Helbing, D., 2013: “Globally networked risks and how to respond.” Nature, v. 497, pp. 51-59, doi: 10.1038/nature12047.
Today’s strongly connected, global networks have produced highly interdependent systems that we do not understand and cannot control well. These systems are vulnerable to failure at all scales, posing serious threats to society, even when external shocks are absent. As the complexity and interaction strengths in our networked world increase, man-made systems can become unstable, creating uncontrollable situations even when decision-makers are well-skilled, have all data and technology at their disposal, and do their best. To make these systems manageable, a fundamental redesign is needed. A ‘Global Systems Science’ might create the required knowledge and paradigm shift in thinking.
Figure 1 from the referenced paper, after a 2011 World Economic Forum report (pdf).
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Devauchelle, O., A.P. Petroff, H.F. Seybold, and D.H. Rothman, 2012: “Ramification of stream networks.” Proceedings of the National Academy of Sciences, v. 109, pp. 20,832–20,836, doi: 10.1073/pnas.1215218109.
The geometric complexity of stream networks has been a source of fascination for centuries. However, a comprehensive understanding of ramification—the mechanism of branching by which such networks grow—remains elusive. Here we show that streams incised by groundwater seepage branch at a characteristic angle of 2π/5 = 72°. Our theory represents streams as a collection of paths growing and bifurcating in a diffusing field. Our observations of nearly 5,000 bifurcated streams growing in a 100 km2 groundwater field on the Florida Panhandle yield a mean bifurcation angle of 71.9° ± 0.8°. This good accord between theory and observation suggests that the network geometry is determined by the external flow field but not, as classical theories imply, by the flow within the streams themselves.
Open Access
Perron, J.T., P.W. Richardson, K.L. Ferrier, and M. Lapôtre, 2012: “The root of branching river networks.” Nature, v. 492, pp. 100-103, doi: 10.1038/nature11672.
Branching river networks are one of the most widespread and recognizable features of Earth’s landscapes and have also been discovered elsewhere in the Solar System. But the mechanisms that create these patterns and control their spatial scales are poorly understood. Theories based on probability or optimality have proven useful, but do not explain how river networks develop over time through erosion and sediment transport. Here we show that branching at the uppermost reaches of river networks is rooted in two coupled instabilities: first, valleys widen at the expense of their smaller neighbours, and second, side slopes of the widening valleys become susceptible to channel incision. Each instability occurs at a critical ratio of the characteristic timescales for soil transport and channel incision. Measurements from two field sites demonstrate that our theory correctly predicts the size of the smallest valleys with tributaries. We also show that the dominant control on the scale of landscape dissection in these sites is the strength of channel incision, which correlates with aridity and rock weakness, rather than the strength of soil transport. These results imply that the fine-scale structure of branching river networks is an organized signature of erosional mechanics, not a consequence of random topology.
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Sanford, S.E., I.F. Creed, C.L. Tague, F.D. Beall, and J.M. Buttle, 2007: “Scale-dependence of natural variability of flow regimes in a forested landscape.” Water Resources Research, v. 43, paper no. W08414, doi: 10.1029/2006WR005299.
The ecological integrity of riverine ecosystems is dependent upon the natural flow regime of the river system. Maintaining natural variability in the flow regime is critical for conserving the structure and function of riverine ecosystems. This research seeks to determine relations between natural variability in the flow regime and basin scale. A distributed hydrologic model was used to characterize the natural flow regime of basins from first to fifth order within tributaries of the Batchawana River in the Algoma Highlands of central Ontario using the range of variability approach (RVA). A 30-year simulated flow record was used to calculate natural variability in the flow regime, defined by the S80 [(90th percentile – 10th percentile)/median]. Flow variability under wetter conditions was similar across all basins, regardless of scale. Conversely, flow variability under drier conditions was scale-dependent, with smaller basins (<600 ha) showing a large range in variability and larger basins (>600 ha) showing a smaller range in variability that converged toward a constant with increasing area. The effect of basin area on flow variability suggested the existence of a representative elementary area (REA). Within the REA, morphometric sources of natural variability were determined through multivariate regression analyses. A combination of indices describing the near-stream riparian area within a basin, median basin residence time, and basin curvature was significantly related to flow variability under drier conditions. These findings present a potential management template for establishing reference conditions against which impacts of disturbance on flows throughout a regional drainage basin may be measured
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Mason, W., and D.J. Watts, 2012: “Collaborative learning in networks.” Proceedings of the National Academy of Sciences, v. 109, no. 3, pp. 764-769, doi: 10.1073/pnas.1110069108.
Complex problems in science, business, and engineering typically require some tradeoff between exploitation of known solutions and exploration for novel ones, where, in many cases, information about known solutions can also disseminate among individual problem solvers through formal or informal networks. Prior research on complex problem solving by collectives has found the counterintuitive result that inefficient networks, meaning networks that disseminate information relatively slowly, can perform better than efficient networks for problems that require extended exploration. In this paper, we report on a series of 256 Web-based experiments in which groups of 16 individuals collectively solved a complex problem and shared information through different communication networks. As expected, we found that collective exploration improved average success over independent exploration because good solutions could diffuse through the network. In contrast to prior work, however, we found that efficient networks outperformed inefficient networks, even in a problem space with qualitative properties thought to favor inefficient networks. We explain this result in terms of individual-level explore-exploit decisions, which we find were influenced by the network structure as well as by strategic considerations and the relative payoff between maxima. We conclude by discussing implications for real-world problem solving and possible extensions.
Open Access
David, C.H., D.R. Maidment, G.-Y. Niu, Z.-L. Yang, F. Habets, and V. Eijkhout, 2011: “River network routing on the NHDPlus dataset.” Journal of Hydrometeorology, v. 12, no. 5, pp. 913-934, doi: 10.1175/2011JHM1345.1.
The mapped rivers and streams of the contiguous United States are available in a geographic information system (GIS) dataset called National Hydrography Dataset Plus (NHDPlus). This hydrographic dataset has about 3 million river and water body reaches along with information on how they are connected into networks. The U.S. Geological Survey (USGS) National Water Information System (NWIS) provides streamflow observations at about 20 thousand gauges located on the NHDPlus river network. A river network model called Routing Application for Parallel Computation of Discharge (RAPID) is developed for the NHDPlus river network whose lateral inflow to the river network is calculated by a land surface model. A matrix-based version of the Muskingum method is developed herein, which RAPID uses to calculate flow and volume of water in all reaches of a river network with many thousands of reaches, including at ungauged locations. Gauges situated across river basins (not only at basin outlets) are used to automatically optimize the Muskingum parameters and to assess river flow computations, hence allowing the diagnosis of runoff computations provided by land surface models. RAPID is applied to the Guadalupe and San Antonio River basins in Texas, where flow wave celerities are estimated at multiple locations using 15-min data and can be reproduced reasonably with RAPID. This river model can be adapted for parallel computing and although the matrix method initially adds a large overhead, river flow results can be obtained faster than with the traditional Muskingum method when using a few processing cores, as demonstrated in a synthetic study using the upper Mississippi River basin.
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Garcia, M., C.D. Peters‐Lidard, and D.C. Goodrich, 2008: “Spatial interpolation of precipitation in a dense gauge network for monsoon storm events in the southwestern United States.” Water Resources Research, v. 44, paper no. W05S13, doi: 10.1029/2006WR005788.
Inaccuracy in spatially distributed precipitation fields can contribute significantly to the uncertainty of hydrological states and fluxes estimated from land surface models. This paper examines the results of selected interpolation methods for both convective and mixed/stratiform events that occurred during the North American monsoon season over a dense gauge network at the U.S. Department of Agriculture Agricultural Research Service Walnut Gulch Experimental Watershed in the southwestern United States. The spatial coefficient of variation for the precipitation field is employed as an indicator of event morphology, and a gauge clustering factor CF is formulated as a new, scale‐independent measure of network organization. We consider that CF < 0 (a more distributed gauge network) will produce interpolation errors by reduced resolution of the precipitation field and that CF > 0 (clustering in the gauge network) will produce errors because of reduced areal representation of the precipitation field. Spatial interpolation is performed using both inverse‐distance‐weighted (IDW) and multiquadric‐biharmonic (MQB) methods. We employ ensembles of randomly selected network subsets for the statistical evaluation of interpolation errors in comparison with the observed precipitation. The magnitude of interpolation errors and differences in accuracy between interpolation methods depend on both the density and the geometrical organization of the gauge network. Generally, MQB methods outperform IDW methods in terms of interpolation accuracy under all conditions, but it is found that the order of the IDW method is important to the results and may, under some conditions, be just as accurate as the MQB method. In almost all results it is demonstrated that the inverse‐distance‐squared method for spatial interpolation, commonly employed in operational analyses and for engineering assessments, is inferior to the ID‐cubed method, which is also more computationally efficient than the MQB method in studies of large networks.
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Overeem, A., H. Leijnse, and R. Uijlenhoet, 2011: “Measuring urban rainfall using microwave links from commercial cellular communication networks.” Water Resources Research, v. 47, paper no. W12505, doi: 10.1029/2010WR010350.
The estimation of rainfall using commercial microwave links is a new and promising measurement technique. Commercial link networks cover large parts of the land surface of the earth and have a high density, particularly in urban areas. Rainfall attenuates the electromagnetic signals transmitted between antennas within this network. This attenuation can be calculated from the difference between the received powers with and without rain and is a measure of the path-averaged rainfall intensity. This study uses a 17-day data set of, on average, 57 single-frequency links from 2009 to estimate rainfall in the Rotterdam region, a densely populated delta city in Netherlands (≈1250 sq km, >1 million inhabitants). A methodology is proposed where nearby links are used to remove signal fluctuations that are not related to rainfall in order to be able to reliably identify wet and dry weather spells. Subsequently, received signal powers are converted to path-averaged rainfall intensities, taking into account the temporal sampling protocol and attenuation due to wet antennas. Link-based rainfall depths are compared with those based on gauge-adjusted radar data. In addition, the rainfall retrieval algorithm is applied to an independent data set of 21 rainy days in 2010 with on average 16 single-frequency links in the same region. Rainfall retrievals are compared against gauge-adjusted radar rainfall estimates over the link path. Moreover, the retrieval algorithm is also tested using high-resolution research link data to investigate the algorithm’s sensitivity to temporal rainfall variations. All presented comparisons confirm the quality of commercial microwave link data for quantitative precipitation estimation over urban areas.
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Sultana, S., and Z. Chen, 2009: “Modeling flood induced interdependencies among hydroelectricity generating infrastructures.” Journal of Environmental Management, v. 90, no. 11, pp. 3272-3282, doi: 10.1016/j.jenvman.2009.05.019.
This paper presents a new kind of integrated modeling method for simulating the vulnerability of a critical infrastructure for a hazard and the subsequent interdependencies among the interconnected infrastructures. The developed method has been applied to a case study of a network of hydroelectricity generating infrastructures, e.g., water storage concrete gravity dam, penstock, power plant and transformer substation. The modeling approach is based on the fragility curves development with Monte Carlo simulation based structural–hydraulic modeling, flood frequency analysis, stochastic Petri net (SPN) modeling, and Markov Chain analysis. A certain flood level probability can be predicted from flood frequency analysis, and the most probable damage condition for this hazard can be simulated from the developed fragility curves of the dam. Consequently, the resulting interactions among the adjacent infrastructures can be quantified with SPN analysis; corresponding Markov Chain analysis simulates the long term probability matrix of infrastructure failures. The obtained results are quite convincing to prove the novel contribution of this research to the field of infrastructure interdependency analysis which might serve as a decision making tool for flood related emergency response and management.
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