Uncertainty in using dispersion models to estimate methane emissions from manure lagoons in dairies
Introduction
Methane has an increasingly important role in causing climate change, with emissions rising more quickly than those of CO2 (Saunois et al., 2016b). Animal agriculture is the source of ~35% of anthropogenic methane emissions globally, and these emissions are increasing along with the number of animals (Saunois et al., 2016a). Methane emissions from animal agriculture derive primarily from enteric fermentation in cattle and from manure management, particularly when waste is treated or stored in anaerobic lagoons. Manure management accounts for nearly 10% of methane emissions in the U.S. (US Environmental Protection Agency, 1990), and in California, more than a quarter (CARB, 2019). However, as pointed out by a report from the National Academies of Sciences, Engineering (2018) these inventories are not supported adequately by measurements. Furthermore, the report concludes that “fundamental research identifying and quantifying uncertainties is needed”. This paper presents results that contribute towards fulfilling this need.
Methane emissions from area sources, such as manure lagoons, have been inferred using several micrometeorological methods, which are critically reviewed in McGinn (2013). This paper focuses on one of these methods, based on using dispersion models, to infer emissions from measurements of the concentrations of the relevant species near the source. Dispersion models have been used by several investigators (Ro et al., 2013; Leytem et al., 2017) to estimate emissions from lagoons and determine their uncertainty. Most have used the WindTrax software, based on the backward Lagrangian particle model developed by Flesch et al. (2005), to infer emissions from path averaged methane concentrations measured upwind and downwind of the lagoon of interest. Some of these studies have quantified the uncertainty in these emissions. Kaharabata et al. (2000) used the approximate solution of the two-dimensional diffusion equation proposed by van Ulden (1978) to infer emission rates from a 4 by 8 m plot with a tracer gas with a known release rate. The uncertainty was the ratio of the inferred to the known emission rate of the tracer gas. 81% of the measurements made near the centerline of the plumes yielded emission estimates within ±20% of the actual source strength and this dropped to 55% and 22% moving away from the centerline. Ro et al. (2013) estimated the uncertainty using a similar approach. The inferred emission estimate was within a range of 0.68 to 1.08 of the actual value. In principle, determining emission uncertainty using tracer releases is more direct. However, a tracer study is not practical for typical lagoons with lengths and widths of the order of 100 m, and the results would be difficult to transfer to conditions that differ from those of the tracer study.
In this study, we estimate methane emissions from waste lagoons in two dairies, one located in Southern California, and the other in Central California. We use two dispersion models to infer these emissions from measurements of atmospheric methane concentrations made around these lagoons. The difference in the results from the two models is one measure of the uncertainty in inferring emissions using dispersion models.
Our application of dispersion models to infer emission rates of methane differs from others in several ways. The first is that the Eulerian model is a numerical solution of the mass conservation equation to model the vertical distribution of concentrations; the eddy diffusivity is specified using Monin-Obukhov similarity theory. Nieuwstadt and van Ulden (1978) show that the solution agrees remarkably well with observations at the surface as well as of the vertical distribution of concentrations measured during the Prairie Grass experiment (Barad, 1958). Thus, we do not have to resort to the often-used Gaussian distribution, which is a useful approximation only under very stable conditions. The numerical solution also avoids specifying the height at which the plume is transported, which is usually chosen arbitrarily or needs to be computed from an implicit equation (van Ulden, 1978). We refer to this model as the Eulerian numerical (EN) model in this paper.
Lagrangian particle methods offer similar advantages and have been used by several investigators (Todd et al., 2011; Ro et al., 2013; Grant et al., 2013; Baldé et al., 2016; Leytem et al., 2017). The model used in this study is that formulated by Flesch et al. (2005) and converted into a free software called WindTrax (http://www.thunderbeachscientific.com/). This model, which computes emissions by tracking particles from the receptor to the source in a turbulent flow field, belongs to a class of models referred to as backward Lagrangian Stochastic (bLS) models. Details of the model can be found in the cited paper.
The second way that this study differs from previous studies is the strategy used to sample atmospheric methane concentrations, which allows us to provide indirect estimates of the uncertainty in the inferred emissions associated with the uncertainty in the model physics. Our approach is to station the measurement platform at several locations around the lagoons to make time averaged measurements of methane accompanied by simultaneous measurements of micrometeorology. These measurements are then fitted to estimates from dispersion models that use the corresponding micrometeorological inputs to yield the unknown emission estimates. We then show how the residuals between model estimates and corresponding measurements can be used to estimate the 95% confidence intervals of the inferred emission rates.
Section snippets
Methodology
Measurements were made near the manure lagoons in two dairies using a mobile platform that circulated around the lagoon complex and a stationary meteorological tower. Atmospheric methane (CH4) mixing ratios were collected with a cavity ring-down spectrometer (Picarro 2210-i) in the mobile platform, a Mercedes Sprinter van. An inlet was located at the front of the vehicle's roof 2.87 m above ground level through which the outside air was pumped and sampled approximately every second by the
Dispersion models
In the model, the manure lagoon is represented as a set of area sources. In the EN model, the contribution of each area source to the concentration at a receptor is an integral over a set of line sources perpendicular to the wind direction. The contribution of each line source is the analytical solution for the concentration distribution resulting from a finite length line source if the horizontal distribution is taken to be Gaussian (Venkatram and Horst, 2006). The number of line sources,
Results
We evaluate the performance of the models in this study using the following statistics: the coefficient of determination (R2) between model estimates and corresponding measurements, the percentage of predicted concentrations within a factor of 2 of the observed concentration (fact2), the geometric mean (mg) and the geometric standard deviation (sg) of the residuals between model estimates and observations. The mg and sg are computed using the following equations,
Discussion
We used two state-of-the-art dispersion models, an Eulerian Numerical (EN) model and a backward Lagrangian Stochastic (bLS) model to infer methane emissions from manure lagoons located in dairies in Southern and Central California. The emissions are obtained by fitting model estimates to corresponding methane concentrations measured at several receptors surrounding the lagoons. The 95% confidence intervals for these emission estimates were computed by bootstrapping the residuals between model
Conclusions
A widely used method to estimate emissions from area sources, such as manure lagoons, is based on using a dispersion model, such as WindTrax, to relate emissions to concentration measurements made in the vicinity of the source. The uncertainty associated with such emission estimates depends on uncertainties in 1) the formulation of the dispersion model used to infer emissions, 2) model inputs that include micrometeorology, physical characteristics of the source, and locations of concentration
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The research described in this paper is supported by the UC Lab Fees Research Program, contract number LFR-18-548581. Work at LBNL was conducted under U.S. Department of Energy contract DE-AC02-05CH. We gratefully acknowledge the participation of the two dairies studied for site access. We also thank Dr. Deanne Meyer, UC Davis, for helping with site access and providing information that helped in computing the bottom-up values of methane emissions.
References (29)
- et al.
Short-term methane emissions from 2 dairy farms in California estimated by different measurement techniques and US Environmental Protection Agency inventory methodology: a case study
J. Dairy Sci.
(2018) - et al.
Measured versus modeled methane emissions from separated liquid dairy manure show large model underestimates
Agric. Ecosyst. Environ.
(2016) Re-examination of empirically derived formulas for horizontal diffusion from surface sources
Atmos. Environ.
(1994)- et al.
Estimating gas emissions from a farm with an inverse-dispersion technique
Atmos. Environ.
(2005) - et al.
Comparison of a backward-Lagrangian stochastic and vertical radial plume mapping methods for estimating animal waste lagoon emissions
Agric. For. Meteorol.
(2013) - et al.
Methane emissions from dairy lagoons in the western United States
J. Dairy Sci.
(2017) Developments in micrometeorological methods for methane measurements
Animal
(2013)- et al.
Measuring gas emissions from animal waste lagoons with an inverse-dispersion technique
Atmos. Environ.
(2013) - et al.
Methane emissions from southern High Plains dairy wastewater lagoons in the summer
Anim. Feed Sci. Technol.
(2011) Simple estimates for vertical diffusion from sources near the ground
Atmos. Environ.
(1978)
Re-formulation of plume spread for near-surface dispersion
Atmos. Environ.
Project Prairie Grass: a field program in diffusion vol II
Geophys. Res. Pap.
Comparison of AERMOD and WindTrax dispersion models in determining PM10 emission rates from a beef cattle feedlot
J. Air Waste Manag. Assoc.
Flux-Profile Relationships in the Atmospheric Surface Layer
J. Atmos. Sci.
Cited by (12)
Methane emissions from animal agriculture: Micrometeorological solutions for challenging measurement situations
2024, Agricultural and Forest MeteorologyCharacterizing NH<inf>3</inf> emissions from a sheep feedlot and a manure composting facility in North China with the inverse dispersion technique
2023, Agricultural and Forest MeteorologyEstimating inputs for dispersion modeling in mobile platform applications
2023, Science of the Total EnvironmentSensing atmospheric flows in aquatic environments using a multirotor small uncrewed aircraft system (sUAS)
2023, Environmental Science: AtmospheresAccounting for Area Sources in Air Pollution Models
2023, International Journal of Environmental Research and Public Health