Understanding Persistence to Avoid Underestimation of Collective Flood Risk

Significance testing of rank cross-correlations between autocorrelated time series with short-range dependence

Statistical dependency measures such as Kendall's Tau or Spearman's Rho are frequently used to analyse the coherence between time series in environmental data analyses. Autocorrelation of the data can, however, result in spurious cross correlations if not accounted for. Here, we present the asymptotic distribution of the estimators of Spearman's Rho and Kendall's Tau, which can be used for statistical hypothesis testing of cross-correlations between autocorrelated observations. The results are derived using U-statistics under the assumption of absolutely regular (or β-mixing) processes. These comprise many short-range dependent processes, such as ARMA-, GARCH- and some copula-based models relevant in the environmental sciences. We show that while the assumption of absolute regularity is required, the specific type of model does not have to be specified for the hypothesis test. Simulations show the improved performance of the modified hypothesis test for some common stochastic models and small to moderate sample sizes under autocorrelation. The methodology is applied to observed climatological time series of flood discharges and temperatures in Europe. While the standard test results in spurious correlations between floods and temperatures, this is not the case for the proposed test, which is more consistent with the literature on flood regime changes in Europe.

Trend Detection in Annual Streamflow Extremes in Brazil

Changes in streamflow extremes can affect the economy and are likely to impact the most vulnerable in society. Estimating these changes is crucial to develop rational adaptation strategies and to protect society. Streamflow data from 1106 gauges were used to provide a comprehensive analysis of change in eight different extreme indices. The modified trend-free prewhitening and the false discovery rate were used to account for serial correlation and multiplicity in regional analysis, issues shown here to distort the results if not properly addressed. The estimated proportion of gauges with significant trends in low and high flows was about 23% and 15%, respectively. Half of these significant gauges had more than 60 years of data and were associated with changes greater than 5% per decade. A clear spatial pattern was identified, where most increasing trends in both low and high flows were observed in Southern Brazil, and decreasing trends in the remaining regions, except for the Amazon, where a pattern is not clear, and the proportion of significant gauges is low. Results based only on gauges unaffected by reservoirs suggest that reservoirs alone do not explain the increasing trends of low flows in the southern regions nor the decreasing trends in high flows in the remaining hydrographic regions.

A Global-Scale Investigation of Stochastic Similarities in Marginal Distribution and Dependence Structure of Key Hydrological-Cycle Processes

To seek stochastic analogies in key processes related to the hydrological cycle, an extended collection of several billions of data values from hundred thousands of worldwide stations is used in this work. The examined processes are the near-surface hourly temperature, dew point, relative humidity, sea level pressure, and atmospheric wind speed, as well as the hourly/daily streamflow and precipitation. Through the use of robust stochastic metrics such as the K-moments and a second-order climacogram (i.e., variance of the averaged process vs. scale), it is found that several stochastic similarities exist in both the marginal structure, in terms of the first four moments, and in the second-order dependence structure. Stochastic similarities are also detected among the examined processes, forming a specific hierarchy among their marginal and dependence structures, similar to the one in the hydrological cycle. Finally, similarities are also traced to the isotropic and nearly Gaussian turbulence, as analyzed through extensive lab recordings of grid turbulence and of turbulent buoyant jet along the axis, which resembles the turbulent shear and buoyant regime that dominates and drives the hydrological-cycle processes in the boundary layer. The results are found to be consistent with other studies in literature such as solar radiation, ocean waves, and evaporation, and they can be also justified by the principle of maximum entropy. Therefore, they allow for the development of a universal stochastic view of the hydrological-cycle under the Hurst–Kolmogorov dynamics, with marginal structures extending from nearly Gaussian to Pareto-type tail behavior, and with dependence structures exhibiting roughness (fractal) behavior at small scales, long-term persistence at large scales, and a transient behavior at intermediate scales.

A Blueprint for Full Collective Flood Risk Estimation: Demonstration for European River Flooding

Floods are a natural hazard evolving in space and time according to meteorological and river basin dynamics, so that a single flood event can affect different regions over the event duration. This physical mechanism introduces spatio-temporal relationships between flood records and losses at different locations over a given time window that should be taken into account for an effective assessment of the collective flood risk. However, since extreme floods are rare events, the limited number of historical records usually prevents a reliable frequency analysis. To overcome this limit, we move from the analysis of extreme events to the modeling of continuous stream flow records preserving spatio-temporal correlation structures of the entire process, and making a more efficient use of the information provided by continuous flow records. The approach is based on the dynamic copula framework, which allows for splitting the modeling of spatio-temporal properties by coupling suitable time series models accounting for temporal dynamics, and multivariate distributions describing spatial dependence. The model is applied to 490 stream flow sequences recorded across 10 of the largest river basins in central and eastern Europe (Danube, Rhine, Elbe, Oder, Waser, Meuse, Rhone, Seine, Loire, and Garonne). Using available proxy data to quantify local flood exposure and vulnerability, we show that the temporal dependence exerts a key role in reproducing interannual persistence, and thus magnitude and frequency of annual proxy flood losses aggregated at a basin-wide scale, while copulas allow the preservation of the spatial dependence of losses at weekly and annual time scales.

General simulation algorithm for autocorrelated binary processes

The apparent ubiquity of binary random processes in physics and many other fields has attracted considerable attention from the modeling community. However, generation of binary sequences with prescribed autocorrelation is a challenging task owing to the discrete nature of the marginal distributions, which makes the application of classical spectral techniques problematic. We show that such methods can effectively be used if we focus on the parent continuous process of beta distributed transition probabilities rather than on the target binary process. This change of paradigm results in a simulation procedure effectively embedding a spectrum-based iterative amplitude-adjusted Fourier transform method devised for continuous processes. The proposed algorithm is fully general, requires minimal assumptions, and can easily simulate binary signals with power-law and exponentially decaying autocorrelation functions corresponding, for instance, to Hurst-Kolmogorov and Markov processes. An application to rainfall intermittency shows that the proposed algorithm can also simulate surrogate data preserving the empirical autocorrelation.