The analysis and estimation of extreme event occurrences is a central problem in many fields of geoscience. Advancements in the study of extreme events have recently been limited, arguably in connection with asymptotic assumptions in the traditional extreme value theory (EVT) and with its focusing on a small fraction of the available observations representing the tail properties of the underlying event generation process. Here we develop a Metastatistical Extreme Value framework (MEV) which relaxes limiting assumptions at the basis of the traditional EVT and accounts for the full distribution of the underlying “ordinary” events. We apply this general approach to the relevant case of daily rainfall and find that the MEV approach reduces the uncertainty in the estimation of high‐quantile extremes by up to 50% with respect to the classical EVT. The improved predictive power of the MEV framework is connected with its recognizing that extremes emerge from repeated sampling of ordinary events, thereby being able to use all available observations.

The estimation of the frequency of intense rainfall events is a crucial step for quantifying their impact on human societies and on the environment. This process is hindered by large gaps in ground observational networks at the global scale, such that extensive areas remain ungauged. The increasing availability of satellite‐based rainfall estimates, while providing data with unprecedented resolution and global coverage, also introduces new challenges: the scale disparity between gridded and rain‐gauge precipitation products on the one hand, and the short length of the available satellite records on the other. Here we propose a statistical framework for the estimation of rainfall extremes that is specifically designed to simultaneously address these two key issues, providing a new way of estimating extreme rainfall magnitudes from space. A downscaling procedure is here introduced to recover the spatial correlation and the probability density function of daily rainfall at the point (gauge) scale from coarse‐scale satellite estimates. The results are then combined with a recent statistical model of extremes (the Metastatistical Extreme Value distribution), which optimizes the use of the information obtained from relatively short satellite observational time series. The methodology is tested using data from the Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis over the Little Washita River, Oklahoma. We find that our approach satisfactorily reproduces downscaled daily rainfall probability density functions and can significantly improve the Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis‐based estimation of quantiles with return times larger than the length of the available data set (19 years here), which are especially important for several water‐related applications.

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The effects of mechanical generation of turbulent kinetic energy and buoyancy forces on the statistics of air temperature and velocity increments are experimentally investigated at the cross over from production to inertial range scales. The ratio of an approximated mechanical to buoyant production (or destruction) of turbulent kinetic energy can be used to form a dimensionless stability parameter ζ that classifies the state of the atmosphere as common in many atmospheric surface layer studies. Here, we assess how ζ affects the scale-wise evolution of the probability of extreme air temperature excursions, their asymmetry and time reversibility. The analysis makes use of high frequency velocity and air temperature time series measurements collected at z=5 m above a grass surface at very large frictional Reynolds numbers Re * = u * z/ν > 1 × 10 5 (u * is the friction velocity and ν is the kinematic viscosity of air). Using conventional higher-order structure functions, temperature exhibits larger intermittency and wider multifractality when compared to the longitudinal velocity component, consistent with laboratory studies and simulations conducted at lower Re * . Moreover, deviations from the classical Kolmogorov scaling for the longitudinal velocity are shown to be reasonably described by the She-Leveque vortex filament model that has no 'tunable' parameters and is independent of ζ. The work demonstrates that external boundary conditions, and in particular the magnitude and sign of the sensible heat flux, have a significant impact on temperature advection-diffusion dynamics within the inertial range. In particular, atmospheric stability affects both the buildup of intermittency and the persistent asymmetry and time irreversibility observed in the first two decades of inertial sub-range scales.

Abstract. Parameterizing incident solar radiation over complex topography regions in Earth System Models (ESMs) remains a challenging task. In ESMs, downward solar radiative fluxes at the surface are typically computed using plane parallel radiative transfer schemes, which do not explicitly account for the effects of a three-dimensional topography, such as shading and reflections. To improve the representation of these processes, we introduce and test a parameterization of radiation-topography interactions tailored to the Geophysical Fluid Dynamics Laboratory (GFDL) ESM land model. The approach presented here builds on an existing correction scheme for direct, diffuse and reflected solar irradiance terms over three-dimensional terrain. Here we combine this correction with a novel hierarchical multivariate clustering algorithm which explicitly describes the spatially varying downward irradiance over mountainous terrain. Based on a high-resolution digital elevation model, this combined method first defines a set of sub–grid land units ("tiles") by clustering together sites characterized by similar terrain-radiation interactions (e.g., areas with similar slope orientation, terrain and sky view factors). Then, based on terrain parameters characteristic for each tile, correction terms are computed to account for the effects of local 3-D topography on shortwave radiation over each land unit. We develop and test this procedure based on a set of Monte Carlo ray tracing simulations approximating the true radiative transfer process over three dimensional topography. Domains located in three distinct geographic regions (Alps, Andes, and Himalaya) are included in this study to allow for independent testing of the methodology over surfaces with differing topographic features. We find that accounting for the sub–grid spatial variability of solar irradiance originating from interactions with complex topography is important as these effects lead to significant local differences with respect to the plane-parallel case, as well as with respect to grid–cell scale average topographic corrections. Finally, we quantify the importance of the topographic correction for a varying number of terrain clusters and for different radiation terms (direct, diffuse, and reflected radiative fluxes) in order to inform the application of this methodology in different ESMs with varying sub-grid tile structure.