Description:FIELD OF THE INVENTION:
The present invention relates to a system and a method thereof for spatiotemporal landslide susceptibility mapping. More particularly, the present invention discloses a system and a method thereof for spatiotemporal landslide susceptibility mapping by applying an advanced statistical prediction model called Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM) that efficiently incorporates spatial dependencies as well as temporal dependencies to include nonlinear functions of time-dependent covariates to assist professionals in hazard forecasting, estimation and management of landslides.

BACKGROUND OF THE INVENTION:
Landslides are a significant natural hazard, causing widespread destruction and loss of life. Among the key triggers for landslides are rainfall and earthquakes. Earthquake-induced landslides are often shallow and rapid, frequently exacerbated by subsequent rainfall. In many instances, these events evolve into deep-seated debris flows. Debris flows, characterized by their substantial volume, pose a severe threat, capable of devastating entire communities within their path.
Landslide susceptibility modeling (LSM), which assesses the probability of landslides, has significantly advanced in recent years due to increased computational capabilities. Several approaches have been employed for LSMs such as: physical models, heuristic models, machine learning models and statistical models.
A number of literatures have been published including patents and non-patent documents in said domain.
According to a non-patent literature titled, “A method for producing digital probabilistic seismic landslide hazard maps an example from the Los Angeles”, by Jibson, R.W., Harp, E.L. and Michael, J.A., published in 1998, physical models derive laws that closely resemble landslide processes. However, the main drawback of these models is that they require extensive datasets representing physical properties and mechanisms. Furthermore, such datasets must include detailed information about the physical properties of every slope in the study region. While these models come close to natural processes observed in situ, the requirement of such detailed datasets frequently makes them impractical. This limitation restricts the range of the model to predict landslides in a few localized slopes.

Another non patent literature titled, “A heuristic approach to global landslide susceptibility mapping”, by Thomas Stanley and Dalia B. Kirschbaum, published in 2017, describes heuristic models for landslide susceptibility mapping that are index-based and give quick estimations of susceptibility. These heuristic models use expert knowledge, empirical observations, and common-sense rules to identify patterns and relationships between landslide occurrences and influencing factors. These models are generally used when there is limited data available, or the data is not sufficient to train more complex machine learning algorithms. While heuristic models are easy to apply, they are often outperformed by data driven models due to their inability to capture intricate patterns and relationships in the data.

Machine learning models estimate the functional relationship between terrain, seismic, morphological properties, and the occurrence of landslides. Such a relationship is usually derived by fitting a parametric class of functions to the data. As per another non patent literature titled, “The elements of statistical learning data mining, inference, and prediction”, by Hastie, Trevor, Tibshirani, Robert, Friedman, Jerome published in second ed. Springer Series in Statistics., in 2009, the relationships that fit the data are generally complicated, and the number of parameters is large.

A patent document, CN-202211420018-A, titled, “Single landslide early warning and forecasting method based on space-time combination”, dated 14th November 2022, brings out a model that uses a machine learning model for prediction/. The drawback of this model is that it is specific to one or a few landslides being field monitored. Additionally, machine learning model employed is often considered “black box” model that provides limited insights into how it arrives at its predictions.

Statistical models follow a similar approach to the machine learning models, but the parameters in the statistical model usually have a direct interpretation and provide information on how predictors influence landslide susceptibility. According to a non-patent literature titled, “ Binary logistic regression versus stochastic gradient boosted decision trees in assessing landslide susceptibility for multiple-occurring landslide events: application to the 2009 storm event in Messina”, by Lombardo, L., Cama, M., Conoscenti, C., Marker, M., and Rotigliano, E., published in Nat. Hazards, in 2015, statistical models are based on probability theory and, unlike machine learning models, reveal the relationship between the input variables. The most common statistical routine used for landslide susceptibility is the Logistic Regression (LR). However, it is to be noted that such statistical models are based on linear dependency of the independent variables with the dependent variable. Moreover, these models do not consider temporal and spatial variation in the occurrence of landslides.

Certain models such as the Hidden Markov Model (HMM) leverage the temporal dependence of prior events to predict the future and estimate the outcome of a certain event using risk states. Besides to overcome the drawbacks many statistical models used in the literature have extended the LR model such as Generalized Additive Model (MS-GAM) that harness non-linear dependence of the independent variables with the dependent variable. However, while GAMs allow non-linear relationships between the covariates and the predicted variable(s), they do not capture the spatiotemporal dependencies present when predicting landslides. Similarly, most models discard the spatial and temporal relationship in the evolution of landslides. Certain models that are termed ‘spatiotemporal’ in the landslide susceptibility literature do not however simultaneously consider spatial and temporal dependencies between land slide occurrences.
Therefore, there is a need for a system and a method thereof for landslide susceptibility mapping that incorporates spatiotemporal terms and non-linearity in the prediction model, consumes lower computational time, captures intricate patterns and relationships in the data, is easy to interpret, that is robust, flexible and cost effective in providing a reliable hazard estimation.

OBJECT OF THE INVENTION:
In order to overcome the shortcomings in the existing state of the art the main object of the present invention is to provide a system for landslide susceptibility mapping by applying an advanced statistical prediction model for landslides called Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM).
Yet another object of the present invention is to provide a method for landslide susceptibility mapping that incorporates an advanced statistical prediction model for landslides called Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM).

Yet another object of the present invention is to provide a system for landslide susceptibility mapping that incorporates both spatial and temporal relationships of landslide occurrence simultaneously in the model for prediction of the occurrence of landslides.

Yet another object of the present invention is to provide a system for landslide susceptibility mapping that incorporates the terms of nonlinear dependencies of the variables in the model for prediction of the occurrence of landslides.

Yet another object of the present invention is to provide a system and method capable of capturing intricate patterns and relationships in the data used in the model for prediction of occurrence of landslides.

Yet another object of the present invention is to provide a system and method for landslide susceptibility mapping that does not require extensive datasets representing physical properties and mechanisms, is practical and provides a prediction model for large geographical areas.

Yet another object of the present invention is to provide a system and method for landslide susceptibility mapping with a prediction model that consumes lower computational time and is easy to interpret.

Yet another object of the present invention is to provide a method for landslide susceptibility mapping that is accurate, robust, flexible and cost effective in providing a reliable hazard estimation.

SUMMARY OF THE INVENTION:
Accordingly, the present invention discloses a system and a method thereof for spatiotemporal landslide susceptibility mapping by applying an advanced statistical prediction model called Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM) that efficiently incorporates spatial dependencies as well as temporal dependencies to include nonlinear functions of time-dependent covariates to assist professionals in hazard forecasting, estimation and management of landslides.

The system and a method thereof for of the invention discloses an advanced and innovative statistical prediction model called Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM). In this model, temporal dependencies are incorporated by using a sequence of hidden risk states, while neighborhood structure incorporates spatial relationships. In terms of model performance, this leads to a much higher sensitivity as landslides tend to occur in clusters and can affect nearby slopes.

The system of the present invention comprises of modules to include a data acquisition module, processing module, a mapping and prediction module etc. The data acquisition module comprises of submodules for acquiring of various data in the form of rainfall, NDVI, terrain attributes, terrain related properties of watersheds, lithological data etc. The processing module comprises of preprocessing submodule for receiving and preparing the acquired data and an advanced statistical prediction tool (MSST-GAM) for processing the acquired data from the Data acquisition module (A) to obtain results in the form of landslide mapping and predictions. The advanced statistical prediction tool incorporates both spatial and temporal dependencies by integrating a plurality of statistical models in specific configuration. Some of the models that are utilized include HMM, MRF, MS-GAM etc. that are configured specifically to obtain the MSST- GAM. The mapping and prediction module displays said results of landslide mapping and predictions.

The method of present invention broadly comprises of steps of but not limited to data acquisition, data preparation, data processing and displaying said predictions for the purpose of spatiotemporal landslide susceptibility mapping in a region of interest for a particular period of time. The data required for extracting variables or covariates related to terrain or climatic conditions are acquired from various repositories or remote sensing facilities. The data is extracted and preprocessed from the raster layers by extracting raster values in the form of covariates, to include a number of static and time dependent covariates. These are utilized as inputs to the processing module wherein the MSST-GAM processes the data to obtain results in the form of landslide mapping and predictions. The processing by the processing module includes steps of correlation of landslide data in different temporal lobes and watersheds, validation, model testing, evaluation, obtaining probabilities for susceptibility mapping and display of the same.

The prediction model MSST-GAM in an embodiment of the present invention is applied to a multi-temporal inventory of post-seismic debris flow in a region affected by the 2008 Wenchuan earthquake. A five-fold spatiotemporal cross-validation is used to evaluate the model’s performance. The innovative model exhibits significantly improved performance over prevalent models such as GAM and Logistic Regression (LR) in terms of AUC-ROC and improves the mean log-likelihood by 24.7% compared to GAM and therefore clearly provides better susceptibility prediction than the other commonly used statistical models, such as the LR and GAM. MSST-GAM can handle the complex correlation among the co-variables to predict the future chain of events with the memory of past landslide events and their contributing factors.

Accordingly, the present invention provides a system and a method thereof for landslide susceptibility mapping that applies an advanced statistical prediction model called MSST-GAM that incorporates spatiotemporal terms and non-linearity, is accurate consumes lower computational time, captures intricate patterns and relationships in the data, is easy to interpret, that is robust, flexible and cost effective in providing a reliable hazard estimation.

BRIEF DESCRIPTION OF DRAWINGS
Figure 1 displays an overview of the system of the invention and its working in the form of a flowchart.
Figure 2 displays a) Study area location in China indicated by a red polygon outlined with a rectangle box in the inset. b) Southeast part of the study area with watersheds. c) Northeast part of the study area with remaining watersheds.
Figure 3 displays a) Temporal distribution of landslide count in five counties within the study area. The 3D plot shows the variation in quarters of the year. b) Rainfall distribution throughout the study
Figure 4 displays the counties have been abbreviated for representation – Anxian (A), Beichuan (B), Mianzhu (MI), Maxzhou (MA), Pengzhou (P), Shifang (S), Dujiangyan (D) and Wenchuan (W). a) Lithological units used in our study, modified from the GLIM database with strengths shown next to the units. b) Slope map. c) Aspect map.
Figure 5 displays pair plot representation of six covariates and the correlation matrix. The values of Channel length have been scaled for presentation in this plot as the values were too large to be shown in the axes.
Figure 6 displays neighborhood graph of connected watersheds, showing the links in orange lines and watershed centroids as black dots.
Figure 7 displays five-fold spatiotemporal cross-validation in two time slices. The testing is always performed in an untrained spatiotemporal data slice.
Figure 8 displays the modeling strategy followed in this study. The GAM is extended with HMM and MRF into MSST-GAM model as presented in this study.
Figure 9 displays a forest plot showing the significance of covariates in the LR model.
Figure 10 displays variation of the nonlinear descriptors in the GAM model, the plot on the left shows the NDVI and the plot on the right shows the rainfall.
Figure 11 displays a) Box plot of the susceptibility in each of the two risk states. b) Rainfall splines for both the risk states. c) NDVI splines for the risk states.
Figure 12 displays ROC curve for each model. Corresponding AUC values from the spatiotemporal cross-validation scheme are shown in Table 5. Higher AUC values represent more accurate predictions.
Figure 13 display a) Actual landslide points in the week WT1. The counties have been abbreviated for representation - Anxian(A), Beichuan(B), Mianzhu (MI), Maxzhou (MA), Pengzhou(P), Shifang(S), Dujiangyan(D), Wenchuan(W). b) The probabilities predicted by the LR model in the week of 18th September 2008. c) GAM probabilities. d) MSST-GAM probabilities.
Figure 14 displays a) Actual landslide points in the week WT2. b) The probabilities predicted by the LR model c) GAM probabilities. d) MSST-GAM probabilities.
Figure 15 displays Rainfall from September 18th to 24th, 2008 and the preceding weeks. a) September 18th to 24th 2008. b) August 28th to September 3rd, 2008.
Figure 16 displays rainfall distribution from August 13th to 19th, 2012 and the preceding weeks. a) August 13th to 19th. b) July 16th to 22nd 2012.

DETAILED DESCRIPTION OF THE INVENTION WITH ILLUSTRATIONS AND EXAMPLES
While the invention has been disclosed with reference to certain embodiments, it will be understood by those skilled in the art that various changes may be made, and equivalents may be substituted without departing from the scope of the invention. In addition, many modifications may be made to adapt to a particular situation or material to the teachings of the invention without departing from its scope.

Throughout the specification and claims, the following terms take the meanings explicitly associated herein unless the context clearly dictates otherwise. The meaning of “a”, “an”, and “the” include plural references. Additionally, a reference to the singular includes a reference to the plural unless otherwise stated or inconsistent with the disclosure herein.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this disclosure belongs. The system, methods, and examples provided herein are only illustrative and not intended to be limiting.
The abbreviations used in the invention are represented in table 1 as below:

Table 1: Legend of abbreviations
S.no. Particulars Legend
1 Markov-switching spatio-temporal generalized
additive model MSST-GAM
2 Generalized additive model GAM
3 Area under the receiver operating characteristic curve. AUC-ROC
4 Landslide susceptibility modelling LSM
5 Land use land cover LULC
6 Coordinated downscaling experiment - European domain. EURO-CORDEX
7 Fast shallow landslide assessment model FSLAM
8 Quantum geographic information system QGIS
9 Long short-term memory networks LSTM
10 Logistic regression LR
11 Generalized linear models GLM
12 Hidden Markov models HMM
13 Markov switching GAM MS-GAM
14 Markov random fields MRF
15 Integrated nested Laplace approximation INLA
16 Global Lithological database GLiM
17 Digital elevation model DEM
18 Climate hazards group infrared precipitation with station data CHIRPS
19 Google earth engine GEE
20 Normalized difference vegetation index NDVI
21 Moderate resolution imaging spectroradiometer MODIS
22 Geographic information system GIS
23 Residual maximum likelihood REML
24 Mixed GAM computation vehicle MGCV
25 Hydro morphological process HMP

The reference numerals used in the present invention are tabulated below in table 2.
Table 2: Legend of Reference numerals
Ser No. Item description Reference signs/ numerals
1 System S
2 Data acquisition module A
Rainfall data submodule A1
NDVI data submodule A2
Terrain information submodule A3
Watershed information submodule A4
Lithological information submodule A5
Multitemporal inventory A6
3 Processing module P
Preprocessing submodule P1
Advanced statistical prediction tool P2
Programming tool P3
4 Mapping and prediction module M
Display submodule M1
User interface submodule M2
5 Computing unit C
6 Power (Po)
7 Storage units (So)

Statistical susceptibility models predict the occurrence of landslides, which is the first step toward landslide hazard estimation. Landslide occurrences depend on complex interactions between geological, geomorphological, hydrological, and climatic processes over space and time. The combination of these factors leads to the formation of distinct spatiotemporal patterns. Understanding these spatiotemporal patterns is crucial for effective landslide susceptibility mapping. However, most of the models in the literature do not consider spatiotemporal dependencies among landslide occurrences.

Accordingly, the present invention discloses a system (S) and a method thereof for spatiotemporal landslide susceptibility mapping by applying an advanced statistical prediction model called Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM) that efficiently incorporates spatial dependencies as well as temporal dependencies to include nonlinear functions of time-dependent covariates to assist professionals in hazard forecasting, estimation and management of landslides.

As per an embodiment of the invention an overview of the system (S) and the method is depicted in the form of a flowchart in Fig. 1. The system (S) for spatiotemporal landslide susceptibility mapping in a predefined region of interest comprises of a data acquisition module (A), processing module (P), mapping and prediction module (M), computing unit (C) and other units such as but not limited to power (Po) and storage unit (So) for operation of said system (S).

The data acquisition module (A) acquires data for landslide susceptibility mapping in the predefined region of interest for a pre-determined period of time and comprises of a rainfall data submodule (A1) to obtain rainfall data from a rainfall data base, an NDVI data submodule (A2) to obtain NDVI data from vegetation repositories, a terrain information submodule (A3) for obtaining terrain attributes from Digital Elevation Model (DEM)s, a watershed information submodule (A4) for obtaining watershed properties in the region of interest from DEMs, a lithological information submodule (A5) for obtaining lithological data from a lithological database and a multitemporal inventory (A6) for obtaining data related to landslide occurrences or watershed properties in the region of interest.

The processing module (P) of the system (S) is utilized for receiving, preparing and processing the acquired data from the data acquisition module (A) and comprises of a preprocessing submodule (P1) for receiving and preparing the acquired data in the form of covariates, an advanced statistical prediction tool (P2) for processing of the prepared data to obtain results in the form of landslide mapping and predictions and a programming tool (P3) to fit said advanced statistical prediction tool (P2).

The mapping and prediction module (M) of the system (S) comprises of a display submodule (M1) for displaying said results of landslide mapping and predictions and a user interface submodule (M2) for facilitating display of the results and for user interaction if required. The computing unit (C) accommodates and facilitates the operation of the data acquisition module (A), the processing module (P) and the mapping and prediction module (M) and is connected to power (Po) and storage unit (So) for smooth operation of said system (S).

The invention is characterized in that the advanced statistical prediction tool (P2) of the processing module (P) incorporates both spatial and temporal dependencies by integrating a plurality of statistical models in specific configurations. The tool (P2) incorporates temporal dependencies by utilizing and applying a statistical model, that estimates the outcome of a certain event using risk states, such as but not limited to Hidden Markov Model (HMM). It incorporates non-linearity in prediction by utilizing and applying statistical model, such as but not limited to Markov Switching Generalized Additive Model (MS-GAM), that includes non-linear dependence of independent variables with dependent variables. The tool (P2) incorporates spatial dependencies by utilizing and applying statistical model such as Markov Random Field (MRF) to model the neighborhood structure in the region of interest. The tool (P2) predicts risk state sequence using nonlinear functions of covariates that include rainfall and NDVI. The data acquisition module (A) acquires and provides optimum number and combination of static and temporal covariates for efficient landslide mapping and prediction. Therefore, the present invention provides a system (S) enabled to perform a spatiotemporal landslide susceptibility mapping that is accurate, consumes lower computational time, captures intricate patterns and relationships in the data, is easy to interpret, is robust, flexible and cost effective in assisting professionals in hazard forecasting, estimation and management of landslides.

The rainfall data in rainfall data submodule (A1) is obtained from rainfall database selected from group of geospatial analysis platforms and remote sensing facilities such as but not limited to CHIRPS from Google Earth Engine (GEE), Global precipitation measurement (GPM) by NASA, site specific rain gauge datasets (if available) etc., preferably CHIRPS from GEE. The NDVI data is obtained from vegetation repositories selected from remote sensing facilities such as MODIS repository, Landsat series from USGS, Advanced Very High Resolution Radiometer (AVHRR) on NOAA, preferably MODIS repository. The terrain information submodule (A3) obtains terrain attributes of region from Digital Elevation Model (DEM)s obtained from databases selected from group of remote sensing earth science data and information systems such as ALOS PALSAR, SRTM 30 m DEM, high accuracy DEM obtained by field investigations using LiDAR or 3D Photogrammetry, preferably ALOS PALSAR. The DEMs also provide watershed properties for watershed information module (A4)
The watershed properties can also be obtained from multitemporal inventories of landslides related hazards. The lithological data for lithological information submodule (A5) is obtained from lithological database selected from GLiM, site specific lithology maps, any other web based databases, preferably GLiM. The multitemporal inventory (A6) is selected from inventories available on landslide affecting hazards in the region of interest such as but not limited to inventories recording the earthquakes in said region, repositories from sciencebase.gov, zenodo.org or any other journal websites etc.
The advanced statistical prediction tool (P2) is encoded in programming languages selected from group of python, C, C++, SPSS, statistical computing and data visualization languages such as R language, etc. preferably R language. The risk states of rainfall and NDVI are utilized as hidden states for generating at least one HMM state transition probability matrix. The advanced statistical prediction tool (P2) of the processing module (P) after integrating the plurality of statistical models in specific configuration is referred as Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM).

MSST-GAM is defined with respect to discrete watersheds as well as watersheds of continuous space and time preferably discrete watersheds. The tool or model of the present invention can be combined with physical models for landslide susceptibility mapping.

The neighborhood structure utilized in MRF is obtained by extracting neighborhood matrix from the shape files of the watersheds. The time dependent or time-varying covariates and counts are segregated into a matrix of three columns per time period such as a week. The static covariates are combined into one single matrix, with each column representing a unique covariate. The risk states are such that for each the occurrence of a landslide would be modelled by a separate Generalized additive model (GAM) and the transitions between risk states over time are estimated from time dependent covariates such as rainfall.

The method of the present invention for spatiotemporal landslide susceptibility mapping in a predefined region of interest for a pre-determined period of time comprises of steps of acquiring data, receiving and preparing of said acquired data, processing of the data and displaying the predictions and correlations for landslide susceptibility mapping. The acquiring of data for landslide comprises of steps of acquiring of rainfall data from a rainfall database such as Google Earth Engine (GEE), acquiring of NDVI data from vegetation repositories such as MODIS repository, obtaining terrain attributes from Digital Elevation Model (DEM)s from remote sensing earth science data and information systems such as ALOS PALSAR, obtaining watershed properties in said region of interest from DEMs or from multitemporal inventories of landslide related hazards in said region of interest, obtaining lithological data from a lithological database such as GLiM and obtaining spatial and temporal information on landslide occurrences from multitemporal inventories of landslide affecting hazards in said region of interest.

The receiving and preparing of the acquired data by the preprocessing submodule (P1) of the processing module (P) of said system (S) is performed by standardizing their raster layers to match their resolution. The data is further prepared by extracting raster values in the form of covariates, in specific combination of static and time dependent covariates in specific numbers using zonal statistics from geographic information system.

The processing of the prepared data by the advanced statistical prediction tool (P2) of the processing module (P) to obtain results in the form of landslide mapping and predictions, comprises of steps of receiving the prepared data as inputs by the advanced statistical prediction tool (P2), correlating of landslide incidences in two temporal lobes T1 and T2 by said tool (P2), correlating simultaneously of landslide incidences in each watershed by said tool (P2), performing validation of tool using spatiotemporal cross validation preferably fivefold spatiotemporal cross-validation, evaluating model performance using statistical measures such as for discrimination and calibration, performing testing of model by choosing a time period in each temporal lobe, obtaining probabilities for landslide susceptibility mapping and plotting predictions in GIS by the tool and performing correlation among said predictions and rainfall, displaying said predictions and correlations as obtained in preceding steps by a mapping and prediction module (M) of said system (S) as landslide susceptibility mapping and predictions and allowing user interaction.

The fivefold spatiotemporal cross-validation is carried out by clustering randomly five spatial splits of watersheds in both temporal lobes followed by training the models in four spatial slices from one of the temporal lobes and testing in a spatial slice from the other. The measures for discrimination and calibration are selected from group of AUC-ROC, mean log likelihoods, the Brier score, the C statistic, the Hosmer-Lemeshow goodness-of-fit measure and R2 measures for binary outcomes, preferably AUC-ROC and mean log likelihoods.

The probabilities of the tool are collected in all the time slices to plot susceptibility classes preferably by splitting the susceptibility into ten deciles based on the total percent of the probabilities. The susceptibility classes formed are by selecting from methods of classification to include natural breaks, quantiles and Head/tail breaks, preferably an extension of the quantile method of classification of landslide susceptibility. The covariates are such that they are not collinear among themselves and the number of covariates ranges from 5 20 preferably 14 to include time dependent covariates such as rainfall and NDVI.

The present invention explores a novel way to extend GAM, a model used in prior arts for LSMs. The invention models temporal dependency between the occurrence of landslides by introducing risk states in the model. For each risk state, the occurrence of a landslide would be modeled by a separate GAM and the transitions between risk states over time are estimated from time varying covariates such as rainfall. The risk states are not observed directly and hence are referred to as latent or hidden states. Models of this kind that estimate said hidden states, transition probabilities between hidden states, and emission probabilities are called Hidden Markov Models (HMMs). An HMM leverages the temporal dependence of prior events to predict the future and is truly a temporal model that estimates the outcome of a certain event using risk states. This paradigm has never been used in landslide susceptibility mapping.

When GAM is used for modeling the transitions and emissions in an HMM, the resulting model is referred to as a Markov switching GAM (MS-GAM). MS-GAM harnesses the flexibility of nonlinear dependence of the independent variables with the dependent variable. This adds
flexibility to the model and retains the temporal nature of the Hidden Markov. The MS-GAM has never been used for LSMs in earth science.

The spatial aspect of LSM is introduced by adding Markov Random Fields (MRFs) to the MS-GAM. MRFs are used in landslide inventory mapping using change recognition in satellite images. MRF introduces a spatial correlation based on a neighborhood structure of adjacent mapping units. The present invention innovatively combines MS-GAM and MRF to provide a spatiotemporal statistical model that can be used for LSM. This model has thus been appropriately called Markov Switching Spatio-Temporal GAM (MSST-GAM). This model has not been used in earth science and landslide literature before.

This work introduced a novel approach incorporating spatial and temporal dependencies using HMM and MRF into LSMs making it a truly spatiotemporal susceptibility model. To demonstrate the efficacy of the model, a multi-temporal inventory of the areas was utilized that were affected by the 2008 Wenchuan earthquake. Fourteen covariates were selected based on collinearity tests to ensure the robustness of the dataset and the time frame of the dataset was divided into two time slices. This novel MSST-GAM was compared with two of the most commonly used models, LR and GAM, for landslide susceptibility. All models were validated in a rigorous five-fold spatio temporal cross-validation scheme. It is observed that the MSST-GAM improved its performance significantly over GAM and Logistic Regression model in terms of AUC-ROC. It was observed that MSST GAM shows an improvement in AUC-ROC by 4% over LR and by 2% over GAM. Similarly, the mean log-likelihood for MSST-GAM is observed to be 24.7% more than the GAM and 20% more than LR. These results clearly show the superior performance of the MSST-GAM in comparison with the other two models. Therefore, model MSST-GAM is a viable alternative for landslide susceptibility mapping. Susceptibility modeling is the first step toward hazard estimation, and integrating MSST-GAM could enhance hazard modeling.

Relevance of this model in Spatiotemporal landslide susceptibility mapping
Presently in the state of the art, two models are prominent in statistical susceptibility mapping viz. Logistic Regression (LR) and GAM. Both these models are not spatiotemporal by nature. The present invention demonstrates the spatiotemporal nature of MSST- GAM using all three models (including MSST-GAM) to map susceptibility in watersheds in China. The MSST-GAM shows a superior performance over the LR and GAM by at least 24.1%. The model was also tested by looking at its performance in specific weeks in the time period, and it is observed that the model of the present invention captures the pattern of rainfall from the previous week in its prediction while the others do not.

The MSST-GAM is defined with respect to discrete watersheds. It can also be extended to continuous space and time watersheds. HMM and Markov switching models require a continuous temporal dataset of landslide occurrences. The Wenchuan inventory provides a detailed spatiotemporal dataset of post-seismic debris flows over five continuous years. The model of the present invention applies to all types of landslides, while the effectiveness regarding post seismic debris flow has been evaluated and illustrated presently. The method and system of the present invention are applicable when used in combination with some physical models that can work as hybrid models.

EXAMPLES
The present invention shall now be explained with accompanying examples. These examples are non-limiting in nature and are provided only by way of representation. While certain language has been used to describe the disclosure, any limitations arising on account of the same are not intended. As would be seeming to a person skilled in the art, various working alterations may be made to the method in order to implement the inventive concept as taught herein. The figures and the preceding description give examples of embodiments. Those skilled in the art will appreciate that one or more of the described elements may well be combined into a single functional element. Alternatively, certain elements may be split into multiple functional elements. Elements from one embodiment may be added to another embodiment. For example, order of steps of method or processes of data flow described herein may be changed and is not limited to the manner described herein. Moreover, the actions of any flow diagram need not be implemented in the order shown; nor do all of the acts need to be necessarily performed. Also, those acts that are not dependent on other acts may be performed in parallel with the other acts. The scope of embodiments is by no means limited by these specific examples.

In an exemplary embodiment, the various components which together form the system (S) along with the working of the invention and the method thereof are illustrated below.

Multi-temporal inventories record the evolution of landslides in any terrain. The MSST-GAM for LSM is demonstrated by using the multi-temporal inventory created by Fan et l. (2019). This inventory consists of post-seismic debris flow data after the Wenchuan earthquake and the area affected by this event hereon is called the study area. It is to be noted that none of the prior art considered temporal and spatial variation in the occurrence of landslides while utilizing the said open inventory.
The Wenchuan earthquake that occurred in the Sichuan region of China on the 12th of May 2008, with a surface rupture of 250 km and a thrust fault movement is reported to be one of the most devastating events in history. The triggered landslide count was reported to be more than 200,000 with a total planimetric area of 1159 km2, causing severe damage to the built environment, disrupting roads and highway networks.

The post-seismic debris flow is reported to be one of the most destructive long-term hazards. Fan et al. (2019) have created a multi-temporal inventory of post-seismic debris flows from the field and satellite images in 8 counties within the Wenchuan area. The dataset contains landslide occurrences in 252 watersheds covering a total surface area of 1581 km2 and 171 km of fault rupture. These watersheds were continuously monitored for over a decade after the earthquake for post-seismic landslides.

Debris flow events have been observed by the concerned researchers in watersheds within the study area in five counties: Anxian, Mianzu, Beichuan, Pengzhou and Wenchuan. Fig. 2a) shows the location of the study area marked in red polygon. In continuation, part (b) of the figure shows the location of watersheds in the northeastern part of the study area, with the boundaries of the counties marked in yellow. Similarly, part (c) represents the watersheds in the southwestern half of the study area, with the epicenter of the Wenchuan earthquake represented by a red star. The bar graph in Fig. 3a) shows the quarterly number of landslides in each county. The figure shows that the majority of landslides occurred in Q3 (July - September) of each year, primarily during the rainy season. Fig. 3b) shows the distribution of rainfall on a quarterly scale in the 2008–2013 time interval. The peak rainfall in those years is observed in Q3, which is also the quarter that experienced the maximum number of landslides as seen in Fig. 3a).

The dataset on post-seismic debris flow included Debris flow points from May 2008, immediately after the Wenchuan earthquake. These events were observed in the field and over satellite images from May 2008 to August 2017. For the development of the system and method of the present invention 520 individual debris flow events triggered between 2008 and 2013 were considered because there were only 7 events recorded from 2014 to 2017. This multi-temporal inventory is most suited to test a model that can evolve over space and time as it best represents actual scenarios. Very few aftershocks with a magnitude Mw > 5.0 were observed during the weeks under consideration. As these did not coincide with the temporal distribution of the landslides, seismic parameters were not considered in the predictions.

There are 9 static covariates provided with the dataset by Fan et al. (2019), as shown in Table 3 that were collected for the work on present invention. In addition, 11 other covariates that represent the terrain and climatic attributes were collected, as shown in Table 4. For the first 4 terrain attributes shown in Table 4, the mean and standard deviation were calculated within the watersheds using zonal statistics. Fig. 4a) shows the lithological map obtained from the Global Lithological database GLiM. The strength of lithological units was assigned on a scale of 0–15 (marked next to the names of the units in Fig. 4a). Terrain attributes such as slope and aspect were calculated from the Digital Elevation Model (DEM) obtained from ALOS PALSAR (ALOS-JAXA, 2023) with a resolution of 12.5m as represented in Fig. 4b) & c). Rainfall was obtained from ‘Climate Hazards Group InfraRed Precipitation with Station data’ (CHIRPS), which has a resolution of 5 km. The weekly rainfall from August 2008 to December 2013 was extracted from CHIRPS using Google Earth Engine (GEE) at the catchment scale (watersheds represented in Fig. 2). NDVI datasets were acquired from the MODIS repository with a resolution of 250m. Each slice of the dataset contains the vegetation for an interval of 16 days (ORNL DAAC, 2018). These slices were further used to extract the mean values in each catchment using zonal statistics in GIS software. The temporal resolution of the rainfall and the NDVI were matched to capture the simultaneous variation of vegetation and precipitation.

Table 3: Default covariates available with the dataset
Properties observed Default covariates
Area Catchment Area
Gradient Catchment Gradient, Channel Gradient & Main channel Gradient
Length Channel Length
Relief Catchment Relief, Channel Relief & Main channel Relief
Drainage density Catchment Drainage density

Table 4: Covariates additionally collected for this study
Acquired covariates Source Resolution Range of values
Slope (μ & σ) DEM ALOS Palsar 12.5m 0° to 80°
Aspect (μ & σ) DEM ALOS Palsar 12.5m 0° to 360°
Planar curvature (μ & σ) DEM ALOS Palsar 12.5m -1.5 to 3
Profile curvature (μ & σ) DEM ALOS Palsar 12.5m -1 to 4.2
Rainfall (weekly μ) CHIRPS (GEE*) 5km 0mm to 250mm
NDVI (16 days μ) MODIS 250m 0 to 1
Lithology GLiM 0.5° 0 to 13

A weekly temporal scale was selected to evaluate the susceptibility within the watersheds, as this gives the right level of granularity. The watershed delineated by Fan et al. (2019) is used as the basic mapping unit. The main outcome, the set of binary variables indicating whether the landslide occurred in a particular week etc. are defined. From the remaining 17 covariates, the rainfall and NDVI are time-dependent, while the rest are static. Three default covariates showed high collinearity and were ignored for further calculations. Using pair plots, Fig. 5 shows the variation of the six most important static covariates. These six covariates were selected based on their significance in the LR model fit that will be represented as a forest plot as explained in subsequent paragraphs. Time-varying covariates and counts are then segregated into a matrix of three columns per week.

On the other hand, the static covariates were combined into one single matrix, with each column representing a unique covariate. The missing data points were imputed based on wavelet shrinkage using the imputeR package. None of the covariates had more than 44 missing entries. Fig. 5 shows the bivariate distributions of the significant static covariates. The other variables and their significance scores are represented on the upper half of the figure, while the actual correlation is represented as contours in the lower half in blue. The stars on the correlation values increase with the significance of the variables. The diagonal represents the marginal distributions of the static covariates. The curvatures planar and profile are highly correlated. The channel length and the profile curvature are uncorrelated, which could be due to the large values of channel length. Similar contours are observed for channel length and area of the watersheds.

There are two ways to represent a neighborhood structure of mapping units for LSMs: First is the distance between the centroids of the mapping units, and second is the neighborhood matrix, which represents the proximity of two mapping units based on shared outlines. The second method was followed and the neighborhood matrix extracted from the shape files of the watersheds. The matrix was used only in the MSST-GAM model and not in the LR and GAM. Fig. 6 represents the neighborhood structure with the watersheds as centroid points (in black) and links (in orange) to the neighbors as connecting lines. Although the figure does not show the neighborhood border structure, this is only a pictorial representation.

The most common model for landslide susceptibility is logistic regression (LR). Such an LR model predicts the log odds ղ of the occurrence of landslides as a linear combination of the m covariates X1 … Xm in the particular watershed over a temporal slice so that
ղ = α1X1+ … + αmXm (1)
The vector of parameters α1 … αm is estimated from the training data using maximum likelihood. This LR model can be extended by allowing nonlinear relationships between the covariates and predicted log odds in the form
ղ = α1s1(X1) + … + αmsm(Xm) (2)
Where the nonlinear transformations s1 … sm are again estimated from the data. The model of the present invention used smoothing splines for these non-linear transformations. Such a model is called logistic Generalized Additive Model (GAM). The most common method to simultaneously estimate regression parameters and smoothing splines is to maximize residual maximum likelihood (Residual maximum likelihood (REML)). The GAM can be further extended by introducing temporal dependencies in the following way. Let Z1, …, Zn denote a latent sequence of binary variables that indicates landslide risk (low or high) in each time slice in a particular watershed. The value of the variable Zk is called the risk state at the kth time slice. In the kth time slice, the log odds for this watershed are predicted by the equation:
ղ={█(〖α_1〗^((0)) 〖s_1〗^((0)) (X_1)+...+ 〖α_m〗^((0)) 〖s_m〗^((0)) (X_m),if Z_k = 0,@〖α_1〗^((1)) 〖s_1〗^((1)) (X_1)+...+ 〖α_m〗^((1)) 〖s_m〗^((1)) (X_m),if Z_k = 1.)┤ (3)
In the simplest case, this allows to model temporal dependencies between the time slices in a watershed by assuming that the sequence Z1, …, Zn forms a binary Markov chain where the transition probabilities are estimated from the data. It is further possible to make the transition probabilities as functions of time-dependent covariates. In the present invention, the transition probability P (Z k+1 = 1| Zk = 0) of switching from a low-risk state to a high-risk state was modeled by a GAM with covariates rainfall and NDVI. Similarly, the transition probabilities P (Z k+1 = 0| Zk = 1) of switching back to a low-risk state are again modeled by the GAM.

Finally, to introduce the spatial dependencies in the model, a Markov Random Field (MRF) was added, where it is assumed that the occurrence of landslides in each pair of neighboring watersheds is positively correlated. While it is possible to estimate individual correlation among coefficients for each pair, a model is used where each correlation is assumed to be equal to an unknown parameter ρ > 0, which is estimated from the data. All models were fitted in R using the built-in GLM function for LR, the package Mixed GAM Computation Vehicle - MGCV for GAM, and the package “hmmTMB” for MSST-GAM.

A fivefold spatiotemporal cross-validation approach was used to compare the performance of the three models. As shown in Fig. 7, the total time frame from 2008 to 2013 is divided into two time slices, T1 from 2008 to 2010 and T2 from 2011 to 2013. A total of five spatial splits of the watersheds are randomly clustered in both temporal slices. Two patterns have been given for the train and test slices, as indicated in the legend in Fig. 7. One validation step includes training the models in four spatial slices from one of the temporal slices and testing in a spatial slice from the other. In summary, a total of 20 iterations are used to train and test all three models in each of the slices.
Each cross-validation replication calculates AUC-ROC and mean log likelihoods for the three models and the mean values were reported. AUC-ROC is selected to evaluate the discrimination ability of the model and mean log-likelihood as a measure to estimate the model calibration. Other measures for discrimination and calibration, such as the Brier score, the C statistic, the Hosmer-Lemeshow goodness-of-fit measure and R2 measures for binary outcomes, were also used for validation and gave similar results.

The modeling strategy used in this study is described in Fig. 8. The figure shows that LR uses independent variables to estimate the model parameters linearly, which is validated over space and time. GAM, on the other hand, estimates the model parameters while considering the non-linear variation of time-dependent covariates. In the MSST-GAM, the time-dependent covariates influence transitions between latent risk states and the neighborhood structure between watersheds is incorporated using MRF. The model performance in each case was then evaluated using AUC-ROC and mean log-likelihood and the susceptibility maps are created from the model predictions.

As per the present invention, the probabilities of each model in all the time slices were collected to plot the susceptibility classes. The susceptibility is split into ten deciles based on the total percent of the probabilities. This is an extension of the quantile method of classification of landslide susceptibility and is more suitable for the dataset here as it can represent the spatial variation in high and low susceptibility values in each watershed.
The results are presented in the following order: First, the significance of the covariates in the LR model for susceptibility is described, followed by the non-linear variation of rainfall and NDVI in the GAM. Next, the transition probabilities of the same two variables for both the risk states in MSST-GAM are presented. Sequentially the performance of the three models is evaluated using AUC-ROC and log-likelihood.

The significance of the covariates in the LR model is represented using a forest plot in Fig. 9. Cubes with minimal confidence intervals that do not cross the y-axis in the plot represent the covariates that are more significant in the model. The time-varying covariates Rainfall and NDVI contribute the most to the prediction of post-seismic landslides. Significant static covariates include the two curvatures, planar and profile, lithology, aspect standard deviation and slope mean.

Rain and NDVI were the only two variables where the non-linear terms are significant and are the most important predictions in the GAM model, and therefore their non-linear relationship is shown in Fig. 10. An increase in NDVI signifies an increase in the density of vegetation, decreasing the susceptibility to landslides. On the other hand, the variation of weekly rainfall shows that landslide susceptibility increases with an increase in rainfall with a peak at 120 mm.

The variation of probability values among the risk states is captured by the box plot in Fig. 11a). Transition probabilities of the MSST-GAM as a function of rainfall are shown in Fig. 11b). In both plots, high-risk states are shown in red and low-risk states in green. If the model is initially in a low-risk state, consistent rainfall of 20 mm or more for an extended period will slowly switch the model back to the high-risk state. This can be observed in the green line of the plot, which has a gentle slope and rises in small increments. If the model is initially in a high-risk state, then with very low rainfall, the model will switch back to a low risk state. The red curve from 0 to 20 mm in the plot shows this behavior of the model. Similarly, Fig. 11c) shows the variation of the NDVI transition probabilities in both the risk states.
The performance metrics of the models are represented in Table 5. Based on AUC-ROC and Mean log-likelihood, it can be observed that the MSST-GAM performs better than the LR and GAM. The plot of the corresponding ROC of all three models is shown in Fig. 12. The performance of LR and GAM is very similar to each other, with a small improvement by the GAM. On the other hand, MSST-GAM has a much higher sensitivity but a lower specificity in Fig. 13. This can be explained by the spatial correlation in the predictions that result in increased susceptibility predictions after long periods of rain or after major debris flow events. Sensitivity is usually the set of true positive values observed in the prediction and Specificity represents the True negatives. High sensitivity of a model is preferable as it can assess the actual days in which a landslide occurs and low specificity implies the model can avoid predicting wrong susceptibility classes.

Table 5 shows that MSST-GAM has the best fit among the three models. While GAM improves the AUC-ROC by around 2% compared to LR, the MSST-GAM further improves over GAM by another 2%. The MSST-GAM model considers the previous occurrences and the neighborhood structure and improves the GAM by another 2% accuracy. Log-likelihood for LR and GAM is almost similar and MSST-GAM is observed to be far superior.
Table 5: Performance scores for all three models.
Models AUC ROC Mean Log-Likelihood
LR 0.900 0.0284
GAM 0.919 0.0275
MSST-GAM 0.941 0.0343

Therefore, the present invention provides an innovative model to predict landslide susceptibility while incorporating temporal and spatial relationships of the landslide occurrence. It is clearly illustrated that MSST-GAM gives better susceptibility prediction than the other commonly used statistical models, such as the LR and GAM. In this model, temporal dependencies are incorporated by using a sequence of hidden risk states, while neighborhood structure incorporates spatial relationships. In terms of model performance, this leads to a much higher sensitivity as landslides tend to occur in clusters and can affect nearby slopes. MSST-GAM can handle the complex correlation among the co-variables to predict the future chain of events with the memory of past landslide events and their contributing factors. The detailed multi-temporal dataset has been used as an input for the MSST-GAM to improve the existing models. This is reflected in the model’s overall performance as measured by the AUC ROC and mean log likelihood as shown by the results.

While the model’s overall performance is essential, it is also important to look at predictions in eventful weeks. To compare the performance of the models in specific weeks in corresponding time slices, the susceptibility maps generated by them are presented within the same time window. Figs. 12 and 13 show the actual distribution of landslides and the predicted susceptibility classes for one week in each time slice T1 and T2. The week chosen in T1 (denoted by WT1) was such that there were a large number of landslides, while the week selected in T2 (denoted by WT2) had a small number of landslides. While the subfigures a) show the actual landslide distribution in each case, the subfigures (b), (c) and (d) show the susceptibilities according to LR, GAM, and MSST-GAM, respectively.

From Fig. 13b) and c), for WT1, it is seen that the LR and GAM models predict higher susceptibility values for landslides in Wenchuan county and low susceptibility in Beichuan county. This is in stark contrast to the actual distribution of landslides. On the other hand, Fig. 13d), clearly indicates that the MSST-GAM predicts higher susceptibility in Beichuan county and correspondingly lower values in Wenchuan county, which is in line with the actual landslide distribution (Fig. 13a). On closer inspection of Fig. 13d), it can be observed that the MSST-GAM even gives better susceptibility estimates in isolated catchments in Mianzhu, Pen gzhou, and Wenchuan counties.

In WT2, Fig. 14a) shows the sparse distribution of debris flows, with most of them occurring in the Anxian, Mianzhu, and Pengzhou counties and one debris flow in the Wenchuan county. As shown in Fig. 14b), the LR model predicts very high susceptibility in northeastern parts of Bei chuan county and lower estimates in Pengzhou, Mianzhu, and Wen chuan counties. GAM on the other hand, predicts well in the Pengzhou, Anxian and Mianzhu counties but also predicts medium susceptibility values in several regions of Beichuan county (orange patches) where no actual landslides occurred.

Like the GAM, the MSST-GAM predicts very well for the Pengzhou, Anxian and Mianzhu counties. In addition, unlike LR and GAM models, the predicted susceptibility values for MSST-GAM in the northeastern regions of Beichuan county are low, which is in agreement with the actual data. Interestingly, the MSST GAM also accurately estimates high susceptibility values in a small region within Wenchuan county, where one landslide point was observed. However, it also predicts medium susceptibility in neighboring watersheds where no landslides occurred.

The above results can be better understood by looking at rainfall distribution during and before WT1 and WT2, as shown in Figs. 15 and 16. As can be seen in Fig. 15a), although a lot of rainfall was observed throughout the study area during WT1, the heaviest rainfall occurred in patches. It is clearly seen that LR and GAM predictions closely followed the highest rainfall for that week. On the other hand, MSST GAM considers that the Beichuan region also received heavy rainfall in the weeks before the landslides (Fig. 15b) than just during WT1. Therefore, the model is not misled by the peak rainfall during WT1, like LR and GAM. It is clear that MSST-GAM is more accurate than LR and GAM in predicting susceptibility. The model considers the temporal evolution of rainfall in its predictions. At the same time, it also considers the spatial distribution of landslides in Wenchuan county to predict high susceptibility in the watersheds that experienced landslides.

Fig. 16a) shows that during WT2, the predictions of the LR and GAM model show a close correlation with heavy rainfall during the week of consideration. In the LR model, odds ratios linearly increase with rain fall which is not in line with the observed landslide points as shown in Fig. 14a). This leads to incorrect predictions in the eastern regions of Beichuan for LR. In contrast, for the GAM model, the influence of rainfall over regression coefficients saturates after 120 mm (Fig. 10). This leads to a slightly better performance of GAM over LR. Still, GAM falls short in its prediction in Beichuan. The MSST-GAM, on the other hand, also incorporates rainfall from the prior weeks (Fig. 16b) and does not solely rely on the rainfall during WT2 for its predictions. Because of this, the MSST-GAM predicts moderate susceptibility in Wenchuan and the northwestern part of Beichuan county due to significant rainfall in these regions in the previous weeks. Thus, MSST GAM shows a more accurate prediction over GAM and LR.

Fig. 11c) shows the contribution of NDVI to the risk states for MSSTGAM. As mentioned earlier, an increase in vegetation stabilizes the slope and decreases the chance of landslides. NDVI exhibits a more minor influence than rainfall in the model. This could be study area specific, as studies in other parts of Wenchuan have observed slopes that have lost vegetation and have experienced landslides for a decade after the earthquake. Additionally, some studies examine the variation of NDVI in other regions where the revegetation significantly improved the stability of slopes.

It is well known that topographic slope angle contributes significantly to landslide susceptibility, with the susceptibility increasing with slope angle. During the working of the present invention, in WT1, the median slope exhibiting maximum landslides was around 32.4◦ in Beichuan county, where most landslides occurred. The WT2, the median slope exhibiting maximum landslides, was 31.6◦ in Pengzhou, Anxian, and Mianzhu counties. This shows that the slopes in landslide-active counties in WT1 and WT2 contributed significantly to debris flow.

From the results of the working of the present invention (Fig. 9), it is observed that aspect mean values within catchments do not contribute to landslide risk, while Aspect standard deviation is a significant factor. This indicates an increase in susceptibility when all the slope faces in a watershed are along a particular direction.

The individual contribution of the slope aspect cannot be used as a major predictor of susceptibility. The curvature also affects the stability of the slope by accumulation of flow within the watersheds. Planar curvature, which is positively correlated with susceptibility, is measured along the strike of the slope and the profile curvature is measured in the direction of the dip. More convex slopes correspond to larger planar curvature values and lower profile curvature values. A convex slope is more susceptible to debris flow as water can accumulate on the slope. Fig. 9 shows that in the working of the present invention, the planar and profile curvature also show opposite effects on the susceptibility. These results are in line with the observations of some prior arts in which it was reported that convex slopes facilitate soil erosion and influence susceptibility more than concave slopes.

In general, lithological units that have low shear strength exhibit more landslide susceptibility. However, in the present case, lithology did not influence susceptibility to a large extent (Fig. 9). This could be because most of the watersheds in the present study area have similar lithology. Most of the landslides observed in Beichuan and Wenchuan counties are abundant in mixed sedimentary rocks having moderate strength. Besides the covariates discussed above, other static covariates only had an insignificant effect on the model.
The hardware components that form part of the system (S) of the present invention that form part of the system (S) are as enumerated below:
Data Processing of the invention is performed on computer with specifications such as but not limited to 8GB RAM, 500GB Hard Disk, Intel core i5 processor.
Power (Po) and storage units (So) may be connected to said computer for smooth operation of the system (S). The storage unit (So) may have a storage capacity of 100 GB or above.

As per an embodiment of the present invention, the other components and their details that form part of the system are as enumerated below:
Availability of data: -
The Multi temporal inventory used in this study is available from https://doi.org/10.5281/zenodo.1405489.

Software: -
Description: Code for fitting the MSST-GAM
Language: R programming language
Libraries required: hmmTMB, https://cran.r-project.org/web/packages/hmmTMB/index.html.
Availability: https://github.com/aadityanphd/msst_gam.

 
, C , Claims:We claim:
1. A system (S) for spatiotemporal landslide susceptibility mapping in a predefined region of interest, said system (S) comprising of:
- at least one data acquisition module (A01, A02,…, An) for acquiring data for landslide susceptibility mapping in said predefined region of interest for a pre-determined period of time, said data acquisition module (A) comprising of:
o at least one rainfall data submodule (A101, A102,…, A1n) to obtain rainfall data of said region of interest from a rainfall data base,
o at least one NDVI data submodule (A201, A202,..., A2n) to obtain NDVI data of said region of interest from vegetation repositories,
o at least one terrain information submodule (A301, A302,…., A3n) for obtaining terrain attributes of said region of interest from Digital Elevation Model (DEM)s,
o at least one watershed information submodule (A401, A402,…., A4n) for obtaining watershed properties in the region of interest from DEMs,
o at least one lithological information submodule (A501, A502,…., A5n) for obtaining lithological data of said region of interest from a lithological database and
o at least one multitemporal inventory (A601, A602,……, A6n) for obtaining data related to landslide occurrences or watershed properties in the region of interest;
- at least one processing module (P01, P02,.., Pn) for receiving, preparing and processing said acquired data from said data acquisition module (A), said processing module (P) comprising of:
o at least one preprocessing submodule (P101, P102,.., P1n) for receiving and preparing said acquired data in the form of covariates,
o at least one advanced statistical prediction tool (P201, P202,…, P2n), for processing of said prepared data to obtain results in the form of landslide mapping and predictions and
o at least one programming tool (P301, P302,…, P3n) to fit said advanced statistical prediction tool (P2);
- at least one mapping and prediction module (M01, M02,…, Mn), said mapping and prediction module (M) comprising of:
o at least one display submodule (M101, M102,…, M1n) for displaying said results of landslide mapping and predictions and
o at least one user interface submodule (M201, M202,…, M2n) for facilitating display of said results and user interaction;
- at least one computing unit (C) that accommodates and facilitates the operation of said data acquisition module (A), processing module (P) and mapping and prediction module (M) and
- power (Po) and storage unit (So) connected to said computing unit (C) for operation of said system (S)
wherein
- said advanced statistical prediction tool (P2) of said processing module (P) of said system (S) incorporates both spatial and temporal dependencies by integrating a plurality of statistical models in specific configuration,
- said advanced statistical prediction tool (P2) of said processing module (P) incorporates temporal dependencies by utilizing and applying a statistical model, that estimates the outcome of a certain event using risk states, such as but not limited to Hidden Markov Model (HMM),
- said advanced statistical prediction tool (P2) of said processing module (P) incorporates non-linearity in prediction by utilizing and applying statistical model, such as but not limited to Markov Switching Generalized Additive Model (MS-GAM), that includes non-linear dependence of independent variables with dependent variables,
- said advanced statistical prediction tool (P2) of said processing module (P) incorporates spatial dependencies by utilizing and applying statistical model such as Markov Random Field (MRF) to model the neighbourhood structure in said region of interest,
- said advanced statistical prediction tool (P2) of said processing module (P) predicts risk state sequence using nonlinear functions of covariates to include rainfall and NDVI and
- said data acquisition module (A) acquires and provides optimum number and combination of static and temporal covariates for efficient landslide mapping and prediction
thereby enabling said system (S) to perform a spatiotemporal landslide susceptibility mapping that is accurate, consumes lower computational time, captures intricate patterns and relationships in the data, is easy to interpret, is robust, flexible and cost effective in assisting professionals in hazard forecasting, estimation and management of landslides.
2. The system (S) as claimed in claim 1, wherein said rainfall data in rainfall data submodule (A) is obtained from rainfall data base selected from group of geospatial analysis platforms and remote sensing facilities such as but not limited to CHIRPS from Google Earth Engine (GEE), Global precipitation measurement (GPM) by NASA, site specific rain gauge datasets (if available) etc., preferably CHIRPS from GEE.
3. The system (S) as claimed in claim 1, wherein said NDVI data is obtained from vegetation repositories selected from remote sensing facilities such as MODIS repository, Landsat series from USGS, Advanced Very High Resolution Radiometer (AVHRR) on NOAA, preferably MODIS repository.
4. The system (S) as claimed in claim 1, wherein said terrain information submodule (A3) obtains terrain attributes from Digital Elevation Model (DEM)s obtained from database selected from group of remote sensing earth science data and information systems such as ALOS PALSAR, SRTM 30 m DEM, high accuracy DEM obtained by field investigations using LiDAR or 3D Photogrammetry, preferably ALOS PALSAR.
5. The system (S) as claimed in claim 1, wherein said watershed information submodule (A4) obtains watershed properties from DEMs or multitemporal inventories.
6. The system (S) as claimed in claim 1, wherein said lithological data is obtained from lithological database selected from GLiM, site specific lithology maps, other web based databases, preferably GLiM.
7. The system (S) as claimed in claim 1, wherein said multitemporal inventory (A6) is selected from inventories available on landslide affecting hazards in the region of interest such as but not limited to inventories recording the earthquakes in said region, repositories from sciencebase.gov, zenodo.org or any other journal websites etc.
8. The system (S) as claimed in claim 1, wherein said advanced statistical prediction tool (P2) is encoded in programming languages selected from group of python, C, C++, SPSS, statistical computing and data visualization languages such as R language, etc. preferably R language.
9. The system (S) as claimed in claim 1, wherein said risk states of rainfall and NDVI are utilized as hidden states for generating at least one HMM state transition probability matrix.
10. The system (S) as claimed in claim 1, wherein said advanced statistical prediction tool (P2) of said processing module (P) formed after integrating said plurality of statistical models in specific configuration is referred as Markov Switching Spatiotemporal Generalized Additive Model (MSST-GAM).
11. The system (S) as claimed in claim 10, wherein said MSST-GAM is defined with respect to discrete watersheds as well as watersheds of continuous space and time preferably discrete watersheds.
12. The system (S) as claimed in claim 10, wherein said MSST-GAM can be combined with physical models for landslide susceptibility mapping.
13. The system (S) as claimed in claim 1, wherein said neighbourhood structure utilized in MRF is obtained by extracting neighbourhood matrix from the shape files of the watersheds.
14. The system (S) as claimed in claim 1, wherein said time dependent or time-varying covariates and counts are segregated into a matrix of three columns per time period such as a week.
15. The system (S) as claimed in claim 1, wherein said static covariates are combined into one single matrix, with each column representing a unique covariate.
16. The system (S) as claimed in claim 1, wherein said risk states are such that for each the occurrence of a landslide would be modelled by a separate Generalized additive model (GAM) and the transitions between risk states over time are estimated from time dependent covariates such as rainfall.
17. A method for spatiotemporal landslide susceptibility mapping, the said method comprising steps of:
- acquiring data for landslide susceptibility mapping in a predefined region of interest for a pre-determined period of time by a data acquisition module (A) of a system (S), said step of acquiring of data comprising of:
o acquiring of rainfall data from a rainfall database such as Google Earth Engine (GEE),
o acquiring of NDVI data from vegetation repositories such as MODIS repository,
o obtaining terrain attributes from Digital Elevation Model (DEM)s from remote sensing earth science data and information systems such as ALOS PALSAR,
o obtaining watershed properties in said region of interest from DEMs or from multitemporal inventories of landslide related hazards in said region of interest,
o obtaining lithological data from a lithological database such as GLiM and
o obtaining spatial and temporal information on landslide occurrences from multitemporal inventories of landslide affecting hazards in said region of interest;
- receiving and preparing of said acquired data by a preprocessing submodule (P1) of a processing module (P) of said system (S) by standardizing their raster layers to match their resolution;
- preparing further of said data from preceding step by extracting raster values in the form of covariates, in specific combination of static and time dependent covariates in specific numbers, using zonal statistics from geographic information system;
- processing of said prepared data by an advanced statistical prediction tool (P2) of said processing module (P) to obtain results in the form of landslide mapping and predictions, said processing of prepared data comprising of steps of:
o receiving said prepared data as inputs by said advanced statistical prediction tool (P2),
o correlating of landslide incidences in two temporal lobes T1 and T2 by said tool (P2),
o correlating simultaneously with previous step of landslide incidences in each watershed by said tool (P2),
o performing validation of tool using spatiotemporal cross validation preferably fivefold spatiotemporal cross-validation,
o evaluating model performance using statistical measures such as for discrimination and calibration,
o performing testing of model by choosing a time period in each temporal lobe,
o obtaining probabilities for landslide susceptibility mapping and plotting predictions in GIS by the tool and
o performing correlation among said predictions and rainfall and
- displaying said predictions and correlations as obtained in preceding steps by a mapping and prediction module (M) of said system (S) as landslide susceptibility mapping and predictions and allowing user interaction.
18. The method as claimed in claim 17, wherein said fivefold spatiotemporal cross-validation is carried out by clustering randomly five spatial splits of watersheds in both temporal lobes followed by training the models in four spatial slices from one of the temporal lobes and testing in a spatial slice from the other.
19. The method as claimed in claim 17, wherein said measures for discrimination and calibration is selected from group of AUC-ROC, mean log likelihoods, the Brier score, the C statistic, the Hosmer-Lemeshow goodness-of-fit measure and R2 measures for binary outcomes, preferably AUC-ROC and mean log likelihoods.
20. The method as claimed in claim 17, wherein said probabilities of the tool are collected in all the time slices to plot susceptibility classes preferably by splitting the susceptibility into ten deciles based on the total percent of the probabilities.
21. The method as claimed in claim 20, wherein said susceptibility classes formed are by selecting from methods of classification to include natural breaks, quantiles and Head/Tail breaks, preferably an extension of the quantile method of classification of landslide susceptibility.
22. The method as claimed in claim 17, wherein said covariates are such that they are not collinear among themselves and number of covariates ranges from 5 to 20 preferably 14 to include time dependent covariates such as rainfall and NDVI.

Dated this the 30th day of January 2025
__________________________
Daisy Sharma
IN/PA-3879
of SKS Law Associates
Attorney for the Applicant

To
The Controller of Patents
The Patent Office, Chennai