Alejandro Tejedor

Delta channel networks: 1. A graph‐theoretic approach for studying connectivity and steady state transport on deltaic surfaces

River deltas are intricate landscapes with complex channel networks that self-organize to deliver water, sediment, and nutrients from the apex to the delta top and eventually to the coastal zone. The natural balance of material and energy fluxes, which maintains a stable hydrologic, geomorphologic, and ecological state of a river delta, is often disrupted by external perturbations causing topological and dynamical changes in the delta structure and function. A formal quantitative framework for studying delta channel network connectivity and transport dynamics and their response to change is lacking. Here we present such a framework based on spectral graph theory and demonstrate its value in computing deltas steady state fluxes and identifying upstream (contributing) and downstream (nourishment) areas and fluxes from any point in the network. We use this framework to construct vulnerability maps that quantify the relative change of sediment and water delivery to the shoreline outlets in response to possible perturbations in hundreds of upstream links. The framework is applied to the Wax Lake delta in the Louisiana coast of the U.S. and the Niger delta in West Africa. In a companion paper, we present a comprehensive suite of metrics that quantify topologic and dynamic complexity of delta channel networks and, via application to seven deltas in diverse environments, demonstrate their potential to reveal delta morphodynamics and relate to notions of vulnerability and robustness.

Delta channel networks: 2. Metrics of topologic and dynamic complexity for delta comparison, physical inference, and vulnerability assessment

Deltas are landforms that deliver water, sediment and nutrient fluxes from upstream rivers to the deltaic surface and eventually to oceans or inland water bodies via multiple pathways. Despite their importance, quantitative frameworks for their analysis lack behind those available for tributary networks. In a companion paper, delta channel networks were conceptualized as directed graphs and spectral graph theory was used to design a quantitative framework for exploring delta connectivity and flux dynamics. Here we use this framework to introduce a suite of graph-theoretic and entropy-based metrics, to quantify two components of a deltas complexity: (1) Topologic, imposed by the network connectivity and (2) Dynamic, dictated by the flux partitioning and distribution. The metrics are aimed to facilitate comparing, contrasting, and establishing connections between deltaic structure, process, and form. We illustrate the proposed analysis using seven deltas in diverse morphodynamic environments and of various degrees of channel complexity. By projecting deltas into a topo-dynamic space whose coordinates are given by topologic and dynamic delta complexity metrics, we show that this space provides a basis for delta comparison and physical insight into their dynamic behavior. The examined metrics are demonstrated to relate to the intuitive notion of vulnerability, measured by the impact of upstream flux changes to the shoreline flux, and reveal that complexity and vulnerability are inversely related. Finally, a spatially explicit metric, akin to a delta width function, is introduced to classify shapes of different delta types.

A review of vulnerability indicators for deltaic social–ecological systems

The sustainability of deltas worldwide is under threat due to the consequences of global environmental change (including climate change) and human interventions in deltaic landscapes. Understanding these systems is becoming increasingly important to assess threats to and opportunities for long-term sustainable development. Here, we propose a simplified, yet inclusive social–ecological system (SES)-centered risk and vulnerability framework and a list of indicators proven to be useful in past delta assessments. In total, 236 indicators were identified through a structured review of peer-reviewed literature performed for three globally relevant deltas—the Mekong, the Ganges–Brahmaputra–Meghna and the Amazon. These are meant to serve as a preliminary “library” of potential indicators to be used for future vulnerability assessments. Based on the reviewed studies, we identified disparities in the availability of indicators to populate some of the vulnerability domains of the proposed framework, as comprehensive social–ecological assessments were seldom implemented in the past. Even in assessments explicitly aiming to capture both the social and the ecological system, there were many more indicators for social susceptibility and coping/adaptive capacities as compared to those relevant for characterizing ecosystem susceptibility or robustness. Moreover, there is a lack of multi-hazard approaches accounting for the specific vulnerability profile of sub-delta areas. We advocate for more comprehensive, truly social–ecological assessments which respond to multi-hazard settings and recognize within-delta differences in vulnerability and risk. Such assessments could make use of the proposed framework and list of indicators as a starting point and amend it with new indicators that would allow capturing the complexity as well as the multi-hazard exposure in a typical delta SES.

Population dynamics, delta vulnerability and environmental change: comparison of the Mekong, Ganges–Brahmaputra and Amazon delta regions

Tropical delta regions are at risk of multiple threats including relative sea level rise and human alterations, making them more and more vulnerable to extreme floods, storms, surges, salinity intrusion, and other hazards which could also increase in magnitude and frequency with a changing climate. Given the environmental vulnerability of tropical deltas, understanding the interlinkages between population dynamics and environmental change in these regions is crucial for ensuring efficient policy planning and progress toward social and ecological sustainability. Here, we provide an overview of population trends and dynamics in the Ganges–Brahmaputra, Mekong and Amazon deltas. Using multiple data sources, including census data and Demographic and Health Surveys, a discussion regarding the components of population change is undertaken in the context of environmental factors affecting the demographic landscape of the three delta regions. We find that the demographic trends in all cases are broadly reflective of national trends, although important differences exist within and across the study areas. Moreover, all three delta regions have been experiencing shifts in population structures resulting in aging populations, the latter being most rapid in the Mekong delta. The environmental impacts on the different components of population change are important, and more extensive research is required to effectively quantify the underlying relationships. The paper concludes by discussing selected policy implications in the context of sustainable development of delta regions and beyond.

Quantifying the signature of sediment composition on the topologic and dynamic complexity of river delta channel networks and inferences toward delta classification

Deltas contain complex self-organizing channel networks that nourish the surface with sediment and nutrients. Developing a quantitative understanding of how controlling physical mechanisms of delta formation relate to the channel networks they imprint on the landscape remains an open problem, hindering further progress on quantitative delta classification and understanding process from form. Here we isolate the effect of sediment composition on network structure by analyzing Delft3D river-dominated deltas within the recently introduced graph-theoretic framework for quantifying complexity of delta channel networks. We demonstrate that deltas with coarser incoming sediment tend to be more complex topologically (increased number of pathways) but simpler dynamically (reduced flux exchange between subnetworks) and that once a morphodynamic steady state is reached, complexity also achieves a steady state. By positioning simulated deltas on the so-called TopoDynamic complexity space and comparing with field deltas, we propose a quantitative framework for exploring complexity toward systematic inference and classification.

Predictability of the large relaxations in a cellular automaton model

A simple one-dimensional cellular automaton model with threshold dynamics is introduced. It is loaded at a uniform rate and unloaded by abrupt relaxations. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to −1. This coincides with the phenomenological Gutenberg–Richter behavior observed in seismology for the cumulative statistics of earthquakes at the regional or global scale. The key point of the model is the zero-load state of the system after the occurrence of any relaxation, no matter what its size. This leads to an equipartition of probability between all possible load configurations in the system during the successive loading cycles. Each cycle ends with the occurrence of the greatest—or characteristic—relaxation in the system. The duration of the cycles in the model is statistically distributed with a coefficient of variation ranging from 0.5 to 1. The predictability of the characteristic relaxations is evaluated by means of error diagrams. This model illustrates the value taking into account the refractory periods to obtain a considerable gain in the quality of the predictions.

The Negative Binomial Distribution as a Renewal Model for the Recurrence of Large Earthquakes

The negative binomial distribution is presented as the waiting time distribution of a cyclic Markov model. This cycle simulates the seismic cycle in a fault. As an example, this model, which can describe recurrences with aperiodicities between 0 and 0.5, is used to fit the Parkfield, California earthquake series in the San Andreas Fault. The performance of the model in the forecasting is expressed in terms of error diagrams and compared with other recurrence models from literature.

One-Way Markov Process Approach to Repeat Times of Large Earthquakes in Faults

A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid’s elastic rebound theory. Here it is proved that in any one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world.

Multiplex Networks: A Framework for Studying Multiprocess Multiscale Connectivity Via Coupled‐Network Theory With an Application to River Deltas

Transport of water, nutrients, or energy fluxes in many natural or coupled human natural systems occurs along different pathways that often have a wide range of transport timescales and might exchange fluxes with each other dynamically. Although network approaches have been proposed for studying connectivity and transport properties on single-layer networks, theories considering interacting networks are lacking. We present a general framework for transport on multiscale coupled-connectivity systems, via multilayer networks which conceptualize the system as a set of interacting networks, each arranged in a separate layer, and with interactions across layers acknowledged by interlayer links. We illustrate this framework by examining transport in river deltas as a dynamic interaction of flow within river channels and overland flow on the islands, when controlled by the flooding level. We show the potential of the framework to answer quantitative questions related to the characteristic timescale of response in the system. Plain Language Summary The physical processes that shape landscapes leave behind patterns of connectivity along which fluxes occur via a multitude of processes, for example, flow through channels, subsurface or overland flow. The connectivity imposed by those processes (e.g., channel networks) exerts a significant control on the evolution and form of the underlying systems. We introduce a framework based on coupled networks, Multiplex, that allows to quantify the connectivity properties emerging from the simultaneous action of different processes, enabling thus to assess the overall system properties and dynamics. We illustrate this framework by examining the case of river deltas, where intermittent flooding and exchange of water, sediment, and nutrients between the channels and the islands maintains the delta top by trapping sediment, stabilizing banks, and enriching rivers with carbon and nutrients. By describing the delta system as a Multiplex—integrating the connectivity imposed by confined (in the channel network) and overland (on the islands) flows as well as the interactions (flux exchange) between them—we show the emergence of system transport properties and dynamics not foreseen by analyzing each process separately, and therefore revealing key information essential to predict the system response under changing forcing.