The Martian global dust storm (GDS) of 2018 began soon after the southern spring equinox, which is quite early in the dust storm season. The origins of early-season GDS, including those of 1977, 2001, and now 2018, have been mysterious, as atmospheric dynamical investigations and numerical modeling experiments have been unable to explain or reproduce the timing of these events. We employ a newly expanded catalog of historic Martian GDS for our investigation, which includes 2018 and the telescopically observed equinoctial dust storms of 1877 and 1909. All of the GDS of this catalog took place either (1) when orbit-spin coupling torques on the Martian atmosphere were near peak values or (2) near times when the orbit-spin coupling torques were changing most rapidly. The second category, here termed “Mode 2,” includes all six of the equinoctial GDS of the historic record, including 2018. Recognition of the existence of two triggering modes for GDS occurrence leads to a significant improvement in temporal resolution for both hindcasting and forecasting. Orbit-spin coupling now provides explanations for the late-season inception dates of the 1924 and 1973 storms, as well as for the equinoctial events. We provide conditional forecasts, with sub-seasonal time resolution, for GDS occurrence and non-occurrence in Mars years 35 through 40. We introduce a detailed working hypothesis for the genesis of equinoctial GDS that may be validated through numerical modeling. The characteristic timescale for frictional damping of an intensified Martian Hadley circulation is estimated to be O(10) sols.

Key Points

We introduce an expanded catalog of Martian planet-encircling dust storms including pre-space-age observations and the 2018 storm
Global dust storms occur near times when orbit-spin coupling torques are peaking and near times when torques are changing most rapidly
The 2018 storm began during the first of two torque episodes that were each separately capable of triggering a global dust storm that year

Plain Language Summary

Spectacular planet-encircling dust storms occur in some Mars years, but not in others. Five Mars years (and 11 Earth years) elapsed between the two most recent global dust storms (GDS) of 2007 and 2018. Until recently, the fundamental causes of the inter-annual variability of GDS occurrence were completely unknown. Since 2015, a series of studies have shown a strong relationship linking changes in the orbital motion of Mars with the occurrence of GDS. GDS preferentially occur when Mars is gaining orbital angular momentum, at the expense of other members of the solar system family, during the southern summer dust storm season on Mars. The underlying orbit-spin coupling hypothesis identifies a torque on the Mars atmosphere that varies strongly with time. GDS tend to happen at times when the torque reaches peak values and also at times when the torque is changing most rapidly. The GDS of 2018 falls in the latter category. Compared to past investigations, much higher precision is attained, in this study, with respect to the question of the timing of these storms within a given Mars year. The new results are important for at least two reasons. First, they will permit more accurate Martian weather forecasts to be made for future years. These may be helpful in the planning of future Mars missions. The results in addition lend impetus to a new scientific question of some interest: Does orbit-spin coupling give rise to variability with time of the atmospheric circulations of planets other than Mars?

1 Introduction

The Martian planet-encircling dust storm of 2018 did not come as a complete surprise. Advance forecasts calling for the occurrence of a global-scale dust storm in 2018 appeared in a series of published studies beginning in 2015 (Shirley, 2015; Mischna & Shirley, 2017; Shirley & Mischna, 2017; Newman et al., 2019). Earlier forecasts were based on empirical studies of solar system dynamical relationships and statistical investigations, with additional support from theoretical work (Shirley, 2017). Two studies employing century-long simulations with atmospheric global circulation models followed (Mischna & Shirley, 2017; Newman et al., 2019). Conditions favoring the occurrence of a global-scale dust storm during the 2018 dust storm season were simulated in both of these studies. Within the context of these studies, the most surprising aspect of the 2018 event was the very early seasonal inception date of the storm. Telescopically observed initial dust storm activity for the 2018 storm began as early as 30 May (L_s ~ 184°), only about a week after the southern spring equinox.

1.1 Equinoctial Global Dust Storms: An Enigma

The seasonal timing of known Martian planet-encircling dust events is illustrated in Figure 1. The center of the figure corresponds to the time of Mars' perihelion; at that time, the solar irradiance attains its maximum value. As indicated in Figure 1, the 2018 event is one of six such storms that started during the first few weeks and months of the dust storm season. These storms began just prior to the time of a major seasonal re-organization of Mars' large-scale circulation; the transition from an equinoctial, twin Hadley cell configuration to the single-cell pattern characteristic to the solstice seasons typically occurs at about L_s = 210° (Kass et al., 2016, Figures 1–3; Barnes et al., 2017, Figure 9.9). (For reference, and as tabulated later, the areocentric longitude corresponding to the inception date of the latest equinoctial event illustrated in Figure 1 [i.e., 1982] was L_s = 208°.)

Details are in the caption following the image — **Figure 1**
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Distribution of global-scale dust storms over the Mars year from aphelion to aphelion (updated; after Shirley, 2015). Time in Earth years is on the abscissa, as this provides a uniform timescale (unlike the solar areocentric longitude L_s, which will be employed hereafter). The dust storm season is identified as the interval between L_s = 160° and 340°, wherein the solar irradiance is ≥600 W m⁻². Also shown is a representative 1-year atmospheric pressure record (scale at right), from the Viking 1 Lander. Peak atmospheric pressure occurs near the time of the southern summer solstice, which lags perihelion by ~20° of L_s. Further discussion and additional information is provided below in section 2.

The underlying mechanisms responsible for the occurrence of equinoctial planet-encircling dust storms on Mars are not yet fully understood. As indicated in Figure 1, the solar irradiance at this season is much reduced, in comparison with the irradiance Mars receives at perihelion. (Atmospheric modeling studies confirm that the vigor of the large-scale circulation depends strongly on the solar energy input to the system.) Similarly, the atmospheric surface pressure, near the time of the southern spring equinox, is substantially reduced (by ~20%) from its annual peak value, as also illustrated in Figure 1. Surface wind stresses (required for lifting dust from the surface into the atmosphere) are proportional to the atmospheric density, which is in turn proportional to the pressure (cf. Mischna & Shirley, 2017, equation (1)).

The above factors, among others, contribute to the difficulty of simulating planet-encircling dust storms within Mars global circulation models (MGCMs) at this season. Prior modeling studies of global dust storm (GDS) occurrence have been unable to reproduce large dust storms starting before L_s = 200° (Basu et al., 2004, 2006; Kahre et al., 2006; Newman et al., 2002a, 2002b; Newman & Richardson, 2015), even when orbit-spin coupling accelerations have been included (Mischna & Shirley, 2017; Newman et al., 2019).

1.2 Incorporating Historic GDS Recorded in Telescopic Observations

For the present study, we wish to employ a catalog of storm years and storm-free years that is as complete as possible. Prior investigations of the influence of orbit-spin coupling on GDS occurrence have made use of a catalog of Martian storm years derived mainly from the work of Martin and Zurek (1993) and Zurek and Martin (1993; hereinafter, ZM93), supplemented by recent events, including those of 1994, 2001, and 2007. The criteria for identifying pre-space-age GDS on Mars employed in ZM93 heavily relied on photographic evidence, with less emphasis given to observational reports by terrestrial telescopic observers. Much additional information regarding the history of Martian dust storm occurrence has become available since the publication of ZM93; in particular, an extensive compilation of telescopic observations appeared in 1999 (McKim, 1999; hereinafter, M99). Our catalog (described in section 2) accordingly includes two additional planet-encircling events (in 1877 and 1909) for which we have strong supporting evidence from the telescopic record. Brief descriptions of the newly added events are found in section 2 of this paper.

The approach and rationale for the present analysis are detailed in section 3. This section includes a brief review of the orbit-spin coupling hypothesis (Shirley, 2017; hereinafter, S17) as it applies to the circulation of the atmosphere of Mars. New calculations addressing timescales for frictional damping of intensified Martian Hadley circulations are also provided in section 3. This is followed in section 4 by the presentation of new results, involving an extensive re-classification (with respect to prior work) of the historic catalog of Martian GDS years and years known to be free of global-scale storms. Two different modes of forcing for global-scale dust storms are now recognized. Mode 1 forcing involves a cumulative incremental loading of the circulation of the atmosphere by angular momentum transferred from the reservoir of the planetary orbital motion, as described in earlier studies (Mischna & Shirley, 2017; hereinafter, MS17; Newman et al., 2019; hereinafter, N19). The GDS of 1971, 1973, and 2007 occurred under Mode 1 forcing conditions. Mode 2 forcing is identified with times when the orbit-spin coupling torques are changing most rapidly. We show that 10 of the 14 currently known Martian global-scale dust storms have occurred under Mode 2 forcing conditions.

Section 5 of the paper introduces and describes a working hypothesis for Mode 2 storm triggering. Pertinent spacecraft observations of the 2018 GDS are reviewed, to provide context for a detailed discussion of the triggering process of the 2018 GDS. In section 6, we digress briefly from questions of storm triggering to introduce new data from telescopic observations describing surface albedo changes engendered by the 2018 storm.

Certain implications of the results of this investigation, together with recommendations for further work, are summarized in section 7. The prospects for global-scale dust storm occurrence during the upcoming dust storm seasons of the years 2020 through 2030 (Mars years 35–40, in the system of Clancy et al., 2000; Piqueux et al., 2015) are discussed in section 8. Conclusions are detailed in section 9.

2 The Historic Record of Martian Global-Scale Dust Storms and GDS-Free Years

Table 1 lists Mars years with planet-encircling and global dust events. (We make no distinction between these categories here. Restricting our attention to the storms known to have completely obscured all latitudes of the planet would greatly reduce the size of the sample.) As previously noted, this catalog was originally drawn from ZM93, with more recent events added (Shirley, 2015; Shirley, Newman, et al., 2019). Detailed descriptions of the individual storms will not be provided here, as these may be found in the above-mentioned papers, in the references included therein, and in other sources, such as the compilation by M99. We will mention key features of several of the listed GDS, at appropriate times, in the sections that follow.

Table 1. Planet-Encircling Dust Storms on Mars, as Illustrated in Figure 1

Year	Mars year	L_s	Calendar dates	Inception date	P ratio	φ_dL/dt	Polarity
1877	−41	186	8 May to 4 Aug	1877.351	0.83	23	T₀
1909	−24	204	3 June to Sept	1909.414	0.88	194	T₁₈₀
1924	−16	310	5 Dec to Jan	1924.962	0.92	93	(+)
1956	1	249	19 Aug to Nov	1956.631	0.99	144	(+)
1971	9	260	22 Sept to Jan	1971.723	1.00	93	(+)
1973	10	300	13 Oct to Dec	1973.808	0.95	44	(+)
1975	11	270	14 July to Sept	1975.532	0.99	303	(−)
1977	12	204	15 Feb to April	1977.123	0.87	233	(−)
1977	12	268	27 May to Oct	1977.233	1.00	233	(−)
1982	15	208	October	1982.789	0.90	82	(+)
1994	21	201	14 Jan to July	1994.038	0.87	70	(+)
2001	25	185	26 June to Oct	2001.482	0.82	272	(−)
2007	28	262	22 June to Oct	2007.471	1.00	82	(+)
2018	34	184	30 May to Aug	2018.460	0.82	65	(+)

Note. The first five columns describe the calendar dates and Martian calendar years (after Clancy et al., 2000; Piqueux et al., 2015) of storm inception and duration. The final three columns contain data that will be referenced later in this paper. Column 6 has the ratio of the atmospheric surface pressure at the storm inception date to the annual peak surface pressure value (see the pressure curve of Figure 1). The phase (φ_dL/dt) and waveform polarity values (column 8) describe aspects of the forcing function dL/dt as introduced and described in SM17. Definitions of these quantities are found in section 3.1 below.

The adopted inception date of the 1994 storm in our earlier publications (cf. Shirley, 2015) has been corrected. The date given previously (L_s = 254°) referred to the time when mature-phase atmospheric temperatures were attained (Wolff et al., 1997). We now provide a range of possible values for the inception date (from L_s = 220° to L_s = 245°). We arrive at this estimate through the following considerations: (1) Clancy et al. (1994) and Clancy et al. (2000) indicate that while no terrestrial microwave observations of Mars were obtained between L_s = 200° and L_s = 254°, the decay phase of the storm, ending at ~L_s = 312°, was reasonably well resolved. (2) We also recognize that the longest-duration GDS in the historic catalog extend for no more than ~90° of L_s. This suggests that the earliest reasonable inception date for the 1994 storm is ~L_s = 220°. (3) In order for mature-phase temperatures to be observed by ~L_s = 254°, it is unlikely that the GDS may have begun later than ~L_s = 245°. In Figure 1, we have thus plotted the 1994 event at L_s = 232°, near the midpoint of the range thus determined. These considerations suggest that the 1994 storm began well after the seasonal date of the transition between the twin-cell (equinoctial) and single-cell (solsticial) Hadley circulations, which occurs at ~L_s = 210°.

A second difference separating the catalog of Table 1 from those employed in previous studies lies in the inclusion of two historic storms (1877 and 1909) that were documented solely by visual observations. We describe the rationale for including these storms in our updated catalog in section 2.1 below.

A third important difference between the catalog of Table 1 and the corresponding lists in prior papers (Shirley, 2015; Shirley & Mischna, 2017; Shirley, Newman, et al., 2019) is found in the inclusion here of 1975 as a GDS year. ZM93 did not discuss Martian dust storm activity in this year (which falls 1 year prior to the Viking Missions). Nonetheless, an encircling storm was recorded and described by terrestrial observers (M99). A brief description of some key observations is provided in section 2.1.

Statistical evaluations of the degree of randomness found in the occurrence times of planet-encircling dust storms (as defined by the phase values in column 7 of Table 1) have been performed in three prior investigations (Shirley, 2015; Shirley & Mischna, 2017; Shirley, Newman, et al., 2019). A slightly different catalog of Mars years was used for each of these evaluations, as the number of years with known outcomes grew from n = 20 in 2015, to n = 21 in 2017, to n = 22 in 2019. Monte Carlo methods were employed in Shirley (2015) and in Shirley, Newman, et al. (2019), while the investigation by Shirley and Mischna (2017; hereinafter, SM17) made use of Schuster's test (a standard test for assessing the degree of randomness in series of angular phases). The Mann–Whitney test was employed in MS17 to assess the significance of modeled differences in surface wind stresses when comparing forced versus control run outcomes. Statistical significance at the 95% level or better was found in all of these investigations.

2.1 Relevant Telescopic Observations of Historic (and Recent) Martian Dust Storms

The first telescopic observation of an identifiable feature on Mars was recorded by C. Huygens in a drawing made in 1659. Huygens soon after measured the rotation period of Mars, by tracking the motion of the dark albedo feature that was later to be named Syrtis Major. Knowledge of Mars' rotation allows the calculation of the Martian meridian of longitude that will appear at the center of the Martian disk during any given period of observation, termed the CML. Together with other visual cues, including the bright polar caps, the color of the body, and Martian albedo markings, it is possible to confidently identify the geographic positions of anomalous or changing features on the Martian surface, such as dust clouds and water ice clouds, when observing conditions are favorable. Due to the similarity of the rotation rates of Mars and the Earth, it is helpful to compile and combine the observations from observers on different continents, in order to build up a complete picture of Martian surface conditions at all longitudes.

More than 100 observers from around the Earth contributed observations to the clearinghouse maintained by the British Astronomical Association during the recent (2018) apparition of Mars (https://britastro.org/node/10908). The earliest report describing the storm inception comes from a summary posted on 8 June 2018. “Images on May 30 by Morales had first shown a patch of bright dust at the SE of Mare Acidalium, covering part of it together with E. Achillis Pons. On May 31 the bright yellow cloud had greatly expanded, and it was now a striking feature upon the images by Boudreau, Maxson, Morales and others.” This location agrees closely with that provided in the weekly MRO/MARCI Mars Weather Report for 28 May to 3 June 2018 (Malin et al., 2018; see also Sánchez-Lavega et al., 2019). The normal practice for identifying the start times of Martian storms in telescopic observations is to employ the date of the start of telescopically observed dust activity (McKim, 2012).

As previously noted, we are here principally concerned with obtaining a listing of historic Martian planet-encircling dust storms that is as complete as possible. On the basis of archival data, some of it recently discovered (McKim et al., 2009), we have added three “new” GDS to the earlier compilation of Shirley, Newman, Mischna, and Richardson (2019). These are the GDS of 1877, 1909, and 1975, as already given in Table 1. For completeness, we next briefly summarize the observational evidence pertaining to these events. Positional information about dust storms observed telescopically is normally given with reference to Martian albedo features. For consistency and clarity, we are therefore obliged to use the old telescopic nomenclature given (for example) in the IAU map of 1957 (and as displayed in Appendix VII of M99).

2.1.1 The 1877 Storm

Strong evidence for the existence of this event was uncovered in 2009, with the discovery of a “lost” notebook of E. L. Trouvelot, one of the most accomplished observers of the time, at Paris Observatory (McKim et al., 2009). The 1877 event occurred well before opposition, and observation was therefore hampered by the small disk diameter. However, drawings made before the start of the event clearly showed recognizable albedo markings. Throughout the event, the dark collar around the south polar cap remained visible, so we assume that dust never covered the cap. The first indications of obscuration were made in apparently poor seeing on 8 May (L_s = 184°). During a much better view on 18 May (L_s = 190°), there was no doubt that major obscuration had already occurred, and a start date of 8 May seems realistic, as the storm must have been at least 1 week old on 18 May.

Trouvelot's drawings showed only the faintest features until late July. During this time, the south polar cap and its dark collar were essentially the only visible features. The duration of the event, from 8 May to 4 August (L_s = 239°), is further indicative of the occurrence of a planet-encircling storm in 1877.

2.1.2 The 1909 Storm

The 1909 event had definitely commenced by 3 June (L_s = 204°) when Solis Lacus had already become heavily obscured, according to observations by P. Lowell and E. C. Slipher (M99). Activity may have begun in NW Hellas-E. Noachis on or shortly after 27 May. Veiling by widespread yellow dust was confirmed on 8 June by G. & V. Fournier. Encirclement appeared to have been achieved in ~13 days. Dust quickly spread to all longitudes, but the high south latitudes above approximately −60°, including the S. polar cap, were not affected. Throughout August, the storm was gradually but irregularly clearing. The event was essentially over by 20 September (L_s = 273°). Aside from photographic evidence by E. E. Barnard, showing only the last few days of the clearing of the event, the above details of the 1909 storm were derived solely from the records and drawings of visual observers.

2.1.3 The 1975 Storm

This event occurred long before the date of opposition, so although there was some photographic coverage, the latter was of poor quality. Activity began south of Solis Lacus (near 35°S, 90°E) on 14 July (L_s = 270°), according to members of the Oriental Astronomical Association of Japan. The initial cloud had covered Solis Lacus and was seen to have expanded over Argyre and Noachis on 19 July. Dust was observed over Mare Sirenum on 18–19 July, over Thaumasia, Ophir and Candor on 21 July, and progressively over Meridiani Sinus, Pandorae Fretum, Sinus Sabaeus, and Mare Serpentis during 28 July to 2 August. A secondary dust core had developed over central Deucalionis Regio (as in 1973) on 26 July (L_s = 277.6°). Syrtis Major began to be veiled on 9 August. A temporary clearing at one longitude seemed to occur around 8–11 August, following which activity irregularly grew more widespread again. Encirclement was essentially complete by mid-August (L_s = 290°).

The final clearing process was irregular. The storm appeared to be abating at some longitudes in mid-September, though several bright dust cores remained. Furthermore, there was another outbreak of dust activity, which seems to have come from the Deucalionis Regio source, leading to renewed obscuration of the Meridiani Sinus-Sinus Sabaeus longitudes around 8–19 October. The estimated end of the storm was on 21 October (L_s = 329°), although the transparency of the atmosphere had not returned to normal until the second half of November.

2.2 An Updated List of Mars Years Without Global-Scale Dust Storms

In some years, the geometric positioning of the Earth and Mars with respect to the Sun may rule out telescopic observations covering the entire period of the dust storm season (ZM93; M99). In such cases, we cannot say with confidence whether or not a planet-encircling dust event may have occurred. Our knowledge of pre-space age atmospheric storms on Mars thus suffers from significant temporal gaps.

We have compiled an updated list of “global storm-free” Mars years. This now includes 17 entries, as listed in Table 2. By comparison with the similar list in Shirley (2015), this list includes seven additional years (MY −31, −7, 8, 16, 19, 32, and 33). Most of these additions were identified by means of an inspection of Figure 4.1 of M99, which outlines the starting and ending dates of telescopic coverage of Mars from 1876–1999. As was the case with Table 1, the original listing of GDS-free Mars years was principally derived from the earlier study by ZM93.

Table 2. Historic Mars Years Without Planet-Encircling Dust Storms

Perihelion year	Mars year	φ_dL/dt	Polarity
1896.440	−31	175	T₁₈₀
1939.714	−8	309	(−)
1941.601	−7	267	(−)
1969.801	8	131	(+)
1984.859	16	75	(+)
1986.722	17	39	T₀
1988.611	18	2	T₀
1990.500	19	75	(+)
1998.029	23	2	T₀
1999.892	24	314	(−)
2003.673	26	213	T₁₈₀
2005.533	27	135	(+)
2009.311	29	38	T₀
2011.201	30	343	T₀
2013.062	31	272	(−)
2014.952	32	175	T₁₈₀
2016.840	33	105	(+)

Note. As in Table 1, the third and fourth columns include data from SM17 that will be referenced in sections 3, 5 below. The phase (φ_dL/dt) and waveform polarity values (column 4) describe diagnostic aspects of the orbit-spin coupling forcing function dL/dt described below in section 3.1.

2.3 Sample Overview

Our knowledge of planetary-scale atmospheric dust storms on Mars has grown to encompass 30 complete Martian dust storm seasons. Fourteen global-scale dust storms were recorded during the 13 Mars years of Table 1, while 17 Mars years are now known to have been free of planet-encircling storms (Table 2). This compares favorably with the catalog employed in Shirley, Newman, et al. (2019) and N19, where only 22 Mars years with known outcomes were assessed.

Nine Mars years have been added to the sample of 21 years that was employed in a formal statistical test of the predictions of the orbit-spin coupling hypothesis in SM17. We ask: What is the impact on the prior statistical results of the addition of nine new events to the sample tested in SM17? To address this question, we performed a statistical evaluation identical to that of SM17 but using the expanded list of phase values shown in column 7 of Table 1. As in the prior study, this exercise yields an outcome that is statistically significant at the 95% level. The method employed and the results obtained are detailed in Text S1 of the supporting information accompanying this paper.

The overall frequency of GDS occurrence in the updated catalog (Tables 1 and 2) is 43.3%. This is somewhat higher than the occurrence probability of ~33% previously estimated by ZM93, on the basis of the shorter historic record available at that time. The many gaps in the historic record make it problematic to rely too heavily on either of these estimates.

3 Approach

The circulation of the Martian atmosphere is principally driven by the solar energy input to the system (cf. Barnes et al., 2017). The large orbital eccentricity of Mars' orbit about the Sun (0.09) dictates a strong annual modulation of the incoming solar energy (Figure 1). In addition, a substantial portion of the mass of the CO₂ atmosphere condenses and is deposited in polar regions during the winter seasons in both hemispheres. Global circulation models have achieved considerable success in simulating the seasonal mean climate of the Mars atmosphere (Forget et al., 1999; Toigo et al., 2012). The models are typically tuned to replicate the diurnal through annual cycles of temperature and pressure as recorded by instruments on orbiters and on landed spacecraft.

Numerical models of the Martian atmosphere have (until recently) generally failed to accurately reproduce the inter-annual variability of the Martian climate, as most dramatically evidenced by the intermittent occurrence of global-scale dust storms. Incorporation of orbit-spin coupling accelerations (S17) within Mars general circulation models (MS17; N19) has significantly improved the correspondence between numerical modeling outcomes and observations (Shirley, Newman, et al., 2019). In this section, we provide a brief review of prior work on the orbit-spin coupling problem, in order to provide context for the subsequent description of the approach taken for the present investigation.

3.1 The Orbit-Spin Coupling Hypothesis

The orbital and rotational motions of extended bodies have traditionally been considered to be independent and uncoupled, aside from small tidal effects. A more consequential form of coupling between the reservoirs of the orbital angular momentum (with respect to inertial frames) and the rotational motion was proposed in S17. Quantitative aspects of the hypothesis were detailed in that study. Any such coupling must necessarily be very inefficient, due to the extraordinary quantities of angular momentum residing in these reservoirs. The efficiency is also constrained by the error levels estimated for planetary ephemerides (S17). To provide context, for Mars, we note that the rotational angular momentum is ~8 orders of magnitude larger than the total angular momentum of the Mars atmosphere, but this quantity is itself dwarfed by the orbital angular momentum, which is >7 orders of magnitude larger still. Even a very tiny exchange of angular momentum between these reservoirs is thus likely to be geophysically significant. Under the orbit-spin coupling hypothesis (S17), the atmosphere of Mars participates in just such an exchange.

In this paper, we will be concerned with atmospheric effects linked with both the first and second time derivatives of Mars' orbital angular momentum with respect to the solar system barycenter (Shirley, 2015). Figure 2 illustrates waveforms of the orbital angular momentum L, and its time derivatives, for the Mars year of the 2018 global-scale dust storm (MY 34). Here, the areocentric longitude of the Sun L_s (a measure of the progression of the seasonal cycle of Mars) provides the time coordinate. The first time derivative of angular momentum dL/dt was identified in S17 and in MS17 as the forcing function for the putative coupling. The second time derivative d²L/dt² is simply the rate of change of that quantity. Arrowhead symbols in Figure 2 denote the inception time of the 2018 global-scale dust storm. This occurred very soon after the time of a minimum of the orbital angular momentum (top panel), which corresponds to a time approaching a positive peak in the time rate of change of the forcing function (bottom panel).

Prior studies have analyzed waveforms for L_Mars (Shirley, 2015) and for dL/dt (SM17). The present study is the first to explore the nature and consequences of atmospheric behaviors and relationships involving d²L/dt².

The following expression for the coupling mechanism, termed the “coupling term acceleration,” or CTA, was derived in S17:

$urn:x-wiley:21699097:media:jgre21322:jgre21322-math-0001$ (1)

Here, L̇ (or dL/dt) represents the rate of change of Mars' orbital angular momentum with respect to the solar system barycenter, ω_α is the angular velocity of Mars' rotation about its spin axis, r is a position vector in the body-fixed coordinate system, and c is a scalar coupling efficiency coefficient. The role and nature of the coefficient c is described in considerable detail in S17 and is also examined in the subsequent investigations (MS17; N19). Those extended discussions will not be repeated here. From a practical standpoint, the goal of past (and future) numerical modeling studies has been (and will be) to determine whether the use of a nonzero value of c within numerical simulations may lead to improved agreement between modeling outcomes and observations. This has been the case in all modeling investigations undertaken to date. (A zero value of c, if found to be preferable, would indicate that no such coupling is taking place.)

Figure 3 provides a global view of the acceleration field described by equation 1.

In Figure 3, the north pole of the body is near the top of the figure. The body rotates “beneath” or “through” the pattern of accelerations shown. A null position (or node) of the acceleration field is visible at the lower right. The displayed pattern can be compared to a force diagram for a belt and pulley system, with the rotation axis of the pulley emerging at the null position. Equation 1 thus describes a torque about an axis lying within the equatorial plane of the body. The accelerations are the largest, and lie in directions parallel to meridians of longitude, at positions 90° removed from the node. As the body rotates, the acceleration vector for most locations will revolve in azimuth through a complete cycle. Thus, during the course of 1 day, particles within an atmosphere will typically experience accelerations that cycle completely in azimuth but are predominantly directed alternately northward and southward (S17, Figure 5).

The variability with time of the magnitude of the cross product (L̇ × ω_α) of equation 1 is dictated largely by dL/dt (since the direction and magnitude of the axial rotation angular velocity vector ω_α remains nearly constant over short time periods). dL/dt however varies in a complex manner with time (SM17; MS17). Two key aspects of this variability must be recognized. First, the somewhat irregular ~2.2-year period of the dL/dt waveform (Shirley, 2015; SM17) is incommensurate with the annual cycle (1.88 years) that dictates the seasons on Mars (Figure 2). Second, when the time derivative dL/dt approaches and transitions through its zero points, the acceleration field illustrated in Figure 3 must necessarily diminish and disappear, thereafter re-emerging with reversed direction (due to the sign change of dL/dt).

3.1.1 Predicted Circulatory Intensification

An intensification of circulatory motions is predicted to occur (S17) during intervals when Mars is either gaining or losing orbital angular momentum, that is, when the dL/dt waveform (Figure 2b) is approaching and near its positive and negative extrema. The intensification results from a slow cumulative addition of small increments of wind velocities, as dictated by the accelerations illustrated in Figure 3 above.

The addition of momentum to atmospheric motions by this process may have a number of consequences. We, for instance, recognize that the accelerations, acting over extended periods, should introduce appreciable changes in the large-scale wind and pressure fields. Increases in atmospheric kinetic and potential energy are an expected consequence. Pressure gradients existing within the forced circulation may be larger than those resolved in model simulations without the external forcing. By these pathways, anomalies of the wind and pressure fields may be induced or strengthened. Increased barotropic and baroclinic instability is an expected result. A destructive interference between the cumulative effects of the applied accelerations and the seasonal-normal circulation patterns may likewise occur. Further discussion of this topic is found in MS17.

The atmosphere may be envisioned as a repository of “stored” momentum accumulated during periods of circulatory intensification. Atmospheric gyres, like the gyres of Earth's oceans, sequester quantities of angular momentum. On Mars, strong topographic relief gives rise to large and persistent stationary eddies within the atmospheric circulation (Pollack et al., 1981; Barnes et al., 2017). Like a flywheel, a single rotating air mass may be loaded during circulatory intensification intervals. It is not too large a step to consider the atmosphere (in a broad sense) to be a collective system of momentum-storing entities, akin to a system of interconnected flywheels. A portion of the angular momentum (arising due to orbit-spin coupling and stored within the atmospheric system) may subsequently be transferred to the solid body, through frictional processes, both during the intensification intervals and during transitional intervals, when the forcing accelerations disappear. The accumulated momentum may in this way provide a previously unsuspected form of memory for the atmospheric system.

3.1.2 Transitional Intervals

No active external forcing of atmospheric motions due to orbit-spin coupling is anticipated during the transitional intervals while the dL/dt waveform amplitude (Figure 2b) is diminishing and passing through zero values. In SM17, this condition was accordingly labeled the “relaxation phase.” SM17 found that none of the historic GDS in their catalog took place in years when the coupling term accelerations given by equation 1 were diminishing and passing through the sign change of the dL/dt waveform near the midpoint of the dust storm season. In that study, the corresponding GDS-free Mars years were accordingly termed “transitional years.”

To summarize: Orbit-spin coupling introduces cycles of circulatory intensification and relaxation, which are superimposed upon the normal annual cycles of atmospheric motions driven by solar energy input to the system. The phasing of the cycle of intensification and relaxation is asynchronous with the annual cycle. This factor introduces inter-annual variability within modeled atmospheric systems (Shirley, 2015; SM17; MS17; N19).

3.1.3 Characteristic Timescales of the Atmospheric Response to Orbit-Spin Coupling

Important insights may be gained through a knowledge of characteristic timescales. The thermal time constant for the Mars atmosphere (Leovy, 2001; Rogberg et al., 2010) is a classic example. The thermal time constant τ describes the likely duration, or persistence, of a thermal anomaly, within the larger circulation. τ for Mars is <2 sols (Rogberg et al., 2010). We wish to obtain an analogous estimate for the frictional damping timescale for energy added to the atmospheric circulation through orbit-spin coupling to ascertain whether the Martian atmosphere may similarly exhibit a form of memory due to this source. We ask: How long may the effects of the added momentum persist within the atmosphere, at times when the forcing is changing most rapidly?

Timescales for momentum buildup within the Mars atmosphere were addressed in MS17. Neglecting friction, MS17 found that appreciable cumulative wind speed differences (tens of ms⁻¹) could result from accelerations of ≤1 × 10⁻⁴ m s⁻² acting on seasonal timescales. However, timescales for the transfer of momentum to the underlying Martian surface were not estimated, either in MS17 or in N19.

We approach this question by considering a mechanical flywheel system with friction along one surface, as an analog for the Martian meridional overturning circulation. This approach allows us to make use of quantitative results obtained in the numerical modeling investigation by MS17. Strengthening of modeled Martian Hadley-type circulations due to orbit-spin coupling torques was a principal finding of that study. The investigation compared model outcomes obtained both with and without orbit-spin coupling accelerations. For the following calculations, we employ derived parameter values pertaining to MY 15 (a strongly forced GDS year).

MS17 plotted and described zonal-mean meridional stream functions for time intervals of 20° of L_s leading up to the inception times of the GDS included in their study. Effects due to the dynamical forcing were demonstrated by differencing the stream functions of control run and forced run simulations, in the sense (forced-control). The resulting stream function difference plot for MY 15 is shown in Figure 4a (after Figure 14 of MS17). Strengthened clockwise circulations are shown in brown colors, while volumes with intensified anticlockwise circulations (with respect to the control run) are shown in green. Peak values of the clockwise flows approach 2 × 10⁹ kg s⁻¹ near the 350-Pa pressure level. This may usefully be compared with the control run stream function peak value (before differencing) of ~1.5 × 10¹⁰ kg s⁻¹ (see Figure 14d of MS17).

Friction between the Martian surface and the moving atmosphere transfers momentum between them, while in the process damping and dissipating the kinetic energy of atmospheric motions. The question may be framed as follows:

What is the time required to go from the driven, or loaded, atmospheric state, as in Figure 4a, to an unloaded, or relaxed state, as exemplified in the control simulations, under the hypothetical assumption of a rapid disappearance of the driving accelerations?

A system diagram for order-of-magnitude flywheel calculations is provided in Figure 4b. A single-cell meridional overturning circulation extends between 4°N and 30°S latitude, a distance of 2,000 km. This latitude range corresponds to that of the boxed area shown in Figure 4a. The overturning circulation is considered to extend in a continuous band around all longitudes of the planet. A little over 28% of Mars's surface lies between 4°N and 30°S latitude, and so in the following, we will accordingly assume that a corresponding proportion of the total atmospheric mass of Mars participates in the illustrated circulation. Topographic variability is not considered in this simple model.

The kinetic energy of a flywheel is given by E = ½ Iω², where I is the moment of inertia of the flywheel and ω is its angular velocity. A typical flywheel takes the shape of a cylindrical solid. The moment of inertia of such a cylinder is I = ½ mr²; however, the particle trajectories of Figure 4b are elliptical (rather than circular) in form. The moment of inertia for a rotating cylinder with an elliptical cross-section is I = ½ m (a² + b²). Here, m is the mass and a and b are the semi-major and semi-minor axes, respectively. (For present purposes, we assume that solid-body rotational motions may adequately describe the atmospheric motions for order-of-magnitude estimates.)

The vertical limit of the circulation identified within the boxed area lies at the 100-Pa pressure level or at an altitude of ~20 km. Thus, the semi-minor axis of the flywheel analog circulation is 10 km, while the semi-major axis is 1,000 km. The elliptical path length c for the circulation is then (4a + 2πb) or 4.1 × 10⁶ m. Assuming a value of 3 × 10¹⁶ kg for the mass of the Mars atmosphere, we estimate that the mass m participating in the flywheel circulation is ~28% of this, or 8.55 × 10¹⁵ kg.

To estimate the stored energy E, we require a value for the angular velocity ω. As an intermediary step, we solve for the linear velocity of the motion in the meridional plane (v′); this may be obtained from the definition of the stream function (Peixoto & Oort, 1992, section 11.2.1.3):

$urn:x-wiley:21699097:media:jgre21322:jgre21322-math-0002$ (2)

Here, ϕ is latitude, ∂Ψ is the stream function maximum (estimated to be 1.8 × 10⁹ kg s⁻¹ from Figure 4a), and ∂p is the difference of pressure between the surface and the core of the circulation (~100 Pa, as also obtained from Figure 4a). (Complete details of all calculations performed in this section are provided in Text S2 of the supporting information.) We obtain v′ = 3.6 ms⁻¹ for the circulation. This value represents the excess velocity above that found for the unforced (control run) overturning circulation of ~25 ms⁻¹. The angular velocity ω is then 2π (c/v′) or 5.6 × 10⁻⁶ radians s⁻¹. The stored energy E of the circulation shown in Figure 4 is then 6.7 × 10¹⁶ J.

We next consider the effects of friction on this system. MS17 provide a table of global mean daytime surface wind stresses (their Table 5) for forced and unforced conditions. As with the stream function of Figure 4a, these represent averages over intervals of 20° of L_s prior to the inception dates of known past GDS. For purposes of this exercise, we have chosen to use a value of 0.001 N m⁻², which is close to the median value of the (forced-control) stress differences of Table 5 of MS17. We justify this estimate as the average surface stress over the entire domain considered and over day and night periods.

To obtain a value of the frictional energy per unit time, we multiply the above stress value by the linear wind velocity v′ obtained previously and integrate this over the surface area lying beneath the overturning circulation illustrated in Figure 4 to yield an integrated stress of ~1.5 × 10¹¹ J s⁻¹. Finally, to obtain a frictional damping time, the flywheel energy E is divided by the summed stresses and converted to sol by dividing by 88,600 s/sol. With the parameters employed, we obtain a frictional damping time of 5.1 sols.

A number of caveats should be noted in connection with this simplified scenario. An instantaneous disappearance of the forcing accelerations, as assumed here, does not occur in reality. The model considers surface friction only, neglecting turbulence and other possible sources of dissipation. We have assumed that the atmospheric motions may be approximated by the flywheel equations for a solid rotating elliptical cylinder. In addition, we have assumed a constant value for the surface wind stress, while in fact that stress depends on the wind velocity. We justify the order-of-magnitude approximation for the stress by noting two factors. First, we are not describing a situation in which either the velocity or the surface stress tends toward a zero value; the driven and control case velocities differ by only a relatively small amount. To be conservative, we have chosen a stress value on the lower end of the range (0.001 N m⁻²); this was the median difference for the nine cases modeled in MS17. The actual daytime surface wind stress difference listed for MY 15 in MS17 is more than twice as large as the value employed here, but the assumed value is preferred, as the average over an entire sol and across the entire surface from 4°N to 30°S.

With the above considerations in mind, we recognize that the damping time obtained here cannot be categorized as a time constant (as with the thermal relaxation time). In reality, the damping time depends nonlinearly on both the wind velocity and the surface stress value, and the surface stress depends nonlinearly on the wind velocity itself. The nonlinearities are subsumed into the model physics and dynamics simulated by MarsWRF in the experiments run in MS17, from which we estimate parameters. Under the assumption that the surface stress may be taken as a constant, we find that more time is required for frictional damping of higher wind velocities. Higher initial values of the surface stress, on the other hand, reduce the damping time, for a given starting difference of the wind velocity.

We conclude that a plausible frictional damping timescale for the Mars atmosphere (under the given conditions) is on the order of 10 sols or less. In addition, given the much longer (seasonal) timescale for momentum buildup (MS17), we conclude that the Martian atmospheric intensification-relaxation process, like our analog flywheel mechanism, is likely to exhibit hysteresis. We will return to this topic in connection with our discussion of storm triggering mechanisms in section 5 below.

The above exercise yields a preliminary estimate for the atmospheric relaxation-recovery timescale. This question should additionally be addressable in a straightforward way via numerical modeling. While the parameterizations of friction within MGCMs may be to some extent model dependent, we believe that suitably designed experiments may nonetheless shed significant light on questions of characteristic timescales.

3.1.4 Nomenclature

Before moving forward, we must define two parameters (or metrics) that allow for efficient characterization and discussion of the similarities and differences of solar system dynamical conditions between different Mars years. These are the phase and the polarity of the dL/dt waveform, as listed in Tables 1 and 2. The phase parameter is defined analogously with the sine function. The upward zero crossing of the dL/dt waveform is assigned a phase value of 0°, with the following positive peak assigned a phase of 90°, and so on (SM17). Different Mars years can be compared on the basis of the phase value at the time of Mars perihelion (L_s ~ 250°) (SM17). The waveform polarity parameter distinguishes between times when Mars is gaining orbital angular momentum (positive polarity) and losing orbital angular momentum (negative polarity). We also recognize two varieties of “transitional polarity” conditions (when the forcing function dL/dt is transitioning through zero values during the dust storm season and near the time of Mars' perihelion). The negative-to-positive transition is labeled T₀, while the positive-to-negative transition is labeled T₁₈₀ (see Tables 1 and 2).

3.2 Open Questions From Prior Investigations

Numerical modeling experiments with orbit-spin coupling (MS17; N19) have been remarkably successful (Shirley, Newman, et al., 2019) in hindcasting GDS occurrence on an annual basis (i.e., with temporal resolution of a single Mars year). The intra-seasonal time resolution of the forced simulations, however, still leaves much to be desired. The models have not thus far shed much light on the reasons for the relatively late onset times of GDS in 1924 (L_s = 310°) and 1973 (L_s = 300°). Likewise, as previously noted, the simulations typically fail to reproduce GDS conditions very early in the dust storm season. The initiation of the 2018 event, at L_s ~ 184°, serves to underscore this point, as the published forecasts of this event by MS17 and N19 both explicitly called for storm initiation nearer to perihelion (L_s ~ 250°).

In prior work, we have largely neglected the possibility of a memory component arising due to a lagged response of the atmospheric system to changes in the external forcing. The early occurrence of the 2018 event forces us to broaden our focus and consider this possibility.

3.3 Approach and Methodology

Intervals when the forcing is rapidly changing are of interest in many dynamical problems. The transitional intervals of the dL/dt waveform meet that criterion. To identify and focus on the time intervals when the dynamical forcing is most rapidly changing, we examine the second time derivative of the angular momentum, that is, d²L/dt², for the time period of the historic record of Tables 1 and 2. d²L/dt² (Figure 2c) is a proxy for the rate of change of the orbit-spin coupling torque. This quantity is most simply obtained by differencing the vector component values of dL/dt and dividing by the time step. Procedures for obtaining dL/dt are described in SM17. A complete listing of the calculated values of d²L/dt² employed for this investigation is provided in Table S3 of the supporting information. Supporting data are also archived on the Mendeley site (Shirley, 2020). The tabulated data cover the time period from 1870 through 2030, which encompasses the time span of the historic planet-encircling storms catalog of Table 1.

As in the earlier studies by Shirley (2015) and in SM17, our approach involves a sorting procedure that segregates the 30 individual Mars years of Tables 1 and 2 into families. As in the prior studies, the criteria for membership in each family are derived from common factors in the phasing of the chosen dynamical waveform with respect to the annual cycle for the year in question. Because we have already defined a phase parameter (φ) (SM17) that has in the past served to characterize the differences between years, there is no need to introduce a new phase identification scheme. We will continue to characterize the years of our sample by means of φ_dL/dt, as listed in Tables 1 and 2. This choice provides continuity with the prior investigations (SM17; MS17; N19).

Examination and interpretation of the waveforms of the rate of change of torque factor d²L/dt² yield three family groupings that suffice for characterizing all of the Mars years of Tables 1 and 2. We first identify and discuss the members of the Mode 1 family, whose members were assigned in previous studies (SM17; MS17) to the positive polarity and negative polarity categories. We retain the transitional years category of SM17, now calling this Mode T, with two subcategories reflecting the upward-crossing (T₀) and downward-crossing (T₁₈₀) transitions of the dL/dt waveform.

We introduce one further category. This is the Mode 2 family, wherein years are classified on the basis of the phasing of the d²L/dt² waveform with respect to the annual cycle. Discussion of the details of the sorting process is deferred to section 4.3 below.

4 Results I: Orbit-Spin Coupling

4.1 Mode 1 Storms and Storm Triggering

The Mode 1 category is a direct descendant of the positive polarity and negative polarity categories of SM17. We accordingly display the dL/dt waveforms here, rather than those for the second time derivative d²L/dt², which will be discussed below in connection with the transitional and Mode 2 years. (Peak times and waveform plots of the d²L/dt² waveforms of Mode 1 years are provided in Table S1 and Figure S1 of the supporting information.)

dL/dt waveforms for the Mode 1 forcing family are illustrated in Figure 5. Eight of the 30 Mars years of Tables 1 and 2, including the GDS years 1971, 1973, and 2007, are assigned to this category (Table 3). (Note the opposed phasing of the positive polarity Mode 1(+) years and negative polarity Mode 1(−) years in the top and bottom rows of Figure 5.) Seven of the events have dL/dt waveform peak dates between L_s = 202° and L_s = 258°, with one outlier (1973, MY 10) at L_s = 302° (Table 3).

Table 3. Mode 1 Forcing Function Peak Dates for the Mars Years Displayed in Figure 5

Year	MY	Mode	GDS date			Component values (dL/dt)			Δt
			(L_s)	L_s	x	y	z	Resultant	(L_s)
1971	9	1 (+)	260	250.456	6.21E − 02	−1.97E − 02	2.08E + 00	2.08E + 00	−9.5
1973	10	1 (+)	300	301.997	2.49E − 02	−1.09E − 02	1.39E + 00	1.39E + 00	2.0
2007	28	1 (+)	262	257.716	7.53E − 02	2.09E − 02	2.22E + 00	2.22E + 00	−4.3
1969	8	1 (+)		207.359	3.79E − 02	−4.63E − 02	1.99E + 00	1.99E + 00
2005	27	1 (+)		202.224	5.21E − 02	−3.62E − 02	1.83E + 00	2.40E − 01
2016	33	1 (+)		235.620	9.61E − 02	3.98E − 03	2.22E + 00	1.83E + 00
								2.23E + 00
1939	−8	1 (−)		209.550	−1.01E − 01	4.24E − 02	−2.76E + 00
1999	24	1 (−)		205.181	−1.11E − 01	6.16E − 02	−3.42E + 00	2.76E + 00

Note. Column 5 identifies the seasonal dates (L_s) of the extrema of the curves shown in Figure 5 falling within the dust storm season. Column 9 (Δt) is the difference between columns 4 (GDS inception dates) and 5. Cartesian components of dL/dt (referenced to the ecliptic coordinate system) are provided in columns 6–8. The signed z component (column 8) is plotted in Figure 5.

Mars is gaining orbital angular momentum, during the second half of the Mars year, in Mode 1(+) years (SM17), while the opposite is true for Mode 1(−) years. No global-scale dust storms have occurred in the Mode 1(−) years of Table3 (see Figure 5c). We note that the waveforms for years with GDS (Figure 5a) are not markedly different, in phasing or amplitude, from some of the storm-free years displayed in Figure 5b. This may indicate that some other factor, aside from the CTA, may play an important role in controlling whether or not a global-scale storm may take place in any given year. The spatial distribution of dust available for lifting from the surface is likely to play an important role (Haberle, 1986; Basu et al., 2006; Szwast et al., 2006; Mulholland et al., 2013; Newman & Richardson, 2015; also see section 6 below). Dust is continuously redistributed over the Martian surface, by dust devils and by local and regional storms, as well as by GDS.

The close agreement in time of the GDS inception dates (Figure 5, arrow symbols) and corresponding waveform extrema is a noteworthy feature of Figure 5a. The calculated time differences are listed in the last column of Table 3. The Δt cover a range of only about 12° of L_s; the mean signed difference of the storm inception dates lies ~4° of L_s later than the waveform peak dates (about 1 week). Also noteworthy, in connection with the 1971, 1973, and 2007 Mode 1 GDS of Figure 5, are the tabulated ratios of the atmospheric pressure at the inception dates to the annual pressure maximum (found in column 6 of Table 1). The values are 1.0, 0.95, and 1.0 respectively; the average is 0.983. Relatively high levels of atmospheric surface pressure may thus be a contributing factor, or possibly a requirement, for the occurrence of Mode 1 GDS.

4.1.1 Overview of Mode 1 Storms and Storm Triggering

The plots of Figure 5 illustrate relationships between the forcing function waveforms and the cycle of solar irradiance during one annual cycle. It is useful at this point to step back and consider temporal relationships with respect to the full time span of Table 3. Figure 6 illustrates the distribution of Mode 1 years with reference to the dL/dt waveform since 1935. As noted earlier in connection with Table 3, the signed mean difference of the initiation dates lies within about 4° of L_s of the Mode 1 forcing function peak times. (The signed mean difference corresponds to the centroid of the distribution of the time differences for the three global storms.)

In Figure 6, we have chosen to place the symbols for storm-free Mode 1 years at the times of the southern summer solstices (L_s = 270°) of the years in question. We justify this choice by noting that the average seasonal inception date for the GDS of Table 3 lies at L_s = 274°. Plotted in this way, the data reveal an apparent difference between the Mode 1 GDS years and the Mode 1 storm-free years; the waveform peak dates correspond well with the times of the solstices in GDS years, while in storm-free years, with the possible exception of MY 33 (2016), they typically do not.

The conceptual model for the origins of Martian GDS developed in prior studies (S17; MS17; N19) involves an incremental addition of momentum to the circulation of the Mars atmosphere, by the cumulative action of small accelerations, applied over appreciable time periods (i.e., on time intervals comparable to seasonal timescales). Our recognition that Mode 1(+) GDS seem to occur preferentially (1) when atmospheric pressures are the highest, and (2) very near the times when the dL/dt waveform is near peak values, generally tends to support this conceptual model for storm triggering.

Numerical modeling of the storm initiation process for the Mode 1(+) GDS of 2007 is discussed in some detail in section 5.2.2 of N19. These authors were successful in simulating a planet-encircling storm, initiating very close to the inception time for the historic storm, within the MarsWRF MGCM.

4.2 Transitional (Mode T) Mars Years

The transitional years category was likewise introduced previously (in SM17). The current Mode T listing includes four Mars years in which no GDS occurred (1896, 1988, 2011, and 2015; Table 4). In prior studies, transitional years were identified as years when the coupling term accelerations given by equation 1 were diminishing and passing through the sign change of the dL/dt waveform near the midpoint of the dust storm season (see Figures 2 and 3 of SM17). No changes to that physical description are implied or called for in the present study. However, the Mode T classification for the present study (Table 4) is additionally made on the basis of a consideration of the times (L_s) when the d²L/dt² waveform attains extreme values within the dust storm season. d²L/dt² waveform extrema (peak dates) for the Mode T events fall between L_s = 250° and L_s = 260°, as listed in the fourth column of Table 4 and as illustrated in Figure 7.

Table 4. Mode T Waveform Peak Dates, for the Global Storm-Free Mars Years Displayed in Figure 7

Year	MY	Mode		Component values (d²L/dt²)
			L_s	x	y	z
1998	23	T₀	251.300	7.17E − 03	−9.00E − 03	4.58E − 01
2011	30	T₀	258.380	−3.93E − 04	−3.51E − 03	2.04E − 01
1896	−31	T₁₈₀	253.663	−5.56E − 03	6.65E − 03	−3.28E − 01
2015	32	T₁₈₀	258.410	−6.12E − 03	4.27E − 03	−1.41E − 01

Note. Column 4 identifies the seasonal dates (L_s) of the extrema of the curves shown in Figure 7 that fall within the dust storm season. Cartesian components of d²L/dt² (referenced to the ecliptic coordinate system) are provided in columns 5–7. The signed z component (column 7) is plotted in Figure 7.

Even though our full sample of years (Tables 1 and 2) is considerably larger than was employed for prior studies (SM17; N19; Shirley, Newman, et al., 2019), the listing of transitional years (Table 4) is shorter than before. Four Mars years from the transitional category of SM17 (MY 17, 18, 26, and 29; i.e., 1986, 1988, 2003, and 2009) have been re-classified as Mode 2 years on the basis of criteria to be described below in section 4.3. No GDS were recorded in any of these years. (A brief tabulation and discussion of the sub-sample of re-classified events is found in Text S3 and Table S2 of the supporting information).

Two of the GDS years added to our catalog for this study (1877 and 1909) would have been assigned to the prior (SM17) transitional years category, if they had been included in that study, on the basis of their phase values (φ_dL/dt) as indicated above in column 7 of Table 1. One of the key findings of SM17 was that no GDS were recorded during the seven transitional Mars years of that study. A revised accounting, using the system of SM17, would now include eight storm-free transitional years, out of a total of 10. Thus, minor modifications to the results and conclusions of SM17 would follow from the addition of the 1877 and 1909 GDS years to the list of Mars years employed for that study.

4.3 Mode 2 Storms and Storm Triggering

We turn now to a consideration of the phasing of the waveform for the second derivative of the orbital angular momentum (d²L/dt²; Figure 2c) with respect to the annual cycle and the inception times of the remaining eleven planet-encircling dust storms of Table 1. Figure 8 illustrates d²L/dt² waveforms for 14 of the 30 Mars years listed in Tables 1 and 2. The selection is made on the basis of the time (L_s) when the rate of change of torque waveforms attains peak values within the dust storm season. As in Shirley (2015) and Figure 1, the dust storm season is defined as a symmetric interval around perihelion, between L_s = 160° and L_s = 340°. d²L/dt² waveform peak dates for the 14 Mars years of Figure 8 fall between L_s = 170° and L_s = 242°, as listed in the fifth column of Table 5.

Table 5. Mode 2 Waveform Peak Dates, for the Mars Years Displayed in Figures 8-10

Year	MY	Mode	GDS date		Component values (d²L/dt²)			Δt
			(L_s)	L_s	x	y	z	(L_s)
1877	−41	2E (+)	186	237.670	4.49E − 03	−4.64E − 03	2.88E − 01	51.7
1982	15	2E (+)	208	172.700	1.45E − 02	1.63E − 03	3.76E − 01	−35.3
1994	21	2E (+)	220–245	201.537	7.13E − 03	1.60E − 03	3.10E − 01
2018	34	2E (+)	184	207.140	5.31E − 03	4.47E − 03	3.33E − 01	23.1
1984	16	2E (+)		197.301	9.65E − 03	6.85E − 03	4.24E − 01
1986	17	2E (+)		219.745	2.19E − 03	3.25E − 03	3.74E − 01
1988	18	2E (+)		241.715	−4.53E − 04	−1.59E − 03	2.06E − 01
1990	19	2E (+)		207.523	5.86E − 04	1.56E − 03	4.48E − 02
2009	29	2E (+)		226.143	1.33E − 05	2.67E − 03	2.41E − 01
1909	−24	2E (−)	204	238.556	2.50E − 03	−1.20E − 03	−1.81E − 01	34.6
1977	12	2E (−)	204	221.531	−2.79E − 03	6.52E − 05	−2.07E − 01	17.5
2001	25	2E (−)	185	182.927	−8.15E − 03	−2.40E − 03	−2.43E − 01	−2.1
1941	−7	2E (−)		189.347	−9.40E − 03	−3.86E − 03	−3.14E − 01
2003	26	2E (−)		227.974	−9.72E − 04	3.65E − 05	−2.24E − 01
1975	11	2S (+)	270	286.272	4.42E − 03	−2.37E − 03	1.03E − 01	16.3
2013	31	2S (+)		308.214	1.49E − 03	−2.87E − 03	9.24E − 02
1924	−16	2S (−)	310	309.276	−1.42E − 02	−6.35E − 04	−2.71E − 01	−0.7
1956	1	2S (−)	249	274.958	−1.53E − 02	1.01E − 02	−4.25E − 01	26.0

Note. Column 5 identifies the seasonal dates (L_s) of the extrema of the curves shown in Figures 8 and 9 falling within the dust storm season. Column 9 (Δt) is the difference (L_s) between columns 4 (GDS inception dates) and 5. Cartesian components of d²L/dt² (referenced to the ecliptic coordinate system) are provided in columns 6–8. The signed z component (column 8) is the quantity plotted in Figures 8-10.

Table 5 includes two categories of Mode 2 years. One category, labeled Mode 2E, for equinoctial, includes the six equinoctial GDS years of Table 1, together with the post-equinoctial 1994 event, and with seven additional global storm-free years of Table 2. The second category, labeled Mode 2S (for “solsticial”), includes four additional Mars years. Among these are the GDS years 1924 (MY −16), 1956 (MY 1), and 1975 (MY 11). Waveforms and relationships for Mode 2S Mars years are discussed below in section 4.3.2.

4.3.1 Equinoctial Mode 2 Storms and Storm-Free Years (Mode 2E)

The first telescopically observed activity associated with the 2018 planet-encircling dust storm began on approximately 30 May, 38 sols prior to the positive peak of the d²L/dt² waveform shown in Figure 8a. As indicated in Figure 8a and in Table5, two other equinoctial GDS (1877 and 1982) occurred under similar forcing conditions. The signed mean difference of the set of Δt values for the Mode 2E(+) storm years is small, at −6.1° of L_s, but the standard deviation is large (41.3°).

Little information is available regarding the initiation sites for the Mode 2E(+) 1877 and 1982 storms, and so we cannot at present identify any other common factors linking these events with 2018. N19 made a special study of the 1982 (MY 15) storm, as simulated within the MarsWRF global circulation model with forcing by orbit-spin coupling. The amplitude of the dL/dt waveform for 1982 (SM17) is the largest found for any year analyzed between 1920 and 2030. N19 obtained a seasonal inception date of L_s ~ 200° for the simulated storm, which is close to the estimated inception time of L_s = 208° for the actual storm (Table 1). This represents the first successful simulation of an equinoctial GDS by a numerical model without prescribed atmospheric dust forcing. N19 also discussed the interaction between the equinoctial, double Hadley cell circulation and the external forcing. In common with prior studies (SM17; MS17), they also commented on the similarity of the dynamical waveforms (dL/dt) between 2018 (MY 34) and the post-equinoctial 1994 (MY 21) event, which likewise appears here as a member of the Mode 2E(+) global storm family in Figure 8a. Much like 1982, the GDS of 1994 began sometime after the peak value of the waveform was attained.

Waveform for five additional Mode 2E(+) Mars years with phasing similar to those of Figure 8a, but without GDS, are given in Figure 8b. Of these, the waveforms for 1984 (MY 16) and 1986 (MY 17) stand out by virtue of their large amplitudes. We speculate that the redistribution of surface dust occurring during the great storm of 1982 (MY 15) may have led to surface conditions unfavorable for the occurrence of GDS in the following two Mars years. Further experiments with realistic surface dust distributions may be required to address this question.

We next turn to the Mode 2E(−) years of Figures 8c and 8d. As indicated, the remaining three equinoctial GDS of the expanded catalog of Table 1 occurred under similar dynamical forcing conditions, that is, near the times of negative extrema of the d²L/dt² waveform. The signed mean difference of the listed time differences (L_s) between the waveform peak dates and the storm inception dates is 5.6° here, with a corresponding standard deviation of 24.5°.

The initiation time of the second planet-encircling storm of 1977 is also indicated in Figure 8c. We cannot be sure if this storm did (or did not) occur independently, with respect to the 1977a storm (MS17; N19), and so we defer further consideration of this event to a later study.

Our knowledge of initiation locations and storm development for the Mode 2E(−) GDS of 1909, 1977a, and 2001 is superior to that for the Mode 2E(+) events. The onset and development of the 2001 (MY 25) storm was observed by the instruments of the Mars Global Surveyor spacecraft, including the Mars Orbiter Camera and the Thermal Emission Spectrometer. Detailed descriptions of the storm are found in Smith et al. (2002), in Strausberg et al. (2005), in Cantor (2007), in McKim (2009), and in Kahre et al. (2017). The 2001 storm began in Hellas. It was preceded by significant cap-edge (local) storm activity (Cantor, 2007; Strausberg et al., 2005). Modeling by Wilson et al. (2008) indicates that dust moving northward from Hellas may have been entrained into the ascending branch of the Hadley circulation (see also Toigo et al., 2018). Such entrainment has often been suggested as a factor possibly contributing to the growth of Martian dust storms from regional to global scale (Haberle, 1986; Haberle et al., 1993; Murphy et al., 1995; Kahre et al., 2017; S17; MS17; Shirley, Kleinböhl, et al., 2019).

The initial stages of the equinoctial 1977a (MY 12) GDS were observed only sparsely by the Viking Orbiter mission. Strausberg et al. (2005) note that “… strong dust activity in Hellas from just before equinox to just after equinox was followed by activation of lifting in Solis, followed by expansion to a global storm and in that respect 2001 and 1977a were similar.”

The waveform for the 1909 equinoctial storm is also included in Figure 8c. As noted in section 2.1.2, the Hellas basin (and Noachis, to the west) is considered to be the most likely location of initiation for this storm as well.

As in the case of Figures 8a and 8b, the waveforms for the storm-free Mars years 1941 and 2003, shown in Figure 8d, are not strongly dissimilar to those of the GDS years of Figure 8c. The amplitude of the 1941 waveform is the largest of any in this family, and quite extensive regional storm activity was observed (M99), but no GDS occurred in this year. This once again indicates that some other factor, such as the spatial distribution of mobile surface dust available for lifting, may play an important role in determining whether or not a GDS may occur in any given Mars year.

Atmospheric pressure ratios (Table 1) for the occurrence times of the equinoctial Mode 2E storms of Table 4 are significantly lower than those for the Mode 1 storms, due to the much earlier seasonal inception dates for Mode 2E events (Figure 1). The mean and standard deviation of the pressure ratios, for the six equinoctial GDS of Table 4, are 0.85 and 0.03, respectively.

All of the known equinoctial GDS of Table 1 appear together in Figures 8a and 8c. The similar phasing of these storms with respect to d²L/dt² is a second common factor linking these enigmatic events, beyond the known common factor of their very early seasonal inception dates.

The results of Figure 8 and Table 5 demonstrate that the coincidence in time of (southern spring) equinoctial atmospheric conditions with intervals when the orbit-spin coupling torque is changing most rapidly is favorable for the occurrence of global-scale dust storms. It is not entirely clear why this should be the case. A new working hypothesis is detailed in section 5 below. While currently speculative, the proposed mechanism is susceptible to testing by means of numerical modeling.

4.3.2 Solsticial Mode 2 Storms and Storm-Free Years (Mode 2S)

Waveform peak times for the remaining three planet-encircling dust storms of Table 1 are given at the bottom of Table 5. As with the Mode 2E events, the Mode 2S selection is made on the basis of the times (L_s) when the d²L/dt² waveforms (Figure 9) attain extreme values within the dust storm season. Waveform extrema (peak dates) for the Mode 2S events fall between L_s = 274° and L_s = 310°, as listed in the fifth column of Table 5.

Of the three planet-encircling storms in this category, the 1924 GDS is noteworthy as an outlier, as this storm has the latest known initiation date for a global dust event (L_s = 312°). Among the other solsticial storms of Figure 1, the 1956 GDS is also an outlier, as this has the second earliest inception date (after the post-equinoctial 1994 event) of that group (L_s = 249°; Figure 1). As indicated in Figure 9, both of these storms began near times when the orbit-spin coupling torque was changing most rapidly.

The initiation date of the Mode 2S(+) GDS of 1975 bears a similar relationship to the d²L/dt² waveform for that year (Figure 9a), although the waveform amplitude is far lower in this case. As indicated in Table 5, the differences in time between the Mode 2S storm initiation dates and the forcing function peak dates are 16.3°, −0.7°, and 26° of L_s, yielding a signed mean time difference of 12.5° of L_s.

Figure 9b illustrates the waveform for one storm-free year (2013; MY 31) with similar phasing to the 1975 event. As illustrated in Figures 4 and 5 of Shirley (2015), solar system dynamical conditions were similar in these years, as in both cases, the Sun was moving with relatively low velocity while in close proximity to the solar system barycenter. The range of variability of the orbital angular momentum of Mars was correspondingly reduced.

The waveform illustrated for comparison purposes in Figure 9d does not correspond to a global storm-free year but instead represents the Mode 2E(+) year 1982. The curve for 1982 reaches a minimum at L_s = 306°, which falls in the 2S(−) range (Figure 9c), following its earlier positive peak at L_s = 172.7° (Table 5); 1982 (MY 15) had the largest waveform amplitude of any year in the study period (1870–2030) (SM17; N19), and so the close spacing of these extrema may represent an unusual or special case. Nonetheless, this example demonstrates that there may be more than one preferred interval for Mode 2 GDS occurrence within a single Mars year. Hypothetically speaking, if a GDS had occurred near L_s = 300° in 1982, instead of near the equinox, we would classify 1982 as a Mode 2S(−) case, rather than as Mode 2E(+).

We next obtain the statistics of the time differences between the GDS inception dates and the waveform peak dates for the full sample of Mode 2 events of Table 5. We exclude 1977b, for reasons noted above, and 1994, due to the uncertainty in the inception date. With n = 9, we have a signed mean time difference of 14.6° of L_s, with a moderately large standard deviation of 25.0°. (The signed mean difference (or centroid) of the storm inception dates precedes the d²L/dt² waveform peak dates in time.)

4.3.3 Mode 2 Overview

Figure 10 illustrates Mode 2 GDS timing with reference to the d²L/dt² waveform. The two panels of Figure 10 cover the entire period of the historic record. The occurrence times typically fall near the times of extrema of the d²L/dt² waveform. The symbol representing the 2018 planet-encircling dust event is found at the right side of the lower panel (b).

The two panels of Figure 10 include all six of the equinoctial GDS of Table 1. The correspondence illustrated in this figure once again highlights one of the main findings of our investigation: The similar phasing of the equinoctial GDS with respect to d²L/dt² is a second common factor linking these enigmatic events, beyond the known common factor of their very early seasonal inception dates.

4.4 Intra-Seasonal Statistics of GDS Occurrence for the Complete Sample

All 14 of the Martian planet-encircling dust storms of Table 1 are included within the Mode 1 and Mode 2 plots of Figures 6 and 10. Combining the time difference statistics for both modes, we have 12 independent events with known inception dates (GDS; not including 1977b or 1994). We obtain a mean signed difference between waveform peak times and storm inception dates of 9.9° of L_s. The standard deviation of the distribution of signed differences is 23.0° of L_s. These quantities will be used to identify candidate temporal windows for the updated forecasts for 2020–2030 of section 8 below.

As with the prior studies of Shirley (2015) and SM17, we recognize that the assignment of storm years and storm-free years into categories based solely on solar system dynamical waveform phase relationships is problematic. The Mars atmosphere is a complex, nonlinear system, and it is naïve and possibly dangerous to rely on one-dimensional or two-dimensional parameterizations for its characterization.

4.5 Mode 1 and Mode 2 Peak Times in Juxtaposition: Torque Episodes

Mode 1 years and phenomena (section 4.1) and Mode 2 phenomena (section 4.3) have until now been described and evaluated separately. Our goal in this subsection is to identify and investigate possible relationships between the two forcing modes. As noted above, in connection with the Mode 2S examples of Figure 9, it is evidently possible to have more than one Mode 2 waveform peak within a single dust storm season. In addition, as shown below, it is likewise possible for a single Mars year to include both Mode 1 and Mode 2 waveform peaks.

To enable comparisons, we require a simple, repeatable, and quantitative method of identifying time intervals of interest associated with waveform peak dates. It will be advantageous if the method may be applied in a consistent way for both storm triggering modes. We will employ the statistical findings of section 4.4 to define preferred intervals in time bracketing individual Mode 1 and Mode 2 waveform peak times. The defined intervals will be termed torque episodes (TE).

We calculate candidate time windows as follows. We first subtract the signed mean difference (9.9°, rounded to 10° for convenience) from the considered waveform peak time(s) of the year under investigation, to identify the center of the preferred time window(s). 1-Sigma ranges about this time are then obtained by adding and subtracting the standard deviation (23°) to (and from) the L_s value obtained. Suppose, for instance, that the (positive or negative) peak value of a given waveform is found at L_s = 270°. The center of the calculated TE window must then lie at L_s = 260°, while the associated time interval must include the range from L_s = 237° to L_s = 283° (±1σ). (TE window ranges will be rounded to integer degrees of L_s.)

We take account of the historic record of GDS occurrence in formulating the following additional rules (or filters) for recognizing TE:

We restrict our attention to the Martian dust storm season, from L_s = 160° to L_s = 340°, as defined previously (Shirley, 2015). Thus, no TE may begin before L_s = 160°, and none may end later than L_s = 340°.
As previously indicated in Figures 5 and 6, no historic Mode 1 GDS have occurred in close proximity to negative extrema of the dL/dt waveform. We thus ignore the negative extrema of the dL/dt waveform in connection with this discussion.
Waveform peak times for all known Mode 1 GDS lie in the range between L_s = 250° and L_s ~ 300° (Table 3). None of the storm-free Mode 1 years of Table 3 have waveform peak times within this range. Extending slightly the ends of the above GDS preferred range by ~5°, we require that a positive peak of the candidate dL/dt waveform must be found between L_s = 245° and L_s = 305° in order to qualify as a Mode 1 TE.
Transitional years: As indicated in Figure 7, for the d²L/dt² waveform, the range between L_s = 250° and L_s = 260° appears to be unfavorable for GDS occurrence. We likewise expand this range by ±5°, yielding a waveform peak qualifying range of L_s = 245° to L_s = 265°, as our criterion for recognition as a transitional case.
Mode 2E and Mode 2S TE time ranges may be similarly constrained by an inspection of the historic record. Extrema of the d²L/dt² waveform for prior Mode 2E cases lie between L_s = 172° and L_s ~ 242° (Table 5). To be recognized as a valid Mode 2E window, we thus require that a peak of the d²L/dt² waveform must lie within the slightly expanded range from L_s = 165° to L_s = 245°.
Observed waveform extrema for Mode 2S cases lie between L_s ~ 275° and L_s ~ 310° (Table 5). To be recognized as a valid Mode 2S window, we thus require that a candidate peak of the d²L/dt² waveform must be found within the slightly extended range from L_s = 270° to L_s = 315°.

We summarize these selection rules in Table 6. The range values for the d²L/dt² cases do not overlap. While some overlap of seasonal dates is present between Mode 1 preferred times and those for the other modes, there cannot be an overlap or other inconsistency in any given year, as peak times of the dL/dt and d²L/dt² waveforms cannot by definition coincide closely in time within any given Mars year (see Figure 2).

Table 6. Adopted Seasonal Filtering Criteria (L_s) for Identifying Torque Episodes (TE)

Mode	Waveform peak times	Waveform	Extended range
Mode	(L_s)		(L_s)
Mode 1 (Table 3)	250–302	dL/dt	245–305
Mode 2E (Table 5)	172–242	d²L/dt²	165–245
Mode 2S (Table 5)	275–310	d²L/dt²	270–315
Mode T (Table 4)	250–260	d²L/dt²	245–265

Applying the above selection criteria to the sample of Mars years with GDS of Table 1 yields the results displayed in Table 7. Taking MY 25 as an example, and looking across the row, we see that only one TE was obtained using our selection rules for MY 25; this is a Mode 2E, with a window extending from L_s = 160° to L_s = 196°. No Mode 1 window could be identified, as the dL/dt waveform peak time for MY 25 lies outside the range given in Table 6. Similarly, the second (positive) peak of the d²L/dt² waveform, occurring at L_s = 317.4° of MY 25, does not lie within the target range for Mode 2S events of Table 6. Thus, as with Mode 1, no MY 25 Mode 2S TE could be defined.

Table 7. Torque Episode (TE) Window Definitions for the GDS Years of Table 1, Calculated Using the Method Specified in This Section and in Table 6

Mars year	dL/dt peak	dL/dt TE	2E d²L/dt² peak	Mode 2E TE	2S d²L/dt² peak	Mode 2S TE
	Date (L_s)	Window (L_s)	Date (L_s)	Window (L_s)	Date (L_s)	Window (L_s)
−41	316.1	None	237.7	205–251	None	None
−24	142.5	None	238.6	206–252	None	None
−16	244.4	None	175	160–188	309.3	276–322
1	198.3	None	130.3	None	275	242–288
9	250.5	217–263	186.1	163–209	317.1	None
10	302.0	269–315	221.5	189–235	None	None
11	None	None	None	None	286.3	253–299
12	102.6	None	221.5	189–235	None	None
15	239.1	None	177.1	160–190	306.8	274–320
21	269.6	237–283	201.5	169–215	335.1	None
25	29.7	None	182.9	160–196	317.4	None
28	257.7	225–271	190.4	160–203	324.8	None
34	274.2	241–287	207.1	174–220	340.2	None

Figure 11 illustrates calculated TE windows for six historic Mars years with GDS. Here Mode 1 TE are shaded in blue, while Mode 2S and Mode 2E TE are shaded in yellow and purple, respectively. These plots differ from those of Figures 5–10 through including both the dL/dt and d²L/dt² waveforms, shown in blue and red, respectively. The dL/dt waveform has been scaled by a factor of 10⁻⁸ for plotting. As before, arrowheads denote the inception dates of the GDS recorded in the year plotted. All six of the storm inception dates fall within calculated windows; however, this need not always be the case. Similar plots for MY −41 and MY −24, provided in Figure S2 of the supporting information, show storm inception dates lying outside the calculated intervals, as the displacements from the waveform peak times for these events were >>23° (i.e., >1σ) (Table 5). This is an expected result, due to our choice of a relatively narrow (±1σ) window width for identifying and displaying TE.

The top row of plots includes MY 25 and MY 34, two early-season storm years, with inception dates of L_s = 185° and L_s = 184°, respectively, while the center row illustrates mid-season storms from MY 1 (L_s = 249°) and MY 28 (L_s = 262°). The bottom row shows late-season examples (MY 10 and MY −16, with L_s = 300° and L_s = 310°, respectively).

Figure 11 includes representative examples of all of the forcing mode combinations present during the time period of study (1870–2030). In three of the six examples, Mode 2E TE are paired with following Mode 1 TE. In two other cases (MY 25 and MY 1), only a single TE is obtained. We additionally see one case where both 2E and 2S windows were identified (MY −16). (Corresponding plots for the seven GDS of Table 7 not shown in Figure 11 are included in Figure S2 of the supporting information. All of the GDS year plots of Figure S2 show relationships similar to those displayed in Figure 11; for instance, the plot for the MY 21 GDS year is closely similar to that for MY 34 [Figure 11b]; while the plots for MY −24 and MY 12 are similar to that for MY 25 [Figure 11a]; etc.)

We next consider the frequency of identified Mode 1, Mode 2, and Mode T episodes, as a function of time, between 1870 and 2030. Table 8 provides this information. Color coding in Table 8 is the same as in Figure 11. The data correspond to the dust storm season only, from L_s = 160° to L_s = 340°. The table covers 86 Mars years (from MY −45 to MY 40). A number of patterns and regularities are evident in Table 8. Mode 2E occurs most frequently (48 cases), followed by Mode 2S (28 cases), Mode 1 (17 cases), and Mode T (16 cases). In one case (MY 40), no plausible TE could be defined (as discussed later in section 8). The higher frequency for Mode 2E may be explained by the greater width of the range of acceptable peak values for that mode shown in Table 6.

Table 8. Frequency of Mode 1, Mode 2, and Mode T Torque Episodes Within the Dust Storm Season from MY −45 to MY 40 (1870–2030)

Mars year	Events	Mode 2E	Mode 1+	Mode T	Mode 2S	Mars	Events	Mode 2E	Mode 1+	Mode T	Mode 2S
Mars year						Year
−45					+	−2		+			−
−44		−				−1		−
−43					+	0				180
−42		+				1	GDS				−
−41	GDS	+				2		+			−
−40					+	3		+
−39					+	4		+
−38		−				5				0
−37		−				6		−
−36				180		7				180
−35					−	8	No GDS				−
−34		+				9	GDS	+
−33		−				10	GDS	+
−32		−				11	GDS				+
−31	No GDS			180		12	GDS	−
−30					−	13				180
−29		+				14					−
−28		+				15	GDS	+			−
−27				0		16	No GDS	+
−26					+	17	No GDS	+
−25		−				18	No GDS	+
−24	GDS	−				19	No GDS	+
−23					−	20		+
−22		+				21	GDS	+
−21					+	22		+
−20		−				23	No GDS			0
−19		−				24	No GDS				+
−18				180		25	GDS	−
−17					−	26	No GDS	−
−16	GDS	+			−	27	No GDS				−
−15		+				28	GDS	+
−14				0		29	No GDS	+
−13		−				30	No GDS			0
−12				180		31	No GDS	−			+
−11					−	32	No GDS			180
−10		+				33	No GDS	+			−
−9				0		34	GDS	+
−8	No GDS				+	35		+
−7	No GDS	−				36				0
−6		−				37					+
−5				180		38		−			+
−4					−	39		−
−3					−	40

Note. As in Figure 11, Mode 1 = blue, Mode 2E = yellow, Mode T = gray, and Mode 2S = purple. Plus and minus symbols identify the polarity of d²L/dt² waveform peaks (as given in Table 5). The Mode T episodes (T₀ or T₁₈₀) are classified as in Table 4.

Fifty-seven of the 86 years analyzed show only a single preferred interval or TE of any type. In particular, we note that none of the 16 Mode T years have accompanying Mode 1 or Mode 2 episodes. There are 25 years with solitary Mode 2E episodes, as in Figure 11a, and 20 years with solitary Mode 2S episodes, as in Figure 11c. Conversely, there are 24 years displaying two TE. Mode 2E and Mode 2S, as in Figure 11f, appear together in seven cases; two of these are historic GDS years (MY −16 and MY 15). Somewhat surprisingly, all 17 of the identified Mode 1 TE of Table 8 are accompanied by Mode 2E TE. Five of the 17 are GDS years; these include the three Mode 1 GDS of Table 3, along with the Mode 2E storm years 1994 (MY 21) and 2018 (MY 34). If we restrict our attention to the Mars years of Table 8 with known outcomes, we obtain 8 years when Mode 2E TE were accompanied by Mode 1 TE. Five of the 8 years were GDS years.

Several other patterns of interest may be noted in Table 8. None of the 86 MY were, for instance, found to include both Mode 1 and Mode 2S intervals. Considering only the subset with known outcomes (n = 30; Table 1 years together with those of Table 2), the frequency of GDS occurrence is somewhat higher in years showing two TE (7/12 or 58%) than it is in years with only one defined interval (6/14 or 43%). In light of the small sample sizes, this difference is unlikely to be statistically significant. Finally, between MY 15 and MY 22, we observe a continuous run of Mode 2E+ TE. We appeal to solar system dynamics for an explanation of this oddity. For about one Mars year, between 1988 and 1990, the Sun experienced an unusual period of retrograde orbital motion about the solar system barycenter (Jose, 1965; Javaraiah, 2005; see also Shirley, 2015). As shown in Figure 21 of MS17, the phasing of the dL/dt waveform with respect to the annual cycle was substantially altered, both during this episode and during the years leading up to and following this episode, such that a nearly invariant phase relationship was maintained in these years. This factor accounts for the continuous run of Mode 2E TE between MY 15 and MY 22.

Our methodology for identifying TE detects intervals wherein the phasing of the dL/dt and/or d²L/dt² waveforms is similar to seasonal phasing relationships obtaining during known historic GDS events. We recognize a number of limitations to this approach. The method takes no account of variations in the amplitudes of the waveforms; as previously noted, this may be significant in some cases. The sample sizes employed for defining the eligibility criteria (Table 6) are small, and the seasonal ranges employed may thus be suboptimal. Other window definitions may be more effective or more appropriate for other investigations. We must be careful not to overinterpret the findings; apparent relationships emerging from analyses by this method may, for instance, not necessarily be representative of real physical effects and causes.

Table 8 additionally shows that the frequency of TE occurrence is much higher than the frequency of GDS occurrence. Not every TE gives rise to a GDS. This aspect clearly limits the hindcasting and forecasting utility of the method. TE in general may thus best be viewed as intervals that may potentially exhibit some instability of the large-scale circulation.

The TE plots of Figure 11 usefully shed light on the temporal relationships of Mode 1 and Mode 2 storm triggering, while Table 8 illustrates the temporal patterns of occurrence of Mode T years with respect to Mode 1 and Mode 2 TE. TE will be employed as one tool for assessing the likelihood of future GDS in MY 35–40 in section 8 below.

5 Mode 2 Storm Triggering and the 2018 GDS

5.1 Working Hypotheses for Mode 1 and Mode 2 Storm Triggering

Orbit-spin coupling is considered to modify the Martian atmospheric circulation through an incremental buildup of atmospheric wind speeds occurring on seasonal timescales (MS17). This buildup must necessarily increase atmospheric momentum and total energy, while introducing, altering, and occasionally strengthening anomalies of the wind and pressure fields. The atmosphere may retain or sequester some portion of this momentum, within meridional circulation cells (section 3.1.3), within atmospheric gyres or stationary eddies, and within large-scale zonal flows. We can collectively refer to these effects as a “spinning up” of the atmosphere that occurs in response to the torque applied.

5.1.1 Working Hypothesis for Mode 1 Storm Triggering

Mode 1 storm triggering, as proposed in S17 and as numerically modeled in MS17 and in N19, takes place near the times when the loading of the atmosphere by this process is at or near peak values. Positive peaks of the dL/dt waveform (Figures 2b, 5, and 6) identify times when Mars is most rapidly gaining orbital angular momentum, at the expense of other members of the solar system family (Shirley, 2015). A type of threshold mechanism has been invoked to explain Mode 1 storm triggering (S17; SM17). In the process envisioned, the accumulated atmospheric momentum and energy may eventually give rise to near-surface wind speeds with velocities sufficient to lift dust that might not be susceptible to lifting under normal, unforced conditions. However, as already noted and discussed in MS17, the cumulative wind speed buildup mechanism was unable to account for the timing of the equinoctial GDS of 1977 and 2001.

Ten of the 14 GDS of the Martian historic record have occurred near times when the second time derivative of the orbital angular momentum d²L/dt² was at or near peak values (section 4.3). These intervals correspond to times when the orbit-spin coupling torque on the Mars atmosphere is changing most rapidly. These are also times when the active forcing of the circulation by orbit-spin coupling is diminishing or is near zero. The temporal relationships observed are incompatible with the above Mode 1 triggering process. We must thus seek some other explanation for Mode 2 GDS.

5.1.2 Working Hypothesis for Mode 2 Storm Triggering

We surmise that when the external forcing is decreasing, the atmosphere will tend to revert to a state driven only by incoming solar energy; however, at such times, it may still possess excess momentum and energy. We thus expect that the atmosphere will respond to the disappearance of the driving accelerations by seeking to restore an equilibrium. Ageostropic winds, flowing down the pressure gradient (across rather than along isobars of pressure), represent one pathway for restoring equilibrium. These may rapidly relieve or adjust pressure gradients within the atmosphere that were built up by the prior cumulative addition of momentum to the system. Readjustment (or relaxation) from this excess momentum condition is likely to result in winds blowing in anomalous or unusual directions (by comparison with the seasonal-normal winds dictated by solar heating, atmospheric tides, and topography). Localized strengthening of near-surface winds may occur during the time period required for re-equilibration of the large-scale wind and pressure fields to take place. The time interval required for this adjustment is likely to be O(10) sols (section 3.1.3). We speculate that short-lived, turbulent, or chaotic episodes, in which cascading effects may give rise to intermittently bursty local wind conditions, are likely.

Locally higher surface wind speeds may thus occur, and dust may be lifted, during the envisioned Mode 2 process of a short-lived re-adjustment of the large-scale circulation. The reorientation of wind directions may expose surface dust deposits or reservoirs that are normally sheltered (by surface roughness or topography) from exposure to seasonal-normal winds. Dust thus lifted will absorb incoming solar energy, which will in turn heat the atmosphere.

We thus propose that the diminution and disappearance of the active dynamical forcing of equation 1 during the transitional intervals may give rise to episodic re-equilibration of the atmospheric wind and pressure fields, as the active forcing decreases. Transfer of momentum to the solid planet, and a frictional damping of accumulated atmospheric energy, as pressure gradients readjust, may aid in generating surface winds with anomalous directions and velocities, near the times when the applied torque on the atmosphere is most rapidly changing. Even in the presence of seasonally lower atmospheric pressure and density, near the equinoxes, these winds may be sufficient to lift dust that subsequently powers up the circulation, through conventional radiative-dynamical positive feedback mechanisms. We thus propose that an “unwinding” of the spun-up atmosphere is an essential factor in the Martian Mode 2 global-scale dust storm initiation process.

5.2 Triggering of the Martian Global-Scale Dust Storm of 2018

In this subsection, we briefly summarize complementary information from other sources pertinent to the triggering process of the MY 34 GDS, including information from applicable numerical modeling investigations and from spacecraft observations, in order to obtain a more complete picture of the MY 34 GDS triggering process. We will consider this complementary information in juxtaposition with solar system dynamical information specific to MY 34, as presented above in Figures 2, 8, 10, and 11.

Numerical modeling may potentially shed light on the underlying details of the triggering processes of the 2018 GDS. Unfortunately, the recent numerical modeling investigations (MS17; N19) wherein orbit-spin coupling accelerations were included, and in which GDS conditions were simulated for MY 34, were optimized for the investigation of Mode 1 triggering. We recognize (in retrospect) that the averaging time interval of 20° of L_s chosen for resolving the differences between forced and unforced model runs in MS17 and N19 was too coarse to reveal essential details of Mode 2 triggering phenomena. The 5° × 5° spatial resolution of the prior simulations may likewise be less than optimal for revealing rapidly evolving details of wind systems developing and evolving in the mesoscale.

Spacecraft observations provide a wealth of information on the inception and development of the 2018 GDS (Guzewich et al., 2018; cf. Kass et al., 2019; Smith, 2019; Heavens et al., 2019; Shirley, Kleinböhl, et al., 2019; Lemmon et al., 2019; Kleinböhl, et al., 2020). As with prior storms, the locations of initial dust lifting and the spatial and temporal development of lifted dust are well characterized by spacecraft visual imaging, nadir sounding, and limb sounding. However, extant spacecraft data do not yet allow us to resolve key details of evolving changes in the large-scale circulatory flows of the atmosphere. (The availability of high spatial and temporal observations of global pressures and winds would enable rigorous testing of the Mode 2 triggering hypothesis of the previous section.)

Circumstantial evidence of a direct role for orbit-spin coupling in the triggering of the 2018 GDS is detailed in Shirley, Kleinböhl, et al. (2019). Atmospheric data obtained by the Mars Climate Sounder (MCS) (McCleese et al., 2007) for the period of initiation of the MY 34 GDS were examined in detail. Seasonal-normal conditions of atmospheric temperatures and dust loading were present on 29 May (L_s = 183.9°). A rapidly growing regional-scale dust storm was well underway within the Acidalia storm track by 4 June (L_s = 187.3°). This storm grew rapidly in latitude and in altitude, while remaining confined within the topographic corridor extending from Acidalia Planitia in the north to Argyre Planitia in the south. By 6 June (L_s = 188.5°), the storm extended more than 120° in latitude, and dust layer peak altitudes extended above 70 km over extensive regions. High-altitude (>50 km) dust hazes had by then encircled all longitudes of the planet. (Typical regional-scale dust storms rarely loft dust above ~45 km in altitude.) By 9 June (L_s = 190.2°), much of the dust lifting activity within the Acidalia Corridor had subsided; however, other lifting centers soon became active (Heavens et al., 2019), and the storm thereafter attained planet-encircling status on about 17 June (L_s = 195°) (Kass et al., 2019).

Various physical mechanisms for rapid storm expansion and for dust lofting to high altitudes were evaluated in Shirley, Kleinböhl, et al. (2019). Intensification of a regional-scale Hadley circulation within the Acidalia Corridor was found to offer the best explanation for the observed spatial and temporal scales of storm development. The existence of an intensified meridional overturning circulation during this period was confirmed by the presence of strong contemporaneous nighttime adiabatic (dynamical) heating at high altitudes (~45 km) in northern and southern high latitudes localized above the Acidalia Corridor.

Intensification of meridional overturning circulations is a fundamental prediction of the orbit-spin coupling hypothesis (section 3.1.1; see also S17; MS17; N19). The duration of the triggering regional-scale storm of early June 2018 is in good agreement with the timescale obtained here in section 3.1.3 for frictional damping of a strengthened meridional overturning circulation cell when active forcing is diminishing. Orbit-spin coupling thus appears to provide a plausible explanation for the events of the earliest days of the 2018 storm as recorded in MCS observations.

The observed rapid intensification of a regional-scale Hadley circulation, as resolved in MCS observations at the start of the 2018 GDS, strongly supports the applicability of the orbit-spin coupling mechanism for the general problem of Martian dust storm occurrence. However, we do not yet possess the high-resolution observations and data required to reach fully definitive conclusions regarding the triggering process of the GDS of 2018.

This section has detailed a working hypothesis for MY 34 storm triggering that may be validated, or disqualified, through future numerical modeling.

6 Results II: The Changing Surface Dust Distribution

Changes from year to year in the spatial distribution of dust available for lifting (Szwast et al., 2006; Newman & Richardson, 2015) have long been considered to represent a possible controlling factor on the occurrence of global-scale storms (Haberle, 1986; Basu et al., 2006; Mulholland et al., 2013). In order to assess the role and importance of this factor with respect to the triggering mechanisms for global storms, it is helpful to first make note of some of the changes in surface albedo effected by the 2018 storm. We approach this question from the perspective of the telescopic observer. Figure 12 indicates a number of locations where changes due to the 2018 storm have been observed. Brief descriptions of the changes are provided in the numbered list below. Place names reference the IAU atlas (M99, Appendix 7).

Syrtis Major was enlarged on the northwest side. Small changes here are not uncommon, but this has been an exceptionally large variation. It has slowly faded with time.
There has been a strong reappearance of the Phasis albedo feature, running between Gallinaria Silva and Aonius Sinus. It comprises a wide dark streak running SE to NW located at the western boundary of Claritas (the eastern boundary of Daedalia). This streak was still obvious as of March 2019.
There is an anomalous dark extension to the SE part of Mare Acidalium at Niliacus Lacus. This extension connects Niliacus Lacus with the northern part of Oxia Palus and is unprecedented in intensity and longevity. It is adjacent to the initiation site of the encircling storm (as first noted on 30 May 2018). As of May 2019, it was still observable with ground-based telescopes.
The classical connection between the aforementioned Oxia Palus and the northern part of Margaritifer Sinus has been effaced by dust fallout.
The northern part of Solis Lacus faded due to dust fallout, though this area is slowly returning to normal. To the north of Site 5, the floor of Valles Marineris was initially brightened by dust fallout, but this is no longer obvious.
The storm produced large patches of bright yellow dust fallout in Hellas and Argyre, enlarging their canonical boundaries, particularly to the east and northeast of Hellas. Both changes were no longer apparent as of February 2019.
The central part of Mare Sirenum was initially affected by dust fallout, but it subsequently nearly recovered its initial intensity. However, a longer-lived change has occurred, resulting in the NW end of the feature darkening and returning to something close to its appearance on the IAU 1957 and Ebisawa 1957 telescopic maps (M99). (It has been faded and truncated in longitude on the western and northwestern side since 1986.)
The NW border of Elysium has contained a variable dark albedo feature since the late 1970s, known as the Aetheria darkening. This was much obscured and faded by dust deposition.
The Mare Serpentis area has darkened, and there was also a notable broadening of Hellespontus, which invaded the eastern part of the Noachis desert. Pandorae Fretum, to the west, was also darkened. This is a very common suite of changes to witness following either regional or encircling storms at or near the Hellas basin. Hellespontus has now reverted to its normal appearance.

The above descriptions confirm expectations of a significant redistribution of surface dust as a consequence of the 2018 storm. It is complementary to forthcoming investigations employing spacecraft observations, which will achieve higher spatial resolution and will be based on quantitative photometric analyses and other techniques. It represents a step toward obtaining an accurate inventory of surface dust reservoirs, including their characteristics and locations. Such an inventory will be valuable for future numerical modeling investigations wherein the surface dust distribution is to be constrained by observations.

6.1 The Surface Dust Distribution as a Factor in the Triggering of Historic GDS

In sections 4.1 and 4.3, we noted that the dynamical forcing in a number of global storm-free years was similar to or stronger than that obtaining in known GDS years with similar phasing. We speculated that an unfavorable distribution of surface dust available for lifting might play a role. In this subsection, we will look more systematically at this question.

The strongest case for a controlling influence of the dust distribution on GDS occurrence comes from the years 1984, 1986, and 2003. The 1984 and 1986 storm-free years (MY 17–18) (Figure 8) followed on the heels of the 1982 storm, which had the strongest forcing of any year in our study. Along with many prior investigators (cf. Szwast et al., 2006), we hypothesize that dust was shifted by the storm into locations that may have been, in effect, sheltered from exposure to the strongest winds of the following years. Similarly, the 2003 dust storm season followed the 2001 equinoctial GDS season. The phasing for 2003 (Figure 8) was much like that of 1909, another equinoctial GDS year.

The situation is more equivocal for the 1941 (Figure 8) and 2016 (Figure 5) storm-free years. Both of these had forcing comparable in phasing and amplitude to other GDS years of our catalog. We are confident that no global storm occurred immediately prior to 1941, that is, in MY −8. However, for 2016, four storm-free Mars years had passed since the prior GDS (2007). Presumably, this interval would allow for a gradual re-arrangement of dust, subsequent to the 2007 event, potentially enabling the occurrence of an event in 2016, under favorable forcing conditions. (Published forecasts calling for a GDS in MY 33 [Shirley, 2015; SM17; MS17] will be discussed in section 7.3 below.) For 1941 and 2016, an unfavorable surface distribution of dust may possibly account for the non-occurrence of GDS; however, support for this explanation is equivocal at best.

In the six remaining storm-free years of Table 2, it appears that there may be no need to invoke an influence of the surface dust distribution on the occurrence or non-occurrence of GDS. In the 2005 dust storm season (MY 27), neither of the MGCM simulations (MS17; N19) generated circulatory changes of a magnitude sufficient to give rise to a global storm in those simulations. Thus, while the phasing for 2005 (Figure 5) was favorable, the magnitude of the forcing may have been insufficient. This may also have been the case for 1969 (MY 8; Figure 5), which had waveform phasing and amplitude similar to that of 2005. Waveform amplitudes are likewise relatively small for 1988 and 2009 (Figure 8) and for 2013 (Figure 9).

On balance, we conclude that a significant influence on GDS occurrence of the surface dust distribution is likely. This implies that efforts to accurately characterize the surface dust distribution, both for 2018 and for past years, should be supported. The results of such investigations will aid in future efforts toward forecasting GDS in support of landed and orbital missions. Maps of the spatial distribution and depth of dust deposits available for lifting could make strong contributions to future numerical modeling efforts. The development and use of “finite dust” models is a key recommendation for moving forward in N19.

7 Discussion

7.1 Overlapping Timescales of Atmospheric Memory Components

Our investigation suggests that a temporary sequestration of orbital momentum within the Mars atmosphere may comprise a form of memory for the large-scale circulation. Here, we compare the dynamical timescales obtained in section 3.1.3 with timescales estimated for several other processes and phenomena. We list and consider these in time order, from the longest to the shortest timescale.

Changes in the surface dust distribution are thought to supply a form of memory for the large-scale circulation (Haberle, 1986; Basu et al., 2006; Mulholland et al., 2013). The results and analysis of section 6 support this hypothesis. This type of memory must evidently operate on timescales from one to several Mars years.

The timescale for the momentum accumulation phase of the orbit-spin coupling intensification and relaxation process (MS17) may encompass time intervals of up to about half of a Mars year.

Characteristic transport timescales of the Martian meridional overturning circulation were investigated by Barnes et al. (1996; see also Barnes et al., 2017). Overturning timescales of 40–60 sols were typically found; however, the ventilation timescales ranged from ~180 sols for equinox conditions to only a few sols for extremely dusty southern summer solstice conditions.

Estimated decay times for atmospheric baroclinic disturbances typically lie in the range of 2–10 sols (Rogberg et al., 2010; Barnes et al., 2017). This timescale is close to that obtained here for frictional damping of a dynamically intensified Hadley cell circulation, that is, O(10) sols.

The Martian atmospheric thermal time constant, most recently estimated to be on the order of <2 sols by Rogberg et al. (2010), is the shortest form of atmospheric memory on this brief list. It plays an extremely important role, given the strong influence of thermal tides on the Martian circulation on semidiurnal and diurnal timescales. τ appears to be somewhat shorter than the dynamical timescale for the relaxation to background conditions we have obtained for an intensified Hadley cell (section 3.1.3).

We note two overlaps with possible implications First, the correspondence between the approximately seasonal timescales for dynamical momentum accumulation and for meridional overturning dovetails with and lends credence to the hypothesis of S17 that orbit-spin coupling may effectively modulate meridional overturning circulations on Mars. Second, there appears to be some overlap between the characteristic timescales for baroclinic disturbances and for frictional damping (section 3.1.3). This correspondence may be entirely coincidental. An interplay, or linkage, between these two processes within the Martian atmosphere, could nonetheless be of interest. Further study is warranted.

7.2 Improved Sub-Seasonal Time Resolution

Early season, mid-season, and late-season dust storms were distinguished on the basis of the phasing of dynamical waveforms in Shirley (2015). Likewise, in SM17 and MS17, different phasing relationships of the dynamical waveforms with the annual cycle were recognized for solsticial GDS and equinoctial GDS. The implied sub-seasonal temporal resolution of storm forcing by orbit-spin coupling in the above cases was, at best, a substantial fraction of a Mars year. From this perspective, the signed mean time difference of 9.9° of L_s separating waveform peak times and GDS inception dates found in the present study represents a considerable step forward. The improvement in temporal precision is largely attributable to the identification here of a second mode of storm triggering. In light of the improved temporal resolution now attained, we are justified in describing the present investigation as a study of the triggering of Martian planet-encircling dust events in general and of the 2018 event in particular. The present results lend credence to the possibility of producing more accurate intra-seasonal dust storm forecasts in future numerical modeling investigations (section 8).

7.3 Revisiting Prior Forecasts for GDS Occurrence in Mars Years 33 and 34

7.3.1 Recapping the MY 33 Forecast

Conditional forecasts favoring the occurrence of a GDS in the perihelion season of MY 33 appeared in Shirley (2015) and in MS17 and SM17. The phasing with respect to the annual cycle of the MY 33 dL/dt waveform is similar to that found for seven historic positive polarity GDS years (SM17). Published forecasts for MY 33 were thus principally based on the positive polarity phasing of the dL/dt waveform for that year. However, the positive polarity preferred phase triggering concept of SM17 has been subsumed within the Mode 1 triggering model of the present study.

Two TE are detected within MY 33; these are illustrated in Figure 13. Figure 13 provides some insight into the failure of the MY 33 forecast. The first TE was of type 2E, and the second was of type 2S. The former episode took place very early in the dust storm season and was quite short, ending by L_s = 183°. The latter episode is more typical, beginning at L_s = 275°, soon after the solstice. As noted in Table 8, only 7 of the 86 Mars years of our study interval exhibit this pattern of TE occurrence. Of those, two were GDS years (MY −16 and MY 15). The MY 33 d²L/dt² waveform amplitude is however considerably lower than was found for those cases (compare Figure 13 with Figure 11f and with Figure S2).

Would the current approach have produced a forecast favorable for GDS occurrence in MY 33? As indicated in Table 8 and in Figure 13, the method of this paper does not resolve a Mode 1 TE for MY 33; the dL/dt waveform peak date is outside the preferred range of Table 6. The resolved Mode 2E TE ends as the dust season is just getting underway (at L_s = 183°); and the d²L/dt² waveform amplitude in both the 2E and the 2S windows is small. These several factors would raise doubts concerning the possible occurrence of a GDS in MY 33. Thus, the present method would not yield a favorable forecast for GDS occurrence in MY 33.

7.3.2 Revisiting the MY 34 Forecast

As noted in section 1, the early-season inception date of the GDS of 2018 came as a surprise, within the context of published forecasts. As was the case with MY 33, the forecasts were predicated on a Mode 1 triggering model.

Figure 11b resolves two TE for MY 34. Both Mode 2E and Mode 1 TE are present. As noted in section 4.5, combinations within a single year of Mode 2E and Mode 1 TE are historically quite favorable for triggering GDS. Two other such examples are shown in Figure 11; in MY 10, and in MY 28, GDS took place within the Mode 1 (second) TE. Thus, by the methods employed here, we now recognize two possible opportunities for GDS triggering in MY 34.

The above example helps to explain the prior success of the positive polarity triggering model (SM17; MS17; N19). Seven positive polarity Mars years with GDS were identified in SM17. This pattern may now be understood either (1) as a result of having multiple TE in positive polarity years, or (2) from another point of view, as a consequence of the inherently lower (seasonal) temporal resolution of the positive polarity phasing criterion. Of the seven positive polarity GDS years of SM17, four are now recognized as hosting Mode 2 events (1924, 1956, 1982, and 1994). In prior studies, these Mode 2 storms could masquerade as positive polarity events. We could not draw clear distinctions between these events and the 1971, 1973, and 2007 Mode 1 storms until the role of the second time derivative d²L/dt² was recognized.

7.4 Future Work

Proof of concept for the orbit-spin coupling hypothesis has now been demonstrated in two numerical modeling investigations (MS17; N19). Our emphasis, moving forward, may justifiably shift from testing focused on verifying the physical hypothesis to more practical studies focused more directly on understanding the consequences of the coupling. An important implication is that a key physics is missing from most currently available MGCMs. In order to more realistically reproduce the inter-annual variability of the Martian atmospheric circulation, it will be necessary to include orbit-spin coupling accelerations within such models. We note in passing that currently available numerical models are not yet able to accurately reproduce the normal seasonal progression of large regional storm activity on Mars (Kass et al., 2016). Tuning of MCGMs to successfully reproduce this form of activity would represent an important step forward in validating MGCM simulations.

Three significant adaptations and enhancements of MGCMs with orbit-spin coupling (MS17; N19) are recognized as key next steps. N19 call for the use of models with finite dust, recognizing that simulations with realistic surface dust inventories would potentially yield more realistic modeling outcomes. N19 also recommend including radiatively active water ice within the simulations, as this is known to have important effects on the dust cycle (Kahre et al., 2012, 2015; Mulholland et al., 2016; Pottier et al., 2017; Lee et al., 2018). Lastly, we recognize that the (spatial) grid spacing employed for the investigations of MS17 and N19 was probably too coarse to resolve important processes occurring at the mesoscale (cf. Richardson & Newman, 2019). This may be particularly important for future simulations of Mode 2E(−) GDS, such as 2001, where relatively small-scale cap-edge storm activity appears to have played an important role in the initiation of the planet-encircling event (Strausberg et al., 2005; Cantor, 2007).

There is much still to be learned concerning the everyday effects of orbit-spin coupling on the Mars atmosphere. Future investigations may, for instance, usefully focus on possible relationships linking the dynamical forcing functions described here with regional-scale dust storm occurrence on Mars. New investigations to verify or disqualify the working hypothesis for Mode 2 storm triggering (section 5) are strongly recommended. Further constraining the timescales for momentum accumulation and release (section 3.1.3) is of particular interest. Modeling activities to address these questions would likely benefit from the MGCM enhancements described above.

From a much broader perspective: Complex variability as a function of time is also found in the orbital angular momenta of all other planets of our solar system. Thus, if orbit-spin coupling gives rise to inter-annual variability of GDS occurrence on Mars, it would be surprising to find that this mechanism may play no similar role in exciting atmospheric variability elsewhere. Future investigations to explore the applicability of orbit-spin coupling to problems of the observed seasonal, inter-annual, and decadal timescale variability of the atmospheric circulations of other solar system bodies are thus justified and are recommended as a potentially fruitful avenue of future research.

8 Forecasts of GDS Occurrence and Non-Occurrence in Future Mars Years

The relative simplicity of the solar system dynamical patterns uncovered in the historic record of GDS occurrence has permitted the formulation of conditional forecasts for future Mars years in a number of past studies (Shirley, 2015; SM17; MS17; N19). As noted in section 1, the occurrence of a global storm in 2018 was anticipated in four prior studies (Shirley, 2015; SM17; MS17; N19). The success of past forecasts has been mixed; in particular, conditions favorable for the occurrence of a planet-encircling storm in MY 33 (2016) were cited in SM17 and in MS17. However, no GDS took place in that year (see section 7.3.1 above).

The recognition of an important role for the rate of change of the orbit-spin coupling torque (d²L/dt²) may enable a significant improvement in the intra-seasonal time resolution for forecasts. As indicated in section 4.4, and as tabulated in Tables 3–5, we obtained a signed mean time difference between waveform peak times and historic GDS inception dates of 9.9° of L_s. In this section, we employ the methodology of section 4.5 for identifying TE as an aid to forecasting. Selection rules for identifying TE are summarized in Table 6 above. The TE approach focuses our attention on time intervals that (based on historic experience) may be more likely to experience future GDS conditions.

Plots of the dL/dt and d²L/dt² waveforms for six future Mars years are given in Figure 14, in a format similar to that employed for the sample of GDS years of Figure 11. (Color coding employed for Figure 14 is similar to that of Figure 11 and Table 8.) In Figure 14, in most cases, d²L/dt² waveforms for similarly phased historic Mars years are provided for purposes of comparison.

The frequency of occurrence of TE in MY 35–40 is shown at the bottom of Table 8. There (and in Figure 14), we note that only one of the upcoming years includes two TE (MY 38). None of the future years of Figure 14 include an identified Mode 1 TE. Both of these factors argue against a high frequency of GDS occurrence in MY 35–40. Future observations of atmospheric phenomena during the upcoming TE of Table 9 may nonetheless prove to be of interest, as these intervals may possibly exhibit increased atmospheric instability, as posited in section 4.5.

Table 9. Waveform Peak Dates and Timing of Torque Episodes (TE) for 2020–2030 (MY 35–40)

Mars year	Perihelion	dL/dt peak	Mode 1 TE	Mode 2E peak	Mode 2E TE	Mode 2S peak	Mode 2S TE
Mars year	Perihelion	Date (L_s)	Window (L_s)	Date (L_s)	Window (L_s)	Date (L_s)	Window (L_s)
35	2020.618	311.2	None	233.8	201–247	None	None
36	2022.536	351.2	None	None	None	261.0	None
37	2024.314	None	None	None	None	284.2	251–297
38	2026.232	35.8	None	179.2	160–192	314.7	282–328
39	2028.149	83.9	None	205.4	172–218	None	None
40	2029.995	113.9	None	None	None	208.4	None

Note. Columns 3 and 5 identify the seasonal dates (L_s) of the extrema of the dL/dt and d²L/dt² curves shown in Figure 14. TE are defined using the methods of section 4.5.

We next discuss relevant dynamical aspects for the six future Mars years of Figure 14, in chronological order, in order to formulate new forecasts based on current understanding. Table 9 provides pertinent quantitative information on TE for each of these years, in a format similar to that employed in Table 7 above.

8.1 2020 (MY 35)

2020 (Figure 14a) is a Mode 2E(+) year, with phasing similar to the 1877 GDS year but with larger amplitude. A GDS was simulated for this year in the modeling study by N19. These two factors favor the occurrence of a planet-encircling dust storm in the 2020 dust storm season. Several other factors dictate caution, however. As indicated in Figure 14a, the storm-free year 1986 (MY 17) is quite similar in phasing and amplitude to MY 35. In MS17, both of these years were assigned to the transitional years category, which was considered to be unfavorable for the occurrence of GDS. We additionally recognize that the 2020 dust storm season follows directly on the heels of the 2018 GDS. Thus, it may be that the distribution of surface dust available for lifting may be unfavorable for GDS occurrence in 2020.

On the basis of the new categorization scheme developed here, we can make a number of other observations. We believe that if a storm does occur in 2020, it is unlikely to be a Mode 1 storm that initiates near or soon after the time of the southern summer solstice. We can in addition state that if a GDS occurs in 2020, it will most likely begin close to or within the forecast window identified in Table 9. The MY 35 TE window center lies at L_s = 224°, and the ±1σ window includes the range from L_s = 201° to L_s = 247°.

Bearing all of the above factors in mind, we cannot presently identify a clear preponderance of evidence for or against the occurrence of a GDS in the 2020 dust storm season.

8.2 2022 (MY 36)

As in SM17 and MS17, 2022 (MY 36) (Figure 14b) is identified as a transitional year, with phase φ_dL/dt = 1° and a Mode T₀ designation (Tables 4, 8, and 9). While the waveform amplitude is large, it is in-family with that for the 1998 season (MY 23). Based on the historic record, we believe that a planet-encircling dust storm is unlikely to occur in this time frame.

8.3 2024 (MY 37)

The d²L/dt² waveform for MY 37 (Figure 14c) is quite similar to that for MY 24 (1999), a global storm-free year. In SM17 and MS17, 2024 was categorized as a negative polarity year, which now receives a Mode 1(−) designation (Table 3). Other years of the Mode 1(−) category have failed to produce global storms.

The waveform shown in Figure 14c for 2024 is similar in form to the Mode 2E(−) years of Figure 8 (see also Figure 14d for this comparison). However, the peak of the MY 37 d²L/dt² waveform (Figure 14c) was attained at L_s = 145.6°, which lies outside the selection range of prior Mode 2E GDS years, as indicated in Tables 6 and 7. The latest date in a 1σ forecast window for this case would lie at L_s = 159°. While no TE could thus be identified for the equinoctial season of MY 37, our methodology does identify a candidate Mode 2S TE, beginning at L_s = 251°. MY 37 is in this way also similar to MY 24, which was an active regional-scale storms year (Wang & Richardson, 2015), with one Mode 2S TE, but which failed to produce a GDS.

It thus appears unlikely, on the basis of the historic record, that a global-scale dust storm will develop on Mars in the 2024 dust storm season.

8.4 2025–2026 (MY 38)

The d²L/dt² waveform for MY 38 (Figure 14d) is a virtual carbon copy of that for the GDS year 2001 (MY 25). The (negative) peak value of the d²L/dt² waveform is attained at L_s = 179.2° (Table 9), compared with L_s = 182.9° for 2001 (Table 7). The center of the TE window then lies at L_s = 169°. Based on the historic record, a GDS inception date much earlier than L_s = 160° seems unlikely, and thus, following the discussion of section 4.5, the beginning of the TE window is placed at L_s = 160°. The upper limit of the 1σ window would then fall at L_s = 192°. Resolving the seasonal timing of this TE is an important first step in the development of a specific forecast for MY 38.

From a purely statistical standpoint, we recognize that a ±2σ time window is substantially more likely to capture the actual start date of the hypothetical future event. We thus add 1σ (23°) to the TE end date above, obtaining a 2σ forecast window upper boundary at L_s = 215°, while leaving the lower boundary unchanged, for the reason cited above and in section 4.5, at L_s = 160°. Our MY 38 GDS forecast window thus extends from 24 October 2025 (L_s = 160°) to 28 January 2026 (L_s = 215°).

In common with the prior investigations (Shirley, 2015; SM17; MS17; N19), we consider that a planet-encircling storm is likely to occur in MY 38. However, we still cannot call this a prediction (Shirley, 2015); instead, we recognize the possibility that other factors may yet play a role; for instance, it is possible that an unfavorable spatial distribution of surface dust reservoirs may exist at that time. The term “forecast” continues to be warranted and appropriate.

We note in passing that MY 38 is unlike MY 25 in containing a second TE (Mode 2S) beginning at L_s = 282°. As indicated in Table 7, the second peak of the d²L/dt² waveform for 2001 lies just outside the limits for 2S TE consideration listed in Table 6.

8.5 2028 (MY 39)

The d²L/dt² waveform for 2028 (Figure 14e) has phasing similar to those for the 1977 GDS year and the 2003 global storm-free year, but with lesser amplitude than both of these. A Mode 2E TE is shown beginning at L_s = 172°. If an equinoctial GDS were to occur in 2028, the 1σ forecast window would indicate a likely inception date between L_s = 172° and L_s = 219°.

In common with MY 35, one may make a case either for the occurrence of a GDS in 2028 or for the non-occurrence of such a storm. The categorization of 2028 as Mode 2E(−) indicates that it is unlikely that a perihelion-season Mode 1 or Mode 2S GDS may occur. MY 39 was previously (SM17, Figure 7) grouped with the negative polarity set, most of whose members are now assigned to Mode 1 (Table 3). That assignment was (and is) considered unfavorable for the occurrence of GDS.

If a planet-encircling dust event occurs in the 2026 dust season, then we believe it is even more unlikely that a similar event may occur in 2028, by analogy with the historic record for 2001 and 2003. Given that the 2028 amplitude is less than for 2003, in contrast with the case for MY 35, our best conditional forecast for 2028 places this in the Mode 2E global storm-free years category (Figure 8d).

8.6 2030 (MY 40)

The nearly featureless d²L/dt² waveform for the 2030 dust season (Figure 14f) is unique among the many waveform plots of this paper. As earlier noted in connection with the years 1975 and 1990, during this Mars year, the barycentric orbital angular momentum of the Sun is much reduced. During these years, the Sun is moving relatively slowly, as it passes in close proximity to the solar system barycenter (Shirley, 2015, Figures 4 and 5). The orbit-spin coupling torques on Mars during this interval are consequently much smaller than normal. Thus, it appears quite unlikely that a GDS could be triggered due to this cause in 2030. Instead, 2030 (MY 40) may represent an unusual example of a year in which the only significant forcing of atmospheric motions throughout much of the year is due to the solar input to the system. Observations from MY 40 could thus be valuable for calibrating the responses of MGCMs under (dynamically) unforced conditions.

8.7 Forecasts Summary

Six Mars years are listed Table 9. Of these, the best candidate year for hosting a future planet-encircling dust event on Mars is 2025–2026 (MY 38). The seasonal timing of the forecasted storm is likely to be similar to that of the 2001 equinoctial GDS. Global-scale dust storms are unlikely to occur in the years 2022, 2024, 2028, and 2030 (MY 36, 37, 39, and 40). The dust storm season of 2020 (MY 35) is here considered a toss-up, as no clear predominance of evidence for or against the occurrence of a storm was found. If a global-scale storm does occur in 2020, it is most likely to initiate between L_s = 201° and L_s = 247°, that is, between 15 May 2020 and 28 July 2020.

The success or failure of these forecasts bears little relationship to the question of the validity of the underlying physical hypothesis. Instead, the relevant metric for assessing that issue lies in the question of whether or not the level of agreement between numerical modeling outcomes and atmospheric observations may be significantly improved by the inclusion of orbit-spin coupling accelerations within such models.

9 Summary and Conclusions

An expanded catalog of Mars years (with and without global-scale dust storms) has been compiled for this study. Catalogs employed in previous investigations have been augmented by the addition of well-documented examples from the telescopic record. The sample employed is ~30% larger than in any prior study. It is unlikely that any significant future additions from historic sources to this catalog may occur. The more comprehensive historic record has enabled a more robust and more nuanced investigation of the putative role of orbit-spin coupling as a contributing factor in Martian GDS occurrence.

The present study has materially advanced our understanding of the physical mechanisms of GDS triggering by orbit-spin coupling. We have for the first time obtained an estimate for the characteristic timescale for frictional damping (to background conditions) of an intensified Martian Hadley cell circulation. A specific set of atmospheric parameters derived from the prior numerical modeling investigation of the 1982 GDS by MS17 was employed to obtain a frictional damping time of O(10) sols for the modeled conditions.

This is, in addition, the first investigation to recognize the significance and characterize the effects of the rate of change of torque parameter d²L/dt². The Martian planet-encircling dust storm of 2018 began within a few weeks of a positive peak in the d²L/dt² waveform. All of the equinoctial GDS of the expanded catalog were initiated under similar external forcing conditions.

Two modes of Martian dust storm triggering (under the orbit-spin coupling hypothesis) are now recognized. Mode 1 forcing, as described in prior work, involves a cumulative incremental loading of the circulation of the atmosphere by angular momentum transferred from the reservoir of the planetary orbital motion. All of the historic Mode 1 storms began near times when the dL/dt waveform, characterizing the external forcing, attained peak values near the midpoint of the dust storm season.

Mode 2 storm triggering, by contrast, is associated with times when the orbit-spin coupling torque is changing most rapidly. The 2018 GDS is our type example. A working hypothesis for Mode 2 dust storm triggering is introduced and described in this paper. The working hypothesis invokes a relatively rapid relaxation, or unwinding, of the previously loaded, spun-up atmosphere. The proposed mechanism may episodically produce ageostrophic winds with directions and speeds that may depart significantly from seasonal norms, facilitating dust lifting from normally sheltered surface locations.

Principal findings of this investigation include the following:

All of the Martian global-scale dust storms evaluated began close to times when (1) orbit-spin coupling torques were attaining peak values or (2) near times when the orbit-spin coupling torques were changing most rapidly.
The orbit-spin coupling storm triggering mechanisms permit and enable both hindcasting and forecasting of Martian GDS events with sub-seasonal time resolution. Orbit-spin coupling now provides explanations both for the previously enigmatic early-season initiation dates of equinoctial storms, such as those of 1977, 2001, and 2018, and for the anomalously late-season inception dates of the 1971 and 1924 events.
A global-scale dust storm is likely to occur early in the Martian dust storm season of MY 38. The preferred (2σ) time window for the forecasted global-scale dust storm of MY 38 extends from L_s = 160° to L_s = 215°, with corresponding calendar dates extending from 24 October 2025 to 28 January 2026.
This investigation provides support for the long-standing hypothesis that the spatial distribution of surface dust available for lifting may play an important role in determining whether or not a GDS may occur in any given Mars year. Orbit-spin coupling accelerations that appear to be sufficient to give rise to GDS in one year may fail to do so in another. The global storm-free years 1984, 1986, and 2003 (MY 16, 17, and 26) are prime examples. An unfavorable spatial distribution of surface dust available for lifting could account for the non-occurrence of GDS in these years.

Surface albedo changes accompanying the 2018 GDS have additionally been mapped and described, through visual inspection of terrestrial telescopic observations of Mars obtained before and after the storm, in this investigation.

The working hypotheses for Mode 1 and Mode 2 storm triggering introduced here may be tested in suitably designed numerical modeling investigations employing Mars general circulation models including orbit-spin coupling. The most recent such investigation (N19), despite a focus on testing Mode 1 triggering only, achieved an unprecedented 78% hindcast success rate in reproducing the historic record of GDS occurrence on Mars (Shirley, Newman, et al., 2019). Future simulations additionally taking account of Mode 2 storm triggering processes are likely to improve on those results.

Acknowledgments

We thank Jim Murphy and Dan McCleese for critical reviews of this manuscript prior to submission. We thank reviewer Mark Richardson and an anonymous reviewer for constructive comments and suggestions during the review phase. We thank Armin Kleinböhl and the members of the MRO-MCS science team for valuable discussions. We thank D. Peach and S. Voltmer for permission to use the Chilescope image of Figure 12. We are grateful to Jon Giorgini for practical and theoretical discussions of planetary dynamics and planetary ephemerides. The accompanying supporting information contain all of the data employed to produce the figures within this paper. These data have additionally been uploaded to the Mendeley archive as cited in the references (Shirley, 2020). Portions of this work were performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Copyright 2019, government sponsorship acknowledged.

Supporting Information

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Citing Literature

Volume125, Issue6

June 2020

e2019JE006077

This article also appears in:

Studies of the 2018/Mars Year 34 Planet-Encircling Dust Storm

Orbit-Spin Coupling and the Triggering of the Martian Planet-Encircling Dust Storm of 2018

Abstract

Key Points

Plain Language Summary

1 Introduction

1.1 Equinoctial Global Dust Storms: An Enigma

1.2 Incorporating Historic GDS Recorded in Telescopic Observations

2 The Historic Record of Martian Global-Scale Dust Storms and GDS-Free Years

2.1 Relevant Telescopic Observations of Historic (and Recent) Martian Dust Storms

2.1.1 The 1877 Storm

2.1.2 The 1909 Storm

2.1.3 The 1975 Storm

2.2 An Updated List of Mars Years Without Global-Scale Dust Storms

2.3 Sample Overview

3 Approach

3.1 The Orbit-Spin Coupling Hypothesis

3.1.1 Predicted Circulatory Intensification

3.1.2 Transitional Intervals

3.1.3 Characteristic Timescales of the Atmospheric Response to Orbit-Spin Coupling

3.1.4 Nomenclature

3.2 Open Questions From Prior Investigations

3.3 Approach and Methodology

4 Results I: Orbit-Spin Coupling

4.1 Mode 1 Storms and Storm Triggering

4.1.1 Overview of Mode 1 Storms and Storm Triggering

4.2 Transitional (Mode T) Mars Years

4.3 Mode 2 Storms and Storm Triggering

4.3.1 Equinoctial Mode 2 Storms and Storm-Free Years (Mode 2E)

4.3.2 Solsticial Mode 2 Storms and Storm-Free Years (Mode 2S)

4.3.3 Mode 2 Overview

4.4 Intra-Seasonal Statistics of GDS Occurrence for the Complete Sample

4.5 Mode 1 and Mode 2 Peak Times in Juxtaposition: Torque Episodes

5 Mode 2 Storm Triggering and the 2018 GDS

5.1 Working Hypotheses for Mode 1 and Mode 2 Storm Triggering

5.1.1 Working Hypothesis for Mode 1 Storm Triggering

5.1.2 Working Hypothesis for Mode 2 Storm Triggering

5.2 Triggering of the Martian Global-Scale Dust Storm of 2018

6 Results II: The Changing Surface Dust Distribution

6.1 The Surface Dust Distribution as a Factor in the Triggering of Historic GDS

7 Discussion

7.1 Overlapping Timescales of Atmospheric Memory Components

7.2 Improved Sub-Seasonal Time Resolution

7.3 Revisiting Prior Forecasts for GDS Occurrence in Mars Years 33 and 34

7.3.1 Recapping the MY 33 Forecast

7.3.2 Revisiting the MY 34 Forecast

7.4 Future Work

8 Forecasts of GDS Occurrence and Non-Occurrence in Future Mars Years

8.1 2020 (MY 35)

8.2 2022 (MY 36)

8.3 2024 (MY 37)

8.4 2025–2026 (MY 38)

8.5 2028 (MY 39)

8.6 2030 (MY 40)

8.7 Forecasts Summary

9 Summary and Conclusions

Acknowledgments

Supporting Information

References

Citing Literature

Figures

References

Related

Information

RESOURCES

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