already noted several deficiencies of
past numerical modeling efforts. In addition, we note
that the triggering mode illustrated in Fig. 1 had not
yet been recognized, and that our temporal sampling
interval (20° of Ls) was too coarse to resolve pulses
of frictional damping in association with episodes of
circulatory reorganization. The c value previously
employed may in addition have been underestimated.
Atmospheric numerical models are unlikely to
correctly represent atmospheric processes if some
key physics is omitted. This applies to model studies
employing data assimilation, as well as to investigations not constrained by concurrent observations.

Incorporation of orbit-spin coupling accelerations
within state-of-the art MGCMs is strongly recommended.
Annotated Bibliography: