We investigated the scaling and topology of engineered urban drainage networks (UDNs) in two cities, and further examined UDN evolution over decades. UDN scaling was analyzed using two power law scaling characteristics widely employed for river networks: (1) Hack's law of length (L)‐area (A) [ L∝Ah] and (2) exceedance probability distribution of upstream contributing area (δ) [ P(A≥δ)∼aδ−ɛ]. For the smallest UDNs (<2 km2), length‐area scales linearly (h ∼ 1), but power law scaling (h ∼ 0.6) emerges as the UDNs grow. While P(A≥δ) plots for river networks are abruptly truncated, those for UDNs display exponential tempering [ P(A≥δ)=aδ−ɛexp(−cδ)]. The tempering parameter c decreases as the UDNs grow, implying that the distribution evolves in time to resemble those for river networks. However, the power law exponent ɛ for large UDNs tends to be greater than the range reported for river networks. Differences in generative processes and engineering design constraints contribute to observed differences in the evolution of UDNs and river networks, including subnet heterogeneity and nonrandom branching.
Cities are the drivers of socioeconomic innovation and are also forced to address the accelerating risk of failure in providing essential services such as water supply today and in the future. Here, we investigate the resilience of urban water supply security, which is defined in terms of the services that citizens receive. The resilience of services is determined by the availability and robustness of critical system elements or “capitals” (water resources, infrastructure, finances, management efficacy, and community adaptation). We translate quantitative information about this portfolio of capitals from seven contrasting cities on four continents into parameters of a coupled system dynamics model. Water services are disrupted by recurring stochastic shocks, and we simulate the dynamics of impact and recovery cycles. Resilience emerges under various constraints, expressed in terms of each city's capital portfolio. Systematic assessment of the parameter space produces the urban water resilience landscape, and we determine the position of each city along a continuous gradient from water insecure and nonresilient to secure and resilient systems. In several cities stochastic disturbance regimes challenge steady‐state conditions and drive system collapse. While water insecure and nonresilient cities risk being pushed into a poverty trap, cities which have developed excess capitals risk being trapped in rigidity and crossing a tipping point from high to low services and collapse. Where public services are insufficient, community adaptation improves water security and resilience to varying degrees. Our results highlight the need for resilience thinking in the governance of urban water systems under global change pressures.
We examine high-resolution urban infrastructure data using every pipe for the water distribution network (WDN) and sanitary sewer network (SSN) in a large Asian city (≈4 million residents) to explore the structure as well as the spatial and temporal evolution of these infrastructure networks. Network data were spatially disaggregated into multiple subnets to examine intracity topological differences for functional zones of the WDN and SSN, and time-stamped SSN data were examined to understand network evolution over several decades as the city expanded. Graphs were generated using a dual-mapping technique (Hierarchical Intersection Continuity Negotiation), which emphasizes the functional attributes of these networks. Network graphs for WDNs and SSNs are characterized by several network topological metrics, and a double Pareto (power-law) model approximates the node-degree distributions of both water infrastructure networks (WDN and SSN), across spatial and hierarchical scales relevant to urban settings, and throughout their temporal evolution over several decades. These results indicate that generic mechanisms govern the networks' evolution, similar to those of scale-free networks found in nature. Deviations from the general topological patterns are indicative of (1) incomplete establishment of network hierarchies and functional network evolution, (2) capacity for growth (expansion) or densification (e.g., in-fill), and (3) likely network vulnerabilities. We discuss the implications of our findings for the (re-)design of urban infrastructure networks to enhance their resilience to external and internal threats.
The security, resilience, and sustainability of urban water supply systems (UWSS) are challenged by global change pressures, including climate and land use changes, rapid urbanization, and population growth. Building on prior work on UWSS security and resilience, we quantify the sustainability of UWSS based on the performance of local sustainable governance and the size of global water and ecological footprints. We develop a new framework that integrates security, resilience, and sustainability to investigate trade-offs between these three distinct and inter-related dimensions. Security refers to the level of services, resilience is the system's ability to respond to and recover from shocks, and sustainability refers to local and global impacts, and to the long-term viability of system services. Security and resilience are both relevant at local scale (city and surroundings), while for sustainability cross-scale and -sectoral feedbacks are important. We apply the new framework to seven cities selected from diverse hydro-climatic and socio-economic settings on four continents. We find that UWSS security, resilience, and local sustainability coevolve, while global sustainability correlates negatively with security. Approaching these interdependent goals requires governance strategies that balance the three dimensions within desirable and viable operating spaces. Cities outside these boundaries risk system failure in the short-term, due to lack of security and resilience, or face longterm consequences of unsustainable governance strategies. We discuss these risks in the context of poverty and rigidity traps. Our findings have strong implications for policy-making, strategic management, and for designing systems to operate sustainably at local and global scales.
This paper was published online on 9 March 2017 with an error in Eq. (1b) and surrounding text and in the caption to Fig. 6. The caption of Fig. 6 should read as "WDN subnets along a gradient of breaking points between the power laws of trunk and tail (k break outliers from panel (d) in Fig. 5): (a) DZ11: k break = 5, p(k) trunk = 0.40k −2.49 and p(k) tail = 0.09 k −1.47 , N = 2425 (dual-mapped nodes); (b) DZ10: k break = 8, p(k) trunk = 1.46k −2.80 and p(k) tail = 0.26k −1.88 , N = 3179; (c) DZ01: k break = 10, p(k) trunk = 1.17k −2.37 and p(k) tail = 0.138k −1.686 , N = 1497; (d) DZ32: in this subnet power-law distributions of trunk and tail converge as the breaking point between the two power laws increases (k break = 20), and p(k) = 1.07k −2.27 (N = 2271)." On page 2, left-hand column, the text above Eqs. (1a) and (1b) should read as "The node degree distributions (NDD) for both types of water networks can be approximated by a Pareto power-law distribution [Eq. (1a); large, mature networks], p(k) = ak −γ , (1a) for k 2, or a double Pareto power-law distribution [Eq. (1b); small, immature networks], described by a two-piece function in the form p(k) trunk = ak −γ trunk , p(k) tail = bk −γ tail , (1b) where k 2 for p(k) trunk and k k break for p(k) tail. The exponent, γ [Eq. (1a)] and γ trunk [Eq. (1b)], for both WDNs and SSNs converges above a threshold of network size, measured as dual-mapped nodes N > 10 2 ." The paper has been corrected as of 25 February 2019. The caption and text are incorrect in the printed version of the journal.
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