Landslides: Compute probability of failure for shallow landslides¶

Landlab component that simulates landslide probability of failure as well as mean relative wetness and probability of saturation.

Relative wetness and factor-of-safety are based on the infinite slope stability model driven by topographic and soils inputs and recharge provided by user as inputs to the component. For each node, component simulates mean relative wetness as well as the probability of saturation based on Monte Carlo simulation of relative wetness where the probability is the number of iterations with relative wetness >= 1.0 divided by the number of iterations. Probability of failure for each node is also simulated in the Monte Carlo simulation as the number of iterations with factor-of-safety <= 1.0 divided by the number of iterations.

Code author: R.Strauch, E.Istanbulluoglu, & S.S.Nudurupati

University of Washington

Ref 1: Strauch et. al. 2017, ‘A hydro-climatological approach to predicting regional landslide probability using Landlab, Earth Surface Dynamics, In prep.

Ref 2: ‘The Landlab LandslideProbability Component User Manual’ @ https://github.com/RondaStrauch/pub_strauch_etal_esurf/blob/master/LandslideComponentUsersManual.docx

Created on Thu Aug 20, 2015 Last edit June 7, 2017

class LandslideProbability(self, grid, number_of_iterations=250, groundwater__recharge_distribution='uniform', groundwater__recharge_min_value=20.0, groundwater__recharge_max_value=120.0, groundwater__recharge_mean=None, groundwater__recharge_standard_deviation=None, groundwater__recharge_HSD_inputs=[], seed=0, **kwds)[source]

Landslide probability component using the infinite slope stability model.

Landlab component designed to calculate probability of failure at each grid node based on the infinite slope stability model stability index (Factor of Safety).

The driving force for failure is provided by the user in the form of groundwater recharge; four options for providing recharge are supported. The model uses topographic and soil characteristics provided as input by the user.

The main method of the LandslideProbability class is calculate_landslide_probability(), which calculates the mean soil relative wetness, probability of soil saturation, and probability of failure at each node based on a Monte Carlo simulation.

Usage:

Option 1 - Uniform recharge:

LandslideProbability(grid, number_of_iterations=250,
groundwater__recharge_distribution='uniform',
groundwater__recharge_min_value=5.,
groundwater__recharge_max_value=121.)


Option 2 - Lognormal recharge:

LandslideProbability(grid, number_of_iterations=250,
groundwater__recharge_distribution='lognormal',
groundwater__recharge_mean=30.,
groundwater__recharge_standard_deviation=0.25)


Option 3 - Lognormal_spatial recharge:

LandslideProbability(grid, number_of_iterations=250,
groundwater__recharge_distribution='lognormal_spatial',
groundwater__recharge_mean=np.random.randint(20, 120, grid_size),
groundwater__recharge_standard_deviation=np.random.rand(grid_size))


Option 4 - Data_driven_spatial recharge:

LandslideProbability(grid, number_of_iterations=250,
groundwater__recharge_distribution='data_driven_spatial',
groundwater__recharge_HSD_inputs=[HSD_dict, HSD_id_dict,
fract_dict])


Examples

>>> from landlab import RasterModelGrid
>>> from landlab.components.landslides import LandslideProbability
>>> import numpy as np


Create a grid on which to calculate landslide probability.

>>> grid = RasterModelGrid((5, 4), spacing=(0.2, 0.2))


Check the number of core nodes.

>>> grid.number_of_core_nodes
6


The grid will need some input data. To check the names of the fields that provide the input to this component, use the input_var_names class property.

>>> sorted(LandslideProbability.input_var_names)
['soil__density',
'soil__internal_friction_angle',
'soil__maximum_total_cohesion',
'soil__minimum_total_cohesion',
'soil__mode_total_cohesion',
'soil__saturated_hydraulic_conductivity',
'soil__thickness',
'soil__transmissivity',
'topographic__slope',
'topographic__specific_contributing_area']


Check the units for the fields.

>>> LandslideProbability.var_units('topographic__specific_contributing_area')
'm'


Create an input field.

>>> grid.at_node['topographic__slope'] = np.random.rand(grid.number_of_nodes)


If you are not sure about one of the input or output variables, you can get help for specific variables.

>>> LandslideProbability.var_help('soil__transmissivity')
name: soil__transmissivity
description:
mode rate of water transmitted through a unit width of saturated
soil - either provided or calculated with Ksat and soil depth
units: m2/day
at: node
intent: in


>>> scatter_dat = np.random.randint(1, 10, grid.number_of_nodes)
>>> grid.at_node['topographic__specific_contributing_area'] = np.sort(
...      np.random.randint(30, 900, grid.number_of_nodes))
>>> grid.at_node['soil__transmissivity'] = np.sort(
...      np.random.randint(5, 20, grid.number_of_nodes), -1)
>>> grid.at_node['soil__saturated_hydraulic_conductivity'] = np.sort(
...      np.random.randint(2, 10, grid.number_of_nodes), -1)
>>> grid.at_node['soil__mode_total_cohesion'] = np.sort(
...      np.random.randint(30, 900, grid.number_of_nodes))
>>> grid.at_node['soil__minimum_total_cohesion'] = (
...      grid.at_node['soil__mode_total_cohesion'] - scatter_dat)
>>> grid.at_node['soil__maximum_total_cohesion'] = (
...      grid.at_node['soil__mode_total_cohesion'] + scatter_dat)
>>> grid.at_node['soil__internal_friction_angle'] = np.sort(
...      np.random.randint(26, 40, grid.number_of_nodes))
>>> grid.at_node['soil__thickness'] = np.sort(
...      np.random.randint(1, 10, grid.number_of_nodes))
>>> grid.at_node['soil__density'] = (2000. * np.ones(grid.number_of_nodes))


Instantiate the ‘LandslideProbability’ component to work on this grid, and run it.

>>> ls_prob = LandslideProbability(grid)
>>> np.allclose(grid.at_node['landslide__probability_of_failure'], 0.)
True


Run the calculate_landslide_probability method to update output variables with grid

>>> ls_prob.calculate_landslide_probability()


Check the output variable names.

>>> sorted(ls_prob.output_var_names)
['landslide__probability_of_failure',
'soil__mean_relative_wetness',
'soil__probability_of_saturation']


Check the output from the component, including array at one node.

>>> np.allclose(grid.at_node['landslide__probability_of_failure'], 0.)
False
>>> core_nodes = ls_prob.grid.core_nodes

Parameters: grid: RasterModelGrid A raster grid. number_of_iterations: int, optional Number of iterations to run Monte Carlo simulation (default=250). groundwater__recharge_distribution: str, optional single word indicating recharge distribution, either ‘uniform’, ‘lognormal’, ‘lognormal_spatial,’ or ‘data_driven_spatial’. (default=’uniform’) groundwater__recharge_min_value: float, optional (mm/d) minium groundwater recharge for ‘uniform’ (default=20.) groundwater__recharge_max_value: float, optional (mm/d) maximum groundwater recharge for ‘uniform’ (default=120.) groundwater__recharge_mean: float, optional (mm/d) mean grounwater recharge for ‘lognormal’ and ‘lognormal_spatial’ (default=None) groundwater__recharge_standard_deviation: float, optional (mm/d) standard deviation of grounwater recharge for ‘lognormal’ and ‘lognormal_spatial’ (default=None) groundwater__recharge_HSD_inputs: list, optional list of 3 dictionaries in order (default=[]) - HSD_dict {Hydrologic Source Domain (HSD) keys: recharge numpy array values}, {node IDs keys: list of HSD_Id values}, HSD_fractions {node IDS keys: list of HSD fractions values} (none) Note: this input method is a very specific one, and to use this method, one has to refer Ref 1 & Ref 2 mentioned above, as this set of inputs require rigorous pre-processing of data. g: float, optional (m/sec^2) acceleration due to gravity. seed: int, optional seed for random number generation. if seed is assigned any value other than the default value of zero, it will create different sequence. To create a certain sequence repititively, use the same value as input for seed.
calculate_factor_of_safety(i)[source]

Method to calculate factor of safety.

Method calculates factor-of-safety stability index by using node specific parameters, creating distributions of these parameters, and calculating the index by sampling these distributions ‘n’ times.

The index is calculated from the ‘infinite slope stabilty factor-of-safety equation’ in the format of Pack RT, Tarboton DG, and Goodwin CN (1998),The SINMAP approach to terrain stability mapping.

Parameters: i: int index of core node ID.
calculate_landslide_probability(**kwds)[source]

Main method of Landslide Probability class.

Method creates arrays for output variables then loops through all the core nodes to run the method ‘calculate_factor_of_safety.’ Output parameters probability of failure, mean relative wetness, and probability of saturation are assigned as fields to nodes.