ALBERT

Description: 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. The main focus of this paper is to provide a formal framework that enables a mathematically accurate description of any given system in a self-contained fashion. In addition, the purpose of this framework is to facilitate the utilization of existing methods and models supporting a practical data analysis. Network theory serves as the mathematical foundation of our framework. A network models the elements of a system as nodes, and their relations (or interactions) as edges. Particularly in the recent past—certainly also due to the deluge of available data—one could notice a large number of publications attempting to augment “traditional” networks, in order to accommodate the increased heterogeneity of data, and to assign labels and values to nodes and edges (e.g., networks of networks and multilayer networks (MLN)). The framework proposed here entails and unifies these approaches, but also generalizes them with two main aspects in mind: (1) Any node and any edge may be assigned possibly distinct types of properties (e.g., a node representing a human being may have “age” as a type of property whose value is a number, and “blood values” as another type of property whose value is a table of labels and numbers) and (2) integration of properties of groups of nodes and their respective interrelations within the same framework. Together, these objectives make it possible to combine different datasets (e.g., climatological and socioecological data or (electro) physiological records of different organs), integrate a priori knowledge of groups of objects and their relations, and carry out an analysis of potential relationships of the respective systems within the same network representation. On the basis of the mathematical work we provide here, the existing network measures can be generalized and new measures developed. Yet, in order to practically conduct data analysis, we also provide a rich software implementation of our framework that integrates into the PyData ecosystem (which comprises various libraries for scientific computing) and offers interfacing methods to popular network packages, making it a considerable general-purpose data analysis toolkit

Description: The scaling behavior of rainfall has been extensively studied both in terms of event magnitudes and in terms of spatial extents of the events. Different heavy‐tailed distributions have been proposed as candidates for both instances, but statistically rigorous treatments are rare. Here we combine the domains of event magnitudes and event area sizes by a spatiotemporal integration of 3‐hourly rain rates corresponding to extreme events derived from the quasi‐global high‐resolution rainfall product Tropical Rainfall Measuring Mission 3B42. A maximum likelihood evaluation reveals that the distribution of spatiotemporally integrated extreme rainfall cluster sizes over the oceans is best described by a truncated power law, calling into question previous statements about scale‐free distributions. The observed subpower law behavior of the distribution's tail is evaluated with a simple generative model, which indicates that the exponential truncation of an otherwise scale‐free spatiotemporal cluster size distribution over the oceans could be explained by the existence of land masses on the globe.

Description: Fires are a fundamental part of the Earth System. In the last decades, they have been altering ecosystem structure, biogeochemical cycles and atmospheric composition with unprecedented rapidity. In this study, we implement a complex networks-based methodology to track individual fires over space and time. We focus on extreme fires—the 5% most intense fires—in the tropical forests of the Brazilian Legal Amazon over the period 2002–2019. We analyse the interannual variability in the number and spatial patterns of extreme forest fires in years with diverse climatic conditions and anthropogenic pressure to examine potential synergies between climate and anthropogenic drivers. We observe that major droughts, that increase forest flammability, co-occur with high extreme fire years but also that it is fundamental to consider anthropogenic activities to understand the distribution of extreme fires. Deforestation fires, fires escaping from managed lands, and other types of forest degradation and fragmentation provide the ignition sources for fires to ignite in the forests. We find that all extreme forest fires identified are located within a 0.5-km distance from forest edges, and up to 56% of them are within a 1-km distance from roads (which increases to 73% within 5 km), showing a strong correlation that defines spatial patterns of extreme fires.

Description: 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.

Description: Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere that play a crucial role in the distribution of freshwater but can also cause natural and economic damage by facilitating heavy precipitation. Here, we investigate the large-scale spatiotemporal synchronization patterns of heavy precipitation events (HPEs) over the western coast and the continental regions of North America (NA), during the period from 1979 to 2018. In particular, we use event synchronization and a complex network approach incorporating varying delays to examine the temporal evolution of spatial patterns of HPEs in the aftermath of land-falling ARs. For that, we employ the SIO-R1 catalog of ARs that landfall on the western coast of NA, ranked in terms of intensity and persistence on an AR-strength scale which varies from level AR1 to AR5, along with daily precipitation estimates from ERA5 with a 0.25∘ spatial resolution. Our analysis reveals a cascade of synchronized HPEs, triggered by ARs of level AR3 or higher. On the first 3 d after an AR makes landfall, HPEs mostly occur and synchronize along the western coast of NA. In the subsequent days, moisture can be transported to central and eastern Canada and cause synchronized but delayed HPEs there. Furthermore, we confirm the robustness of our findings with an additional AR catalog based on a different AR detection method. Finally, analyzing the anomalies of integrated water vapor transport, geopotential height, upper-level meridional wind, and precipitation, we find atmospheric circulation patterns that are consistent with the spatiotemporal evolution of the synchronized HPEs. Revealing the role of ARs in the precipitation patterns over NA will lead to a better understanding of inland HPEs and the effects that changing climate dynamics will have on precipitation occurrence and consequent impacts in the context of a warming atmosphere.

Description: Humans profoundly alter fire regimes both directly, by introducing changes in fuel dynamics and ignitions, and indirectly by increasing the release of greenhouse gases and aerosols from fires, which can alter regional climate and, as a consequence, modify fuel moisture and availability. Interactions between vegetation dynamics, regional climate change, and anthropogenic pressure lead to high heterogeneity in the spatio-temporal fire distribution. We use the new FireTracks Scientific Dataset that tracks the spatio-temporal development of individual fires to analyse fire regimes in the Brazilian Legal Amazon over the period 2002-2020. We analyse fire size, duration, intensity, and rate of spread in six different land-cover classes. Particular combinations of fire features determine the dominant and characteristic fire regime in each of them. We find that fires in savannas and evergreen forests burn the largest areas and are the most long-lasting. Forest fires have the potential for burning at the highest intensities, whereas higher rates of spread are found in savannas. Woody savanna and grassland fires are usually affected by smaller, shorter, less-intense fires compared with fires in evergreen forest and savanna. However, fires in grasslands can burn at rates of spread as high as savanna fires as a result of the easily flammable fuel. We observe that fires in deciduous forests and croplands are generally small, short, and low-intense, although the latter can sustain high rates of spread due to the dry post-harvest residuals. The reconstructed fire regimes for each land cover can be used to improve the simulated fire characteristics by models, and thus, future projections.

Description: The character and health of ecosystems worldwide is tightly coupled to changes in Earth’s climate. Theory suggests that ecosystem resilience—the ability of ecosystems to resist and recover from external shocks such as droughts and fires—can be inferred from their natural variability. Here, we quantify vegetation resilience globally with complementary metrics based on two independent long-term satellite records. We first empirically confirm that the recovery rates from large perturbations can be closely approximated from internal vegetation variability across vegetation types and climate zones. On the basis of this empirical relationship, we quantify vegetation resilience continuously and globally from 1992 to 2017. Long-term vegetation resilience trends are spatially heterogeneous, with overall increasing resilience in the tropics and decreasing resilience at higher latitudes. Shorter-term trends, however, reveal a marked shift towards a global decline in vegetation resilience since the early 2000s, particularly in the equatorial rainforest belt.