Lagrangian Stochastic Model Research Articles

Unique stochastic Lagrangian particle dispersion models for inhomogeneous turbulent flows

It is well established that Lagrangian particle dispersion models, for inhomogeneous turbulent flows, must satisfy the ‘well-mixed condition’ of Thomson (J. Fluid Mech., vol. 180, 1987, pp. 529–556) in order to produce physically reasonable results. In more than one dimension, however, the well-mixed condition is not sufficient to define the dispersion model uniquely. The non-uniqueness, which is related to the rotational degrees of freedom of particle trajectories, permits models with trajectory curvatures and velocity autocorrelation functions which are clearly unphysical. A spin condition is therefore introduced to constrain the models. It requires an ensemble of particles with fixed initial position and velocity to have, at short times, expected angular momentum, measured relative to the mean position and velocity of an ensemble of fluid particles with initially random velocity, equal to the relative angular momentum of the mean flow at the ensemble mean location. The resulting unique model is found explicitly for the canonical example of inhomogeneous Gaussian turbulence and is characterised by accelerations which are exponential in the particle velocity. A simpler unique model with a quadratic acceleration is obtained using a weaker version of the spin condition. Unlike previous models, the unique models defined by the spin condition lead to particles having the correct (ensemble mean) angular speed in a turbulent flow in solid-body rotation. The properties of the new models are discussed in the settings of a turbulent channel flow and an idealised turbulent atmospheric boundary-layer flow.

Pollen productivity estimates strongly depend on assumed pollen dispersal II: Extending the ERV model

Pollen productivity estimates (PPEs) are a key parameter for quantitative land-cover reconstructions from pollen data. PPEs are commonly estimated using modern pollen-vegetation data sets and the extended R-value (ERV) model. Prominent discrepancies in the existing studies question the reliability of the approach. We here propose an implementation of the ERV model in the R environment for statistical computing, which allows for simplified application and testing. Using simulated pollen-vegetation data sets, we explore sensitivity of ERV application to (1) number of sites, (2) vegetation structure, (3) basin size, (4) noise in the data, and (5) dispersal model selection. The simulations show that noise in the (pollen) data and dispersal model selection are critical factors in ERV application. Pollen count errors imply prominent PPE errors mainly for taxa with low counts, usually low pollen producers. Applied with an unsuited dispersal model, ERV tends to produce wrong PPEs for additional taxa. In a comparison of the still widely applied Prentice model and a Lagrangian stochastic model (LSM), errors are highest for taxa with high and low fall speed of pollen. The errors reflect the too high influence of fall speed in the Prentice model. ERV studies often use local scale pollen data from for example, moss polsters. Describing pollen dispersal on his local scale is particularly complex due to a range of disturbing factors, including differential release height. Considering the importance of the dispersal model in the approach, and the very large uncertainties in dispersal on short distance, we advise to carry out ERV studies with pollen data from open areas or basins that lack local pollen deposition of the taxa of interest.

Modelling of three-dimensional particle rebound from an anisotropic rough wall

In gas-solid confined flows, particle rebound on a rough wall may have a great influence on the macroscopic properties of both phases. Existing simulation methods use simplified approaches where surface roughness is modelled as two-dimensional or isotropic. To improve the accuracy of such simulations, an anisotropic virtual rough wall statistical approach and the corresponding Lagrangian stochastic particle-wall collision model are proposed. From deterministic simulations of the impact of particles on the anisotropic virtual wall given as correlated bi-Gaussian surface, wall-normal vector angle statistics are used for model development. Rebound angle statistics computed from deterministic simulations and using the proposed stochastic model are in very good agreement. Incident particles in vertical planes not collinear with one of the principal directions of the anisotropic rough surface are bouncing with a mean transverse angle towards the principal direction of lower roughness.

Reexamining the framework for intermittency in Lagrangian stochastic models for turbulent flows: A way to an original and versatile numerical approach

The characterization of intermittency in turbulence has its roots in the refined similarity hypotheses of Kolmogorov, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in an attempt to reproduce it. The first contribution of this work is to propose a requirement list to be satisfied by models designed within the Lagrangian framework. Multifractal stochastic processes are a natural choice to retrieve multifractal properties of the dissipation. Among them, we investigate the Gaussian multiplicative chaos formalism, which requires the construction of a log-correlated stochastic process X_{t}. The fractional Gaussian noise of Hurst parameter H=0 is of great interest because it leads to a log correlation for the logarithm of the process. Inspired by the approximation of fractional Brownian motion by an infinite weighted sum of correlated Ornstein-Uhlenbeck processes, our second contribution is to propose a stochastic model: X_{t}=∫_{0}^{∞}Y_{t}^{x}k(x)dx, where Y_{t}^{x} is an Ornstein-Uhlenbeck process with speed of mean reversion x and k is a kernel. A regularization of k(x) is required to ensure stationarity, finite variance, and logarithmic autocorrelation. A variety of regularizations are conceivable, and we show that they lead to the aforementioned multifractal models. To simulate the process, we eventually design a new approach relying on a limited number of modes for approximating the integral through a quadrature X_{t}^{N}=∑_{i=1}^{N}ω_{i}Y_{t}^{x_{i}}, using a conventional quadrature method. This method can retrieve the expected behavior with only one mode per decade, making this strategy versatile and computationally attractive for simulating such processes, while remaining within the proposed framework for a proper description of intermittency.

Assessment of the inverse dispersion method for the determination of methane emissions from a dairy housing

Methane (CH4) emissions from dairy housings, mainly originating from enteric fermentation of ruminating animals, are a significant source of greenhouse gases. The quantification of emissions from naturally ventilated dairy housings is challenging due to the spatial distribution of sources (animals, housing areas) and variable air exchange. The inverse dispersion method (IDM) is a promising option, which is increasingly used to determine gaseous emissions from stationary sources, as it offers high flexibility in the application at reasonable costs. We used a backward Lagrangian stochastic model combined with concentration measurements by open-path tunable diode laser spectrometers placed up- and downwind of a naturally ventilated housing with 40 dairy cows to determine the CH4 emissions. The average emissions per livestock unit (LU) were 317 (±44) g LU−1 d−1 and 267 (±43) g LU−1 d−1 for the first and second campaign, in September – October and November – December, respectively. For each campaign, inhouse tracer ratio measurements (iTRM) were conducted in parallel during two subperiods. For simultaneous measurements, IDM showed average emissions which were lower by 8% and 1% than that of iTRM, respectively, for the two campaigns. The differences are within the uncertainty range of any of the two methods. The IDM CH4 emissions were further analysed by wind direction and atmospheric stability and no differences in emissions were found. Overall, IDM showed its aptitude to accurately determine CH4 emissions from dairy housings or other stationary sources if the site allows adequate placement of sensors up- and downwind in the prevailing wind direction. To acquire reliable emission data, depending on the data loss during measurements due to quality filtering or instrument failure, a measuring time of at least 10 days is required.

Development of a Backward–Forward Stochastic Particle Tracking Model for Identification of Probable Sedimentation Sources in Open Channel Flow

As reservoirs subject to sedimentation, the dam gradually loses its ability to store water. The identification of the sources of deposited sediments is an effective and efficient means of tackling sedimentation problems. A state-of-the-art Lagrangian stochastic particle tracking model with backward–forward tracking methods is applied to identify the probable source regions of deposited sediments. An influence function is introduced into the models to represent the influence of a particular upstream area on the sediment deposition area. One can then verify if a specific area might be a probable source by cross-checking the values of influence functions calculated backward and forward, respectively. In these models, the probable sources of the deposited sediments are considered to be in a grid instead of at a point for derivation of the values of influence functions. The sediment concentrations in upstream regions must be known a priori to determine the influence functions. In addition, the accuracy of the different types of diffusivity at the water surface is discussed in the study. According to the results of the case study of source identification, the regions with higher sediment concentrations computed by only backward simulations do not necessarily imply a higher likelihood of sources. It is also shown that from the ensemble results when the ensemble mean of the concentration is higher, the ensemble standard deviation of the concentration is also increased.

Effect of the local wind reduction zone on seed dispersal from a single shrub element on sparsely vegetated land.

Accurate predictions of seed dispersal kernels are crucial for understanding both vegetation communities and landscape dynamics. The influences of many factors, including the physical properties of seeds, the time-averaged wind speed and the wind turbulence, on seed dispersal have been studied. However, the influence of local wind speed reduction around a single shrub element (e.g. a small patch of scrub) on seed dispersal is still not well understood. Here, the spatial distribution of the wind intensity (represented by the wind friction speed u*) around a single shrub element is described, with an emphasis on the variation in the streamwise direction, and assuming that the time-averaged lateral and vertical speeds are equal to zero. The trajectories of the seeds were numerically simulated using a Lagrangian stochastic model that includes the effects of wind turbulence and particle inertia. The patterns of seed deposition with and without the effect of local wind reduction were compared. The variation in seed deposition with changing wind intensity, release height and shrub porosity were also simulated. The simulation results revealed that the local wind reduction increased seed deposition in nearby regions and therefore decreased seed deposition in the regions farther away. Local wind reduction had a greater impact on short-distance dispersal than on long-distance dispersal. Moreover, the dispersal in the circumferential direction decreased once the motion of a seed moving in the streamwise direction was reduced due to the local wind reduction. As the wind intensity and release height increased, the effect of local wind reduction on seed dispersal weakened. Seed dispersal was both wider and farther as the shrub porosity increased. These results may help explain the disagreement between the mechanistic models and the fitting curves in real cases. In addition, the results of this study may improve the currently used mechanistic models by either increasing their flexibility in case studies or by helping explain the variations in the observed distributions.

A Lagrangian Stochastic Model of a Volcanic Eruption Column

AbstractWe present a Lagrangian stochastic model (LSM) of a volcanic plume in which the mean flow is provided by an integral plume model of the eruption column and fluctuations in the vertical velocity are modeled by a suitably constructed stochastic differential equation. This model is based on that of Bisignano and Devenish (2015, http://doi.org/10.1007/s10546-015-0055-3) with the mean flow provided by the integral plume model of Devenish (2013, http://doi.org/10.1016/j.jvolgeores.2013.02.015). The LSM is applied to the two eruptions considered by Costa et al. (2016, http://doi.org/10.1016/j.jvolgeores.2016.01.017) for the volcanic‐plume intercomparison study with no ambient wind and to the hypothetical cases with ambient wind considered by Aubry et al. (2019, http://doi.org/10.1029/2019GL083975). Vertical profiles of the mass concentration computed from the LSM are compared with equivalent results from large eddy simulations (LES). The LSM captures the order of magnitude of the LES mass concentrations and aspects of their profiles: for example, in contrast with a standard integral plume model, that is, without fluctuations, the mass concentration computed from the LSM decays (to zero) toward the top of the plume consistent with the LES plumes. In the lower part of the plume, we show that the presence of ash leads to a peak in the mass concentration at the level at which there is a transition from a negatively buoyant jet to a positively buoyant plume. A quantitative analysis of the cases with ambient wind shows generally good agreement between the LSM and the LES for a number of quantities including the maximum concentration, the level at which it occurs, the maximum rise height, and the total erupted mass.

Concentration Fluctuations of Single Particle Stochastic Lagrangian Model Assessment with Experimental Field Data

A single particle Lagrangian Stochastic model has been developed and applied with the purpose of simulating the concentration fluctuations dispersion. This model treats concentration variance as a quantity whose motion is driven by an advection-diffusion process so that it can be studied by a single particle model. A parameterization for both velocity standard deviations and Lagrangian time-scales is required as input to the model. The paper is focused on the estimation of the best parameterization needed to simulate both mean and standard deviation concentrations in a case study. We consider the FFT-07 field experiment. The trials took place at Dugway Proving Ground, UTAH (USA) and consist of a dispersion analysis of a gas emitted from a point-like source in different atmospheric conditions with a continuous emission technique. The very small spatial scales (a few hundred meters) and short duration (about 10 minutes) that characterize the trials make the comparison with model results very challenging, since traditional boundary layer parameterizations fail in correctly reproducing the turbulent field and, as a consequence, the dispersion simulation yields unsatisfactorily results. We vary the coefficients of the turbulence parameterization to match the small-scale turbulence. Furthermore, we show that the parameterization for the variance dissipation time-scale, already tested in neutral conditions, can be used also in stable and unstable conditions and in low-wind speed conditions. The model gives good results as far as mean concentration is concerned and rather satisfactory results for the concentration standard deviations. Comparison between model results and observation is shown through both statistical and graphical analyses.

An Urban Lagrangian Stochastic Dispersion Model for Simulating Traffic Particulate-Matter Concentration Fields

The accumulated particulate matter concentration at a given vertical column due to traffic sources in urban area has many important consequences. This task, however, imposes a major challenge, since the problem of realistic pollutant dispersion in an urban environment is a very demanding task, both theoretically and computationally. This is mainly due to the highly inhomogeneous three dimensional turbulent flow regime in the urban canopy roughness sublayer, which is far from “local equilibrium” between shear production and dissipation. We present here a mass-consistent urban Lagrangian stochastic model for pollutants dispersion, where the flow field is modeled using a hybrid approach by which we model the surface layer based on the typical turbulent scales, both of the canopy and in the surface layer inertial sub-layer. In particular it relies on representing the canopy aerodynamically as a porous medium by spatial averaging the equations of motion, with the assumption that the canopy is laterally uniform on a scale much larger than the buildings but smaller than the urban block/neighbourhood, i.e., at the sub-urban-block scale. Choosing the spatial representative averaging volume allows the averaged variables to reflect the characteristic vertical heterogeneity of the canopy but to smooth out smaller scale spatial fluctuations caused as air flows in between the buildings. This modeling approach serves as the base for a realistic and efficient methodology for the calculation of the accumulated concentration from multiple traffic sources for any vertical column in the urban area. The existence of multiple traffic sources impose further difficulty since the computational effort required is very demanding for practical uses. Therefore, footprint analysis screening was introduced to identify the relevant part of the urban area which contributes to the chosen column. All the traffic sources in this footprint area where merged into several areal sources, further used for the evaluation of the concentration profile. This methodology was implemented for four cases in the Tel Aviv metropolitan area based on several selected summer climatological scenarios. We present different typical behaviors, demonstrating combination of source structure, urban morphology, flow characteristics, and the resultant dispersion pattern in each case.

Upscaling bimolecular reactive transport in highly heterogeneous porous media with the LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model

The LAgrangian Transport Eulerian Reaction Spatial (LATERS) Markov model was developed to predict upscaled bimolecular reactive transport in a flow around an array of solid cylinders. This method combines the stochastic Lagrangian Spatial Markov model (SMM) to predict transport and a volume averaged reaction rate equation to predict reactions of the form $$A+B\rightarrow \emptyset$$ . Here, we extend the LATERS Markov model to upscale bimolecular reactive transport in a Darcy flow through an idealized heterogeneous porous medium. In agreement with previous literature, the accuracy of the prediction is a function of the Damkohler (Da) numbers, i.e., high Da are more challenging because of incomplete mixing. It was found that a key component which must be incorporated into the upscaled model in these high Da systems is the idea that nearby A and B particles should be more likely to react than those that are farther apart. This is here achieved by appropriately reducing the resolution of the spatial grid employed to resolve the reactive process.

Relative pollen productivity estimates of savanna taxa from southern Africa and their application to reconstruct shrub encroachment during the last century

To understand the resilience of African savannas to global change, quantitative information on the long-term dynamics of vegetation is required. Past dynamics can be reconstructed with the REVEALS model, which requires pollen productivity estimates (PPE) that are calibrated using surface pollen and vegetation data. Here we calculated PPE values for five savanna taxa using the extended R-value (ERV) model and two pollen dispersal options: the Gaussian plume model (GPM) and the Lagrangian stochastic model (LSM). The ERV calculations failed to produce a reliable PPE for Poaceae. We therefore used Combretaceae as the reference taxon – although values obtained with Poaceae as the reference taxon are presented in the supplement. Our results indicate that Combretaceae is the taxon with the highest pollen productivity and Grewia the taxon with the lowest productivity. Acacia and Dichrostachys are intermediate pollen producers. We find no clear indication of whether the GPM PPEs or the LSM PPEs are more realistic, but the differences between these values confirmed that the pollen fall speed has a greater effect in the modelling of GPM than in the LSM. We also applied REVEALS to the pollen record of Lake Otjikoto (northern Namibia) and obtained the first quantitative reconstruction of the last 130 years of vegetation history in the region. Cover estimates for Poaceae indicate the predominance of a semi-open landscape throughout the 20th century, while cover values below 50% since the 21st century correspond to a thick savanna. This change in grass cover is associated with the spread of Vachellia, Senegalia and Grewia reflecting an encroached state.

A dry deposition scheme for particulate matter coupled with a well-known Lagrangian Stochastic model for pollutant dispersion

A 3D dry deposition scheme for particulate matter (PM) is presented as a Free-Libre and Open-Source Software (FOSS) library, DePaSITIA (RSE SpA). This combines some advanced formulations for the deposition mechanisms of sedimentation, inertial impaction, turbulent impaction and interception. The scheme also considers bouncing effects. The input quantities relate to the canopy elements (Leaf Area Density, leaf equivalent diameter, leaf shape, orientation and roughness parameters), the transporting fluid (local mean velocity, friction velocity) and the particulate matter (PM local mean concentration, median diameter and density). The deposition scheme is coupled with a well-known Lagrangian Stochastic model for pollutant dispersion, the Open-Source code SPRAY-WEB (Universita del Piemonte Orientale et al.). The coupled numerical solution is validated on a laboratory test case representing the dispersion of particulate matter from two line sources within a canopy atmospheric boundary layer. The deposition interfaces are represented by the trees of a scaled spruce forest. Validation refers to the average vertical profile of the deposited mass (not the mean concentration) normalized by the above-canopy mean concentration. Some inter-comparisons are also reported considering uniform Leaf Area Density, the additional effects of molecular diffusion, the height-dependent relative contribution of each deposition mechanism and an alternative deposition scheme. The results of this test case are available as a FOSS tutorial. Considering the Fractional Bias obtained for the deposited mass (FB = 27%), this numerical solution seems suitable to simulating stationary dispersion phenomena within complex canopy boundary layers, assessing the height-dependent dry deposition fluxes of atmospheric PM. The current numerical solution might be improved and applied to elevated obstacles such as electric insulators.

Dispersion of Buoyant and Sinking Particles in a Simulated Wind‐ and Wave‐Driven Turbulent Coastal Ocean

AbstractIn shallow coastal oceans, turbulent flows driven by surface winds and waves and constrained by a solid bottom disperse particles. This work examines the mechanisms driving horizontal and vertical dispersion of buoyant and sinking particles for times much greater than turbulent integral time scales. Turbulent fields are modeled using a wind‐stress driven large eddy simulation (LES), incorporating wave‐driven Langmuir turbulence, surface breaking wave turbulent kinetic energy inputs, and a solid bottom boundary. A Lagrangian stochastic model is paired to the LES to incorporate Lagrangian particle tracking. Within a subset of intermediate buoyant rise velocities, particles experience synergistic vertical mixing in which breaking waves (BW) inject particles into Langmuir downwelling velocities sufficient to drive deep mixing. Along‐wind dispersion is controlled by vertical shear in mean along‐wind velocities. Wind and bottom friction‐driven vertical shear enhances dispersion of buoyant and sinking particles, while energetic turbulent mixing, such as from BW, dampens shear dispersion. Strongly rising and sinking particles trapped at the ocean surface and bottom, respectively, experience no vertical shear, resulting in low rates of along‐wind dispersion. Crosswind dispersion is shaped by particle advection in wind‐aligned fields of counter‐rotating Langmuir and Couette roll cells. Langmuir cells enhance crosswind dispersion in neutrally to intermediately buoyant particles through enhanced cell hopping. Surface trapping restricts particles to Langmuir convergence regions, strongly inhibiting crosswind dispersion. In shallow coastal systems, particle dispersion depends heavily on particle buoyancy and wave‐dependent turbulent effects.

Simulated Dust Transport in the Convective Boundary Layer

AbstractSoil dusts are an important source of aerosol in agricultural regions and can affect the Earth's radiation budget through the modification of cloud properties, and in particular, through their ability to act as ice nucleating particles. In order to impact cloud properties, agricultural soil dusts need to be transported from the point of emission to cloud‐relevant altitudes. Vertical transport within the planetary boundary layer is strongly controlled by turbulence and is challenging to represent accurately in regional and global models. Large‐eddy simulations (LES) are run at resolutions capable of resolving most of the turbulent energy directly and can thus better simulate vertical transport. In this study, we leverage the LES ARM Symbiotic Simulation and Observation (LASSO) large‐eddy simulations to simulate vertical transport of agricultural dust within the turbulent boundary layer using a modified version of the stochastic dispersion model FLEXPART‐WRF. We find that the modified model is better capable of simulating particle transport due to turbulence, and that particle size was the greatest factor in determining particle lifetime. Individual meteorology and particle density had intermediate effects upon particle transport, while release height had little effect upon simulation results. Finally, we utilize a quasi‐single column model (QSCM) approach to determine how our results compare to a parameterized treatment of turbulence. The QSCM simulations led to greater tracer transport out of the boundary layer, with ramifications for any studies utilizing a Lagrangian stochastic model to understand tracer dispersion. These results highlight the importance of accurately simulating turbulence for understanding particle transport.

Collision rate of bidisperse, hydrodynamically interacting spheres settling in a turbulent flow

Abstract

Calculation of NH3 Emissions, Evaluation of Backward Lagrangian Stochastic Dispersion Model and Aerodynamic Gradient Method

Two campaigns measuring ammonia (NH3) emissions with different measurement techniques were performed on a large grass field (26 ha) after the application of liquid animal manure. The aim was to compare emissions from a confined area estimated from either (i) concentration measurements, both point and line-integrated measurements, combined with backward Lagrangian stochastic (bLS) dispersion modeling or by (ii) estimation of the vertical flux by the aerodynamic gradient method (AGM) with and without footprint correction approximated by the bLS model estimates of the flux footprint. The objective of the comparison is to establish the best practice to derive NH3 emissions from a large field. NH3 emissions derived from bLS agreed well when comparing point and line-integrated measurements. Simple point measurements combined with bLS yield good emission estimations for the confined area. Without footprint correction, the AGM underestimates the emissions by up to 9% compared to the footprint-corrected AGM results. The sensitivity of the measurement methods makes it possible to quantify NH3 emissions with diurnal patterns even five days after a field application of liquid animal manure under wet conditions. The bLS model proves to be a strong tool to determine the NH3 emissions from point concentration measurements inside a large field after a slurry application.

Measuring N2O Emissions from Multiple Sources Using a Backward Lagrangian Stochastic Model

Nitrous oxide (N2O) emissions from agricultural soil are substantially influenced by nitrogen (N) and field management practices. While routinely soil chambers have been used to measure emissions from small plots, measuring field-scale emissions with micrometeorological methods has been limited. This study implemented a backward Lagrangian stochastic (bLS) technique to simultaneously and near-continuously measure N2O emissions from four adjacent fields of approximately 1 ha each. A scanning open-path Fourier-transform infrared spectrometer (OP-FTIR), edge-of-field gas sampling and measurement, locally measured turbulence, and bLS emissions modeling were integrated to measure N2O emissions from four adjacent fields of maize production using different management in 2015. The maize N management treatments consisted of 220 kg NH3-N ha−1 applied either as one application in the fall after harvest or spring before planting or split between fall after harvest and spring before planting. The field preparation treatments evaluated were no-till (NT) and chisel plow (ChP). This study showed that the OP-FTIR plus bLS method had a minimum detection limit (MDL) of ±1.2 µg m−2 s−1 (3σ) for multi-source flux measurements. The average N2O emission of the four treatments ranged from 0.1 to 2.3 µg m−2 s−1 over the study period of 01 May to 11 June after the spring fertilizer application. The management of the full-N rate applied in the fall led to higher N2O emissions than the split-N rates applied in the fall and spring. Based on the same N application, the ChP practice tended to increase N2O emissions compared with NT. Advection of N2O from adjacent fields influenced the estimated emissions; uncertainty (1σ) in emissions was 0.5 ± 0.3 µg m−2 s−1 if the field of interest received a clean measured upwind background air, but increased to 1.1 ± 0.5 µg m−2 s−1 if all upwind sources were advecting N2O over the field of interest. Moreover, higher short-period emission rates (e.g., half-hour) were observed in this study by a factor of 1.5~7 than other micrometeorological studies measuring N2O-N loss from the N-fertilized cereal cropping system. This increment was attributed to the increase in N fertilizer input and soil temperature during the measurement. We concluded that this method could make near-continuous “simultaneous” flux comparisons between treatments, but further studies are needed to address the discrepancies in the presented values with other comparable N2O flux studies.

Methane flux from flowback operations at a shale gas site

ABSTRACT We report measurements of methane (CH4) mixing ratios and emission fluxes derived from sampling at a monitoring station at an exploratory shale gas extraction facility in Lancashire, England. Elevated ambient CH4 mixing ratios were recorded in January 2019 during a period of cold-venting associated with a nitrogen lift process at the facility. These processes are used to clear the well to stimulate flow of natural gas from the target shale. Estimates of CH4 flux during the emission event were made using three independent modeling approaches: Gaussian plume dispersion (following both a simple Gaussian plume inversion and the US EPA OTM 33-A method), and a Lagrangian stochastic transport model (WindTrax). The three methods yielded an estimated peak CH4 flux during January 2019 of approximately 70 g s−1. The total mass of CH4 emitted during the six-day venting period was calculated to be 2.9, 4.2 ± 1.4(1σ) and 7.1 ± 2.1(1σ) tonnes CH4 using the simple Gaussian plume model, WindTrax, and OTM-33A methods, respectively. Whilst the flux approaches all agreed within 1σ uncertainty, an estimate of 4.2 (± 1.4) tonnes CH4 represents the most confident assessment due to the explicit modeling of advection and meteorological stability permitted using the WindTrax model. This mass is consistent with fluxes calculated by the Environment Agency (in the range 2.7 to 6.8 tonnes CH4), using emission data provided by the shale site operator to the regulator. This study provides the first CH4 emission estimate for a nitrogen lift process and the first-reported flux monitoring of a UK shale gas site, and contributes to the evaluation of the environmental impacts of shale gas operations worldwide. This study also provides forward guidance on future monitoring applications and flux calculation in transient emission events. Implications: This manuscript discusses atmospheric measurements near to the UK’s first hydraulic fracturing facility, which has very high UK public, media, and policy interest. The focus of this manuscript is on a single week of data in which a large venting event at the shale gas site saw emissions of ~4 tonnes of methane to atmosphere, in breach of environmental permits. These results are likely to beresults are likely to be reported by the media and may influence future policy decisions concerning the UK hydraulic fracturing industry.

Abyssal Pathways and the Double Silica Maximum in the Northeast Pacific Basin

AbstractThis study examines causes of the double silica maximum in the deep interior Northeast Pacific Basin using a stochastic Lagrangian tracer model based on steady‐state advective fields and diapycnal diffusion established by a hydrographic inverse method that conserves potential vorticity and salinity. Lateral diffusion, unresolved by the inverse model, is adjusted for overall agreement with radiocarbon distribution. The double silica maximum in vertical profiles arises from an eastern‐intensified single maximum in the North Pacific Deep Water along the northern domain boundary (originating in the western Pacific), and a strong subarctic bottom source supplying silica to Upper Circumpolar Deep Water density surfaces that successively intersect the seafloor over a broad area east of 150°W, associated geostrophically with southward flow. The existence of the double silica maximum requires weak diapycnal transport in the deep interior, with broader implications for the conceptual picture of meridional overturning circulation in the North Pacific.