Maria Manuela Portela

Spatial and temporal variability of droughts in Portugal

[1] An analysis of droughts in mainland Portugal based on monthly precipitation data, from September 1910 to October 2004, in 144 rain gages distributed uniformly over the country is presented. The drought events were characterized by means of the Standardized Precipitation Index (SPI) applied to different time scales (1, 6, and 12 consecutive months and 6 months from April to September and 12 months from October to September). To assess spatial and temporal patterns of droughts, a principal component analysis (PCA) and K-means clustering (KMC) were applied to the SPI series. In this way, three different and spatially well-defined regions with different temporal evolution of droughts were identified (north, central, and south regions of Portugal). A spectral analysis of the SPI patterns obtained with principal component analysis and clusters analysis, using the fast Fourier transform algorithm (FFT), showed that there is a manifest 3.6-year cycle in the SPI pattern in the south of Portugal and evident 2.4-year and 13.4-year cycles in the north of Portugal. The observation of the drought periods supports the occurrence of more frequent cycles of dry events in the south (droughts from moderate to extreme approximately every 3.6 years) than in the north (droughts from severe to extreme approximately every 13.4 years). These results suggest a much stronger immediate influence of the NAO in the south than in the north of Portugal, although these relations remain a challenging task.

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.

SPI Modes of Drought Spatial and Temporal Variability in Portugal: Comparing Observations, PT02 and GPCC Gridded Datasets

Regional drought modes in Portugal are identified applying the Principal Component Analysis (PCA) and Varimax rotation to the Standardized Precipitation Index (SPI) computed on various time scales using the three precipitation datasets covering the period 1950–2003: (i) The observation dataset composed of 193 rain-gauges distributed almost uniformly over the country, (ii) the PT02 high-resolution gridded dataset provided by the Portuguese Meteorological Institute, and (iii) the GPCC dataset with 0.5° spatial resolution. Results suggest that the three datasets well agree in identifying the principal drought modes, i.e. two sub-regions in northern and southern Portugal with independent climate variability. The two sub-regions appear stable when the SPI time scale is varied from 3- to 24-month, and the associated rotated principal component scores (RPCs) do not show any statistically significant linear trend. The degree of similarity between the rotated loadings or REOFs of different SPI time scales for the three used datasets was examined through the congruence coefficients, whose results show a good agreement between the three datasets in capturing the main Portuguese sub-regions. A third spatial mode in central-eastern Portugal was identified for SPI-24 in PT02, with the associated RPC characterized by a statistically significant downward trend. The stability of the identified sub-regions as a function of studied time period was also evaluated applying the same methodologies to a set of three different time windows and it was found that the southern sub-region is very stable but the northern and central-eastern sub-regions are very sensitive to the selected time window.

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.

A new plotting position concept to evaluate peak flood discharges based on short samples

A model to improve the estimates of the peak flood discharges given by the statistical analysis applied to small samples of annual maximum instantaneous discharges, Qami, is presented. The model combines a new probability plotting position technique – by means of a sorting operator, SO – with the Gumbel law with parameters evaluated by the least square method. It should be stressed that other statistical laws compatible with the previous parameter estimation method should be possible. For a given watershed, the SO modifies the rank of each element of the sample of Qami by taking into account the magnitude of the floods in a nearby watershed where more records are available. The two watersheds must belong to the same homogenous hydrologic region and must be geographically close in order to be valid to consider that the extreme flood events in both watersheds are likely due to the same extreme rainfall events. The results achieved showed that the model allows for better estimates, especially when applied to short samples, as those more often provided by the Portuguese network of stream gages.

Investigation on the properties of the relationship between rare and extreme rainfall and flood volumes, under some distributional restrictions

The fact that rainfall data are usually more abundant and more readily regionalized than streamflow data has motivated hydrologists to conceive methods that incorporate the hydrometeorologial information into flood frequency analyses. Some of them, particularly those derived from the French GRADEX method, involve assumptions concerning the relationship between extreme rainfall and flood volumes, under some distributional restrictions. In particular, for rainfall probability distributions exhibiting exponential-like upper tails, it is possible to derive the shape and scale of the probability distribution of flood volumes by hypothesizing the basic properties of such a relationship, under rare and/or extreme conditions. This paper focuses on a parametric mathematical model for the relationship between rare and extreme rainfall and flood volumes under exponentially-tailed distributions. The model is analyzed and fitted to rare and extreme events derived from hydrological simulation of long stochastically-generated synthetic series of rainfall and evaporation for the Indaiá River basin, located in south-central Brazil. The paper also provides a sensitivity analysis of the model parameters in order to better understand flood events under rare and extreme conditions. By working with hydrologically plausible hypothetical events, the modeling approach proved to be a useful way to explore extraordinary rainfall and flood events. The results from this exploratory analysis provide grounds to derive some conclusions regarding the relative positions of the upper tails of the probability distributions of rainfall and flood volumes.

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.

Hydraulic–hydrologic model for water resources management of the Zambezi basin

The paper focuses on the development of the hydraulic–hydrological model used to simulate water resources management scenarios in the Zambezi River basin. The main challenges of the implementation of the model are the scarcity of continuous reliable discharge data and the significant influence of large floodplains. The Soil and Water Assessment Tool, a semi-distributed physically based continuous time model, was chosen as simulation tool. Given the complexity and the size of the basin under study, an automated calibration procedure was applied to optimize the relative error and the volume ratio at multiple stations. Using data derived from satellite observations, the model is first stabilized during two years, then calibrated over six years and finally validated over three years. The study evidences the importance of evaluating the model at different points of the basin and the complementarities between performance indicators.

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.