Debris flow is one of the main causes of loss of life and infrastructure damage
in mountainous areas. This hazard should be recognized in the early stage of
land development planning. According to field investigation and expert
experience, a scientific and effective quantitative susceptibility
assessment model was established in Pinggu District of Beijing. This model
is based on geographic information system (GIS) combined with grey
relational, data-driven and fuzzy logic methods. The influence factors,
which are divided into two categories and consistent with the system
characteristics of a debris flow gully, are selected, but also a new important
factor is proposed. The results of the 17 models are verified using data
published by the authority and validated by two other indexes, as well as
area under curve (AUC). Through the comparison and analysis of the results,
we believe that the streamlining of factors and scientific classification
should attract attention from other researchers to optimize a model. We also
propose a good perspective to make better use of the watershed feature
parameters. These parameters fit well with the watershed units. With full
use of insufficient data, scientific calculation and reliable results, the
final optimal susceptibility map could potentially help decision makers in
determining regional-scale land use planning and debris flow hazard
mitigation. The model has advantages in economically weak areas with
insufficient data in mountainous areas because of its simplicity,
interpretability and engineering usefulness.
Introduction
Debris flows are processes of rapid transport of water and soil materials in
mountain watersheds, with sudden and destructive outbreaks (Di et al.,
2019). Some debris flows can often cause devastating disasters and huge
losses (Zhang et al., 2021), seriously threaten the lives and
properties of people in the mountains and the safety of major projects, and
restrict social and economic development (Iverson, 1997; Hungr et al.,
2005; Hu et al., 2011; Takahashi, 2014; Wu et al., 2019). Mass movements in
Beijing range in scale from shallow slope failures and rockfalls to
catastrophic rock avalanches frequently mobilize to form debris flows,
threatening the ecological environment of the mountainous area (Zhong et
al., 2004). Especially in recent years, due to the superposition of extreme
rainstorm weather and human engineering activities, debris flow events have
increased gradually (Z. Li et al., 2021). As the capital of China, Beijing
also has strong influence at home and abroad where geological
disasters are widely concerned (Xie et al., 2004; Li et al., 2020b). With
the deepening understanding of debris flow disaster and the updating of a
database, a new and more accurate evaluation is also very necessary.
Therefore, it is of great significance to establish an accurate and scientific debris flow susceptibility map.
Through previous studies, it can be summarized that the current research on
debris flow mainly focuses on the following aspects: study on mechanism of
debris flow, study on early warning and prediction of debris flow, study on
numerical simulation of debris flow, and study on debris flow hazard
analysis. Especially studies on debris flow hazard analysis gain the
attention of the researchers as soon as they appear (Dong et al., 2009).
Communicating information about debris flow hazard analysis is a crucial
component of preparedness and hazard mitigation (Chiou et al., 2015).
Susceptibility assessment, an important part of a hazard assessment of
geological processes, is more flexible (Y. Li et al., 2021). In the early
days, the susceptibility assessment of debris flows was mainly qualitative
research using geomorphological information (Guzzetti et al., 1999).
In 1976, the United Nations commissioned the International Union of
Engineering Geology to conduct a risk assessment of debris flows, which
marked the beginning of research on the susceptibility assessment of debris
flows as an important research direction for disaster prevention and
prediction (Li et al., 2020b). Many methods and techniques have
been proposed to evaluate debris flow susceptibility assessment based on
different qualitative and quantitative approaches along with
geo-environmental information (Liu and Wang, 1995), such as the analytic
hierarchy process (Wu et al., 2016), logistic regression method (Regmi et al., 2013; Conoscenti et al., 2015), information value
(Akbar and Ha, 2011; Melo et al., 2012), support vector
machine (Pourghasemi et al., 2017),
frequency ratio (FR) (Sun et al., 2018), certainty factor (CF)
(Tsangaratos and Ilia, 2015), neural network (Lee et al.,
2003; Liu et al., 2005) and Bayesian network algorithm (Liang et al., 2012; Tien Bui et al., 2012). These
methods have corresponding advantages and limitations for research subjects
with different geological conditions. Generally speaking, it is easier to
get satisfactory results by combining and comparing various methods
(Meyer et al., 2014; Di Napoli et al., 2020; Fang et al., 2020). In
summary, with the development of mathematical theory, the susceptibility
assessment of debris flows has been extensively and quantitatively studied,
and the research methods have also changed from single to comprehensive.
The economy in mountainous areas is often limited; we cannot supervise and
verify every basin due to limited funds. The debris flow susceptibility
assessment can give decision makers a basis for rational allocation of
resources and determine which gullies should be focused on. In other words,
the study plays a link role for other studies. Recently, with the
development of mathematical theory, computer technology and the application of
3S (remote sensing, geography information systems, global positioning
systems), the susceptibility assessment of debris flows has been extensively
and quantitatively studied (Li et al., 2020a). As research progresses,
debris flows are increasingly seen as an open system. There are many factors
influencing the system, the combination of factors is nonlinear, and the
interactions are chaotic. Therefore, it is very difficult to find a unified
and standard evaluation model. At present, when the information is
insufficient, field investigation and the experience of experts are necessary.
However, the experience is often subjective and needs a lot of professional
experience accumulation. It is very important to express the experience of
experts objectively and understandably to serve decision makers. The
application of fuzzy set theory in geographic information system (GIS) environments is effective for similar
problems (Luo and Dimitrakopoulos, 2003; Porwal et al., 2006).
The main objective of this paper is to propose a GIS-based model. The results of expert experience
scoring and site surveys are used as guidance and reference in the modeling
process. We have tried to apply methods that can indicate the nonlinearity
of the debris flow system. Finally, the modeling process should respect the
laws of geomorphological evolution and the geological basis. Otherwise, the
result will tend to be simply data fitting (Porwal et al., 2006).
Study area
The study area is located to the northeast of Beijing, China (Fig. 1), with
a total area of 948.24 km2. The elevation of Pinggu is high in
the northeast and low in the southwest. It is surrounded by mountains and
accounts for about two-thirds of the total area on three sides in the
southeast and north. The central and southern parts are alluvial plains. The
area, geologically, is the west extension of the famous Jixian section,
whose bedrock is mainly Middle and Late Proterozoic
dolomite (Lü et al., 2017). The administrative unit of Pinggu
District is used as the study area boundary, mainly considering that
geological hazards frequently influence human economic activities, so
political factors must be taken into account. Within the administrative
region, inconsistent decision-making can be effectively avoided.
Study area.
Data and methodology
In this study, the susceptibility assessment of debris flow hazard was based
on the drainage basin unit. In such a model, a hydrological response unit can
fully represent the hillside hydrological process and will make the
results more meaningful (Khan et al., 2013, 2016; Zou et al.,
2019). First, drainage networks were extracted from the ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) digital elevation model (DEM) by using
the ArcGIS ArcHydro Toolbox, and regions without obvious watershed
characteristics were directly deleted. Then for each drainage basin, 19
controlling and triggering factors divided into two types were calculated.
In addition, since these factors have different characteristics, different
methods were used to calculate the fuzzy membership for different type
factors. Field investigation is generally required in geological hazard
surveys. If these data are applied to the model, it can help with the model
building and reduce the time for model training. The weights derived from
the grey relational analysis method used in the following section (Sect. 3.4.1) are based on the data from the field investigation. While geology and
geomorphology factors are independent of watershed characteristics, it is
suitable to use statistical methods to determine the objective weight.
Finally, the debris flow susceptibility index (DFSI) map was derived by
overlaying the factor thematic layers with the fuzzy logic method. The workflow
of debris flow susceptibility assessment is shown in Fig. 2. First, a DEM
map of the Pinggu area was downloaded. Then, the basin units were generated
from the DEM map using the ArcHydro tool. The derived results were analyzed,
and units that did not fit the characteristics of the watershed were
removed. During the analysis, the field investigation data and Google images
were referenced. After that, the controlling and triggering factors for the
remaining 135 catchments were counted. For the fuzzy memberships, watershed
characteristic parameters were determined by grey correlation, and the
geological and geomorphological factors were determined by the frequency
ratio (FR) method and the cosine amplitude method. Finally, the individual
layers were overlaid by fuzzy logic operations to obtain the final map. As
there were different combinations of factors, 17 results were derived. Three
indexes (area under curve, AUC, accuracy ratio, AR, and resolution ratio, RR) were used to evaluate advantages and disadvantages
of these results.
Workflow of debris flow susceptibility assessment.
Debris flow basin division and inventory
There are many geological hazard points in mountainous areas, so it is not
realistic to monitor them completely by professional teams. According to the
monitoring and prevention staff and the villagers, the detailed field
investigation (Fig. 3) for the evidence collection of debris flows will be
carried out at the reported disaster point, aiming at recording the loose
material, delineating the basin and exploring other important information on
the debris flow gullies. Moreover, field investigation is also very
important for model modification. Then based on the hydrology module in
ArcGIS 10.2, the research object can be determined. Compared with grid unit
and slope unit, the hydrological response unit for susceptibility of debris flow
has greater advantages (Z. Li et al., 2021b; Zou et al., 2019).
Finally, referring to the result of the field investigation and the remote
sensing image, 135 basins are divided after removing the flat and irregular
areas (Fig. 4), and of them 48 basins were investigated in the field, accounting
for 36 %.
Field investigation photos. (a) Loose material, (b) Middle and Late Proterozoic dolomite, (c) colluvium deposit,
(d) slope fracture and (e) channel erosion phenomenon.
Debris flow basin division and inventory. Note: the data of debris flow points come from the Beijing Municipal Commission
of Planning and Natural Resources websites
(Beijing Municipal Commission of Planning and Natural Resources, 2022).
Debris flow controlling and triggering factors
The basic requirement for the assessment of debris flows is that some
factors included are easily obtainable, meaningful for susceptibility
assessment, and can be used for evaluating the need for passive or active
debris flow mitigation. According to previous studies, 19 factors are
selected in this study. The factors are divided into two types (Table 1)
because of their different characteristics. Watershed characteristic factors
(Type A) can be directly quantified once the basin is determined (Fig. 5).
The influence of these parameters is bounded by the watershed; geology and
geomorphology factors (Type B) need to be further processed even if the
watershed is determined. The scope of these parameters is independent of the
watershed boundary.
Factors for susceptibility assessment.
Factors and description SignificanceObtaining waysWatershed characteristic factors (Type A)A1The planimetric (projected) area of the catchmentGeometric parameter; affecting the accumulative total volume of water and representing the potential magnitude (Zhang et al., 2011; Cao et al., 2016; Chang and Chien, 2007)Derived from DEMA2The curved surface area of the catchmentReal contact area between rainfall and basinDerived from DEMA3The surface roughness of the catchmentDimensionless parameters, reflecting the fragmentation degrees of the surface and the ground surface micro-topography; Wu et al. (2019) believe the factor can further reflect the ability of the earth to resist wind erosionCalculated by A3=A2/A1A4The perimeter of catchmentGeometric parameter, controlling the boundaries of a watershedDerived from DEMA5Form factorHydrologic parameter, related to the distribution of flow rate hydrograph (Chang and Chien, 2007)Calculated by A5=A42πA1A6The curve length of the main channelImportance for the travel distance of materials and affecting the potential of erosive agents to dislodge and transport materials (Gómez and Kavzoglu, 2005)Derived from DEMA7The straight length of the main channelGeometric parameter, representing the change in material source in spaceDerived from DEMA8Bending coefficient of the main channelAffecting the discharge situation of debris flows (Li et al., 2020a; Zhang et al., 2013)Calculated by A8=A6/A7A9The gradient of the main channelHydraulic gradient parameter, affecting water transport capacityCalculated by A9=A12/A6A10Maximum elevation in the catchmentAffecting vegetation and bedrock exposureDerived from DEMA11Minimum elevation in the catchmentAffecting vegetation and bedrock exposure slightlyDerived from DEMA12Maximum relative relief in the catchmentThe higher the value of A12 is, the large relative relief provides more favorable terrain conditions for the initiation of the debris flow sourceCalculated by A12=A10-A11A13Basin volume: the volume above the level of the minimum elevation in the basinRepresenting the maximum material source that can be produced in an ideal state, loose material volumeDerived from DEMA14Drainage densityRepresenting the geological structure, lithology and the degree of rock weathering comprehensively and affecting the range of lateral erosions and retrogressive (Cao et al., 2016; Zhang et al., 2011)The ratio of the total length of river network lines to A1
Continued.
Factors and description SignificanceObtaining waysGeology and geomorphology factors (Type B)B1LithologyAffecting the rock mass shear strength and permeability (Donati and Turrini, 2002)Derived from 1:50000 geological mapsB2Proximity to faultsCorrelated with slope failures by generally reducing the strength of the rock mass (Dramis and Sorriso-Valvo, 1994; Korup, 2004; Kellogg, 2001; Kritikos and Davies, 2015)Derived from 1:50000 numerical geological mapsB3Slope (∘)Correlated with the probability of landslide occurrence (Dai and Lee, 2002; Lee and Choi, 2004; He and Beighley, 2008). The greater the slope, the greater the vertical component of gravity (Donati and Turrini, 2002) and the higher the frequency of slope failures (Lee and Sambath, 2006; Lee and Talib, 2005)Derived from DEMB4Slope aspectAffecting slope instability directly or indirectly as a result of drying winds, sunlight, rainfall and vegetation (Dai and Lee, 2002; Dai et al., 2001)Derived from DEMB5CurvatureAffecting slope stability; Lee and Talib (2005) and Ohlmacher (2007) argue on how curvature affects slope stabilityDerived from DEM
Note: the geological maps are provided by the Beijing Institute of Geological
and Prospecting Engineering, and the digital elevation model (DEM) of the study
area is from the Shuttle Radar Topography Mission (SRTM) DEM with a resolution of 30 m (http://www.gscloud.cn/sources/accessdata/310?pid=302, last access: 25 June 2022).
Graphical illustration of some Type A factors. A1 is the planimetric (projected) area of the
catchment, A2 is the curved surface area of the
catchment, A4 is the perimeter of the catchment,
A6 is the curve length of the main channel,
A7 is the straight length of the main
channel, and A13 is basin volume.
Fuzzy logic in susceptibility modeling
Fuzzy set theory is proposed by Zadeh (1965). It is an efficient way
of expressing the concept of partial set membership degree. This concept
differs from classical binary (0–1 value) logic. More words with
transitional fuzzy descriptions (such as low, medium and high) are used
(Kritikos and Davies, 2015). This fuzzy expression is particularly
applicable to geological hazard classification. In the theory of fuzzy sets,
elements have different degrees of membership in the interval [0, 1]: 1
represents complete membership, and 0 represents non membership. Ross (1995) showed that fuzzy systems are useful in two general situations
(Kritikos and Davies, 2015). The method is very consistent with the
characteristics of debris flow system, whose predisposing factors are fuzzy
in nature and whose mechanism is complex and not fully understood. In the application of the fuzzy logic method, the critical step is to find the suitable fuzzy membership of factors. Fuzzy membership degree is equivalent to the
weight in the expert scoring method, which is calculated by the objective method
rather than given subjectively.
Fuzzy membershipsGrey relational analysis (GRA) in susceptibility modeling
GRA is proposed by Deng (1982), and it is an important part of grey
system theory (Wang et al., 2014). Comparing with mathematical
statistics methods which need lots of sample data, typical probability
distribution and large calculations, GRA is applicable to small sample size
with the data whether regular or not. There will be no inconsistency between
qualitative analysis and quantitative analysis (Deng, 1988). Moreover, it
is to excogitate the leading and potential factors that affect the
development of the system and quantitatively describe the development and
change trend of the system by studying whether the relative change trend of
the grey factor variables with complex relationship is consistent in the
process of system development and evolution (Liu et al., 2004). Thus,
grey correlation analysis is introduced to quantify the correlation between
each factor and the evaluation results according to field investigation and
expert experience. First, the procedure of GRA is to translate the
performance of every alternative into a comparability sequence (Lin and
Lin, 2002; Kuo et al., 2008; Wei et al., 2017). Therefore, according to
the technical standard “Specification of geological investigation for debris
flow stabilization (DZ/T0220-2006)” (Ministry of Natural Resources of the People’s Republic of China, 2006), published by the China Ministry of
Lands and Resources, the preliminary assessment results of debris flow
susceptibility are obtained, which are used as the reference sequence of
the grey relation method (Table 2). Second, the grey correlation coefficient of
all A factors is calculated by Eq. (1). Finally, the average grey relational
coefficient (the correlation degree) is calculated by Eq. (2) as the fuzzy
memberships (Table 3).
ξik=miniminkx0k-xik+0.5maximaxkx0k-xikx0k-xik+0.5miniminkx0k-xik,
where ξi(k) is the grey relational coefficient, i= 1, 2,
…, n are the number i of type A factors, k= 1, 2, …,
n are the number of basins, x0(k) is the reference sequence (ideal
target sequence), and xi(k) is the number i of the Type A factor sequence.
ri=1N∑i=1nξi(k),
where ri is the correlation degree in the range (0, 1). N is the total
number of basins in Table 2
Quantitative evaluation grade standard table for debris flow susceptibility.
Note: 130 ≥ score ≥ 116, VH; 115 ≥ score ≥ 87, M; 86 ≥ score ≥ 44, L; and 43 ≥ score ≥ 15, N. VH is very high susceptibility, M is moderate susceptibility, L is low
susceptibility, and N is non-debris flow.
The fuzzy memberships of Type A factors.
FactorA1A2A3A4A5A6A7Fuzzy membership0.770.770.630.60.540.550.67FactorA8A9A10A11A12A13A14Fuzzy membership0.710.550.550.590.610.790.54Data-driven method in susceptibility modeling
Landslide is one of the main fixed sources of debris flow in mountainous
area. Shallow landslides are one of the most common categories of
landslides. They frequently involve large areas and different soils in
various climatic zones (Benda and Dunne, 1987; Selby, 1982; Borrelli et
al., 2014). Great debris flows may result from numerous, small slope
failures that subsequently coalesce (Fairchild, 1987; Roeloffs,
1996), from flow enlargement due to incorporation of bed and bank debris
(Pierson et al., 1990; Bovis and Dagg, 1992), or from large,
individual landslides that mobilize partially or almost totally
(Vallance and Scott, 1997; Iverson et al., 1997). Debris
flows may also scour steep channels to bedrock and accelerate sediment
delivery to downstream, lower-gradient channels. The spatial and temporal
distribution of shallow landslides are important controls on landscape
evolution and a major component of both natural and management-related
disturbance regimes in mountain drainage basins (Tsukamoto et al., 1982;
Dietrich et al., 1986; Benda and Dunne, 1987; Crozier et al., 1990). Therefore, the
landslide susceptibility assessment methods can be used for reference to
debris flow susceptibility assessment.
For Type B factors which cannot be characterized by a specific number, the
frequency ratio (FR) method and the cosine amplitude method can be used to
derive their fuzzy memberships. The FR ratio defined as Eq. (3). Considering
the fuzzy membership must be in the interval [0, 1], the FR values of the
different categories are normalized by the largest FR value (Lee, 2006;
Pradhan, 2010, 2011a, b) within the same type factor (Table 4) in order to
derive the function.
FR=N(Di)/N(Ci)N(D)/N(A),
where N(Di) is the number of debris flow pixels in the category i,
N(Ci) is the total number of pixels in the category i, N(D) is total number
of debris flow pixels in the study area, and N(A) is the total number of
pixels in the study area.
Factor categories and their fuzzy membership degrees.
The cosine amplitude method (Ross, 1995) is also widely used
(Ercanoglu and Gokceoglu, 2004; Kanungo et al., 2006,
2009; Ercanoglu and Temiz, 2011) to establish relationships among elements
of two or more datasets (Kritikos and Davies, 2015). Assuming that n is
the number of data samples (categories of a factor used in the analysis)
represented as an array X= {x1,x2, …, xn}
and that each of its elements, xi, is a vector of length m (i.e. the
size of the raster image) and can be expressed as X={xi1,xi2, …, xim}, then each
element of a relation rij results from a pairwise comparison of a factor
category xi with a category of the debris flow distribution layer
xj (debris flow or non-debris flow). The memberships can be calculated by Eq. (4):
rij=∑k=1mxikxjk∑k=1mxik2∑k=1mxjk2.
As an analogy with the study of Kanungo et al. (2006), we defined
the rij value for any given factor category as the ratio of the
total number of debris flow pixels in the category to the square root of the
product of the total number of pixels in that category and the total number
of debris flow pixels in the area. Values of rij close to 1 indicate
similarity, whereas values close to 0 indicate dissimilarity between the two
datasets (Kritikos and Davies, 2015). What is more, every thematic layer
must use the same pixel size to use the method properly.
DFSI map
To derive the debris flow susceptibility index (DFSI) map by overlaying the
factor thematic layers using the fuzzy logic method, the “fuzzified” factors
represented by information layers in raster format with values ranging from
0 to 1 need to be combined. Compared with the other four fuzzy operators, fuzzy gamma (Eq. 5) is more suitable for the research (Kritikos and Davies,
2015). To determine the appropriate γ value, the results of
different gamma values were compared by the greatest distance (Kritikos
and Davies, 2015) between the average DFSI curves of the debris flow
locations and non-debris flow locations (for example, flat pixels) (Fig. 6).
Finally, 0.9 is determined for the γ value because there is the
greatest difference between debris flow and non-debris flow location
areas. In order to illustrate the superiority of our model through a
comparison, 17 results are calculated in ArcGIS.
μ(x)=1-∏i=1n1-μiγ⋅∏i=1nμi1-γ,
where μ(x) is the combined membership value, μi is the
fuzzy membership function for the ith map, i= 1,2, …, n are
the numbers of thematic layers to be combined, and γ is a parameter
in the range (0, 1).
Effect of γ value on debris flow susceptibility index (DFSI).
Curves d, e and f correspond to debris flow pixels, and curves a, b and c
correspond to non-debris flow area where a debris flow is unlikely.
According to curve i, the maximum difference between the average DFSI values
is observed for γ≈0.9.
To find the optimal model, 17 results were compared (Table 5). According to
the distribution map of potential geological hazard points and
susceptibility map in Pinggu District published by the Beijing Municipal
Commission of Planning and Natural Resources (Beijing Municipal Commission of Planning and Natural Resources, 2022), three
indexes are used to verify the validity and accuracy of the model.
Predictive performance of different models.
Result and description AUCTwo-category test Performance indexAccuracy ratioResolution ratio(centesimal grade)(AR)(RR)A factors only or B factors onlyR1B factors with rij0.460–––R2B factors with FR0.687–––R3B factors with FRR0.602–––R4All A factors0.7860.3040.70083R5Selected A factors0.7600.3910.75094All factors as a single thematic layerR6All A factors and B factors with rij0.7760.2610.66774R7All A factors and B factors with FR0.7790.2830.68478R8All A factors and B factors with FRR0.7530.3260.60076R9Selected A factors and B factors with rij0.7460.3480.72786R10Selected A factors and B factors with FR0.7610.3480.72787R11Selected A factors and B factors with FRR0.7400.3480.72785A factors combined into one thematic layer,R12All A factors and B factors with rij0.7080.5000.51182B factor combined into another thematic layerR13All A factors and B factors with FR0.7530.8480.39499R14All A factors and B factors with FRR0.7110.8700.40496R15Selected A factors and B factors with rij0.7260.3480.66780R16Selected A factors and B factors with FR0.7680.7390.442100R17Selected A factors and B factors with FRR0.7400.4570.60088
Note: selected A factors with fuzzy membership more than 0.6; FRR represents
the product of FR and rij; performance index is normalized by the
largest FR value.
The results of the model are independent of the model itself, so the
predictive performance of the final map is not just “the goodness of fit”
of the data (Chung et al., 1995; Remondo et al., 2003). A
relatively reliable technique for quantitatively assessing how good a model
is is the construction of validation or success rate curves (Chung and
Fabbri, 1999; van Westen et al., 2003; Remondo et al., 2003; Frattini et al.,
2010) based on a comparison between the spatial distribution of debris flows
and modeled debris flow susceptibility. The curves illustrate the debris
flow recorded in the area with respect to susceptibility values also
expressed as cumulative percentages of the total area. The area under the
curve (AUC) defines the success rate (Marjanović et al., 2011).
Generally, AUC values above 0.7 indicate model performance can be
acceptable, while below 0.7, the performance is considered poor
(Kritikos and Davies, 2015).
Although AUC is an effective evaluation method, the results are not
comprehensive as mathematical features for selecting the best measurement
model because of insufficient data for validation. In order to ensure the
objectivity of the results, we can only effectively use the recorded debris
flow gully as positive and the others as negative. Thus, a two-category
test is proposed to verify the model in this paper. First, the DFSI map of
each model is divided into two categories by the natural breaks (Jenks) method
(Fig. 7). Then the accuracy ratio (AR) is defined as the frequency of the
number of debris flows both classified by model and simultaneously recorded
on site to the number of debris flows recorded on site. The resolution ratio
(RR) is defined as the number of debris flows classified by model and
simultaneously recorded on site to the total number of debris flows classified
by the model (in red color). Take R4, for example; there are in total 135
basins in the research area but only 46 records of debris flows (Fig. 3). In the results of two categories by the natural breaks (Jenks) method, 20 basins are divided into debris flow, while there are only 14 debris flows
among them. Then 14 divided by 46 is AR, and 14 divided by 20 is RR.
Results of two categories by natural breaks (Jenks) method.
Debris flow susceptibility maps. Note: AUC results of R1–R4 below 0.7 are not shown. VH represents very high susceptibility area, H represents high susceptibility area, M represents moderate susceptibility area, L represents low susceptibility area, and VL represents very low susceptibility area.
The higher the two values are, the better the susceptibility map is. Finally, the
performance of models (P value) can be obtained by Eq. (6). AUC values
less than 0.6 are directly eliminated. Comparing the results of the rest of the models,
the result of R16 is optimal, and the results of the DFSI map are in good
agreement with those of field investigation (Fig. 8).
P=AUC+(AR⋅RR)
Results and discussion
Through the modeling process, relatively satisfactory results are obtained
in this paper. The predictive performance of the output debris flow
susceptibility maps, obtained from 17 different models, is verified by
comparing them with maps published by relevant authorities. By comparing the results, the following results are discussed.
Firstly, comparing R1, R2, R3, R4 and R5, it can be
concluded that the model based on field investigation and expert experience
is more effective than data driven directly when the information is
insufficient. This is mainly because when the basin area reaches a certain
size, it is no longer controlled by one or several factors but becomes a
complex system. It is not only the factors that affect the system, but also
the system will react to each factor. Geomorphic evolution is basically the
result of the interaction of the endogenic and exogenic geological processes. A geological period can be regarded as the beginning of one endogenic
geological process to the next one. In the early stage of the geological
period, endogenic geological processes play a major role, and in the later
relatively stable period, exogenic geological processes will take on more
important parts. In this large cycle, a small cycle of energy accumulation and release occurs in the basin continuously, which leads to extremely complex
system changes. In addition, there is a contradiction between the scale of
geological evolution and the scale of engineering activities. So limited
information can be obtained under these conditions, which leads to the
unreliability of data-driven evaluation. Therefore, in the current period,
field investigation and expert experience are fundamental.
Secondly, by comparing R4 and R5, R6 and R9, R7 and
R10, R8 and R11, R12 and R15, R13 and
R16, and R14 and R17, it can be concluded that the accuracy and
resolution of the model can be improved by simplifying the factors, which
will eliminate the ones with weak correlation and independence. In practical
applications, even if the susceptibility map is obtained, the classification
of the susceptibility degree is still a very difficult problem because
everyone's subjective definition of “susceptibility degree” is different. By simplifying the factors, the main ones can be selected, which magnifies the differences between basins, so the boundaries between different
susceptibility degrees are more obvious.
Thirdly, by comparing R6 and R12, R7 and R13, R8
and R14, R9 and R15, R10 and R16, and R11 and
R17, it can be concluded that the appropriate classification of factors is helpful to optimize the susceptibility assessment model because the properties of the factors divided into one category are relatively consistent, as well as the impact on the debris flow system. We can also infer that the nonlinear combination
characteristics between different types are stronger and scientific
classification can improve the performance of the model.
Fourthly, comparing R12 and R13, as well as R15 and R16, it can be
concluded that the frequency ratio method is better than the cosine
amplitude method in the study. Different from the study of Kritikos and
Davies (2015), the watershed unit rather than the grid unit is used, which
indicates that the former has a wide range of applications, while the latter
has a disadvantage of strict conditions.
Based on the results of the above four analyses, the most optimal model
should have the features of being based on expert experience, using selected
factors, classifying factors before using them and using the frequency ratio
method. Then the model R16 is selected according to the features, which
is well in accordance with theoretical method performance score, and gets
fine mutual verification.
There is also the selection of factors to discuss, which is still a very
complex dilemma. Although 19 factors selected cannot fully evaluate the
character of a basin, it is necessary to consider that they are easily and
relatively accurately obtainable for each basin. This will facilitate a wide
range of applications. Moreover, rainfall and total amount of loose material
source are also very important influencing factors. But according to the
Beijing hydrological manual, the rainfall change in the study area is not
obvious, so it is excluded in the model. The total amount of loose material
source cannot be obtained for the watershed without on-site investigation,
so calculations are impossible. In fact, we indirectly consider the
influence of natural loose material source by evaluating geological
conditions but cannot consider the impact of human activities. As for the
factors describing debris flow magnitude, usually several channels have the
recorded data.
The scientific and systematic principle of model building is another
challenge. To correctly classify the factors, it is necessary to grasp the
characteristics of the formation, movement and accumulation of debris flow.
Therefore, the classification should comprehensively consider the
development background (geology, geomorphology, climate, hydrology, soil,
vegetation, human activities and other factors). What the practical principle
refers to is that the study should not only fully obtain scientific and
accurate results but also make the professional results be understood by
decision makers. Although the susceptibility grade and susceptibility value
of each watershed are obtained, the results are relatively effective in this
study area. In addition, with the development of technology and theory, we
should replace some traditional factors which are not easy to quantify with
more precise quantitative factors to improve the efficiency and accuracy of
evaluation, such as surface roughness instead of drainage density.
We would like to further discuss the results derived from Table 3. It
can be seen from the results that the occurrence of debris flow is highly
correlated with basin volume, basin area and main gully bending coefficient
with fuzzy membership above 0.7 in the Beijing area. Rainfall in the study area
is abundant to induce the debris flow. Loose sources and sinks in the total
volume of the catchment become more important. The watershed area determines the
total volume of the catchment. For the same rainfall, generally, the larger the
area is, the larger the catchment is. The bending coefficient reflects the
replenishment sources along the channel. The greater the coefficient is, the
slower the flow is. Then loose source along the channel has more time to
replenish. Basin volume characterizes the maximum amount of loose material
that can be supplied. These three features reflect the development
characteristics of debris flow in the study area. It also provides ideas for
disaster prevention and mitigation.
Finally, we should consider decision making under uncertainty because the
debris flow phenomenon is extremely complex. The classification of
geologists (high, moderate and low) is ambiguous for decision makers. It is
more beneficial for them to use mathematically rigorous definitions.
Considering that geological conditions tend to vary greatly from region to
region, it is not appropriate to define a fixed limit. The Jenks method
(chosen in this paper) can be used to classify sensitivity maps according to
the characteristics of the data. We can also further process the data
according to the needs of decision makers, such as identifying 10 % of the
watersheds in the entire region as high risk. However, the applicability of
the model to extreme rainfall and seismic conditions is not considered.
Conclusion
In this study, a new combination model for debris flow susceptibility based
on GIS was developed in Pinggu. The objective and motivation of this study
are to demonstrate a simple, extensible and convenient analytical model for
the debris flow prediction. Three methods are selected in the model, each with
their own advantages. GRA has great advantages in the case of fewer samples,
the data-driven method is mainly used to reduce subjectivity, and fuzzy logic is
fitted to solve nonlinear problems with fuzzy classification. The output
optimal debris flow susceptibility maps demonstrated satisfactory
performance with the relative higher susceptibility values corresponding to
AUC = 0.768. The predictive performance of the susceptibility maps and the
spatial correlation of debris flow gully with H and VH susceptibility with
recorded debris flows illustrate that the assessment at regional scale using
the proposed method is feasible. Compared with the previous
results (Li et al., 2020b) based on grid units, the evaluation
results are basically the same, but the model is more targeted at debris
flow disasters for decision makers. Moreover, considering that the meaning of
the factors used is clear and the data are easy to obtain, these conditions
mentioned enable the model to be widely applied. In addition, a new factor
(basin) is proposed in our study, which contributes greater weight – up to
0.79. From our 17 results by comparing the control variables, we suggest
that other scholars should pay more attention to the classification and
streamlining of factors, whose potential value to improve
model accuracy has been indicated. It was also found that the watershed characteristic
parameters can better reflect the advantages of the watershed unit, but further
development is needed.
In short, an effort has been made to develop a cost- and time-efficient
debris flow susceptibility assessment model. The model has an acceptable
degree of accuracy for regional-scale planning and helps to make
susceptibility and risk maps more accessible to individuals and local
authorities. The GIS-based methods and modern data availability especially
through online databases are significantly beneficial to this aim. However,
a challenge remains in producing results with practical accuracy for the
scale of planning using available resources. Previous studies highlight
that the effectiveness of the final map depends on the quality of input
data. Updating and improving existing debris flow catalogues and inventories
are crucial for the development of reliable susceptibility and risk
assessment methods.
Data availability
The data presented in this research are available from the first or corresponding author upon reasonable request.
Author contributions
YZ contributed to the conceptualization, investigation, data collection and analyses, methodology, and model visualization. In addition, YZ wrote the original manuscript. JC contributed to conceptualization, methodology, validation and funding acquisition. JC also critically reviewed and edited the manuscript. QW contributed to funding acquisition and data curation. CT contributed to resources and supervision. YL contributed to the investigation, data collection and methodology. XS contributed to methodology. YL contributed to data collection. All authors have read and agreed to the published version of the manuscript.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special issue statement
This article is part of the special issue “Advances in flood forecasting and early warning”. It is not associated with a conference.
Acknowledgements
This research was financially supported by the Key Project of NSFC-Yunnan
Joint Fund (grant no. U1702241) and the National Key Research and
Development Plan (grant no. 2018YFC1505301). The authors would like to thank Yuchao Li, Zhihai Li, Jiejie Shen, Feifan Gu, Zhu Liang and Meng Yao for their contributions
to the collection of field data, as well as the editor and anonymous reviewers for their comments and suggestions which helped a lot in making this paper
better.
Financial support
This research has been supported by the Key Project of NSFC-Yunnan Joint Fund (grant no. U1702241) and the National Key Research and Development Program of China (grant no. 2018YFC1505301).
Review statement
This paper was edited by Heidi Kreibich and reviewed by three anonymous referees.
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