Lagrangian Stochastic Model Research Articles

Cannabis pollen dispersal across the United States

For the recently legalized US hemp industry (Cannabis sativa), cross-pollination between neighboring fields has become a significant challenge, leading to contaminated seeds, reduced oil yields, and in some cases, mandated crop destruction. As a step towards assessing hemp cross-pollination risk, this study characterizes the seasonal and spatial patterns in windborne hemp pollen dispersal spanning the conterminous United States (CONUS). By leveraging meteorological data obtained through mesoscale model simulations, we have driven Lagrangian Stochastic models to simulate wind-borne hemp pollen dispersion across CONUS on a county-by-county basis for five months from July to November, encompassing the potential flowering season for industrial hemp. Our findings reveal that pollen deposition rates escalate from summer to autumn due to the reduction in convective activity during daytime and the increase in wind shear at night as the season progresses. We find diurnal variations in pollen dispersion: nighttime conditions favor deposition in proximity to the source, while daytime conditions facilitate broader dispersal albeit with reduced deposition rates. These shifting weather patterns give rise to specific regions of CONUS more vulnerable to hemp cross-pollination.

Applicability of the inverse dispersion method to measure emissions from animal housings

Abstract. Emissions from agricultural sources substantially contribute to global warming. The inverse dispersion method (IDM) has been successfully used for emission measurements from various agricultural sources. The IDM has also been validated in multiple studies with artificial gas releases mostly in open fields. Release experiments from buildings have rarely been conducted and were partly affected by additional nearby sources of the target gas. Specific release studies for naturally ventilated animal housings are lacking. In this study, a known and predefined amount of methane (CH4) was released from an artificial source inside a barn that mimicked a naturally ventilated dairy housing, and IDM recovery rates, using a backward Lagrangian stochastic (bLS) model, were determined. For concentration measurements, open-path devices (OPs) with a path length of 110 m were placed in a downwind direction of the barn at fetches of 2.0h, 5.3h, 8.6h, and 12h (h equals the height of the highest obstacle), and a 3D ultrasonic anemometer (UA) was placed in the middle of the first three OP paths. Upwind of the barn, an additional OP and a UA were installed. The median IDM recovery rates determined with the UA placed upwind of the barn and the downwind OP ranged between 0.55–0.75. It is concluded that, for the present study case, the effect of the building and a tree in the main wind axis led to a systematic underestimation of the IDM-derived emission rate probably due to deviations in the wind field and turbulent dispersion from the underlying assumptions of the used dispersion model.

Lagrangian Perspectives on the Small-scale Structure of Alfvénic Turbulence and Stochastic Models for the Dispersion of Fluid Particles and Magnetic Field Lines in the Solar Wind

Lagrangian perspectives on the small-scale structure of anisotropic Alfvénic turbulence are adopted. We are interested in relating the statistical properties of the Eulerian field increments evaluated along the fluid particle trajectories, in the direction perpendicular to the guiding magnetic field and along the magnetic field lines. We establish the basis for a unified multifractal phenomenology of Eulerian and Lagrangian Alfvénic turbulence. The critical balance condition is generalized to structure functions of an order different than 2. A Lagrangian perspective is not only useful for investigating the small-scale structure of Alfvénic turbulence, it is also tailored to the modeling of large-scale turbulent transport. Therefore, we develop Lagrangian stochastic models for the dispersion of fluid particles and magnetic field lines in the solar wind. The transport models are based on the integrated Ornstein–Uhlenbeck process that is not Markov, yielding smooth stochastic fluid particle trajectories and magnetic field lines. Brownian diffusion is recovered by tending the integral scale parameter to zero while keeping the diffusivity finite.

Stochastic Lagrangian wall deposition model for RANS prediction of deposition in turbulent gas–solid flows

In industrial-scale Reynolds Averaged Navier–Stokes (RANS) simulations, a wall-modeled approach is often employed, specifically choosing a dimensionless wall-cell height much greater than one. However, in gas–solid flows, a coarse description of the boundary layer may lead to inaccurate results in terms of particle dispersion and deposition. In this study, we conducted an investigation on stochastic RANS dispersion models with deposition on smooth walls using a wall-modeled approach. These models were applied to turbulent channel flows in both vertical and horizontal orientations. The modeling approach involved the adoption of the Euler–Lagrange formalism and the RANS k−ϵ turbulence model in OpenFOAM®. To assess particle behavior first, a simple homogeneous isotropic stationary turbulence (HIST) case was examined. Fluid elements were also tracked in an inhomogeneous turbulence for dispersion analysis. These tests gave the good formulation for the dispersion model to be used for particle tracking coupled with turbulent channel flow simulation. However, the deposition results in turbulent channel using such stochastic dispersion model in the wall-cell were found to be consistently overestimated across various scenarios for low-inertia particles. To address these limitations arising from the coarse description of the boundary layer, we examined, implemented, and evaluated a Lagrangian stochastic wall deposition model. The activated deposition model demonstrated good agreement with experimental data.

Potential of using CO2 observations over India in a regional carbon budget estimation by improving the modelling system

Abstract. Devising effective national-level climate action plans requires a more detailed understanding of the regional distribution of sources and sinks of greenhouse gases. Due to insufficient observations and modelling capabilities, India's current carbon source–sink estimates are uncertain. This study uses a high-resolution Lagrangian transport model to examine the potential of available CO2 observations over India for inverse estimation of regional carbon fluxes. We use four different sites in India that vary in the measurement technique, frequency and spatial representation. These observations exhibit substantial seasonal (7.5 to 9.2 ppm) and intra-seasonal (2 to 12 ppm) variability. Our modelling framework, a high-resolution Weather Research and Forecasting Model combined with the Stochastic Time-Inverted Lagrangian Transport model (WRF–STILT), performs better in simulating seasonal (R2=0.50 to 0.96) and diurnal (R2=0.96) variability (for the Mohali station) of observed CO2 than the current-generation global models (CarboScope, CarbonTracker and ECMWF EGG4). The seasonal CO2 concentration variability in Mohali, associated with crop residue burning, is largely underestimated by the models. WRF–STILT captures the seasonal biospheric variability over Nainital better than the global models but underestimates the strength of the CO2 uptake by crops. The choice of emission inventory in the modelling framework alone leads to significant biases in simulations (5 to 10 ppm), endorsing the need for accounting for emission fluxes, especially for non-background sites. Our study highlights the possibility of using the CO2 observations from these Indian stations for deducing carbon flux information at regional (Nainital) and suburban to urban (Mohali, Shadnagar and Nagpur) scales with the help of a high-resolution model. On accounting for observed variability in CO2, the global carbon data assimilation system can benefit from the measurements from the Indian subcontinent.

Lagrangian Stochastic Modeling of Stratified Atmospheric Boundary Layer

A single-column turbulence model for stratified atmospheric boundary layer (ABL), which solves the transport equations of turbulence probability density function (PDF) using a Lagrangian stochastic modeling (LSM) approach, is proposed in this study. This study adopts previously developed stochastic differential equations (SDEs) for particle velocity and temperature and extends the LSM to simulate inhomogeneous turbulence. The proposed LSM is tested for its ability to fully simulate statistics of inhomogeneous stratified turbulence. In the model, particles evolve by SDEs, and turbulence statistics are calculated by averaging the properties of particles. The model provides a full representation of turbulence PDF and simulates turbulent transport without any modeling assumption. The model performance is evaluated against large-eddy simulation (LES) results in the simulations of convective and stable ABL cases. For the convective ABL, LSM realistically simulates the entrainment process with the temperature and heat flux profiles that closely match with LES. The joint PDF simulated by LSM reproduces a curved and highly skewed shape, and some distinct features, like the asymmetric distribution of vertical velocity and the separation of the PDF in the entrainment zone, are simulated. LSM also reproduces the entrainment enhancement by wind shear in the simulation of sheared convective ABL. The LSM simulation of stable ABL predicts realistic turbulence intensity and mean field profiles, where Gaussian-like PDFs are simulated both in LSM and LES.

Designing additional CO2 in-situ surface observation networks over South Korea using bayesian inversion coupled with Lagrangian modelling

Efforts to enhance greenhouse gas (GHG) emission reduction in East Asia play a pivotal role on both global and regional scales in advancing climate mitigation strategies. This study aimed to better constrain anthropogenic CO2 emission estimates by expanding the network of near-surface in-situ stations for CO2 observations across South Korea. To achieve an optimal CO2 network design, we conducted an Observing System Simulation Experiment (OSSE) coupled with the Stochastic Lagrangian Transport model (STILT), utilizing meteorological data from the Korean Integrated Model (KIM). Our inversion setup incorporated two CO2 emission datasets with a 0.1o resolution: EDGAR v6 for prior emissions and GRACED for truth emissions. A uniform model-mismatch error of 3 ppm was introduced across sites. The effectiveness of the existing five in-situ stations, termed the base network, in South Korea was evaluated to gauge their ability to constrain CO2 surface flux estimates. However, the findings revealed a reduction in flux uncertainty of only 29.2%, which fell short of the desired uncertainty reduction goal. In this base network, the Lotte World Tower (LWT: 37.5126°E, 127.1025°E) in Seoul and the Anmyeondo (AMY: 36.538576° N, 126.330071° E) site in Taean county stood as major contributors, with estimated reductions of 17.48% and 6.35%, respectively. Consequently, we proposed and developed an extended network, identifying seven candidate sites based on consideration of logistical factors, existing infrastructures, and proximity to the emission source regions. An incremental optimization scheme ranked their contributions, resulting in an additional 25% reduction, bringing the total to 54.13%. However, it is noteworthy that diminishing returns (ranging from 13% to less than 0.1%) were observed with an increase in station count mainly due to the possibility that adding a station earlier in the sequence might render subsequent stations redundant. Despite this, the proposed CO2 network successfully reduced uncertainty in emissions, narrowing the gap with the objectives of the Global Greenhouse Gas Watch (G3W).

Accurate Lagrangian stochastic model on homogeneous turbulence under two shear orientations

The paper reports a numerical modelisation of homogeneous and stratified turbulence under vertical and horizontal shear by way of Lagrangian stochastic model (LSM) versus Froude number. Vertical and horizontal shear (θ = 0 and θ = π/2) are adopted. First, a comparison of predictions by LSM with results of direct numerical simulation of Jacobitz (DNSJ) is carried out. Current results obtained by LSM demonstrate the existence of asymptotic equilibrium states for various parameters of the problem particularly for the horizontal shear. Compared to the case of a vertical shear, an excellent agreement between predictions of LSM related to the case of horizontal shear and results of DNSJ is detected for growth rate, ratio kinetic energy to total energy and potential energy to total energy beyond τ = 40. For two shear orientations, results of normalized production and turbulence dissipation are comparable with different approaches for τ ≥ 70. Second, a comparative study of various thermal and dynamic parameters governing the considered problem for horizontal and vertical shear is performed versus Froude number. This study indicates that the LSM can present a significant contribution for numerical modelisation of stratified and homogeneous turbulence especially in the presence of a horizontal shear.

Evaluation of Turbulence Depending Drag Coefficient in Plume Rise Model for Fire Smoke Dispersion

It is well-known that the correct modeling of the plume rise is fundamental for a proper description of pollutants dispersion, especially for highly buoyant plumes like those emitted by wildfires. In this work, we want to investigate the role of the drag coefficient (CD) in our plume rise scheme. We evaluate different formulations taken from the literature and suggest the best option for the plume rise scheme embedded in the Lagrangian Stochastic model SPRAY-WEB. As a matter of fact, previous works on plume rise models are based on the drag coefficient which is a quantity that should be determined. There is not a general consensus on the best values for CD. Some values suggested in the literature are simply constants that do not directly depend on the meteorological and turbulent variables. In order to evaluate the model performances obtained using different CD formulations we simulate a field experiment, carried out in August 2013 in Idaho (USA), in which prescribed fires were observed and the physical and chemical parameters were measured. As a matter of fact, plumes emitted from fires are affected by strong buoyancy and very low or even negligible initial vertical momentum. These conditions are very different from traditional plumes from stacks for which the classical plume rise models are built. For this reason, the case studies chosen for the tests are very challenging and they allow us to assess the scheme here proposed in the best way. Comparison among the results obtained with different CD parameterizations are presented and discussed. Three of the four CD models tested derive from an extension of the Stokes’ law; the fourth one is a more refined model derived from the Shanks transformation of the Goldstein series. This last model seems to give better results as regards the maximum height of the plume, but is the one that underestimates most CO concentrations.

Steady-State Supersaturation Distributions for Clouds under Turbulent Forcing

Abstract The supersaturation equation for a vertically moving adiabatic cloud parcel is analyzed. The effects of turbulent updrafts are incorporated in the shape of a stochastic Lagrangian model, with spatial and time correlations expressed in terms of turbulent kinetic energy. Using the Fokker–Planck equation, the steady-state probability distributions of supersaturation are analytically computed for a number of approximations involving the time-scale separation between updraft fluctuations and phase relaxation, and droplet or ice particle size fluctuations. While the analytical results are presented in general for single-phase clouds, the calculated distributions are used to compute mixed-phase cloud properties—mixed fraction and mean liquid water content in an initially icy cloud—and are argued to be useful for generalizing and constructing new parameterization schemes. Significance Statement Supersaturation is the fuel for the development of clouds in the atmosphere. In this paper, our goal is to better understand the supersaturation budget of clouds embedded in a turbulent environment by analyzing the basic equations of cloud microphysics. It is found that the turbulent characteristics of an air parcel substantially affect the cloud’s supersaturation budget and hence its life cycle. This is also shown in the context of mixed-phase clouds where, depending on the turbulent regime, different liquid-to-ice ratios are found. Consequently, the theoretical approach of this paper is crucial to develop tools to parameterize small-scale atmospheric features, like clouds, into global circulation models to improve climate projections for the future.

QES-Plume v1.0: a Lagrangian dispersion model

Abstract. Low-cost simulations providing accurate predictions of transport of airborne material in urban areas, vegetative canopies, and complex terrain are demanding because of the small-scale heterogeneity of the features influencing the mean flow and turbulence fields. Common models used to predict turbulent transport of passive scalars are based on the Lagrangian stochastic dispersion model. The Quick Environmental Simulation (QES) tool is a low-computational-cost framework developed to provide high-resolution wind and concentration fields in a variety of complex atmospheric-boundary-layer environments. Part of the framework, QES-Plume, is a Lagrangian dispersion code that uses a time-implicit integration scheme to solve the generalized Langevin equations which require mean flow and turbulence fields. Here, QES-Plume is driven by QES-Winds, a 3D fast-response model that computes mass-consistent wind fields around buildings, vegetation, and hills using empirical parameterizations, and QES-Turb, a local-mixing-length turbulence model. In this paper, the particle dispersion model is presented and validated against analytical solutions to examine QES-Plume’s performance under idealized conditions. In particular, QES-Plume is evaluated against a classical Gaussian plume model for an elevated continuous point-source release in uniform flow, the Lagrangian scaling of dispersion in isotropic turbulence, and a non-Gaussian plume model for an elevated continuous point-source release in a power-law boundary-layer flow. In these cases, QES-Plume yields a maximum relative error below 6 % when compared with analytical solutions. In addition, the model is tested against wind-tunnel data for a uniform array of cubical buildings. QES-Plume exhibits good agreement with the experiment with 99 % of matched zeros and 59 % of the predicted concentrations falling within a factor of 2 of the experimental concentrations. Furthermore, results also emphasize the importance of using high-quality turbulence models for particle dispersion in complex environments. Finally, QES-Plume demonstrates excellent computational performance.

Modeling wind-driven seed dispersal using a coupled Lagrangian particle tracking and 1-D [formula omitted]-[formula omitted] turbulence model

We present a one-dimensional k-ɛ model and a Markov chain stochastic Lagrangian particle tracking model to study wind-driven dispersal of forest and grassland seeds. The turbulence model within and above the canopy is implemented for transient winds so that time series of profiles of mean velocity, turbulence kinetic energy, dissipation rate, and the root-mean-square of fluctuating velocity components can be modeled. We validate the model for steady state conditions using observations in a wide range of canopies, and apply the model for predicting time series of seed dispersal of Andropogon gerardii in a tall grass prairie in Missouri, United States. The stochastic seed dispersal model is validated against experimental data from a Quercus-Carya (oak-hickory) forest where seeds were released from different heights for a range of wind speeds. Using the model, we explore the detailed seed movement trajectories, instantaneous velocities, and investigate the relationship between dispersal distance and the seed falling duration and the mean fluctuating velocity during the falling. Moreover, examining the role of individual turbulent velocity components, we elucidate the different roles of horizontal and vertical velocity fluctuations, i.e., the horizontal component mainly contributes to the seed spreading in the wind direction, while the vertical component enhances the long tail of the distribution in the downstream direction, i.e., promoting long-distance-dispersal of seeds by wind.

Modeling the Distribution of Radionuclides in the Air and on the Soil Surface

Mathematical and numerical methods are used to simulate physical and chemical processes when building models of pollutants dispersion in the air and on the soil surface. Based on meteorological data and information on the source of emissions, these models characterize both the primary pollutants entering the atmosphere directly and the secondary ones formed as the result of complex chemical reactions. These models are important for the air quality management system, as they allow monitoring emissions into the atmosphere, predicting their distribution, as well as developing effective strategies intended for reducing harmful substances in the atmosphere. The article presents an overview of computational methods used to simulate the pollutants dispersion in atmospheric air and on the soil surface, such as the Gaussian torch model, the Lagrangian dispersion stochastic model, and the Eulerian model of atmospheric diffusion. The practical application of the considered models showed sufficient reliability and validity of the air and soil pollution levels forecast. The simulation uses computer programs that include algorithms for solving the mathematical equations that control pollutant dispersion. The dispersion models are used to estimate the concentration of air pollutants or toxins. They can also be used to predict future concentrations under certain scenarios. They are useful for studying the pollutants that disperse over long distances and can initiate reactions in the atmosphere. Such software products are as follows: AEROPOL, AERMOD, GRAL, TAPM CSIRO, CALPUFF, HYSPLIT, etc. A method of processing information about the pollution sources and the environmental parameters, based on the HYSPLIT program, is proposed to form maps of the volume and surface activity of radionuclides. This method was applied to analyze the process of the plutonium isotopes dispersion as a result of the movement of air masses in the places of fires in April 2020 in the exclusion zone of the Chornobyl NPP, as well as the associated hazard for the population health and the environment.

Effect of Covering Deep Litter Stockpiles on Methane and Ammonia Emissions Analyzed by an Inverse Dispersion Method

Ammonia (NH3) and methane (CH4) emission rates from cattle deep litter and horse manure deep litter in farm-scale stockpiles were measured using an inverse dispersion method based on the backward Lagrangian Stochastic (bLS) model. The aims of the study were to (i) evaluate the effects of timing and carefulness of covering a stockpile, (ii) measure emissions from handling and storing deep litter, (iii) compare emissions from manure stored in a container and stockpile, (iv) determine emissions from cattle and horse manure deep litter, and (v) evaluate potential effects of pile temperature on emissions. New emission data with relatively high temporal resolution are provided. High variability in CH4 emissions was observed with no clear effects on the timing of covering, even though the temperatures inside the piles were different. NH3 emissions occur immediately after pile establishment and the emissions were highly influenced by the timing of covering. In the first week of storage, covering reduced NH3 emissions by 92 ± 9% when comparing the emissions from a noncovered and totally covered stockpile. This demonstrates the effect of applying a cover immediately to avoid NH3 emissions. The long-term effects of covering strategies as well as the influence of temperature and season are also discussed. For horse manure deep litter, storage in a closed (covered) container instead of a covered stockpile was observed to reduce CH4 emissions by 50 ± 58% and NH3 emissions by 67 ± 37%.

Simulation of Inertial Droplet Dispersion and the Spray Mediated Fluxes in the Atmospheric Boundary Layer Above Waved Water Surface: A Lagrangian Stochastic Model Versus Direct Numerical Simulation

Simulation of Inertial Droplet Dispersion and the Spray Mediated Fluxes in the Atmospheric Boundary Layer Above Waved Water Surface: A Lagrangian Stochastic Model Versus Direct Numerical Simulation

Lagrangian stochastic model for the orientation of inertialess spheroidal particles in turbulent flows: An efficient numerical method for CFD approach

In this work, we propose a model for the orientation of inertialess spheroidal particles suspended in turbulent flows. This model consists in a stochastic version of the Jeffery equation that can be included in a statistical Lagrangian description of particles suspended in a flow. It is compatible and coherent with turbulence models that are widely used in CFD codes for the simulation of the flow field in practical large-scale applications. In this context, we propose and analyze a numerical scheme based on a splitting scheme algorithm that decouples the orientation dynamics into its main contributions: stretching and rotation. We detail its implementation in an open-source CFD software. We analyze the weak and strong convergence of both the global scheme and of each sub-part. Subsequently, the splitting technique yields to a highly efficient hybrid algorithm coupling pure probabilistic and deterministic numerical schemes. Various numerical experiments were implemented and the results were compared with analytical predictions of the model to assess the algorithm efficiency and accuracy.

Lagrangian Stochastic Model for the Motions of Magnetic Footpoints on the Solar Wind Source Surface and the Path Lengths of Boundary-driven Interplanetary Magnetic Field Lines

In this work, we extend Leighton’s diffusion model describing the turbulent mixing of magnetic footpoints on the solar wind source surface. The present Lagrangian stochastic model is based on the spherical Ornstein–Uhlenbeck process with drift that is controlled by the rotation frequency Ω of the Sun, the Lagrangian integral timescale τ L, and the root-mean-square footpoint velocity V rms. The Lagrangian velocity and the positions of magnetic footpoints on the solar wind source surface are obtained from the solutions of a set of stochastic differential equations, which are solved numerically. The spherical diffusion model of Leighton is recovered in the singular Markov limit when the Lagrangian integral timescale tends to zero while keeping the footpoint diffusivity finite. In contrast to the magnetic field lines driven by standard Brownian processes on the solar wind source surface, the interplanetary magnetic field lines are smooth differentiable functions with finite path lengths in our model. The path lengths of the boundary-driven interplanetary magnetic field lines and their probability distributions at 1 au are computed numerically, and their dependency with respect to the controlling parameters is investigated. The path-length distributions are shown to develop a significant skewness as the width of the distributions increases.

Heterogenous Canopy in a Lagrangian-Stochastic Dispersion Model for Particulate Matter from Multiple Sources over the Haifa Bay Area

The Haifa Bay area (HBA) is a major metropolitan area in Israel, which consists of high volume transportation routes, major industrial complexes, and the largest international seaport in Israel. These, which lie relatively near densely populated residential areas, result in a multitude of air pollution sources, many of whose emissions are in the form of particulate matter (PM). Previous studies have associated exposure to such PM with adverse health effects. This potential consequence serves as the motivation for this study whose aim is to provide a realistic and detailed three-dimensional concentration field of PM, originating simultaneously from multiple sources. The IIBR in-house Lagrangian stochastic pollutant dispersion model (LSM) is suitable for this endeavor, as it describes the dispersion of a scalar by solving the velocity fluctuations in high Reynolds number flows. Moreover, the LSM was validated in urban field experiments, including in the HBA. However, due to the fact that the multiple urban sources reside within the canopy layer, it was necessary to integrate into the LSM a realistic canopy layer model that depicts the actual effect of the roughness elements’ drag on the flow and turbulent exchange of the urban morphology. This was achieved by an approach which treats the canopy as patches of porous media. The LSM was used to calculate the three-dimensional fields of PM10 and PM2.5 concentrations during the typical conditions of the two workday rush-hour periods. These were compared to three air quality monitoring stations located downstream of the PM sources in the HBA. The LSM predictions for PM2.5 satisfy all acceptance criteria. Regarding the PM10 predictions, the LSM results comply with three out of four acceptance criteria. The analysis of the calculated concentration fields has shown that the PM concentrations up to 105 m AGL exhibit a spatial pattern similar to the ground level. However, it decreases by a factor of two at 45 m AGL, while, at 105 m, the concentration values are close to the background concentrations.

Stochastic model for the alignment and tumbling of rigid fibers in two-dimensional turbulent shear flow

Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess, rod-shaped particles embedded in a two-dimensional turbulent flow with homogeneous shear. A Lagrangian stochastic model for the rods angular dynamics is introduced and compared to the results of direct numerical simulations. The model consists in superposing a short-correlated random component to the steady large-scale mean shear, and can thereby be integrated analytically. To reproduce the single-time orientation statistics obtained numerically, it is found that one has to properly account for the combined effect of the mean shear, for anisotropic velocity gradient fluctuations, and for the presence of persistent rotating structures in the flow that bias Lagrangian statistics. The model is then used to address two-time statistics. The notion of tumbling rate is extended to diffusive dynamics by introducing the stationary probability flux of the rods unfolded angle. The model is found to reproduce the long-term effects of an average shear on the mean and the variance of the fibres angular increment. Still, it does not reproduce an intricate behaviour observed in numerics for intermediate times: the unfolded angle is there very similar to a L\'evy walk with distributions of increments displaying intermediate power-law tails.

Full-Scale Investigation of Methane and Ammonia Mitigation by Early Single-Dose Slurry Storage Acidification

The effects of early acidification with sulfuric acid of animal slurry in concrete storage tanks to pH 5 on methane and ammonia emissions have been investigated on two cattle and two pig slurry storage tanks in full scale. The tanks’ up- and down-wind concentrations were measured online by cavity ring-down spectroscopy (CRDS). The inverse-dispersion method (IDM), using a backward Lagrangian stochastic (bLS) model, was used to determine the emission rates. The results show that CH4 emissions after single-dose acidification of slurry tanks in the early summer were reduced by 95 ± 14% and 95% ± 6% for cattle and pig manure, respectively, compared to the emissions measured before acidification. The reductions occurred even though pH increased during the storage with and without addition of fresh slurry. After acidification, NH3 emissions were comparable to or lower than when a natural crust was present. A supplementary experiment on small-scale slurry containers was conducted to investigate the pH development when fresh slurry was added to the acidified slurry. The influence of pH development on the long-term emission dynamics of methane is discussed by comparing the large-scale and small-scale studies. The study presents the first full-scale documentation that slurry acidification is a promising technology for mitigation of methane from slurry storage.