Artur Tiago Silva

On some aspects of peaks-over-threshold modeling of floods under nonstationarity using climate covariates

This paper discusses some aspects of flood frequency analysis using the peaks-over-threshold model with Poisson arrivals and generalized Pareto (GP) distributed peak magnitudes under nonstationarity, using climate covariates. The discussion topics were motivated by a case study on the influence of El Niño–Southern Oscillation on the flood regime in the Itajaí river basin, in Southern Brazil. The Niño3.4 (DJF) index is used as a covariate in nonstationary estimates of the Poisson and GP distributions scale parameters. Prior to the positing of parametric dependence functions, a preliminary data-driven analysis was carried out using nonparametric regression models to estimate the dependence of the parameters on the covariate. Model fits were evaluated using asymptotic likelihood ratio tests, AIC, and Q–Q plots. Results show statistically significant and complex dependence relationships with the covariate on both nonstationary parameters. The nonstationary flood hazard measure design life level (DLL) was used to compare the relative performances of stationary and nonstationary models in quantifying flood hazard over the period of records. Uncertainty analyses were carried out in every step of the application using the delta method.

On peaks-over-threshold modeling of floods with zero-inflated Poisson arrivals under stationarity and nonstationarity

The peaks-over-threshold (POT) model with Poisson arrivals and generalized Pareto (GP) distributed exceedances remains a popular and useful tool for modelling hydrologic extremes. The use of the Poisson–GP model for flood frequency analysis requires the validation of the hypothesis that the distribution of the annual number of flood events may be described by a Poisson distribution. Such hypothesis is not always valid in practical applications. The present study concerns the use of an alternative distribution for modelling the annual number of floods—the zero-inflated Poisson (ZIP) distribution with two parameters. A ZIP–GP model for flood frequency analysis is proposed. This model is less restrictive than the Poisson–GP model since it allows for a more accurate description of the occurrence process in a POT framework if the fraction of years with no exceedances is significantly higher than the theoretical mass at zero of the Poisson distribution. Furthermore, a nonstationary model (NSZIP–GP) is presented, in which the parameters of the ZIP are allowed to change in time as a function of a covariate, which, even for stationary peak magnitudes, affects the annual maximum flood quantiles with a given non-exceedance probability. Applications of the ZIP–GP model to flood data from Northern Portugal and the evaluation of its performance relative to the Poisson–GP model, including assessments of quantile uncertainty, are presented. An illustrative application of the NSZIP–GP model, using the North Atlantic Oscillation as a covariate is also presented. The applications of both models include assessment of quantile uncertainty.

A Bayesian peaks-over-threshold analysis of floods in the Itajaí-açu River under stationarity and nonstationarity

In this paper we revisit the case study of Silva et al. (Stoch Env Res Risk A. doi:10.1007/s00477-015-1072-y, 2015), the Itajaí-açu River at Apiúna (Southern Brazil), with an augmented data set and Bayesian inferential techniques. Nonstationary Poisson-GP models are used to study the joint influence of El Niño-Southern Oscillation (ENSO) and of upstream flood control structures on the flood regime at the study site. The Niño3.4 DJF index and a dimensionless reservoir index are used as covariates. Prior belief about the GP shape parameter is elicited by fitting the GEV distribution to AMS samples from 138 sites in Southern Brazil with 40 or more years of data and deriving the distribution from the estimates of that parameter. Following a data-driven exploratory analysis, a Markov chain Monte Carlo (MCMC) procedure is used to sample from the posterior distribution of parameters. Model evaluation and selection used Bayes factors and two information criteria. Results show evidence that, while upstream dams play a significant, though small, role in reducing flood hazard, the influence of the climate covariate is stronger, and an increase in ENSO amplitude in the last decades has led to the occurrence of higher annual maximum floods. MCMC samples are used to derive the Bayesian predictive distribution of annual flood quantiles and design life levels. Uncertainty analyses based on the posterior distribution of parameters and quantiles are presented.

Analysis of Temporal Variability of Droughts in Southern Paraguay and Northern Argentina (1961-2011)

The study presents an analysis of droughts using monthly rainfall data, from January 1961 to December 2011, from 11 rain gauges located in Paraguay and Northern Argentina. The characterization of the drought events used the standardized precipitation index (SPI) applied at different time scales (3, 6, and 12 consecutive months). The temporal variability of the droughts in the study period was analyzed in terms of changes in their frequency—regardless of the severity, has the frequency of droughts increased or decreased?—and in their severity—are we experiencing more severe droughts or not? The results achieved, despite proving the suitability of the approaches applied, did not reveal any trend towards an increase or a decrease either in the frequency of the droughts or in their severity in the studied area.

Generation of monthly synthetic streamflow series based on the method of fragments

Synthetic time series generation has long been an important tool for the planning and management of water resources systems. This technique allows for a significant reduction of the uncertainty associated with hydrological phenomena. In this article a procedure is proposed for generating synthetic series of annual and monthly flows that combines two models, a probabilistic one, applied at an annual level, and at a monthly level, a deterministic disaggregation model. The modeling of the annual flow series is based on the random sampling of the log-Pearson III law of probability. The disaggregation of annual flows into monthly flows uses the method of fragments. For the application of this method, a new procedure was developed and tested for the automatic definition of the classes of fragments, reducing the need for intervention of the modeler, resulting in a more general and robust approach. The combination of the two models was tested on a data set of 54 streamflow samples from gauging stations geographically spread over Mainland Portugal. For each gauging station, 1200 synthetic series were generated, with a length equal to that of the corresponding sample. The quality of the generated series was evaluated by their capacity to preserve the most significant statistical characteristics of the samples of annual and monthly flows, namely the mean, standard deviation, and skewness coefficient. Confidence intervals were established for this evaluation, and the results show that, generally, the statistics of the samples are contained in these intervals. Thereupon it was concluded that the developed procedure is adequate.

Design of a multimode reconfigurable sigma-delta converter for 4G wireless receivers

This paper presents a multi-standard reconfigurable sigma-delta modulator, which is able to support the predictable standards of fourth generation of mobile communication systems (4G). Furthermore, the proposed architecture halves the number of required analog-to-digital converters in parallel receivers, by processing concurrently two different signals. The major design issues are outlined and operation modes are detailed. A system-level simulation is performed to demonstrate the feasibility of the presented solution.

Introduction to Bayesian Analysis of Hydrologic Variables

In Sect. 3.4 of Chap. 3, Bayes’ theorem is introduced in a setting of random events in a sample space. It is also shown how the theorem allows for the updating of the current knowledge about the probability of a certain event, in light of new information. In this context, the conditional probability arising from Bayes’ theorem is proportional to the inverse probability given by the theorem of total probability. This chapter explores Bayesian methods in more detail, with the aim of providing the reader with a basic overview of this important branch of statistics, which has extensive application opportunities in the modeling and inference of hydrologic random variables.

Erratum to: Disaggregation Modelling of Annual Flows into Daily Streamflows Using a New Approach of the Method of Fragments

Abstract For many decades, synthetic streamflow series have been utilized in hydrology to analyze numerous stochastic problems whose solutions depend on the values of the streamflows and their temporal pattern. The stochastic generation of synthetic streamflows at a given time level can adopt two general approaches: the generation at the required time level by applying an appropriate model; or the generation of annual flows using a suitable annual model, followed by their disaggregation into flows at the required time level. The first approach is feasible for a seasonal or monthly level, but not for a daily level, while the latter can be applied to any level. It also has the advantage of allowing the preservation of the historical statistical properties at both the upper (year) and the lower (season, month or day) time levels. One of the simplest disaggregation models is the method of fragments. Based on the extensive application of that method to the generation of monthly flow series in more than 50 Portuguese river gauges (Silva and Portela, 2011, Hydrol Sci J 57(5): 942–955. doi: 10.1080/02626667.2012.686695 , 2012), it was possible to establish a deterministic criterion to define the classes of fragments and to select the fragments that proved to be very robust. That criterion was revisited and modified and applied to the generation of synthetic daily flow series, with even better results. This paper describes the revisited method, presents the results from its application to a few case studies and discusses its relevance to analyze the uncertainty due to the temporal variability of the flow regime.

Continuous Random Variables: Probability Distributions and Their Applications in Hydrology

The probability distributions covered in this chapter refer to models of continuous random variables. Emphasis is given to the models that are generally employed in frequency analysis of hydrologic continuous random variables. Following the formal description of each model, the reader will find, in most cases, a brief example of its application in hydrology. The list of models detailed in this chapter is not exhaustive, as it does not include all distributions that have possible uses in Statistical Hydrology. However, the list includes other models that are not currently employed in the frequency analysis of hydrologic continuous random variables but are key elements in setting out the foundations of statistical inference, such as the sampling distributions, as well as other generally useful models, like the uniform and beta distributions. Throughout the chapter, the focus is deliberately kept on describing the models, their main shape characteristics, and usual applications, and not on systematically providing mathematical proofs for expected values and other population descriptors. By the end of the chapter, the normal bivariate model and the principles for building copulas, for describing the dependence structure between variables, are introduced, as an illustration of multivariate probability distributions.

Using Climate-Flood Links and CMIP5 Projections to Assess Flood Design Levels Under Climate Change Scenarios: A Case Study in Southern Brazil

The Intergovernmental Panel on Climate Change (IPCC) assessed with medium confidence that there has been an anthropogenic influence in the intensification of heavy rainfall at the global scale. Nevertheless, when taking into account gauge-based evidence, no clear climate-driven global change in the magnitude or frequency of floods has been identified in recent decades. This paper follows up on a previous nonstationary flood frequency analysis in the Itajaí River, which is located in the Southeastern South America region, where evidence of significant and complex relationships between El Niño-Southern Oscillation (ENSO) and hydrometeorological extremes has been found. The identified climate-flood link is further explored using sea surface temperature (SST) output from CMIP5 models under different representative concentration pathway (RCP) scenarios. Results are inconclusive as to whether it is possible to make a statement on scenario-forced climate change impacts on the flood regime of the Itajaí river basin. The overall outcome of the analysis is that, given that sample sizes are adequate, stationary models seem to be sufficiently robust for engineering design as they describe the variability of the hydrological processes over a large period, even if annual flood probabilities exhibit a strong year-to-year dependence on ENSO.