A 10×10 m high-resolution Digital Elevation Model (DEM) of the area is generated from the Cartosat stereo pair satellite images where ground control points (GCPs) were mapped using differential global positioning system (DGPS). The DEM is used to run the Index of Connectivity (IC) and Flow-R. IC and Flow-R are used to delineate geomorphic areas that are connected as source and sink of debris flows and to simulate the extension of flow events considering probable source areas. The Flow-R model is particularly applied for detecting triggering areas. Different thematic layers consisting of topographic data diagnostic to debris flows occurrence are also extracted from the DEM and then used for probabilistic based prediction of debris flow occurrence using weights of evidences (WOEs) method.

## 3.2 Index of connectivity (IC)

Index of connectivity (IC) or sediment connectivity is a spatial parameter established to understand the degree of linkage between sediment sources and downstream affected areas (Cavalli et al. 2013). IC depends on coupling between hill slopes where sediments are being produced and valleys where sediments are transported. It is crucial to model the potential efficiency of sediment transfer from source to sink in a catchment scale for hydrological hazard monitoring. We used a method developed by (Cavalli et al. 2013) that runs on ArcGIS 10.1 and 10.3 (ESRI 2012) modified after (Borselli et al. 2008). This model is specially designed for mountain catchments to tackle debris flows. It is based on two aspects: (1) sediment delivery (2) sediment coupling-decoupling between source and sink. Index of connectivity is defined as

$$IC={log}_{10}\left(\frac{{D}_{up}}{{D}_{dn}}\right)$$

2

Where *D**up* and *D**dn* are upslope and downslope components of connectivity.

*D* *up* is the sediment routing potential of the upslope area expressed as

Where W is the average weighing factor of the upslope contributing area. Here we use roughness index (*RI*) as the weighing factor as suggested by (Cavalli et al. 2013), *S* is the average slope gradient of the upslope contributing area (m/m) and *A* is the upslope contributing area in *m**2*.

The *D**dn* quantifies the length of flow path that sediment particle has to travel from the source to the nearest sink defined as

$${D}_{dn}=\sum _{i}{d}_{i}/{W}_{i}{S}_{i}$$

4

Where *d**i* is the length of flow path of a particle along the maximum downward slope along the *i**th* cell, *W**i* is the weighing factor and *S**i* is the slope gradient of the *i**th* cell.

## 3.3 Flow-R model

Flow-R is a Matlab based debris flow susceptibility mapping tool developed at the University of Lausanne by (Horton et al. 2013) particularly for regional susceptibility mapping that only requires DEM and its derivatives. This model has been tested in South Korea, Switzerland, France, Norway, Italy, Pakistan and is proved to be effective in modeling debris flows susceptibility (Fischer et al. 2014; Horton et al. 2013, 2010; Hürlimann et al. 2003; Kang and Lee 2018; Kappes et al. 2011). Flow-R is used to identify (1) potential source areas and (2) their propagation extent.

Certain criteria/thresholds were used to identify potential source areas such as slope gradient and upslope contributing area and then choose the algorithms to assess the flow propagation. A threshold of 15° slope is selected (Rickenmann and Zimmermann 1993; Takahashi 1981). Upslope contributing area of a channel should be large enough to supply enough sediments and water for extreme flows to occur. Here 0.01 km2 is used as the minimum contributing area which is designed for rare extreme flows (Rickenmann and Zimmermann 1993; Heinimann 1998). The source area identification is purely based on the topographic aspect rather than physical verification. It is assumed that areas with upslope catchment larger than 0.01 km2 and slopes higher than 15° contain sufficient debris. Base on this criteria all pixels are classified as favorable when initiation is probable, excluded if not or ignored when no decision is feasible. The program used to run in the present study is designed for extreme events. (Rickenmann and Zimmermann 1993; Horton et al. 2013). The equation (5) for slope threshold is established from debris flow in Central Alps area.

\(tan{\beta }_{thres}=0.31{S}_{uca}^{-0.15} if {S}_{uca}<2.5{km}^{2}\) (5)

$$tan{\beta }_{thres}=0.26 if {S}_{uca}\ge 2.5{km}^{2}$$

Where βthres is the slope threshold, and Suca the surface of the upslope contributing area.

The propagation routine is based on previously studied source areas and it utilizes spreading algorithms and frictional laws (Huggel et al. 2003). Spreading algorithm determines the path and down slope spread of flows whereas frictional laws determines run out distance (Horton et al. 2013). These are directly depended on the slope and persistence which will eventually estimate the down slope extension of flows. In present study the program uses a flow direction algorithm developed by Holmgren. 1994 that contains an exponent x that allows control of divergence with some modifications by Horton et al. 2013-

\({p}_{i}^{fd}={\left(tan{\beta }_{i}\right)}^{x}/{\sum }_{j=1}^{8}{\left(tan{\beta }_{j}\right)}^{x}\) for all tanβ > 0 (6)

x є [1; +∞]

where i, j are the ଂow directions, \({p}_{i}^{fd}\) is the susceptibility proportion in direction *i*, *tan β**i* is the slope gradient between the central cell and the cell in direction i, and *x* the variable exponent. We use the exponent, x=4 following the experimental result of Claessens et al. (2005). Another criterion is the inertial parameter or persistence function which assesses the weights of flow direction. This is based on the change of flow direction with respect to the previous flow direction following the equation developed by Gamma, 2000 (Horton et al. 2013)-

$${p}_{i}^{p}={\omega }_{\alpha \left(i\right)}$$

7

Where \({p}_{i}^{p}\)is the flow proportion in direction *i* according to the persistence, and *α(i)* the angle between the previous direction and the direction from the central cell to cell *i.*

The susceptibility is calculated from the flow direction and the persistence weights (see details in Horton et al., 2013). The run out distance is calculated by implementing a frictional law using the equation-

$${E}_{kin}^{i}={E}_{kin}^{0}+{\varDelta E}_{pot}^{i}-{E}_{f}^{t}$$

8

Where \({E}_{kin}^{i}\) is the kinetic energy of the cell in direction i, \({E}_{kin}^{0}\)is the kinetic energy of the central cell, \({E}_{pot}^{1}\) is the change in potential energy to the cell in direction i, and \({E}_{f}^{1}\) is the energy lost in friction to the cell in direction i. Travel angle of 11° and velocity of 15 meters per second is used following Rickenmann and Zimmermann 1993.

## 3.4 Weights of evidence method

Weights of evidence (WoE) method is a Bayesian data analysis approach used for establishing hypothesis using statistical relationship of certain evidences with occurred events (Bonham-Carter and F. 1994). Here two types of data sets are used: (1) Training data and (2) Factors. Training data consist of locations of known occurred events. Factors are variables directly or indirectly related to occurrence of that event. In this study training data consist of debris flows inventory prepared using combination of flows mapped in the field and extracted from a previous work (Stolle et al. 2015) (Fig. 1). We use TWI, SPI, STI, slope, plan curvature, stream density and aspect as factors (Fig. 3). In the absence of proper evidential data, prior probability (*P{D}*) is calculated to assess probability of occurring events due to unknown factors (Eq. 9).

$$P\left\{D\right\}=N\left\{D\right\}/N\left\{A\right\}$$

9

Where N{D} is the total number of pixels containing the debris flows and N{A} is the total number of pixels of the study area.

When enough evidential layers are available this is modified to calculate conditional probability. Conditional probability is more reliable as it is based on the presence or absence of different factors (Fig. 3). The expression to calculate the presence of debris flow D in the presence of causative factor F in the area A is as follows

$$P\left\{\frac{D}{F}\right\}=\frac{P\left\{D\cap F\right\}}{P\left\{F\right\}}=Npix\left\{D\cap F\right\}/Npix\left\{F\right\}$$

10

where *Npix* is the number of pixels.

Four possible combinations of probability is calculated for each evidential layers using the numbers of pixels: *Npix1*- when flows occur in the presence of a conditioning factor, *Npix2* – the absence of it, *Npix3*- absence of flows but factor is present, *Npix4*- absence of both flows and a particular factor (Fig. 4). The W+ and W- which are positive and negative weights are then calculated and the degree of correlation of a causative factor with the flows is quantified using the formula (Bonham-Carter and F. 1994).

$${W}^{+}=ln(P\left\{\frac{F}{D}\right\}/\left\{F/\overline{D}\right\}$$

11

W+= ln((Npix1*(Npix3+Npix4)/(Npix1+Npix2)*Npix3) (12)

$${W}^{-}=ln(P\left\{\frac{\overline{F}}{D}\right\}/\left\{\overline{F}/\overline{D}\right\}$$

13

$${W}^{-}= \text{l}\text{n}\left(\right(\text{N}\text{p}\text{i}\text{x}2\text{*}(\text{N}\text{p}\text{i}\text{x}3+\text{N}\text{p}\text{i}\text{x}4)/\left(\right(\text{N}\text{p}\text{i}\text{x}1+\text{N}\text{p}\text{i}\text{x}2\left)\text{*}\text{N}\text{p}\text{i}\text{x}4\right)$$

14

Where F is the factor and D is the debris flow

Positive weight (W+) quantifies the correlation between a causative factor and the flows whereas negative weight (W-) indicates the absence of correlation. The weight contrast factor is then calculated as

C=W+ - W− (15)

Following are the parameters that are used in of weights of evidence method: *Topographic wetness index* (TWI): It is a steady state index used to assess topographic control of wetness conditions of catchments. It is a function upslope contributing area with n of slope and

respect to a point, often used to assess water saturated areas and soil moisture patterns (Chen and Yu 2011; Grabs et al. 2009). TWI is mathematically defined as

$$TWI=\text{ln}\left(\frac{\text{A}\text{s}}{\text{t}\text{a}\text{n}{\beta }}\right)$$

16

where *As* is the local upslope area draining to a particular point and *β* is the local slope in radians. Areas with similar TWI will respond similarly during rainfall or any other hydrological event (Qin et al. 2011). Higher TWI is suggestive of higher soil saturation such as in landslide bodies whereas lower TWI suggest high run offs.

**Stream power index (SPI)**

It is a measure of potential erosive power of a flow on a given topographic surface. It is also based on slope and contributing area.

$$SPI=\text{l}\text{n}\left(As tan\beta \right)$$

17

where As is the upslope contributing area and β is the slope of the grid cell.

**Sediment transport capacity index (STI)**

It is a parameter that quantifies maximum amount of sediment that a flow can carry. This is also based on slope and contributing area, defined as

$$STI={\left(\frac{As}{22.13}\right)}^{0.6}*{\left(\frac{sin\beta }{0.896}\right)}^{1.3}$$

18

where As is the upslope contributing area and β is the slope of the grid cell (Moore and Burch 1986).

**Slope and curvature**

Slope is the rate of change of elevation from a pixel to another neighboring cell towards the downward direction of maximum rate of change of elevation in the DEM.

$$Slope=({y}_{2}-{y}_{1})/({x}_{2}-{x}_{1})$$

19

Where *x*2-*x*1 represents the distance and *y*2-*y*1 represents the difference in elevation between the two neighboring cells.

Curvature is the second derivative of slope which tells whether a terrain is concave up or concave down. Curvature is generally uses as a factor that controls the formation of gullies and also determines whether a flow will accelerate or decelerate (Kang and Lee 2018). It can also influence run off erosion (Conoscenti et al., 2013).

**Drainage density**

It is the ratio of the sum of drainage lengths per unit area.

$$Drainage density=m/{m}^{2}$$

20

Where *m* is the total length of all streams and channels of an area and *m**2* is the area. Drainage density depends on multiple factors such as infiltration capacity, sediment texture, geology, slope, rainfall etc. Areas with high drainage density are susceptible to higher water supply and sediment flux.

**Aspect of slope**

It is the orientation of slope measured clockwise in degrees from 0 to 360 where 0 is north facing, 90 is east facing, 180 is south facing and 270 is west facing. As rainfall and intensity of sunlight differ in different directions of slope, aspect can be an influencing factor on erosion intensity and regolith thickness.

Based on this method weights are assigned for each class of evidential layer and the layer itself (Table 1).

Table 1

Data used for Weights of Evidence and the outcomes (weights).

Features | Class | Class pixels | Debris flows pixels | w+ | w- | Weights of each classes | Final if weights each layers |

**Slope** | 0-10 | 1585882 | 52908 | 1.512 | -1.639 | 3.151 | 2.144 |

10-15 | 521117 | 4278 | 0.192 | -0.013 | 0.205 |

15-25 | 1447541 | 2822 | -1.330 | 0.140 | -1.470 |

25-40 | 3946910 | 2707 | -2.403 | 0.602 | -3.005 |

40-55 | 673970 | 138 | -3.530 | 0.076 | -3.606 |

55-90 | 108113 | 0 | 0.000 | 0.006 | 0.000 |

**TWI** | -2- 1 | 4235 | 0 | 0.000 | -0.007 | 0.000 |

1- 5 | 3875382 | 10119 | -1.064 | 0.453 | -1.518 |

5- 10 | 4124467 | 46826 | 0.409 | -0.683 | 1.092 | 2.154 |

10- 15 | 243317 | 4885 | 1.257 | -0.059 | 1.316 |

15- 20 | 34303 | 1016 | 0.000 | -0.020 | 0.000 |

20- 25 | 1823 | 7 | 0.000 | -0.008 | 0.000 |

25- 30 | 6 | 0 | 0.000 | -0.008 | 0.000 |

**SPI** | -7- -3 | 50666 | 4 | 0.000 | -0.002 | 0.000 | 2.437 |

-3- -2 | 276271 | 147 | -2.415 | 0.024 | -2.439 |

-2- -1 | 348411 | 575 | -1.342 | 0.026 | -1.368 |

-1- 0.15 | 2044735 | 46005 | 1.109 | -1.040 | 2.149 |

0.15-0.5 | 2056325 | 13222 | -0.148 | 0.043 | -0.192 |

0.5- 1 | 2364888 | 2509 | -1.955 | 0.291 | -2.246 |

1- 1.5 | 876662 | 316 | -2.988 | 0.100 | -3.088 |

1.5- 2 | 202572 | 70 | -2.733 | 0.016 | -2.749 |

2- 9 | 63003 | 5 | 1.465 | 0.000 | 1.465 |

**STC** | 0- 1 | 8091210 | 12686 | -1.583 | 3.826 | -5.409 | 1.947 |

1-5 | 168587 | 50165 | 4.126 | -1.587 | 5.714 |

5-10 | 16672 | 2 | 0.000 | -0.006 | 0.000 |

10- 15 | 4443 | 0 | 0.000 | -0.007 | 0.000 |

15-25 | 1847 | 0 | 0.000 | -0.007 | 0.000 |

25-40 | 485 | 0 | 0.000 | -0.008 | 0.000 |

40-60 | 146 | 0 | 0.000 | -0.008 | 0.000 |

60-100 | 132 | 0 | 0.000 | -0.008 | 0.000 |

100-1701 | 11 | 0 | 0.000 | -0.008 | 0.000 |

**Drainage density** | 0.18-2 | 1916937 | 3429 | -1.427 | 0.202 | -1.6281 | 1.246 |

2-2.5 | 5165867 | 26923 | -0.375 | 0.418 | -0.793 |

2.5-3 | 810812 | 24054 | 1.432 | -0.387 | 1.818 |

3-3.3 | 297756 | 4673 | 0.949 | -0.048 | 0.997 |

3.3-3.5 | 63299 | 2452 | 6.571 | -0.040 | 6.610 |

3.5-3.7 | 20155 | 1004 | 0.000 | -0.021 | 0.000 |

3.7-4 | 8707 | 318 | 0.000 | -0.012 | 0.000 |

**Aspect** | 1 | 1020736 | 2364 | -1.138 | 0.087 | -1.225 | 2.747 |

2 | 467715 | 708 | -1.483 | 0.040 | -1.522 |

3 | 735012 | 2557 | -0.705 | 0.044 | -0.750 |

4 | 1044018 | 7025 | -0.072 | 0.010 | -0.082 |

5 | 1267511 | 16141 | 0.555 | -0.137 | 0.693 |

6 | 1396134 | 19971 | 0.667 | -0.204 | 0.872 |

7 | 1347360 | 10872 | 0.095 | -0.019 | 0.114 |

8 | 1005047 | 3215 | -0.814 | 0.070 | -0.884 |

**Plan curvature** | 1060- -200 | 148 | 0 | 0.000 | -0.008 | 0.000 | 1.000 |

-200- 100 | 457 | 0 | 0.000 | -0.008 | 0.000 |

-100- -10 | 24248 | 7 | 0.000 | -0.005 | 0.000 |

-10- 25 | 8106699 | 4024 | -2.734 | 4.170 | -6.904 |

25- 100 | 6410 | 8 | 0.000 | -0.007 | 0.000 |

100- 300 | 563 | 0 | 0.000 | -0.008 | 0.000 |

300- 770 | 32 | 0 | 0 | -0.0077 | 0 |