Nonlinear model reduction for uncertainty quantification in large-scale inverse problems : application to nonlinear convection-diffusion-reaction equation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 147-152).There are multiple instances in science and engineering where quantities of interest are evaluated by solving one or several nonlinear partial differential equations (PDEs) that are parametrized in terms of a set of inputs. Even though well-established numerical techniques exist for solving these problems, their computational cost often precludes their use in cases where the outputs of interest must be evaluated repeatedly for different values of the input parameters such as probabilistic analysis applications. In this thesis we present a model reduction methodology that combines efficient representation of the nonlinearities in the governing PDE with an efficient model-constrained, greedy algorithm for sampling the input parameter space. The nonlinearities in the PDE are represented using a coefficient-function approximation that enables the development of an efficient offline-online computational procedure where the online computational cost is independent of the size of the original high-fidelity model. The input space sampling algorithm used for generating the reduced space basis adaptively improves the quality of the reduced order approximation by solving a PDE-constrained continuous optimization problem that targets the output error between the reduced and full order models in order to determine the optimal sampling point at every greedy cycle. The resulting model reduction methodology is applied to a highly nonlinear combustion problem governed by a convection-diffusion-reaction PDE with up to 3 input parameters. The reduced basis approximation developed for this problem is up to 50, 000 times faster to solve than the original high-fidelity finite element model with an average relative error in prediction of outputs of interest of 2.5 - 10-6 over the input parameter space. The reduced order model developed in this thesis is used in a novel probabilistic methodology for solving inverse problems.(cont) The extreme computational cost of the Bayesian framework approach for inferring the values of the inputs that generated a given set of empirically measured outputs often precludes its use in practical applications. In this thesis we show that using a reduced order model for running the Markovby David Galbally.S.M

Nonlinear Model Reduction for Uncertainty Quantification in Large-Scale Inverse Problems

We present a model reduction approach to the solution of large-scale statistical inverse problems in a Bayesian inference setting. A key to the model reduction is an efficient representation of the non-linear terms in the reduced model. To achieve this, we present a formulation that employs masked projection of the discrete equations; that is, we compute an approximation of the non-linear term using a select subset of interpolation points. Further, through this formulation we show similarities among the existing techniques of gappy proper orthogonal decomposition, missing point estimation, and empirical interpolation via coefficient-function approximation. The resulting model reduction methodology is applied to a highly non-linear combustion problem governed by an advection–diffusion-reaction partial differential equation (PDE). Our reduced model is used as a surrogate for a finite element discretization of the non-linear PDE within the Markov chain Monte Carlo sampling employed by the Bayesian inference approach. In two spatial dimensions, we show that this approach yields accurate results while reducing the computational cost by several orders of magnitude. For the full three-dimensional problem, a forward solve using a reduced model that has high fidelity over the input parameter space is more than two million times faster than the full-order finite element model, making tractable the solution of the statistical inverse problem that would otherwise require many years of CPU time.MIT-Singapore Alliance. Computational Engineering ProgrammeUnited States. Air Force Office of Scientific Research (Contract Nos. FA9550-06-0271)National Science Foundation (U.S.) (Grant No. CNS-0540186)National Science Foundation (U.S.) (Grant No. CNS-0540372)Caja Madrid Foundation (Graduate Fellowship

The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with residual minimization; it delivers computational efficency by a hyper-reduction procedure based on the `gappy POD' technique. Originally presented in Ref. [1], where it was applied to implicit nonlinear structural-dynamics models, this method is further developed here and applied to the solution of a benchmark turbulent viscous flow problem. To begin, this paper develops global state-space error bounds that justify the method's design and highlight its advantages in terms of minimizing components of these error bounds. Next, the paper introduces a `sample mesh' concept that enables a distributed, computationally efficient implementation of the GNAT method in finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability of GNAT for parameterized problems is highlighted with the solution of an academic problem featuring moving discontinuities. Finally, the capability of this method to reduce by orders of magnitude the core-hours required for large-scale CFD computations, while preserving accuracy, is demonstrated with the simulation of turbulent flow over the Ahmed body. For an instance of this benchmark problem with over 17 million degrees of freedom, GNAT outperforms several other nonlinear model-reduction methods, reduces the required computational resources by more than two orders of magnitude, and delivers a solution that differs by less than 1% from its high-dimensional counterpart

Uncertainties in models of tropospheric ozone based on Monte Carlo analysis: Tropospheric ozone burdens, atmospheric lifetimes and surface distributions

Recognising that global tropospheric ozone models have many uncertain input parameters, an attempt has been made to employ Monte Carlo sampling to quantify the uncertainties in model output that arise from global tropospheric ozone precursor emissions and from ozone production and destruction in a global Lagrangian chemistry-transport model. Ninetyeight quasi-randomly Monte Carlo sampled model runs were completed and the uncertainties were quantified in tropospheric burdens and lifetimes of ozone, carbon monoxide and methane, together with the surface distribution and seasonal cycle in ozone. The results have shown a satisfactory degree of convergence and provide a first estimate of the likely uncertainties in tropospheric ozone model outputs. There are likely to be diminishing returns in carrying out many more Monte Carlo runs in order to refine further these outputs. Uncertainties due to model formulation were separately addressed using the results from 14 Atmospheric Chemistry Coupled Climate Model Intercomparison Project (ACCMIP) chemistry-climate models. The 95% confidence ranges surrounding the ACCMIP model burdens and lifetimes for ozone, carbon monoxide and methane were somewhat smaller than for the Monte Carlo estimates. This reflected the situation where the ACCMIP models used harmonised emissions data and differed only in their meteorological data and model formulations whereas a conscious effort was made to describe the uncertainties in the ozone precursor emissions and in the kinetic and photochemical data in the Monte Carlo runs. Attention was focussed on the model predictions of the ozone seasonal cycles at three marine boundary layer stations: Mace Head, Ireland, Trinidad Head, California and Cape Grim, Tasmania. Despite comprehensively addressing the uncertainties due to global emissions and ozone sources and sinks, none of the Monte Carlo runs were able to generate seasonal cycles that matched the observations at all three MBL stations. Although the observed seasonal cycles were found to fall within the confidence limits of the ACCMIP members, this was because the model seasonal cycles spanned extremely wide ranges and there was no single ACCMIP member that performed best for each station. Further work is required to examine the parameterisation of convective mixing in the models to see if this erodes the isolation of the marine boundary layer from the free troposphere and thus hides the models' real ability to reproduce ozone seasonal cycles over marine stations

Long-term changes in tropospheric ozone

Tropospheric ozone changes are investigated using a selected network of surface and ozonesonde sites to give a broad geographic picture of long-term variations. The picture of long-term tropospheric ozone changes is a varied one in terms of both the sign and magnitude of trends and in the possible causes for the changes. At mid latitudes of the S.H. three time series of ∼20 years in length agree in showing increases that are strongest in the austral spring (August–October). Profile measurements show this increase extending through the mid troposphere but not into the highest levels of the troposphere. In the N.H. in the Arctic a period of declining ozone in the troposphere through the 1980s into the mid-1990s has reversed and the overall change is small. The decadal-scale variations in the troposphere in this region are related in part to changes in the lowermost stratosphere. At mid latitudes in the N.H., continental Europe and Japan showed significant increases in the 1970s and 1980s. Over North America rises in the 1970s are less than those seen in Europe and Japan, suggesting significant regional differences. In all three of these mid latitude, continental regions tropospheric ozone amounts appear to have leveled off or in some cases declined in the more recent decades. Over the North Atlantic three widely separated sites show significant increases since the late-1990s that may have peaked in recent years. In the N.H. tropics both the surface record and the ozonesondes in Hawaii show a significant increase in the autumn months in the most recent decade compared to earlier periods that drives the overall increase seen in the 30-year record. This appears to be related to a shift in the transport pattern during this season with more frequent flow from higher latitudes in the latest decade

Crop Updates 2005 - Farming Systems

This session covers forty four papers from different authors: PLENARY 1. 2005 Outlook, David Stephens and Nicola Telcik, Department of Agriculture FERTILITY AND NUTRITION 2. The effect of higher nitrogen fertiliser prices on rotation and fertiliser strategies in cropping systems, Ross Kingwell, Department of Agriculture and University of Western Australia 3. Stubble management: The short and long term implications for crop nutrition and soil fertility, Wayne Pluske, Nutrient Management Systems and Bill Bowden, Department of Agriculture 4. Stubble management: The pros and cons of different methods, Bill Bowden, Department of Agriculture, Western Australia and Mike Collins, WANTFA 5. Effect of stubble burning and seasonality on microbial processes and nutrient recycling, Frances Hoyle, The University of Western Australia 6. Soil biology and crop production in Western Australian farming systems, D.V. Murphy, N. Milton, M. Osman, F.C. Hoyle, L.K Abbott, W.R. Cookson and S. Darmawanto, The University of Western Australia 7. Urea is as effective as CAN when no rain for 10 days, Bill Crabtree, Crabtree Agricultural Consulting 8. Fertiliser (N,P,S,K) and lime requirements for wheat production in the Merredin district, Geoff Anderson, Department of Agriculture and Darren Kidson, Summit Fertilizers 9. Trace element applications: Up-front verses foliar? Bill Bowden and Ross Brennan, Department of Agriculture 10. Fertcare®, Environmental Product Stewardship and Advisor Standards for thee Fertiliser Industry, Nick Drew, Fertilizer Industry Federation of Australia (FIFA) SOIL AND LAND MANAGEMENT 11. Species response to row spacing, density and nutrition, Bill Bowden, Craig Scanlan, Lisa Sherriff, Bob French and Reg Lunt, Department of Agriculture 12. Investigation into the influence of row orientation in lupin crops, Jeff Russell, Department of Agriculture and Angie Roe, Farm Focus Consultants 13. Deriving variable rate management zones for crops, Ian Maling, Silverfox Solutions and Matthew Adams, DLI 14. In a world of Precision Agriculture, weigh trailers are not passé, Jeff Russell, Department of Agriculture 15. Cover crop management to combat ryegrass resistance and improve yields, Jeff Russell, Department of Agriculture and Angie Roe, Farm Focus Consultants 16. ARGT home page, the place to find information on annual ryegrass toxicity on the web, Dr George Yan, BART Pty Ltd 17. Shallow leading tine (SLT) ripper significantly reduces draft force, improves soil tilth and allows even distribution of subsoil ameliorants, Mohammad Hamza, Glen Riethmuller and Wal Anderson, Department of Agriculture PASTURE ANS SUMMER CROP SYSTEMS 18. New annual pasture legumes for Mediteranean farming systems, Angelo Loi, Phil Nichols, Clinton Revell and David Ferris, Department of Agriculture 19. How sustainable are phase rotations with Lucerne? Phil Ward, CSIRO Plant Industry 20. Management practicalities of summer cropping, Andrea Hills and Sally-Anne Penny, Department of Agriculture 21. Rainfall zone determines the effect of summer crops on winter yields, Andrea Hills, Sally-Anne Penny and David Hall, Department of Agriculture 22. Summer crops and water use, Andrea Hills, Sally-Anne Penny and David Hall, Department of Agriculture, and Michael Robertson and Don Gaydon, CSIRO Brisbane 23. Risk analysis of sorgum cropping, Andrea Hills and Sally-Anne Penny, Department of Agriculture, and Dr Michael Robertson and Don Gaydon, CSIRO Brisbane FARMER DECISION SUPPORT AND ADOPTION 24. Variety release and End Point Royalties – a new system? Tress Walmsley, Department of Agriculture 25. Farming system analaysis using the STEP Tool, Caroline Peek and Megan Abrahams, Department of Agriculture 26. The Leakage Calculator: A simple tool for groundwater recharge assessment, Paul Raper, Department of Agriculture 27. The cost of Salinity Calculator – your tool to assessing the profitability of salinity management options, Richard O’Donnell and Trevor Lacey, Department of Agriculture 28. Climate decision support tools, Meredith Fairbanks and David Tennant, Department of Agriculture 29. Horses for courses – using the best tools to manage climate risk, Cameron Weeks, Mingenew-Irwin Group/Planfarm and Richard Quinlan, Planfarm Agronomy 30. Use of seasonal outlook for making N decisions in Merredin, Meredith Fairbanks and Alexandra Edward, Department of Agriculture 31. Forecasts and profits, Benefits or bulldust? Chris Carter and Doug Hamilton, Department of Agriculture 32. A tool to estimate fixed and variable header and tractor depreciation costs, Peter Tozer, Department of Agriculture 33. Partners in grain: ‘Putting new faces in new places’, Renaye Horne, Department of Agriculture 34. Results from the Grower group Alliance, Tracey Gianatti, Grower Group Alliance 35. Local Farmer Group Network – farming systems research opportunities through local groups, Paul Carmody, Local Farmer Group Network GREENHOUSE GAS AND CLIMATE CHANGE 36. Changing rainfall patterns in the grainbelt, Ian Foster, Department of Agriculture 37. Vulnerability of broadscale agriculture to the impacts of climate change, Michele John, CSIRO (formerly Department of Agriculture) and Ross George, Department of Agriculture 38. Impacts of climate change on wheat yield at Merredin, Imma Farré and Ian Foster, Department of Agriculture 39. Climate change, land use suitability and water security, Ian Kininmonth, Dennis van Gool and Neil Coles, Department of Agriculture 40. Nitrous oxide emissions from cropping systems, Bill Porter, Department of Agriculture, Louise Barton, University of Western Australia 41. The potential of greenhouse sinks to underwrite improved land management in Western Australia, Richard Harper and Peter Ritson, CRC for Greenhouse Accounting and Forest Products Commission, Tony Beck, Tony Beck Consulting Services, Chris Mitchell and Michael Hill, CRC for Greenhouse Accounting 42. Removing uncertainty from greenhouse emissions, Fiona Barker-Reid, Will Gates, Ken Wilson and Rob Baigent, Department of Primary Industries - Victoria and CRC for Greenhouse Accounting (CRCGA), and Ian Galbally, Mick Meyer and Ian Weeks, CSIRO Atmospheric Research and CRCGA 43. Greenhouse in Agriculture Program (GIA), Traci Griffin, CRC for Greenhouse Accounting 44. Grains Greenhouse Accounting framework, D. Rodriguez, M. Probust, M. Meyers, D. Chen, A. Bennett, W. Strong, R. Nussey, I. Galbally and M. Howden CONTACT DETAILS FOR PRINCIPAL AUTHOR

Tropospheric Ozone Assessment Report: Tropospheric ozone from 1877 to 2016, observed levels, trends and uncertainties

From the earliest observations of ozone in the lower atmosphere in the 19th century, both measurement methods and the portion of the globe observed have evolved and changed. These methods have different uncertainties and biases, and the data records differ with respect to coverage (space and time), information content, and representativeness. In this study, various ozone measurement methods and ozone datasets are reviewed and selected for inclusion in the historical record of background ozone levels, based on relationship of the measurement technique to the modern UV absorption standard, absence of interfering pollutants, representativeness of the well-mixed boundary layer and expert judgement of their credibility. There are significant uncertainties with the 19th and early 20th-century measurements related to interference of other gases. Spectroscopic methods applied before 1960 have likely underestimated ozone by as much as 11% at the surface and by about 24% in the free troposphere, due to the use of differing ozone absorption coefficients. There is no unambiguous evidence in the measurement record back to 1896 that typical mid-latitude background surface ozone values were below about 20 nmol mol–1, but there is robust evidence for increases in the temperate and polar regions of the northern hemisphere of 30–70%, with large uncertainty, between the period of historic observations, 1896–1975, and the modern period (1990–2014). Independent historical observations from balloons and aircraft indicate similar changes in the free troposphere. Changes in the southern hemisphere are much less. Regional representativeness of the available observations remains a potential source of large errors, which are difficult to quantify

Methylobacterium Genome Sequences: A Reference Blueprint to Investigate Microbial Metabolism of C1 Compounds from Natural and Industrial Sources

Methylotrophy describes the ability of organisms to grow on reduced organic compounds without carbon-carbon bonds. The genomes of two pink-pigmented facultative methylotrophic bacteria of the Alpha-proteobacterial genus Methylobacterium, the reference species Methylobacterium extorquens strain AM1 and the dichloromethane-degrading strain DM4, were compared. Methodology/Principal Findings The 6.88 Mb genome of strain AM1 comprises a 5.51 Mb chromosome, a 1.26 Mb megaplasmid and three plasmids, while the 6.12 Mb genome of strain DM4 features a 5.94 Mb chromosome and two plasmids. The chromosomes are highly syntenic and share a large majority of genes, while plasmids are mostly strain-specific, with the exception of a 130 kb region of the strain AM1 megaplasmid which is syntenic to a chromosomal region of strain DM4. Both genomes contain large sets of insertion elements, many of them strain-specific, suggesting an important potential for genomic plasticity. Most of the genomic determinants associated with methylotrophy are nearly identical, with two exceptions that illustrate the metabolic and genomic versatility of Methylobacterium. A 126 kb dichloromethane utilization (dcm) gene cluster is essential for the ability of strain DM4 to use DCM as the sole carbon and energy source for growth and is unique to strain DM4. The methylamine utilization (mau) gene cluster is only found in strain AM1, indicating that strain DM4 employs an alternative system for growth with methylamine. The dcm and mau clusters represent two of the chromosomal genomic islands (AM1: 28; DM4: 17) that were defined. The mau cluster is flanked by mobile elements, but the dcm cluster disrupts a gene annotated as chelatase and for which we propose the name “island integration determinant” (iid).Conclusion/Significance These two genome sequences provide a platform for intra- and interspecies genomic comparisons in the genus Methylobacterium, and for investigations of the adaptive mechanisms which allow bacterial lineages to acquire methylotrophic lifestyles.Organismic and Evolutionary Biolog

Attachment goes to court: child protection and custody issues

Attachment theory and research are drawn upon in many applied settings, including family courts, but misunderstandings are widespread and sometimes result in misapplications. The aim of this consensus statement is, therefore, to enhance understanding, counter misinformation, and steer family-court utilisation of attachment theory in a supportive, evidence-based direction, especially with regard to child protection and child custody decision-making. The article is divided into two parts. In the first, we address problems related to the use of attachment theory and research in family courts, and discuss reasons for these problems. To this end, we examine family court applications of attachment theory in the current context of the best-interest-of-the-child standard, discuss misunderstandings regarding attachment theory, and identify factors that have hindered accurate implementation. In the second part, we provide recommendations for the application of attachment theory and research. To this end, we set out three attachment principles: the child’s need for familiar, non-abusive caregivers; the value of continuity of good-enough care; and the benefits of networks of attachment relationships. We also discuss the suitability of assessments of attachment quality and caregiving behaviour to inform family court decision-making. We conclude that assessments of caregiver behaviour should take center stage. Although there is dissensus among us regarding the use of assessments of attachment quality to inform child custody and child-protection decisions, such assessments are currently most suitable for targeting and directing supportive interventions. Finally, we provide directions to guide future interdisciplinary research collaboration