Spatial Support in Landslide Hazard Predictions Based on Map Overlays

Transcription

1 Spatial Support in Landslide Hazard Predictions Based on Map Overlays Andrea G. Fabbri International Institute for Aerospace Survey and Earth Sciences (ITC), Hengelosestraat 99, 7500 AA Enschede, The Netherlands Chang-Jo F. Chung Geological Survey of Canada, 601 Booth Street, Ottawa, Canada K1A 0E8 Abstract This contribution considers the predictions of mass movements that have yet to take place and the support provided by spatial databases for the prediction. Conventional hazard maps tend to compile the neighbourhoods and dynamic types of the known past landslides, assuming that they satisfactorily represent the locations of future landslides. The latter, however, may also occur elsewhere. Spatial prediction models, instead, isolate the spatial relationships of all distinct mass movements and the presence of elementary or basic map units that accompany those movements. An operational strategy is presented that has the power to assess the degree of support provided by the combination of individual map units in the spatial databases used to compute the predictions. In particular, using validation techniques on the predictions, three aspects of spatial support assessment are considered: (1) How to interpret a prediction in terms of future landslides; (2) How much scarp area should be used to generate a prediction, or similarly, how the scarp area definition affects the analysis; and (3) How to extend a prediction to a neighbouring area. The strategy is based on the spatial validation of the prediction maps using a variety of temporal or spatial subsets of the distribution of the past landslide trigger areas. Two different application examples on the same spatial database are used to document a strategy for temporal and spatial predictions that can be adopted also in situations or models of more general nature than landslide hazard mapping 1. Introduction The representation of spatially distributed data today covers a large variety of digital products ranging from base maps with topography and infrastructures to special thematic maps containing the integrated results of computations, simulations and predictions such as mineral potential, flooding risk or landslide hazard. The trend in all physical sciences is towards digital representations based on spatial quantitative models that combine the distribution of spatial features in several monothematic maps (e.g., elevation, slope angle, drainage, surficial lithology, land use, mass movement distribution, flooding events) into a comprehensive theme (e.g., propensity to failure of the slope, flooding risk). The spatial models are to identify the physical conditions that are common to the occurrence of the events to be represented so that the

2 corresponding thematic maps can be used to define safer or more desirable land use patterns. One basic issue in the application of existing spatial models is to establish the degree of support that the various monothematic maps provide to the resulting integrated theme. Such support is unavoidably a function of the acceptable validity of the integration results. This contribution considers the predictions of mass movements that have yet to take place and the support provided by spatial databases for the prediction. Conventional hazard maps tend to compile the neighbourhoods and dynamic types of the known past landslides, assuming that they satisfactorily represent the locations of future landslides. The latter, however, may also occur elsewhere. Spatial prediction models, instead, isolate the spatial relationships of all distinct mass movements and the presence of elementary or basic map units that accompany those movements. The information on the distribution of the known mass movements and on the map units is stored and analyzed in spatial databases. Expert geomorphologists consider those units as characteristic of the geomorphologic conditions favouring or leading to the occurrence of the trigger zones of the mass movements. Spatial databases, however, only partially represent those conditions. Therefore, the results obtained from them have to be validated. Examples of prediction models applied to landslide hazards have been discussed by the authors during the past six years (Chung et al., 1995; Chung and Fabbri, 1998, 1999, and 2001a). Emphasis has been initially placed on the predictive models for which a unified and general framework has been proposed and termed Favourability Function by Chung and Fabbri (1993). FF models can be based on probability, belief or fuzzy set theories, depending on the interpretation of the relative frequencies of the observed events (the individual dynamic types of landslide) and of the corresponding or accompanying factors observed in their neighbourhoods (slope, land use, soil type, lithology, etc.). More recently the emphasis has been directed towards the application strategies that allow coping with varying data quality, quantity and spatial distributions (Chung and Fabbri 2001b; Fabbri et al., 2001; Remondo et al., 2001). The mathematical models have been developed and applied to landslide hazard mapping using geographical information systems as computational platforms. The models generally assume that: (a) spatial databases are used that contain information of quality and quantity to allow estimating the predictions; (b) satisfactory prediction methods are available; (c) a feasible strategy is selected to generate and interpret the predictions; and (d) explicit arguments can be provided to communicate the prediction results to decision makers. This contribution discusses an operational strategy that satisfies those model assumptions and that has the power to assess the degree of support provided by the combination of individual map units in the spatial databases used to compute the predictions. In particular, three aspects of spatial support assessment are considered: (1) How to interpret a prediction in terms of future landslides; (2) How much scarp area should be used to generate a prediction, or similarly, how the scarp area definition affects the analysis; and (3) How to extend a prediction to a neighbouring area. The strategy is based on the spatial validation of the prediction maps using a variety of temporal or spatial subsets of the distribution of the past landslide trigger 2

3 areas. The empirical validation allows the extraction of the support by data mining, i.e., the exploration of the combined presence of the map units and the frequency of occurrence of the mass movement neighbourhoods. The validation identifies the added value of the information (presence of the map units) enabling to infer their causality or causal factor properties. Two different application examples on the same spatial database are used to document a strategy for temporal and spatial predictions that can be adopted also in situations or models of more general nature than landslide hazard mapping or zonation. 2. The Fabriano case study in central Italy A first study of the Fabriano area in central Italy has been documented by Luzi and Fabbri (1995). The area is affected by earth-and-debris-flow dynamic types of landslides and a database compiled by Luzi (1995) was used to generate landslide hazard-zonation maps. Its geographical coordinates are longitude E , latitude N (upper left corner); and longitude E , latitude N (lower right corner). In that spatial database it was pretended that the time of the study was the year 1955 and that all the spatial data available in 1955 were compiled including the distribution of the landslides that had occurred prior and up to that year. These were used to construct the fuzzy set membership function between the distribution of the two undivided dynamic types of landslides and the remainder of the input data set of causal factors. The predictions based on the membership functions were validated by comparing the map pattern of predicted hazard classes with the distribution of the landslides that had occurred after 1955, i.e., during the period The landslide hazard prediction at each point in the data set is considered as a member of the fuzzy set consisting of the fact that: the point will be affected by a future landslide given the information from the supporting input data at that point. Chung and Fabbri (2001b) have discussed the use of fuzzy set theory in favourability-function modeling of landslide hazard. Of the many layers of spatial data collected by Luzi (1995), the following six are significantly related to landslide hazard: (1) engineering geology map units; (2) slope angle map classes; (3) aspect angle map classes; (4) land use map classes; (5) classes of distance from the nearest drainage lines; and (6) classes of distance from fault lines. Each map layer was digitized from 1:50,000 and 1:25,000 maps into images consisting of 922x515 pixels (= 474,830 pixels) where each pixel corresponded to a 30m x 30m area on the ground. In this application example, the database was cropped to a smaller rectangular sub-area of 870 x 490 pixels (= 426,300 pixels) and the two dynamic types of landslides, earth flows and debris flows, have been grouped into one consisting of 123 separate mass movements. Plate 1 shows the distribution of the 123 earth-and-debris flows in the Fabriano study area in central Italy, on the background of the elevations of the digital elevation model (DEM). In the illustration a separation has been made between the pre-1955 and the post-1955 landslides (i.e., between 1956 and 1993) and between the full 3

4 scarps and the topographically highest 50% of the scarps of the landslides. In addition, the study area has been subdivided into an upper (northern) sub-area and a lower (southern) sub-area of exactly the same size (see Plates 4 and 5). The following two applications will take advantage of those time and space partitions. 3. Assessing temporal relevance of predictions Strictly speaking, a prediction is a representation of what will happen in the future. To have significance in time, a spatial database for landslide-hazard zonation should provide the time intervals in which the landslides have occurred. By separating in time both the groups of landslides and the map units that accompany them, the corresponding dated spatial relationships can be assessed with favourability-function models. They generate a prediction that applies to the time interval used to validate it (Chung and Fabbri, 1999). For instance, Plate 2 shows a prediction of landslide hazard in the Fabriano study area using the full pre-1955 landslide scarps (red/yellow areas in Plate 1), and Plate 3 shows a similar prediction using the topographically highest 50% of the same scarps (the corresponding yellow areas only). For simplicity from now on, we will refer to them as full scarps and reduced scarps, and pre-1955 and post-1955 landslides, respectively. While the prediction results in Plate 2 are based on the pre full scarps, those in Plate 3 are based on the pre-1955 reduced scarps. For visualization in the prediction images, the fuzzy-set membership-function predicted values, ranging from 0 to 1 at each pixel, were sorted in ascending order. The pixel with the largest predicted value was given the value 1/426,300 or % and the value 1 or 100% was assigned to the pixel with the smallest predicted value. The top 1% predicted class consists of all the pixels whose revised values are smaller than 0.01 or 1% and it occupies 1% of the whole study area. Similarly the top 5% predicted class is based on all the pixels whose values are smaller than Successive colours of a pseudo-colour look-up table were then assigned to 5% subdivisions: purple indicating the highest values and blue the lowest values. This is shown by the colour bar beside the illustrations in Plates 2 through 5. A way to assess and study the behaviour of the prediction, in one or more experiments, is to compute a function to relate those revised pixel values ranging 0 and 1 to the distribution of landslide scarps. To validate the prediction results in Plate 2 then, the distribution of the post-1995 full scarps (landslides) was used and the prediction rate curve, shown in Figure 1, was computed. Full scarps were used to generate the prediction in Plate 2 based on the fuzzy set algebraic sum operator (see Chung and Fabbri, 2001b for a discussion of the fuzzy sets as Favourability-Function models). The predictions were computed by using the 93 pre-1955 landslides and were subsequently validated by using the 30 post-1955 landslides. Figure 1 shows the prediction-rate curves obtained by comparing the prediction map in Plate 2 with the distribution of the full scarps of the post-1955 landslides, shown in Plate 1. It is a cumulative distribution function. To compare the landslide distribution and one particular class in the prediction map, the overlap 4

5 between the landslide and the class can range from 0% to 100% of the landslide scarp. If we assume that the landslide in the post-1955 (group) is predicted by the class if only one pixel of its full scarp is contained by the class, then the predictionrate curve shown in Figure 1 is orange and labelled One pixel. If we assume that the post-1955 landslides are predicted by the class, when 100% (all) of its full scarp is contained by the class, then the prediction-rate curve is blue and labelled as All pixels. Similarly, other curves in Figure 1 have different colours and are labelled as 10% to 90%. From many experiments on this database and on other ones and in the authors experience, a 50% containment of the scarps within a class seems to be a reasonable median representation. This representation will be used in the remainder of this contribution. In Figure 1b, when we use the green curve as the prediction-rate curve, we can see that the top 15% class predicts approximately 75% of the post-1955 landslides. In establishing a spatial relationship between a landslide scarp (or trigger area) and the corresponding units in the accompanying map layers, it becomes important to isolate the scarps from the rest of the scar that also contains the deposit (i.e., the mass that has moved from the scarp). Such a separation is also critical where the distribution of the validation landslides is used to generate the prediction-rate curve. It leads to the next experiment. Whenever this descriptive aspect of the landslides is not anticipated during the data collection in the field, experiments such as the ones made in Figures 1 and 2 become essential. The reduced scarps were used to generate the prediction in Plate 3 but using the same model as in Plate 2, the fuzzy set algebraic sum operator. The prediction was also computed by using the 93 reduced scarps of the pre-1955 landslides and was subsequently validated by using the 30 post-1955 landslides. The difference was that in the prediction in Plate 3 the reduced scarps were used (instead of the full scarps for Plate 2) to evaluate the effectiveness of the prediction with respect to the future landslides. The two prediction images were compared with the distribution of 50% of each of the post-1955 landslides (with respect to the corresponding full and reduced scarps) and the statistics obtained from the comparison are shown in Figure 2. In the illustration the two prediction-rate curves exhibit a similar pattern in which they intersect at several points. The green Plate 2 prediction-rate curve is also shown in Figure 1 where it is labelled 50%. The red Plate 3 prediction-rate curve will be used as a term of comparison in the next application. As shown in Figure 2, if we consider as satisfactory the result of 83% (Plate 3) or 97% (Plate 2) of the post-1955 landslides contained in the top 20% predicted class, the prediction looks ahead 38 years, i.e., from 1956 to All that we can empirically say then, is that in time we are able to predict for the next 38 years (using the Uniformity Principle assumption!). Should we use all the available 123 scarps, although we would not be able to validate the results, we could only hope that the prediction would apply to the subsequent 38 years. This application considers a time subdivision of the spatial database to generate statements or predictions from one time slice to another that follows. We can say that it assesses the time robustness of the prediction. An additional problem is to extend the prediction in space, i.e., given the data in our study area, to apply the results to an 5

6 adjacent geologically and geomorphologically similar area. A different strategy can provide such space robustness and is exemplified in the next application section. 4. Assessing spatial relevance of predictions The second application to the study area aims to establish whether and to what extent a prediction can be extended, in space, to neighbouring areas with similar geomorphology or geology. A different predictive strategy can be followed in which spatial partitioning of the study area and of the corresponding database is of assistance. It represents a form of data mining where the study area and the respective database are subdivided into two or more parts so that the spatial data from one part is used to compute the prediction over the entire area, and the scarp distribution from another part is used to validate it. Then, the predicted parts that can be validated can be assembled into a mosaic of predictions. To illustrate this strategy, let us consider two landslide hazard representations in which the same parts of the database are used but for different computations. The Fabriano study area has been subdivided into an upper (northern) sub-area and a lower (southern) sub-area. This was because the geological trend runs in the north-south direction so that greater similarity exists between north-south than eastwest sub-areas, and the corresponding database subdivisions. Plate 4 shows a first experiment of spatial partitioning in which all 123 landslide scarps known to have occurred have been used as follows: (i) the 59 reduced scarps distributed in the upper sub-area together with the corresponding spatial data base were used to compute the upper sub-area favourability function, and (ii) similarly the 67 scarps in the lower sub-area with the corresponding spatial data base were used to compute a second function, the lower sub-area favourability function. We can assemble them into a mosaic of the two representations, as was done for Plate 4, however, that is not a prediction that can be validated to provide an empirical measure of its significance. That has to be obtained differently as follows. A second mosaic of two favourability-function representations is shown in Plate 5. It has been generated by using the prediction model from the lower sub-area favourability function to predict in the upper sub-area. Similarly, the prediction model from the upper sub-area favourability function, was used for the lower subarea. For this reason, the image in Plate 5 is a true prediction and its validation is shown in the prediction-rate curve of Figure 3. In the illustration it can be seen that the top 20% predicted class contains 88% of the reduced scarps. The blue line was tagged with All landslides to stress that all the available information in the database was used, but that was with a strategy that allows validation, differently from what was done to obtain Plate 4. The Plate 5 spatial prediction and the corresponding prediction-rate curve in Figure 3 provide a measure of spatial robustness. It is logical to assume that the result applies to adjacent areas to the south and to the north if similar geological/geomorphological conditions are expected. At this point in the analysis, we may wonder how this prediction in space, that provides a measure of spatial significance for neighbouring areas, compares with the temporal prediction in the previous section. Again, the prediction-rate curve is of 6

7 assistance, so that in Figure 3, beside the blue All landslides curve, we can plot the red line (also shown in Figure 2) for the prediction in time in which the post-1955 landslide scarps were used for validation. The similarity of the two curves, 88% versus 83% validation, respectively, for the top 20% predicted class, verifies that the predictions are robust in time and in space. The similarity is in terms of the data-layer units, and the scarps, that are present in the sub-areas. 5. Concluding remarks In this contribution we have exemplified how data mining can be used to assess the degree of support provided by the spatial data that were used to represent the physical conditions in the neighbourhoods of the known landslides and to extrapolate them to those of other unknown or of future landslides. The validation techniques used here have assisted in: (1) interpreting the predictions in terms of future landslides; (2) providing a test of how the scarp area can affect the analysis; and (3) extending a prediction to neighbouring areas. In the first application example, data mining can help in isolating the portions of the landslide scars that correspond to the trigger areas of the mass movement and that generate relatively better predictions with respect to the validation set of landslides. In the second application example we have seen how the study-area sub-divisions constrain the spatial support in predictions in which a sub-area for computing the prediction and another sub-area is used for validating it. Alternatively, when time partitioning of the landslide distribution is not possible or available, a random spatial partition of the known landslides can be used to compute the prediction and another to validate it. Again, the degree of support of the partitions and of the spatial data layers can be assessed by validation. Owing to the spatial partitioning of the landslide distribution in the second example, the data-mining strategy provides some empirical measures of support in the prediction of where the landslides are likely to occur. Owing to the time subset of the known landslide scarps in the first application example, the data-mining strategy predicts, to a limited extent, when the future landslides are likely to occur, i.e., where they are likely to occur in the more recent time interval (38 years). A prediction strategy aiming at establishing where and when would require a detailed compilation of the years in which each landslide took place and also of the spatial data sets of the corresponding vintage. We must stress that significance of the prediction is only within the validation results or degree of satisfaction for the spatial matching of hazard ranges and the relative distribution of validation landslide scarps. Different predictions for different time intervals would represent true time predictions. At present, this points at an added value in old air-photograph coverage s and of base and thematic maps that could be established through validations of prediction models. Similarly, this can be envisaged for the current or future cartographic products. The authors are continuing in such a research endeavour (Remondo et al., 2001). 7

8 Acknowledgements This research work was partly financed by the following two Projects of the European Community: NEWTECH, Contract ENV-CT (CEC Environment Programme), and GETS, Contract ERBFMRCT (CEC Training & Mobility of Researchers Programme). One of the authors (CFC) is presently supported as a visiting professor by a Foreign Researcher Fellowship at the Institute for Environmental Sciences of the University of Tokyo, Japan. References Chung, C. F. and Fabbri, A. G., 1993, Representation of geoscience data for information integration. Jour. of Non-renewable Resources, v.2, no. 2, p Chung, C. F., and Fabbri, A. G., 1998, Three Bayesian prediction models for landslide hazard. In, A. Buccianti, ed., Proceedings of International Association for Mathematical Geology 1998 Annual Meeting (IAMG 98), Ischia, Italy, October 3-7, 1998, p Chung, C. F., and Fabbri, A. G., 1999, Probabilistic prediction models for landslide hazard mapping. Photogrammetric Engineering & Remote Sensing (PE&RS), v. 65, no.12, p Chung, C. F., and Fabbri, A. G. 2001a, Validation of spatial prediction models for landslide hazard mapping. Natural Hazards, in press. Chung, C. F. and Fabbri, A. G., 2001b, Prediction models for landslide hazard using fuzzy set approach. In, M. Marchetti and V. Rivas, eds., Geomorphology and Environmental Impact Assessment, A.A. Balkema, Rotterdam, p Chung, C. F., Fabbri, A. G., Van Westen, C. J., 1995, Multivariate regression analysis for landslide hazard zonation. In, Carrara, A. and Guzzetti, F., eds,. Geographical Information Systems in Assessing Natural Hazards. Dordrecht, Kluwer Academic Publishers, p Fabbri, A. G., Chung, C. F., Cendrero, A., and Remondo, J., 2001, Is prediction of future landslides possible with a GIS? Natural Hazards, in press. Luzi, L., 1995, GIS for Slope Stability Zonation in the Fabriano Area, Central Italy. ITC, Enschede, The Netherlands, unpublished M.Sc. thesis, 261 p. Luzi, L. and Fabbri, A. G., 1995, Application of favourability modelling to zoning of landslide hazard in the Fabriano area, central Italy. Proc. Joint European Conference and Exhibition on Geographic Information, JEC-GI 95, Den Haag, March 26-31, from Research to Application through co-operation, v.1, p Remondo, J., González-Díez, A., Díez de Terán, J. R., Cendrero, A., Chung, C.F., and Fabbri, A. G., 2001, Strategies for landslide hazard map validation. Some examples and applications. Natural Hazards, in press. 8

9 Pre-1955 landslides (Full scarps) Post-1955 landslides (Full scarps) 50% of the scarps (Reduced scarps) Plate 1. Distribution of the 123 earth-and-debris flows in the Fabriano study area. Blue indicates the scarps of the pre-1955 landslides, and red the post landslides. The yellow colour identifies the topographically higher 50% of the scarps. The study area was further subdivided into an upper (northern) sub-area and a lower (southern) sub-area in Plates 4 and 5. Both time and space subdivisions have been used for generating predictions. 9

10 Non-Hazardous area 0% - 50% 50% - 55% 55% - 60% 60% - 65% 65% - 70% 70% - 75% 75% - 80% 80% - 85% 85% - 90% 90% - 95% 95% - 100% Hazardous area Plate 2. Time prediction of landslide hazard for the Fabriano study area in central Italy, based on the full scarps of the pre-1955 earth-anddebris flows using the algebraic sum fuzzy set operator. The colour bar identifies the pseudo-colours used to indicate successively lower predicted-value ranges in fixed area percentages of 0.5%. The same colour look-up tables have been used for Plates 3, 4, and 5. To evaluate the effectiveness of the prediction with respect to future landslides, this prediction map was compared with the 50% of the post landslides and the statistics obtained from this comparison are shown in Figure 2. 10

11 All pixels 90% 75% 50% 25% 10% One pixel Portion of study area predicted as hazardous Portion of post-1955 landslides Portion of post-1955 landslides Portion of study area predicted as hazardous A B Figure 1. Prediction-rate curves for the Fabriano study area using the 93 pre-1955 earth-and-debris flows to compute the fuzzy-set favourability function (algebraic sum operator with gamma =1). The post-1955 landslides are used for validating the prediction. In (a) the complete curves are shown that were obtained using different area percentages of the post-1955 scarps from One pixel to All pixels. In (b) an enlargement of the grey rectangle area in (a) is shown. Note that the 50% green curve is also shown in Figure 2. 11

12 Non-Hazardous area 0% - 50% 50% - 55% 55% - 60% 60% - 65% 65% - 70% 70% - 75% 75% - 80% 80% - 85% 85% - 90% 90% - 95% 95% - 100% Hazardous area Plate 3. Time prediction of landslide hazard for the Fabriano study area in central Italy, based on the restricted scarps of the pre-1955 earthand-debris flows using the algebraic sum fuzzy set operator. The colour bar identifies the pseudo-colours used to indicate successively lower predicted-value ranges in fixed area percentages of 0.5%. The same colour look-up tables have been used for Plates 3, 4, and 5. To evaluate the effectiveness of the prediction with respect to future landslides, this prediction map was compared with the 50% of the post-1955 landslides and the statistics obtained from this comparison are shown in Figure 2. 12

13 Plate 3 and 50% of the reduced scarps Plate 2 and 50% of full scarps Portion of post-1955 landslides Portion of study area predicted as hazardous Figure 2. Comparison of two predictions that used the full scarps and the reduced scarps, respectively, of the pre-1955 landslides, shown in Plates 2 and 3. Only 50% of the post-1955 scarps are used for validation. The Plate 2 and 50% of full scarps green curve is also shown in Figure 1; the Plate 3 and 50% of the reduced scarps red curve is also shown in Figure 3. 13

14 Non-Hazardous area 0% - 50% 50% - 55% 55% - 60% 60% - 65% 65% - 70% 70% - 75% 75% - 80% 80% - 85% 85% - 90% 90% - 95% 95% - 100% Hazardous area Plate 4. Representation of landslide hazard in the study area. A mosaic of two favourability functions (fuzzy set algebraic sum operator, gamma=1) generated using the restricted scarps of the 59 landslides occurring in the upper sub-area for the upper-sub-area, and the corresponding 67 landslide scarps occurring in the lower sub-area for the lower sub-area. This is not a prediction because all 123 scarps were used (i.e., no validation is possible). 14

15 Non-Hazardous area 0% - 50% 50% - 55% 55% - 60% 60% - 65% 65% - 70% 70% - 75% 75% - 80% 80% - 85% 85% - 90% 90% - 95% 95% - 100% Hazardous area Plate 5. Prediction of landslide hazard in the study area as a mosaic of two predictions. The upper sub-area used the prediction computed in the lower sub-area based on the restricted scarps of the 67 landslides occurring in the lower sub-area. The lower sub-area used the corresponding 59 scarps of the upper sub-area. This is a true prediction in space that can be validated, as shown in Figure 3. 15

16 All landslides Post-1955 landslides l Plate 5 and 50% of the reduced scarps Plate 3 and 50% of the reduced scarps Portion of landslides Portion of study area predicted as hazardous Figure 3. Comparison of the two predictions shown in Plates 3 and 5, the time and the space predictions, respectively. Note that the Plate 3 and 50% of the reduced scarps red curve is also shown in Figure 2. 16