Characteristics and development of steepland gullies in the dry valleys of Southwest China

Use of spatiotemporal ergodic indicators for studying the development of steepland gullies

When utilizing the space-for-time substitution method to investigate the evolution of river geomorphology, it is necessary to ensure that the selected experimental objects are situated at an equivalent watershed level and have comparable watershed morphologies; in other words, the chosen experimental subjects should share a similar or identical developmental environment (Fryirs, Brierley & Erskine, 2012). In this study, we selected a representative region featuring steepland gullies within a dry valley. This area exhibits well-developed geological structures, steep terrain gradients, concentrated precipitation patterns, and sparse vegetation cover, as well as fragmented rock and soil compositions; these provide the basic conditions necessary for the formation of erosion gullies. Moreover, various stages of steepland gully evolution have been preserved within the study area, thereby forming a relatively comprehensive sequence.

Space-for-time substitution often employs ergodic indicators to reflect the spatiotemporal development of individual landforms and thus represent the changing characteristics of research objects. In studies on the evolution of geomorphology, many researchers have utilized morphological measurement parameters such as distance, location, and geomorphologic dimension or complexity as ergodicity indices (Huang et al., 2019). Micallef et al. (2014), Yang et al. (2021b), and others used space-for-time substitution to investigate the evolution of gullies and selected the gully length as an ergodic indicator to represent the different stages of gully development. In this study, this method was adopted for sorting and numbering the steepland gullies based on the length of the main gully.

Morphological indicators used to represent the spatiotemporal development of steepland gullies

The selected gully parameters were first extracted using the ArcGIS software to obtain DEM data for the steepland gullies. Referring to earlier studies (Micallef et al., 2014), the indicators that can effectively reflect the morphological changes during the development of steepland gullies were selected: the coefficient of the main and tributary gullies, vertical gradient, gully elongation, and gully openness. Descriptions of these indicators are given below. (1) The coefficient of the main and tributary gullies, R, is the ratio of the length of the main gully to the total length of the gully: (1)${\displaystyle R=\frac{L}{L_0}}$ where L is the length of the main gully, and L ₀ is the total length of the gully. (2) The vertical gradient, I, is the ratio of the difference in elevation between the gully’s head and tail to its length: (2)${\displaystyle I=\frac{H_2-H_1}{L}}$ where H ₂ is the elevation of the gully head, H ₁ is the elevation of the gully tail, and L is the length of the gully. (3) The gully elongation, F, is the ratio of the gully’s width to its length: (3)${\displaystyle F=\frac{W}{L}}$ where W represents the width of the gully, and L represents its length.

The gully elongation quantifies the relationship between the length and width of the rectangle formed by enclosing the gully along the direction of the normal to the slope. It also indirectly classifies the gully according to the type of tail: according to Huang Jinlv’s proportion standard, F < 0.618 corresponds to a “slender” tail, F = 0.618 corresponds to a tail of the “Huang Jinlv type”, and F > 0.618 corresponds to a “short, coarse” tail. (4) The gully openness, K, is a measure of the topographic openness of the gully: (4)${\displaystyle K=\frac{W}{H}=\frac{1000A}{L\cdot H}}$ where W is the width, A is the area, L is the length, and H is the relative height difference of the gully.

A gully with K > 0.65 is defined as “open”, 0.35 < K < 0.65 corresponds to a “semi-open gully”, and an “incised” gully has K < 0.35.

Steepland gully cross-section indicators

During the process of gully development, the cross-section morphology serves as a significant indicator of gully dynamics. The VF indicator, a measure of the width-to-height ratio of a valley, can be employed to quantitatively assess a gully’s cross-sectional characteristics and thus provide insight into regional uplift patterns. Given the specific conditions prevailing in the study area, for each gully, we selected five cross-sections for analysis: these were named upper gully, upper-middle gully, middle gully, lower-middle gully, and lower gully (Fig. 3). The average VF value was then calculated for each cross-section (Bull & Mcfadden, 1977). A low VF value (VF < 1.0) was considered to indicate a V-shaped valley with rapid regional uplift and intense downcutting erosion by a river. A high VF value (VF > 1.0) was considered to correspond to a wider valley where tectonic activity is relatively weak and lateral erosion dominates over downcutting erosion. The value of the VF indicator was calculated as (5)${\displaystyle VF=\frac{2VFfw}{\left[\left(Eld-Esc\right)+\left(Erd-Esc\right)\right]}}$ where Ffw represents the width of the valley floor, Eld and Erd represent the elevations of the shoulders on the two sides of the valley, and Esc represents the average elevation of the valley floor.

Empirical volume–length relationship

There is a power function relationship between the volume and length of the erosion trench, which usually closely fits the data set, so the volume–length (V–L) model can be used to predict the volume of the gully (Frankl et al., 2013b). (6)${\displaystyle V=a\cdot L^b.}$

Here, V represents the volume of the gully, and L represents its length. The higher the absolute value of a is, the stronger the correlation between V and L; b reflects the rate at which the volume changes in response to variations in gully length.

Planar characteristics

Based on the lengths of the main gullies, the steepland gullies in the study area were sorted and numbered (Fig. 4); gully G1 was the shortest at 82.29 m, and gully G11 was the longest at 498.82 m. Gully G3 was the narrowest (width = 11.12 m), and gully G11 was the widest (width = 145.87 m). The shallowest gully, designated G3, had a depth of 3.57 m, whereas G11 was the deepest at 41.57 m. As steepland gullies develop, their length, width, depth, area, and volume increase (Table 1).

An empirical model, V = 0.2 ×L^2.61, which accurately describes the relationship between the length and volume of the steepland gullies in the dry valleys, was established. This model exhibits a high coefficient of determination (R² = 0.98), indicating a strong correlation between the length and volume (Fig. 5A). The area and volume of the steepland gullies were found to increase nonlinearly with the length of the main gully (Figs. 5A and 5B). During steepland gully development, the longitudinal and transverse forces are exerted, leading to continuous growth, widening, and increased erosion amount. In the early stages of development, expansion is slow; however, in the later stages, the expansion rates accelerate rapidly. The gully elongation increases linearly with the width, length, and depth of the gully (Figs. 5C, 6A and 7A), where ductility values remain below 0.618 according to the Huang Jinlv’s proportion standard, classifying it as a slender gully type. The gully openness also increases linearly with the width, length, and depth of the gully (Figs. 5D, 6B and 7B). Based on the openness degree, gullies G1–G7 were found to correspond to the incised type (K <0.35), whereas gullies G8–G11 were found to correspond to the semi-open type (0.35 < K < 0.65). These results show that, as gullies develop, the amount of undercutting continues to increase as a result of hydraulic action. The vertical gradient decreases nonlinearly with the width, length and depth of the gully (Figs. 5E, 6D and 7D), and the coefficient of the main and tributary gullies decreases nonlinearly with the width, length, and depth (Figs. 5F, 6C and 7C). These two results indicate that the early stages of gully development are rapid; the rate of development later slows down until it becomes constant.

Profile characteristics

Based on the actual situation in the study area, four representative gullies were selected, and the five cross-sections described in “Steepland gully cross-section indicators” were drawn for each of them (Fig. 8); the average VF values for these cross-sections were then calculated. It was observed that the VF values gradually increased as the gullies developed (Fig. 9). The range falls between 0.38 and 1.35, where G1–G9 represent V-shaped gullies (VF < 1), while G10 and G11 represent U-shaped gullies (VF > 1).

As illustrated in Fig. 8, the cross section of the gully exhibits a gradual transition from wide to narrow, which is indicative of a wide gully head and a narrow gully tail. The four selected gullies have undergone progressive deepening and widening over time, transitioning from shallow V-shaped gullies to having a more pronounced U-shaped morphology. Initially, the cross-sections exhibit distinct V-shapes with smooth walls, primarily due to hydraulic scouring and undercutting. Subsequently, the gullies gradually evolve into broader V-shaped gullies characterized by the formation of noticeable fractures and steps on their slopes; gravity-induced collapse also becomes increasingly prominent during this stage. At the same time, lateral erosion continues to widen the gullies, and surface tributaries develop. This leads to the slopes becoming less steep until stability is achieved within the U-shaped gullies.