A New Method to Evaluate the Combined Performance of Check Dams and Afforestation on Debris Flows Mitigation in a Dry-hot Valley

Debris ows in waterways can transport large amounts of sediment downstream, which can cause serious damage and economic losses. The vegetation cover in the valley of the Xiaojiang River in Yunnan Province, China—classied as a dry-hot valley—was signicantly reduced by logging in the 1950s. Soil erosion intensied and 107 gullies developed, which led to debris ows along the 86 km length of the river. Jiangjia Gully is a tributary of the Xiaojiang River. Historically, debris ows have occurred frequently, blocking the Xiaojiang River seven times between 1957 and 2000. Since 2000, the construction of check dams and afforestation have decreased the volume of debris ows in the three tributaries of Jiangjia Gully. However, different combinations of check dams and afforestation were adopted in the three tributaries of Jiangjia Gully, which has led to the different trends in debris ows behaviour. A new method was established to evaluate the mitigative effect of check dams and afforestation on debris ows. We found that the debris ow volume was proportional to the gravity energy of soil and rock on the gully bank and inversely proportional to the vegetation coverage in a dry-hot valley setting. The method revealed that under different gravity energy conditions, the implementation order of check dam construction and afforestation is important for debris ow mitigation.


Elevation of the gully bed
The bed elevation of the lower Jiangjia Gully between 1964 and 2020 was assessed between the observation points (D 1 -PL 1 ) shown in Fig. 1. A geophysical exploration was performed with georadar along Jiangjia Gully (D 1 -PL 1 ). This exploration provided the accurate depth of the interface between sediment deposits and the underlying bedrock and gave the thickness of the sediment deposits (Lyu et al. 2020). Although the earliest record of a large debris ow was in 1957, there was no observational data of the bed. The bed elevation of the lower Jiangjia Gully (D 1 -PL 1 ) in 1957 was assumed to be the interface between sediment deposits and the underlying bedrock.

Estimating the annual volume of debris ows
The estimation of the sediment volume mobilized by a debris ow can be carried out by the differences of pre-and post-events DEMs (Simoni et al., 2020). But the DEMs before and after a debris ow event is di cult to be obtained timely (Mohammad and Ali, 2017;Hassan and Banihabib 2016;Schürch et al. 2011). Based on the laboratory work of Lyu et al. (2016;2017a), the volume of the potentially unstable rock mass on the gully banks was expected to play an important role in the volume of debris ows. Most of sediment transported to the outlet of the gully was originated from the potentially unstable rock mass on the gully banks. The volume of potentially unstable rock mass on the gully banks was estimated according to the method introduced by Blothe et al. (2015) in gure 3. First, the quantity of potentially unstable rock mass, de ned as the rock located between the toe of the gully bank and an idealized topography with slope equal to the threshold hillslope angle, α, is computed (Fig. 3). Second, the potential volume of debris ow is de ned as the increased volume of the potentially unstable rock mass, S, by gully bed incision (Fig. 3). Third, the proportion of particle percentage in the debris ow and in the original rock mass and soil was used as a measure of soil particle erodibility (Ali et al., 2017). According to the grain size distribution, 10% of the potential volume, S, ushed into the debris ow per year (Lyu, 2019), is estimated as the actual annual debris ow volume, D. The collapse deposits on the bank were loose with average slope angles of 35 (Liu, 2010). So, in the present analysis, α= 35° in this gully was adopted for the potentially unstable rock mass. The slopes on both sides of the tributaries are between 35° and 65°. The debris ow volume of the Menqian (1957Menqian ( , 1964Menqian ( , 1997Menqian ( , 2005Menqian ( and 2020 and the Duozhao (1957Duozhao ( , 1974Duozhao ( , 1982Duozhao ( , 1985Duozhao ( and 1990 was derived from the changes in the gully bed and potentially unstable rock mass (Fig. 3).
The annual debris ow volume, D of the Daaozi (1957Daaozi ( , 1974Daaozi ( , 1982Daaozi ( , 1985Daaozi ( , 2010Daaozi ( and 2020  There are no data about the annual debris ow volume trapped by check dams, D τ , in the Duozhao. However, 6×10 5 m 3 of sediments were trapped in total from 1974 to 2005. Because the debris ows only occurred in 1974, 1982, 1985, 1990, 1997 and 2005, we assumed that 10 5 m 3 of sediments were trapped on average in each debris ow year (Table 1).

Energy of source material on the slope
The debris ow is triggered by the slide of the unstable lateral mass and the mass laying on the channel bed. The kinetic energy of debris ows is related to the transformation of gravitational energy and is released by creeping or by landslides on the gully bank (Weinmeister, 2007). The gravitational energy, E, above the critical slope, α, on both banks (hereinafter referred as the source energy) is calculated as follows ( Fig. 3): where γ s is the unit weight, B is the width, Z is the height, and H is the height of the highest point. For gully incision, the source energy adopts Eq (2), and ΔH is the incision height. For gully deposition, the source energy adopts Eq (3), and H D is the deposition thickness (Fig. 3).
The check dams in the Duozhao tributary were full of sediment until 2005, so the source energy of the Duozhao that was affected by check dams, E r , can be calculated by the bed elevation change and Eq (3).

Vegetation coverage
The normalized difference vegetation index (NDVI) is used to represent the vegetation coverage and is recognized as an integrated indicator of elevation change and ood frequency (Casco et al., 2005;Marchetti and Aceñolaza, 2012). Positive NDVI values indicate increasing vegetation and negative or zero values indicate water or a surface that has no vegetation. In debris ow gullies, an increase in NDVI re ects the conversion of bare surfaces to vegetation.
vegetation coverage rate data, V, before 1992 came from the Dongchuan Forestry Bureau, and the vegetation coverage rate after 1992 was calculated using NDVI (Yang, 2018). The change in the vegetation coverage rate, V f , by humans (afforestation and deforestation) from 1957 to 2020 was sourced from the Dongchuan Forestry Bureau (Table 1).

Debris ow deposition and incision in Jiangjia Gully
The middle and upper reaches of Jiangjia Gully (upstream of D 1 ) were increasingly incised by debris ows from 1957 to 2005, but the incision rate slowed between 2005 and 2020 (Fig. 4b). The lower reach (downstream of D 1 ) was deposited by the debris ows, which extended into the Xiaojiang River from 1997. The maximum thickness of the debris ow deposition in the lower Jiangjia Gully was 80 m according to the georadar method (Fig. 4a).  The vegetation growth may be another reason for the inconsistent pace between the debris ow volume decrease and the energy decrease of source material from 1990. As the afforestation and vegetation growth, the soil shear strength is found to increase due to developed root tensile forces and soil-root bonding (Wu et al., 1979;Bischetti et al., 2009). Morgan (2009) showed that vegetation decreases surface water runoff and sediment erosion. Compared with the bare slop, the vegetated deposits have higher erosion resistance and are resistant to erosion even under more intense rainfall (Shen et. al, 2017). Hence, the threshold hillslope angle, α, in gure 3 has increased due to the vegetation growth and decreased the energy of source material. In this study, the change of threshold hillslope angle due to vegetation are not considered.
The change rate of debris ow volume in Jiangjia gully, , was negative with the increase of vegetation coverage, V, and positive with the increase of the source energy, E (Fig. 6, 8 and 10). Afforestation and check dams could form a soil and water conservation system (Shi et al., 2019). Combination of check dams and afforestation could greatly mitigate debris ow or landslide formation and motion (Promper et al., 2014).
Debris ow has an eruption cycle, and its volume decreases within a certain period of time after the eruption. Therefore, the change rate of debris ow volume was negative in relation to the volume of the last debris ow (Lyu, 2017).
The change rate of source energy in Jiangjia gully, , was negative because of the increase of vegetation coverage, V, and was positive because of the increase of the debris ow volume, D (Fig. 6, 8 and 10). Check dams could control the gully incision, thus the potential energy for bank erosion was greatly reduced (Wang and Zhang, 2019). Check dams could promote revegetation by stabilizing gully slopes and controlling soil erosion. Vegetation development also affected erosion and potential energy (Kosmas et al., 2000). It takes three to ve years or more for afforestation to play a signi cant role in the areas with landslides and creeping (Cui and Lin, 2013). Wang et al. (2005) developed the vegetation-erosion model, which analyzed the relations among the rate of soil erosion, vegetation cover, and human activities in Xiaojiang River. The varying rate of vegetation () in Wang's model was proportional to the vegetation but negatively proportional to the erosion rate. However, Wang's model did not consider the potential energy for bank erosion. It is necessary to develop a model including the vegetation coverage and source energy in serious bank erosion or gravity erosion area to evaluate the combined effect of afforestation and check dams for debris ow mitigation.
Equation (4) was established based on vegetation-erosion model, and the source energy was added as one factor. The change rate of vegetation coverage was negatively to source energy ( Fig. 8 and 10). And the annual volume of debris ows replaced erosion rate in the model, because debris ow (gravity erosion) was the main erosion type in Jiangjia gully. The varying rate of source energy and debris ow volume were also assumed to be linear with other factors.
where parameter a depends on the local rainfall, environmental and plant composition; c represents the destructive effect of source energy on vegetation; g represents the destructive effect of the debris ow volume on vegetation; b depends on the local source energy; f represents the effect of vegetation coverage on source energy; h represents the effect of incision by debris ow on the source energy; i represents the impact of the debris ow volume on the next debris ow volume; j represents the inhibitory effect of vegetation on debris ow volume, where the increase in vegetation coverage is bene cial; and k represents the promoting effect of the source energy on the debris ow volume.
Using values of vegetation coverage, V, source energy, E, debris ow volume D, and human activities on vegetation coverage, , source energy, , debris ow volume, , in Table 1, and Eq (4), the values of parameters a, b, c, f, g, h, i, j, and k were obtained by a trial-and-error method (Li and Wang, 2016). Table 2 shows that parameters a, j, and f were highest in the Daaozi tributary, which indicates that vegetation coverage had the greatest impact on the debris ow control in the Daaozi. The maximum values of parameters b, c, and k were in the Duozhao, which indicates that, here, check dam construction had the greatest impact on debris ow control. Owing to the construction of the check dams in the Duozhao, the destructive effect of debris ow on vegetation coverage was small, and most trees survived, so the value of g in the Duozhao was the lowest. By substituting the values for parameters, vegetation coverage, and source energy in Table 2 into Eq (4) to calculate the debris ow volume in different years, Fig. 10 shows that the calculated value and the actual value were consistent for the debris ow trend.
The vegetation coverage-source energy-debris ow volume dynamics model in equation (4) may be representative for similar debris ow processes in in serious bank erosion or gravity erosion area and dry-hot valleys such as the Loess plateau, the Yungui plateau and Tibet plateau in China. There were spatial differences in the physical and mechanical properties of different combinations of vegetation and rock-soil media in the dry-hot valleys. Therefore, the parameters in the vegetation coverage-source energy-debris ow volume dynamics model differed. Obtaining parameter values in different regions through eld surveys and indoor experiments can guide combined models of check dam construction and afforestation in different dry-hot valleys.
The V-E plane in gure 11 can be divided into three zones by the lines and (Fig. 12), as follows.
1. Zone A (V′<0, E′> 0): The vegetation coverage is decreasing and the source energy is increasing. This is the area in which debris ow disasters are aggravated.
2. Zone B (V′>0, E′> 0): The vegetation coverage is increasing and the source energy is increasing. This is the transition area for debris ow disasters.
3. Zone C (V′>0, E′< 0): The vegetation coverage is increasing and the source energy is decreasing. This is the area in which debris ow disasters are reduced.
For the Menqian and Duozhao tributaries, which had higher source energy, afforestation cannot fully control debris ow. Check dams should be constructed rst to reduce the source energy. Then afforestation can disrupt the accumulation of material sources, and control debris ows (such as in the Duozhao tributary). For tributaries with a low source energy, afforestation can control debris ows (such as in the Daaozi tributary).

Conclusion
The good performance of the combined model supports the physical interpretation of the debris ow trends in the Jiangjia gully. Debris ow volume was proportional to the source energy and inversely proportional to the vegetation coverage. Owing to the different combinations of check dams and afforestation in the three tributaries, the trend of debris ow development differed. Check dam construction and afforestation worked simultaneously in the Duozhao while afforestation was the main reason for the debris ow reduction in the Daaozi. As the main tributary of Jiangjia Gully, the Menqian tributary had only one check dam, which was destroyed in 1974. Afforestation did not seem to control debris ows in this tributary. The vegetation coverage-source energy-debris ow volume dynamics model could explain the effect of different factors on the trends of debris ow development in the three tributaries. Using only afforestation in low source energy gullies can control debris ow, whereas high source energy gullies require the construction of check dams rst, followed by afforestation.  Source energy distribution of the three tributaries in 2020 The relationship between debris ow volume (D), source energy (E) and vegetation coverage (V) in the three tributaries from 1957 to 2020