OpenMARS: A global record of martian weather from 1999 2015

The Open access to Mars Assimilated Remote Soundings (OpenMARS) dataset is a reanalysis product combining past spacecraft observations with a Mars Global Circulation Model (GCM). The OpenMARS product is a global surface/atmosphere reference database of surface and atmospheric properties for almost nine Mars years that can be used by Mars scientists and engineers interested in global surface/atmospheric conditions and the physical, dynamical and chemical behaviour of the atmosphere for the recent past on Mars. In the OpenMARS dataset, spacecraft observations of temperature, dust and water vapour from the Thermal Emission Spectrometer (TES) instrument on the NASA Mars Global Surveyor spacecraft, temperature and dust from the Mars Climate Sounder (MCS) instrument aboard NASA ’ s Mars Reconnaissance Orbiter spacecraft and ozone from the Spectrometer for the Investigation of the Characteristics of the Atmosphere of Mars (SPICAM) instrument on the European Space Agency (ESA) Mars Express orbiter are combined with a Mars GCM used at the Open University.


Introduction
A reference dataset for the martian atmosphere and surface that provides the best estimate of the past weather on Mars has for a long time been sought by scientists and engineers looking to send satellites to orbit Mars and for landing rovers and surface platforms on the surface, resulting in the creation of the Mars Climate Database (Lewis et al., 1999), perhaps the most prevalent reference dataset used so far. While it has been extensively validated with current observations, it does not combine output from the Mars global circulation model (GCM) with current and past retrievals; a process which is commonplace on Earth in particular for forecasting the global weather and providing the best dataset of the past climate (Dee et al., 2011). A synergism of retrievals of the atmosphere of Mars with one of the world's leading Mars global circulation models is a key next step towards this goal in providing accurate forecasting and reanalyses akin to what we have available to us on Earth.
To address some of the limitations noted above, we have created the Open access to Mars Assimilated Remote Soundings (OpenMARS) dataset to be used as a reference dataset of the actual global weather occurring on Mars from 1999 to 2015. This dataset is able to sit alongside the MCD dataset that provides a smoothed seasonal climatology for varying dust scenarios. While the MCD datset provides multiple different scenarios that can be used to explore the parameter space of key variables of high importance to landing a rover on Mars (for example), the OpenMARS dataset provides the best estimate of the atmospheric state for the past 9 Mars years, with the global state of the atmosphere constrained by observational datasets and physical laws in the Mars GCM (in particular for spatio-temporal regions for which observations are not available nearby). The OpenMARS dataset would therefore be more appropriate to use as the best estimate of the atmospheric state when re-processing past satellite observations of the martian atmosphere, or for investigating specific past weather events that have occurred on Mars from 1999 to 2015. The OpenMARS dataset however does not contain simulations of the thermosphere, or several trace gases (such as CO and odd hydrogen species) that are present in the martian atmosphere, so it would be more appropriate to use the MCD for these investigations. If the user would also prefer to look at a wider parameter space of atmospheric dust content, for quick and easy estimates of potential extreme conditions upon atmospheric entry of a spacecraft as an example, the MCD would be more appropriate than the OpenMARS reanalysis dataset.
Two other reanalyses products for the Mars atmosphere have previously been created to this date. The Ensemble Mars Atmosphere Reanalysis System (EMARS) is fully described in Greybush et al. (2012), and has recently been made publicly available (Greybush et al., 2019a,b). In the EMARS reanalysis product, retrievals of Thermal Emission Spectrometer (TES) and Mars Climate Sounder (MCS) temperature profiles are assimilated into the Geophysical Fluid Dynamics Laboratory Mars GCM (Greybush et al., 2019a,b) that includes a finite volume dynamical core based on a longitude-latitude coordinate system. The EMARS reanalysis uses the Local Ensemble Transform Kalman Filter assimilation scheme (Hunt et al., 2007) to assimilate the temperature profiles, with fundamental surface and atmospheric variables output on a 5 latitude by 6 longitude grid and on 28 vertical levels up to around 90 km. A second reanalysis, the Mars Analysis Correction Data Assimilation (MACDA) dataset has been created and detailed by Montabone et al. (2014) using a past version of the same Mars GCM used to create the OpenMARS reanalysis product. The MACDA dataset is a reanalysis of TES temperature profiles and TES dust column optical depth retrievals over almost three Mars years. The data are publicly available from the National Centre for Atmospheric Science British Atmospheric Data Centre, with the aim of fostering scientific analyses and to allow applications of the long-term martian dust climatology, and contain two-hourly output of fundamental atmospheric and surface variables on a 5 longitude-latitude grid extending on 25 vertical levels from the surface to an altitude of around 100 km.
For times at which observational data are available (and over a defined time window around each observation), the Analysis Correction (AC) data assimilation scheme (Lorenc et al., 1991) is used to update the temperature and column dust optical depth fields (using TES temperature profiles and column dust optical depth retrievals respectively). In the case of assimilation of TES temperature profiles, the assimilation scheme also updates the wind fields to ensure that any changes balance the thermal data input into the GCM. In the case of local column dust optical depth, when no further retrievals are available for assimilation, the column dust optical depth remains fixed until further retrievals are assimilated into the GCM.
The MACDA reanalysis dataset has been used to study multiple different topics related to Mars, including transient eddies (Mooring and Wilson, 2015), energetics of the martian atmosphere (Battalio et al., 2016) and the structure of the polar vortices (Waugh et al., 2016) which also includes a comparison of the EMARS and MACDA reanalysis products. There are, however, a few limitations of the MACDA reanalysis. The dust particles in the GCM were prescribed in both the horizontal and vertical dimensions and therefore not transported. The EMARS reanalysis allowed for the vertical transport of dust particles with the horizontal distribution constrained by observations (Montabone et al., 2015). The vertical distribution of the dust is analytically prescribed in the MACDA dataset using a modified form of the Conrath distribution (Conrath, 1975), which following the discoveries of detached dust layers (Heavens et al., 2014) is less valid than previously thought. Observational data are also available for later Mars years from more recent spacecraft, such as the Mars Reconnaissance Orbiter (MRO). For any statistical studies using the MACDA dataset a longer time series would be preferable, and assimilation of additional observational datasets to extend the timescale covered by the MACDA reanalysis would provide a more robust reanalysis product. The above limitations are some of the more pertinent reasons for the creation of the OpenMARS dataset.
In this paper, we detail the OpenMARS reanalysis product, a dataset containing directly assimilated temperature, dust opacity, water vapour column and ozone column from multiple observational datasets. Section 2 gives an overview of the observational data, the Mars GCM and the data assimilation scheme used to create the OpenMARS reanalysis product and section 3 displays an overview of the output contained in the OpenMARS reanalysis product. Section 4 describes a comparison of the OpenMARS reanalysis product to assimilated observations, while section 5 details the format of the OpenMARS reanalysis data files. Finally, section 6 describes how an interested user can access the OpenMARS reanalysis product.

Components of the OpenMARS dataset
To create the OpenMARS dataset observations of the martian atmosphere from several different instruments on multiple orbiters have been combined with a Mars GCM using the AC data assimilation scheme. These three components are now detailed in the following sections.

Observational data
The following section describes the observational datasets that have been assimilated to create the OpenMARS dataset, which cover almost 9 Mars years of observation and provide the largest spatio-temporal reanalysis dataset for the martian atmosphere.

TES data
The Thermal Emission Spectrometer (TES) instrument, aboard the Mars Global Surveyor (MGS) spacecraft operates in the thermal infrared between 6 and 50 μm (200-1600 cm -1 ). The spectrometer began its mapping operations on March 1, 1999 (L S ¼ 104 , MY 24) and ended on August 31, 2004 (L S ¼ 81 , MY 27). MGS completed 12 orbits each sol, creating two sets of 12 narrow strips of data, running roughly north-south and separated by around 30 in longitude. The two sets of data contain observations at local times around 2 a.m. and 2 p.m. respectively, with the variation larger near the poles (for example, in the polar regions the daytime observations range between 12:30-14:30).
The temperature retrievals used in the assimilation, along with the retrieval methods, are described in detail by Smith et al. (2000) and Smith (2004). Temperature profiles are retrieved from nadir radiances in the 15 μm CO 2 band, and extend up to an altitude of around 40 km. The vertical resolution is around one pressure scale height (around 10 km), though the temperature retrievals provided for assimilation have a vertical sampling on a one-quarter pressure scale height (around 2.5 km). Uncertainties for each profile are around 2 K, but are larger in the lowest scale height above the ground because of possible errors in estimating the surface pressure Smith, 2004). While systematic errors are present for each retrieval, they peak with values greater than 5 K in retrievals over the winter polar regions because the absolute radiometric calibration affects the retrievals most strongly under cold atmospheric and surface conditions . Evidence for systematic errors was found in retrievals with temperatures lower than the CO 2 condensation temperature: it would be expected that the latent heat released during condensation would keep the temperature close to the CO 2 condensation temperature of around 145 K. Fig. 1 displays the number of TES temperature profiles that are assimilated to form part of the OpenMARS reanalysis product. Throughout its lifetime, the TES instrument retrieved approximately 46 million temperature profiles. Fewer temperature profiles are available during the majority of MY 25 as the TES instrument during this period was observing at a higher spectral resolution that took twice as long to acquire compared to running at the lower resolution for the rest of the time period covered by the observations.
The TES instrument in nadir-viewing geometry measured dust opacity at 1075 cm -1 in the infrared, with the retrievals method detailed in Smith et al. (2000). Using the TES spectra, an equivalent column-integrated opacity of pure absorbers as a function of wavenumber is first computed. Then, the contribution of dust to the total opacity is estimated by fitting predetermined spectral shapes (opacity as a function of wavenumber) for dust, water ice, and the effect of a non-unit emissivity surface to the observed opacity spectrum. Fig. 2 displays the number of TES column dust optical depth retrievals that are assimilated to form part of the OpenMARS reanalysis product. Over the time period used for the present reanalysis, around 16 million TES dust opacity retrievals are available for assimilation. There is a notable lack of coverage of column dust optical depth retrievals at high latitudes during polar winter of each Mars years, a result of the minimal thermal contrast between the surface and atmosphere preventing a reliable retrieval being derived. Fewer retrievals of column dust optical depth are also available during the majority of MY 25 for the exact same reason detailed in the description of the TES temperature profiles, namely that the TES instrument during this time was observing at a higher spectral resolution.
The quality control applied to the TES temperature profiles follows the procedure described in Lewis et al. (2007). Profiles marked as bad by the retrieval algorithm are automatically rejected, with remaining retrievals filtered to remove any profiles that fall significantly below the CO 2 saturation curve in a similar method to Montabone et al. (2014). This additional filtering is applied in order to remove excessively high or low temperatures which may cause problems with the model's physical schemes, and also removes some of the retrievals affected by possible systematic errors in the radiometric calibration. The filtering removes around 0.5% of the available observations.
For dust opacity, the quality control procedure is also detailed fully in Lewis et al. (2007). Following Smith et al. (2000), only opacities where the surface temperature was greater than 220 K were retained. This requirement, for a good surface-atmosphere temperature contrast, unfortunately further restricts the dust information to daytime. Most dust information is in the equatorial region and the southern hemisphere. Finally, checks were run to see that the dust opacity and the simultaneously retrieved water ice opacity were both positive and that the total fit residual was not too large (Lewis et al., 2007).

MCS data
The Mars Climate Sounder (MCS) instrument, aboard the MRO spacecraft, employs a nearly continuous limb viewing strategy in order to achieve greatly increased sensitivity to minor and trace constituents (McCleese et al., 2007). The instrument is a passive radiometer which retrieves in 9 spectral bands covering the visible and mid-to far-infrared channels. It is capable of retrieving vertical profiles of water ice and dust opacity alongside temperature profiles with a greater vertical resolution than TES (5 km for MCS as opposed to around 10 km for TES). The vertical coverage of the profiles is from the surface up to altitudes of around 85 km (as opposed to around 40 km for TES). The MCS observations comprise two sets of twelve narrow strips of data, separated by around 30 in longitude, a similar pattern to that observed by the TES instrument, with only along-track MCS profiles currently included. Due to the Sun-synchronous orbit of MRO, the MCS observations away from the pole occur at local times around 3 a.m. and 3 p.   of the MCS instrument (A1-3) in the far-infrared. The radiative transfer equation is inverted to determine the temperature from the radiance using an iterative method. For this process, a 'first guess' is needed for the temperature profile, although the success of this retrieval method is shown to be insensitive to this initial guess (Kleinb€ ohl et al., 2009). The algorithm is processed for each limb profile with 30 iterations, to converge on the final vertical profile of temperature. The error on the retrieval is reduced in the lower atmosphere (0.5 K) and increases at higher altitudes due to the reduction in signal-to-noise ratio (> 1 K above 40 km) and in situations where the atmosphere is opaque. Fig. 3 displays the number of MCS temperature profiles that are assimilated to form part of the OpenMARS reanalysis product. After quality control, around 7.5 million temperature profiles retrieved by the MCS instrument are assimilated. An increased number of MCS temperature profiles are noticeable at the end of MY 28, as a result of a dedicated campaign to observe as much as possible of the martian atmosphere during a high dust loading dust storm season. Periods in which there are no data at all (e.g. at the end of MY 29) are as a result of the MCS instrument being switched off during this time period.
The retrieval of dust opacity profiles from the MCS measured radiance is also extensively covered in Kleinb€ ohl et al. (2009). Details of how the column dust optical depth is retrieved are presented in Montabone et al. (2015) and briefly detailed here. For any given successful limb retrieval, the full profile of dust extinction opacity produced by the retrieval algorithm (MCS retrievals from version v4.3 are used for the current version of the OpenMARS reanalysis product) is integrated to produce a column dust optical depth. The profile is extended upward and downward under the assumption of well mixed dust, based on the last valid value. The MCS dust profiles cannot be retrieved down to the surface using only limb observations, and the dust in the un-retrieved part of the profile can potentially account for a significant fraction of the total dust column. Therefore estimates of column dust optical depth from MCS observations have the possibility of errors attributable to either the extrapolation to the surface under the well mixed assumption or the use of dust opacity values at altitudes where the fit to observed radiances is not within the standard threshold. The well mixed assumption in particular is less valid with the discovery of detached dust layers found in MCS profiles (Heavens et al., 2014). Fig. 4 displays the number of MCS column dust optical depth retrievals that are assimilated to form part of the OpenMARS reanalysis product. During the time period covered by the MCS instrument, around 4 million column dust optical depth retrievals are assimilated. The retrieval method allows for a reliable measurement of dust optical depth during the daytime and nighttime during polar winter over this time period. As with the MCS temperature profiles, more retrievals are available at the end of MY 28 as a result of the dedicated campaign to observe as much as possible during the high dust loading dust storm season.
The quality control applied to the MCS temperature profiles is described in Lewis et al. (2007) and is precisely the same process as is described for the TES temperature profiles in the previous section. Quality control for the derived MCS column dust optical depth retrievals is fully described in Montabone et al. (2015) and briefly detailed here. Estimates of the MCS column dust optical depth can be fairly inaccurate if the lowest retrieved level of dust opacity is above around 20 km altitude, depending on the time of the year and the dust/water ice conditions. The dataset therefore largely consists of nighttime retrievals that correspond to dust extinction profiles with valid values at or below 25 km altitude, and only retrievals with local times between 12 p.m. and 6 p.m. when the corresponding extinction profile has valid values at or below 8 km altitude are accepted. Finally, estimates of column dust optical depth where the temperature profile dropped below the condensation temperature of carbon dioxide at some of the pressure levels are rejected, because CO 2 ice opacity is currently not taken into account in the retrieval algorithm but can affect retrievals of dust opacity at those levels.

SPICAM total ozone data
The Spectrometer for the Investigation of the Characteristics of the Atmosphere of Mars (SPICAM) instrument, aboard the Mars Express (MEx) spacecraft, is comprised of a dual UV/IR spectrometer. In the UV spectral range, it observed from 115 to 310 nm and is capable of ozone column density retrievals due to the strong Hartley band of ozone absorption around 250 nm. SPICAM was the first orbiting instrument capable of providing a global total ozone climatology with decent spatial and temporal coverage (Perrier et al., 2006).
The retrieval of total ozone from the Hartley band of intense absorption (220-280 nm) is described fully in Perrier et al. (2006). The outcome of the retrieval process is just over 27,000 high signal-to-noise ratio observations for almost one and a half martian years (L S ¼ 341 in MY 26 to L S ¼ 121 in MY 28). The binned number of retrievals from SPICAM is shown in Fig. 5. The algorithm to retrieve the ozone column from the solar backscattered UV radiation in this version is a relative method, with the measured spectra divided by a reference spectrum, taken to be over Olympus Mons. This location is used since it is a region known to have extremely low ozone density values and minimal dust and aerosols in the atmospheric column owing to the low surface pressure and total column mass. The division by the reference spectrum filters out instrumental effects.
A forward radiative transfer model, containing assumptions on surface pressure, vertical ozone profile and temperature, is computed taking into account the geometry of the considered observation. The vertical distribution of dust follows the Conrath profile (Conrath, 1975) which was analytically derived from considerations of particle sedimentation and eddy mixing to vary the height that dust can reach in the atmosphere at different times of a Mars year. The a priori information is taken from the Laboratoire de M et eorologie Dynamique (LMD) GCM, with a two-step method used to perform the retrieval. The model first computes the spectra assuming a dust-free atmosphere, and then in the second step the modelled spectra are adjusted to the observed spectra by least square minimisation to retrieve the ozone column density, surface albedo and dust opacity, which are the three free parameters. To remove observations which have a low signal-to-noise ratio, observations with a solar zenith angle less than 85 and emission angle less than 30 are rejected. The relative method used does not currently take into account the effect of clouds, although any biases introduced due to the neglect of clouds has been investigated previously by Perrier et al. (2006). Using synthetic realistic spectra and the forward model, they found the retrieval error increased to almost 100% with high cloud opacity (cloud opacity greater than 1) but this occurs infrequently on Mars and primarily in polar winter regions where there are no SPICAM retrievals. An average error of 10-15% in total ozone was calculated for much more common thinner clouds (cloud optical depth between 0.1 and 0.2). The ground resolution of the SPICAM observations at pericentre is around 4 km 2 . Before the SPICAM retrievals are assimilated to create part of the OpenMARS reanalysis product, they are subject to further quality control measures which are detailed in Holmes et al. (2018). For the almost 27,000 retrievals from SPICAM available, each individual SPICAM retrieval R i is compared to the retrieval R iAE1 either side of it in time. Spurious retrievals are then flagged up using three criteria; | R i - and | S i -S iAE1 | < 1 where L i and S i are the latitude and sol of observation i respectively. A value of 10 μm-atm was chosen to avoid rejection of retrievals which are realistic due to the sharp gradient on the boundaries of the high polar ozone abundance. This quality control method removes only 7 retrievals from the dataset.

TES water vapour column data
The only water vapour column data currently publicly available for assimilation into the OpenMARS reanalysis product are from the TES instrument aboard the MGS spacecraft, described in Section 2.1.1. Water vapour column retrievals are obtained by comparing synthetic spectra with TES spectra from rotation bands in the 28-42 μm region. In this region, the TES signal-to-noise ratio is relatively high, and the contribution to the spectrum from water vapour can easily be separated from the dust, water ice and surface contributions (Smith, 2002). When calculating the synthetic spectra, water vapour is assumed to be well mixed up to the condensation level, and zero above. The estimated uncertainties in the vapour column abundance caused by random errors are 3-5 pr-μm, while uncertainty in the pressure broadening of water vapour by CO 2 results in a systematic error likely to be much less than 25%.
Full details of the quality control are in Steele et al. (2014b). Because of the restrictions of the retrieval algorithm, water vapour retrievals are only provided for locations where the surface temperature is greater than 220 K, which excludes data from the nighttime orbits and over the winter polar regions. The number of TES retrievals varies with time, but in full operational mode each strip of data typically contains around 700 retrievals, spaced around 0.15 (10 km) apart in latitude. The TES instrument retrieved approximately 13 million water vapour columns during its lifetime, with the number of retrievals binned into discrete latitude-time periods shown in Fig. 6, although the OpenMARS reanalysis product currently only includes retrievals from L S ¼ 173 For the vapour column observations, the variation with latitude can be quite large due to differences in topography and temperature, but nearby measurements should conform to within a specified threshold. To investigate possible spurious observations, a buddy-check was applied on each strip of data after all retrievals had been scaled to the 610 Pa pressure level to remove the effects of topography. For each observation, the buddy-check compares the value to the mean of all the observations within a specified meridional distance d either side of it. The observation is highlighted as a possible error if its value differs by some threshold value δ vap . As the vapour column is strongly dependent on latitude, applying a buddy-check with large values of d removes observations with natural variation. Conversely, small values of d results in too few observations to perform a meaningful statistical analysis. Numerous tests showed that comparing observations over a distance d ¼ 300 km (around 5 in latitude), and excluding any observations where δ vap > 3σ (around 4-10 pr-μm depending on location and season) from the mean, gave the best combination of a large enough sample of data for comparison, the removal of spurious observations and the retention of observations with natural variation. Only a small fraction of the water vapour column observations are discarded (around 0.5%) by the buddy-check algorithm and so it does not negatively impact on the amount of data available for assimilation into the OpenMARS reanalysis product.

Mars Global Circulation Model
The GCM used to create the OpenMARS reanalysis product is the UK version of the LMD GCM (hereafter MGCM), which has been developed in a collaboration of the Laboratoire de M et eorologie Dynamique, the Open University, the University of Oxford and the Instituto de Astrofisica de Andalucia. This model uses physical parameterisations shared with the LMD GCM, which are coupled to a UK-only spectral dynamical core alongside an energy and angular momentum conserving vertical finitedifference scheme. Tracers such as CO 2 , water vapour and dust are transported by a UK-only semi-Lagrangian advection scheme (Newman et al., 2002) with mass conservation (Priestley, 1993).
The MGCM used to create the OpenMARS reanalysis product is similar to the model used in Montabone et al. (2014) for a previous reanalysis dataset but the MGCM used for the OpenMARS reanalysis product includes additional sub-models. CO 2 is now transported as an additional tracer providing a better representation of the CO 2 cycle, with condensation and sublimation of carbon dioxide on the ground and in the atmosphere calculated from the local temperature and pressure state (Forget et al., 1998). A thermal plume model is used to better represent turbulent structures in the planetary boundary layer (Colaïtis et al., 2013), of importance for the evolution of tracers. A 'semi-interactive' two-moment scheme is used to freely transport dust in the model (Madeleine et al., 2011), although the dust column optical depth at each grid point is scaled to match the observed dust distribution from TES/MCS (depending on the time period covered) that is assimilated into the OpenMARS reanalysis product (Montabone et al., 2015). The MGCM is also coupled with the LMD photochemical module (Lef evre et al., 2004(Lef evre et al., , 2008 and uses a microphysical scheme for the water cycle (Navarro et al., 2014) to track and evolve 16 different chemical species in the atmosphere and on the surface including ozone and water vapour. Radiatively active clouds are not included, since previous modelling work has shown that it can introduce discrepancies as well as improvements to the temperature structure (Madeleine et al., 2012). The model is truncated at wavenumber 31 resulting in a 5 physical longitude-latitude grid (and 3.75 longitude-latitude grid for the dynamical core) with 35 vertical levels extending to an altitude of around 105 km. The time-stepping regime for the physical and dynamical parts of the MGCM is 15 and 1.5 min respectively.

Data assimilation scheme
To assimilate the observations and create the OpenMARS reanalysis product, the MGCM uses the AC scheme (Lorenc et al., 1991) with necessary parameters adapted to martian conditions. The AC scheme has previously been used to assimilate thermal and dust opacity retrievals from TES (Lewis and Barker, 2005) to indirectly study the thermal tides and also create the MACDA dataset (Montabone et al., 2014). The dust opacity retrievals have also been used to perform a multi-annual study of interannual dust variability (Montabone et al., 2005(Montabone et al., , 2015, indicating localised regions which triggered the onset of the global dust storm in MY 25 and also found dust lifting by dust devils to contribute little. Observations during the TES aerobraking phase have been assimilated indicating an atmospheric warming at the onset of northern hemisphere winter due to the dust storm in MY 23 (Lewis et al., 2007). The AC scheme has also been validated against radio occultation (RO) measurements (Montabone et al., 2006), with the assimilation of TES thermal and dust opacity retrievals improving the agreement between the MGCM and the RO profiles. Recent work with the AC scheme has moved on to the assimilation of chemically passive water vapour and water ice (Steele et al., 2014b, a) to investigate the martian water cycle and radiative effect of water ice clouds respectively and chemically active species such as ozone (Holmes et al., 2018) and carbon monoxide (Holmes et al., 2019). The AC scheme is a form of successive corrections in which analysis steps are interleaved with each model dynamical time step. The modified successive corrections equation used by the scheme is where x a is the analysis vector, x ba is the model background, y o is the observation vector, H is the observation operator and W ¼ BH T R À1 and Q are matrices of weights and normalization factors respectively, with B the background error covariance matrix, H the linearization of the observation operator and R the sum of the observation and observation operator error covariance matrices. In each analysis step, the above equation is split into separate vertical and horizontal stages in order to spread the analysis increments from the observation locations to the surrounding model grid points. This is followed by the derivation of multi-variate increment fields for dynamical balance where applicable (e.g. after assimilating temperatures, balanced thermal wind increments are applied). Observations are inserted over an asymmetrical specified time window of 6 h (5 h before an observations valid time until 1 h after), optimally selected so that the assimilation will not unrealistically smooth out any inherent model variation. The asymmetrical time window is also used as it is beneficial because it biases the assimilation gains to regions ahead of the satellite ground track, which have not recently been observed. Spreading in time was also found to be beneficial in the case of relatively sparse data, where it is often better to use an observation from a slightly different time, with a reduced weight, rather than release the model which would then quickly relax back toward a temperature determined principally by its dust distribution, since the radiative timescale of the martian atmosphere is only 1-2 sols. Temperature profiles from the TES and MCS instruments were assimilated into the OpenMARS reanalysis product using parameters which have previously been defined as optimal from numerous tests on the parameter space (Lewis et al., 1996(Lewis et al., , 1997(Lewis et al., , 2007. A normalised radius of influence for each observation equal to 3.5 correlation scales (equivalent to around 1200 km) is used for the temperature retrievals, consistent with previous assimilation of temperature profiles. This is equivalent to any temperature retrieval on the equator affecting the nearest four model grid points at its valid time with a weight dependent on the time factor and horizontal correlation scale (see Fig. 1 of Lewis et al. (2007)) and horizontal distance from the actual location of the retrieval assimilated.
Retrievals of column dust optical depth from the TES and MCS instruments were assimilated into the OpenMARS reanalysis with a slight alteration in parameters from those used for the MACDA reanalysis (Montabone et al., 2014). The normalised radius of influence for each observation is increased to 5 from 3.5 (used for MACDA) in an attempt to minimise the 'checkerboard' effect that can happen due to the spacing of the retrievals.

Sample output from the OpenMARS reanalysis product
The zonal-mean atmospheric temperature distribution at 60 Pa and 3 p.m. local time for the first three Mars years covered by the OpenMARS reanalysis product (i.e. covering the majority of the TES assimilation period) is shown in Fig. 7. Increased atmospheric heating of up to 15 K can be seen leading up to perihelion in MY 25 when compared to the  MY 26 are as a result of the lack of assimilated temperature retrievals over time periods of greater than 2 sols and short radiative timescale on Mars, with the OpenMARS reanalysis therefore reverting to the 'control' model state. Fig. 8 displays the visible column dust optical depth covering the majority of the TES assimilation period. The observed absorption-only IR optical depth at 9.3 μm is converted to an IR extinction optical depth using a factor of 1.3 from Wolff and Clancy (2003), and then converted into a visible extinction optical depth at 0.67 μm using a factor of 2 from Madeleine et al. (2011). The global dust storm in MY 25 stands out with visible dust optical depths greater than 2. Levels of dust during the polar winter of both hemispheres seem initially to be quite varied from year to year, however in this region there are no TES column dust optical depth retrievals to assimilate (see Fig. 2). The assimilation process results in the last previous assimilated column dust optical depth being kept until updated by the next available retrievals in time, similar to the process used by MACDA (Montabone et al., 2014).
While no column dust optical depth retrievals were available in polar winter during the TES assimilation period, derivations of the column dust optical depth from vertical profiles of dust retrieved from the MCS instrument are available for later Mars years. The zonally averaged column dust optical depth for MY 27 to MY 29 is shown in Fig. 9. The observed MCS IR extinction optical depths are converted into an absorption-only IR optical depth at 9.3 μm using the method described in Montabone et al. (2015) without normalising onto a reference pressure level, and then converted into a visible extinction optical depth at 0.67 μm using a factor of 2 from Madeleine et al. (2011). In the polar winter of both hemispheres the visible column dust optical depth is reduced during the MCS period particularly when comparing with polar winter in MY 26 (see Fig. 8). Retrievals of column dust optical depth from the MCS instrument do not cover the full complete column of the atmosphere however, and so the column dust optical depth value in reality is likely to be somewhere between the values derived in the polar winter during the MCS assimilation period.
Local dust storms are evident at high northern latitudes during the start of each Mars year observed by the MCS instrument, generally occurring at around 60 N at the start of the year and steadily increasing in latitude to around 85 N by L S ¼ 90 . These local dust storms have also been observed by the Mars Orbiter Camera and Mars Color Imager instruments (Cantor et al., 2010) on the same spacecraft as TES and MCS respectively. Local dust storms during the TES period at high northern latitudes after northern polar winter are likely to be obscured initially in the OpenMARS reanalysis by the visible column dust optical depth values carried through northern polar winter that correspond to the last available TES retrieval at the beginning of polar winter.

A comparison of the OpenMARS reanalysis product to assimilated observations
One method of use to indicate whether the data assimilation process has had a beneficial impact on the model output is by comparing assimilated observational data to the reanalysis and a 'control' simulation (i.e. with no data assimilation of any observations). For a successful reanalysis, the deviation of the assimilated variable from the observations assimilated should be lower in the reanalysis than when comparing the assimilated observations to a control simulation. To determine if this is the case when assimilating temperature profiles for the OpenMARS reanalysis product, a case study covering time periods of MY 28 is conducted. A time period covering the assimilation of MCS data is chosen since the MCS temperature profiles extend to a greater altitude than TES temperature profiles. Mars Year 28 is chosen as it covers a period in which a large number of MCS temperature profiles are assimilated, in particular around aphelion (see Fig. 3). Also, the TES temperature profiles have previously been compared to a similar reanalysis dataset in Lewis et al. (2007), the TES water vapour retrievals have been compared to a similar reanalysis dataset in Steele et al. (2014b) and the SPICAM ozone retrievals have been investigated in Holmes et al. (2018).
A comparison of the 3 p.m. zonal-mean atmospheric temperature at different pressure levels averaged over L S ¼ 120-150 MY 28 in a control simulation and OpenMARS reanalysis dataset with MCS daytime retrievals is shown in Fig. 10. The comparison of the MCS temperature retrievals with the OpenMARS reanalysis dataset and control simulation is not exactly direct because the MCS tmperature retrievals used for the comparison range in local time from 9 a.m. to 9 p.m., although the majority of MCS temperature retrievals will have local times close to 3 p.m. Below 100 Pa, a control simulation can be up to 10 K cooler than the MCS temperature retrievals, while the OpenMARS reanalysis dataset is primarily within AE5 K of the MCS temperature retrievals. In the middle atmosphere (i.e. from 100 to 1 Pa), a control simulation displays a global warm bias, with the largest warm bias of greater than 20 K peaking at around 60 S at 10 Pa. In the OpenMARS reanalysis dataset, the middle atmosphere warm bias is greatly reduced, with a factor of two reduction in the largest middle atmosphere temperature bias identified in a control simulation.
Above 1 Pa in the atmosphere, the temperature bias in a control simulation and OpenMARS reanalysis dataset are reasonably similar although generally around 1-2 K smaller in the OpenMARS reanalysis dataset. Globally, it is clear that the temperature distribution in the OpenMARS reanalysis dataset around aphelion (L S ¼ 120-150 ) displays a reduced bias when compared to a control simulation.
An identical comparison has also been performed covering the time period L S ¼ 210-240 MY 28 and is shown in Fig. 11. During this time period, the MCS instrument retrieved more temperature profiles of the atmosphere than at any other time period covered by this instrument (see Fig. 3). The increased dust in the atmosphere did however prevent the retrieval of temperature at altitudes closer to the surface, in particular in the mid-latitude region. The largest temperature bias in a control simulation, when compared to the MCS retrievals of temperature, is a cold bias greater than 20 K centred at 60 N and 100 Pa. As seen in the previous time period investigated (Fig. 10), the OpenMARS reanalysis dataset greatly reduces the cold bias by a factor of at least two. A weaker cold bias of just over 5 K is present over the southern polar region in a control simulation below 10 Pa, which is reduced to around AE5 K in the Open-MARS reanalysis dataset.
The polar warming over the northern polar region from 10 to 1 Pa is up to 20 K too warm in a control simulation, but is well captured in the OpenMARS reanalysis dataset. The OpenMARS reanalysis dataset again displays temperature biases of at most around AE5 K for the majority of the atmosphere, with the largest temperature bias present above 0.1 Pa over the equator.
The final time period used for the investigation of temperature biases when comparing the OpenMARS reanalysis dataset and a control simu-  lation against MCS daytime temperature retrievals is L S ¼ 300-330 MY 28 (shown in (Fig. 12). The largest temperature bias in a control simulation is again centred at around 60 N near the surface, indicating a cold bias greater than 20 K. The weak cold bias near the surface at southern polar latitudes during L S ¼ 210-240 ( Fig. 11) has strengthened by L S ¼ 300-330 to match the strong cold bias at 60 N. Both of these large biases are non-existent in the OpenMARS reanalysis dataset, which deviates from the MCS daytime retrievals by less than 5 K in the same regions. A warm temperature bias of up to around 15 K across all latitudes at around 1 Pa in a control simulation is also reduced in the OpenMARS reanalysis dataset to around 5 K, with the OpenMARS reanalysis dataset more in line with the MCS temperature retrievals than a control simulation for the entirety of the atmosphere.

Format of the OpenMARS reanalysis product
In many respects, the format of the OpenMARS dataset is consistent with the MACDA dataset described in Montabone et al. (2014). The reanalysis produced for this dataset covers almost nine complete Mars years, with any particular data file covering 30 sols. The data files are provided in netCDF4 format which are easily accessible by common scripting software such as Python (a sample python script for accessing the dataset is included in the dataset repository). The OpenMARS reanalysis product is split into four separate datasets: the MY 24-27 standard database (covering the TES time period of L S ¼ 98

Dimensions
The dimensions of the reanalysis data files are listed in Table 1. The surface and atmospheric reanalysis output in the data files depend on three (longitude, latitude, time) and four dimensions (longitude, latitude, level, time) respectively, with the exceptions being the visible column dust optical depth, water vapour column and ozone column which depend on only three (longitude, latitude, time) dimensions. The horizontal grid spacing is 5 in both longitude and latitude, with fourdimensional atmospheric variables defined on model sigma levels σ (where σ ¼ p=p s , p is atmospheric pressure and p s is surface pressure) that are non-dimensional terrain-following levels. There are 35 vertical levels in the OpenMARS reanalysis data product extending to an altitude of around 105 km.
The primary time variable used for each data file is the Martian sol (see Table 2 for all time variables). For ease of conversion and since the majority of the Mars science community use solar longitude and Mars year, these values are also included. The OpenMARS dataset employs the same calendar used by Montabone et al. (2014) which means there is a consistent bias of around 6 h between the model solar longitude and astronomical solar longitudes, and is therefore currently not consistent with the Mars24 algorithm (Allison, 1997).
The surface and atmospheric variables are output every 2 Martian hours starting at 2 a.m. on sol 241 of MY 24 for the MY 24-27 standard dataset, sol 2911 (sol 235 of MY 28) for the MY 28-32 standard dataset and on sol 361 of MY 24 for the water vapour column dataset, with sol 0 corresponding to L S ¼ 0 MY 24. The ozone column dataset is output every 3 Martian hours starting at 3 a.m. on sol 2011 (sol 4 of MY 27), and hence only has 240 values of output for the time dimension.

Surface variables
The surface variables included in the OpenMARS MY 24-27 and MY 28-32 standard reanalysis data files are listed in Table 3. Although only the surface pressure is included in the reanalysis data files, the atmospheric pressure can be calculated for each vertical level of the atmosphere by multiplying the surface pressure variable ps by the corresponding sigma value of each vertical level in lev. Although none of the surface variables are directly assimilated in the OpenMARS reanalysis product, each one is altered indirectly as a result of the assimilation of temperature profiles and column dust optical depth. No surface variables are included in the water vapour column dataset (because they can be found in the MY 24-27 standard dataset of the corresponding time period) and the ozone column dataset (since no temperature retrievals were assimilated for this particular dataset).

Atmospheric variables
The atmospheric variables included in the OpenMARS MY 24-27 and MY 28-32 standard reanalysis data files are listed in Table 4. As previously mentioned, as the variable dustcol is a column value it only has three dimensions whereas the other atmospheric variables are all fourdimensional. The zonal wind u and meridional wind v are positive in the eastward and northward direction respectively. Although not directly assimilated, u and v are both indirectly altered as a result of the assimilation procedure.
The atmospheric variables of temperature and dust column are not included in the final OpenMARS water vapour reanalysis product, as they can already be found in the OpenMARS MY 24-27 standard database, with only the water vapour column included in the water vapour column dataset (see Table 5).
Only atmospheric variables that were assimilated into the time period for the of SPICAM retrievals are included in the final OpenMARS ozone column reanalysis product (see Table 6). The data contained in the OpenMARS ozone column reanalysis product is identical to the assimilation investigated by Holmes et al. (2019).

Accessing and use of the OpenMARS reanalysis product
The OpenMars reanalysis dataset can be accessed freely through the Open Research Data Online (ORDO) repository at https://ordo.open.ac. uk/collections/OpenMARS/_database/4278950 (DOI: https://doi.or g/10.21954/ou.rd.c.4278950.v1), with a sample Python script providing an example of how to access the dataset also provided in the repository along with a reference manual. The OpenMARS dataset has multiple different uses for scientists and engineers interested in Mars, such as an updated and extended investigation of transient eddies, energetics and the structure of the polar vortex. The dataset can also be used as improved boundary conditions for smaller scale studies (which generally use boundary conditions from a GCM), as expected conditions for entry, descent and landing of rovers and surface platforms on Mars and as a priori for retrievals of temperature, dust, water vapour and ozone.

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.