Forward Transport Model Research Articles

Recovery of sparse urban greenhouse gas emissions

Abstract. To localize and quantify greenhouse gas emissions from cities, gas concentrations are typically measured at a small number of sites and then linked to emission fluxes using atmospheric transport models. Solving this inverse problem is challenging because the system of equations often has no unique solution and the solution can be sensitive to noise. A common top–down approach for solving this problem is Bayesian inversion with the assumption of a multivariate Gaussian distribution as the prior emission field. However, such an assumption has drawbacks when the assumed spatial emissions are incorrect or not Gaussian distributed. In our work, we investigate sparse reconstruction (SR), an alternative reconstruction method that can achieve reasonable estimations without using a prior emission field by making the assumption that the emission field is sparse. We show that this assumption is generally true for the cities we investigated and that the use of the discrete wavelet transform helps to make the urban emission field even more sparse. To evaluate the performance of SR, we created concentration data by applying an atmospheric forward transport model to CO2 emission inventories of several major European cities. We used SR to locate and quantify the emission sources by applying compressed sensing theory and compared the results to regularized least squares (LSs) methods. Our results show that SR requires fewer measurements than LS methods and that SR is better at localizing and quantifying unknown emitters.

Real-world wintertime CO, N2O, and CO2 emissions of a central European village

Abstract. Although small rural settlements are only minor individual sources of greenhouse gases and air pollution, their high overall occurrence can significantly contribute to the total emissions of a region or country. Emissions from a rural lifestyle may be remarkably different than those of urban and industrialized regions, but nevertheless they have hardly been studied so far. Here, flux measurements at a tall-tower eddy covariance monitoring site and the footprint model FFP are used to determine the real-world wintertime CO, N2O, and CO2 emissions of a small village in western Hungary. The recorded emission densities, dominantly resulting from residential heating, are 3.5, 0.043, and 72 µg m−2 s−1 for CO, N2O, and CO2, respectively. While the measured CO and CO2 emissions are comparable to those calculated using the assumed energy consumption and applying the according emission factors, the nitrous oxide emissions exceed the expected value by a magnitude. This may indicate that the nitrous oxide emissions are significantly underestimated in the emission inventories, and modifications in the methodology of emission calculations are necessary. Using a three-dimensional forward transport model, we further show that, in contrast to the flux measurements, the concentration measurements at the regional background monitoring site are only insignificantly influenced by the emissions of the nearby village.

Markov chain Monte Carlo with neural network surrogates: application to contaminant source identification

Subsurface remediation often involves reconstruction of contaminant release history from sparse observations of solute concentration. Markov Chain Monte Carlo (MCMC), the most accurate and general method for this task, is rarely used in practice because of its high computational cost associated with multiple solves of contaminant transport equations. We propose an adaptive MCMC method, in which a transport model is replaced with a fast and accurate surrogate model in the form of a deep convolutional neural network (CNN). The CNN-based surrogate is trained on a small number of the transport model runs based on the prior knowledge of the unknown release history. Thus reduced computational cost allows one to reduce the sampling error associated with construction of the approximate likelihood function. As all MCMC strategies for source identification, our method has an added advantage of quantifying predictive uncertainty and accounting for measurement errors. Our numerical experiments demonstrate the accuracy comparable to that of MCMC with the forward transport model, which is obtained at a fraction of the computational cost of the latter.

The impacts of fossil fuel emission uncertainties and accounting for 3-D chemical CO2 production on inverse natural carbon flux estimates from satellite and in situ data

Atmospheric carbon dioxide (CO2) inversions for estimating natural carbon fluxes typically do not allow for adjustment of fossil fuel CO2 emissions, despite significant uncertainties in emission inventories and inadequacies in the specification of international bunker emissions in inversions. Also, most inversions place CO2 release from fossil fuel combustion and biospheric sources entirely at the surface. However, a non-negligible portion of the emissions actually occurs in the form of reduced carbon species, which are eventually oxidized to CO2 downwind. Omission of this ‘chemical pump’ can result in a significant redistribution of the inferred total carbon fluxes among regions. We assess the impacts of different prescriptions of fossil fuel emissions and accounting for the chemical pump on flux estimation, with a novel aspect of conducting both satellite CO2 observation-based and surface in situ-based inversions. We apply 3-D carbon monoxide (CO) loss rates archived from a state-of-the-art GEOS chemistry and climate model simulation in a forward transport model run to simulate the distribution of CO2 originating from oxidation of carbon species. We also subtract amounts from the prior surface CO2 fluxes that are actually emitted in the form of fossil and biospheric CO, methane, and non-methane volatile organic compounds (VOCs). We find that the posterior large-scale fluxes are generally insensitive to the finer-scale spatial differences between the ODIAC and CDIAC fossil fuel CO2 gridded datasets and assumptions about international bunker emissions. However, accounting for 3-D chemical CO2 production and the surface correction shifts the global carbon sink, e.g. from land to ocean and from the tropics to the north, with a magnitude and even direction that depend on assumptions about the surface correction. A GOSAT satellite-based inversion is more sensitive to the chemical pump than one using in situ observations, exhibiting substantial flux impacts of 0.28, 0.53, and −0.47 Pg C yr−1 over tropical land, global land, and oceans, due to differences in the horizontal and vertical sampling of the two observation types. Overall, the biases from neglecting the chemical pump appear to be minor relative to the flux estimate uncertainties and the differences between the in situ and GOSAT inversions, but their relative importance will grow in the future as observational coverage further increases and satellite retrieval biases decrease.

A new inverse method for contaminant source identification under unknown solute transport boundary conditions

Abstract A new solute transport inverse method is proposed for estimating plume trajectory and source release location under unknown solute transport boundary conditions in a steady-state, non-uniform groundwater flow field. Solute concentration is modeled by proposing a set of local approximation solutions (LAS) of transport that are discretized over the problem domain. At a given time step, the inverse method imposes continuities of concentration and total solute mass flux at a set of collocation points in the inversion grid, whereas the LAS are conditioned to measured breakthrough concentrations. By enforcing transport physics at selected points in space and time, the inverse problem becomes well-posed and a single system of inversion equations is assembled and solved with a parallel iterative solver. Unlike most of the inversion techniques that minimize a model-data mismatch objective function, the inverse method does not require the simulation of a forward transport model for optimization, thus both solute initial and boundary conditions can be recovered. Assuming dispersivity estimates are available, the method was demonstrated using synthetic breakthrough data from various sampling densities and designs, i.e., irregular versus uniformly spaced well networks. Different measurement errors and source release histories (e.g., uniform-in-time, single, and multiple pulses) were also investigated. Results suggest that for the source release histories tested, 1) inversion is stable under increasing measurement errors up to 5% of the maximum observed concentration; 2) accurate plume trajectory and source release location can be estimated from solute breakthrough concentrations; 3) inversion accuracy appears the most sensitive to sampling well density and its information content.

Deep Autoregressive Neural Networks for High‐Dimensional Inverse Problems in Groundwater Contaminant Source Identification

AbstractIdentification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly heterogeneous media often results in a high‐dimensional inverse problem. In this study, a deep autoregressive neural network‐based surrogate method is developed for the forward model to allow us to solve efficiently such high‐dimensional inverse problems. The surrogate is trained using limited evaluations of the forward model. Since the relationship between the time‐varying inputs and outputs of the forward transport model is complex, we propose an autoregressive strategy, which treats the output at the previous time step as input to the network for predicting the output at the current time step. We employ a dense convolutional encoder‐decoder network architecture in which the high‐dimensional input and output fields of the model are treated as images to leverage the robust capability of convolutional networks in image‐like data processing. An iterative local updating ensemble smoother algorithm is used as the inversion framework. The proposed method is evaluated using a synthetic contaminant source identification problem with 686 uncertain input parameters. Results indicate that, with relatively limited training data, the deep autoregressive neural network consisting of 27 convolutional layers is capable of providing an accurate approximation for the high‐dimensional model input‐output relationship. The autoregressive strategy substantially improves the network's accuracy and computational efficiency. The application of the surrogate‐based iterative local updating ensemble smoother in solving the inverse problem shows that it can achieve accurate inversion results and predictive uncertainty estimates.

TransCom model simulations of hourly atmospheric CO2: Analysis of synoptic‐scale variations for the period 2002–2003

The ability to reliably estimate CO2 fluxes from current in situ atmospheric CO2 measurements and future satellite CO2 measurements is dependent on transport model performance at synoptic and shorter timescales. The TransCom continuous experiment was designed to evaluate the performance of forward transport model simulations at hourly, daily, and synoptic timescales, and we focus on the latter two in this paper. Twenty‐five transport models or model variants submitted hourly time series of nine predetermined tracers (seven for CO2) at 280 locations. We extracted synoptic‐scale variability from daily averaged CO2 time series using a digital filter and analyzed the results by comparing them to atmospheric measurements at 35 locations. The correlations between modeled and observed synoptic CO2 variabilities were almost always largest with zero time lag and statistically significant for most models and most locations. Generally, the model results using diurnally varying land fluxes were closer to the observations compared to those obtained using monthly mean or daily average fluxes, and winter was often better simulated than summer. Model results at higher spatial resolution compared better with observations, mostly because these models were able to sample closer to the measurement site location. The amplitude and correlation of model‐data variability is strongly model and season dependent. Overall similarity in modeled synoptic CO2 variability suggests that the first‐order transport mechanisms are fairly well parameterized in the models, and no clear distinction was found between the meteorological analyses in capturing the synoptic‐scale dynamics.

Temporal and spatial variations of the atmospheric CO2 concentration in China

In order to understand the variations of atmospheric greenhouse gases over the Chinese mainland, an air sampling network was established in March 2003 that included one GAW global station, three GAW regional stations and three cooperative stations. Flask air samples were taken every week at the stations for 3 years. The secular increase and the seasonal variation in the CO2 concentration are clearly observable at all the stations, reflecting global as well as the regional terrestrial biospheric and human activities, as well as the local meteorological conditions. The average CO2 concentration depends on the station, with the lowest value observed at Mt. Waliguan and relatively high values observed at Fukang and Lin‐an stations, located in the westernmost and eastern parts of China, respectively. The observed CO2 concentration variations are also discussed within the context of forward transport model simulations using CO2 fluxes derived by time‐dependent inversion.

Constraints on the 232Th/238U ratio (κ) of the continental crust

This study examines constraints on the 232Th/238U ratio of the continental crust (κC) imposed by heat flow, Th‐U systematics and Pb isotope ratios. The 232Th/238U ratio of the depleted upper mantle (κUM) as sampled by mid‐ocean ridge basalt is well‐constrained to be 2.5 ± 0.1. The 232Th/238U ratio of the lower mantle (κLM) can be constrained as follows. Oceanic island basalts (OIB) have average κ of 3.78. If OIB are derived from mantle plumes and if plumes are representative of the lower mantle, then κLM ≤ 3.78. Alternatively, if the lower mantle is “primitive”, then κLM is similar to the chondritic 232Th/238U ratio of κS = 4 ± 0.2. Mass balance calculations assuming κUM = 2.5, and κLM ≤ 4 with heat production constraints suggest that κC is in the range 5–6. Further support for κC substantially greater than 4 comes from the Pb isotopic composition of the continental crust. We estimate the 208Pb/204Pb of the lower continental crust to be 37.36 to 37.84 and the 208Pb*/206Pb* ratio of the total continental crust to be 1.046 to 1.059, which corresponds to a time‐integrated 232Th/238U ratio (κC(Pb)) of 4.25 − 4.30. A four‐reservoir (upper and lower continental crust, depleted upper mantle, and primitive lower mantle) forward transport model of Pb isotope evolution that reproduces the difference in κUM and κUM(Pb) values in the depleted mantle suggests that to achieve a κC(Pb) of 4.25, the present 232Th/238U ratio in the crust (κC) must be ≈5. Thus several lines of evidence converge on a value κC of around 5 or slightly higher.

Modelling the isotopic evolution of the Earth.

We present a flexible multi-reservoir (primitive lower mantle, depleted upper mantle, upper continental crust, lower continental crust and atmosphere) forward-transport model of the Earth, incorporating the Sm-Nd, Rb-Sr, U-Th-Pb-He and K-Ar isotope-decay systematics. Mathematically, the model consists of a series of differential equations, describing the changing abundance of each nuclide in each reservoir, which are solved repeatedly over the history of the Earth. Fluxes between reservoirs are keyed to heat production and further constrained by estimates of present-day fluxes (e.g. subduction, plume flux) and current sizes of reservoirs. Elemental transport is tied to these fluxes through 'enrichment factors', which allow for fractionation between species. A principal goal of the model is to reproduce the Pb-isotope systematics of the depleted upper mantle, which has not been done in earlier models. At present, the depleted upper mantle has low (238)U/(204)Pb (mu) and (232)Th/(238)U (kappa) ratios, but Pb-isotope ratios reflect high time-integrated values of these ratios. These features are reproduced in the model and are a consequence of preferential subduction of U and of radiogenic Pb from the upper continental crust into the depleted upper mantle. At the same time, the model reproduces the observed Sr-, Nd-, Ar- and He-isotope ratios of the atmosphere, continental crust and mantle. We show that both steady-state and time-variant concentrations of incompatible-element concentrations and ratios in the continental crust and upper mantle are possible. Indeed, in some cases, incompatible-element concentrations and ratios increase with time in the depleted mantle. Hence, assumptions of a progressively depleting or steady-state upper mantle are not justified. A ubiquitous feature of this model, as well as other evolutionary models, is early rapid depletion of the upper mantle in highly incompatible elements; hence, a near-chondritic Th/U ratio in the upper mantle throughout the Archean is unlikely. The model also suggests that the optimal value of the bulk silicate Earth's K/U ratio is close to 10000; lower values suggested recently seem unlikely.