Elliptic Cylinder Airborne Sampling and Geostatistical Mass Balance

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Elliptic cylinder airborne sampling and geostatistical mass balance approach for quantifying local greenhouse gas emissions Jovan M. Tadi#, Anna M Michalak, Laura T. Iraci, Velibor Ilic, Sébastien C. Biraud, Daniel R Feldman, Thaopaul V Bui, Matthew S. Johnson, Max Loewenstein, Seongeun Jeong, Marc L. Fischer, Emma L. Yates, and Ju-Mee Ryoo Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b03100 • Publication Date (Web): 20 Jul 2017 Downloaded from http://pubs.acs.org on August 6, 2017

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Environmental Science & Technology

ACS Paragon Plus Environment


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Elliptic cylinder airborne sampling and geostatistical mass balance approach

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for quantifying local greenhouse gas emissions

Jovan M. Tadić1,*,†, Anna M. Michalak1, Laura Iraci2, Velibor Ilić3, Sébastien C. Biraud4 Daniel R. Feldman4, Thaopaul Bui2, Matthew S. Johnson2, Max Loewenstein2, Seongeun Jeong5, Marc L. Fischer5, Emma L. Yates2 and Ju-Mee Ryoo2

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1

Department of Global Ecology, Carnegie Institution for Science, Stanford CA 94305 USA

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2

Earth Science Division, NASA Ames Research Center, Moffett Field CA, USA

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3

RT-RK Institute for Computer Based Systems, 21000 Novi Sad, Serbia

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4

Earth and Environmental Sciences Area, Lawrence Berkeley National Lab, Berkeley CA 94720 USA

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5

Energy Technologies Area, Lawrence Berkeley National Lab, Berkeley CA 94720, USA

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† Now at Earth and Environmental Sciences Area, Lawrence Berkeley National Lab, Berkeley CA 94720 USA * Corresponding author at: Department of Climate Sciences, Lawrence Berkeley National Laboratory,

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Berkeley CA 94720.

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E-mail address: [email protected] (J. M. Tadić).

1 ACS Paragon Plus Environment

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Graphical abstract:

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Abstract: In this study, we explore observational, experimental, methodological and practical aspects

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of the flux quantification of greenhouse gases from local point sources by using in-situ airborne

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observations, and suggest a series of conceptual changes to improve flux estimates. We address the major

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sources of uncertainty reported in previous studies by modifying (1) the shape of the typical flight path,

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(2) the modeling of covariance and anisotropy, and (3) the type of interpolation tools used. We show that

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a cylindrical flight profile offers considerable advantages compared to traditional profiles collected as

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curtains, although this new approach brings with it the need for a more comprehensive subsequent

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analysis. The proposed flight pattern design does not require prior knowledge of wind direction and

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allows for the derivation of an ad hoc empirical correction factor to partially alleviate errors resulting

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from interpolation and measurement inaccuracies. The modified approach is applied to a use-case for

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quantifying CH4 emission from an oil field south of San Ardo, CA, and compared to a bottom-up CH4

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emission estimate.



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Keywords: Local sources, Urban domes, Anthropogenic emissions, Greenhouse gases, In-situ measurements, Anisotropy, Kriging * Corresponding author at: Department of Climate Sciences, Lawrence Berkeley National Laboratory, Berkeley CA 94720.

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E-mail address: [email protected] (J. M. Tadić).

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1. Introduction

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Atmospheric measurements at local scales can be used to provide a top-down constraint on emissions

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as well as to validate and improve bottom-up emission inventories. Local scale measurements can target

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various local sources, ranging from the anthropogenic (urban centers, industrial activities, agriculture,

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traffic, landfills) to the natural (volcanoes, wild fires, marshlands). The lack of a standardized verification

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protocol for measuring GHG fluxes from point sources has led to uncertainty in quantifying, and by

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extension, mitigating these point sources. This situation is particularly problematic because urban

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populations are expected to double by 2050(1) and will significantly influence GHG emissions, but

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mechanisms to characterize these emissions are lacking.

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Quantitative measurement, reporting, and verification (MRV) will be critical to any international

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climate treaty, as emphasized by a 2010 National Research Council (NRC) report,2 and by the

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Intergovernmental Panel on Climate Change.3 Verification based on direct observations of atmospheric

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GHG concentrations could provide estimates of emission reductions.4

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To fill this need, the quantification of GHG emissions at high spatial resolutions has become an area

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of active research. The highly heterogeneous nature of anthropogenic emissions does not lend itself well

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to the application of inverse modeling tools developed primarily for regional/continental scale estimation

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of biospheric fluxes.5 Several recent studies have examined the feasibility of constraining greenhouse gas

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emissions at local scales using ground-based,4,6 airborne,7-11 and space-based12 observations. Airborne

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observations, in particular, offer an opportunity to capture GHG concentrations in the air entering and


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exiting a focus area. Flux studies using airborne measurements have also been conducted at local scales

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from sources such as forest fires,13 volcanoes,14 leaks from natural gas and oil operations

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accidents,15 emissions from dairy farms,17,18 and landfills.18

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and related

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Early applications of airborne observations for quantifying local and urban emissions have exposed

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the high uncertainties associated with baseline mass balance approaches at spatial scales of 10s to 100s of

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km. For example, a study in Indianapolis7 reported uncertainties of 80% (19.2 ± 15.4 µmol/m2s) for CO2

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emissions, and 71% (0.14 ± 0.10 µmol/m2s) (±1σ) for CH4. The flux quantification method used in that

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study relied on airborne observations along a single downwind “curtain” in combination with a kriging

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scheme, presuming direction-independent (constant) variability and mass balance. In more recent studies,

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uncertainty estimates were reduced to ~43% (±1σ) for CH4 emissions from Indianapolis,19 ~30% (±1σ)

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for CH4 and SO2 emissions from Alberta oil sands operations,11 and ~29% (95% confidence interval (CI))

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for CH4 emissions from the Barnett Shale basin.20 The uncertainty reduction is achieved through more

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sophisticated quantification protocols: (a) introduction of a second, up-wind curtain8,10,11 that captures

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both the upwind and downwind concentration profiles, and (b) the reduction of measurement time by

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using a second aircraft flying dense horizontal transects to reduce interpolation errors.

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More recent work using aircraft to measure GHG emissions at small (~ 1 km) spatial scales has

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claimed that methane emissions from an individual facility can be measured to better than 20% by

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combining in-situ measurements of winds and GHG concentration measurements using mass-flux

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integration over controlled flight patterns covering the vertical extent of plumes downwind of individual

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facilities15.

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The factors contributing to uncertainties in the quantification of fluxes from localized or point sources

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using airborne measurements are listed and analyzed in Cambaliza et al. (2014).9 The factors for these

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large uncertainties generally fall into four categories: (1) observational, related to the ability of the flight

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plan or sampling scheme to capture urban emissions and background concentrations, the requirement for

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many horizontal transects to get reasonable coverage, and the necessity to know wind direction in

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advance for flight path planning; (2) experimental, related to the availability of reliable, accurate, and



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high frequency airborne sensors for all measured quantities, including wind speeds and GHG

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concentrations; (3) practical, involving air traffic control problems encountered around urban centers; and

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(4) methodological, pertaining to the availability of post-processing/modeling tools that accurately and

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precisely translate the observed spatiotemporal GHG concentration patterns into GHG fluxes and their

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associated uncertainties and the failure to exploit existing and observed spatial concentration trends

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(especially characterizing the concentration field below the aircraft profile).

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In this study, we focus on the major observational, experimental and methodological factors limiting

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the precision of GHG flux estimation at local/facility scales. We explore if and how modifying sampling

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protocols might be expected to reduce uncertainty for these facility-scale flux estimates and perhaps

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larger spatial scales if large-scale entrainment and convection can be estimated. Our suggested

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modifications include (1) changes in flight patterns, (2) interpolation techniques and associated modeling

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of spatial variability, (3) reduction in sampling time, and (4) a revised the approach to mass balance. For

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the first modification, we use a flight pattern design that maximizes capture of inflow and outflow, and

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eliminates the need for prior knowledge of the predominant wind direction (Section 2.1). For the second

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modification, we develop a geostatistical approach that accounts for anisotropy (zonal or directionally

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dependent variability) and variable spatial means of atmospheric GHGs (Section 2.2.2, 2.2.3 and

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Supporting information). For the third modification, we use winds measured by the aircraft simultaneous

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to the GHG concentration measurements. For the final modification, we use a mass balance approach not

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only to quantify the flux of the atmospheric constituent of interest, but also to derive an empirical

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correction factor to account for dynamic effects of mass convergence within the domain of field

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measurements. (Section 2.2.4).

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These tools and approaches apply broadly to a range of local/urban domains and choices of single or

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multiple airborne platforms, including aircraft and unmanned aerial systems (UAS) and can reduce

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uncertainty in mass balance characterization across spatial domains of tens of km.

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2. Methodology and materials

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2.1 Aircraft and instruments

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We developed and tested the cylindrical sampling and geostatistical mass balance approach by

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collecting and analyzing data from a flight covering a 4×9 km area surrounding an oil field about 8 km

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south of San Ardo, CA (35º57’ N, 120º52’ W), on 10/01/2015. This area includes the eighth largest oil-

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producing field in California with 7.8 million barrels of oil, and ~1 million Mcf of natural gas produced in

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2015.21 The flight took place at around 20:30 UTC (local time 12:30 PM), a time when the planetary

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boundary layer (PBL) has not yet reached its peak. Due to quick sampling (10–15 minutes), it is

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reasonable to assume that the PBL top remains at a stable height during the aircraft sampling period.

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Measurements were collected using an aircraft (Alpha Jet) based at the National Aeronautics and

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Space Administration (NASA) Ames Research Center, equipped with a Picarro 2301-m cavity ring-down

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instrument for CO2, CH4 and H2O measurements, GPS and inertial navigation systems that provide

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latitude, longitude and altitude, and a Meteorological Measurement System (MMS), which measures both

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dynamic and static state variables. MMS, a NASA Ames-developed airborne instrument package,

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provides calibrated, science-quality, in situ measurements of static pressure, static temperature, wind in

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three dimensions, GPS positions, velocities, accelerations, pitch, roll, yaw, heading, angle of attack, angle

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of sideslip, dynamic total pressure, and total temperature. The primary products of MMS are barometric

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pressure (precision of 0.1 hPa with an accuracy of ± 0.3 hPa), air temperature (0.1°K, ± 0.3°K), horizontal

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wind

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(https://airbornescience.nasa.gov/instrument/MMS). Other derived parameters are potential temperature,

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true air speed, turbulence dissipation rate, and Reynolds number. This instrument has been installed in

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several NASA aircraft in addition to the Alpha Jet, including the ER-2, the DC-8, and the Global Hawk

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unmanned aircraft, the WB-57F, and is flexible in terms of flight pattern (i.e., not limited to straight or

(0.1

ms-1,

±

1

ms-1),

and

vertical

wind


(0.1

ms-1,

±

0.3

ms-1)


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level flights only). Further details of the aircraft and instruments can be found in previous publications22-

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.

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2.2 Theory

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2.2.1 Optimization of the projection grid

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Cylinder-shaped profiles offer a substantial advantage over the “curtain” type flight profile, because

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they can necessarily adapt to any wind direction. In other approaches, the wind direction needs to be

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determined either ahead of the flight or at the start of the sampling phase, whereas in this approach this

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constraint is relaxed. However, this approach requires a more sophisticated subsequent analysis for

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calculating fluxes (Section 2.2.4).

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Before the fitting, interpolations and flux calculation, all spatially referenced data are converted to a

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Universal Transverse Mercator (UTM) (Euclidean) coordinate system, so that distances and angles can be

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computed using Euclidean geometry over short distances.25 The GPS instrument records raw data in

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latitude/longitude/altitude format based on WGS84 spheroid earth model26. The additional uncertainty in

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the position of the aircraft introduced by the spatial distortions in conversion to UTM system is < 1mm

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and is therefore negligible compared to the 3–4 m horizontal uncertainty in position reported by the GPS

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instrument.

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An optimal 3D elliptical grid is fitted to the flight trajectory following a three-step approach. First, we

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fit the optimal ellipse into a vertically projected set of coordinates representing the flight trajectory. Next

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we place an arbitrary number of equidistant points (300 in this case) along the perimeter of the ellipse

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optimized in the first step. In general, the optimal number of points depends on the observed spatial

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variability of all relevant variables. The potential dependence of the results on details of optimal grid

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construction and projection can be considered heuristically. The third step is the extension of the

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discretized elliptical profile obtained in the second step and involves matching the ceiling of the flight

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trajectory (every 50 m up to ~2550 m).


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Only nodes of the grid that reside above the ground level are contained in the final projection grid,

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and

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(https://developers.google.com/maps/documentation/elevation/intro) is used to eliminate underground

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points on the grid. The result is an optimal 3D projection grid used for interpolation, projection, and flux

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calculation.

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customized

software

built

on

Google

Maps

elevation

data

2.2.2 Original product-sum model and proposed modifications

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In this study we develop an alternative kriging approach for modeling an anisotropic environment, using a

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product-sum covariance model.27-29

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This product-sum was initially developed for different purposes - to model spatio-temporal covariance

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structures in which a common unit of the distance between points does not exist because of the different

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natures of spatial and temporal axes. We observe that there is an analogy between problems of modeling

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spatio-temporal covariance and covariance in anisotropic conditions. In modeling spatio-temporal

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variability, it is necessary to deal with two qualitatively different spatiotemporal subspaces. Formally, the

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variability in these spatiotemporal subspaces could require different theoretical variogram models, and

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requires different units of distance.30 In anisotropy, we face an analogous situation, with potentially

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different types of variability in different directions. Therefore, the product-sum model is applicable to

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anisotropic conditions, and, as we show in this study, equivalent to the classical model of zonal

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anisotropy in the case where horizontal and vertical directions represent principal anisotropic axes (i.e.,

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when anisotropy splits the space into two subspaces). We show that there is a partial mathematical

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equivalency between these two models, in the sense that every admissible set of sill parameters in the

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classical model (3 sill parameters, 7 parameters in total) can be expressed as an admissible set of sill

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parameters (3 sill parameters, 6 parameters in total) in the product-sum model. The sill is the expected

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value of the semi-variance between two observations as the lag distance tends to infinity30.

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There is one important area for improvement in the manner that the product-sum model has been applied

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in the past. The original procedure27 assumed separate modeling of the spatial and temporal covariance



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(variograms) and their later unification into a spatio-temporal model in the final step. In our study, this is

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equivalent to separating modeling the vertical and horizontal covariance, if we assume temporal

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stationarity of the wind and concentration fields (this assumption could be problematic in that there is a

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risk of using the same air parcel as it advects to a different location, which, when combined with the

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potential that the field is actually non-stationary in composition, could lead to artifacts in the analysis).

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The procedure requires observations approximately in the same horizontal location at multiple different

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altitudes. However, aircraft trajectories are often not perfectly horizontally collocated at different

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altitudes. As a result, we would need to define a tolerance in order to apply the original approach, which

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is also a part of the genuine modeling approach suggested in De Iaco et al., 2001.27 To avoid defining a

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tolerance, in this study we cater to specific properties of aircraft trajectories and alter the original

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procedure by estimating all covariance parameters simultaneously.

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We broadly define the covariance as follows: , ℎ , ℎ = COV + ℎ , + ℎ , ,

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(1)

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The equation shows that covariance (Ch,v) between two points (Z) depends on their distance in horizontal

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direction (hh) and distance in vertical direction (hv). lh and lv denote arbitrary horizontal and vertical

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coordinate within the domain. The product–sum covariance model is given as: , ℎ , ℎ = ℎ ℎ + ℎ + ℎ

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(2)

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where Cv and Ch are valid vertical and horizontal covariance models, respectively27,29. This model

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corresponds to the horizontal-vertical variogram: , ℎℎ , ℎ = , ℎ , 0 + , 0, ℎ − , ℎ , 0, 0, ℎ

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(3)

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where γh,v(hh,0) and γh,v(0, hv) are spatio-temporal variograms for hv=0 and hh=0, respectively (see Figure

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1 (red lines)). In the original procedure, separately estimated horizontal (“spatial”) and vertical


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(“temporal”) variogram components are subsequently combined into a horizontal-vertical variogram

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model, equivalent to spatio-temporal variogram in the genuine embodiment of the approach.

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Parameter k is estimated from the data: =

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, ,

(4)

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where 0 and 0 are horizontal and vertical sills (variances) obtained in modeling of separate

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horizontal and vertical variograms. The only condition k has to fulfill in order to create an admissible

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covariance model is 0

Elliptic Cylinder Airborne Sampling and Geostatistical Mass Balance

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