The substrate into which the gullies have incised is identified based on the following criteria.

LDM/glacial deposits – any crater whose gullies incise walls that appear to be softened by the drape of smooth mantling material with polygonal cracks is inferred to have an LDM as the substrate within which gullies have incised (e.g., Mustard et al., 2001; Kreslavsky and Head, 2002; Levy et al., 2009a; Conway et al., 2018; De Haas et al., 2019a) (Fig. 2a and b). The gully alcoves on the walls of these craters may be partially to completely filled by the LDM, and in some cases, polygonized LDM materials may be seen covering the alcove walls (e.g., Christensen, 2003; Conway et al., 2018; De Haas et al., 2019a). These infilled alcoves on the crater walls are not the alcoves of gullies formed within the LDM substrate; instead, they represent the alcoves that were formed prior to the LDM emplacement epoch. Additionally, gullied craters that show evidence in the form of arcuate ridges at the foot of the walls and VFFs that cover part or the entire crater floor are inferred to have been modified by one or multiple episodes of glaciation (e.g., Arfstrom and Hartmann, 2005; Head et al., 2010; Milliken et al., 2003; Hubbard et al., 2011) (Fig. 2c). These craters host gullies that are often partially or fully covered by LDM deposits and are also inferred to incise LDM deposits.

The measurements we made of each gully system include alcove area, alcove perimeter, alcove length, alcove width, alcove gradient, fan area, fan length, fan width, and fan gradient (Fig. 3). In total, we derived 18 morphometric variables to characterize each gully fan and its alcove. The morphometric variables are classified into geometry, relief, gradient, and dimensionless variables (e.g., form factor, elongation ratio, and circularity ratio), and they are calculated with established mathematical equations shown in Table 2. For the gradient measurement using the DTM, the topographic profile from (1) the crest of the alcove to the apex of the fan was extracted for the alcove, and (2) the apex to the foot of the fan was extracted for the fan.

We have selected only those gully systems for morphometric measurements in which (i) the depositional fan from an alcove–channel system is not superimposed by or interfingering with the fans from the neighboring channels, (ii) there is clear association between the primary channel emanating from the alcove that extends downslope and then deposit its respective fan, (iii) no evidence of extensive cross-cutting is seen with the neighboring channels on the walls, (iv) no evidence of extensive mantling by dust/aeolian deposits is apparent, and (v) no evidence of channel/fan superposition on any topographic obstacle on the walls or the floor of the crater is apparent, which may have influenced the morphometry. If in any case the fans superimpose or channels cross-cut, we have carefully demarcated the alcove–channel–fan boundary to minimize the inaccuracies in the measurements. Note that the selection of the gully systems was also constrained by the coverage of HiRISE DTMs used for morphometric analysis.

We have two groups of gullies in our study: (1) gullies whose source areas are incised into LDM/glacial deposits and (2) gullies whose source areas are incised into the bedrock. First, for both groups, we have calculated descriptive statistics for each of the morphometric variables shown in Table 2. The significance of the difference between the values of each of the morphometric variables calculated for each group was tested using a Student's t test. To apply t tests, we have transformed the morphometric variables to remove skewness by taking their natural logarithm. The Pearson correlation analysis has been used to investigate the correlation between the selected morphometric attributes of gully alcoves and fans. We infer strong positive correlations between variables if the correlation coefficient value is more than 0.7 and strong negative correlations if the value is less than -0.7. A very strong positive correlation between variables is inferred if the correlation coefficient is ≥ 0.9. Further, we used canonical discriminant analysis (CDA) to determine morphometric variables that provide the most discrimination between the groups of gullies. In CDA, functions are generated according to the number of groups, until a number equal to n-1 functions is reached (n is the number of groups) (McLachlan, 2005). For the two groups of gullies in our study, there is going to be a function for which there is a standardized canonical discriminant function coefficient associated with the morphometric variable. The higher the magnitude of this coefficient for a particular morphometric variable, the higher the role of that variable in separating the groups of gullies (Conway et al., 2015). Standardization was done by dividing each value for a given variable by the maximum value.

Out of the 29 gullied craters analyzed in this work, we have found that there are 24 craters influenced by LDM and/or VFFs. The remaining 5 craters have gullies incised into the exposed underlying bedrock on the wall of the crater. Below we describe the substrates identified in the studied craters and then compare the morphology of the gullies formed into those substrates.

Out of 24 craters, 4 craters (i.e., Raga, Roseau, unnamed crater in Newton basin, and unnamed crater-1 in Terra Sirenum) have gullies that are only influenced by an LDM. In these craters, we have found morphological evidence of an LDM in the form of polygonized, smooth textured material on the pole-facing walls of the craters. Morphological evidence of VFFs is not evident in these craters. In these craters, the gully alcoves and gully channels appear to have been incised into the polygonized LDM material, and the gully fan deposits are mantled. A typical example of this can be found in the unnamed crater formed inside the Newton basin (Fig. 4a). The Roseau crater, in particular, contains a large number of gully systems whose alcoves and fans are extensively mantled (Fig. 4b). The remaining 20 craters out of the 24 craters contain evidence for gullies that are influenced by both LDM and glacial deposits (Table 1). The base of the pole-facing walls and the floor of the craters within which the gully systems have formed host linear-to-sinuous arcuate ridges and VFFs, respectively. Typical examples of VFFs can be found in craters of Corozal, Talu, unnamed craters in Terra Sirenum and Argyre basin, Langtang, Dechu, and Dunkassa (Fig. 4c). In majority of the gullied craters (except Raga, Roseau, and unnamed crater-1 in Terra Sirenum) influenced by LDM and glacial deposits, gully alcoves are found to have a distinctive V-shaped cross section in their mid-section (Fig. 4d and e), they do not extend up to the crater rim, and gully systems often show multiple episodes of activity, inferred by the presence of fresh channel incision on the gully fan surfaces (Fig. 4d and e).

Istok, Galap, Gasa, Los, and an unnamed crater in the Terra Sirenum contain gully systems on the pole-facing walls that are not associated with an LDM and VFFs (Table 1). The gully alcoves inside these craters have a crenulated shape and appear to have formed by headward erosion into the bedrock of the crater rim (Fig. 4f). These craters have formed large gully systems on their pole-facing walls, with brecciated alcoves, comprising of multiple sub-alcoves and hosting many clasts/boulders (Fig. 4f).

We have found that the gully systems formed in LDM/glacial deposits and bedrock can, using discriminatory analysis, be distinguished from one another in terms of perimeter and relief of gully alcoves (Table 3). Additionally, we have found statistically significant differences between the perimeters and reliefs of gully alcoves formed in LDM/glacial deposits and bedrock (Fig. 5). It is likely that these differences in the perimeters and reliefs of gully alcoves formed within morphologically distinct substrates could be due to the integral nature of the surface material within which the gully alcoves have formed. In other words, it is possible that the differences in the physical properties of the sediments (namely grain size, compactness etc.) within which gully alcoves have formed played a key role in erosion of the substrate, leading to differences in their morphometric variables. Below, we elaborate on the uniqueness of the substrates within which gully alcoves have formed and discuss further the relationships between the morphometric variables of the morphologically distinct gully systems.

On Mars, VFFs contain high-purity glacial ice with a debris cover (Sharp, 1973; Squyres, 1978, 1979; Squyres and Carr, 1986; Holt et al., 2008; Plaut et al., 2009; Petersen et al., 2018). Their surfaces have been interpreted to comprise of finer, reworked debris derived from sublimation of the underlying ice (Baker et al., 2010; Plaut et al., 2009). It has been suggested that the smooth, meters-thick draping unit on the walls of formerly glaciated craters is derived from the atmosphere as a layer of dust-rich ice primarily constituted of fine-grained materials (Kreslavsky and Head, 2000; Mustard et al., 2001). The fine-grained materials are loosely packed, unconsolidated materials exhibiting low thermal inertia values (Mellon et al., 2000; Putzig et al., 2005). Typically, gullies formed within this substrate display a smooth surface texture wherein evidence of individual clasts or meter-scale boulders is not resolvable in HiRISE images, substantiating the dominant component of fine-grained materials within the LDM (e.g., Levy et al., 2010; De Haas et al., 2015a). Additionally, it has been found that gully alcoves incised into the LDM always have a distinctive V-shaped cross section in their mid-section (Fig. 4d and e), which when compared with similar-scaled systems on Earth, also corresponds to the presence of loose sediments constituting the LDM (Conway et al., 2018). The gully alcoves with V-shaped cross sections are found to be elongated, likely indicating incision within ice-rich unlithified sediments (Aston et al., 2011). In the studied craters, we have found that gullies incised into LDM/glacial deposits do have an elongated, V-shaped cross section in their mid-sections (Fig. 4). We propose that the presence of fine-grained, loosely packed, unconsolidated materials within LDM/glacial deposits has facilitated the formation of elongated gully alcoves with perimeters and reliefs relatively higher than that of gully alcoves formed in coarse-grained bedrock substrate. This is consistent with the previous studies suggesting that gullies eroding into LDM/glacial deposits have elongated catchments (Aston et al., 2011), whereas gullies eroding into the bedrock have more amphitheater-shaped catchments (Levy et al., 2009b). For this reason, the estimated length of gully alcoves formed in LDM/glacial deposits is found to be relatively higher than that of gully alcoves formed in bedrock (Fig. 5). Furthermore, statistical analysis has revealed a significant difference between the length of gully alcoves formed in LDM/glacial deposits and bedrock (Fig. 5). Additionally, the presence of finer-grained sediments in LDM/glacial deposits is the likely cause of the V-shape of the incision of gully alcoves investigated in this study (Aston et al., 2011). On Earth, it has been observed that V-shaped incisions through glacial ice-rich moraines have occurred during the paraglacial phase of glacial retreat (Bennett et al., 2000; Ewertowski and Tomczyk, 2015) (Fig. 7). The paraglacial phase refers to a terrestrial post-glacial period that represents the response of changing environment to deglaciation (Bennett et al., 2000; Ewertowski and Tomczyk, 2015).

The next most important difference between these two types of gullies is the mean gradient of gully fans. At the foot of the fans, mean gradient of the fans influenced by LDM/glacial deposits is < 15∘ for 61 % of the studied fans. For bedrock, 84 % of the studied fans have a mean gradient > 15∘ at the foot of the fans. Hence, gully fans formed in bedrock are emplaced at a relatively steeper gradient than the fans formed from gullies in LDM/glacial deposits. We propose that the nature of the mobilized material can explain this difference, with the finer-grained sediments that are characteristic of the LDM/glacial type gullies being easier to mobilize and being entrained to lower slope angles than the coarser sediments found within the bedrock type gullies.

On Earth, alcove–fan systems can roughly be subdivided in flood-dominated, debris-flow-dominated, and colluvial systems. Following the terminology of De Haas et al. (2015b) and Tomczyk (2021), we define these systems as follows:

Flood-dominated systems – these are systems dominated by fluid-gravity flows, i.e., water floods, hyperconcentrated floods, and debris floods. The fans of such systems are commonly referred to as fluvial or alluvial fans (e.g., Ryder, 1971; Blair and McPherson, 1994; Hartley et al., 2005).

Although these systems may be dominated by one type of geomorphic process, it is important to stress that other processes may also occur. For example, on Earth, water floods are not uncommon on many debris-flow-dominated systems, while debris-flow deposits are commonly recognized on colluvial cones.

To compare the morphometric characteristics of the Martian gully systems to terrestrial systems, we have compiled morphometric data of gully alcoves and fans across several continents, mountain ranges, climate zones, and process types on Earth. This dataset includes published data from the Himalayas, Ladakh, India (Stolle et al., 2015), the tropical Andes, Columbia (Arango et al., 2021), Spitsbergen, Svalbard (Tomczyk, 2021), British Columbia, Canada (Kostaschuk et al., 1986; Jackson et al., 1987; and newly presented data), the southern Carpathians, Romania (Ilinca, 2021), the Southern Alps, New Zealand (de Scally and Owens, 2004; de Scally et al., 2010), the North Cascade Foothills, USA, the European Alps (including Switzerland, Italy, France, and Austria), and the Pyrenees (from multiple authors compiled by Bertrand et al., 2013). The dataset comprises information from colluvial, debris-flow-dominated, and flood-dominated (also including debris flood) systems. In total, it contains 231 colluvial systems, 749 debris-flow-dominated systems, and 369 flood-dominated systems. In total, data were compiled for 1349 systems, although not all information was available for all systems, with data availability ranging from 729 sites for alcove length to all 1349 systems for Melton index and process type. Based on these data, we have made a heatmap of the probability of conditions dominated by flood, debris flow, or colluvial systems for combinations of Melton ratio with alcove length and fan gradient to which we compare the Martian gullies (Fig. 8). We have specifically chosen the combinations of Melton ratio with alcove length and fan gradient to infer the Martian gully formative mechanism because they have been widely used in discriminating terrestrial drainage basins and fans prone to flooding from those subject to debris flows, debris floods, and floods (e.g., de Scally and Owens, 2004; Wilford et al., 2004). We have found that the Martian gullies are indeed in the debris-flow regime on Earth. Moreover, their transition is closer to the smaller and steeper colluvial cones than to the flood-dominated fans. As expected, bedrock systems in Fig. 8d and e are closer to the colluvial systems than the LDM systems.

According to the previous reports of debris-flow-like deposits found in Martian gullies (e.g., Johnsson et al., 2014; Sinha et al., 2019, 2020), the morphological attributes of debris-flow-like deposits typically include overlapping tongue-shaped lobes with embedded clasts, channels with medial deposits, and channels with clearly defined lateral levees. However, it is still not clear whether the formation of these deposits in gullies are from sublimation of CO2 ice or due to meltwater generation. De Haas et al. (2019b) showed that CO2 sublimation may lead to flow fluidization on Mars in a manner similar to fluidization by water in terrestrial debris flows – a concept supported by the recent finding of lobate deposits and boulder-rich levee formation during the present day in the Istok crater (Table 1) (Dundas et al., 2019). The formation of these morphologically similar deposits during the present day is attributed to sublimating CO2 frost, which likely produces the necessary fluidization by gas generated from entrained CO2 frost (Dundas et al., 2019). On the basis of these recent reports (De Haas et al., 2019b; Dundas et al., 2019) and based on our own findings in this study, we argue that a debris-flow-like process similar to those operated in the terrestrial gully systems has likely dominated the flow types that lead to gully formation on Mars. Present-day sublimation of CO2 ice on Mars may have provided the necessary flow fluidization for the emplacement of deposits similar to terrestrial debris-flow-like deposits (De Haas et al., 2019b).