Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. It is particularly appropriate when one wishes to approximate the states at a few points in time without time marching from the initial conditions. We prove some interesting characteristics of the scheme including an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and conductive heat transfer - a nonlinear parabolic PDE with a random field model for the thermal conductivity.Comment: 28 pages, 8 figures, 2 table

Biomass burning at Cape Grim: exploring photochemistry using multi-scale modelling

We have tested the ability of a high-resolution chemical transport model (CTM) to reproduce biomass burning (BB) plume strikes and ozone (O3) enhancements observed at Cape Grim in Tasmania, Australia, from the Robbins Island fire. The CTM has also been used to explore the contribution of near-field BB emissions and background sources to O3 observations under conditions of complex meteorology. Using atmospheric observations, we have tested model sensitivity to meteorology, BB emission factors (EFs) corresponding to low, medium, and high modified combustion efficiency (MCE), and spatial variability. The use of two different meteorological models (TAPM–CTM and CCAM–CTM) varied the first (BB1) plume strike time by up to 15 h and the duration of impact between 12 and 36 h, and it varied the second (BB2) plume duration between 50 and 57 h. Meteorology also had a large impact on simulated O3, with one model (TAPM–CTM) simulating four periods of O3 enhancement, while the other model (CCAM) simulating only one period. Varying the BB EFs, which in turn varied the non-methane organic compound (NMOC) ∕ oxides of nitrogen (NOx) ratio, had a strongly non-linear impact on simulated O3 concentration, with either destruction or production of O3 predicted in different simulations. As shown in previous work (Lawson et al., 2015), minor rainfall events have the potential to significantly alter EF due to changes in combustion processes. Models that assume fixed EF for O3 precursor species in an environment with temporally or spatially variable EF may be unable to simulate the behaviour of important species such as O3. TAPM–CTM is used to further explore the contribution of the Robbins Island fire to the observed O3 enhancements during BB1 and BB2. Overall, TAPM–CTM suggests that the dominant source of O3 observed at Cape Grim was aged urban air (age  = 2 days), with a contribution of O3 formed from local BB emissions. This work shows the importance of assessing model sensitivity to meteorology and EF and the large impact these variables can have in particular on simulated destruction or production of O3 in regional atmospheric chemistry simulations. This work also shows the importance of using models to elucidate the contribution from different sources to atmospheric composition, where this is difficult using observations alone

Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models

Computational inverse problems related to partial differential equations (PDEs) often contain nuisance parameters that cannot be effectively identified but still need to be considered as part of the problem. The objective of this work is to show how to take advantage of a reduced order framework to speed up Bayesian inversion on the identifiable parameters of the system, while marginalizing away the (potentially large number of) nuisance parameters. The key ingredients are twofold. On the one hand, we rely on a reduced basis (RB) method, equipped with computable a posteriori error bounds, to speed up the solution of the forward problem. On the other hand, we develop suitable reduction error models (REMs) to quantify in an inexpensive way the error between the full-order and the reduced-order approximation of the forward problem, in order to gauge the effect of this error on the posterior distribution of the identifiable parameters. Numerical results dealing with inverse problems governed by elliptic PDEs in the case of both scalar parameters and parametric fields highlight the combined role played by RB accuracy and REM effectivity

Terahertz Security Image Quality Assessment by No-reference Model Observers

To provide the possibility of developing objective image quality assessment (IQA) algorithms for THz security images, we constructed the THz security image database (THSID) including a total of 181 THz security images with the resolution of 127*380. The main distortion types in THz security images were first analyzed for the design of subjective evaluation criteria to acquire the mean opinion scores. Subsequently, the existing no-reference IQA algorithms, which were 5 opinion-aware approaches viz., NFERM, GMLF, DIIVINE, BRISQUE and BLIINDS2, and 8 opinion-unaware approaches viz., QAC, SISBLIM, NIQE, FISBLIM, CPBD, S3 and Fish_bb, were executed for the evaluation of the THz security image quality. The statistical results demonstrated the superiority of Fish_bb over the other testing IQA approaches for assessing the THz image quality with PLCC (SROCC) values of 0.8925 (-0.8706), and with RMSE value of 0.3993. The linear regression analysis and Bland-Altman plot further verified that the Fish__bb could substitute for the subjective IQA. Nonetheless, for the classification of THz security images, we tended to use S3 as a criterion for ranking THz security image grades because of the relatively low false positive rate in classifying bad THz image quality into acceptable category (24.69%). Interestingly, due to the specific property of THz image, the average pixel intensity gave the best performance than the above complicated IQA algorithms, with the PLCC, SROCC and RMSE of 0.9001, -0.8800 and 0.3857, respectively. This study will help the users such as researchers or security staffs to obtain the THz security images of good quality. Currently, our research group is attempting to make this research more comprehensive.Comment: 13 pages, 8 figures, 4 table

Gridded global surface ozone metrics for atmospheric chemistry model evaluation

The concentration of ozone at the Earth's surface is measured at many locations across the globe for the purposes of air quality monitoring and atmospheric chemistry research. We have brought together all publicly available surface ozone observations from online databases from the modern era to build a consistent data set for the evaluation of chemical transport and chemistry-climate (Earth System) models for projects such as the Chemistry-Climate Model Initiative and Aer-Chem-MIP. From a total data set of approximately 6600 sites and 500 million hourly observations from 1971-2015, approximately 2200 sites and 200 million hourly observations pass screening as high-quality sites in regionally representative locations that are appropriate for use in global model evaluation. There is generally good data volume since the start of air quality monitoring networks in 1990 through 2013. Ozone observations are biased heavily toward North America and Europe with sparse coverage over the rest of the globe. This data set is made available for the purposes of model evaluation as a set of gridded metrics intended to describe the distribution of ozone concentrations on monthly and annual timescales. Metrics include the moments of the distribution, percentiles, maximum daily 8-hour average (MDA8), sum of means over 35 ppb (daily maximum 8-h; SOMO35), accumulated ozone exposure above a threshold of 40 ppbv (AOT40), and metrics related to air quality regulatory thresholds. Gridded data sets are stored as netCDF-4 files and are available to download from the British Atmospheric Data Centre (doi:10.5285/08fbe63d-fa6d-4a7a-b952-5932e3ab0452). We provide recommendations to the ozone measurement community regarding improving metadata reporting to simplify ongoing and future efforts in working with ozone data from disparate networks in a consistent manner

Composition of Clean Marine Air and Biogenic Influences on VOCs during the MUMBA Campaign

Volatile organic compounds (VOCs) are important precursors to the formation of ozone and fine particulate matter, the two pollutants of most concern in Sydney, Australia. Despite this importance, there are very few published measurements of ambient VOC concentrations in Australia. In this paper, we present mole fractions of several important VOCs measured during the campaign known as MUMBA (Measurements of Urban, Marine and Biogenic Air) in the Australian city of Wollongong (34°S). We particularly focus on measurements made during periods when clean marine air impacted the measurement site and on VOCs of biogenic origin. Typical unpolluted marine air mole fractions during austral summer 2012-2013 at latitude 34°S were established for CO2 (391.0 ± 0.6 ppm), CH4 (1760.1 ± 0.4 ppb), N2O (325.04 ± 0.08 ppb), CO (52.4 ± 1.7 ppb), O3 (20.5 ± 1.1 ppb), acetaldehyde (190 ± 40 ppt), acetone (260 ± 30 ppt), dimethyl sulphide (50 ± 10 ppt), benzene (20 ± 10 ppt), toluene (30 ± 20 ppt), C8H10 aromatics (23 ± 6 ppt) and C9H12 aromatics (36 ± 7 ppt). The MUMBA site was frequently influenced by VOCs of biogenic origin from a nearby strip of forested parkland to the east due to the dominant north-easterly afternoon sea breeze. VOCs from the more distant densely forested escarpment to the west also impacted the site, especially during two days of extreme heat and strong westerly winds. The relative amounts of different biogenic VOCs observed for these two biomes differed, with much larger increases of isoprene than of monoterpenes or methanol during the hot westerly winds from the escarpment than with cooler winds from the east. However, whether this was due to different vegetation types or was solely the result of the extreme temperatures is not entirely clear. We conclude that the clean marine air and biogenic signatures measured during the MUMBA campaign provide useful information about the typical abundance of several key VOCs and can be used to constrain chemical transport model simulations of the atmosphere in this poorly sampled region of the world. © 2019 The Author

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

Global Distribution and Trends of Tropospheric Ozone: An Observation-Based Review

Tropospheric ozone plays a major role in Earth's atmospheric chemistry processes and also acts as an air pollutant and greenhouse gas. Due to its short lifetime, and dependence on sunlight and precursor emissions from natural and anthropogenic sources, tropospheric ozone's abundance is highly variable in space and time on seasonal, interannual and decadal time-scales. Recent, and sometimes rapid, changes in observed ozone mixing ratios and ozone precursor emissions inspired us to produce this up-to-date overview of tropospheric ozone's global distribution and trends. Much of the text is a synthesis of in situ and remotely sensed ozone observations reported in the peer-reviewed literature, but we also include some new and extended analyses using well-known and referenced datasets to draw connections between ozone trends and distributions in different regions of the world. In addition, we provide a brief evaluation of the accuracy of rural or remote surface ozone trends calculated by three state-of-the-science chemistry-climate models, the tools used by scientists to fill the gaps in our knowledge of global tropospheric ozone distribution and trends

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category