An eight-year climatology of the martian northern polar vortex

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Introduction
The winter atmosphere of Mars at both hemispheres is dominated by the presence of a polar vortex, a region of the atmosphere characterised by low temperatures and circumscribed by a powerful (westerly) jet.These polar vortices are important features which play key roles in the global atmospheric circulation and local thermal structure.The cold temperatures within the vortex itself enable the predominantly carbon dioxide atmosphere to condense onto the surface, dramatically altering the global atmospheric budget on a seasonal timescale (Haberle et al., 2008).The strong temperature gradient between the poles and lower latitudes results in a strong circumpolar jet via the thermal wind relation, and this westerly jet can form an effective barrier to the polar transport of atmospheric aerosols and chemical species including water vapour (Holmes et al., 2017).The interaction between this jet and planetary stationary topographic waves also helps control the shape of the polar hood cloud belt (Haberle et al., 2019;Streeter et al., 2021).In addition to its importance in the contemporary atmosphere, understanding of the polar vortices can provide insight into Mars' historical climate, recorded in alternating layers of ice and dust at the permanent polar caps (Seu et al., 2018).
Polar vortices have been observed in the atmospheres of several Solar System planets and moons, both terrestrial and gas giants (Mitchell et al., 2021), and are therefore likely ubiquitous in atmospheres across the universe.However, Mars' polar vortices have several distinctive characteristics which distinguish them from other known polar vortices.One example is the martian vortices' peculiar potential vorticity (PV; a useful way to diagnose the strength of the polar vortex, see discussion below) structure.In Earth's polar vortices, PV increases monotonically towards the pole itself.By contrast, previous studies have shown Mars' vortices to have an annular PV structure, where PV is at a maximum in a ring around the pole before decreasing again over the pole itself (Mitchell et al., 2015;Waugh et al., 2016).This annular PV structure is most prominent and coherent when averaged over multiple sols (e.g.Waugh et al., 2016, Fig. 9), but can still be easily identifiable even in instantaneous PV snapshots (e.g.Waugh et al., 2016, Fig. 12).According to theory, an isolated band of PV should in most cases be unstable to perturbation and therefore not https://doi.org/10.1016/j.icarus.2023.115864Received 8 July 2023; Received in revised form 1 November 2023; Accepted 7 November 2023 persist; this makes the seasonal-level persistence of Mars' annular PV structure surprising (Seviour et al., 2017), suggesting the presence of some external stabilising mechanism.Modelling implies that this mechanism is likely the latent heat release from CO 2 condensation over the winter pole, warming the lower atmosphere and thereby weakening the vortex over the pole itself (Toigo et al., 2017;Scott et al., 2020;Rostami et al., 2018).
Another notable feature of Mars' polar vortices is their elliptical morphology, most evident in the northern vortex (Waugh et al., 2016).This shape can be seen in the PV structure of the northern polar vortex, both in instantaneous snapshots (e.g.Mitchell et al., 2015, Fig. 8) and averaged over tens of sols (e.g.Waugh et al., 2016, Fig. 9).Recent modelling work strongly suggests that this characteristic morphology in the north is due to the pattern of the stationary planetary waves induced by the zonal mean topography of the northern mid-latitudes (Seviour et al., 2017;Streeter et al., 2021;Mester, 2022), agreeing with previous theorising (Mitchell et al., 2015;Rostami et al., 2018).
Martian dust storms and background atmospheric dust loading have complex effects on the polar vortices.The most spectacular examples of martian atmospheric dust phenomena are global dust storms (GDS), which tend to occur in the dustier perihelion season ( s = 180-360 • ) every few martian years and loft dust into the air for months at a time, with dramatic consequences for the atmospheric temperature and dynamics (e.g.Gierasch, 1974;Leovy and Zurek, 1979;Haberle et al., 1982).However, martian dust events are well-known to occur at a diverse range of spatial and temporal scales (e.g.Battalio and Wang, 2021), from smaller local dust storms which occur frequently and can last for periods of sols, through regional-scale dust storms with a much greater surface area that can have global effects on the circulation, to GDS.
Of particular interest are regional-scale or regional dust storms (RDS), dust events sufficiently extended in both area and time to significantly impact the background atmospheric state; using this criterion, they have been estimated from modelling to be at least 10 6 m 2 and 10 sols respectively (Toigo et al., 2018).Analysis of temperature and dust observations from satellites has indicated a striking interannual similarity in the timings, locations, and structure of these events for years without a GDS (Kass et al., 2016).In the notation of Kass et al. (2016), ''A'' and ''C'' storms are tropical/mid-latitude events which occur towards the beginning and end of Mars' dusty season respectively, while ''B'' storms occur closer to solstice and are confined to the southern seasonal cap edge.Mars' meridional circulation is dominated by Hadley cells of air rising at tropical latitudes and being transported poleward before descent (Haberle et al., 1993).''A'' and ''C'' regional dust storms (RDS-A and RDS-C) will therefore have greater impacts on global dynamics, and have greater influence on the northern polar vortex in particular, than the southern polar region-confined RDS-B.
Both RDS and GDS have been shown to have noteworthy effects on Mars' polar vortices, these effects having a strong seasonal dependence.Mitchell et al. (2015) investigated the vortices in a reanalysis dataset and found that vortex variability was almost exclusively linked to changes in the Hadley circulation caused by dust loading.A specific RDS-C in Mars Year (MY) 26 caused the centre point of the northern vortex to be shifted ∼10 • in latitude away from the pole, along with an overall weaker polar circulation (Mitchell et al., 2015).Guzewich et al. (2016) and Ball et al. (2021) found from modelling that interannual variability in dust atmospheric loading (such as from RDS) helps drive interannual variability in the zonal asymmetry of the northern vortex.
GDS have been shown to have significant effects on the polar vortices, unsurprisingly given the radical impacts they have on other aspects of Mars' global meteorology.Simulating solstitial global scaledust events in a Mars global climate model (MGCM) in both southern and northern hemispheres, Guzewich et al. (2016) found that these could cause sudden transient warming of the vortex by shifting the downwelling branch of the Hadley cell poleward, resulting in disruption of the northern vortex for up to 10s of sols.Kleinböhl et al. (2020) used retrievals from the orbital Mars Climate Sounder (MCS) instrument during the MY 34 GDS to identify a significant change to the southern polar vortex morphology, with the storm destroying the nightside vortex and leaving only a dayside remnant.Assimilating MCS and Atmospheric Chemistry Suite (ACS) retrievals for the MY 34 GDS, Streeter et al. (2021) also noted this substantial diminishment of the southern vortex, while finding that the northern vortex remained relatively robust in its intensity, and pointed out the potential importance of seasonal timing in determining GDS effects.Most recently, Ball et al. (2021) also used an assimilation of MCS retrievals to find that the solstitial MY 28 GDS had the effect of effectively destroying the northern polar vortex.
This article presents a climatology of the martian north polar vortex for a period of eight Mars Years, covering MY 28-35 inclusive, from an assimilation of MCS temperature and dust retrievals into an MGCM.This multi-annual record allows for characterisation of the typical seasonal patterns and variability of the vortex.This period contains within it two global dust storms, one solstitial (MY 28) and one equinoctial (MY 34), as well as numerous regional dust storms, thus offering an ideal opportunity for investigation of the impacts of global and regional scale dust events on the northern vortex.In particular, the importance of seasonal timing and dust loading in determining storm effects are explored in the results, giving greater insights into the complex relationship between polar dynamics and dust storms across several spatio-temporal scales.

OpenMARS dataset
The dataset used in this study is OpenMARS (Open access to Mars Assimilated Remote Soundings), a publicly available reanalysis of the martian atmosphere constructed through the use of data assimilation (Holmes et al., 2020(Holmes et al., , 2019a)).This technique combines a climate model with atmospheric observations to reconstruct the past state of the atmosphere.The model used in this case was the Planetary Climate Model, UK spectral variant (PCM-UK) (Forget et al., 1999), with a spectral dynamical core (Hoskins and Simmons, 1975), and used extensively by the Open University.The model was run at a spectral resolution of T31, or approximately 5 • horizontal resolution, with 35 vertical levels.The dust distribution in the vertical dimension is allowed to evolve without constraint, according to local transport, while the horizontal dust distribution is constrained by available MCS observations which are assimilated.The assimilation scheme used was a modified version of the Analysis Correction scheme (Lorenc et al., 1991), tuned for the case of Mars' atmosphere (Lewis et al., 1997(Lewis et al., , 2007)).OpenMARS assimilates remote sensing observations of geophysical quantities from various martian orbiters; for the time period examined in this article, the main source of observations was the Mars Climate Sounder (MCS) and its retrievals of temperature profiles and column dust optical depth (CDOD) (Kleinböhl et al., 2017).See Holmes et al. (2020) for more details on the OpenMARS dataset including the model, retrievals, and assimilation scheme.
The full OpenMARS dataset contains periods where the GCM was run with assimilation of MCS retrievals , and where it was run with assimilation of retrievals from the Thermal Emission Spectrometer (TES) aboard the Mars Global Surveyor (MY 24-27).Unfortunately the two instruments did not overlap in their measurements.For this analysis we have decided to focus exclusively on the MCS years for several reasons.Firstly, the MCS dataset is significantly larger than the TES dataset in terms of temporal coverage, and continues to grow in size as MCS is still operating.The eight MCS MY analysed here provide an internally consistent climatology so the focus can be on real atmospheric phenomena, rather than potential instrumental differences affecting the reanalysis.This leads into the second reason: the fact that there are noted and significant differences between TES and MCS years in reanalyses.Studying the EMARS (Ensemble Mars Atmosphere Reanalysis System) reanalysis dataset, Greybush et al. (2019) noticed significant differences in large-scale dynamics between TES and MCS years including in eddy amplitudes, atmospheric temperature variability, and the expression of the solstitial pause.Such systematic differences are unlikely to be in the true state of the martian atmosphere, and therefore are a result of differences in the observation systems and (by extension) in their assimilation into the GCM.These include vertical coverage, spatial coverage, vertical resolution, local time biases, orbital constraints, and others.Disentangling the effects of real atmospheric phenomena from the effects of different observational systems would add another layer of complexity.We have therefore concluded that the extensive MCS dataset and the internal self-consistency of a reanalysis using only one observational system is the best option for this analysis of polar dynamics.

Potential vorticity diagnostics
A frequently employed diagnostic in this and similar studies is Ertel's potential vorticity, or PV.PV is derived using the vorticity (dynamical component) and stratification/static stability (thermodynamic component) of the atmosphere, and is valuable due to its tracer-like conservation under adiabatic processes (Haynes and McIntyre, 1987).This property makes it especially useful in the study of polar dynamics, and polar vortices are frequently defined as regions of high PV around the poles, with a sharp PV gradient on the outer edge marking the boundary of the vortex.Another highly useful fact is that PV cannot be created or destroyed on, or transported between, isentropic surfaces (surfaces of constant potential temperature) (Haynes and McIntyre, 1987).A large-scale PV reduction at a certain location on an isentropic surface therefore implies significant mixing along the surface, often associated with diabatic and/or frictional processes.
PV can be defined as: where  is the gravitational acceleration (3.72 m/s 2 on Mars),  is the relative isentropic vorticity (the relative vorticity of the air mass on that particular isentropic surface),  is the Coriolis parameter (the vorticity associated with the planetary rotation at a particular latitude;  = 2sin() where  is the planet's rotation rate and  is the latitude),  is the potential temperature, and  is the pressure.In this study, PV is calculated and reported as values on isentropic surfaces.Throughout, the 300 K isentropic surface is often used as a default for consistency with previous studies of Mars' polar atmosphere (e.g.Waugh et al., 2016;Streeter et al., 2021;Ball et al., 2021).This surface corresponds to an approximate altitude range of 20-30 km (usually towards the higher end of this range over the winter pole).
PV is typically positive/negative in the northern/southern hemisphere and, for a given height/isentropic level, increases in magnitude towards the poles due to the value of  and the increasing vertical gradient of potential temperature.This study focuses on the northern hemisphere, and so PV values are generally positive, especially at higher latitudes.For simplicity and in line with previous studies (Streeter et al., 2021;Ball et al., 2021), throughout this article 1 '' MPVU'' (Mars potential vorticity unit) is defined as 1 ×10 −4 K m 2 kg −1 s −1 , or 100 PVU (a standard unit used for terrestrial studies).
PV as calculated in Eq. ( 1) has an exponential variation with height, which can make it difficult to investigate (for example) vertical crosssections of PV in the atmosphere (Lait, 1994).To address this issue, Lait (1994) introduced a modified form of PV which has similar conservation properties but removes the exponential variation with altitude, known as Lait PV (LPV).
The use of a dimensionless scaling factor allows easier interpretation of PV with altitude, while maintaining the key conservation property of the impermeability theorem: that PV on isentropic surfaces cannot be destroyed, created, or transported between isentropic surfaces (unless they intersect topography) (McIntyre, 2003).
LPV is defined as where  is potential temperature,  0 is a reference potential temperature value (for this work,  0 = 200 K, in line with previous studies (Waugh et al., 2016;Ball et al., 2021)), and the value of   ∕ for Mars is 3.89.Note that this value differs from previous values used in these kinds of analysis, such as 4.4 (Mitchell et al., 2015) and 4 (Waugh et al., 2016;Ball et al., 2021).We use 3.89 to be consistent with the internal value used in the MGCM.

Results
Throughout this section, the term ''zonal annularity'' is used as a metric to describe the zonally-averaged polar vortex.Here, it is defined to mean the latitudinal distance of the maximum of (absolute) PV from the pole itself.Greater/lesser zonal annularity indicates that the location of greatest PV magnitude is further equatorward/poleward.It should be noted that due to the nature of zonal averaging, a change in zonal annularity could represent a change in the radius of the vortex PV annulus; a change in the location of the centre of the annulus (ie.whether the entire ring structure is shifted off-pole); or some combination of the two.

Seasonal trends and deviations
This section describes the seasonal characteristics and behaviour of Mars' northern polar vortex over the eight MY period investigated in this article.Fig. 1 shows zonally-averaged potential vorticity (PV) at the 300 K isentropic surface for the northmost 45 • for each MY.Presented below the PV plots are plots of column dust optical depth (CDOD), averaged over the tropics (30 • S-30 • N).
The zonally-averaged northern vortex at 300 K shows a high degree of interannual repeatability in its structure and intensity, with the notable exception of GDS periods and periods without MCS data for assimilation.The general pattern appears to be as follows.The vortex first appears some time between  s = 160-170 • and is initially nonzonally annular in its PV structure.It grows in intensity gradually throughout this early dusty/perihelion season until reaching an approximate temporal local maximum in PV at around  s = 200-210 • .At this point, the vortex is still non-zonally annular, with the local PV maximum being located around the pole itself.After reaching this temporal local maximum in PV, PV at the pole then decreases and the local PV maximum drifts equatorward, forming a zonally annular PV structure.The local PV maximum remains at ∼80 • N, with a zonally annular vortex structure, during approximately  s = 220-330 • .After this time, the local PV maximum once more returns poleward, and the vortex becomes non-zonally annular for the brief remainder of its duration.
Similar plots to those shown in Fig. 1 were also created for the 260 K (approximately 10-20 km altitude) and 400 K (approximately 40-50 km altitude) isentropic surfaces, but not shown here.The general pattern of timings of inception, evolution (including zonal annularity and drift of the local PV maximum), and decay remains reasonably consistent across these different isentropic surfaces.That said, there are certain systematic differences between the PV structure of the vortex at the different isentropic surfaces.The vortex has a greater zonal annularity at the 260 K isentropic surface, which decreases at higher isentropic surfaces (greater altitudes).Specifically, at 260 K the local PV maximum (when the vortex is zonally annular) is located at ∼75 • N, while at 400 K it is located at ∼85 • N.This implies a cone-like vertical PV structure, sloping towards the pole with altitude/isentrope.
While this high interannual similarity holds in general, there are notable exceptions which can be divided into three main categories.The first, and the most salient to this study, is that of dust events with spatial extent greater than the model horizontal resolution; henceforth, ''model resolution-scale dust events''.This category will be returned to momentarily.The second is that of periods when the model is free-running due to a lack of MCS data for assimilation: for example,  s ∼270-280 • of MY 34, as seen in Fig. 1.At these periods, it can be seen in Fig. 1 that there is a dramatic change in the PV structure of the vortex compared to adjacent periods with MCS data to assimilate, as well as compared to the equivalent period in other MYs when there is MCS data to assimilate.In general, PV during these free-run periods is higher at all latitudes but especially near the pole itself, and there is a complete absence of a zonally annular PV structure.The difficulties experienced by some free-running MGCMs in reproducing Mars' characteristic annular vortices have been discussed elsewhere (e.g.Toigo et al., 2017;Seviour et al., 2017) and are beyond the scope of this study.
Finally, the third category is that of small PV perturbations which do not appear to be linked to (model resolution-scale) dust events.These perturbations mostly appear at very high (>75 • N) latitudes and have relatively short (<5  .This is nowhere close to being an exhaustive list, and examples of this kind can be found in every MY in Fig. 1 and across the whole season when the northern vortex is present.This list is simply intended to point out some examples of this phenomenon for reference.The examples listed tend to have two main (but likely linked) morphological features.The first is a sharp increase in PV at the northernmost latitudes (>82.5 • N).The second is a corresponding sharp drop in PV at the location of the local PV maximum (when the vortex is zonally annular, this is usually at ∼80 • N at the 300 K isentropic surface).The concurrent nature of these two features suggests a short-lived and rapid redistribution of PV poleward, but is not obviously linked to large-scale tropical dust loading.This category of small-scale PV perturbations requires its own separate study and will be studied in future work.
Returning to the first category of (model resolution-scale) dust events, there are numerous cases in Fig. 1 where there are large-scale perturbations of the northern polar vortex PV structure which can be linked to significant tropical CDOD changes.The most spectacular examples are the two GDS events which occur in this period: in MY 28  s = 265-300 • , and in MY 34  s = 190-240 • .The specific effects of these events have been discussed in greater detail elsewhere (e.g.Streeter et al., 2021;Ball et al., 2021), and so only a brief summary is provided here.The MY 28 GDS occurred around solstice and almost entirely destroyed the northern polar vortex, with local PV reductions of up to 100% at the peak of its impact around  s = 280 • .This peak in local PV reduction also corresponds to local PV increases at lower latitudes (at least down to 45 • N from 60 • N), suggesting PV redistribution to lower latitudes.After this peak, the vortex was somewhat reestablished but with a notably diminished size relative to other MYs at the same time, and lacking the characteristic zonally annular structure normally present at this season.The zonally annular structure did not return until  s = 310 • .
Despite similarly high CDOD values, the MY 34 GDS had markedly different effects on the northern polar vortex compared to the MY 28 GDS.The MY 34 event occurred around equinox and had relatively limited impacts (in the north), causing compression of the vortex poleward and some local PV reduction, but nowhere near the same order of magnitude as that caused by the MY 28 GDS.The zonally annular morphology of the vortex was also delayed in its appearance relative to other MYs, not being established until well into the dusty/perihelion season around  s = 240 • .Even then, the latitude of the local PV maximum remained a few degrees higher than in other MYs, before returning to background levels at around  s = 285 • (after a gap in MCS data).More details of the effects of the MY 34 GDS on both northern and southern polar vortices can be found in Streeter et al. (2021).
The other example of (model resolution-scale) dust events which perturb the PV field are regional-scale dust storms, discussed in Section 3.2, ''Regional dust storm impacts''.

A brief note on the southern polar vortex
This study focuses on the northern polar vortex, as it occurs during the dusty martian perihelion season and is therefore more subject to interannual variability from dust storms.The clearer aphelion season is by contrast quieter.However, it is worth a brief discussion here in the interests of completeness.
Fig. 2 shows the behaviour of the zonally-averaged southern polar vortex during the period  s = 0-180 • for MY 28-35.It is apparent that interannual repeatability in the vortex structure and behaviour is even greater than in the north, likely at least in part due to the lack of major dust storm activity.That said, even the relatively (compared to climatology) large and rare event of the regional dust storm at around  s = 40 • of MY 35 appeared to have minimal impacts on the southern polar vortex.As in the north, the local absolute PV maximum (in the south, PV minimum) is located off-pole for most of the lifespan of the vortex, at around 70 • S between around  s = 45-140 • .
One possible hint of long-lasting interannual variability can be found in the magnitude of the PV minimum band between  s = 75-120 • , at the greatest extent of the vortex.This band appears relatively weaker in MY 29, but grows in magnitude by up to 10 MPVU by the same period in MY 34.In MY 35, however, it appears to have diminished back to a similar magnitude as in MY 30.One possible explanation is that both MY 28 and 34 were GDS years.This would imply that GDS have a small but noticeable effect in diminishing or suppressing the southern polar vortex, perhaps via dust redistribution and resulting changes to surface albedo (and therefore atmospheric temperatures), as described in Bapst et al. (2022).This effect would then lessen over the following non-GDS years as surface dust distributions (and albedoes) return back to their pre-GDS state.

Regional dust storm impacts
This section examines the impacts of RDS on the northern polar vortex via its effects on the (zonally-averaged and non-zonally-averaged) 300 K isentropic surface PV, and the vertical Lait PV structure.

300 K isentropic surface
Fig. 1 shows the impact of multiple RDS on the zonally-averaged PV field at northern high latitudes.The convention for referring to RDS followed is that of Kass et al. (2016), which defines A, B, and C storms in the dusty/perihelion season.RDS-B are excluded from this analysis due to their location at the southern cap edge, as they are therefore not expected to have any significant impact on norther polar dynamics.RDS-A and RDS-C occur at the tropics/mid-latitudes, and therefore might be expected to affect northern polar dynamics via their modification of the large-scale atmospheric temperature structure and the meridional circulation.
Table 1 contains the dates of RDS-A, RDS-C, and GDS for MY 28-35 as defined for the purposes of this study.To maintain consistency between storms, the time periods for GDS are restricted to the 10 •  s periods with the greatest dust loading, despite the fact that the full GDS lasted for significantly longer.
There were RDS-A in all of the MYs investigated except for two, MY 28 and MY 34, which instead had GDS.These events, as defined for the purposes of this study, all occurred some time between  s = 210-255 • .It is apparent from Fig. 1 that there is some diversity in the impacts of RDS-A on the zonally-averaged PV structure of the northern polar vortex.The MY 29 RDS-A, a high opacity event, appeared to compress the vortex poleward, removing the zonally annular structure which had developed and increasing PV at the polemost latitudes for around 5 • of  s .The MY 30 RDS-A, despite occurring at a very similar time, was significantly weaker in opacity, and appeared to have minor-tonegligible effects.The MY 31, MY 32, and MY 33 RDS-A were all earlier events (near the beginning of the dusty/perihelion season) of moderate, high, and low opacity, respectively.Interestingly, all are linked to more defined zonally annular PV structures, with a higher local off-pole PV maximum, than either the periods immediately preceding them or the same periods in MY with later RDS-A (MY 28-30, MY 35).Finally, the RDS-A in MY 35 had a timing closer to that of MY 29 and a high opacity, and had a similar effect to the MY 29 event in compressing the vortex poleward and removing the zonal annularity of the vortex for around 5 • of  s .
There were RDS-C in all of the MYs investigated, occurring between  s = 315-345 • .However, the MY 29 RDS-C occurred entirely during a gap in MCS data, and so the MGCM was run freely during this period; this RDS-C is therefore excluded from this analysis.The MY 28 RDS-C occurred late (ie.further from solstice) and had a relatively low opacity; it also appeared to have minor-to-negligible effects on the northern pole PV structure.The MY 30 RDS-C occurred earlier but also with low opacities, and was linked to a minor poleward shift of the local PV maximum by up to ∼5 • and a temporary loss of zonal annularity.The effects were short-lived, with zonal annularity returning after ∼2 • of  s .It should be noted, though, that the MY 30 vortex appeared to lose its zonal annularity earlier than in other MYs; MY 30 was also the year with the lowest dust loading in the period studied.The MY 31 RDS-C was an early event with moderate opacity, and had a significant effect on the northern polar PV structure: first causing a reduction in PV at the local PV maximum, before compressing the vortex to the pole itself and removing the zonally annular structure for at least 5 • of  s .The MY 32 RDS-C occurred at the same time (for the purposes of this study; the MY 32 RDS-C had an odd double-peak structure in opacity with time, but the first peak was chosen for this analysis despite a small data gap) with low-moderate opacity, and had similar effects to the MY 31 RDS-C event.However, there was a lesser initial reduction in PV, and the loss of zonal annularity in the vortex persisted for less time.
The MY 33 RDS-C again occurred ∼10 • of  s later than the previous two, with moderate-high opacity.Though, as with the previous two events, there was an initial reduction in PV at the local PV maximum followed by a shifting of PV maximum poleward, the poleward shift was insufficient to remove the zonal annularity of the vortex.The MY 34 RDS-C also occurred reasonably later in the season, with a high opacity.Despite much higher dust loading, the effects were not dissimilar to those of the MY 33 event, and indeed less pronounced than those of

Vertical structure
The use of Lait-scaled PV (LPV), described in Section 2, allows the investigation of the vertical vortex structure and its response to RDS (and GDS), as seen in Figs. 3 for RDS-A and 4 for RDS-C.These plots show effects relative to the same period in MY 30, the year with the lowest dust loading of the eight MYs investigated in this study.Also included are contour plots of the (Eulerian) mean meridional circulation (MMC), a diagnostic parameter which gives an indication of the strength and direction of the zonally-averaged meridional flow.The MMC is calculated as the zonal-average meridional mass flow streamfunction which satisfies considerations of thermal wind balance and conservation of angular momentum (see Holton, 2004).Positive streamfunction contours imply anticlockwise circulation in the plane of the figure (Figs. 3 and 4) and contours are labelled in units of 10 9 kg∕s.On Mars, this circulation is dominated by thermally-direct (Hadley) cells which upwell at subsolar latitudes and downwell at mid-high latitudes, depositing angular momentum and warmer tropical air.The structure of these cells is seasonally dependent: around equinox it is roughly axisymmetrical, with both Hadley cells upwelling around the equator; around solstice it is characterised by a dominant cross-equatorial Hadley cell upwelling in the summer hemisphere and downwelling at mid-high latitudes in the winter hemisphere (e.g.Read et al., 2015;Barnes et al., 2017).
Fig. 3 shows the impacts of RDS-A and the MY 28 and MY 34 GDS on the vertical LPV and MMC structures for each MY.The MY 28 GDS clearly caused a significant PV reduction at the latitudes of the polar vortex, linked to a dramatically strengthened dominant Hadley cell.At this time of year (solstice), the dominant south-tonorth cross-equatorial Hadley cell is already at its peak strength and latitudinal extension, and the GDS boosted the strength of this existing structure by up to double relative to MY 30, driving warmer tropical air further poleward and reducing the temperature stratification of the polar atmosphere.In general, the RDS-A had markedly similar effects relative to MY 30: causing a compression of the vortex poleward, signified by a redistribution of LPV from lower to higher latitudes.The greatest LPV changes in absolute terms occurred between 30-50 km, and LPV generally decreased between 50-75 • N and increased between 75-90 • N. The greatest changes to absolute LPV from RDS-A occurred in MY 29, MY 33, and MY 35.These were all also the latest RDS-A to occur.The MY 33 RDS-A did occur at the same time as the MY 32 RDS-A, but interestingly with a lower dust opacity.The earlier storms, and including the MY 34 GDS, appeared to have a reduced impact on LPV.
Fig. 4 shows the impacts from RDS-C.In general there was a reduced impact on absolute LPV compared to RDS-A, though it should be noted that the averaged LPV at these time periods is less than at RDS-A periods.The exception was MY 29; however, as mentioned earlier, there was lack of MCS data to assimilate at this time and so the MGCM was allowed to run freely.This RDS-C is therefore excluded from this analysis.Most RDS-C showed a similar pattern of LPV impacts as RDS-A: a redistribution of LPV poleward, at similar latitudes and altitudes, and matching with a boosted meridional circulation.The greatest LPV changes appeared to be during the MY 31, MY 34, and MY 35 RDS-C, and the least during the MY 28 and MY 33 RDS-C, with the MY 32 RDS-C occupying something of a middle ground.The MY 31, MY 32, MY 34, and MY 35 RDS-C were all relatively early events while the MY 28 and MY 33 events occurred later.This appears to be the main distinguishing factor in determining RDS-C impacts, as the MY 35 RDS-C had a slightly greater effect on LPV than the MY 34 event despite much lower dust loading, while the MY 31 RDS-C had only a slightly greater effect on LPV than the MY 32 event despite a greater dust loading; both of these events occurred at the same time.

Zonal structure
Figs. 5 and 7 show the northern polar PV structure during the RDS-A and RDS-C respectively, while Figs.6 and 8 show the difference between that and the same period during MY 30, the MY with lowest dust activity in those investigated for this analysis.In this section, ''annular'' is used to refer to a non-monotonic PV structure where the PV maximum is located in an annulus, and absolute PV decreased again inside the annulus.respectively, though with the exception of the MY 33 RDS-A which occurred at the same time as the MY 32 event.As noted previously, however, the MY 32 RDS-A had a significantly greater dust loading than its immediate successor.
Comparing these PV structures to the same period in MY 30, as in Fig. 6, reveals a consistent general pattern of differences.Both RDS-A and GDS increased PV over and close to the pole itself, and reduced it at lower latitudes, indicating a redistribution of PV from lower to higher latitudes.The magnitude and latitudes of these changes show some variation, however.Interestingly, the MY 28 GDS and MY 34 GDS had the greatest and least PV impacts respectively, likely related to their respective timings at solstice and equinox.Of the RDS-A, the greatest PV impacts occurred during MY 29, MY 33, and MY 35, with lesser impacts during MY 31 and MY 32.Again, the key determining factor appears to be seasonal timing: later events had a greater PV impact.And again, the difference between the MY 32 and MY 33 RDS-A would seem to be linked to the greater dust loading of the MY 32 event, with the weaker event counterintuitively having the greater PV impact.
Another notable feature from Fig. 6 is the zonal asymmetry of PV changes caused by RDS-A.The greatest decreases in PV occurred at longitudes 0-60 • W and 120-180 • E, which correspond to the locations of the greatest extension of the elliptical polar vortex.Preferential PV decrease at these longitudes therefore corresponds to a reduced ellipticity of the vortex, similar to that induced by the MY 34 GDS as shown in previous modelling work (Streeter et al., 2021).This is apparent in the RDS-A of MY 31,32,33,and 35.This similar pattern is despite the lower dust loadings of the RDS-A compared to the MY 34 GDS, suggesting that the later seasonal timing of the RDS-A may compensate for the lower dust loadings to generate a similar impact in reducing northern polar vortex ellipticity, via the mechanisms described in Streeter et al. (2021) of a shifting of the northern polar jet poleward and away from the northern mid-latitude regions of high mechanical forcing responsible for the usual characteristic wavenumber-2 stationary wave pattern.
The vortex structure during RDS-C can be seen in Fig. 7, and is annular for all MY except for MY 29; as mentioned, this was a period without MCS data to assimilate, and so MY 29 is excluded from this analysis.All MY except for MY 28 and MY 29 also show a similar zonal asymmetry in the annular structure: the central local PV minimum is offset from the pole by several degrees, and centred around longitudes 0-120 • E (ie. the eastern hemisphere).In most cases, these longitudes also correspond to the location of the greatest magnitude of the local PV maximum in the annulus, such as in MY 30,MY 31,MY 34,and MY 35.Comparing the RDS-C periods to the same period in MY 30, in Fig. 8, there is a similar pattern to the effects of RDS-A: an increase in PV near the pole itself, and a decrease at lower latitudes.The striking exception is in MY 28, the latest RDS-C, which experienced the opposite effect.Overall, the later RDS-C (MY 28, MY 33, MY 34) appeared to have lesser PV impacts, even when dust loading was very high (MY 34).There was also the same zonal asymmetry in PV effects as seen in the RDS-A case.In addition, however, the western hemisphere appeared to experience greater PV decrease (seen in MY 31,MY 32,MY 33,MY 35); this zonal asymmetry may help explain the apparent zonal asymmetry of the annuli in Fig. 7.

Discussion
Mars' northern polar vortex in general displays a strong interannual repeatability, including in its response to regional-scale dust storms, though with notable exceptions.The OpenMARS reanalysis shows a consistent pattern of northern polar vortex inception, growth, the development of an annular PV structure, and finally decay, which does not vary significantly between martian years in the absence of large dust events (a crucial caveat).As noted in other studies (e.g.Ball et al., 2021), the vertical structure of the vortex shows a sloping morphology, with the local PV maximum extending further poleward at higher altitudes until its structure is no longer annular.The annular structure present on the 300 K isentropic surface only develops ∼40-50 • of  s after the inception of the vortex, from around  s = 220 • , and persists until close to the end of the dusty/perihelion season at around  s = 330 • .As this annular structure has been linked to latent heat release from CO 2 condensation (e.g.Toigo et al., 2017), and given the short radiative timescales involved (e.g.Seviour et al., 2017), this behaviour has potentially interesting links to the martian CO 2 cycle and its behaviour at the north pole, including rates of condensation and CO 2 ice cloud microphysics.
The reaction of the northern polar vortex to the two global dust storms within this period, the MY 28 and MY 34 GDS, agrees well with previous studies.The solstitial MY 28 GDS caused an enormous PV reduction in the northern polar vortex, effectively destroying it for at least 10 • of  s , as reported by Ball et al. (2021).The equinoctial MY 34 GDS, by contrast, had a much more limited effect on the northern vortex, temporarily stunting its usual development but not causing the magnitude of PV reduction seen in MY 28; this agrees with Streeter et al. (2021).These cases, both intense GDS with similarly high dust loadings, therefore support the idea that the seasonal timing of dust events is critical in determining their impacts on the northern polar vortex.In particular, this highlights the importance of their closeness to solstice/perihelion (close together in Mars' current orbital configuration), when the dominant cross-equatorial Hadley cell is at its maximum strength and latitudinal extent.
A and C type regional scale dust storms also had notable effects on the northern polar vortex.Both RDS-A and RDS-C had the generally consistent effect of redistributing PV poleward, decreasing the radius of the PV annulus and in some cases removing annularity entirely.This redistribution occurred across multiple isentropic surfaces, and most strongly in the roughly 30-50 km altitude range.An off-pole shift of the centre of the vortex by several degrees of latitude, and generally towards the eastern hemisphere, was also observed, consistent with a previous RDS-C study (Mitchell et al., 2015).These PV effects correlated with enhanced mean meridional circulation patterns, specifically of the dominant cross-equatorial Hadley cell.For both RDS-A and RDS-C, there was a clear pattern where storms closer to solstice (i.e.later RDS-A and earlier RDS-C) had a more pronounced effect on PV; this pattern is also fit by the two GDS, which occurred at solstice and equinox.
Dust loading associated with RDS-A and RDS-C did not appear to have a straightforward correlation with impacts on the northern polar vortex.The MY 32 and MY 33 RDS-A occurred at the same time, but despite the MY 32 event having significantly higher opacity, it appeared to cause slightly less PV redistribution than its successor.Likewise, the MY 31 and MY 35 RDS-C occurred at the same time, but despite the significantly higher opacities in the latter event, the PV impact appeared to be very similar.And of course the MY 34 GDS, despite its much greater opacities than any RDS-A, had similar or lesser effects on PV.These results suggest that the CDOD of dust events is far less important in determining their polar vortex impacts than the time of year at which they occur.That said, it is also evident that dust loadings in excess of background climatological values have some impact on the vortex, both from these results and from previous work (e.g.Guzewich et al., 2016;Ball et al., 2021;Streeter et al., 2021).There may therefore be some critical value or threshold, possibly seasonally dependent, beyond which increased CDOD has radically diminished or even reversed effects.These ideas are supported by work investigating the relative importance of CDOD and planetary obliquity on specific martian polar dynamical phenomena.Toigo and Waugh (2022) found that while obliquity always had a strong correlation with modelled dynamical impacts, the correlation with CDOD was weaker and contingent.This was found to be due to the relative importance of each factor in affecting the underlying mechanism: the Hadley circulation, and its extent.
From these results, the dominant impacts of RDS (and GDS) on the northern polar vortex appear to be determined by the seasonal timing of the storm, with the tropical CDOD showing little to no relation with effects on PV redistribution.These effects appear to be mediated via impacts on the mean meridional circulation, and specifically the crossequatorial south-to-north Hadley cell which is the dominant meridional circulatory feature for most of the dusty/perihelion season.This circulatory structure is broadly determined by the time of year via the subsolar point and the distance of Mars from the Sun.CDOD around the tropics and the latitude of the upwelling branch of the Hadley cell(s) can also have an impact in boosting the strength and latitudinal extent of the existing Hadley cell, but the gross morphology is ultimately controlled by the season.This gross morphology, once boosted by some degree of CDOD higher than climatological background levels, is what determines the impacts on the northern polar vortex PV structure.

Conclusions
The sophistication of modern numerical models of the martian atmosphere, combined with the high volume of contemporary observations of it, afford an excellent opportunity to examine multi-year trends in polar dynamics.We investigated the behaviour and characteristics of Mars' north polar vortex over eight recent martian years, using the OpenMARS meteorological reanalysis of Mars' atmosphere.We present our main conclusions below.
1.The north polar vortex structure displays high interannual repeatability in its structure and seasonal behaviour, including its latitudinal extension, time of inception, pattern of growth, time over which it becomes zonally annular in structure, and its decay.2. Large-scale perturbations to this climatological structure are due to the effects of regional and global scale dust storms, which act to compress the vortex poleward and reduce the radius of the vortex annulus (via redistribution of PV from lower to higher latitudes), as well as shifting the vortex centre off-pole.3. The seasonal timing of these large dust events appears to be the key factor in determining impacts on vortex PV structure: large dust events closer to southern summer solstice appear to have greater impacts on the north polar vortex, independent of tropical dust loading.4.This importance of seasonal timing is likely due to the seasonal background meridional circulation, as the dominant crossequatorial Hadley cell reaches its peak in strength and latitudinal extent around this time.Dust-induced enhancement of this background circulatory structure therefore allows greater transport of heat into high latitude, including north polar, regions.
Better understanding of the general and perturbed behaviour of Mars' contemporary polar atmosphere will be valuable for many aspects of martian study including the transport of tracers (such as aerosols and chemical species), the shape of cloud features, and the general large-scale circulation.In addition, it could provide insights into past martian climate via linking contemporary polar deposition patterns to the record of past deposition located in the polar layered deposits.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Northern polar PV and tropical CDOD.Periods lacking MCS data for assimilation are indicated with grey shading; during these periods, the MGCM was allowed to run freely.The overlaid black dashed line indicates latitude of maximum PV value at each time.

Fig. 2 .
Fig. 2. Southern polar PV and tropical CDOD.Periods lacking MCS data for assimilation are indicated with grey shading; during these periods, the MGCM was allowed to run freely.The overlaid black dashed line indicates latitude of maximum (absolute) PV value at each time.Note the difference in CDOD colour scale from the previous figure.

Fig. 3 .
Fig.3.Vertical Lait PV difference (relative to same period in MY 30) for the period of each A type storm for MY 28-35 (note that these are GDS for MY 28 and 34).Overlaid are contours of mean meridional circulation (MMC), with red contours showing the averaged MMC for that MY and period, and blue contours showing the averaged MMC for the same period in MY 30.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 .
Fig. 4. Vertical Lait PV difference (relative to same period in MY 30) for the period of each C type storm for MY 28-35.Overlaid are contours of mean meridional circulation (MMC), with red contours showing the averaged MMC for that MY and period, and blue contours showing the averaged MMC for the same period in MY 30.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .
Fig. 5. Northern polar PV for the period of each RDS-A for MY 28-35, on the 300 K isentropic surface.Plots are in a northern stereographic projection, with latitude circles at 10 • intervals.The innermost latitude circle is at 80 • N. PV values are averaged over the  s interval indicated for each subplot.

Fig. 6 .
Fig. 6.Northern polar PV difference relative to MY 30 for the period of each RDS-A for MY 28-35, on the 300 K isentropic surface.Plots are in a northern stereographic projection, with latitude circles at 10 • intervals.The innermost latitude circle is at 80 • N. PV values are averaged over the  s interval indicated for each subplot.

Fig. 7 .
Fig. 7. Northern polar PV for the period of each RDS-C for MY 28-35, on the 300 K isentropic surface.Plots are in a northern stereographic projection, with latitude circles at 10 • intervals.The innermost latitude circle is at 80 • N. PV values are averaged over the  s interval indicated for each subplot.The structure of the northern polar vortex during RDS-A, as seen in Fig.5, is annular except for in MY 29; it is also non-annular during the MY 28 and MY 34 GDS.The annular structure has a higher local

Fig. 8 .
Fig. 8. Northern polar PV difference relative to MY 30 for the period of each RDS-C for MY 28-35, on the 300 K isentropic surface.Plots are in a northern stereographic projection, with latitude circles at 10 • intervals.The innermost latitude circle is at 80 • N. PV values are averaged over the  s interval indicated for each subplot.

Table 1
Table of RDS-A, RDS-C, and GDS storm dates as defined for the purposes of this study.All dates are in • of  s .