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The potential for changes in environmental extremes is routinely investigated by fitting change-permitting extreme value models to long-term observations, allowing one or more distribution parameters to change as a function of time or some other covariate. In most extreme value analyses, the main quantity of interest is typically the upper quantiles of the distribution, which are often needed for practical applications such as engineering design. This study focuses on the changes in quantile estimates under different change-permitting models. First, metrics which measure the impact of changes in parameters on changes in quantiles are introduced. The mathematical structure of these change metrics is investigated for several change-permitting models based on the Generalised Extreme Value (GEV) distribution. It is shown that for the most commonly used models, the predicted changes in the quantiles are a non-intuitive function of the distribution parameters, leading to results which are difficult to interpret. Next, it is posited that commonly used change-permitting GEV models do not preserve a constant coefficient of variation, a property that is typically assumed to hold for environmental extremes. To address these shortcomings a new (parsimonious) model is proposed: the model assumes a constant coefficient of variation, allowing the location and scale parameters to change simultaneously. The proposed model results in changes in the quantile function that are easier to interpret. Finally, the consequences of the different modelling choices on quantile estimates are exemplified using a dataset of extreme peak river flow measurements in Massachusetts, USA. It is argued that the decision on which model structure to adopt to describe change in extremes should also take into consideration any requirements on the behaviour of the quantiles of interest.

Extreme value theory is routinely applied to estimate rainfall frequency for several accumulation periods. Typically, it is found that sub‐daily precipitation has power‐type tails, meaning that the probability of observing increasingly large magnitudes decreases as a power law. Physical arguments, however, suggest it should have lighter, stretched exponential, tails. Here, we reconcile these perspectives showing that part of the contradiction is caused by precipitation process heterogeneity. We examine hundreds of sub‐daily precipitation records in the Greater Alpine Area, for which a classification of storms into homogeneous types is available. We find that an apparent heavy‐tail behavior is reported at scales of 1–6 hr, and is explained by the coexistence of stratiform and convective processes, both characterized by stretched exponential tails. Our results challenge the assumptions which justify the use of extreme value theory for sub‐daily precipitation, with important implications for how design values are determined.

Drought management frameworks are dependent on methods for monitoring and prediction, but quantifying the hazard alone is arguably not sufficient; the negative consequences that may arise from a lack of precipitation must also be predicted if droughts are to be better managed. However, the link between drought intensity, expressed by some hydrometeorological indicator, and the occurrence of drought impacts has only recently begun to be addressed. One challenge is the paucity of information on ecological and socioeconomic consequences of drought. This study tests the potential for developing empirical drought impact functions based on drought indicators (Standardized Precipitation and Standardized Precipitation Evaporation Index) as predictors and text-based reports on drought impacts as a surrogate variable for drought damage. While there have been studies exploiting textual evidence of drought impacts, a systematic assessment of the effect of impact quantification method and different functional relationships for modeling drought impacts is missing. Using Southeast England as a case study we tested the potential of three different data-driven models for predicting drought impacts quantified from text-based reports: logistic regression, zero-altered negative binomial regression (hurdle model), and an ensemble regression tree approach (random forest). The logistic regression model can only be applied to a binary impact/no impact time series, whereas the other two models can additionally predict the full counts of impact occurrence at each time point. While modeling binary data results in the lowest prediction uncertainty, modeling the full counts has the advantage of also providing a measure of impact severity, and the counts were found to be reasonably predictable. However, there were noticeable differences in skill between modeling methodologies. For binary data the logistic regression and the random forest model performed similarly well based on leave-one-out cross validation. For count data the random forest outperformed the hurdle model. The between-model differences occurred for total drought impacts and for two subsets of impact categories (water supply and freshwater ecosystem impacts). In addition, different ways of defining the impact counts were investigated and were found to have little influence on the prediction skill. For all models we found a positive effect of including impact information of the preceding month as a predictor in addition to the hydrometeorological indicators. We conclude that, although having some limitations, text-based reports on drought impacts can provide useful information for drought risk management, and our study showcases different methodological approaches to developing drought impact functions based on text-based data.

Generalized linear models are a widely used method to obtain parametric estimates for the mean function. They have been further extended to allow the relationship between the mean function and the covariates to be more flexible via generalized additive models. However, the fixed variance structure can in many cases be too restrictive. The extended quasilikelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covariates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this article, we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples.

The use of historical data can significantly reduce the uncertainty around estimates of the magnitude of rare events obtained with extreme value statistical models. For historical data to be included in the statistical analysis a number of their properties, e.g. their number and magnitude, need to be known with a reasonable level of confidence. Another key aspect of the historical data which needs to be known is the coverage period of the historical information, i.e. the period of time over which it is assumed that all large events above a certain threshold are known. It might be the case though, that it is not possible to easily retrieve with sufficient confidence information on the coverage period, which therefore needs to be estimated. In this paper methods to perform such estimation are introduced and evaluated. The statistical definition of the problem corresponds to estimating the size of a population for which only few data points are available. This problem is generally refereed to as the German tanks problem, which arose during the second world war, when statistical estimates of the number of tanks available to the German army were obtained. Different estimators can be derived using different statistical estimation approaches, with the maximum spacing estimator being the minimum-variance unbiased estimator. The properties of three estimators are investigated by means of a simulation study, both for the simple estimation of the historical coverage and for the estimation of the extreme value statistical model. The maximum spacing estimator is confirmed to be a good approach to the estimation of the historical period coverage for practical use and its application for a case study in Britain is presented.

This study presents a depth–duration–frequency (DDF) model, which is applied to the annual maxima of sub-hourly rainfall totals of selected stations in England and Wales. The proposed DDF model follows from the standard assumption that the block maxima are generalised extreme value (GEV) distributed. The model structure is based on empirical features of the observed data and the assumption that, for each site, the distribution of the rainfall maxima of all durations can be characterised by common lower bound and skewness parameters. Some basic relationships between the location and scale parameters of the GEV distributions are enforced to ensure that frequency estimates for different durations are consistent. The derived DDF curves give a good fit to the observed data. The rainfall depths estimated by the proposed model are then compared with the standard DDF models used in the United Kingdom. The proposed model performs well for the shorter return periods for which reliable estimates of the rainfall frequency can be obtained from the observed data, while the standard methods show more variable results. Although the standard methods used no or little sub-hourly data in their calibration, they give fairly reliable estimates for the estimated rainfall depths overall.

This article provides, for the first time, direct information on the levels and trends of nitrogen oxides and particulate matter measured by a recently installed air-quality monitoring station in the city of Venice (Italy). High levels of air pollution affect human health and built cultural heritage with corrosion, loss of material due to chemical attack, and soiling: this is particularly dangerous in a World Heritage city like Venice. The pollution levels measured in the historical city are compared to those of a background station in the city of Venice and of urban and background stations in the mainland, also investigating climate factors which might affect pollution in all stations. The first results of the investigation are that the NO2, as well as the PM10, annual average levels in Venice definitely exceeded the limit values set by EU directives. This is an astonishing and unexpected result in a car free city. To contrast the poor air quality, the Venice Municipality decreed in spring 2019 to limit traffic in one of the most overcrowded Venice canals. To investigate the usefulness of the implemented policy we performed a comparative study in which Generalized Additive Models are employed to model the potential reduction in measured nitrogen dioxide in the urban station as compared to the background station. This is done for stations in the historical city of Venice and in the mainland, to give a stronger indication of whether detected changes can be attributable to the traffic policy and no other exogenous factors. The policy is found to have a minor impact in the reduction of measured nitrogen dioxide.

The traditional approach to design flood estimation (for example, to derive the 100-year flood) is to apply a statistical model to time series of peak river flow measured by gauging stations. Such records are typically not very long, for example in the UK only about 10% of the stations have records that are more than 50 years in length. Along-explored way to augment the data available from a gauging station is to derive information about historical flood events and paleo-floods, which can be obtained from careful exploration of archives, old newspapers, flood marks or other signs of past flooding that are still discernible in the catchment, and the history of settlements. The inclusion of historical data in flood frequency estimation has been shown to substantially reduce the uncertainty around the estimated design events and is likely to provide insight into the rarest events which might have pre-dated the relatively short systematic records. Among other things, the FEH Local project funded by the Environment Agency aims to develop methods to easily incorporate historical information into the standard method of statistical flood frequency estimation in the UK. Different statistical estimation procedures are explored, namely maximum likelihood and partial probability weighted moments, and the strengths and weaknesses of each method are investigated. The project assesses the usefulness of historical data and aims to provide practitioners with useful guidelines to indicate in what circumstances the inclusion of historical data is likely to be beneficial in terms of reducing both the bias and the variability of the estimated flood frequency curves. The guidelines are based on the results of a large Monte Carlo simulation study, in which different estimation procedures and different data availability scenarios are studied. The study provides some indication of the situations under which different estimation procedures might give a better performance.

Estimating peak river discharge, a critical issue in engineering hydrology, is essential for designing and managing hydraulic infrastructure such as dams and bridges. In the UK, practitioners typically apply the Flood Estimation Handbook (FEH) statistical method which estimates the design flood as the product of a relatively frequent flow estimate (the index flood, IF) and a regional growth factor. For gauged catchments the IF is estimated from observations. For ungauged catchments it is computed through a multiple regression model. While the FEH IF method provides peak flow estimates that are statistically robust, it does not readily take into account catchment heterogeneity or effect of environmental change on river flows. This study presents a new methodology to estimate the IF at national scale using continuous simulation from a physically based hydrological model (Grid-to-Grid). The methodology is tested across Great Britain and compares well with IF estimates at 550 gauging stations (R2 = 0.91). The promising results for Great Britain support the aspiration that continuous simulation from large-scale hydrological models coupled with increasing availability of global weather and climate products, could be used to estimate design floods in regions with limited gauge data or affected by environmental change.

The open-source programming language R has gained a central place in the hydrological sciences over the last decade, driven by the availability of diverse hydro-meteorological data archives and the development of open-source computational tools. The growth of R's usage in hydrology is reflected in the number of newly published hydrological packages, the strengthening of online user communities, and the popularity of training courses and events. In this paper, we explore the benefits and advantages of R's usage in hydrology, such as the democratization of data science and numerical literacy, the enhancement of reproducible research and open science, the access to statistical tools, the ease of connecting R to and from other languages, and the support provided by a growing community. This paper provides an overview of a typical hydrological workflow based on reproducible principles and packages for retrieval of hydro-meteorological data, spatial analysis, hydrological modelling, statistics, and the design of static and dynamic visualizations and documents. We discuss some of the challenges that arise when using R in hydrology and useful tools to overcome them, including the use of hydrological libraries, documentation, and vignettes (long-form guides that illustrate how to use packages); the role of integrated development environments (IDEs); and the challenges of big data and parallel computing in hydrology. Lastly, this paper provides a roadmap for R's future within hydrology, with R packages as a driver of progress in the hydrological sciences, application programming interfaces (APIs) providing new avenues for data acquisition and provision, enhanced teaching of hydrology in R, and the continued growth of the community via short courses and events.