A software approach to spatial predictions of natural hazards and consequent risks
A. G. Fabbri1, C.-J. F. Chung2 & D.-H. Jang3 1SPINlab, Vrije Universiteit, Amsterdam, The Netherlands 2Geological Survey of Canada, Ottawa, Canada 3Gong-Ju National University, Gong-Ju, Korea
Abstract
This contribution proposes the development of a computer system for spatial analysis in order to meet the requirements of predictive mapping of natural hazards. The approach is new in that it complements existing GIS and image analysis systems with advanced analytical procedures based on validation techniques to construct risk-assessment spatial representations for decision makers. A three-stage strategy has been developed that consists of: (i) construction of a hazard prediction map using spatial databases for time-partitioned distributions of “future” hazardous events, such as landslides, avalanches, subsidence or floods, and supporting data layers such as DEMs, and land use, surficial deposit, geology, geomorphology, and other thematic maps; (ii) validation/reliability of prediction results and estimation of the probability of occurrence for each predicted hazard level; and (iii) generation of risk maps with the introduction of socio-economic factors representing assumed or established vulnerability levels by combining the prediction map in the first stage and the estimated probabilities in the second stage with socio-economic data.
The approach should be interactive and provide several mathematical prediction models (fuzzy sets, empirical likelihood ratio, and multivariate statistical models such as logistic and linear models) and a variety of procedural flows for the analysis of layer-by-layer and multi-layer inputs, the generation and display of prediction-rate functions and tables, cross-validation analysis of grouped occurrences, sequentially-selected, sequentially excluded occurrences by iterative processes, and the use of the fuzzy boundary concept of class boundaries to represent spatial uncertainties. An application from a study area affected by mass movements in Korea is used to exemplify the analytical structure and modeling power implied in the software approach proposed here to provide a fundamental tool for decision making. Keywords: landslide hazard, risk, prediction, cross-validation, software, mathematical models, analytical strategy.
This contribution discusses the generation of spatial predictions via computer models and processing strategies that should be developed to overcome the limitations of past and present natural hazard/risk assessments.
Predictions here imply the partial understanding of natural processes so that the reoccurrence of their effects on society is anticipated and maps can be provided of their distribution in space, and where possible, in time. Experts make predictions based on their past experience of the natural processes and of their distribution in typical settings. The responsibilities of predictions, however, are limited by their uncertainty due to the stochastic manifestation of natural hazards, limited understanding of the natural processes and the constraints of existing digital databases.
For instance, landslides, floods, subsidence, soil erosion or earthquakes, all have basically a probabilistic character so that absolute certainty of their occurrence or reoccurrence cannot be obtained but only some relative measure of likelihood can be provided as estimates. The term hazard refers to the probability of occurrence of a damaging natural process at a given location within a given time frame. When such a process is likely to affect human activities, we use the term risk that associates the hazard intensity of the natural process with the exposure of vulnerable assets and socioeconomic activities. Vulnerability is the probability that the element at risk will be damaged when the natural process occurs and risk is the assessed level of damage in a given area due to a given hazardous event.
Clearly, we are dealing with complex situations that involve natural processes known or studied by experts and that affect socioeconomic activities managed by public administrations in charge of protecting society’s welfare and safety. Structuring complex situations is not only a technical process but also a subtle managerial and psychological task with innumerable feedbacks and repercussions. For instance, it has been customary for earth scientists and engineering geologists to produce geomorphologic compilation maps of all known landslide events because they describe the past and present occurrences of the mass movements. From such maps of geomorphologic elements, relative hazard maps can be constructed by the same experts to group into classes all the areas that are thought to have similar geomorphologic behaviour and are inferred to maintain it in the future. They are classified in terms of their semi-quantitative level of hazard, such as high, medium or low. Several examples of these relative hazard maps have been discussed in a manual by Varnes et al. (1984) [1]. Those authors represented a committee of experts that concluded that (p. 10): “Many hundreds of maps of landslides or of their deposits old or new or active, have been made throughout the world …” but there are a “far fewer number of studies that go further and attempt to assign degrees of hazard to mapped areas.” To go beyond the assessment of past hazards and seek future hazards requires a further acceptance of the responsibility to select and declare the prediction model used along with the level of certainty associated with the map of future hazards. The past hazards are mostly known, however, the future
ones are those of greater concern to society. The maps of the future hazards have to locate in space and, when possible, in time the future hazardous events, i.e., the ones that have not yet occurred but that are likely to occur within a meaningful time frame, given the quality of the prediction models used and the relative assumptions.
Let us suppose that there are experts who are willing to take such responsibilities because, with modern data capture and data processing technology (e.g., sensors, GIS and image processing systems) it is possible to systematically describe the landscape properties by integrating spatial data layers (geology, soil, land use, land cover, elevation, slope, insolation, interpreted aerial photographs that show the distribution of past hazardous events, etc.). How can they provide public administrations and developers with representations that assist in taking action on differential land uses and land values? How can the technical know-how be shared with non-experts decision-makers?
A review by the authors [2] has found very few examples of hazard prediction maps and most of them are affected by limitations that make them hardly usable in practice by decision-makers. The impression is that the current practice in hazard maps is of hiding the facts, of failing to perform and use systematic evaluations of hazards and risks, of refusing to release spatial estimates for fear of the social impact and of consequent misunderstandings. The consequence of this is the ignorance of the laymen, or of the “electorate” who cannot then force the decision-makers to greater transparency and responsible management of natural disasters by prevention and mitigation.
To overcome such an impasse, a new approach was sought by the authors who provided initially a mathematical unified framework to predictions models in spatial analysis [3], and later proposed new analytical strategies based on cross-validation techniques [4]. Validation provides not only a means of checking the reliability of the prediction results, and interpreting and comparing them, but it can be used to estimate the probability of occurrence of future hazardous events given some realistic scenarios related with the risk evaluation. The additional introduction of socioeconomic data layers in parallel with the scenarios, allows a totally new representation of the risks that is compatible with the evidential support needed by decision-makers in the public and private administrations.
Recently, a Spatial Prediction Modeling System has been developed to follow in part the new approach proposed here. That system will also be described in this contribution. First the overall analytical strategy is presented, to be followed by a description of an ideal set of requirements and of the proposed software that is GIS independent. Then an application is discussed that provides an account of the operational power of the system.
2 The strategy
The mathematical background to general purpose spatial prediction models has been discussed by [3] who used the term Favourability Function, FF, to indicate a unified framework for spatial databases that represent the distribution of mapping units, of either categorical or continuous data, and the corresponding
distribution of future events such as resource discoveries, or hazardous occurrences, or negative environmental impacts. As further discussed [5, 6, 7 and 8], several representations can be used as FFs, for example the probability functions, the likelihood ratio functions, the Dempster-Shafer belief functions, and the Fuzzy set membership functions. For simplicity the application to follow will use the Fuzzy set membership function as a prediction model [7]. The selection of a prediction model is part of an overall analytical strategy proposed for landslide hazard zonation [4, 9, and 10].
In landslide risk assessment, the risk, R, at a given sub-area S, is defined by the following expression: R = E ⋅ V ⋅ H, where E is the element at risk in S, such as population, economic activities and/or infrastructures, V is the vulnerability, expressing the degree of loss of the element at risk resulting from the occurrence of a landslide, and H is the probability of the occurrence of a future landslide within a specified period of time in S. We are proposing a three-stage strategy, to risk assessment, farther subdivided in steps as describe below.
Stage 1: HAZARD MAP PREDICTION - Construction of a landslide hazard map dividing the study area into a number of classes by using a Favourability Function technique. Each class shows the relative hazard of occurrences of future landslides.
Step 1.1 Input data preparation to generate the causal data layers and the distribution of homogeneous landslide dynamic types;
Step 1.2 Estimation and prediction using one of the FF models to generate the hazard classes.
Stage 2: ESTIMATION OF PROBABILITY, H - In each sub-area (class), estimate the probability that future landslides will occur in the class through a cross-validation technique under a set of assumptions and scenarios. To estimate the risk, the probability H, is the only component related to the occurrence of future landslides in the sub-area S: hence, it is the most challenging but critical requirement.
Step 2.1 Partition in time or in space of the database to obtain the estimation and the validation groups of landslides, and to validate the reliability of the prediction;
Step 2.2 Cross-validation and generation of a prediction-rate table; Step 2.3 Estimation of the probability of occurrence of landslides for each
hazard class under the assumptions of scenarios on damaged areas by future landslides.
Stage 3: RISK ASSESSMENT MAP, R - In each pixel, estimate RISKS (the expected losses in $-value and in human life) by combining, (a) socio-economic indicators (elements), such as the spatial distribution of the population density, road and housing developments, (b) the vulnerability of elements, (c) the landslide hazard map (from Stage 1), and (d) the estimated probability (from Stage 2).
Step 3.1 Generation of socioeconomic indicator layers. Each socioeconomic indicator layer to be provided as input, such as the population distribution or the road network, contains a number of categories of the element. A corresponding table should be generated containing the vulnerability and $-value of each category of the elements. How to estimate the vulnerability and the $-value of a category of the elements is not a simple task [11].
Step 3.2 Integration of socioeconomic indicators with the corresponding vulnerability/$-value tables and the predicted hazard map with the probability table to construct the landslide risk map.
Step 3.3 Visual displays of risk maps in monetary scale and as expected number of human casualties; including 3-D renderings and other contextual risk-related information.
The three-stage strategy proposed here is to overcome some of the difficulties in estimating the probabilities of occurrence of damaging natural phenomena to obtain a spatial risk assessment that can be comprehended by a decision-maker. For this, the degree of demonstrated support is critical. In the following section the desirable characteristics of a spatial prediction system are discussed.
3 The software
The strategy described above requires computer software to facilitate the representations and analyses listed in the subsequent steps. Many geographical information systems offer some processing tools that partly allow some of the steps. An integrated software approach, however, would need a variety of tools presently not available within a single platform. Next we will describe the desirable tools and then discuss a new system that, while it comes short of offering all of them, it has the potential to eventually satisfy many more requirements.
3.1 What we should have as a general-purpose spatial prediction modeling tool
Spatial data analysis for prediction modeling is the main target of processing for identifying spatial relationships that can be extrapolated in space and in time to allow risk assessments. This is obtained from multiple data layers of similar, or even varying resolutions that need to be integrated quantitatively with the guidance of expert knowledge. The assumption is that the available spatial database sufficiently describes the typical settings of the occurrences of the hazardous processes. Let us consider then, the desirable features that a spatial decision support system should have to perform hazard prediction and risk analysis.
The following is a list of desirable software features:
(1) Easiness of use by earth scientists; (2) Practical transfer of spatial and tabular data in and out of the system;
(3) Ability to work under a common platform and operating system in conjunction with existing GIS, image processing systems, spreadsheets and other statistical packages;
(4) Permit the simultaneous analysis of continuous and thematic data layers without a conversion of one type of data layers to the other type. For instance, most existing prediction models make use of either all thematic data layers or of all continuous data layers [12, 13, 14];
(5) Provide the basic statistical properties of each layer with and without the distribution of the occurrences of damaging phenomena;
(6) Allow the use of all or most of the existing prediction models; (7) Permit cross-validation procedures by subdividing the number of
occurrences spatially and temporally in many different ways; (8) Offer simple iterative procedures for repeated analytical tasks; (9) Allow the spatial computation and representation of vulnerability
values; (10) Perform sensitivity analysis of the contribution of the data layers for
each model; (11) Allow the comparative analysis of different prediction models; (12) Permit the identification of influent and non influent data layers in
different combinations; (13) Integrate the spatial support of mixtures of continuous and categorical
data layers; (14) Maintain the statistic links with the sequential and iterative calculations; (15) Maintain records of the processing steps for each prediction via
automated log files; (16) Allow both step-by-step analyses and pipelined procedures for
multilayer predictions; (17) Use a fuzzy boundary concept where the different resolutions (or scales)
are expressed; (18) Allow different resolutions of data layers; (19) Ability to handle different resolutions within a data layer for arbitrary
sets of features; (20) Provide input to special display and visualization programs to visit and
interpret the prediction landscapes; (21) Be available a modeling tool independently of, and adaptable to,
specific application areas. The following subsection provides a partial solution to the programming of
such a system.
3.2 A modeling system for spatial prediction: the SPMS
Because it is not yet possible to have all of the above mentioned desirable features in a single system to date, a spatial prediction modeling system, SPMS, has been programmed under the supervision of the authors, to satisfy the main desiderata (www.spatialmodels.com). The SPMS provides a set of tools that offers both pipelined and step-by-step processing sequences. It was programmed to eventually satisfy all requirements listed in the previous sub-section and
includes a Data Preparation module, DP, Spatial Prediction modeling modules, SP, a Cross Validation module, CV, and a prototypal Risk analysis module, RISK. The present capabilities of the DP, SP, CV and RISK modules are as follows.
DP allows the conversion of raw raster image files of continuous and thematic data, boundary binary images of thematic data, and occurrence data (representing the distribution of damaging phenomena possibly separated into types, periods, spatial groups, or trigger and non-trigger areas). Indexed image files can be generated for non-connected individual occurrences in the occurrence data layer.
SP associates the distribution of the occurrences and the various continuous and thematic data layers to generate the respective empirical distribution functions and thematic frequency tables. A “Spread Parameter” can be used for continuous data layers to adjust the smoothness of the empirical distribution functions with kernels or for representing the level of resolution of the continuous data layer. A “number of neighbourhood pixels parameter” is used for thematic map layers to apply the fuzzy boundary concept to class boundaries to account for image scale: this parameter is an integer value that has to be empirically determined. The choice of prediction models include: Fuzzy Set, Empirical Likelihood Ratio, Logistic and Linear, and Bayesian Prediction Models. Here several processing modes have been anticipated. The Layer-By-Layer approach examines the contribution of individual layers to a prediction. The Two-Step approach is to examine the distribution functions or the frequency tables in the analysis before choosing a prediction model, for instance adjusting the spread parameter for continuous distributions. The One-Step Multi-Layer Prediction Image Generating Programs provide a pipelined way to obtain integrated prediction images for which all the above parameters and prediction models have been selected. The result is a 32-bit Multi-Layer Prediction Image file of scores for further processing and an 8-bit prediction image file for prediction model; comparison via the prediction-rate table program and for export to external graphic display programs. Prediction-rate, empirical distribution and thematic-frequency tables can be easily converted into diagrams using a spreadsheet program. The Prediction-rate table and curve can be generated when comparing the prediction power of subsets of the occurrences for spatial or temporal partitions. A prediction-rate curve is used to validate the prediction images of a Portion of Occurrences Predicted (number of occurrences in the area divided by the total number of occurrences in the map) versus the portion of the area occupied by a given occurrence favourability (ordered progressively from the most favourable to the least). It is obtained by comparing 200 prediction classes in the 8-bit prediction image and the 16-bit indexed occurrence map, and counting the number of occurrences within each of the 200 classes.
CV, the Cross Validation module, evaluates the predictive ability of the models in SPMS, for a given data set for: User-Defined Grouped Occurrences, Sequentially-Selected Occurrences, and Sequentially-Excluded occurrences. It will repeat the prediction runs using the same input of the SP programs but using different partitions of the occurrences. Some new parameters need to be
specified. One is the fraction of occurrence pixels that must lie within a predicted occurrence-favourability class that are to be considered as a successful prediction result when validating, i.e., the minimum number of occurrence pixels coinciding with a given favourability class divided by the total number of pixels representing that type of occurrence. For the User-Defined Grouped Occurrence Programs, The Grouped Occurrence Number and File name need to be specified. The number of Sequentially Selected Occurrences is required for validation to specify the ones to sequentially include in the generation of a prediction model whose predictive value will be tested using the remaining occurrences in the file. This parameter will allow an iterative process for all possible group combinations of predictions and validations. Similarly, the Number of Excluded Occurrences is required to specify the occurrences to sequentially exclude in a prediction model whose capability to predict the excluded occurrences will be measured. This parameter, like the previous one, will start an iterative process for all possible group combinations. The 16-bit indexed occurrence file is an input to the CV programs. The Cross Validation module output is a prediction-rate table with as many columns as the groups of occurrences used.
RISK, the Risk Analysis Module uses the prediction-rate table from the cross validation to identify, the acceptable/convenient portion of the prediction-rate curve that isolates the most hazardous areas that contain numbers of predicted occurrences well above a random distribution. RISK uses the statistic of the cross validation obtained from the scenario used for estimating the probability of occurrence of the hazardous events in Stage 2 (see Step 2.3), i.e., the predicted hazard map and the estimated probability of occurrence. These are then combined with the spatial distribution of socioeconomic indicator layers and their associated value and vulnerability tables.
3.3 Considerations on the SPMS
In particular CV allows the sensitivity analysis of each prediction, and the comparative analyses of several predictions. Processing can be directed to the identification of good predictor occurrences or to the separation of “well predicted”, “poorly predicted” and “non-predicted” occurrences. Furthermore, CV can identify the better predicting models and separate the “influent” from “non influent” data layers. Another analytical aspect of the implied strategy in the system is the computation of the probability of occurrences via scenarios and the associated assumption using validation techniques. Applications of the SPMS are obviously much more general than the landslide hazard/risk example presented in the next section. Many of these issues have been discussed in previous contributions by the authors [15, 16, 17, and 18].
However, several limitations still exist. For instance, a thematic data layer may consist of several resolutions, so that different fuzziness is required within one map sheet, something that SPMS does not yet allow. Also, the SPMS interface with the most common GISs is not straightforward, and the system does not include display facilities because it assumes that a GIS, spreadsheets and other ancillary software are available on the same PC platform. Furthermore, user-tailored interfaces for specific interaction have not been programmed,
nevertheless the present interface is simple and straightforward for an analyst. The current processing tasks are limited to sets of 20 data layers of up to 2000 x 2000 pixels on a conventional PC. With all these limitations, the SPMS is the only system in existence that allows cross validation procedures in a simple manner, i.e., the key to the whole process.
To exemplify both the 3-stage analytical strategy and the potential of the system, an application in a Korean study area affected by landslides is discussed next.
4 An application example
The Boeun study area in South Korea consists of 584 km2 with 45,600 inhabitants living in 15,000 households. The available spatial database consists of digital images of 1624 x 1444 pixels of 5m x 5m resolution and contains the DEM, surficial geology, forest coverage, land use, drainage and 420 past landslides of surficial debris flow type that occurred up to the year 1997. The socioeconomic indicator layers in the database include:
(1) the distribution of population density; (2) the distribution of road networks and types of the roads, the construction
costs (such as: paved road $ 8,000/5m; and unpaved road $ 4,000/5m) and traffic density of each segment of road networks to compute the economic damages due to the interruption of the road. Figure 1 shows a simplified example of road network infrastructure data layer with two accompanying tables containing $-values and vulnerability values;
(3) the spatial distribution of buildings including houses, industrial
infrastructures, farm infrastructures, business infrastructures and types and costs of the constructions;
(4) the distribution of drainage patterns and the construction costs (such as
embankment, $ 140,000/5m; river bank 1st grade, $ 5,300/5m; 2nd grade, $ 3,200/5m; etc.).
In 1998, 44 landslides occupying approximately 2000 pixels caused
approximately $200,000 of man-made property damages, that were eventually paid by the local government, and three injuries to persons. In this case study, we wish to examine the three-stage risk assessment methodology proposed in the light of the actual damages and casualties due to the 1998 landslides using the pre-1997 data.
Stage 1. Using the spatial database including the 420 pre-1997 landslides with the Fuzzy set model, a landslide-susceptibility prediction score was generated at every pixel. Based on the prediction scores, the whole study area was divided into 200 hazard classes, each of 2.92 km2 (i.e., 0.05% of the study area). The 200 hazard classes are shown in Figure 2.
Figure 2: Landslide hazard prediction obtained in the Boeun study area,
North Korea, using 1997 data on 420 past surficial debris flow type landslides, the DEM, surficial geology, drainage and forest coverage. Image resolution is 5m x 5m pixels and size is 1624 x 1444 pixels, to cover 584 km2. The model estimates the Fuzzy set membership function using the gamma operator with gamma = 0.5 to integrate the functions of the different data layers. For each data layer, as empirical distribution function, we have used the likelihood ratio function, the ratio of the empirical frequency distribution function of the “landslide areas” and the empirical distribution function of the “non landslide areas.” The UTM coordinates of the 4 corner pixels are in Figure 5.
Stage 2. To evaluate the reliability of the prediction results, the 420 landslides were randomly divided into two groups of 210 landslides each. The second prediction map with 200 hazard classes (each class covering 2.92 km2 on the ground) was constructed using the first group of 210 landslides. These 200 hazard classes were then compared with the distribution of the second group of 210 landslides by counting their number in each class. Similarly, a third prediction map, again with 200 hazard classes, was constructed this time using the second group of 210 landslides.
These 200 hazard classes were compared with the distribution of the first group of 210 landslides, again counting the number of the 210 landslides located in each class. Using these two comparisons, the prediction-rate table and graph
were generated that are shown as black bars in Figure 3. Depending on how to randomly divide the two groups of 210 landslides each, the corresponding table and graph fluctuate slightly, but not significantly. Theoretically speaking, the black bars should provide a monotonically decreasing function but, as can be observed in the illustration, this is not quite so.
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Figure 3: The prediction-rate table of landslide hazard in the Boeun study
area, South Korea. To obtain the table, the 420 landslides were randomly divided into two groups of 210 landslides. The prediction map with 200 hazard classes was constructed using the first group of 210 landslides and each class covers 2.92 km2 on the ground. These 200 hazard classes were compared with the distribution of the second group of 210 landslides by counting their number in each class. Similarly a second prediction map, also with 200 hazard classes, was constructed using the second group of 210 landslides. These second 200 hazard classes were compared with the distribution of the first group of 210 landslides by counting their number in each class. Using these two comparisons, the prediction-rate table shown as black bars was generated. Theoretically speaking, the black bars should represent a monotonically decreasing function but, as can be observed in the illustration, class 195, for example, with value 0.038 (hosting 8 of 210 landslides) has a higher value than class 196 which has value 0.024 (hosting 5 of 210 landslides), although class 196 is considered as a more hazardous class than class 195. One way to modify the function is to lump a number of adjacent classes into new larger classes. In this way we can generate the monotonically decreasing function shown with grey bars in the background of the empirical prediction-rate table. Note that only the top 100 classes out of 200 are in the diagram.
Estimated probability that a pixel in the class will bedamaged assuming that 2000 pixels will be affected
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Figure 4: Estimated probability table of H for the risk expression: R =
E ⋅ V ⋅ H. It was obtained from the monotonically decreasing grey bars in Figure 3, assuming that 2000 pixels will be affected by the occurrences of future landslides. The graph estimates, for example, that the probability of a pixel in prediction class 200 of being damaged by a future landslide is 0.008. The assumption that the total number of pixels to be damaged is 2000 is critical to the estimation. Only the first or most hazardous 100 classes out of 200 are in the diagram.
For instance, class 195 with value 0.038 (that contains 9 of the first 210 landslides and 7 of the second 210 landslides) is greater than class 196 with value 0.024 (containing 5 of both groups of 210 landslides), although class 196 has been classified as a more hazardous class than class 195. Lumping the number of classes into a new broader class, we can easily obtain the monotonically decreasing function shown as grey bars behind the black bars from the empirical prediction-rate table.
Stage 3. As a realistic scenario, we assume that 2000 pixels will be affected in 1998. Using the monotonically decreasing function shown as grey bars in Figure 3, we estimate the conditional probability of the occurrence of future landslides at each pixel from each class. The estimated probabilities are shown in Figure 4. For instance, the estimated probability that a pixel in prediction class 200 will be damaged by a future landslides is 0.008, assuming that the total number of pixels to be damaged is 2000. We will combine the estimated probability and the prediction map obtained in Stage 1 with the socioeconomic data layers using the expression R = E ⋅ V ⋅ H. We have obtained two risk maps, casualty-risk map and risk map to man-made infrastructure. The latter map is shown in Figure 5.
Figure 5: Risk assessment for man-made infrastructures in 1997 for the Boeun study area, South Korea. The risk map at the top was placed on an enhanced DEM. A fatality took place in 1998 in the damaged house located in the black square and shown at the bottom. The inset in the middle left is an enlargement of the sub-area close to the damaged house. The inset in the middle right is the corresponding population density map also containing the distribution of buildings. The property damages amount to $ 200,000.00 US., i.e., less than one $ per pixel in the top class! While the risk seems low for individual 5m x 5m pixels, R is spread all over the area. Collectively R is high: only the expression per pixel seems low. Once we have an accident, the risk becomes high. Compare with a car insurance: on individual basis risk is low but after an accident it become high. At the house at the bottom the risk is relatively high.
The total expected costs were estimated as $106,396.80, i.e., about half of the actual damages of $200,000 that had been paid out by the local government. The three highest expected costs of damages were to the houses, estimated as $31,041.16, to the road networks, estimated as $34,280.19, and to the traffic blockages, estimated as $30,710.91. The estimated damages due to business, farms, and industrial infrastructures were not significant. This was because the locations of those infrastructures are far from the hazardous areas. The fact that the estimated damages are about half of the actual damages paid out by the government indicates that either the estimated probabilities are too small or the damages paid by the local government are much higher than the actual costs of the infrastructures. However, the total expected casualties were estimated as 3.14, almost coinciding with the actual casualty number of 3. Classes 117 to 134 are the most hazardous, and not classes 180 to 200, because the lower population densities in the areas corresponding with classes 178 to 200. The house damaged shown in the inset of Figure 5 is in hazard class 124. This is the location of one of the casualties reported.
Owing to the fact that the estimated casualties are almost identical to the actual casualties, the estimated probabilities of the pixels should be considered as "reasonable." It may imply that the discrepancy between the estimated infrastructure damages and the actual $-value paid by the local government was mainly due to the fact that the damages paid were to include not only the costs of the infrastructure damage but also the maintenance and other associated costs such as that of the content of the buildings. Another interesting observation is that the high risk areas do not correspond to the most hazardous classes identified by the prediction models. This is because only a few socioeconomic infrastructures exist in the high hazard areas. The highest risk areas are in fact the middle hazard areas predicted by the analysis.
5 Considerations on requirements and assumptions
This contribution has discussed the need for a software approach that can provide evidential support of spatial predictions to be used by decision-makers. A 3-stage strategy for prediction modeling was proposed that puts the emphasis on cross validation to estimate the probability of occurrence of hazardous events for risk analysis via the introduction of scenarios and socioeconomic data into spatial databases. This requires the assumption of how many pixels will be damaged in the future. Such an assumption should not be looked upon lightly: it requires solid historical data. Without such an assumption, that probability cannot be estimated.
Furthermore, it is important not to forget that prediction models, like most models, are only a simplified version of a complex reality, in this case the natural processes. In real life things are bound to be different. For this particular reason, all models need cross validations to maintain scientific significance. In this way, we make no assumptions but just empirically account for their presence and distribution.
This research is being partly supported by a research network project on the “Assessment of Landslide Risk and Mitigation in Mountain Areas, ALARM” (Contract EVG1-CT-2001-00038) of the European Commission’s Fifth Framework Programme (http://www.spinlab.vu.nl/alarm). This research was also partly supported by the Gong-Ju National University that granted a one-year fellowship to Dr. Dong-Ho Jang as visiting scientist with the Geological Survey of Canada. Additional partial support was provided by the “Sustainable Development Through Knowledge Integration” or SDKI Program of the Pathways Project of Natural Resources Canada’s Earth Science Sector.
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