Carlo De Michele

Tree-grass co-existence in savanna: Interactions of rain and fire

The mechanisms permitting the co-existence of tree and grass in savannas have been a source of contention for many years. The two main classes of explanations involve either competition for resources, or differential sensitivity to disturbances. Published models focus principally on one or the other of these mechanisms. Here we introduce a simple ecohydrologic model of savanna vegetation involving both competition for water, and differential sensitivity of trees and grasses to fire disturbances. We show how the co-existence of trees and grasses in savannas can be simultaneously controlled by rainfall and fire, and how the relative importance of the two factors distinguishes between dry and moist savannas. The stability map allows to predict the changes in vegetation structure along gradients of rainfall and fire disturbances realistically, and to clarify the distinction between climate- and disturbance-dependent ecosystems.

The derivation of areal reduction factor of storm rainfall from its scaling properties

We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is widely used in reducing point rainfall to obtain areal average values for the same duration, probability of exceedance, and specified area. The concepts of scaling and multiscaling, developed in recent years, provide a powerful framework for studying spatial and temporal variability of hydrological processes. It is our view that ARF must reflect the scaling properties of rainfall in space and time. We develop a simple statistical approach to the ARF of extreme storm rainfall based on the scaling properties of the underlying process in space and time. We derive the scaling relations of mean rainfall intensity over an area A and for a duration T using the concepts of dynamic scaling and statistical self-affinity. A new physically based formula for the ARF is then obtained. Applications are made to observations from the metropolitan area of Milan, Italy, and to data in the United Kingdom, as given in the Natural Environmental Research Council Flood Studies Report. These studies indicate that storm rates in space and time are scaling for extreme events, and hence this concept is shown to provide a useful practical approach to the evaluation of design storms for specified areas.

From generalized Pareto to extreme values law: Scaling properties and derived features

Given the fact that, assuming a generalized Pareto distribution for a process, it is possible to derive an asymptotic generalized extreme values law for the corresponding maxima, in this paper we consider the theoretical relations linking the parameters of such distributions. In addition, temporal scaling properties are shown to hold for both laws when considering proper power-law forms for both the position and the scale parameters; also shown is the relation between the scaling exponents of the distributions of interest, how the scaling properties of one distribution yield those of the other, and how the scaling features may be used to estimate the parameters of the distributions at different temporal scales. Finally, an application to rainfall is given.

Multivariate Extreme Value Methods

Multivariate extremes occur in several hydrologic and water resources problems. Despite their practical relevance, the real-life decision making as well as the number of designs based on an explicit treatment of multivariate variables is yet limited as compared to univariate analysis. A first problem arising when working in a multidimensional context is the lack of a “natural” definition of extreme values: essentially, this is due to the fact that different concepts of multivariate order and failure regions are possible. Also, in modeling multivariate extremes, central is the issue of dependence between the variables involved: again, several approaches are possible. A further practical problem is represented by the construction of multivariate Extreme Value models suitable for applications: the task is indeed difficult from a mathematical point of view. In addition, the calculation of multivariate Return Periods, quantiles, and design events, which represent quantities of utmost interest in applications, is rather tricky. In this Chapter we show how the use of Copulas may help in dealing with (and, possibly, solving) these problems.

Phase Space Parameterization of Rain: The Inadequacy of Gamma Distribution

We show that the Gamma distribution is not an adequate fit for the probability density function of drop diameters using the Kolmogorov-Smirnov goodness of fit test. We propose a different parametrization of drop size distributions, which not depending by any particular functional form, is based on the adoption of standardized central moments. The first three standardized central moments are sufficient to characterize the distribution of drop diamters at the ground. These parameters together with the drop count form a 4-tuple which fully describe the variability of the drop size distributions. The Cartesian product of this 4-tuple of parameters is the rainfall phase space. Using disdrometer data from 10 different locations we identify invariant, not depending on location, properties of the rainfall phenomenon.

Modeling flood event characteristics using D-vine structures

The authors investigate the use of drawable (D-)vine structures to model the dependences existing among the main characteristics of a flood event, i.e., flood volume, flood peak, duration, and peak time. Firstly, different three- and four-dimensional probability distributions were built considering all the permutations of the conditioning variables. The Frank copula was used to model the dependence of each pair of variables. Then, the appropriate D-vine structures were selected using information criteria and a goodness-of-fit test. The influence of varying the data length on the selected D-vine structure was also investigated. Finally, flood event characteristics were simulated using the four-dimensional D-vine structure.

Comparing COSMO-CLM simulations and MODIS data of snow cover extent and distribution over Italian Alps

Abstract Snow cover maps from Earth Observation (EO) satellites are valuable datasets containing large-scale information on snow cover extent, snow cover distribution and snow cover duration. In evaluating the performances of Regional Climate Models, EO data can be a valid piece of information alternative to in-situ measurements, which require a dense network of stations covering the entire altitudinal range and techniques for interpolating the values. In this context, MODIS snow products play a leading role providing several types of snow cover maps with high spatial and temporal resolutions. Here, we assess snow cover outputs of a high resolution Regional Climate Model (RCM) using MODIS maps of snow covered area over the Po river basin, northern Italy. The dataset consists of 9 years of MODIS data (2003–2011) cleaned from cloud cover by means of a cloud removal procedure. The maps have 500 m spatial resolution and daily temporal resolution. The RCM considered is COSMO-CLM, run at 0.0715° resolution (about 8 km) and coupled with the soil module TERRA_ML. The ERA-Interim reanalyses are used as initial and boundary conditions. The results show a good agreement between observed and simulated snow cover duration and extension. COSMO-CLM is able to reproduce the inter-annual variabilities of snow cover features as well as the seasonal trend of snow cover duration and extension. Limitations emerge when the RCM simulates the progressive depletion of the snow cover in spring. Simulated snowmelt occurs faster than the observed one. Then, we investigate the influence of the spatial resolution of the climate model. The simulation at 0.0715° (about 8 km) is compared to a simulation performed at 0.125° (about 14 km). The comparison highlights the benefits provided by the higher spatial resolution in the accumulation season, reflecting the improvements obtained in temperature and precipitation fields.

Johnson SB as general functional form for raindrop size distribution

Drop size distribution represents the statistical synthesis of rainfall dynamics at particle size scale. Gamma and Lognormal distributions have been widely used in the literature to approximate the drop diameter variability, contrarily to the natural upper boundary of the variable, with almost always site-specific studies and without the support of statistical goodness-of-fit tests. In this work, we present an extensive statistical investigation of raindrop size distribution based on eight data sets, well distributed on the Earths surface, which have been analyzed by using skewness-kurtosis plane, AIC and BIC indices and Kolmogorov-Smirnov test. Here for the first time, the Johnson SB is proposed as general functional form to describe the drop diameter variability specifically at 1 min time scale. Additional analyses demonstrate that the model is well suitable even for larger time intervals (≥1 min).

The discrete charm of rain

Weather reports and many scientific models treat rainfall as a continuous process, but to truly understand rain and its effects, one must consider its fundamentally discrete nature.

Tree cover bimodality in savannas and forests emerging from the switching between two fire dynamics.

Moist savannas and tropical forests share the same climatic conditions and occur side by side. Experimental evidences show that the tree cover of these ecosystems exhibits a bimodal frequency distribution. This is considered as a proof of savanna–forest bistability, predicted by dynamic vegetation models based on non-linear differential equations. Here, we propose a change of perspective about the bimodality of tree cover distribution. We show, using a simple matrix model of tree dynamics, how the bimodality of tree cover can emerge from the switching between two linear dynamics of trees, one in presence and one in absence of fire, with a feedback between fire and trees. As consequence, we find that the transitions between moist savannas and tropical forests, if sharp, are not necessarily catastrophic.