A copula-based joint deficit index for droughts.

We examine the scaling law $B \propto M^{\alpha}$ which connects organismal metabolic rate $B$ with organismal mass $M$, where $\alpha$ is commonly held to be 3/4. Since simple dimensional analysis suggests $\alpha=2/3$, we consider this to be a null hypothesis testable by empirical studies. We re-analyze data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting $\alpha=2/3$ in favor of $\alpha=3/4$. For mammals, we find a possible breakdown in scaling for larger masses reflected in a systematic increase in $\alpha$. We also review theoretical justifications of $\alpha=3/4$ based on dimensional analysis, nutrient-supply networks, and four-dimensional biology. We find that present theories for $\alpha=3/4$ require assumptions that render them unconvincing for rejecting the null hypothesis that $\alpha=2/3$.

https://arxiv.org/pdf/physics/0007096.pdf

Re-examination of the "3/4-law" of Metabolism

The Standardized Precipitation Index (SPI), a well-reviewed meteorological drought index recommended by the World Meteorological Organization (WMO), and its more recent climatic water balance variant, the Standardized Precipitation-Evapotranspiration Index (SPEI), both rely on selection of a univariate probability distribution to normalize the index, allowing for comparisons across climates. Choice of an improper probability distribution may impart bias to the index values, exaggerating or minimizing drought severity. This study compares a suite of candidate probability distributions for use in SPI and SPEI normalization using the 0.5° × 0.5° gridded Watch Forcing Dataset (WFD) at the continental scale, focusing on Europe. Several modifications to the SPI and SPEI methodology are proposed, as well as an updated procedure for evaluating SPI/SPEI goodness of fit based on the Shapiro-Wilk test. Candidate distributions for SPI organize into two groups based on their ability to model short-term accumulation (1-2 months) or long-term accumulation (>3 months). The two-parameter gamma distribution is recommended for general use when calculating SPI across all accumulation periods and regions within Europe, in agreement with previous studies. The generalized extreme value distribution is recommended when computing the SPEI, in disagreement with previous recommendations.

https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/joc.4267

Candidate Distributions for Climatological Drought Indices (SPI and SPEI)

Savannas are known as ecosystems with tree cover below climate-defined equilibrium values However, a predictive framework for understanding constraints on tree cover is lacking We present (a) a spatially extensive analysis of tree cover and fire distribution in sub-Saharan Africa, and (b) a model, based on empirical results, demonstrating that savanna and forest may be alternative stable states in parts of Africa, with implications for understanding savanna distributions Tree cover does not increase continuously with rainfall, but rather is constrained to low ( 75%, "forest") Intermediate tree cover rarely occurs Fire, which prevents trees from establishing, differentiates high and low tree cover, especially in areas with rainfall between 1000 mm and 2000 mm Fire is less important at low rainfall ( 2000 mm), where fire is rare This pattern suggests that complex interactions between climate and disturbance produce emergent alternative states in tree cover The relationship between tree cover and fire was incorporated into a dynamic model including grass, savanna tree saplings, and savanna trees Only recruitment from sapling to adult tree varied depending on the amount of grass in the system Based on our empirical analysis and previous work, fires spread only at tree cover of 40% or less, producing a sigmoidal fire probability distribution as a function of grass cover and therefore a sigmoidal sapling to tree recruitment function This model demonstrates that, given relatively conservative and empirically supported assumptions about the establishment of trees in savannas, alternative stable states for the same set of environmental conditions (ie, model parameters) are possible via a fire feedback mechanism Integrating alternative stable state dynamics into models of biome distributions could improve our ability to predict changes in biome distributions and in carbon storage under climate and global change scenarios

Tree cover in sub-Saharan Africa: rainfall and fire constrain forest and savanna as alternative stable states.

Pan-European comparison of candidate distributions for climatological drought indices, SPI and SPEI

A multivariate model of sea storms using copulas

[1] Droughts, like floods, are extreme expressions of the river flow dynamics. Here, droughts are intended as episodes during which the streamflow is below a given threshold, and are described as multivariate events characterized by two variables: average intensity and duration. In this work, we introduce the new concept of Dynamic Return Period, formulated using the theory of Copulas, and calculated via a Survival Kendall's approach. We show how it can be used (i) to monitor the temporal evolution of a drought event, and (ii) to perform real time assessment. In addition, a randomization strategy is introduced, in order to get rid of repeated measurements, which may adversely affect the statistical analysis of the available data, as well as the calculation of the return periods of interest: a practical example is shown, involving the fit of the drought duration distribution. The case study of the Po river basin (Northern Italy) is used as an illustration.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/wrcr.20551

Multivariate assessment of droughts: Frequency analysis and dynamic return period

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.

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

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

A comparison is provided between parametric and nonparametric approaches for the calculation of two drought indices: the standardized precipitation index (SPI) and the standardized streamflow index (SSI). The parametric approach has been implemented considering two possibilities: (1) a unique probability distribution for the variable of interest with parameters depending on the month of the year, and (2) the probability distribution depending on the month of the year. The parameters’ estimation is made using the maximum likelihood method, while the distribution selection is operated using the Kolmogorov-Smirnov goodness-of-fit test. For the nonparametric approach, the Weibull plotting position has been used to calculate the cumulative frequency. For both indices, the 1-month, 3-month, and 12-month time scales have been considered. As a case study, two 80-year-long monthly time series in Italy are considered: Roma Collegio Romano for precipitation, and Tevere River Basin at Ripetta for streamflow, ...

/pdf/comparison-between-parametric-and-nonparametric-approaches-1z1xi8nhmv.pdf

Renata Vezzoli

Papers

A multivariate model of sea storms using copulas

Multivariate assessment of droughts: Frequency analysis and dynamic return period

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

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

Comparison between Parametric and Nonparametric Approaches for the Calculation of Two Drought Indices: SPI and SSI