TY - JOUR A1 - Niven, Robert K. A1 - Abel, Markus A1 - Schlegel, Michael A1 - Waldrip, Steven H. T1 - Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications JF - Entropy N2 - The concept of a "flow network"-a set of nodes and links which carries one or more flows-unites many different disciplines, including pipe flow, fluid flow, electrical, chemical reaction, ecological, epidemiological, neurological, communications, transportation, financial, economic and human social networks. This Feature Paper presents a generalized maximum entropy framework to infer the state of a flow network, including its flow rates and other properties, in probabilistic form. In this method, the network uncertainty is represented by a joint probability function over its unknowns, subject to all that is known. This gives a relative entropy function which is maximized, subject to the constraints, to determine the most probable or most representative state of the network. The constraints can include "observable" constraints on various parameters, "physical" constraints such as conservation laws and frictional properties, and "graphical" constraints arising from uncertainty in the network structure itself. Since the method is probabilistic, it enables the prediction of network properties when there is insufficient information to obtain a deterministic solution. The derived framework can incorporate nonlinear constraints or nonlinear interdependencies between variables, at the cost of requiring numerical solution. The theoretical foundations of the method are first presented, followed by its application to a variety of flow networks. KW - maximum entropy analysis KW - flow network KW - probabilistic inference Y1 - 2019 U6 - https://doi.org/10.3390/e21080776 SN - 1099-4300 VL - 21 IS - 8 SP - 776 PB - MDPI CY - Basel ER - TY - GEN A1 - Waldrip, Steven H. A1 - Niven, Robert K. A1 - Abel, Markus A1 - Schlegel, Michael T1 - Consistent maximum entropy representations of pipe flow networks T2 - AIP conference proceedings N2 - The maximum entropy method is used to predict flows on water distribution networks. This analysis extends the water distribution network formulation of Waldrip et al. (2016) Journal of Hydraulic Engineering (ASCE), by the use of a continuous relative entropy defined on a reduced parameter set. This reduction in the parameters that the entropy is defined over ensures consistency between different representations of the same network. The performance of the proposed reduced parameter method is demonstrated with a one-loop network case study. Y1 - 2017 SN - 978-0-7354-1527-0 U6 - https://doi.org/10.1063/1.4985365 SN - 0094-243X VL - 1853 IS - 1 PB - American Institute of Physics CY - Melville ER - TY - GEN A1 - Waldrip, Steven H. A1 - Niven, Robert K. A1 - Abel, Markus A1 - Schlegel, Michael T1 - Maximum entropy analysis of transport networks T2 - AIP conference proceedings N2 - The maximum entropy method is used to derive an alternative gravity model for a transport network. The proposed method builds on previous methods which assign the discrete value of a maximum entropy distribution to equal the traffic flow rate. The proposed method however, uses a distribution to represent each flow rate. The proposed method is shown to be able to handle uncertainty in a more elegant way and give similar results to traditional methods. It is able to incorporate more of the observed data through the entropy function, prior distribution and integration limits potentially allowing better inferences to be made. Y1 - 2017 SN - 978-0-7354-1527-0 U6 - https://doi.org/10.1063/1.4985364 SN - 0094-243X VL - 1853 IS - 1 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Seroussi, Helene A1 - Nowicki, Sophie A1 - Payne, Antony J. A1 - Goelzer, Heiko A1 - Lipscomb, William H. A1 - Abe-Ouchi, Ayako A1 - Agosta, Cecile A1 - Albrecht, Torsten A1 - Asay-Davis, Xylar A1 - Barthel, Alice A1 - Calov, Reinhard A1 - Cullather, Richard A1 - Dumas, Christophe A1 - Galton-Fenzi, Benjamin K. A1 - Gladstone, Rupert A1 - Golledge, Nicholas R. A1 - Gregory, Jonathan M. A1 - Greve, Ralf A1 - Hattermann, Tore A1 - Hoffman, Matthew J. A1 - Humbert, Angelika A1 - Huybrechts, Philippe A1 - Jourdain, Nicolas C. A1 - Kleiner, Thomas A1 - Larour, Eric A1 - Leguy, Gunter R. A1 - Lowry, Daniel P. A1 - Little, Chistopher M. A1 - Morlighem, Mathieu A1 - Pattyn, Frank A1 - Pelle, Tyler A1 - Price, Stephen F. A1 - Quiquet, Aurelien A1 - Reese, Ronja A1 - Schlegel, Nicole-Jeanne A1 - Shepherd, Andrew A1 - Simon, Erika A1 - Smith, Robin S. A1 - Straneo, Fiammetta A1 - Sun, Sainan A1 - Trusel, Luke D. A1 - Van Breedam, Jonas A1 - van de Wal, Roderik S. W. A1 - Winkelmann, Ricarda A1 - Zhao, Chen A1 - Zhang, Tong A1 - Zwinger, Thomas T1 - ISMIP6 Antarctica BT - a multi-model ensemble of the Antarctic ice sheet evolution over the 21st century JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - Ice flow models of the Antarctic ice sheet are commonly used to simulate its future evolution in response to different climate scenarios and assess the mass loss that would contribute to future sea level rise. However, there is currently no consensus on estimates of the future mass balance of the ice sheet, primarily because of differences in the representation of physical processes, forcings employed and initial states of ice sheet models. This study presents results from ice flow model simulations from 13 international groups focusing on the evolution of the Antarctic ice sheet during the period 2015-2100 as part of the Ice Sheet Model Intercomparison for CMIP6 (ISMIP6). They are forced with outputs from a subset of models from the Coupled Model Intercomparison Project Phase 5 (CMIP5), representative of the spread in climate model results. Simulations of the Antarctic ice sheet contribution to sea level rise in response to increased warming during this period varies between 7:8 and 30.0 cm of sea level equivalent (SLE) under Representative Concentration Pathway (RCP) 8.5 scenario forcing. These numbers are relative to a control experiment with constant climate conditions and should therefore be added to the mass loss contribution under climate conditions similar to present-day conditions over the same period. The simulated evolution of the West Antarctic ice sheet varies widely among models, with an overall mass loss, up to 18.0 cm SLE, in response to changes in oceanic conditions. East Antarctica mass change varies between 6 :1 and 8.3 cm SLE in the simulations, with a significant increase in surface mass balance outweighing the increased ice discharge under most RCP 8.5 scenario forcings. The inclusion of ice shelf collapse, here assumed to be caused by large amounts of liquid water ponding at the surface of ice shelves, yields an additional simulated mass loss of 28mm compared to simulations without ice shelf collapse. The largest sources of uncertainty come from the climate forcing, the ocean-induced melt rates, the calibration of these melt rates based on oceanic conditions taken outside of ice shelf cavities and the ice sheet dynamic response to these oceanic changes. Results under RCP 2.6 scenario based on two CMIP5 climate models show an additional mass loss of 0 and 3 cm of SLE on average compared to simulations done under present-day conditions for the two CMIP5 forcings used and display limited mass gain in East Antarctica. Y1 - 2020 U6 - https://doi.org/10.5194/tc-14-3033-2020 SN - 1994-0416 SN - 1994-0424 VL - 14 IS - 9 SP - 3033 EP - 3070 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Waldrip, S. H. A1 - Niven, Robert K. A1 - Abel, Markus A1 - Schlegel, M. T1 - Reduced-Parameter Method for Maximum Entropy Analysis of Hydraulic Pipe Flow Networks JF - Journal of hydraulic engineering N2 - A maximum entropy (MaxEnt) method is developed to predict flow rates or pressure gradients in hydraulic pipe networks without sufficient information to give a closed-form (deterministic) solution. This methodology substantially extends existing deterministic flow network analysis methods. It builds on the MaxEnt framework previously developed by the authors. This study uses a continuous relative entropy defined on a reduced parameter set, here based on the external flow rates. This formulation ensures consistency between different representations of the same network. The relative entropy is maximized subject to observable constraints on the mean values of a subset of flow rates or potential differences, the frictional properties of each pipe, and physical constraints arising from Kirchhoff’s first and second laws. The new method is demonstrated by application to a simple one-loop network and a 1,123-node, 1,140-pipe water distribution network in the suburb of Torrens, Australian Capital Territory, Australia. KW - Maximum entropy method KW - Water distribution systems KW - Hydraulic networks KW - Pipe networks KW - Hydraulic models KW - Nonlinear analysis KW - Probability Y1 - 2017 U6 - https://doi.org/10.1061/(ASCE)HY.1943-7900.0001379 SN - 0733-9429 SN - 1943-7900 VL - 144 IS - 2 PB - American Society of Civil Engineers CY - Reston ER - TY - JOUR A1 - Meister, Claudia-Veronika A1 - Liperovsky, Viktor A. A1 - Schlegel, K. A1 - Haldoupis, Ch. T1 - Currents and turbulence in and near mid-latitude sporadic e-layers caused by strong acoustic impulses JF - Preprint NLD Y1 - 1995 VL - 11 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Liperovsky, Viktor A. A1 - Meister, Claudia-Veronika A1 - Haldoupis, Ch. A1 - Schlegel, K. T1 - Electrical currents and Farley-Buneman turbulence in mid-latitude sporadic E-layers Y1 - 1994 ER - TY - JOUR A1 - Waldrip, S. H. A1 - Niven, R. K. A1 - Abel, Markus A1 - Schlegel, M. T1 - Maximum Entropy Analysis of Hydraulic Pipe Flow Networks JF - Journal of hydraulic engineering KW - Maximum entropy method KW - Water distribution systems KW - Hydraulic networks KW - Pipe networks KW - Hydraulic models KW - Non-linear analysis KW - Probability Y1 - 2016 U6 - https://doi.org/10.1061/(ASCE)HY.1943-7900.0001126 SN - 0733-9429 SN - 1943-7900 VL - 142 SP - 332 EP - 347 PB - American Society of Civil Engineers CY - Reston ER -