RESUMO
The attribution of changing intensity of rainfall extremes to global warming is a key challenge of climate research. From a thermodynamic perspective, via the Clausius-Clapeyron relationship, rainfall events are expected to become stronger due to the increased water-holding capacity of a warmer atmosphere. Here, we employ global, 1-hourly temperature and 3-hourly rainfall data to investigate the scaling between temperature and extreme rainfall. Although the Clausius-Clapeyron scaling of +7% rainfall intensity increase per degree warming roughly holds on a global average, we find very heterogeneous spatial patterns. Over tropical oceans, we reveal areas with consistently strong negative scaling (below -40%∘C-1). We show that the negative scaling is due to a robust linear correlation between pre-rainfall cooling of near-surface air temperature and extreme rainfall intensity. We explain this correlation by atmospheric and oceanic dynamics associated with cyclonic activity. Our results emphasize that thermodynamic arguments alone are not enough to attribute changing rainfall extremes to global warming. Circulation dynamics must also be thoroughly considered.
RESUMO
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. Particularly in recent years, a great progress has been made by augmenting "traditional" network theory in order to account for the multiplex nature of many networks, multiple types of connections between objects, the time-evolution of networks, networks of networks and other intricacies. However, existing network representations still lack crucial features in order to serve as a general data analysis tool. These include, most importantly, an explicit association of information with possibly heterogeneous types of objects and relations, and a conclusive representation of the properties of groups of nodes as well as the interactions between such groups on different scales. In this paper, we introduce a collection of definitions resulting in a framework that, on the one hand, entails and unifies existing network representations (e.g., network of networks and multilayer networks), and on the other hand, generalizes and extends them by incorporating the above features. To implement these features, we first specify the nodes and edges of a finite graph as sets of properties (which are permitted to be arbitrary mathematical objects). Second, the mathematical concept of partition lattices is transferred to the network theory in order to demonstrate how partitioning the node and edge set of a graph into supernodes and superedges allows us to aggregate, compute, and allocate information on and between arbitrary groups of nodes. The derived partition lattice of a graph, which we denote by deep graph, constitutes a concise, yet comprehensive representation that enables the expression and analysis of heterogeneous properties, relations, and interactions on all scales of a complex system in a self-contained manner. Furthermore, to be able to utilize existing network-based methods and models, we derive different representations of multilayer networks from our framework and demonstrate the advantages of our representation. On the basis of the formal framework described here, we provide a rich, fully scalable (and self-explanatory) software package that integrates into the PyData ecosystem and offers interfaces to popular network packages, making it a powerful, general-purpose data analysis toolkit. We exemplify an application of deep graphs using a real world dataset, comprising 16 years of satellite-derived global precipitation measurements. We deduce a deep graph representation of these measurements in order to track and investigate local formations of spatio-temporal clusters of extreme precipitation events.
