Random forests (RF) is a supervised machine learning algorithm, which has recently started to gain prominence in water resources applications. However, existing applications are generally restricted to the implementation of Breiman’s original algorithm for regression and classification problems, while numerous developments could be also useful in solving diverse practical problems in the water sector. Here we popularize RF and their variants for the practicing water scientist, and discuss related concepts and techniques, which have received less attention from the water science and hydrologic communities. In doing so, we review RF applications in water resources, highlight the potential of the original algorithm and its variants, and assess the degree of RF exploitation in a diverse range of applications. Relevant implementations of random forests, as well as related concepts and techniques in the R programming language, are also covered.

[1] We develop methods to estimate the intensity-duration-frequency (IDF) curves for three rainfall models with local multifractal behavior and varying complexity. The models use the classical notion of exterior and interior process, respectively, for the variation of rainfall intensity at (approximately) storm and substorm scales. The exterior process is nonscaling and differs in the three models, whereas the interior process is stationary multifractal in all cases. The model-based IDF curves are robust, against outliers, and can be obtained from only very few years of rainfall data. In an application to a 24-year rainfall record from Florence, Italy, the models closely reproduce the empirical IDF curves and make similar extrapolations for return periods longer than the historical record.Citation: Langousis, A., and D. Veneziano (2007), Intensity-duration-frequency curves from scaling representations of rainfall,

[1] The multifractal representation of rainfall and its use to predict rainfall extremes have advanced significantly in recent years. This paper summarizes this body of work and points at some open questions. The need for a coherent overview comes in part from the use of different terminology, notation, and analysis methods in the literature and in part from the fact that results are dispersed and not always readily available. Two important trends have marked the use of multifractals for rainfall and its extremes. One is the recent shift of focus from asymptotic scaling properties (mainly for the intensity-durationfrequency curves and the areal reduction factor) to the exact extreme distribution under nonasymptotic conditions. This shift has made the results more relevant to hydrologic applications. The second trend is a more sparing use of multifractality in modeling, reflecting the limits of scale invariance in space-time rainfall. This trend has produced models that are more consistent with observed rainfall characteristics, again making the results more suitable for application. Finally, we show that rainfall extremes can be analyzed using rather rough models, provided the parameters are fitted to an appropriate range of large-deviation statistics.Citation: Veneziano, D., A. Langousis, and P. Furcolo (2006), Multifractality and rainfall extremes: A review, Water Resour. Res., 42, W06D15,

In extreme excess modeling, one fits a generalized Pareto (GP) distribution to rainfall excesses above a properly selected threshold u. The latter is generally determined using various approaches, such as nonparametric methods that are intended to locate the changing point between extreme and nonextreme regions of the data, graphical methods where one studies the dependence of GP‐related metrics on the threshold level u, and Goodness‐of‐Fit (GoF) metrics that, for a certain level of significance, locate the lowest threshold u that a GP distribution model is applicable. Here we review representative methods for GP threshold detection, discuss fundamental differences in their theoretical bases, and apply them to 1714 overcentennial daily rainfall records from the NOAA‐NCDC database. We find that nonparametric methods are generally not reliable, while methods that are based on GP asymptotic properties lead to unrealistically high threshold and shape parameter estimates. The latter is justified by theoretical arguments, and it is especially the case in rainfall applications, where the shape parameter of the GP distribution is low; i.e., on the order of 0.1–0.2. Better performance is demonstrated by graphical methods and GoF metrics that rely on preasymptotic properties of the GP distribution. For daily rainfall, we find that GP threshold estimates range between 2 and 12 mm/d with a mean value of 6.5 mm/d, while the existence of quantization in the empirical records, as well as variations in their size, constitute the two most important factors that may significantly affect the accuracy of the obtained results.

Abstract. This paper discusses the relative performance of several climate models in providing reliable forcing for hydrological modeling in six representative catchments in the Mediterranean region. We consider 14 Regional Climate Models (RCMs), from the EU-FP6 ENSEMBLES project, run for the A1B emission scenario on a common 0.22 • (about 24 km) rotated grid over Europe and the Mediterranean region. In the validation period (1951 to 2010) we consider daily precipitation and surface temperatures from the observed data fields (E-OBS) data set, available from the EN-SEMBLES project and the data providers in the ECA&D project. Our primary objective is to rank the 14 RCMs for each catchment and select the four best-performing ones to use as common forcing for hydrological models in the six Mediterranean basins considered in the EU-FP7 CLIMB project. Using a common suite of four RCMs for all studied catchments reduces the (epistemic) uncertainty when evaluating trends and climate change impacts in the 21st century. We present and discuss the validation setting, as well as the obtained results and, in some detail, the difficulties we experienced when processing the data. In doing so we also provide useful information and advice for researchers not directly involved in climate modeling, but interested in the use of climate model outputs for hydrological modeling and, more generally, climate change impact studies in the Mediterranean region.