1 Introduction

Landslide damming of laterally confined rivers is reported with increasing frequency (Knapp et al. 2018; Fan et al. 2019; Ermini and Casagli 2003; Chen et al. 2013; Guo et al. 2021). If these dams breach, the subsequent outburst floods may induce catastrophic casualties and major damage to property downstream (Fan et al. 2020c; Bonnard 2006; Wang et al. b; Ding et al. 2021; An et al. 2021; Zhang et al. 2020). They delivered about 18.7 × 106m3 and 6.3 × 106m3 of sediment, blocking the **sha River and forming landslide-dammed lakes (Chen et al. 2021a, b; Ouyang et al. 2019). After each dam formed, the barrier lake breached and the outburst floods caused flood disaster damage downstream. The landslide dams blocked the **sha River for 44 h and 13 days, respectively. The dam heights were 47 m and 72 m, and the subsequent lake that formed extended 45 km and 70 km, and the peak storage capacity reached 0.29 × 109m3 and 0.58 × 109m3. There was significant infrastructure damage, and the whole of Boluo Town was inundated (Chen et al. 2021a, b; Gao et al. 2021; ** outburst floods using a collaborative learning method based on temporally dense optical and SAR data: a case study with the Baige landslide dam on the **sha river. Tibet Remote Sens 13(11):2205" href="/article/10.1007/s11069-022-05776-z#ref-CR66" id="ref-link-section-d118754862e702">2021), notably because of poor image quality. The one-dimensional HEC–RAS hydraulic model has been used to simulate the flood (Fan et al. 2020d; Gao et al. 2021), but its precision is insufficient because it relies on cross section density and struggles to reproduce spatial patterns of inundation when there is substantial flux of water on the floodplain rather than in the channel. Improvements in hydraulic modelling are needed, to allow for a better assessment of inundation patterns in two dimensions. The aim of this paper is to develop a coupled approach to landslide dam failure and two-dimensional hydraulic modelling for assessing downstream flood risk, applied here to the Baige landslide.

2 Overview of the landslide and the study area

The Baige landslide is located at Boluo Town, Jiangda County, in the Tibet Autonomous Region, China (31.082336°N, 98.704722°E). It periodically dams the **sha River of the Tibetan Plateau. It is in the **sha River suture zone and is associated with strong tectonic activity; the tectonic setting of the area is quite complex; faults and folds are well developed. Proterozoic, Carboniferous, and Triassic strata are the major rocks in the study area. The major faults in the area generally strike NW–SE, and the Boluo–Muxie Fault is the nearest one to the slides which strike N30° W and dip 50 to 70° to SW. The fault is 146 km long, and its fault belt is 100 to 300 m wide. The **sha River undercuts the plateau forming a V-shaped valley which allows for the Baige landslide to readily block the river.

According to field investigations and remote sensing, a total of 41 towns were affected by two Baige outburst floods, with a maximum inundated area of about 102 km2 in the second flood. This paper focuses on a 9 km reach at Zhubalong Town in the **sha River in Batang County (Fig. 1). Zhubalong Town was selected for the focus as it is a city of considerable importance in terms of infrastructure. It was 180 km downstream of the dam but still experienced serious flood impacts. The study reach is representative of other reaches impacted by the floods in that it comprises a wide floodplain.

Fig. 1
figure 1

Location of the Baige landslide and the study area. a, c Baige landslide flood impact extent. b Study area satellite image. d Baige landslide aerial image

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3 Overall methodology and data sources

Figure 2 provides an overview of the outburst flood analysis presented in the paper. It is based upon coupling and upstream analysis of likely dam breach risk and impact in terms of an extreme discharge event with a two-dimensional hydrodynamic model, applied here to a downstream reach at Zhubalong Town. It focuses on the largest of the 2018 events, which provides for validation of the analysis. Then, the hydrodynamic model is applied to determine the inundation for possible future dam breach scenarios. This approach, whilst determining locally specific data for model application and calibration is generic and therefore of wider use.

Fig. 2
figure 2

Flow chart of the outburst flood analysis

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3.1 Data sources

The flood hazard assessment in this work was based upon numerical simulation, satellite imagery, Digital Elevation Model (DEM) data, and hydrological information. First, the PlanetScope satellite imagery data were obtained from the “Planet Developer Resource Centre (Planet Explorer)”. PlanetScope data are based upon approximately 130 satellites and can image the entire land surface of the Earth daily. PlanetScope images are approximately 3 m or 3.7 m per pixel resolution and are generally divided into 4 bands (B, G, R, and NIR) (Table 1). These data were used to identify maximum flood extent during the event (see below). The flood has a clear signature in terms of maximum extent due to extensive fine sediment deposition. Second, the ALOS (Advanced Land Observing Satellite) DEM data, produced using ALOS panchromatic three-line images, were used for the hydrodynamic model. These data have a spatial resolution of 5 m and were obtained from the Geographical Survey Institute of Japan. Finally, discharge data were provided from the Batang gauging station in the **sha River (Fig. 3), providing reliable real-time monitoring data (Gao et al. 2021; Chen et al. 2021a, b). A peak discharge of 20,900 m3s−1 was recorded during the second flood (Fig. 3).

Table 1 Satellite image and DEM data source
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Fig. 3
figure 3

Discharge hydrograph measured for the Batang County reach

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3.2 Methods

3.2.1 Remote sensing interpretation

The outburst floods occurred on 12 October and 13 November 2018. 7 October and 15 November 2018 were selected as dates with cloud-free imagery from before to after the two events; as the second flood was larger, 15 November data are likely representative of this event. The imagery records the extent of the flood’s impact, and it can be used to distinguish between inundated and non-inundated zones (vegetation-covered zone). The maximum inundated extent impacted by the outburst floods was mapped by comparing imagery from before to after the flood. The eCogition Developer version 9.0 software was used to conduct the remote sensing. First, the RGB bands were displayed (Fig. 4a). Second, a multi-resolution segmentation algorithm (MESA; Benz et al. 2004) was applied at the pixel scale. This algorithm starts with individual pixels and merges them with adjacent pixels according to their homogeneity. The MRSA was applied with a scale parameter of 25 m (Fig. 4b). Third, the Normalised Difference Vegetation Index (NDVI) was determined (Fig. 4c):

$$ {\text{NDVI}} = \frac{{{\text{NIR}}_{{{\text{mean}}}} - R_{{{\text{mean}}}} }}{{{\text{NIR}}_{{{\text{mean}}}} + R_{{{\text{mean}}}} }} $$
(1)
Fig. 4
figure 4

Method to delineate flood inundation extent using remote sensing

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The NDVI is used to detect vegetation growth state, vegetation coverage and eliminate partial radiation error. It reflects well on the characteristics of plant distribution and is easy to distinguish from inundated zones. Fourth, the imagery was classified into vegetation zones (non-inundated zone) and inundated zones based upon a threshold value of the NDVI. In this study, the NDVI of the vegetation zones was between 0.16 and 1.0 (Fig. 4d). Fifth, a manual classification was undertaken to provide validation data got assessing the automated classification (Fig. 4e). Sixth, the classes were merged to produce non-inundated zones (vegetation-covered zones) and inundated zones (Fig. 4f).

3.2.2 Determination of potential landslide dam height

The secondary failure and landslide-dammed lake risk of the Baige landslide are high with the continuous deformation of the landslide edge and rear (Chen et al. 2021a, b; Zhang et al. 2021; Zhou et al. 2022). Crack zones have been identified in several detailed field investigations, which implies that the area of landslide potential high-risk zones can be determined (Fig. 5a–e). A deep displacement monitoring instrument (SINCO) was used to detect slope deformation and to identify the landslide sliding surface with manual measurement, once per month on average. The total monitoring time was from June 2019 to December 2021. The potential landslide volume was calculated based upon surface area and the estimated depth to the shear plane.

Fig. 5
figure 5

Deformation characteristics of the Baige landslide. a Deformation area and crack distribution of the Baige landslide edge and rear. b Boundary crack of the Baige landslide rear. c Historical deformation scarp. d Crack propagation in engineering cutting area. e Severe deformation zone

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The potential landslide dam height was determined based upon the landslide volume, dam shape, and the shape of the deposit (dam breach deposit) that formed downstream from the breach. For the two 2018 breaches, distinctive dam breach deposit shapes were identified (Fig. 6a). These deposits then determined the required landslide mass needed to create a landslide dam during future landslide failures (Fig. 6a). The landslide dam shape, especially the back and front slope, could be extracted to restrict the crest of the dam assuming that the landslide accumulation process operates in a similar way (Fig. 6b, c). Using this approach, it was possible to identify landslide dam heights at risk of future breaching.

Fig. 6
figure 6

a Landslide dam cross sections and dam breach deltas for the two flood events. b Longitudinal profile for the first 2018 event. c Longitudinal profile for the second 2018 event

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3.2.3 Hydrodynamic model

The simulation of inundation was based upon the shallow water equations which solve for continuity (conservation of mass or volume) and momentum to calculate the propagation of shallow water flows over natural topography. There are four aspects that must be considered: (1) the form of the terms use to describe conservation of mass and momentum; (2) numerical solution of the associated partial differential equations; (3) parameterization (as shown in Table 2), notably of flow resistance which is generally the parameter that has most impact on flood inundation prediction; and (4) the description of channel and floodplain geometry (Lane 1998; Worni et al. 2013).

Table 2 Parameters of the BASEMENT model simulation outburst flood
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The two-dimensional numerical model BASEMENT (Zischg et al. 2018) was used to investigate and simulate flood inundation in the study reach. BASEMENT has been designed as a tool for application to the study of flood inundation and coupled water–sediment processes (Lala et al. 2018). The 2D shallow water Eqs. (2) through (4) are solved with an explicit finite-volume method on an unstructured mesh (Worni et al. 2013). The water depth h and specific discharges (q = uh, r = vh) are the primary variables in the coordinate directions.

$$ \frac{\partial h}{{\partial t}} + \frac{\partial (uh)}{{\partial x}} + \frac{\partial (\nu h)}{{\partial y}} = 0 $$
(2)
$$ \frac{\partial }{\partial t}(hu) + \frac{\partial }{\partial x}\left( {hu^{2} + \frac{1}{2}gh^{2} } \right) + \frac{\partial }{\partial y}(huv) = - gh\frac{{\partial Z_{B} }}{\partial x} - \frac{{\tau_{Bx} }}{\rho } $$
(3)
$$ \frac{\partial }{\partial t}(hv) + \frac{\partial }{\partial x}(huv) + \frac{\partial }{\partial y}\left( {hv^{2} + \frac{1}{2}gh^{2} } \right) = - gh\frac{{\partial Z_{B} }}{\partial x} - \frac{{\tau_{By} }}{\rho } $$
(4)

where u is the velocity in x direction, v is velocity in y direction, g is the gravitational acceleration, ρ is the fluid density, and ZB is the bottom elevation. The bed shear stresses (τBx, τBy) act in the direction of depth-averaged velocities and are determined using the quadratic resistance law with cf being the dimensionless friction factor as (5). Flow resistance is generally described by the empirical Strickler (Range: 7 ~ 40 m1/3 s−1) or Manning coefficients (Range: 0.025 ~ 0.143 m−1/3 s) (Vanzo et al. 2021).

$$ \tau_{{{\text{B}}x}} = \rho \sqrt {u^{2} + v^{2} u} /c_{{\text{f}}}^{2} ,\quad \tau_{{{\text{B}}y}} = \rho \sqrt {u^{2} + v^{2} v} /c_{{\text{f}}}^{2} $$
(5)

Generating an irregular triangle mesh is a fundamental step in the process. DEM data were used to generate the nodes, each with an elevation value. Triangular meshes were generated by using the pre-processing plug-in in QGIS software, as shown in Fig. 7. Finally, with execution of the BASEMENT model, flood data on water depth, velocity, and water surface elevation (WSE) were obtained.

Fig. 7
figure 7

Irregular triangulation mesh for the BASEMENT flood simulation of the study reach

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The study area has low forest coverage and housing density, and so, the Manning’s friction was set as 0.03 (Chow et al. 1988). The run time of the flood simulation was set as 46,800 s, noting the peak discharge occurred at 10,800 s and that the maximum inundation extent was reached well before the end of this time for the second flood. The boundary condition was set as the stage-discharge curve of Batang County upstream and a normal depth condition downstream. The associated parameters are shown in Table 2.

3.2.4 Accuracy analysis of model predictions

Kappa-based contingency analysis (Cohen 1960) was used to assess the accuracy of the BASEMENT simulation flood result using predicted and observed inundation patterns. The foundation of all accuracy assessments is an error matrix (Fig. 8). With two classes, inundated or not, the error matrix is a 2 × 2 space (Fig. 8). Here, n11 and n22 are represented the numbers of cells of consistent wet and consistent dry classes in both the simulation and the actual results. n12 and n21 are represented the number of cells of the ‘wet versus dry’ and the ‘dry versus wet’ between the simulation and the actual results.

Fig. 8
figure 8

Error matrix for the Kappa accuracy analysis

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The overall accuracy is identified from Eq. (6) as the sum of the correctly predicted cells divided by the total number of cells (Yu and Lane 2006). However, this statistic takes no account of random level of agreement in the contingency table.

$$ {\text{Overall}}\;{\text{accuracy}} = \frac{{\sum\nolimits_{i = 1}^{k} {n_{ii} } }}{n} $$
(6)

Following Cohen (1960), we therefore used Kappa analysis, and a discrete multivariate technique that is used to allow statistical analysis of model performance and to test if one error matrix is different from the actual result (Fig. 6) (Bishop et al. 1975).

$$ K = \frac{{n\sum\nolimits_{i = 1}^{k} {n_{ii} } - \left( {\sum\nolimits_{i = 1}^{k} {n_{i1} + \sum\nolimits_{j = 1}^{k} {n_{ij} } } } \right) \times \left( {\sum\nolimits_{i = 1}^{k} {n_{i2} + \sum\nolimits_{j = 1}^{k} {n_{2j} } } } \right)}}{{n^{2} - \left( {\sum\nolimits_{i = 1}^{k} {n_{i1} + \sum\nolimits_{j = 1}^{k} {n_{ij} } } } \right) \times \left( {\sum\nolimits_{i = 1}^{k} {n_{i2} + \sum\nolimits_{j = 1}^{k} {n_{2j} } } } \right)}} $$
(7)

Equation (7) is essentially expressing the ratio of the observed excess over chance agreement to the maximum possible excess over chance agreement, with K = 1.0 at perfect agreement and K = 0.0 when observed agreement equals chance agreement (Everitt 1998). Data required for this assessment were based upon the spatial extent of the modelled domain.

3.2.5 Calculation of the potential outburst flood peak discharge

We aimed to quantify how inundation changes as a function of different magnitudes of river valley blockage by the landslides. This needed simulations of outburst flood magnitudes for different dam heights and their attenuation with distance downstream. The peak discharge is the key parameter that determines the submergence range, scour intensity, and the arrival time of floods downstream. Empirical models and hydrological experiments are the main two ways to determine the peak discharge for potential dam breaching (Costa 1985; Costa and Schuster 1988b, a; Costa and Schuster 1991; Walder and O’Connor 1997; Fread 1988; Peng and Zhang 2012; Habib et al. 2014; Li et al. 2021). Empirical models vary in their complexity. For example, Costa’s (1985) empirical model only considered dam height (Hd) for calculating peak flow (Qp), and Costa and Schuster (1988b, a, 1991) only considered dam height (Hd) and barrier lake storage capacity (Vl). Peng and Zhang (2012) proposed an empirical model to calculate peak discharge, which has been successfully applied to the peak discharge calculation of glacier lake and landslide dam outburst flood (Rivas et al. 2015; Shi et al. 2017). The method was based upon a database of 1239 landslide dams, including 257 dams formed during the Wenchuan earthquake on May 12, 2008. The model considered dam height, dam width, dam volume, reservoir storage capacity of barrier lake, and dam erodibility. The model is shown in (7):

$$ \frac{{Q_{{\text{p}}} }}{{g^{1/2} H_{{\text{d}}}^{5/2} }} = \left( {\frac{{H_{{\text{d}}} }}{{h_{{\text{r}}} }}} \right)^{ - 1.371} \left( {\frac{{V_{1}^{1/3} }}{{H_{{\text{d}}} }}} \right)^{1.536} e^{a} $$
(7)

where Qp is the peak discharge at dam burst (m3s−1), Hd is dam height (m), Hr = 1 m (Peng and Zhang 2012), Vl is storage capacity of barrier lake (m3), g = 9.8 ms−1, and e = 2.718, and ɑ is the dam erodibility parameter which can be divided into three grades: high (1.236), medium (− 0.380), and low (− 1.615) (Peng and Zhang 2012; Briaud 2008; Hanson and Simon 2001).

The spatial analysis tool in Arcgis 10.2 was used to calculate the storage capacity (Vl) and, as a by-product, the inundation area upstream of different height. The SRTM 30 m spatial resolution DEM data were combined with the dam height to determine the water level height and its intersection with valley topography upstream. This was then overlain on the DEM and, using the cut fill tool of the Arcgis 10.2, allowed the volume of water stored for each dam to be determined. Table 3 illustrates example calculations and also the sensitivity to the dam erodibility parameter ɑ. In this case, we could also back-validate the Peng and Zhang (2012) model against the measured peak discharge calculation for the Baige landslide. For the first outburst flood, and using ɑ = − 0.38, the landslide dam height was 47 m corresponding to an actual outburst flood peak discharge of 10,000 m3s−1. Equation (7) gives 9590 m3s−1 for that dam height (47 m). The modelled peak discharge is very close to the actual result, which means Peng and Zhang (2012) model is likely to be effective. For the second outburst flood, the landslide dam height was 72 m corresponding to an actual outburst flood peak discharge of 31,000 m3s−1. Equation (7) gives 11,347 m3s−1 for that dam height (72 m) with using ɑ = − 0.38. This model result appears distorted compared with the second peak discharge with the dam height significantly increasing. This deviation likely implies that the dam erodibility parameter (ɑ) of this model is not correct. In addition, with the dam height increasing, the estimation of the peak discharge may be too small. However, the dam height for 47 m close to the future potential dam heights considered herein of 30, 35, and 51 m presented a good result.

Table 3 Peng and Zhang (2012) model validation for potential peak discharge of the dam breaching
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Whilst this analysis gives the peak discharge at the dam breach, it was also necessary to quantify the evolution of the peak discharge with distance downstream due to attenuation. Data suggested that the shape of the hydrograph retained similarity as the flood wave moved downstream. This allowed the shape of the simulated hydrographs to be scaled to the estimated peak discharge (Figs. 9 and 10).

Fig. 9
figure 9

Dam downstream outburst hydrographs. a First dam breach: October 2018. b Second dam breach: November 2018; here, the black dotted line represented the water level change of Boluo town 20 km upstream of the dam

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Fig. 10
figure 10

Potential peak discharge attenuation downstream of the dam

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4 Result

4.1 Validation of flood inundation simulations

Figure 11 shows the estimated active river bed before the second flood and then, after, the latter likely indicating the maximum inundation extent. The remote sensing results suggest that the river was inundated to an extent of 1.5 km2 (i.e. in the first flood, before the second flood) and that this area increased by 1.6 km2 in the second flood, such that the total flooded area in the study area is 3.1 km2. The remote sensing results are used to define the actual flooded area.

Fig. 11
figure 11

November dam outburst flood illustrating the active zone of the river before the flood (a), after the flood (b), and the estimated flood area that results (c)

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Figure 12 superimposes the modelled and predicted inundation and is visually encouraging. The modelled result is in good accordance with the actual result suggesting that the data sources used, and the model parameterization are appropriate. This was confirmed quantitatively with an overall accuracy reaches of 0.956 and a Kappa value of 0.911. Figure 13 confirms a qualitatively good agreement between the measured and the modelled water depths. Mismatches in this figure are likely to reflect inaccuracies in the DEM data and local inconsistencies relating to minor topographical details. The spatial resolution is a significant difference between the DEM data (30 m) and the imagery data (3 m) which may also cause the mismatches.

Fig. 12
figure 12

Flood extent measured using remote sensing (a), modelled (b), and difference between the two (c)

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Fig.13
figure 13

Flooded depth difference between the interpretation and the simulation result

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4.2 Potential landslide dam heights

Investigation and monitoring results show that CZ1-1, CZ1-2, and CZ2-1 were at the highest risk of potential failure (Fig. 5a). Their volumes were about 0.8 × 106m3, 0.8 × 106m3, and 3.3 × 106m3. In addition, there is about 1.0 × 106m3 of landslide debris residue in the landslide groove created from the last landslide event. Although the volume of potential material (total 5.9 × 106m3) is lower than for the past two landslide events, its potential hazards will likely be similar and so potentially serious because the breach of the last landslide dam was only small in size. Notably, CZ1-1, CZ1-2, and CZ2-1 are the highest risk zones now. The crack zone boundary is further up-slope, and the extent of potential slope instability may be bigger (Fig. 5).

Based on the shape of the 2018 dams, the dam breach deposit shape, and potential landslide volume, the potential dam height can be calculated. Figure 14 shows three scenarios for potential landslide failures in terms of the high-risk zone covering ‘CZ1-1’, ‘CZ1-1 + CZ2-1’, and ‘CZ1-1 + CZ1-2 + CZ2-1’. The three scenarios are as follows: ‘CZ1-1’ is likely the first failure because of the highest risk; CZ1-1 and CZ2-1 (‘CZ1-1 + CZ2-1’) are likely simultaneous start-ups considering the most severe deformation; CZ1-1, CZ1-2, and CZ2-1 (‘CZ1-1 + CZ1-2 + CZ2-1’) are likely simultaneous failures because the crack zones are interconnected (Fig. 5). The associated landslide failure volumes are 1.3 × 106m3, 2.6 × 106m3, and 5.9 × 106m3 and form landslide dams 30 m, 35 m, and 51 m high, respectively (Fig. 14).

Fig. 14
figure 14

Potential dam heights caused by future blockage by the Baige landslide

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4.3 Flood simulations for the November 2018 event

The main three simulation outputs were depths, velocities, and the maximum flood inundated area of the outburst flood. The total simulation time is 46,800 s, which has been divided into four steps that included 10,800 s, 21,600 s, 324,00 s, and 43,200 s for visualization. Because the landslide dam breaching process was slow, the flood process lasted a long time; whilst the study area was only 9 km long, the flood lasted more than 13 h. The peak discharge time was at 10800 s (Figs. 15 and 16). As shown in Fig. 15, the maximum flood depth was about 27 m at 10,800 s, and it then sharply decreased to 15 m by 43,200 s. As shown in Fig. 16, the largest flood velocity occurred during the peak discharge stage of 10,800 s and reach up to ~ 19 ms−1. Most of the flood discharges are below 16 ms−1, but there are locally high velocities due to a bedrock valley constraint. The maximum flood inundation at the 10,800 s stage is shown in Figs. 15 and 16.

Fig. 15
figure 15

Outburst flood depth evolution process based on the BASEMENT model

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Fig. 16
figure 16

Outburst flood velocity evolution process based on the BASEMENT model

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4.4 Upstream impacts of different landslide dam scenarios

The 30 m, 35 m, and 51 m dam height scenarios induce a storage capacity up to 142 × 106 m3, 182 × 106 m3, and 331 × 106 m3, with the back-flow extending upstream by 32 km, 40 km, and 50 km, respectively (Table 4 and Fig. 17). The potential flooded area upstream of these dams is 5.0 km2, 6.1 km2, and 9.1 km2, respectively (Table 4). Compared with the two landslide dam flood events of October and November 2018, the flooded area and back-flow distance of the potential events are lower, but the impacts would be no less serious. Take Boluo Town as an example, located 20 km upstream of the landslide dam, the 2018 floods inundated the whole town. The scenario of the 51 m dam height will also inundate the whole town (Fig. 17). There is a nonlinear relationship between the storage capacity and the inundated area, which reflects the form of the valley upstream of the Baige landslide (Fig. 18). The increasing velocity of the flooded area is greater than the storage capacity (Fig. 18).

Table 4 Dam upstream potential landslide dam disasters. The table shows data for the measured 2018 events and the three simulated dam heights
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Fig. 17
figure 17

Upstream inundation extent for different dam heights

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Fig. 18
figure 18

Dam height, storage capacity, and dam volume relation upstream

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4.5 Outburst flood impacts downstream of the simulated dams

Following from the peak discharge calculation and application of attenuation, the peak discharges at the study area located at Batang county reach are 5300 m3s−1, 5644 m3s−1, and 6664 m3s−1 for dam heights 30 m, 35 m, and 51 m, respectively. The BASEMENT simulation results show that the potential flood areas are 0.18 km2, 0.34 km2, and 0.43 km2 on both sides of the river under the three different dam height scenarios (Fig. 19). These compare with a proportionately much higher flooded area for the inundated area of the 72 m height dam failure in November 2018, and this reflects the fact that the inundated width of the floodplain increases markedly for the discharges associated with the higher case (Fig. 20).

Fig. 19
figure 19

Flooded area and water depth downstream for failure at different dam heights. Note that only one of the measured events is simulated

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Fig. 20
figure 20

Relation between dam height and potential inundated area for the study reach

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5 Discussion

The Baige landslide is continuously deforming due to gravity, and this resulted in landslide dams that breached on two closely spaced dates in 2018 (Fan et al. 2020d; Chen et al. 2021a, b; Liu et al. 2021; Yang et al. 2021). The potentially unstable slope continues to erode and is likely already blocking the **sha River again. This paper, using the Baige landslide as a case study, focussed on quantifying how the dam drives inundation both upstream and downstream of the dam, the former due to storage of water upstream, and the latter due to an outburst flood with impacts downstream. Remote sensing was combined with the hydrodynamic model BASEMENT to estimate flood extent and with a good agreement between measurements and model predictions (Figs. 12, 13) reflected in Kappa value > 0.9. This approach was aided by high quality remotely sensed imagery for validation. The BASEMENT modelling, however, is crucially dependent upon estimates of the size of the flood discharge and hence, dam heights, the liberation of water during failure and attenuation of the discharge wave as it moves downstream.

First, the potential dam heights were impacted by the dam shape, dam breach deposit volume, and landslide volume. Based upon the landslide accumulation process, the dam shape and dam breach deposit size are easily determined after the breach. However, accurately determining landslide volume before the breach is harder. The volume calculation appeared distinct differences between different scholars even in the failed Baige landslide events (Fan et al. 2020d; Xu et al. 2018; Chen et al. 2021a, b; Gao et al. 2021). Fan and Xu et al. (Fan et al. 2020d; Xu et al. 2018) calculated the Baige landslide volume to be ~ 30.0 × 106 m3 in the first and 12.0 × 106m3 in the second by superposing estimated topography before and after failure; Chen et al. (Chen et al. 2021a, b) calculated the volumes to be 27.0 × 106 m3 in the first and 8.0 × 106m3 in the second also using topographic superposition methods; Chen et al. (2021a, b), Gao et al. (2021) calculated the volumes to be 18.7 × 106 m3 in the first and 6.3 × 106m3 in the second using field measurements and before and after topographic superposition methods. The potential deformation range and unstable zones of the Baige landslide themselves have also differed according to the methods adopted (Fan et al. 2020d; Chen et al. 2021a, b). This work shows that the dam height has an important and nonlinear impact upon both upstream inundation (Fig. 18) and notably downstream outburst flood extent (Fig. 20), emphasising that determining the potential landslide volume and the form of the dam it produces is a key challenge for flood hazard assessment.

Second, the peak discharge is a critical driver of the outburst flood simulation. Although there is a long history in the application of empirical determinations of peak discharge, it is not clear that a universal model exists and that it is suitable for all landslides within a region let alone for all regions (Costa and Schuster 1988b, a; Walder and O’Connor 1997; Fread 1988). Most empirical models only undertake simple fitting of geometrical parameters for different dams in a particular area and use few parameters (Costa 1985; Evans 1986; Cenderelli 2000; Pierce et al. 2010; Habib et al. 2014; Li et al. 2021). Many researchers have captured the geometry and size of landslide dams (such as dam volume, dam height, and breach depth and width) and barrier lakes (for example lake depth and storage capacity) to drive the empirical formula for calculating the peak discharge of the dam breaching (e.g. Evans 1986; Cenderelli 2000; Pierce et al. 2010; Liu et al. 2016 Fan et al. 2012). The dam height (or water depth), storage capacity, and breach size are very frequently used parameters. The dam height controls the storage capacity upstream, whereas the storage capacity exerts strong pressure on the dam and controlled the potential of the peak discharge (Cenderelli 2000; Pierce et al. 2010). Despite the size and shape of the dam breach being very effective parameters for calculating the peak discharge, they generally can only be determined reliably after the dam break. Fortunately, predictive models that represent the dam break process is now being developed based upon dam failure statistics, experiments, and numerical modelling (Peter et al. 2018; Xue et al. 2021), which could be used to calculate the peak discharge before the dam break. However, most of the models rarely consider dam materials and internal structures.

The estimations of peak discharge can be highly sensitive to the model used, as shown for the Baige landslide (Table 5). It implies that specific models need to be selected according to the specific study area. More challenging is the fact that the correct discharge height model may depend on landslide height. With only two landslide events available to calibrate such models, this uncertainty is extreme and a major weakness with the work presented in this paper. The model of Peng and Zhang (2012) is appropriate to calculate the potential peak discharge of the Baige landslide dam because it not only applied the geometry of the dam but also considered the erodibility of the dam. This model is based upon a large database of 1239 landslide dams and has been successfully applied to other sites (Rivas et al. 2015; Shi et al. 2017). A distinct deficiency is likely that the erodibility (ɑ) value divided into high (1.236), medium (− 0.380), and low (− 1.615) needs a finer resolution formulation as well as further testing data. In this paper, we select the medium value (− 0.380) as the erodibility (ɑ) value because the Baige landslide is neither a soil landslide nor a rock landslide but somewhere between the two.

Table 5 Empirical models of the peak discharge calculation of the Baige first two landslides
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Third, the inundation extent downstream is not only a function of the magnitude of the dam breach but also the attenuation of the flood wave. In this case, empirical evidence suggested a relatively simple decline in peak discharge with distance downstream (Fig. 11) and little change in flood wave shape (Fig. 10). This facilitated the analysis. However, there is some evidence that the form of these decay curves (Figs. 10, 11) depends on the dam height with a more nonlinear decay in peak discharge with distance for the first and smaller of the two dam breach events. This suggests that hydraulic modelling of flood wave attenuation should be explored.

Finally, the BASEMENT model validation was surprisingly good given that the model had not been optimised against remotely sensed inundation extent. That said, there are a range of known impacts of hydraulic model parameters on flood extent, notably roughness (e.g. Yu and Lane 2006) as represented here by the Manning friction coefficient, and also the quality of floodplain topography. As shown in Table 6, the choice of the Manning friction coefficient depended on the land-use types (Chow et al. 1988; Jeremy et al. 2015). The study area is located in the dry hot and deep valley segment of the **sha River. Meadow and bare land are the primary land covers, and the forest and infrastructure and covers are not extensive. According to the land-use type, we value the Manning friction coefficient as 0.3 (Table 2). Other research (e.g. Yu and Lane 2006) has shown that flood inundation predictions are relative insensitive to parameterizations of flood plain roughness; the specification of roughness in the channel, which determines the discharge at which out-of-bank flow starts, is much more important. The mesh used for model solution may also have a significant impact (Lala et al. 2018). Testing of mesh effects may be worthwhile, especially as these interact with model parameters and notably friction parameterization. A crucial finding of this work was that the relationship between dam height and downstream flood extent is likely to be nonlinear (Fig. 20) emphasising the importance of using hydrodynamic models for evaluating the downstream impacts of outburst flood events.

Table 6 Land-use type corresponds to the manning coefficient
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6 Conclusion

The Baige landslide dam has failed and twice-triggered severe outburst floods. Unfortunately, the Baige landslide is continuously deforming and continues to be a significant potential hazard. As such, it is representative of a wider set of known flood risk cases where the risk cascades from an initial event (e.g. a landslide that blocks a valley) through a secondary event (e.g. landslide breach) through to a downstream risk (e.g. flood inundation) that can be catastrophic. In this paper, we developed a coupled approach to evaluating this problem showing how it is both necessary and possible to couple analysis of a landslide, to estimation of the dam that it may form in the valley below, to estimation of inundation downstream if that dam then breaches. We tested it successfully on the Baige landslide DEM case and it would merit being tested for a wider number of cases. We emphasise that volume of sediment may produce empirical relationships for dam breaching and the likely outflow flood that results and application of a suitable hydrodynamic model. In terms of the latter, we showed that BASEMENT is an accurate and effective hydrodynamic model for simulating outburst flooding process, and associated scenarios can be used to assess future flood hazard. This was confirmed here by comparison with remotely sensed data.

Three key conclusions follow for the case study consider here. First, remote sensing showed that the second time the Baige dam breached, and it triggered an inundated area reaching up to 3.1 km2 within a length 9 km of downstream river valley. Second, the Baige landslide is continuously deforming which implies a high probability of future outburst flood events. Third, there is some evidence that the relationships between landslide height and both upstream inundation extent and downstream outburst flood extent are nonlinear. This emphasises that the likely consequences of an outburst flood will depend upon the size of the landslide dam and also the time since the last failure event. This hypothesis could be a very major consequence for river valleys at risk of landslide dam (or other) outburst floods and so merits assessment in other cases.