A Triad of Networks and a Triad of Fusions for the Other Climate Crisis

TL;DR

The paper reframes climate science around a triad of networks—networks of data, climate data over networks, and networks for climate data—and shows how bridges within and between these layers can operationalize the Shaw-Stevens agenda that critiques Large Scale Determinism. It grounds the triad in the Tsonis network tradition, surveys geophysical networks and covariance on metric graphs, and presents three ML-enabled model families (GSP, PGMs, GNNs) as tools for data-driven climate tasks. A suite of bridges links discrete-network perspectives with continuum modelling and governance, culminating in a reflexive meta-fusion—the Shaw-Stevens network ecosystem—that aims to co-produce climate knowledge and policy in an adaptive, multiscale, and interpretable framework. The work argues that this ecosystem enables more robust detection of discrepancies, supports hierarchical design, and fosters governance-ready, uncertainty-aware decision making through a dynamically evolving, self-validating architecture.

Abstract

Shaw and Stevens call for a new paradigm in climate science criticizes Large Scale Determinism in favor of (i) embracing discrepancies, (ii) embracing hierarchies, and (iii) create disruption while keeping interpretability. The last 20 years have seen a plethora of contributions relating complex networks with climate data and climate models. We provide a view of climate networks through a triad of frameworks and associated paradigms: (a) networks of data, where both (geographical) nodes and their links (arcs) are determined according to some metrics and/or statistical criteria; (b) climate data over networks, where the structure of the network (for both vertices and edges) is topologically pre-determined, and the climate variable is continuously defined over the (nonlinear) network; finally, (c) networks for data, referring to the huge machinery based on networks within the realm machine learning and statistics, with specific emphasis on their use for climate data. This paper is not a mere description of each element of the network triad, but rather a manifesto for the creation of three classes of fusions (we term them bridges). We advocate and carefully justify a fusion within to provide a corpus unicuum inside the network triad. We then prove that the fusion within is the starting point for a fusion between, where the network triad becomes a condition sine qua non for the implementation of the Shaw-Stevens agenda. We culminate with a meta fusion that allows for the creation of what we term a Shaw-Stevens network ecosystem.

Figures (9)

• Figure 1: A representation of different Tsonis networks with their degree distributions.
• Figure 2: A graph with Euclidean edges, where the bijections between the edges $e_1$ and $e_2$ and their abstract segments $s(e_1)$ and $s(e_2)$ have been highlighted. Figure adapted from filosi_temporally-evolving_2025.
• Figure 3: A physical network (left), its associated resistor graph (center) and distances between some couple of nodes (right). Distances are always measured in meters. $d_{SP}$ denotes the shortest-path distance, while $d_R$ is the resistance distance.
• Figure 4: Left: monthly global land temperature anomalies since 1950. Right: precipitation anomalies in May 2025 on a $2.5^\circ \times 2.5^\circ$ grid. Data for the first figure and the second figure has been taken from NOAA_climate_data.
• Figure 5: Left: Clearwater River Basin in Idaho (USA) and $50$ points of interest on it. Right: how a river basin can be modeled through an (oriented) tree.