Research ArticleANTHROPOLOGY

The demise of Angkor: Systemic vulnerability of urban infrastructure to climatic variations

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Science Advances  17 Oct 2018:
Vol. 4, no. 10, eaau4029
DOI: 10.1126/sciadv.aau4029
  • Fig. 1 Location of the study site.

    (A) Location of the medieval city of Angkor in modern Cambodia. Angkor was the primate city to a kingdom that incorporated most of mainland Southeast Asia at its peak in the 11th and 12th centuries CE. (B) Archeological map of Greater Angkor, after (29, 33, 46, 47). Limit of the study area indicated on (B) represents the watershed boundary.

  • Fig. 2 Schematic of the numerical model of erosion and sedimentation, illustrated for a single bifurcation in the network.

    Channels (edges) are depicted as dark blue lines and junctions (nodes) as pale blue circles. The flow on each edge corresponds to the thickness of the blue lines. Initially, flow is distributed evenly. In response to a heterogeneous increase in flow, one edge begins to erode, increasing its capacity and diverting water away from the neighboring edge. Sedimentation on this depleted edge, in turn, decreases its capacity and diverts more water along the eroded path, resulting in a damaged state in which the initial flow volume is unevenly distributed.

  • Fig. 3 Scaling of topological damage (Q) as a function of α and β (κ = 1, γ = 1) demonstrates three distinct regions of parameter space.

    The color plot in (A) represents the entire parameter space in α and β with the transition between regions (i) and (ii) dependent only on the erosion threshold, while the plots in (B) illustrate higher-resolution scans of “alpha” for fixed “beta” values, demonstrating a transition between regions (ii) and (iii) dependent on the thresholds for both erosion and sedimentation. Each datum point presented here corresponds to an average of 100 different flood configurations.

  • Fig. 4 Effects of flood magnitude (γ) on Q.

    (A and B) Plots of Q as a function of α for κ = 1, β = 0.001 (A), and β = 0.5 (B). (C) Color plot of Q as a function of α and β for γ = 5 and κ = 1.

  • Fig. 5 A map representing the average damage distribution in the network.

    This map was generated for control parameters γ = 1, α = 0.9, and β = 0.9 [region (iii)]. The color of each edge represents the average Q value for that edge 〈Qin, calculated from n = 3000 independent runs.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/10/eaau4029/DC1

    Supplementary Text

    Fig. S1. Conversion of archeological maps of 14th century Angkor into a directed, acyclic network topology.

    Fig. S2. A map representing the Angkor network with supersource (S) and supersink (T) included.

    Fig. S3. A generic network showing equilibrium flow distribution at initialization.

    Fig. S4. To induce damage, random flood flows are added to each edge.

    Fig. S5. Final flow distribution resulting from the perturbation shown above, for α = 0.9, β = 0.9, and ΔQmin = 2 × 10−3.

    Fig. S6. Results of the model on a generic topology.

    Fig. S7. Probability distribution for indegree and outdegree of each node in the final network representation of Angkor’s water distribution network, with supersource and supersink omitted.

    Table S1. List of symbols for control parameters accompanied by their purpose in the overall algorithm (role), brief description, and units.

    Table S2. List of symbols for noncontrol parameters, accompanied by their purpose in the overall algorithm (role), brief description, and units.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fig. S1. Conversion of archeological maps of 14th century Angkor into a directed, acyclic network topology.
    • Fig. S2. A map representing the Angkor network with supersource (S) and supersink (T) included.
    • Fig. S3. A generic network showing equilibrium flow distribution at initialization.
    • Fig. S4. To induce damage, random flood flows are added to each edge.
    • Fig. S5. Final flow distribution resulting from the perturbation shown above, for α = 0.9, β = 0.9, and ΔQmin = 2 × 10−3.
    • Fig. S6. Results of the model on a generic topology.
    • Fig. S7. Probability distribution for indegree and outdegree of each node in the final network representation of Angkor’s water distribution network, with supersource and supersink omitted.
    • Table S1. List of symbols for control parameters accompanied by their purpose in the overall algorithm (role), brief description, and units.
    • Table S2. List of symbols for noncontrol parameters, accompanied by their purpose in the overall algorithm (role), brief description, and units.

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