The use of a deterministic fractal‐multifractal (FM) representation to model high‐resolution rainfall time series via projections of fractal interpolating functions weighed by multifractal measures is reported. It is shown that the intrinsic shape and variability of an 8‐hour Boston storm recorded every 15 s on October 25, 1980, may be encoded wholistically, employing the fractal geometric methodology. It is illustrated that the FM methodology provides very faithful descriptions of both major trends and small (noisy) fluctuations for this storm, resulting in preservation of not only classical statistical characteristics of the records but also multifractal and chaotic properties present in them. These results, and those for other storms, suggest that a stochastic framework for rainfall may be bypassed in favor of a deterministic representation based on projections.

Abstract. A distributed model (TETIS), a semi-distributed model (TOPMODEL) and a lumped model (HEC HMS soil moisture accounting) were used to simulate the discharge response of a tropical high mountain basin characterized by soils with high water storage capacity and high conductivity. The models were calibrated with the Shuffle Complex Evolution algorithm, using the Kling and Gupta efficiency as objective function. Performance analysis and diagnostics were carried out using the signatures of the flow duration curve and through analysis of the model fluxes in order to identify the most appropriate model for the 5 study area for flood early warning. The impact of varying grid sizes was assessed in the TETIS model and the TOPMODEL in order to chose a model with balanced model performance and computational efficiency. The sensitivity of the models to variation in the precipitation input was analysed by forcing the models with a rainfall ensemble obtained from Gaussian simulation.The resulting discharge ensembles of each model were compared in order to identify differences among models structures. The results show that TOPMODEL is the most realistic model of the three tested, albeit showing the largest discharge ensemble 10 spread. The main differences among models occur between HEC HMS soil moisture accounting and TETIS, and HEC HMS soil moisture accounting and TOPMODEL, with HEC HMS soil moisture accounting producing ensembles in a range lower than the other two models. The ensembles of TETIS and TOPMODEL are more similar.

Abstract. In this paper a method is proposed to identify mountainous watersheds with the highest flood risk at the regional level. Through this, the watersheds to be subjected to more detailed risk studies can be prioritised in order to establish appropriate flood risk management strategies. The prioritisation is carried out through an index composed of a qualitative indicator of vulnerability and a qualitative flash flood/debris flow susceptibility indicator. At the regional level, vulnerability was assessed on the basis of a principal component analysis carried out with variables recognised in literature to contribute to vulnerability, using watersheds as the unit of analysis. The area exposed was obtained from a simplified flood extent analysis at the regional level, which provided a mask where vulnerability variables were extracted. The vulnerability indicator obtained from the principal component analysis was combined with an existing susceptibility indicator, thus providing an index that allows the watersheds to be prioritised in support of flood risk management at regional level. Results show that the components of vulnerability can be expressed in terms of three constituent indicators: (i) socio-economic fragility, which is composed of demography and lack of well-being; (ii) lack of resilience and coping capacity, which is composed of lack of education, lack of preparedness and response capacity, lack of rescue capacity, cohesiveness of the community; and (iii) physical exposure, which is composed of exposed infrastructure and exposed population. A sensitivity analysis shows that the classification of vulnerability is robust for watersheds with low and high values of the vulnerability indicator, while some watersheds with intermediate values of the indicator are sensitive to shifting between medium and high vulnerability.

Usage of a deterministic fractal-multifractal (FM) procedure to model high-resolution rainfall time series, as derived distributions of multifractal measures via fractal interpolating functions, is reported. Four rainfall storm events having distinct geometries, one gathered in Boston and three others observed in Iowa City, are analyzed. Results show that the FM approach captures the main characteristics of these events, as the fitted storms preserve the records' general trends, their autocorrelations and spectra, and their multifractal character.

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A large family of deterministic measures built as projections off fractal functions has been introduced recently.1,2 These constructed measures, which transform either simple multifractals as defined by deterministic cascades3 or uniform measures via fractal interpolating functions,4,5 range from nontrivial multifractals to absolutely continuous measures, and include as a limiting case the Gaussian distribution.6 In this work, examples of deterministic measures which possess multiscaling properties when analyzed following the multifractal formalism are given. It is shown that suitable measures which not only preserve the singularity spectrum of turbulence but also capture the inherent details present in turbulent data sets may be obtained. These results suggest a plausible deterministic framework for the study of intermittent phenomena via a new geometric approach — one which closely evokes Plato's ideas that all we observe may be "shadows" of simple objects.7

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Successful usage of a large family of deterministically generated measures to model complex nonlinear phenomena (e.g. rainfall, turbulence and groundwater contaminant transport) has been reported recently. 1-7 As these measures, generated as derived distributions of multifractal measures via fractal interpolating functions (FIF), i.e. the fractal-multifractal (FM) approach, have been found to share the inherent character of natural sets, the present study further investigates their dynamical (chaotic or stochastic) properties. It is shown, through a variety of examples and via the use of power spectrum, mass exponents and false nearest neighbors in the state-space, that the FM approach indeed generates deterministic measures whose behavior (depending on their parameters) may be classified as low-dimensional and chaotic or as highdimensional and stochastic. These results suggest the general suitability of the FM approach for understanding and modeling nonlinear natural phenomena.