Selecting Erosion- and Deposition-Dominated Zones in the Jezero Delta Using a Water Flow Model for Targeting Future In Situ Mars Surface Missions

Abstract

Identifying surface sites with significant astrobiological potential on Mars requires a comprehensive understanding of past geological processes and conditions there, including the shallow subsurface region. Numerical modelling could distinguish between regions dominated by erosion and those characterized by sediment accumulation in ancient wet environments. The target area of Jezero Crater is relatively well explored and thus is an ideal site to evaluate model calculations; however, important works are still missing on expectations related to its shallow subsurface . In this work, the best available approaches were followed, and only surface morphology was considered (supposedly formed by the last fluvial episode). The shallow subsurface became an important target recently, and this model could provide new inputs in this area. Erosion–accumulation models are suitable for terrestrial surface features, but few have been applied to Mars. This work addresses this challenge using the SIMWE (SIMulated Water Erosion) model on the Jezero Crater delta, the landing site of the Perseverance rover. For calculations, the average grain size according to the THEMIS TI data was applied to the target area. The flow depth varied between 1.89 and 34.74 m (average of 12.66 m). The water-filled channel width ranged from 35.3 to 341.42 m. A flow velocity of 0.008–11.6 m/s, a maximum erosion rate of 5.98 g/m²/h, and a deposition 4.07 g/m²/h were estimated. These calculated values are close to the range of estimations from other authors assuming precipitation of 1–20 mm/h and discharges of 60–400 m³/s. The model was able to distinguish between erosion- and accumulation-dominated areas about 1 m above Jezero Crater’s delta that are not visible from above. This model helps to identify the accumulation-dominated areas with the finest grain size with good preservation capability for the shallow but invisible subsurface.

1. Introduction

Ongoing and upcoming in situ Mars missions, e.g., NASA’s Perseverance Rover and ESA’s Rosalind Franklin Rover (former ExoMars Rover), are poised to investigate Mars’s surface and shallow subsurface regions. These missions play a pivotal role in selecting scientifically significant sample return targets [1] and locations that were important for past habitability and are also suitable for potential future human habitation [2]. Mars astrobiology research is primarily centered around locations where liquid water endured over substantial durations [3,4,5], boasting strong potential for weathering and organic material preservation, notably in phyllosilicate-rich areas [6]. Although phyllosilicate-rich areas are observable from orbit, the challenge arises from the fact that astrobiological indicators are likely to be preserved not on the surface but only within the Martian subsurface [7]. Additionally, phyllosilicate detection of bedrock from orbit can be obscured by surficial dust deposits [8]. Hence, while both the Perseverance Rover and Rosalind Franklin Rover possess subsurface sampling capabilities, the precise identification of subsurface drilling targets before the acquired sample can be analyzed there or returned to the Earth for more detailed investigation remains poorly constrained. The modeling-based approach presented in this work might help, but its verification requires on-site shallow subsurface confirmation in the future, which could be conducted by future missions. Regarding the verification of the used and calculated numerical values, beside expected numerical uncertainties (see the last part of the Section 4), as other published models mainly calculate discharge but rarely consider sediment transport, comparison to other models cannot be performed in detail.

This study explores the model-based identification and evaluation of surface or shallow subsurface sites with potential astrobiological significance, which are characterized by extended periods of past wet conditions and the presence of clay-like sediment accumulation in low-energy ancient fluvial settings. The model allows the identification of areas where fine sediment has likely accumulated and subsequently undergone lithification but where surface layers have not been covered or resurfaced much by later processes (e.g., aeolian ripples). The Jezero delta is such a target, where the undulating surface suggests the possibility that substantial differences in flow conditions and directions could emerge, thus revealing accumulation- and sedimentation-dominated areas close to each other to allow the testing of this model. The future sample return of cores collected by Perseverance could undergo detailed Earth-based laboratory analysis of fluvial sediments there (including the smallest grain size), which would support the development of this and similar models. This work goes beyond the morphological analysis of surface features with numerical calculations linked to the observed morphology.

The aim of this research is to provide examples and experience with an Earth-tested specific surface erosion accumulation model for flowing liquid water called SINWE as applied to Mars. Although it is an Earth-type planet, there are several poorly known aspects of how the fluvial process and related erosion known on Earth happens on Mars, including specific numerical parameters (see the Section 2), as differences are expected due to the different gravity acceleration of solid grain fallout related to Stoke’s law and different behavior of vortex formation in the flowing medium. This paper aims to make one step forward in applying Earth-based modelling to Mars. While images provide information only on the surface, the model-based approach provides information on the shallow subsurface, which is not visible from above but might be an important target in the future. The adaptation of any specific model to another planet is difficult and a long-lasting procedure; thus, here, only an early test was conducted in order to see how effectively such a model could be applied to Mars and reveal the possibilities and benefits of its usage. Beside various physical parameters, including the reduced surface gravity of Mars compared to those of the Earth, the surface topography on Mars influences the results substantially—thus, such terrains are useful for the tests, which have not been modified much since the last fluvial activity there. The surface of the Jezero delta seems to be such an area.

Due to the unavailability of subsurface stratigraphic information extending beyond the visible surface (radar data do not show the shallow subsurface and neutron spectrometry indicates only the hydrogen content), our aim is to reconstruct only the topmost layers accessible to in situ missions (both considering planetary geology [9] and astrobiology, plus mission relevance). In this shallow subsurface region, the stratigraphy is expected to be variable with different sedimentary features that exist within about 1 m of depth [10,11], which will be reachable by shallow drilling in the near future to sample specific fluvial sedimentary units. Although the topographic data and infrared-data-based grain size values exhibit lower resolutions than optical images, they can still offer valuable insights to identify the potential locations of shallow buried sediments and support methodological development, especially being a global coverage dataset. The importance of this work is that such locations may not be directly observable in HiRISE images but can be inferred through erosion and accumulation modelling.

In this work, the SIMWE method is applied to a specific example area: the delta in Jezero Crater, the landing site of the Mars 2020 Perseverance rover. This location was examined in order to demonstrate the rationality of such analysis and show the type of results and uncertainties that emerge. The work aims to enhance a new type of model focused on reconstructing late fluvial events at the upper part of the delta, using observable topographical data, excluding the comprehensive delta-building process of deeper units. This SIMWE model can estimate runoff and related precipitation from the topography and the eroded/deposited volumes without the direct measurement of precipitation, a value that is not currently constrained for ancient Mars. The rationale for employing the current topography to reconstruct ancient processes by concentrating on the shallow subsurface, rather than deeper regions (largest volume unit of the delta), is partly that the observable topography gives the only possibility for this type of reconstruction. Also, upcoming rover missions in the next few years lack deep but have shallow drilling capabilities. Although the forthcoming Rosalind Franklin Rover can drill down to 2 m, drilling deeper would likely necessitate a stable platform, which is currently unable to achieve sampling from old fluvial sedimentary locations. This advanced drilling capability is anticipated in the more distant future, making the shallow subsurface the primary focus for the coming decade(s).

Similar types of modelling-based analysis have been performed for Mars surface missions that primarily rely on the remote or in situ direct identification of key surface features, such as sediments [12] and phyllosilicates [13], to draw conclusions regarding ancient Martian surface conditions. However, the full potential of process-based modelling is still awaiting exploitation. Existing models generally aim to reconstruct large scale processes at low resolutions, such as global precipitation patterns, with few performing detailed analyses of specific locations [14,15,16] at high spatial resolution. Examples of models simulating ancient environmental conditions at specific locations include models of climate-related river transport [17], glaciation at Erebus Montes [18], Hesperian aged aeolian bedforms in Gale crater [19], paleohydraulic conditions in Ebro Basin [20], widespread formation of an ice layer in the shallow mid-latitude region [21], silica precipitation from ancient water [22], pedogenic weathering [23], and rainfall estimation [24]. Although complex landscape evolution for Mars has rarely been modelled, a few published examples include models exist of Endeavour crater [25], Gale crater [26], aeolian ripple formation [27], and general paleoclimatic evolution [28]. Few numerical, calculation-based models have been presented for a fluvial erosion/deposition.

Limited efforts have been undertaken to employ numerical methods in estimating erosion and accumulation processes, particularly to discern the areas conducive for the accumulation of specific materials, such as fine-grained clays, and where liquid water persisted for extended periods. These models have been limited in capability, though some of them could be adapted to environments other than the Earth by modifying the physical parameters of the target area, e.g., Martian surface gravity, hypothetical flow depth (water thickness on each pixel), grain size, erodibility, and other parameters of soil or regolith. The main advantage of this SIMWE model is that it estimates erosion/deposition without data on the precipitation and provides a step toward estimating the occurrence of sedimentary features (as different ones are expected to occur in different location types). Thus, the authors of this work were motivated to apply modelling approaches for rover-acquired sampling at localization on Mars to reveal the spatial arrangement of sediment accumulation in Jezero Crater. In particular, this open-source model uses the global THEMIS dataset, which can work without precipitation data and which no one has applied to Mars before. The target area of this work is the sedimentary structure at the termination of the main inlet at Neretva Vallis in Jezero Crater. At present, many of these depositional areas are covered with aeolian ripples, resulting in partly obscured deposits. However, at the analyzed target, only a few, scattered sand ripples are present, thus providing a useful target structure for evaluating fluvial features related to erosional and depositional processes. The erosion accumulation model presented in this study examines the changes that occur during a specified rainfall event. The intensity and duration of the rainfall event exert an influence on the flow depth and flow discharge values that are measured in the study area. The model is capable of discerning the erosion and accumulation processes occurring in the area under study during a rainfall event based on the derived data (e.g., flow velocity, shear stress) and the grain size data of the area, with the latter determined from the THEMIS TI data. In accordance with precedent, cross-sectional sampling is employed, whereby the hydrological and subsequent erosion/accumulation values for a specified valley are estimated from the data derived from the cross-sections.

The southern highlands of Mars are incised by vast arrays of fluvial valleys that have been explored by numerous studies [29,30,31,32,33]; however, paleo-discharge values are poorly constrained but important for climatic reconstruction. Surface material transport models for Mars have also been applied to understand precipitation, infiltration, and runoff [34]; various aspects of fluvial systems [35,36,37]; sediment deformation [38]; and sediment deposition [39]. The specific target area for the model tested here is the top surface of the Jezero delta, where a range of fluvial features are available, and with this being a landing site, high-resolution topographic data are also available.

The delta in Jezero Crater was deposited during the early wet period on Mars before the Noachian/Hesperian transition, when fluvial activity was present across the planet [31]. Data retrieved by the Perseverance rover indicates that the western margin of the deposit shows delta/alluvial fan stratigraphy [40], which likely formed in the Late Noachian–Early Hesperian (~3.6–3.8 Ga) [41,42], on the top of a volcanic basement [43]. Dip and strike measurements of sedimentary beds identified in Mastcam-Z stereo-images indicate an increasing, subaqueous fan by deposition of meter-scale, gravity driven, sediment-rich flows [44]. Deposition of variable grain size fractions in the bottom sets was observed (from Devils Tanyard to Knob Mountain members), with a change to siltstones at Hogwallow Flats. Coarser-grained sandstones (Rocky Top) might have been deposited as turbidity currents. Folding deformation is visible mainly in the lower members, with tight folding sandwiched between the sub-horizontal layers, while many folds present in soft sediment deformation features were formed by vertical loading [45]. The Shenandoah Formation spans more than 50 m of vertical stratigraphy at the delta front, where filled fractures imply late-phase fluid flow with cementation and lithification [46]. Some evidence indicates that hydrodynamic sorting has had an effect on mineralogy related to temporal changes in the watershed [47], and spectral data of the delta front records variable aqueous conditions at a range of redox parameters, both during deposition and post-deposition due to alteration by fluids [48], with aqueous alteration minerals like Fe/Mg smectites, alumino-phyllosilicates, serpentines, and Fe/Mg carbonates [49]. The original size of the delta was likely larger than that is currently visible, which is partly indicated by the sedimentary geometry feature with Gilbert-like succession [50], especially at Kodiak Butte, located 1 km away from the front of the continuous deposit structure of the delta [51]. Similarly, Hawksbill Gap also presents stratigraphic patterns similar to those at Kodiak [48].

There is a proposed localized variation in meanders and bars formed in the depositional regime during the later stages of this delta’s history [52]. For example, there is a wide range of various fluvial features on the top of the delta, including point bar strata in meandering channels, inverted channel-filling deposits by alluvial distributary channels, and incised valley deposits with very few post-fluvial dune stripes. Although in theory it is possible that the very topmost part of the original delta has been eroded away, there are no signatures supporting this possibility; thus, we consider that the currently observable upper surface of the delta is representative of the last fluvial episode. The deposit is mainly composed of finer-than-conglomerate (sand and cobble grain size) lithologies, resembling pebbly sandstones, and locally holds boulders within the topset, indicating episodic high-discharge floods. It shows the presence of phosphate, carbonate, olivine, and sulphates, with certain variations between bedforms [53]. Horvath and Andrews-Hanna (2022) [54] ran hydrological models for the formation of the deposit and found that under semiarid conditions, a lake might have been stable there. Analyses of the modern and paleo-topography of Jezero Crater reveals no strong evidence for lake terraces or shorelines. However, analyses of the deposit at the end of Neretva Vallis, such as the stratigraphic sequence, the thicknesses, and the dip angles measured, all indicate an increasing delta deposit, suggesting a lake was present in Jezero at one time.

At the top of the delta, there are several inverted channel forms that are not covered by sand or other, later aeolian sediment, and only a few sands of aeolian origin are found on the walls of the delta front [55] in general. The original rock material of the delta is prominently exposed in various locations, with multiple outcrops of the same sediment. Although it is possible that the top surface was modified by post-fluvial erosion, like wind scour or sand deposition and cementation, such morphological features could not be identified at the top of the delta, while several fluvial-related features are still present. However, these ripples are really small and cover only a small fraction of the area, below 0.1%. Beside this aspect, there is no other possibility than using the currently available surface topography for modelling. In this work we target such shallow subsurface locations where the top layer, influenced by flowing water, could be visited by mobile rovers—and the last flowing-water-influenced top layer could be analyzed, regarding the influence of the direction, speed, etc., of the last liquid flow. The reconstruction of such a terrain evolution that produced the large delta-like structure of a dozen meters’ thickness is beyond the scope of this work; here, only a simpler, related starting step was undertaken. The main benefit of the approach and methodology presented in this work is not the identification of deltas on Mars but the numerical evaluation of erosion and sedimentation from fluvial activity, which helps in the reconstruction of ancient processes.

The method presented in this work could serve as an additional line of evidence in determining the dimensions and locations of accumulation- and erosion-dominated zones, partly as a complementary approach of higher resolution geomorphological data. These predictions come from the present-day topography, which is the best-established available data, although in the future, subsurface fluvial features might be observed in theory by shallow radar or at frequent and nearby deep outcrops, which would expose subsurface settings. But till such data become available, we need to rely on the present-day, observable topography. This is a reasonable approach as there are no signatures indicating that substantial thickness of further, even-younger layers had been deposited there but were eroded away from the current top surface.

2. Materials and Methods

This section provides a concise summary of prior models for context, an overview of available datasets for calculations, and an introduction to the applied specific modelling system, including the rationality of the parameters used.

Surface evolution models emphasizing the balance of erosion and deposition have been applied and validated in terrestrial contexts [56,57,58], though further improvements are needed to apply them to another planet. Studies using the Universal Soil Loss Equation (USLE) are inherently complex and rely on numerous experimentally derived values and constants from terrestrial studies [59]. In contrast, Mars lacks the range of specific parameters necessary for implementing the USLE model for the Red Planet, demanding a more generalized approach. The parameters highly specific to Earth include the rainfall erosivity factor (R) and the cropping management factors (C—cover management factor, P—conservation practice factor). Given the unmeasurable nature of factors P and C, their application to the Martian environment is not viable. Alternatively, the SIMWE (SIMulated Water Erosion) model, relying on more calculable, simpler physical parameters and fewer empirical ones, can be employed. In this study, we adapted this numerical erosion and sedimentation model for Mars, with its primary parameters influenced by shear stress, detachment, and transport coefficients. However, most of these parameters have not been adjusted for Mars as no Earth-based laboratory tests are available, excluding the data on the local gravity acceleration on Mars and the remote-sensing-acquired grain size distribution. These parameters can be estimated based on theoretical principles using accessible Martian datasets, such as the THEMIS (Thermal Emission Imaging System) for dominant grain size; HiRISE (High Resolution Imaging Experiment), CTX (Context Camera), and HRSC (High Resolution Stereo Camera) data for surface morphological evaluation; and topography from stereo images.

In this work, the SIMWE model [60] was applied and adapted to Mars using erosion and accumulation estimations based on surface grain size and topography. This model relies only on calculated physical parameters, making it particularly suitable for Mars, where empirical data are scarce. The core of this model comprises two scripts integrated into GRASS GIS (an open-source GIS) for numerical calculations. The r.sim.sediment script focuses on erosion and accumulation processes and requires the following parameters: grain size, sediment detachment coefficient (D_c), transport coefficient (T_c), topographic elevation, x and y derivatives of the slope (where x is the first order partial derivative of the slope in the E-W direction, and y is the first order partial derivative in the N-S direction), critical shear stress (τcr), Manning’s value, and the infiltration rate. For further technical explanation, see the abbreviations part. It is essential to specify a time interval to match the value set in the r.sim.water script (a landscape simulation method with overland flow dominated hydrological simulation using the path sampling method, with inputs: elevation, flow gradient vector, and a surface roughness coefficient given by Manning’s n), which can be divided into 60 min units what is easily convertible to other time units. 60 min was selected to make a simple approach that is relevant for moderately short precipitation event characteristic in desert-like terrains, possibly connected with chaotic terrain formation or snow melting by hot volcanic dust fall [61], which are relevant for Mars—however, the durations of such events are very poorly constrained for Mars.

The following datasets were used in this study: The DTM and the THEMIS TI datasets were initially digitized to two different coordinate systems and have different spatial resolutions. For consistency between datasets, we reprojected the HRSC DTMs from the initial MARS_Sinusoidal coordinate system to the Simple_Cylindrical_Mars coordinate system [62], the coordinate system of the THEMIS TI dataset. The values of the DTM were then re-interpolated at the resolution of the THEMIS TI dataset. These conversions were made in ESRI ArcMap using the Project Raster tool. Such steps were necessary to result in a homogeneous topographic dataset of the whole target area.

The optical CTX images (D15_033216_1989_XN_18N282W and D20_035141_1987_XN_18N282W), HRSC DTM-h5270_0000_dt4, and the THEMIS infrared image (a clip from the original dataset) were analyzed for surface morphology (Figure 1) were used. On the right side of the geological map from [63], the units colored with different shades of blue mark the fluvial features, including those that are situated at the top of the delta structure and considered to represent the remnants of the last observable fluvial episode. For further details on these topographic fluvial morphological features, please see the last part of the Section 1. HRSC [64] Digital Terrain Models (DTM—50 m/pixel) were used for analysis. THEMIS TI [65] (TI for Thermal Inertia—Mars Odyssey Mission), which has a 100 m/pixel spatial resolution, shows the thermal behavior of the surface material and was utilized to indicate the dominant grain size.

This method offers the ability to estimate an average grain size for extensive terrains due to THEMIS’s resolution limitations. In the future, an improved grain size estimation method will be needed, but here, we had to apply the available global dataset first to test the methodology in general. The grain size data from THEMIS are based on the thermal inertia measurement, and larger grains provide slower daytime warming and slower nighttime cooling, while smaller grains are composed of material that undergoes faster temperature change. It stands as the sole remote method available for obtaining meaningful grain size estimations across almost all Martian terrains by assessing the target’s thermal characteristics. The distinctive advantage of global coverage of thermal inertia is that it facilitates erosion and deposition calculations across all Martian fluvial surface structures, not only the few sites where some ground truth is available.

One limitation of employing THEMIS for grain size estimation is the potential subpixel variations in grain size, introducing uncertainties to the method (

Table A1. The relationship between THEMIS TI values and grain size [13].

Name	Phi	Diameter	Thermal Inertia J m−2 s−0.5 K−1
Pebbles	−4 to −2	4–16 mm	417–580
Granules	−2 to −1	2–4 mm	353–417
Very coarse sand	−1 to 0	1–2 mm	300–353
Coarse sand	0 to 1	0.5–1 mm	254–300
Medium sand	1 to 2	250–50 µm	215–254
Fine sand	2 to 3	125–250 µm	182–215
Very fine sand	3 to 4	63–125 µm	155–182
Coarse silt	4 to 5	31–63 µm	131–155
Medium silt	5 to 6	16–31 µm	112–131
Fine silt	6 to 7	8–16 µm	95–112
Very fine silt	7 to 8	4–8 µm	80–85
Clay	8+	<4 µm	<80

). The potential drawbacks stemming from THEMIS’s restricted resolution and its provision of average grain size data are offset by the model’s capacity for analyzing erosion–deposition processes along the extensive, meandering former fluvial channel, spanning a significant number of THEMIS pixels; thus, it still provides a starting point for model development. Consequently, the spatial scale for assessing variations in surface alterations due to fluvial activity exceeds THEMIS’s threshold, as indicated by the grain size range presented in Table 1 later. Thus, the grain size estimation needs to be further improved, but the THEMIS data still provide a starting point for model development.

The THEMIS TI values can be matched to the different sediment size classes, and these sediment sizes also can be roughly matched to the corresponding shear stress and critical shear stress values [66]. Hence, several raster operations were applied to this dataset: (1) to classify the THEMIS TI (Thermal Inertia) images to average grain size per pixel (in mm); (2) to determine the Shields parameter (Y) to characterize the initiation of motion in a fluid flow related to shear stress for the average grain size; and (3) to determine the critical shear stress (τcr) [66]. To convert the THEMIS TI values to sediment size classes and also to shear stress values, the following formula was used in the QGIS raster calculator tool:

((THEMIS TI image ≥ x AND THEMIS TI image < y)z) + […]

In this formula, the x and y represent the minimum and the maximum value of the THEMIS TI for the considered target area to approach a realistic range, while z is the sediment grain size class value. Although the calculated values obtained in this way might differ from the real average grain size due to THEMIS subpixel mixing and possible adhesion-driven flocculation during the fluvial sediment transport (which could enlarge the grain size during the wet phase transport compared to the dry sediment relevant grain size), the approach is reasonable for testing the method using only remote observations, which is currently applicable for any Martian surface currently.

Prior to executing the erosion–accumulation model, the HRSC DTM underwent modifications using the GRASS GIS r.hydrodem tool. This tool serves to fill enclosed topographic depressions, such as small impact craters, and rectify errors and noise within the DTM. This depression-filling process is essential for preventing anomalies in the simulation arising from the DTM and from small crater depressions. These depressions, likely formed after the period of fluvial activity (as observable impact craters formed later, overprinting fluvial features, while former craters are buried by the fluvial sedimentation), would otherwise serve as flow terminators, leading to pooling rather than continued flow. This uncertainty is unavoidable but, as will be demonstrated later, does not change the general outcome of the modelling.

The erodibility of the surface reflects the resistance of the rocks there against the force of the erosive mechanism, in this case the fluvial incision. In this paper, the Dg model [67] was applied for the estimation of the USLE-K factor, where K is the erodibility and Dg is the geometric mean diameter of the surface particle (mm). In this model, the K formula was chosen because all of the other related equations use different particle sizes like clay, which can also be used to calculate the K factor. The weight percentage of the particle size fraction (%) is the arithmetic mean of the particle size limits, and n is the number of the particles in the given size fraction.

D_g can be estimated with the following equation:

$$D_g=\mathrm{e}\mathrm{x}\mathrm{p}(0.01\sum _{i=1}^n{f}_i{l}_n{m}_i)$$

The SIMWE model was run in the GRASS GIS 7.8 software environment. The model contains two different scripts, called r.sim.water and r.sim.sediment, which estimate the flow depth (m) and flow discharge (m³/s) from given precipitation values (r.sim.water) and the erosion–accumulation balance of the analyzed area. The T_c and D_c were used as the main parameters for the r.sim.sediment tool. In this work, only the r.sim.sediment tool was applied.

This K value is part of the main detachment coefficient (D_c), where D_c [68] is calculated as:

$$D_c=K\left(\tau -{\tau }_c\right)$$

where the shear stress ($\tau )$ and the critical shear stress (${\tau }_c)$ in Pa are considered. Although there are many empirically acquired parameters for the Earth in discharge estimations, these two stress parameters could be calculated for Mars too, as they are based on physical characteristics of the given granular material and can be calculated from the Shields parameter (Y) [69] both as normal and critical values, as follows:

$$Y={\displaystyle \frac{\tau }{D_s\left({\rho }_s-\rho \right)g_M}}$$

where D_s is the diameter of the sediment (in meters); ${\rho }_s$ is the density of the sediment, which was estimated using onsite data-based analogue rock types from the Earth; $\rho$ is the density of water; and g is the gravity of the given planet, in this case Mars. The threshold shield parameter on Earth is around 0.03–0.07 m²/s, though overall the Shields parameter has a certain error that should have been accounted for in sediment hiding and erosion/accumulation, but without a better approach, it is worth applying here.

To determine the transport coefficient (T_c), the specific volumetric transport rate (m²/s) [70] was used. For the volumetric sediment transport, the shear stress was calculated for the bedload (particles in a flowing fluid that are transported along the bottom of the stream bed). The transport coefficient was calculated with the following formula:

$$T_c=\left({\displaystyle \frac{\lambda }{1-\lambda }}\right)\ast \beta \ast {\left(R\ast g_M\right)}^{0.5}\ast {D_g}^{({\displaystyle \frac{3}{2}})}$$

where β is the nondimensional transport parameter, and R is the relative submerged density. β can calculated with the following formula:

$$\beta =\left({\displaystyle \frac{0.1}{f}}\right)\ast Y^{2.5}$$

where f is the friction factor. The flow depth was calculated using the following equation:

$$h=w\ast {\displaystyle \frac{s^{0.2}}{7}}$$

(1)

where w is the flow width and s is the slope of the upstream channel [71], which was later calculated in GrassGis with the r.stream.direction tool. The estimation of the flow width was made in SAGA GIS with the multiple flow direction (MFD) method [72]. This is a useful means to describe the downslope movement. The logic behind the MFD algorithms is similar to the single direction method, but the MFD diverts the flow to multiply downslope cells in proportion to the slope between them. The upstream slope values were calculated based on the filled DTM’s flow accumulation and flow direction parameters. The flow depth (h) is equal to the estimated water depth in the channel or valley, not to be confused with the valley depth, which is the estimated total depth of the valley or channel according to the topography. The valley depth was estimated with the valley depth tool in SAGA GIS. The flow width was considered using the same tool in SAGA GIS. The Manning roughness was set as Mars relevant at 0.0545, and the roughness value obtained by [73] was used.

Considering the presented images, which visualize the targets and the results of this work, Figure 1 shows the target area, Figure 2 shows the flow route calculation-related results, and Figure 3 shows the calculated accumulation and erosion values in the target areas; Figure 4 also shows erosion- and accumulation-related specific parameters (sediment size, flow width, flow velocity, and flow depth map); Figure 5 shows the rover-recorded image of the delta front, from which the profiles are marked, presented, and graphed as values along them in Figure 6.

Table 1. Summary of the parameters used for the model.

Parameter Name	Background Physics	Values on the Earth	Mars Relevant Aspects	Future Directions for Improvement
DTM-based surface topography	Slope-related processes and gravity action	Resolutions have a wide range from km/px to cm/px	Available HRSC (50 m/px) or HiRISE (~1 m/px) images based DTM	Improved automatized stereo images based on high-resolution DTM generation
Grain diameter of surface-covering material (D50)	Influence the adhesion and erodibility of target material; however, the role of cementation is as yet poorly constrained	0.95 nm–256 mm	THEMIS TI dataset-based calculations, some surface in situ measurements	Improved grain size estimation fusing ground truth at all of the planet surface and remote data
Shear stress between transportable grains (τ)	Force of the friction from a flowing fluid acting on a body/grain	Depends on the local sediment’s hydrological properties	Estimation from classified diameter; however, little information on cementation is available	Improved evaluation of future landing sites, implementation of laboratory tests to support model calculations
Shields number (Y)	Dimensionless number related to the fluid force and the particle weight used to calculate the initiation of the motion of a grain by the transport media	Depends on the shear stress	From equation	Improved Earth-based laboratory analysis and theoretical modelling might provide a better understanding of the Shields parameter under Martian conditions
Transport coefficient (Tc)	Maximum potential soil transport by overland flow	Equal to the volumetric transport rate	Equal to the volumetric transport rate	Inferred data from the calculation, future theoretical evaluation
Detachment coefficient (Dc)	Maximum potential soil detachment by overland flow	From different equations	From different equations	Inferred data from the calculation, future theoretical evaluation

Table 1. Summary of the parameters used for the model.

Parameter Name	Background Physics	Values on the Earth	Mars Relevant Aspects	Future Directions for Improvement
DTM-based surface topography	Slope-related processes and gravity action	Resolutions have a wide range from km/px to cm/px	Available HRSC (50 m/px) or HiRISE (~1 m/px) images based DTM	Improved automatized stereo images based on high-resolution DTM generation
Grain diameter of surface-covering material (D50)	Influence the adhesion and erodibility of target material; however, the role of cementation is as yet poorly constrained	0.95 nm–256 mm	THEMIS TI dataset-based calculations, some surface in situ measurements	Improved grain size estimation fusing ground truth at all of the planet surface and remote data
Shear stress between transportable grains (τ)	Force of the friction from a flowing fluid acting on a body/grain	Depends on the local sediment’s hydrological properties	Estimation from classified diameter; however, little information on cementation is available	Improved evaluation of future landing sites, implementation of laboratory tests to support model calculations
Shields number (Y)	Dimensionless number related to the fluid force and the particle weight used to calculate the initiation of the motion of a grain by the transport media	Depends on the shear stress	From equation	Improved Earth-based laboratory analysis and theoretical modelling might provide a better understanding of the Shields parameter under Martian conditions
Transport coefficient (Tc)	Maximum potential soil transport by overland flow	Equal to the volumetric transport rate	Equal to the volumetric transport rate	Inferred data from the calculation, future theoretical evaluation
Detachment coefficient (Dc)	Maximum potential soil detachment by overland flow	From different equations	From different equations	Inferred data from the calculation, future theoretical evaluation

3. Results

To see the effectivity of this modelling method, in this section, the general parameters used are outlined first, and the calculated variables second. Our calculations reveal that the water level of the final flow event that formed the top part of the Jezero western delta ranged between 1.89 and 34.74 m, and the mean water depth was 12.66 m, while the depth of the deep, engraved channels ranged up to 385.54 m. The flow width, which is the width of the water (not of the whole valley), ranged between 35.3 and 341.42 m, while the valley width was up to 1200 m based on a CTX-image-based measurement. The channel parameters used here may have been a slightly different at the time of their formation due to long-term aeolian erosion and sedimentation—however, not much difference is expected (see the related part in the Section 4). Flow velocity rates varied between 0.008 and 11.6 m²/s for the whole period (Figure 3), considering no substantial erosion happened after the formation of the delta top surface. This range is large, but further development of this model and further background parameter acquisition for the equations will decrease it. Better parameter acquisition might also improve it. For example, improved grain parameters or better resolution data will provide a basis for more-detailed calculations but also more spatially heterogeneous results in the future. These values (and the sediment diameter plus the formerly calculated coefficients, which are summarized in Table 1) influence the results of the erosion–accumulation simulation. The script is able to estimate the erosion/deposition values for each pixel in a given timestep; in this article we used a single, 60 min-long simulation. The estimation of the detachment coefficient (D_c) is based on a calculation from the sediment diameter dataset (in mm), which is divided by 1000 to give the numerical value of the diameter in meters.

A simulation with a duration of 60 min resulted in a maximum erosion of 5.986 g/m² and maximum deposition of 4.072 g/m² (Figure 2), which should be considered as a rough approach only, but useful for testing the model, which should be further improved. The rationality of selecting only 60 min for the tested duration of precipitation is twofold: As a first attempt to apply this model to Mars, it is easier to start interpreting the results from shorter duration events and under simpler conditions to see the realization of model runs, and also to make interpretations easier. However, longer tests in the future could be also realized if the model gets further validation. The second reason is that this current paleoclimate model favors short episodic precipitation events on Mars [74,75] instead of a long-term, stable, humid climate [76,77].

Figure 2. Results of the SIMWE erosion–accumulation model of the western part of Jezero Crater (18.48°N; 77.37°E), where the rim can be followed by the most obvious thick, red-and-blue arc-shaped curve at the middle part of the image, curving from top right to lower left. The blue color represents the net erosion (negative values in the model), and the red color shows the net accumulation (positive values) that characterize the area. The black lines in the center left represent the proposed possible traverse plan made by NASA for 2023 and later periods. Note that the visualized area is almost the same as in Figure 1, but here, the erosion–accumulation rates are indicated.

Figure 2. Results of the SIMWE erosion–accumulation model of the western part of Jezero Crater (18.48°N; 77.37°E), where the rim can be followed by the most obvious thick, red-and-blue arc-shaped curve at the middle part of the image, curving from top right to lower left. The blue color represents the net erosion (negative values in the model), and the red color shows the net accumulation (positive values) that characterize the area. The black lines in the center left represent the proposed possible traverse plan made by NASA for 2023 and later periods. Note that the visualized area is almost the same as in Figure 1, but here, the erosion–accumulation rates are indicated.

Figure 3. Flow depth (blue) and river routes (red) based on model calculations in the target area. Note that the edge of the Jezero Crater runs as an arc-shaped darker blue (steep and thus small flow depth, dominated by fast runoff) area, from the upper right toward lower left. The indicated terrain is the same as in Figure 4 at 18.48°N; 77.37°E.

Figure 3. Flow depth (blue) and river routes (red) based on model calculations in the target area. Note that the edge of the Jezero Crater runs as an arc-shaped darker blue (steep and thus small flow depth, dominated by fast runoff) area, from the upper right toward lower left. The indicated terrain is the same as in Figure 4 at 18.48°N; 77.37°E.

This 60 min simulation time is a test time and can be freely changed in the r.sim.sediment script. The diameter of the sediment used in the simulation is between 0.0031 and 1.6 m based on the THEMIS data pixels from the target area (Figure 4a inset). This range is quite wide but helps to see how the simulations run under the observed and available THEMIS values. These values of maximum erosion and deposition are unrepresentative of the entire system, as they are only present in one pixel of the modelled domain, but they provide an objective calculations-based approach that is available today. The erosion–accumulation model results show that at the front, the delta is dominated by accumulation. The sedimentation-dominated areas are continuous and large, covering approximately 60–70% of the whole analyzed area, while the erosion-dominated areas are scattered plus isolated and mainly connected to the steep slope angle areas, with a size between roughly 500 and 1000 m. It is a fallacy to assume that accumulation areas are necessarily linked to the erosion areas that are in closest proximity to them. Due to the characteristics of the surface in question, material from accumulation areas may in fact originate from areas that are more erosion dominated, yet a larger proportion of the accumulated material is more likely to originate from the nearest erosion-dominated area.

Figure 4. Overview of the generated maps used for the erosion–accumulation simulation. The visualized area is the same as in Figure 2 and Figure 3 (18.48°N; 77.37°E). Note that the crater rim runs from top right toward lower left as a curved feature, while the delta structure is located at the middle of the four images. Inset (a): sediment size map (m); inset (b): flow width map (m); inset (c): flow velocity map (m/s); inset (d): calculated flow depth map (m). Please note that the calculated depth is only a model-based approach that should be further improved in the future. The coarse sand fraction grains are primarily located in the riverbed that flows into the Jezero Crater.

Figure 4. Overview of the generated maps used for the erosion–accumulation simulation. The visualized area is the same as in Figure 2 and Figure 3 (18.48°N; 77.37°E). Note that the crater rim runs from top right toward lower left as a curved feature, while the delta structure is located at the middle of the four images. Inset (a): sediment size map (m); inset (b): flow width map (m); inset (c): flow velocity map (m/s); inset (d): calculated flow depth map (m). Please note that the calculated depth is only a model-based approach that should be further improved in the future. The coarse sand fraction grains are primarily located in the riverbed that flows into the Jezero Crater.

Altogether, seven cross-sectional-profiles were made crossing the frontal outcrop of the Jezero Crater’s delta. The result of the model shows that the area in the field of view (FOV) in front of the rover is dominated by erosion, in agreement with the expectations. The area in which erosion and accumulation are balanced (i.e., the area not dominated by erosion or accumulation) is approximately 1.02 km² (~33% of the whole area of the FOV). The erosion–accumulation survey was made along the seven cross-sectional profiles (Figure 5), which are located about ~460 m from each other along the delta front. The average length of the profiles is ~3000 m. On average, along the profiles, the erosion-dominated area is ~200 m shorter than the accumulation-dominated area.

The slopes at the accumulation sites are gentle at the analyzed profiles. In most cases, the slope values range from around 3 to 2 degrees (Figure 5). The steepest accumulation area can be found at profile seven, where the slope values change between 9.1 and 1.7 degrees in a short, 500 m distance. The lowest slope angle change can be found at profile three, where the change is only 0.6 degrees along 750 m (Figure 5).

Figure 5. Location of the cross-sectional profiles (from Figure 6) in the FOV of the rover’s image with the following insets (the area is part of the target region indicated in Figure 1): In inset (a), the locations with numbers represent the cross-profiles from Figure 6. The names scarp A, B etc., were given by the authors to specifically mark certain locations along the frontal edge of the delta that the rover recorded by images. Inset (b) is an example image, from the area of the interest. Inset (c) shows a magnified version of the boxed area in inset (b) with two examples of large boulders below fine layering. The image was taken by Perseverance rover’s Mastcam-Z in 2021. Several images were stacked to take the final mosaic. Inset (d) shows a Mastcam Z image taken by Perseverance on sol 402 and shows an example of the layered sediment on the Jezero delta’s wall. This outcrop is located at cross-section profile scarp 3. (NASA/JPL-Caltech/LANL/CNES/CNRS/ASU/MSSS).

Figure 5. Location of the cross-sectional profiles (from Figure 6) in the FOV of the rover’s image with the following insets (the area is part of the target region indicated in Figure 1): In inset (a), the locations with numbers represent the cross-profiles from Figure 6. The names scarp A, B etc., were given by the authors to specifically mark certain locations along the frontal edge of the delta that the rover recorded by images. Inset (b) is an example image, from the area of the interest. Inset (c) shows a magnified version of the boxed area in inset (b) with two examples of large boulders below fine layering. The image was taken by Perseverance rover’s Mastcam-Z in 2021. Several images were stacked to take the final mosaic. Inset (d) shows a Mastcam Z image taken by Perseverance on sol 402 and shows an example of the layered sediment on the Jezero delta’s wall. This outcrop is located at cross-section profile scarp 3. (NASA/JPL-Caltech/LANL/CNES/CNRS/ASU/MSSS).

A further example of the results of the applied model can be seen in Figure 3, focusing on local runoff rate and regional flow route estimations. Here, these two different aspects are indicated: the local slope-related flow thickness (indicated by blue color), where the shades indicate how fast the water runs off downward from every pixel, and the larger flow depth (darker shade) marking lower slope angle pixels, where water flowed down slower. The brighter shades of blue mark larger slope angles (steeper terrains in each pixel), where the water has flowed away and run off faster, producing a smaller water thickness at a hypothetical moment. The red lines mark the reconstructed flow routes, e.g., ancient riverbeds with the main flow directions where the water convergence happened, producing a hierarchical system (Figure 3). These later lines help to reconstruct former flow-produced channel locations.

4. Discussion

In this section, first, the links between the model and the delta structure are summarized; secondly, the strengths of the modelling approach are presented; thirdly, knowledge gaps that would further advance the model are given; and fourthly, an overview of how such an approach can specifically support future missions is discussed.

Our prior iteration of the Mars-specific SIMWE model employed a hypothetical precipitation value [78] that produced the ancient flow paths using the best available approach, providing a realistic simulation of the locations of former water flow tracks. However, we acknowledge that multiple processes could lead to the poor reconstruction of ancient flow paths on Mars, such as later topographic modification [29], or the newly acknowledged potential of Martian aeolian–fluvial interactions [79]. However, this work employs a unique and moderately simple methodology that has not yet been applied to Mars using the currently available topography. The updated model is capable of roughly identifying the flow paths, which are observable as remnant surface morphology, and delineating erosion–accumulation zones for the top of the Jezero Crater delta system.

Erosion dominates certain areas, such as the steep walls of the main valley, larger crater interiors, peaks, and the edges of the delta. Deposition or accumulation zones are located near erosion sources and spread out from those areas along low-slope-angle terrains. The amount of accumulated material decreases as the distance from the erosion source increases (Figure 3).

The coarse sand fraction grains are primarily located in the riverbed that flows into the Jezero Crater (Figure 5, inset a, red rectangle), as well as in craters and other depressions within the delta. Sediments with similar grain sizes are also present in the foreground of the delta. The simulation suggests that sediment in the accumulation areas has a finer grain size, possibly due to the reduced flow speed of the fluvial process during the last wet period. Gravel and other larger blocks are rare or sparsely distributed throughout the valley. The flow velocity (as shown in Figure 4, inset c) is closely related to the slope of the terrain. Therefore, steeper slopes exhibit higher values than the observable confined large channels.

Cross-sectional profiles show that the dominant accumulation areas are in a transition zone between the end of the steep slopes and the surrounding flat surface of the crater bottom (Figure 4). Here, the simulated water velocity is low enough to deposit fine-grained sediment and prevent further sediment movement. This agrees with the fact that the fluvial sediment possibly accumulated close to the wall of the delta and appears as a gentle slope near the delta’s wall (Figure 5). This fluvial sediment might be partly buried by aeolian material, which is visible on the last image of the Perseverance rover (Figure 6) taken from the edge of Jezero’s delta, but the aeolian coverage rate is small in general.

Figure 6. Results of the erosion/accumulation calculations along the selected profiles (for profile locations, please refer to the Figure 5). The blue lines show the HRSC (100 m/pixel) profile, and the red lines show the results of the SIMWE model, which all were situated almost perpendicular to the frontal edge of the currently visible delta. The number of the insets corresponds to the number of the profiles in Figure 5. The profiles extend radially from the rover’s position on 17 April 2021 to the present-day topographic front of the Jezero delta system. The numbers between the accumulation marker arrows represent the slope in degrees. Although errors exist in the data used for the visualization, it is useful to roughly estimate the related specific values (making error envelopes around the curves) as there are too many parameters to firmly use such error values.

Figure 6. Results of the erosion/accumulation calculations along the selected profiles (for profile locations, please refer to the Figure 5). The blue lines show the HRSC (100 m/pixel) profile, and the red lines show the results of the SIMWE model, which all were situated almost perpendicular to the frontal edge of the currently visible delta. The number of the insets corresponds to the number of the profiles in Figure 5. The profiles extend radially from the rover’s position on 17 April 2021 to the present-day topographic front of the Jezero delta system. The numbers between the accumulation marker arrows represent the slope in degrees. Although errors exist in the data used for the visualization, it is useful to roughly estimate the related specific values (making error envelopes around the curves) as there are too many parameters to firmly use such error values.

The inset c shows scarp A, where larger boulders transported by a former high discharge are located below layers composed of smaller grain sizes, indicating a temporal decrease in the discharge and transition from more to less erosive periods. Such locations could be estimated using this model purely from the remotely accessible data, which are much more available than in situ images from the surface. In the case of further-improved DTM (both by remote sensing and surface roving missions) with higher spatial resolution, the 1–10 m scale features identified by on-site images could be linked to model-based data, validating the method to find favorable sites for fine-grained accumulation. In addition to surface morphometry, grain size and estimated flow depth also strongly influence the model adapted to Mars.

The presented method for determining grain size is important as it could be sampled for all of the Martian surface using THEMIS data, and the resulting grain size distribution is the best available approach to test the methodology. However, the method clearly should be improved in the future.

The original bedrock of the delta is visible in several Mastacam Z images (Figure 5, inset d). These layered sediments are evidence of former fluvial activity. During the lifetime of the last fluvial activity of the Jezero delta, these previously deposited sediments were eroded and redeposited further from the currently visible wall of the delta. These last accumulation fields could be covered with aeolian sand and dust. An example of a layered sediment outcrop is located at cross-section profile three, shown in Figure 5. These sedimentary layers are on the top and edge of the delta’s wall, where the last fluvial erosion event occurred, and the eroded material could be accumulated, as shown by the result of the simulation.

Although this model is not able to directly separate sites showing the accumulation of boulders vs. clays, fine grains are expected to deposit at the locations of lowest flow speed. To find these sites, further development of the model focusing on separating different depositional regimes is needed and could probably be achieved, supported by the results of this work as a first step. The strength of this model lies in its application to ancient Martian fluvial features in the future, using only remote data without in situ information and lacking exact knowledge of ancient precipitation. Although specific in situ data would have made the calculations more accurate, such information from Mars is poorly available and scattered, while remote-sensing-based data are abundant. These conditions allow the comparison of differently aged fluvial networks, supporting the identification of the temporal climatic changes that happened during the geological history of the planet. However, such work requires the usage and testing of this model by the community on other, already analyzed fluvial networks.

A possible traverse plan according to NASA communication (Press Release 13 September 2021) was overlain on the erosion/sedimentation color code map in Figure 2 as black lines. These proposed tracks mainly cross sedimentation-dominated areas (indicated by yellow-red colors); however, there are several possibilities for passing by erosion-dominated locations (smaller, isolated blue areas). The comparison of Mastcam images from the Perseverance rover of erosion- and sedimentation-dominated areas will provide opportunities to further link this model to observations and identify areas in need of improvement. If on high-resolution images sedimentary- versus erosion-dominated features were visible (possible at steep outcrops), this model could be verified by such on-site images from Mars in the future. This should be conducted after Perseverance has passed along a route of several km and sampled enough sites to correlate several THEMIS pixel-based values to grain size values measured on local, nearby recorded images. A further possibility in the coming years is to evaluate the accumulation-/erosion-dominated locations by the analysis of outcrops on other missions’ images, if a large enough number of outcrops can be found and recorded—unfortunately, at the time of this writing (early 2024) few such matching locations have been recorded, with most images at less than the ideal resolution and quality.

Besides the planned on-site activities, Earth-based laboratory analysis also helps the advancement of this model. One important problem in such development is that the pH and chemistry of possible flowing waters on Mars are poorly known (salt concentrations with melting point decreases would present in the water), which influence flocculation, grain aggregation, and thus deposition processes. Another critical point is the different gravity regimes on Mars compared to those on Earth, which limit our understanding of vortex formation and their intensity inside Martian flowing rivers, which influence the sedimentation as well. However, possibilities for improvement also exist, especially the determination of other parameters used here, like the detachment coefficient, which requires microscopic-scale physical tests.

The model’s uncertainties stem from various sources, as outlined in Table 1 (parameter numbers correspond to table rows): Parameter 1—Uncertainties in the DTM introduced variability in the calculated accumulation and erosion values, but do not significantly impact the locations of these processes, as topographic undulations below the DTM spatial resolution do not change the flow path direction. These errors are expected to be distributed uniformly across the terrain, thus minimally affecting the overall erosion/accumulation pattern. Parameter 2—The grain size determination is based on THEMIS TI values, which introduce subpixel-level variations and related errors into the model. Additionally, the presence of non-fluvial sediments (e.g., aeolian deposits) can contribute to uncertainties, especially with very small grain size, although this proportion is estimated to be less than 1% based on examples from Goudge et al. (2018) [55]. Parameters 3 to 6 represent mechanical properties for those values that could be determined through laboratory tests. However, due to the limited number of such tests conducted under Mars-relevant conditions, the potential errors associated with these parameters remains poorly understood.

When testing the sensitivity of the approach used here, by increasing the duration or the intensity of the precipitation event, the final total erosion or accumulation values increase linearly. The length of the rainfall event and its magnitude exert the greatest influence on the final results, namely the erosion/accumulation rate, flow depth, the derived flow velocity and flow discharge values. However, precipitation of high-intensity but short-duration results in erosion and accumulation rates that are similar to or somewhat more pronounced than those resulting from less intense but longer-duration precipitation. The increase in shear stress as one basic parameter also modifies the final outcome: a twofold increase (along with the increase in simulated flow speed and water thickness) enhances the maximal erosion rate from 21.55 to 28.24 kg/ha/h, and the accumulation increases by roughly the same scale also. Despite the various uncertainties in the parameters used, the spatial pattern of the erosion-/accumulation-dominated locations do not change, though the absolute values were modified. These indicate that the method used to find the targets of accumulation sites with the longest duration and lowest flow speed related looks to be useful already in its current state. Nevertheless, the equations that use both transport and detachment coefficients and shear stress values should be further tested, bearing in mind that when introducing a new modeling approach, the error level of the method is always uncertain. However, through continuous improvement and comparison to other erosion/deposition models, our understanding of these uncertainties will gradually decrease and became better known in the future.

The primary focus of this article was to develop a model for identifying erosion and deposition at the analyzed site based on a hypothetical precipitation event. The exact temporal duration could not be considered, but the total amount of rain (fallen vertical water thickness) was used. This study applied the hypothetical duration of the rainfall event to be 60 min, without specifying its intensity. However, a comprehensive model encompassing the entire delta’s evolution is planned for future iterations. To provide a context to better understand how the gained results fit with other researchers’ projects, we compare our numerical values to estimates from other studies. The mean flow rate, as determined in the study for the entire area, is 35,524.24 m³/s, which falls between previously cited values. Although comparison of different models is difficult, the following values give insight into the correctness of this model and its rough relation to other models. Grotzinger et al. [80] estimated a peak discharge of 1 to 5 million m³s⁻¹. Tate et al. [81] employed Darcy–Weisbach equations to estimate discharge rates for the area, including Kodiak Butte, ranging from 1.63 to 8.64 ms⁻¹ for velocities and 76 to 3000 m³s⁻¹ for discharge. They calculated discharge rates for the western portion of the delta at around 500 m³s⁻¹. The mean flow rate, as determined in the study for the entire study area, is 35,524.24 m³/s, which falls between previously cited values. It is crucial to acknowledge that these discharge figures represent estimated flow discharge data, reflecting the maximum possible value for the given methodology and morphology. In this study, the flow discharge was calculated using the Darcy–Weisbach equation. For a broader perspective, considering other fluvial systems on Mars, highland valley networks typically form with discharges of 300 to 3000 m³/s [82], while outflow valleys feature the largest discharges, reaching around one billion m³/s [83,84]. The model presented here proves to be valuable not only for identifying accumulation-dominated sites, but especially for comparing them regarding the expected grain size of sediments there and the rate of the finest grade grains. Such comparison could not be performed from the optical observations from above, but on-site verification will require shallow drill-based sampling in the future. The identified accumulation-dominated areas, characterized by the lowest slope angles and slowest flow speeds, are most likely to host fine-grained deposits, particularly clay-sized particles, which favor organic preservation [41,80,81,82,83,84]. It is also worth noting that the model applied here is available for the community from now and could be further used and tested with different input parameters for different Mars surface locations.

Possible Future Usage of the Modelling Approach

Recent Mars surface missions have exhibited increased sophistication, encompassing both traverse or rover route planning and instrumental enhancements [85], while landing accuracy has also been improved [86]; thus, sophisticated targeting is also needed. For the planned international Mars Sample Return project, meticulous site selection and safe access are critical prerequisites. The advanced modelling approach outlined in this work could prove valuable in determining the potential sites of sample acquisition. While not directly applicable to landing site selection, this model could be employed to evaluate and select one or more surface targets among several potential rover destinations, particularly where lithologies of interest have been obscured by aeolian deposits but reachable for shallow drilling. This model allows the identification of such former accumulation-dominated sites, even if their morphology is not readily evident from the results above. This enables a more precise identification of accumulation-dominated fluvial sites even without conspicuous indicative surface features.

The model’s output facilitates comparisons between accumulation and sedimentation patterns, particularly for identifying locations with prolonged wet periods that favor the deposition of fine grains, enhancing the preservation of ancient organics and biosignatures. Improved future versions could also support and guide future research and potentially even on-site analysis and target selection [85,86].

Although waterborne sediments could deposit in accumulation-favoring locations, they are typically found within depressions that are challenging for rovers to traverse and analyze. Yet, in the future, if a rover identifies multiple depositional locations, this model could assist in selecting the most promising one among them by providing context to compare these different locations based on the volume of water that flowed through them or the expected rate of former material accumulation.

As a summary, this model aids in the identification of locations that might not be discernible through orbital optical imagery, such as concealed sedimentary formations and minor drainage pathways [78].

5. Conclusions

For proper targeting of Martian fluvial features for the purpose of astrobiology-related in situ analysis, shallow subsurface targets are of import due to their preservation potential. The identification of such locations is somewhat difficult from visual imagery alone, and although locations with abundant phyllosilicates can be detected as evidence of prominent former water abundance, these need to be exposed at the surface. The modelling approach shown in this article could support the identification of sites where drilling is able to reach former accumulation-dominated locations at reachable shallow depths.

The SIMWE erosion model was applied to Mars, in the Jezero Crater fluvial delta deposit, with parameters adjusted for Martian conditions. For identifying the erosion- and accumulation-dominated areas formed during the last flow episode, using the top part of the delta surface in the FOV of the recent Perseverance images (Figure 5), we estimated the area (in km²) and the size (in m) of the best possible areas for acquiring fine-grained deposited sediment samples. Although the currently observable surface need not reflect the real final flow episode, it still provides the best currently available approach for estimating these last flow features and related accumulation locations. At a few hundred meters to a kilometer away from the current delta front, some isolated hills are present (with similar appearances of height and a flat top, together with a spatial correlation with the edge of the delta), which could be classified as outliers [81], representing the former, more extended but eroded remnants of a larger original delta. However, this is only a possibility and does not influence the currently observable topography of the remnant delta. At any site, there are no such surface features visible that would indicate that thicker or thinner deposits have accumulated there before. The finest grains accumulated during the last fluvial event, with the probable occurrence of the smallest grain size when the vanishing discharge supported low flow speed, thus providing the potential location for finding deposited weathering products. The longest ponding sites favor the sedimentation of the smallest grains with possible bound organics.

Using the model calculations with a hypothetical short 60 min precipitation event, the average flow depth is 12.66 m, the maximum erosion is 5.98 g/m², and the maximum deposition is 4.07 g/m². The average size of the accumulation-dominated areas by the cross-section profiles (Figure 6) is ~1000 m. The erosion-dominated areas have an average size of ~800 m, which are typically found along the steep walls, including the major craters or various peaks. The rate of accumulation decreases as the erosion moves away from the source, and accumulation areas are located immediately next to erosion-dominated areas at a lower elevation.

The model can be further advanced as there are current knowledge gaps, such as sediment size estimation and surface reconstruction from the last fluvial activity. The correlation of the model-based erosion-/deposition-dominated area types is possible by high-resolution on-site images, although analysis of more locations (at further landing sites) could greatly improve such connections. Better sediment detachment coefficient modelling is also needed, which future laboratory tests and theoretical calculations might also help to obtain. However, it is apparent that the model, even in its current state, is already useful for identifying potential locations of shallow subsurface deposits of interest, dominated by small grain size accumulation during the latest phase of fluvial activity. This approach is valuable for uncovering such areas, which are likely concealed beneath surficial covers of alluvial material that increases shielding plus preservation, and it could be applied at future landing sites, including those of the Rosalind Franklin Rover, which plans to drill to a depth of 2 m.