Reply on RC1

Natural Hazards, 2022

Debris flows, and landslides in general, are worldwide catastrophic phenomena. As world population and urbanization grow in magnitude and geographic coverage, the need exists to extend focus, research, and modeling to a continental and global scale. Although debris flow behavior and parameters are local phenomena, sound generalizations can be applied to debris flow susceptibility analyses at larger geographic extents based on these criteria. The focus of this research is to develop a global debris flow susceptibility map by modeling at both a continental scale for all continents and by a single global model and determine whether a global model adequately represents each continent. Probability Density, Conditional Probability, Certainty Factor, Frequency Ratio, and Maximum Entropy statistical models were developed and evaluated for best model performance using fourteen environmental factors generally accepted as the most appropriate debris flow predisposing factors. Global models and...

Natural Hazards and Earth System Science, 2014

Predictive spatial modelling is an important task in natural hazard assessment and regionalisation of geomorphic processes or landforms. Logistic regression is a multivariate statistical approach frequently used in predictive modelling; it can be conducted stepwise in order to select from a number of candidate independent variables those that lead to the best model. In our case study on a debris flow susceptibility model, we investigate the sensitivity of model selection and quality to different sample sizes in light of the following problem: on the one hand, a sample has to be large enough to cover the variability of geofactors within the study area, and to yield stable and reproducible results; on the other hand, the sample must not be too large, because a large sample is likely to violate the assumption of independent observations due to spatial autocorrelation. Using stepwise model selection with 1000 random samples for a number of sample sizes between n = 50 and n = 5000, we investigate the inclusion and exclusion of geofactors and the diversity of the resulting models as a function of sample size; the multiplicity of different models is assessed using numerical indices borrowed from information theory and biodiversity research. Model diversity decreases with increasing sample size and reaches either a local minimum or a plateau; even larger sample sizes do not further reduce it, and they approach the upper limit of sample size given, in this study, by the autocorrelation range of the spatial data sets. In this way, an optimised sample size can be derived from an exploratory analysis. Model uncertainty due to sampling and model selection, and its predictive ability, are explored statistically and spatially through the example of 100 models estimated in one study area and validated in a neighbouring area: depending on the study area and on sample size, the predicted probabilities for debris flow release differed, on average, by 7 to 23 percentage points. In view of these results, we argue that researchers applying model selection should explore the behaviour of the model selection for different sample sizes, and that consensus models created from a number of random samples should be given preference over models relying on a single sample.

Ecological Modelling, 1996

In the present paper, the principles of Empirically Based Uncertainty Analysis (EBUA) are described. EBUA is based on the evaluation of 'performance indices' that express the level of agreement between the model and sets of empirical independent data collected in different experimental circumstances. Some of these indices may be used to evaluate the confidence limits of the model output. The method is based on the statistical analysis of the distribution of the index values and on the quantitative relationship of these values with the ratio 'experimental data/model output'. Some performance indices are described in the present paper. Among these, the so called 'functional distance' (d) between the logarithm of model output and the logarithm of the experimental data, defined as d 2= ~]'(ln M i -In Oi)2/l'l where M i is the ith experimental value, O i the corresponding model evaluation and n the number of the couplets 'experimental value, predicted value', is an important tool for the EBUA method• From the statistical distribution of this performance index, it is possible to infer the characteristics of the distribution of the ratio 'experimental data/model output' and, consequently to evaluate the confidence limits for the model predictions. This method was applied to calculate the uncertainty level of a model developed to predict the migration of radiocaesium in lacustrine systems. Unfortunately performance indices are affected by the uncertainty of the experimental data used in validation. Indeed, measurement results of environmental levels of contamination are generally associated with large uncertainty due to the measurement and sampling techniques and to the large variability in space and time of the measured quantities. It is demonstrated that this non-desired effect, in some circumstances, may be corrected by means of simple formulae•

Reliability Engineering & System Safety, 1997

Safety Science, 1997

New techniques in uncertainty analysis are illustrated with simplified examples from recent applications of interest for safety science. The applications are: BLEVE (boiling Bquid expanding vapor explosions) models, satellite life distributions, dispersion coefficients and modeling contamination in food chains. The examples illustrate the importance of carefully modeling dependence in uncertainties. They also illustrate new uses of conditional Monte Carlo sampling. 0 1997 Elsevier Science Ltd.

Eos, Transactions American …, 2007

Although environmental processes at large scales are to a great degree the resultant of processes at smaller scales, models representing these processes can vary considerably from scale to scale. There are three main reasons for this. Firstly, different processes dominate at different scales, and so different processes are ignored in the simplification step of the model development. Secondly, input data are often absent or of a much lower quality at larger scales, which results in a tendency to use simpler, empirical models at the larger scale. Third, the support of the inputs and outputs of a model changes with change of scale, and this affects the relationships between them. Given these reasons for using different models at different scales, application of a model developed at a specific scale to a larger scale should be treated with care. Instead, models should be modified to suit the larger scale, and for this purpose uncertainty analyses can be extremely helpful. If upscaling disturbed the balance between the contributions of input and model error to the output error, then an uncertainty analysis will show this. Uncertainty analysis will also show how to restore the balance. In practice, application of uncertainty analysis is severely hampered by difficulties in the assessment of input and model error. Knowledge of the short distance spatial variability is of paramount importance to input error assessment with a change of support, but current geographical databases rarely convey this type of information. Model error can only be estimated reliably by validation, but this is not easy because the support of model predictions and validation measurements is usually not the same.

Stochastic Environmental Research and Risk Assessment, 2018

Landslides are one of the most dangerous types of natural disasters, and damage due to landslides has been increasing in certain regions of the world because of increased precipitation. Policy decision makers require reliable information that can be used to establish spatial adaptation plans to protect people from landslide hazards. Researchers presently identify areas susceptible to landslides using various spatial distribution models. However, such data are associated with a high amount of uncertainty. This study focuses on quantifying the uncertainty of several spatial distribution models and identifying the effectiveness of various ensemble methods that can be used to provide reliable information to support policy decisions. The area of study was Inje-gun, Republic of Korea. Ten models were selected to assess landslide susceptibility. Moreover, five ensemble methods were selected for the aggregated results of the 10 models. The uncertainty was quantified using the coefficient of variation and the uncertainty map we developed revealed areas with strongly differing values among single models. A matrix map was created using an ensemble map and a coefficient of variation map. Using matrix analysis, we identified the areas that are most susceptible to landslides according to the ensemble model with a low uncertainty. Thus, the ensemble model can be a useful tool for supporting decision makers. The framework of this study can also be employed to support the establishment of landslide adaptation plans in other areas of the Republic of Korea and in other countries.

Risk Analysis, 1994

In recent years the U.S. Environmental Protection Agency has been challenged both externally and internally to move beyond its traditional conservative single-point treatment of various input parameters in risk assessments. In the first section, we assess when more involved distribution-based analyses might be indicated for such common types of risk assessment applications as baseline assessments of Superfund sites. Then in two subsequent sections, we give an overview with some case studies of technical analyses of (A) variabilityheterogeneity and (B) uncertainty. By "interindividual variability" is meant the real variation among individuals in exposure-producing behavior, in exposures, or some other parameter (such as differences among individual municipal solid waste incinerators in emissions). In contrast, "uncertainty" is a description of the imperfection in knowledge of the true value of a particular parameter or its real variability in an individual or a group. In general uncertainty is reducible by additional information-gathering or analysis activities (better data, better models), whereas real variability will not change (although it may be more accurately known) as a result of better or more extensive measurements. The purpose of the rather long-winded exposition of these two final sections is to show the differences between analyses of these two different things, both of which are described using the language of probability distributions.

Erdkunde, 2009

Statistical disposition models are used both in geomorphology and in natural hazards research to spatially predict the occurrence of mass movements, other geomorphic processes or landforms. This is achieved by establishing some statistical relationship between an inventory of mapped occurrences and relevant geofactor maps. Statistical approaches rely, among others, on the assumption that future events will take place under the same conditions as they did in the past. In the present paper, the Certainty Factor (one of the favourability functions) is used to quantify the association of debris flow initiation sites with the geofactors landcover, slope and CIT index in three alpine study areas. The transferability of the models, i.e. their applicability to other study areas, is investigated using a comparison of model results (CF parameters) from different study areas and an extensive cross-validation. It is shown that, in similar study areas, the model parameters are generally very similar, indicating that the geofactors represent well enough the relevant conditions and processes that lead to debris flow initiation. The cross-validation is generally successful, independent of the similarity of the area for which the model has been established and the target area. Therefore, it can be concluded that statistical disposition models such as the CF model are, in principle, transferable between study areas. Nevertheless, some critical issues such as data quality have to be kept in mind when trying to apply a model to another study area.