**4. Results and discussion**

The soil loss, and its consequent degradation, can occur in many ways. In general, after a degradation process, the soil becomes thin and stony, giving rise to severe impacts for the surrounding environment, such as those specified below:


### **Figure 6.**

*Mars global climate zones [18], based on temperature, modified by topography, albedo, actual solar radiation. A = glacial (permanent ice cap); B = polar (covered by frost during the winter which sublimates during the summer); C = north (mild) transitional (Ca) and C south (extreme) transitional (Cb); D = tropical; E = low albedo tropical; F = subpolar lowland (basins); G = tropical lowland (chasmata); H = subtropical highland (mountain).*

It is evident, after analyzing the shape and dimensions of the cross-section profiles made in the study area, that the main channel has the typical shape of a gully. In a broad sense, a gully is a deep depression, channel or ravine, very active for the natural drainage of a liquid fluid that flows through the surface. Although gullies can be continuous and discontinuous, it should be taken into account that the last one appears when the gully bed has a lower slope level than the general slope of the surrounding terrain.

On the other hand, it is also known that, in a gully, runoff is channeled into trenches that deepen over time to form a marked front (head) with very steep faces (walls). The gullies extend and deepen in an upward direction due to cascading erosion and progressive collapses of their upper parts. Similarly, gully slopes can collapse due to seepage of water, as well as undermining the flow of water within the gully.

With regard to the Earth (**Figure 7**), it should be noted that gullies tend to form where the slopes are long and there has been a logical loss of vegetation. This fact has as a consequence an increase in surface runoff. In particular, they tend to be dominant in areas where the soil is composed of deep silty or clay materials, in soils with unstable clays (as in the case of sodium soils), under bare rocky surfaces and on very steep slopes subject to water infiltration and earthmoving.

In another vein, and in relation to the cross-sectional profiles obtained, **Table 1** shows the area of each one of them. As can be seen, from cross-section profile number 8 (km 347 from start in **Figure 8**), inclusive, there is a significant increase in the surface of the gully, perhaps due to the contribution made by an effluent or another contributing watershed, such as [19] specifies.

Regarding the volume of soil lost (Eq. 1) in the study area, it should be noted that a result of 10,817.812 km3 has been obtained. If this result is compared with that obtained by [19–21] (**Table 2**), it can be seen that the methodology used affects the calculation of the volume, so much so that, if Eq. (3) would have been used

*Prediction of the Transported Soil Volume by the Presence of Water in the Vicinity… DOI: http://dx.doi.org/10.5772/intechopen.102985*

**Figure 7.** *Gullies of Cerro Negro (Castilla La Mancha, Spain).*


**Table 1.**

*Area in each cross-sectional profiles.*

(**Figure 9**), the soil lost volume, in the present work, would have been 11,553.29 km<sup>3</sup> . Calculation of this volume using the Topocal 2022-v9.0.811 software resulted in 12,700 km3 .

$$V(\text{km}^3) = \frac{d}{6}(A\_1 + 4 \times A\_m + A\_2) \tag{3}$$

Regarding the RCI shown in Eq. (2), each of its variables has been obtained as follows:

### *Arid Environment - Perspectives, Challenges and Management*

### **Figure 8.**

*Relationship between the area of each cross-section profile and its distance to start.*


### **Table 2.**

*Soil lost volume in Ma'adim Vallis by different methodologies.*

### **Figure 9.**

*Sketch to obtain the volume by the prismatoid equation.* A*<sup>m</sup> is the mean cross-section area between* A*<sup>1</sup> and* A*2.*

The *Q*'<sup>s</sup> value, dependent on the mass ("*m*" in g) of soil lost and of the contributing watershed area ("*A*" in m<sup>2</sup> ). According to [22], the average density of soil on Mars is 2.58 g/cm<sup>3</sup> . Taking into account, as soil lost volume, for having been calculated according to the MOLA data, that corresponding to that obtained through Topocal 2022-v9.0.811, that is, 12,700 km<sup>3</sup> , the soil mass amounts to the value of:

*Prediction of the Transported Soil Volume by the Presence of Water in the Vicinity… DOI: http://dx.doi.org/10.5772/intechopen.102985*

$$m = 12700 \text{ km}^3 \times 2.58 \frac{\text{g}}{\text{cm}^3} \times \frac{10^{15} \text{ cm}^3}{1 \text{ km}^3} = 3.28 \times 10^{19} \text{ g} \tag{4}$$

According to [16], the contributing watershed area is 208,500 km<sup>2</sup> (2.085 1011 m<sup>2</sup> ), so the *Q*'<sup>s</sup> value is:

$$Q'\_s = \frac{3.28 \times 10^{19} \text{ g}}{2.085 \times 10^{11} \text{ m}^2} = 1.57 \times 10^8 \frac{\text{g}}{\text{m}^2} \tag{5}$$

If the soil lost volume is converted to an equivalent per km<sup>2</sup> , it is obtained (12,700 km<sup>3</sup> /208,500 km<sup>2</sup> ) 0.0609 km<sup>3</sup> /km<sup>2</sup> .

In order to obtain the average elevation ("*H*" in m) of the study area, data shown in **Figure 3** were taken into account. It should be noted that the average elevation does not refer to that calculated with respect to level 0, since, in this case, the result varies depending on the absolute elevation at which the study area is located, which does not would make sense. For this reason, the average elevation is obtained taking into account that level 0 is the lower level of Ma'adim Vallis, so *H* will be the average elevation at said level, that is, 2 km (431 m � 1569 m).

In order to infer the average slope ("*S*" in °) of the contributing watershed, and knowing that the gully length is 771 km, it will only be necessary to perform the following calculation:

$$S = \tan^{-1} \left( \frac{2 \text{ km}}{771 \text{ km}} \right) = 0.149^{\circ} \tag{6}$$

Finally, substituting all the numerical values in Eq. (2), the following valid expression for Ma'adim Vallis is obtained:

$$\text{RCI} = e^{\frac{1.56 + \log\left(\frac{1.57 + 1.08}{t'}\right) - 0.46 \times \log\left(2000\right) \times \tan\left(0.149\right)}{2.6}} = e^{\frac{1.56 + \log\left(\frac{1.57 + 1.08}{t'}\right)}{2.65}}\tag{7}$$

It is necessary to emphasize that the developed model has been calculated taking into account the runoff of liquid water due to rainfall in the form of rain that, in the past, would have occurred on Mars. In addition, as is well known, on the red planet the sublimation of groundwater, in low pressure atmospheric conditions, can cause a landslide analogous to that produced by runoff of liquid water flowing on the surface, a phenomenon that should be taken into account in future studies in order to be able to obtain all the causes that can affect the soil loss on Mars.
