Non-Gaussian bivariate modelling with application to atmospheric trace-gas inversion

Atmospheric trace-gas inversion is the procedure by which the sources and sinks of a trace gas are identified from observations of its mole fraction at isolated locations in space and time. This is inherently a spatio-temporal bivariate inversion problem, since the mole-fraction field evolves in space and time and the flux is also spatio-temporally distributed. Further, the bivariate model is likely to be non-Gaussian since the flux field is rarely Gaussian. Here, we use conditioning to construct a non-Gaussian bivariate model, and we describe some of its properties through auto- and cross-cumulant functions. A bivariate non-Gaussian, specifically trans-Gaussian, model is then achieved through the use of Box--Cox transformations, and we facilitate Bayesian inference by approximating the likelihood in a hierarchical framework. Trace-gas inversion, especially at high spatial resolution, is frequently highly sensitive to prior specification. Therefore, unlike conventional approaches, we assimilate trace-gas inventory information with the observational data at the parameter layer, thus shifting prior sensitivity from the inventory itself to its spatial characteristics (e.g., its spatial length scale). We demonstrate the approach in controlled-experiment studies of methane inversion, using fluxes extracted from inventories of the UK and Ireland and of Northern Australia.Comment: 45 pages, 7 figure

Spatio-temporal bivariate statistical models for atmospheric trace-gas inversion

Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a data-assimilation flavour, which implicitly consider univariate statistical models with the flux as the variate of interest. This univariate approach typically assumes that the flux field is either a spatially correlated Gaussian process or a spatially uncorrelated non-Gaussian process with prior expectation fixed using flux inventories (e.g., NAEI or EDGAR in Europe). Here, we extend this approach in three ways. First, we develop a bivariate model for the mole-fraction field and the flux field. The bivariate approach allows optimal prediction of both the flux field and the mole-fraction field, and it leads to significant computational savings over the univariate approach. Second, we employ a lognormal spatial process for the flux field that captures both the lognormal characteristics of the flux field (when appropriate) and its spatial dependence. Third, we propose a new, geostatistical approach to incorporate the flux inventories in our updates, such that the posterior spatial distribution of the flux field is predominantly data-driven. The approach is illustrated on a case study of methane (CH$_4$) emissions in the United Kingdom and Ireland.Comment: 39 pages, 8 figure

Estimation of trace gas fluxes with objectively determined basis functions using reversible-jump Markov chain Monte Carlo

Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved

Process Oscillations in Continuous Ethanol Fermentation with Saccharomyces cerevisiae

Based on ethanol fermentation kinetics and bioreactor engineering theory, a system composed of a continuously stirred tank reactor (CSTR) and three tubular bioreactors in series was established for continuous very high gravity (VHG) ethanol fermentation with Saccharomyces cerevisiae. Sustainable oscillations of residual glucose, ethanol, and biomass characterized by long oscillation periods and large oscillation amplitudes were observed when a VHG medium containing 280 g/L glucose was fed into the CSTR at a dilution rate of 0.027 h1. Mechanistic analysis indicated that the oscillations are due to ethanol inhibition and the lag response of yeast cells to ethanol inhibition. A high gravity (HG) medium containing 200 g/L glucose and a low gravity (LG) medium containing 120 g/L glucose were fed into the CSTR at the same dilution rate as that for the VHG medium, so that the impact of residual glucose and ethanol concentrations on the oscillations could be studied. The oscillations were not significantly affected when the HG medium was used, and residual glucose decreased significantly, but ethanol maintained at the same level, indicating that residual glucose was not the main factor triggering the oscillations. However, the oscillations disappeared after the LG medium was fed and ethanol concentration decreased to 58.2 g/L. Furthermore, when the LG medium was supplemented with 30 g/L ethanol to achieve the same level of ethanol in the fermentation system as that achieved under the HG condition, the steady state observed for the original LG medium was interrupted, and the oscillations observed under the HG condition occurred. The steady state was gradually restored after the original LG medium replaced the modified one. These experimental results confirmed that ethanol, whether produced by yeast cells during fermentation or externally added into a fermentation system, can trigger oscillations once its concentration approaches to a criterion. The impact of dilution rate on oscillations was also studied. It was found that oscillations occurred at certain dilution rate ranges for the two yeast strains. Since ethanol production is tightly coupled with yeast cell growth, it was speculated that the impact of the dilution rate on the oscillations is due to the synchronization of the mother and daughter cell growth rhythms. The difference in the oscillation profiles exhibited by the two yeast strains is due to their difference in ethanol tolerance. For more practical conditions, the behavior of continuous ethanol fermentation was studied using a self-flocculating industrial yeast strain and corn flour hydrolysate medium in a simulated tanks-in-series fermentation system. Amplified oscillations observed at the dilution rate of 0.12 h1 were postulated to be due to the synchronization of the two yeast cell populations generated by the continuous inoculation from the seed tank upstream of the fermentation system, which was partly validated by oscillation attenuation after the seed tank was removed from the fermentation system. The two populations consisted of the newly inoculated yeast cells and the yeast cells already adapted to the fermentation environment. Oscillations increased residual sugar at the end of the fermentation, and correspondingly, decreased the ethanol yield, indicating the need for attenuation strategies. When the tubular bioreactors were packed with ½” Intalox ceramic saddles, not only was their ethanol fermentation performance improved, but effective oscillation attenuation was also achieved. The oscillation attenuation was postulated to be due to the alleviation of backmixing in the packed tubular bioreactors as well as the yeast cell immobilization role of the packing. The residence time distribution analysis indicated that the mixing performance of the packed tubular bioreactors was close to a CSTR model for both residual glucose and ethanol, and the assumed backmixing alleviation could not be achieved. The impact of yeast cell immobilization was further studied using several different packing materials. Improvement in ethanol fermentation performance as well as oscillation attenuation was achieved for the wood chips, as well as the Intalox ceramic saddles, but not for the porous polyurethane particles, nor the steel Raschig rings. Analysis for the immobilized yeast cells indicated that high viability was the mechanistic reason for the improvement of the ethanol fermentation performance as well as the attenuation of the oscillations. A dynamic model was developed by incorporating the lag response of yeast cells to ethanol inhibition into the pseudo-steady state kinetic model, and dynamic simulation was performed, with good results. This not only provides a basis for developing process intervention strategies to minimize oscillations, but also theoretically support the mechanistic hypothesis for the oscillations

Quantifying the UK's carbon dioxide flux: An atmospheric inverse modelling approach using a regional measurement network

We present a method to derive atmosphericobservation-based estimates of carbon dioxide (CO 2 ) fluxes at the national scale, demonstrated using data from a network of surface tall-tower sites across the UK and Ireland over the period 2013-2014. The inversion is carried out using simulations from a Lagrangian chemical transport model and an innovative hierarchical Bayesian Markov chain Monte Carlo (MCMC) framework, which addresses some of the traditional problems faced by inverse modelling studies, such as subjectivity in the specification of model and prior uncertainties. Biospheric fluxes related to gross primary productivity and terrestrial ecosystem respiration are solved separately in the inversion and then combined a posteriori to determine net ecosystem exchange of CO 2 . Two different models, Data Assimilation Linked Ecosystem Carbon (DALEC) and Joint UK Land Environment Simulator (JULES), provide prior estimates for these fluxes. We carry out separate inversions to assess the impact of these different priors on the posterior flux estimates and evaluate the differences between the prior and posterior estimates in terms of missing model components. The Numerical Atmospheric dispersion Modelling Environment (NAME) is used to relate fluxes to the measurements taken across the regional network. Posterior CO2 estimates from the two inversions agree within estimated uncertainties, despite large differences in the prior fluxes from the different models. With our method, averaging results from 2013 and 2014, we find a total annual net biospheric flux for the UK of 8±79 TgCO 2 yr -1 (DALEC prior) and 64±85 TgCO 2 yr -1 (JULES prior), where negative values represent an uptake of CO 2 . These biospheric CO 2 estimates show that annual UK biospheric sources and sinks are roughly in balance. These annual mean estimates consistently indicate a greater net release of CO 2 than the prior estimates, which show much more pronounced uptake in summer months

Advancing Scientific Understanding of the Global Methane Budget in Support of the Paris Agreement

The 2015 Paris Agreement of the United Nations Framework Convention on Climate Change aims to keep global average temperature increases well below 2 °C of preindustrial levels in the Year 2100. Vital to its success is achieving a decrease in the abundance of atmospheric methane (CH4), the second most important anthropogenic greenhouse gas. If this reduction is to be achieved, individual nations must make and meet reduction goals in their nationally determined contributions, with regular and independently verifiable global stock taking. Targets for the Paris Agreement have been set, and now the capability must follow to determine whether CH4 reductions are actually occurring. At present, however, there are significant limitations in the ability of scientists to quantify CH4 emissions accurately at global and national scales and to diagnose what mechanisms have altered trends in atmospheric mole fractions in the past decades. For example, in 2007, mole fractions suddenly started rising globally after a decade of almost no growth. More than a decade later, scientists are still debating the mechanisms behind this increase. This study reviews the main approaches and limitations in our current capability to diagnose the drivers of changes in atmospheric CH4 and, crucially, proposes ways to improve this capability in the coming decade. Recommendations include the following: (i) improvements to process‐based models of the main sectors of CH4 emissions—proposed developments call for the expansion of tropical wetland flux measurements, bridging remote sensing products for improved measurement of wetland area and dynamics, expanding measurements of fossil fuel emissions at the facility and regional levels, expanding country‐ specific data on the composition of waste sent to landfill and the types of wastewater treatment systems implemented, characterizing and representing temporal profiles of crop growing seasons, implementing parameters related to ruminant emissions such as animal feed, and improving the detection of small fires associated with agriculture and deforestation; (ii) improvements to measurements of CH4 mole fraction and its isotopic variations—developments include greater vertical profiling at background sites, expanding networks of dense urban measurements with a greater focus on relatively poor countries, improving the precision of isotopic ratio measurements of 13CH4, CH3D, 14CH4, and clumped isotopes, creating isotopic reference materials for international‐scale development, and expanding spatial and temporal characterization of isotopic source signatures; and (iii) improvements to inverse modeling systems to derive emissions from atmospheric measurements—advances are proposed in the areas of hydroxyl radical quantification, in systematic uncertainty quantification through validation of chemical transport models, in the use of source tracers for estimating sector‐level emissions, and in the development of time and spaceresolved national inventories. These and other recommendations are proposed for the major areas of CH4 science with the aim of improving capability in the coming decade to quantify atmospheric CH4 budgets on the scales necessary for the success of climate policies. Plain Language Summary Methane is the second largest contributor to climate warming from human activities since preindustrial times. Reducing human‐made emissions by half is a major component of the 2015 Paris Agreement target to keep global temperature increases well below 2 °C. In parallel to the methane emission reductions pledged by individual nations, new capabilities are needed to determine independently whether these reductions are actually occurring and whether methane concentrations in the atmosphere are changing for reasons that are clearly understood. At present significant challenges limit the ability of scientists to identify the mechanisms causing changes in atmospheric methane. This study reviews current and emerging tools in methane science and proposes major advances needed in the coming decade to achieve this crucial capability. We recommend further developing the models that simulate the processes behind methane emissions, improving atmospheric measurements of methane and its major carbon and hydrogen isotopes, and advancing abilities to infer the rates of methane being emitted and removed from the atmosphere from these measurements. The improvements described here will play a major role in assessing emissions commitments as more cities, states, and countries report methane emission inventories and commit to specific emission reduction targets. </div