The case study presented here is based on measurements performed by a team from the Netherlands Organisation for Applied Scientific Research (TNO) during the ROMEO campaign in Romania. The measurements were taken in Parhova County at oil well 1474 in Dărmănești. The county is located in the region between the Transylvanian Alps and Bucharest, which is characterized by plains in the south and the Carpathian mountains in the north. The actual site is located in the central part of the county, where the two distinct landscapes meet. The measurements were performed on the road downwind from an oil well over the course of 3 h. The length of the road segment on which the plume was measured was 150 m, while the distance from the middle of road to the well was 78 m. The measured well and the adjacent road on which measurements were performed is shown in Fig. b, and the vehicle used to perform the measurements is shown in Fig. a.

The measurements were performed in the afternoon (14:30–17:30 LT (UTC+3 h)) on 17 October 2019. The weather at the location was characterized by very low speed winds and no cloud cover, as confirmed by the participants of the campaign. To analyze the overall synoptic situation over Europe and Romania in particular, we used the geopotential height and temperature chart obtained from ERA5 . The weather over Romania was characterized by very low gradients in both temperature and pressure (Fig. a), resulting in low wind speeds and advection during the campaign. Hence, we expect that the conditions were strongly influenced by local convection.

Fig.  shows the surface net solar radiation and the sensible and latent heat fluxes in the region (panels b and c, respectively) retrieved from the ERA5 data. The surface heat fluxes are comparable, indicating dry conditions (Fig. b), and the solar radiation indicates no clouds were present. Furthermore, it was inferred from the ERA5 data that the temperature maximum at the surface was 22 ∘C and that the boundary layer (BL) depth reached 700 m at 12:00 UTC (not shown). The ERA5 height wind profiles show wind turning with height. Maxima in wind speeds in opposite direction from those at the ground were seen at approximately 1000 m height or just above the BL top. For the duration of the measurements, the mean horizontal wind at the surface showed variation of 10∘ (not shown).

As will be presented later in Fig. , we find that, for the duration of the measurements, the temperature at the 1000 hPa level remained almost constant and showed an almost linear decrease with height. Similarly, the specific humidity showed peak values at the surface and constant values in the mixing layer above it. Above the BL, specific humidity decreased with height. The near-constant-in-time height profiles of specific humidity and temperature confirm that the contribution of large-scale advection was negligible during the campaign. As a result, the time evolution of temperature and humidity was determined by local processes. This leads to a complex pattern in vertical baroclinicity, which is a challenge for both collecting experimental data and simulation studies.

The measurement device used was a dual-laser trace gas monitor based on tunable infrared laser direct absorption spectroscopy (TILDAS; Aerodyne Research Inc., Billerica, USA) that measures methane and ethane (CH4 and C2H6) simultaneously. The ethane data are used to discriminate methane plumes originating from fossil-fuel-related sources (which contain ethane) and agricultural or biomass degradation methane emissions. The instrument also measures H2O, CO2, CO and N2O. The molar fractions of these components are measured at sub-ppb resolution with one measurement per second (1 Hz). Molar fractions were calibrated versus working standards for CH4 (B20 flasks with compressed air at 2800 and 5000 ppb) that are linked to the Integrated Carbon Observation System (ICOS) and the National Oceanic and Atmospheric Administration (NOAA) standards used at the Cabauw tall tower in the Netherlands. B20 flasks are 20 L cylinders that hold 2000 L of gas at the pressure of 100 bar. Besides that, during the Romania campaign, calibration cylinders from Utrecht University were used, with molar fractions of 6.3, 27 and 130 ppm for the higher molar fraction measurements. The instrument measured CH4, C2H6, N2O, CO2 and CO simultaneously at 1 Hz with a precision of 2.4, 0.1, 386.3 and 2. ppb, respectively. Here, precision is reported as 3 times the standard deviation of 6 min constant molar fraction readings. The instrument was placed into a vehicle that drove along the closest road and its position was logged at 1 Hz with a GPS system. The inlet of the measurement device was placed at the top of the vehicle at a height of 3 m. A delay-time correction is applied to the data to compensate for the 1.5 s delay between the logged GPS location and actual measurement in the TILDAS instrument.

A controlled release of tracer gas N2O was conducted simultaneously with the CH4 measurements. N2O was released using a critical orifice of 0.65 mm2 at 5 bar. Before and after the release, the mass of the cylinder was determined. Release was 0.59 ± 0.02 g s-1

The wind speeds (u, v, w) were measured from a battery-operated Gill R3 sonic anemometer placed close to the source and at 1.8 m above ground level. The sonic data were stored at 20 Hz, and 1 Hz values were transmitted with a wireless link to the central computer in the van. For this analysis, 1 min averages of wind speeds were used.

Due to the varied road conditions, the vehicle speed varied from transect to transect. Therefore, the measured plumes have a different number of measured points, and the exact distribution of these points over the measurement transect differs. To obtain a uniform dataset, two end points were selected that encompass all plumes. Values of the vehicle location, CH4 and N2O data were linearly interpolated on a 250 point grid.

The LES was performed in a three-dimensional domain of 4.8 × 4.8 × 3.085 km (x, y and z directions, respectively). The domain was discretized on a 960 × 960 × 480 (x, y, z) grid. This results in uniform horizontal resolution of 5 m, while the vertical direction is resolved on a stretched grid with 2 m resolution in the first 1 km of the domain and 50 m at the top. The resolution was chosen with computational feasibility in mind such that the grid was dense enough for the dispersion to be well represented but still have the domain large enough to capture the meteorological effects relevant for this study.

A constant source of passive scalar was added as a two-dimensional Gaussian placed on the bottom of the domain. The Gaussian had the 1σi (i=x, y) value equal to the size of one grid box; therefore, 97 % of the source was spread on the 20 × 20 m2 grid. It has been shown in laboratory studies of plume dispersion that the ratio of the source size and the size of larger-scale eddies has a significant impact on plume statistics . To circumvent this issue, the size of the source should be larger than the size of one grid box. Recently, investigated the influence of resolution on the flow and plume statistics in LES. They have shown that the scalar variances converge for the sources resolved by at least 43 grid nodes. We have placed the source in the top right corner of the domain at the position (3600, 3600) m, where the domain origin is defined at the lower left corner. The scalar was emitted with a constant flux of 1 g s-1.

In order to reproduce meteorological conditions encountered on the measurement day, the simulation was nudged according to height profiles of horizontal wind speed, temperature and specific humidity obtained from the ERA5 data. Large-scale forcing was imposed through geostrophic wind with the Coriolis parameter for this latitude being fC=1.0305×10-4 s-1. Furthermore, roughness lengths of z0h=0.001 m and z0m=0.05 m were imposed on the lower boundary for scalar and momentum, respectively.

The simulation was run for 7.5 h in total. A spin-up time was imposed to have the boundary layer fully developed and resembling field conditions as closely as possible. First, the fields from ERA5 were initiated at 07:00 UTC, and the simulation was started with an integration time step of 6 s. The simulation was run for 7.5 h with vertical profiles being nudged towards ERA5 profiles every hour. At 11:00 UTC, the source was activated in the simulation. The instantaneous plume concentrations c; wind components u, v, and w; and liquid potential temperature θl were recorded on various two-dimensional cross-sections of the domain.

The mean wind in this simulation shows fluctuating behavior, which influences the direction of the plume dispersion. Here, we assume that the local wind that influenced the dispersion was governed by local influences that are not captured in ERA5. To be able to still compare the plume at different simulation times, the mean wind speed between observations and simulation should be aligned. Therefore, we performed another simulation in which the mean wind was directed along the x axis, while keeping all the other specifics, apart from the source location, identical. These two simulations will be further on referred to as realistic and idealized for the first and second simulations, respectively. The overview of the specifics of the two simulations is given in Table . Note that in the idealized simulation the nudging profiles for potential temperature and specific humidity still originate from the ERA5 dataset. For the wind, however, we set the height profile of the v component in the nudging profiles to zero and set the u profile to a constant value of 3 m s-1. This wind speed was chosen through manual tuning to get a good match with the measured wind speed at 2 m height. In this way the wind direction was kept constant without loosing the general characteristics of the realistically simulated boundary layer.

Source quantification from one-dimensional transect measurements is often performed using a mass balance approach. This method compares the total line-integrated flux of the time-averaged plume from an unknown source with the flux from a known source under the same atmospheric conditions and at the same downwind distance from the source. This method has been used in conjunction with either a tracer release or – if no tracer is co-emitted – with simple plume transport models such as the Gaussian plume model (e.g., ). The equation used for this approach reads as follows: 1Qestim=∑yCmeasumeas‾∑yCrefuref‾×Qref.

Here the Qestim is the emission rate of the unknown source (in g s-1); C (g kg-1) and u‾ (m s-1) denote the time-averaged measurements and the mean wind speed, respectively. Subscripts “ref” and “meas” refer to the reference tracer with known source Qref and measured tracer, respectively. Note that the reference plume can be either measured or inferred from a model.

Finally, we present a short overview of the statistical moments calculated for the simulated plumes that will be discussed in Sect. –. Higher-order statistics can provide further insight into the behavior of the measured plume but are often unattainable from the measurements due to insufficient spatial and temporal resolution. Figure  shows a scheme of an idealized plume emitted from a ground point-source. Let z be the vertical position of a particle in an instantaneous plume at a distance x from the source. This plume is characterized by its centerline position zm defined as its center of mass: 2zm(x,t)=∫c(x,y,z,t)zdzdy∫c(x,y,z,t)dzdy.

An ensemble of such instantaneous plumes will have its own centerline position zm‾ defined as the mean over all the realizations. Now the fluctuations of the instantaneous plume around these mean positions can be defined. The absolute fluctuation z′ is the displacement of the particle in the plume from the mean centerline position zm‾, relative fluctuation zr′ is the displacement from the instantaneous plume centerline zm and the fluctuation of the instantaneous plume centerline zm′ is the displacement from the mean position zm‾. These can be written as 3z′=z-zm‾,zr′=z-zm,zm′=zm-zm‾.

The mean plume positions and the displacements in the y direction can be defined in a similar manner.

Following the definition of , the absolute plume dispersion (or the second-order moment) in the vertical direction is written as 4σza2(x,t)=∫c(x,y,z,t)z′2dydz∫c(x,y,z,t)dydz.

The absolute plume dispersion can be decomposed into its meandering and relative contributions: dispersion due to movement of the plume centerline (or meandering) and diffusion of particles from the plume centerline. Therefore, it holds that 5σza2=σzm2+σzr2,

where 6σzm2(x,t)=∫c(x,y,z,t)zm′2dydz∫c(x,y,z,t)dydz,σzr2(x,t)=∫c(x,y,z,t)zr′2dydz∫c(x,y,z,t)dydz.

The third-order moment is therefore 7za‾3(x,t)=∫c(x,y,z,t)z′3dydz∫c(x,y,z,t)dydz,zr‾3(x,t)=∫c(x,y,z,t)zr′3dydz∫c(x,y,z,t)dydz,zm‾3(x,t)=∫c(x,y,z,t)zm′3dydz∫c(x,y,z,t)dydz. Similar expressions hold for moments in the y direction. Lastly, we define skewness here as Si=i3‾σi3, where i=(y,z).

Figure  shows multiple instantaneous x–y cross-sections of the simulated plume from the realistic simulation. The cross-sections have been taken at 3 m above the ground, i.e., the inlet height on the vehicle used during the campaign (Fig. a). It can be seen that the variation of the plume direction is pronounced throughout the simulation. This behavior is caused by very low mean wind speeds that change direction frequently in the simulated turbulent flow field. As was demonstrated in Sect. , the large-scale wind and temperature fields showed no pronounced gradients above the area on the simulated day. Therefore, local effects likely governed the flow that was measured at the site. Since ERA5 does not resolve these local effects, the discrepancies between modeled and measured wind are to be expected. To correct for this, the idealized simulation was set up.

Simulated and nudging profiles for the idealized run are compared in Fig. . Note that we replaced the ERA5 wind profiles. The simulated profiles were obtained as spatial averages over the whole domain that were time averaged over 1 h. Throughout the run, θl and qt show very good agreement with the ERA5 profiles. The profiles show hardly any variability over time and are constant with height in the lower ≈ 700 m. This indicates that the spin-up time of the run was sufficiently long for the development of a well-mixed boundary layer. The u wind profile in the idealized run shows virtually no variation. A well-mixed layer above the surface is clearly visible, with stronger and constant winds above 700 m, which correspond to the nudging profiles, and a logarithmic decline towards the surface. The simulated v profiles agree with the imposed zero nudging profiles.

Figure a shows the measured CH4 and N2O plumes. The plumes in the figure are shown with the background subtracted. Background subtraction follows the procedure described in . To help with the interpretation of the plumes, N2O was released from a cylinder 20 cm above the well head with a constant rate of (0.59 ± 0.02) g s-1 for the duration of the measurements.

The measured horizontal wind speed (Fig. b) was low during the whole day, varying from 0.8 to 2.8 m s-1 (1 min averages) during the measurements. A weak periodicity of approximately 55 min can be noticed in the wind speed data. It is possible that it is caused by influences from the local orography, since the area is in the vicinity of hills. The closest elevated area is about 5 km away towards the west (W), and higher mountains are located approximately 10 km towards the N and NW. It was shown in the work of that the mountains can have a considerable effect on atmospheric variability on scales of 4 to 80 km. To verify the possible influence of the mountains in this case, however, the wind data measurements should be considerably longer. The observed periodicity is not present in the simulated wind (Fig. b). This is caused by the imposed flat orography in the domain and the constant wind forcing through the nudging on the lateral boundaries. If the surrounding hills would be included in the simulation, fluctuations in the wind direction would likely be simulated. However, the high-resolution domain would have to be expanded far beyond the measurement site. With the current computing resources, this endeavor is unfeasible. In our restricted domain, the simulated and measured wind speeds show good agreement. This is also visible in the 1 min averages of the instantaneous wind direction (Fig. c). Since the mean wind direction in the idealized simulation was set to be easterly, the wind was rotated to match the mean wind direction from the observations. It can be seen that the wind angle in the idealized simulation fluctuates comparable to the observations. The standard deviation in wind direction was σWD,obs=16.9∘ for the measured wind and σWD,LES=18.6∘ for the simulation.

Time-averaged plumes from the measurements are given in Fig. . The measured plumes were averaged over half-hour increments, and they are shown here together with the mean wind speed and direction for the corresponding time period. The mean horizontal wind direction did not change significantly during the measurement period, except for the first half hour, which deviates by ≈ 40∘. The mean wind speed for the whole period was low and did not exceed 2.4 m s-1. Since the measurements were collected on a public road, the number of averaged plumes varies from one half-hourly period to another. The number of plumes per half-hourly time period amounts to n=[3,6,8,4,9,10] starting from 11:30 until 14:30 UTC.

On the right-hand panel of Fig. , the corresponding time-averaged simulated plumes are shown. Transects through the plume were sampled according to the observations: at 3 m height and 80 m downwind from the source. Plume transects were taken every 1 min, resulting in 150 transects for the entire simulation. After 14:00 UTC the surface flux of sensible heat turns negative, and that is when the simulation stops. For that reason, the set of time-averaged plumes from LES contains one less element than the measurement set. The half-hour averages of the simulated plumes are smoother compared to the corresponding measured plume averages. This follows from comparing the average skewness of the mean plumes defined as S=1xmax‾N(∑i=1N(xi-x‾)3)1/3, where x is the half-hour average from either measurement or simulation, x‾ is the mean value of that half-hour average, N in the number of averages and xmax‾ is a maximum value of the total mean plume (red line in Fig. ). As a result, the LES, CH4 and N2O measurements have an average skewness of SLES=0.32, SCH4=0.44 and SN2O=0.42. The smoother averages in the LES are likely caused by the fact that the number of plumes averaged per half-hour increment is much lower in the measurements compared to the simulation.

The angle over which the wind direction varies during the simulated period amounts to 18∘, with the exception of the last half-hourly period, in which the wind direction deviated from the mean by ≈ 50∘.

We used Eq. () to infer the unknown CH4 emission rate from the oil well using the LES plume as the reference. To this end, we compare the time-averaged measured CH4 plume from the oil well (red line in Fig. b), combined with the measured mean horizontal wind speed (umeas‾=1.93 m s-1), to the corresponding flux of the time-averaged LES plume (red line in Fig. c), combined with the simulated wind speed (uref‾=1.72 m s-1). This leads to the estimated emission rate of Qestim,CH4= (1.11 ± 0.34) g s-1. Using the same principle, we estimate an N2O emission rate of Qestim,N2O= (0.53 ± 0.15) g s-1 (true emission strength was QN2O= (0.59 ± 0.02) g s-1). To benchmark the performance of LES in this experiment, we also estimate the unknown CH4 source using the N2O gas as reference, and we obtain an emission rate of Qestim,CH4= (1.23 ± 0.12) g s-1. Note here that the standard deviations have been calculated using the source strength estimation from the half-hour averages. The discrepancies between both methods can have various reasons. Firstly, even though the mean wind in the LES is very close to the measured mean wind, their magnitudes and variations are not identical, which can also contribute to the error. However, the most notable cause for the estimation error might arise from the averaging time of the measurements, which is likely too short. It can be observed from Fig.  that the time-averaged plumes are not Gaussian shaped, which indicates that turbulent eddies of various sizes still influenced the time averages. The deviation from the normal distribution can be estimated using the Shapiro–Wilk test , and the p values are calculated as p= [9 × 10-6, 6 × 10-16, 1 × 10-16] for the LES, CH4 and N2O plumes, respectively. Therefore, the measured plumes deviate from the expected Gaussian profile and are not as smooth as the LES plume due to the much smaller set of plumes being averaged. Nevertheless, this analysis shows that LES is a useful tool in source estimation in real-atmosphere conditions, e.g., in cases for which the source location is inaccessible for a tracer release.

Finally, we will present concentration statistics in the absolute and relative coordinate systems. Additionally, we will compare these statistics to parametrizations that are commonly used in fluctuating plume models . These fluctuating plume models have been validated against dispersion studies in laboratory channel flows, often by taking line transects through the plume (e.g., ). Here we aim to utilize the high spatial and temporal resolution of LES to estimate dispersion parameters, needed in these models. Figure  (first and second row) shows y–z transects through the time-averaged plume (average of 287 instantaneous plumes) in the absolute (left) and relative (right) coordinate systems. In the relative system, the instantaneous plumes were aligned with the center of mass of the mean plume (ym‾, zm‾). It can be seen that close to the source (top row) the two plumes are similar in shape since the maximum of concentration and centerline position still coincide. Further downwind, there is a clear difference between the plumes since the plume entered the regime in which it was more frequently carried upwards by strong ejections (see e.g., Fig. ). For the distances furthest downwind (Fig. , bottom row), the two plumes again attain similar shapes. Here, the relative dispersion is the dominant mechanism, and the centerlines of the instantaneous plumes do not move far from its mean position by meandering motions. For the two distances closer to the source, the edges of the plumes show large variability, despite the large number of plume transects that was used in time-averaging. This is caused by the plume behavior. Close to the source, the plume tends to stay close to the ground. The large spatial variability away from the ground is caused by occasional ejections by strong upwards motions. Further downwind, the plumes attain a more uniform shape, resembling a Gaussian distribution.