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In recurrence analysis, the tau-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations.
However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis.
We introduce a novel method to decompose the tau-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization.
We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series.
We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.
Meteorological extreme events have great potential for damaging railway infrastructure and posing risks to the safety of train passengers. In the future, climate change will presumably have serious implications on meteorological hazards in the Alpine region. Hence, attaining insights on future frequencies of meteorological extremes with relevance for the railway operation in Austria is required in the context of a comprehensive and sustainable natural hazard management plan of the railway operator. In this study, possible impacts of climate change on the frequencies of so-called critical meteorological conditions (CMCs) between the periods 1961-1990 and 2011-2040 are analyzed. Thresholds for such CMCs have been defined by the railway operator and used in its weather monitoring and early warning system. First, the seasonal climate change signals for air temperature and precipitation in Austria are described on the basis of an ensemble of high-resolution Regional Climate Model (RCM) simulations for Europe. Subsequently, the RCM-ensemble was used to investigate changes in the frequency of CMCs. Finally, the sensitivity of results is analyzed with varying threshold values for the CMCs. Results give robust indications for an all-season air temperature rise, but show no clear tendency in average precipitation. The frequency analyses reveal an increase in intense rainfall events and heat waves, whereas heavy snowfall and cold days are likely to decrease. Furthermore, results indicate that frequencies of CMCs are rather sensitive to changes of thresholds. It thus emphasizes the importance to carefully define, validate, andif neededto adapt the thresholds that are used in the weather monitoring and warning system of the railway operator. For this, continuous and standardized documentation of damaging events and near-misses is a pre-requisite.
Flood risk analyses are often estimated assuming the same flood intensity along the river reach under study, i.e. discharges are calculated for a number of return periods T, e.g. 10 or 100 years, at several streamflow gauges. T-year discharges are regionalised and then transferred into T-year water levels, inundated areas and impacts. This approach assumes that (1) flood scenarios are homogeneous throughout a river basin, and (2) the T-year damage corresponds to the T-year discharge. Using a reach at the river Rhine, this homogeneous approach is compared with an approach that is based on four flood types with different spatial discharge patterns. For each type, a regression model was created and used in a Monte-Carlo framework to derive heterogeneous scenarios. Per scenario, four cumulative impact indicators were calculated: (1) the total inundated area, (2) the exposed settlement and industrial areas, (3) the exposed population and 4) the potential building loss. Their frequency curves were used to establish a ranking of eight past flood events according to their severity. The investigation revealed that the two assumptions of the homogeneous approach do not hold. It tends to overestimate event probabilities in large areas. Therefore, the generation of heterogeneous scenarios should receive more attention.