Methodology and Uncertainty Analysis of Methane Flux Measurement for Small Sources Based on Unmanned Aerial Vehicles

Abstract

The top–down emission rate retrieval algorithm (TERRA) method for calculating the net flux out of a box has been employed by other researchers to assess large sources of methane release. This usually requires a manned aircraft drone with powerful performance to fly over the boundary layer. Few studies have focused on low-altitude box sampling mass balance methods for small sources of methane release, such as at maximum flight altitudes of less than 100 m. The accuracy and sources of uncertainty in such a method still need to be determined as they differ from the conditions of large sources. Nineteen flights were conducted to detect methane emissions from Chinese oil field well sites using a measurement system consisting of a quadcopter and methane, wind speed, wind direction, air pressure, and temperature sensors. The accuracy and uncertainty of the method are discussed. The average absolute relative error of the measurement is 18.5%, with an average uncertainty of 55.75%. The uncertainty is mainly caused by the wind speed and direction, and the background CH₄ concentration. The main paths to reduce uncertainty and improve accuracy for low-altitude box sampling include subtracting the background concentration during flux retrieval, enhancing the accuracy of methane measurements, selecting a period of downwind dominant or wind direction change of less than 30 degrees, and ensuring a maximum flight height greater than 50 m with a horizontal distance from the pollution source center of less than 75 m. The results show that TERRA-based low-altitude box sampling is suitable for quantifying methane release rates from small sources.

1. Introduction

Methane is an important greenhouse gas, and methane emissions have serious consequences in terms of global climate change [1]. Approximately 56% of the methane in the atmosphere is emitted from anthropogenic sources directly related to human activities. The oil and gas (OG) industry is the second largest contributor to anthropogenic methane emissions [2]. Methane emissions from sources relating to oil well sites are an essential target for reducing emissions.

Traditionally, bottom–up approaches based on self-reporting or emission inventory methods with engineering models and emission variables, such as emission factors serving as the foundation for the estimation, have been employed to estimate pollution site- or equipment-level methane emissions [3]. However, these approaches have limitations in accurately measuring in real and complex environments, and many unexpected fugitive emissions are usually ignored, raising questions about the representativeness of bottom–up approaches [4]. Recent developments in sensor technology and navigation systems have made drones a robust and reliable basis for professional data acquisition [5]. Aircraft-based measurements of air pollutants have provided a practical top–down approach for estimating total integrated source emissions, ranging from individual stacks to large industrial complexes and cities [6,7,8,9,10]. Here, the measurement principle lies in the mass balance on the plume’s cross-section in the prevailing wind’s downwind direction [11]. Flight patterns can be grouped into (a) single-height transects, (b) upwind and downwind spirals, (c) single-screen flights, and (d) box flights [12]. The quantitative results of different flight patterns correspond to various uncertainties. The single-transect method relies on steady horizontal wind speed assumptions and a well-mixed planetary boundary layer. Its potential uncertainties range from 65% to 100%. The upwind and downwind spirals and single-screen flights have had reported uncertainties varying from 30 to 80%. The total uncertainty of the box mass balance technique ranges from 5% to 28% [13,14]. Data processing methods range from simple average flux [15] and spatial interpolation screen integration [16] to the top–down emission rate retrieval algorithm (TERRA) method for calculating net flux out of the box [17]. Though the use of mass-balanced methods to measure methane emissions has made significant progress in terms of sampling patterns and data processing methods, uncertainties persist in the estimation of methane emissions across different studies [3]. The accuracy of this measurement method heavily relies on the climatic conditions during the measurement. Parameters that cause severe uncertainty in measurement results include wind speed, background CH₄, boundary layer depth, and the interpolation technique used [18]. For mass-balance box flights, extrapolation to the ground is often the most significant error source due to the minimum flight altitude limit, nearing ∼30% when the bottom of the plume is not captured [17].

Airborne mass-balance box flight methods involve flying multiple closed-loop patterns around a site of interest at increasing altitudes to fully sample upwind and downwind of a source and the entire vertical extent of a plume [19]. This method depends on the assumption of a stable boundary layer and that the emission plume is captured at the top of the box and does not change during sampling (i.e., that the conditions are stationary) [7]. Therefore, it is required that unmanned aerial vehicles (UAV) can reach or exceed the top of the boundary layer, usually with a height of several kilometers [20,21]. This requires a powerful UAV that can fly higher and have long-endurance capabilities. However, these requirements will simultaneously increase costs. Most box flight case studies have focused on large pollution sources based on fixed-wing unmanned aerial vehicles, which can fly high enough to reach the top of a plume. However, for small pollution sources, the vertical diffusion range of the plume is relatively small, which may not require high-altitude sampling. Thus, we assume that low-altitude box flight methods may suit small methane sources. In this research, the TERRA-based low-altitude sampling method is tested and verified to determine whether it can work in such cases. The advantages of the proposed method include the use of less expensive side-rotor drones and decreased sampling time. This kind of methane monitoring system’s best monitoring height is generally below 100 m. Few research results have been established on the accuracy and uncertainty of the box method at such flight altitudes. Whether such a flight altitude can cover the entire plume is still unclear, as are the accuracy, uncertainty, and optimized measurement conditions.

In this study, we compared emissions estimated using the data from 15 box flights for the oil well sites of the China National Petroleum Corporation in 2023. The main objective was to test the accuracy of emissions estimates from the TERRA algorithms with low flight altitudes for small pollution sources, assess the uncertainty, analyze the sources, and provide possible explanations. Consequently, we hope to provide some advice on optimizing the measurement conditions to reduce the uncertainty of CH₄ emissions estimates of small sources.

2. Method

2.1. Aircraft and Instrumentation

The Sniffer4D multi-gas detection system of the Soarability Corporation, ShenZhen city, China was employed to measure CH₄ concentrations, wind speed and direction, air temperature (T), and pressure (P). Aircraft state parameters (latitude, y; longitude, x; and ellipsoid height altitude, h) are also measured by a GPS in the system. The instrumentation of the system was installed aboard the flying platform DJI Matrice 300-RTK from Shenzhen Dajiang Innovation Technology Co., Ltd., Shenzhen city, China. The maximum flight time of DJI M300-RTK is 55 min with a maximum load of 2.7 kg, and the maximum wind speed can be 12 m/s. The CH₄ concentration detection method relied on Cavity Ring-Down Spectroscopy (CRDS)-based Tunable Diode Laser Absorption Spectroscopy (TDLAS). The weight of the instrument was less than 250 g. Its measuring error was ±5%FS with a per-second monitoring frequency and a 24 h CH₄ sensor drift (±1%FS). The time used to stabilize the instrument before the start is about 15 min. Considering the characteristics of the pollution sources, meteorological characteristics of the measurement site, legal restrictions on flight altitude, and battery endurance, a flight altitude of less than 100 m is recommended for small, unorganized emission sources. The box method used for onboard wind measurements (as in this study) or a weather station on the ground will affect the uncertainties relating to the large temporal and spatial variability of meteorological conditions during the measurement. An ultrasonic sensor was used to measure wind speed and direction with a LICOR sensor, model LI-550. Ultrasonic wind speed and direction measuring instruments were employed to measure meridional wind ($V_{i,N}$), zonal wind ($V_{i,E}$), and wind direction with a sampling frequency of 1 Hz. The wind speed and direction detection module has a UAV translational motion compensation algorithm, a UAV posture compensation algorithm, and a UAV rotational motion compensation algorithm. No matter how the UAV flies, it can output accurate wind speed and direction data relative to the ground in real time. The wind speed measurement uncertainty is estimated at 0.1 m∙s⁻¹.

The operation of UAV rotors causes significant disruptions to the natural airflow and gas-transported fields, which can negatively impact measurements [22]. Guidance has also been provided that the area directly above the drone appears to be the optimal place to mount the sensor or sensor inlet [23]. The installation position of the instruments is shown in Figure 1. The anemometer is mounted above the drone, with a 37 cm height distance from the eight propellers (4 × 2).

2.2. Studied Areas

Small sources are defined as unorganized emission sources at the well sites of oil and gas fields. These sources usually comprise leakage from various pipe fittings, valve packings, and compressor seals and have source strengths of less than 1 kg/h. The aircraft flew 19 flights over the Jidong oilfield region in Hebei province, the Liaohe oilfield region in Liaoning province, and the Changqing oilfield region in Shanxi province, China between 13 June and 11 October 2023. The pollution sources include 15 oilfield facilities and four torch systems in the oil field well sites. Each box flight path was designed to fly around the boundary of the oil field well site. The maximum flight height used in a box flight (top of the box) ranges from 35 to 100 m, and the lowest flight altitude is 5 m. The flight radius is about 35–78 m, and the drone flew in a square around the source every 5–10 m in altitude. The 5–10 circles form a closed screen around the detection target, obtaining the corresponding methane volume concentration, wind speed, temperature, pressure, longitude and latitude, and the relative height of each detection point. The flight trajectory is shown in Figure 2.

2.3. TERRA Method

Emissions are determined by flying in a pattern approximating a rectangular box surrounding the oil site boundaries. According to [12], the TERRA was described as area emission rates within oil site boundaries. It was estimated using the divergence theorem, which equates the change in mass within the rectangular box with the integrated mass flux through the walls of a rectangular box. Compared to advective flux, turbulent flux can be neglected. This gives a mass balance in the control volume for a given compound (C):

$$E_C=E_{A,H}+E_{C,V}+E_{C,S},$$

(1)

where $E_C$ is the rate of generation/emission of mass within volume; $E_{A,H}$ is the horizontal advective flux of compound (C), $E_{C,V}$ is the box-top advective flux of compound (C), and $E_{C,S}$ is the processes such as surface deposition and the rate at which mass is accumulated/stored within the volume of the box. According to [12], horizontal advective flux accounts for more than 97.7% of the total advective flux on average. The deposition to the surface and the mass change within the box volume due to chemical changes and air density ($E_{C,S}$) can also be neglected. Formula (1) can be again simplified as follows:

$${E_C=E}_{A,H}=E_{out}-E_{in},$$

(2)

where $E_{out}$ denotes horizontal advective flux leaving the surface of the box and $E_{in}$ denotes horizontal advective flux entering the surface of the box.

In solving Equation (2), the three-dimensional space is expanded into a two-dimensional plane along the trajectory and height, the entire plane is discretized into grids, the net flux of each grid is calculated, and then the release rate of the source can be obtained by summarizing. The three-dimensional coordinates of the sampling points were expanded along the two-dimensional plane formed by the flight trajectory line and relative height. The coordinate conversion formula for the flight trajectory line of the ith sampling point is as follows:

$$S_i=\sqrt{({x_i{-x}_0)}^2+({y_i{-y}_0)}^2},$$

(3)

where $S_i$ is the trajectory coordinate of sampling point i, m; $x_i$ is the longitude projection value of the ith sampling point; $y_i$ is the latitude projection value of the ith sampling point; $x_0$ is the longitude projection value of any sampling point as the starting point, which can be defined any a sample point; $y_0$ is the latitude projection value of any sampling point as the starting point. The coordinate of the starting point can be defined as $(0,h)$. The distance between two adjacent points in the counterclockwise direction are calculated and then accumulated to obtain the coordinates of each point along the trajectory line. Here, it creates a unique coordinate so that the flight path can be unrolled from two dimensions to one dimension. In this way, the three-dimensional coordinates of the sampling points are converted into two-dimensional coordinates with trajectory and height. Calculating the normal wind speed of each sampling point in the flight trajectory line:

$$V_i={\displaystyle \frac{V_{i,N}·\partial S_i/\partial x_i-V_{i,E}·\partial S_i/\partial y_i}{\sqrt{{(\partial S_i/\partial x_i)}^2+{(\partial S_i/\partial y_i)}^2}}},$$

(4)

where $V_i$ is the normal wind speed of sampling point i; $V_{i,N}$ is the meridional wind speed of sampling point i; $\partial S_i$ is the trajectory distance between sampling points i and (i−1); $\partial x_i$ is the distance between sampling points i and (i−1) in the x direction of the projection coordinate; $V_{i,E}$ is the zonal t wind speed of sampling point i; $\partial y_i$ is the distance between sampling points i and (i−1) in the y direction of the projection coordinate.

Furthermore, the formula for converting the volume concentration of methane detection at each sampling point into mass concentration is as follows:

$$C=M_R·C_v·{\rho }_{air},$$

(5)

where $C$ is the mass concentration of methane, g/m³; $M_R$ is the molecular weight of methane; $C_v$ is the volumetric concentration of methane, ppm; and ${\rho }_{air}$ is the molar density of the atmosphere, mol/m³, which can be calculated by using the Ideal Gas Law:

$${\rho }_{air}={\displaystyle \frac{P}{RT}},$$

(6)

where P is atmospheric pressure, Pa; R is the universal gas constant, 8.314; T is atmospheric temperature, K.

Furthermore, kriging interpolation is performed on the normal wind speed and methane mass concentration, respectively; the methane emission rate for each interpolation grid is calculated:

$$Q_i=(C_i-C_b)·V_i·A,$$

(7)

where $Q_i$ is the methane emission rate of grid i; $C_i$ is the methane concentration of grid i; $C_b$ is the background value of methane concentration; $V_i$ is the orthogonal wind speed of grid i; A is the grid area of kriging interpolation. The formula for the total emission rate of methane is as follows:

$$Q={\sum }_{i=1}^n{Q}_i,$$

(8)

where Q is the total methane emission rate; n is the total number of grids.

2.4. Uncertainty Analysis

In calculation methods, types of uncertainty include uncertainty in parameters and assumptions (structures) [24]. The parameter uncertainties are based upon the variability and uncertainty in each variable of the mass balance equation (Equation (7)), including uncertainties for wind speed and wind direction, the molar density of the atmosphere, and the enhanced CH₄ mole fraction, which consist of measurement uncertainty and temporal variation. However, the molar density of the atmosphere varies little at low attitudes and is neglected in this study. The assumption uncertainties include the simplified ignored items in the TERRA method, that is, the six terms on the right side of the equation (Equation (1) in [12]), except for horizontal advective flux ($E_{C,H}$). According to the importance of uncertain impacts and the sampling pattern in this paper, we only calculate the uncertainty caused by sampling height. Therefore, the uncertainties in the calculated emission rates refer to five subcomponents: the wind speed and wind direction uncertainties (${\sigma }_W)$ consist of measurement and kriging interpolation uncertainty and temporal variation, which are summed in quadrature. Here, the measured wind speed and direction are provided in the form of orthogonal wind components ($V_{i,N},V_{i,E}$); therefore, the variation in wind direction is also reflected in the variation of orthogonal wind components. Temporal variability is estimated as the standard deviation (1σ) of variables (mean $V_{i,N}$ and $V_{i,E}$) over time. The volumetric concentration of methane (${\sigma }_M$) consists of measurement uncertainty and kriging interpolation error; uncertainty concerning the background value of the methane concentration $\left({\sigma }_B\right)$ is estimated by using the standard deviation (1σ) of the background value at the same oil field; there are also uncertainties caused by incomplete plume monitoring (${\sigma }_I$).

We derive the total uncertainty by using the error propagation model:

$${\sigma }_Q=\sqrt{{\left({\displaystyle \frac{\partial Q}{\partial W}}{\sigma }_W\right)}^2+{\left({\displaystyle \frac{\partial Q}{\partial M}}{\sigma }_M\right)}^2+{{\left({\displaystyle \frac{\partial Q}{\partial B}}{\sigma }_B\right)}^2+\left({\displaystyle \frac{\partial Q}{\partial I}}{\sigma }_I\right)}^2},$$

(9)

$${\sigma }_W=\sqrt{w_m^2+w_k^2+w_s^2},$$

(10)

$${\sigma }_M=\sqrt{m_c^2+m_k^2},$$

(11)

where $w_m$ is the wind speed measurement error; $w_k$ is the kriging interpolation error of wind speed; $w_s$ is the standard deviation (1σ) of variables (mean $V_{i,N}$ and $V_{i,E}$) over time; $m_c$ is the methane concentration measurement error; $m_k$ is the kriging interpolation error of the methane concentration.

Assuming that the divergence of the pollutants along the altitude direction has a Gaussian distribution, methane divergences at different heights (D(h)) can be estimated using the following formula:

$$D\left(h\right)=D_0+{\displaystyle \frac{A}{\sigma \sqrt{\pi /2}}}{e}^{-2{\displaystyle \frac{{\left(h-\mu \right)}^2}{{\sigma }^2}}},$$

(12)

where $\mu$ is the average value of methane divergence at different heights; $\sigma$ is the standard deviation of values for methane divergence at different heights, $D_0$; $A$ is estimated parameters of the normal distribution function. The percentage of methane flux not included in the box $F\left(h>h_{max}\right)$ can be estimated as follows:

$$F\left(h>h_{max}\right)=1-{\int }_0^{h_{max}}D\left(h\right)dh,$$

(13)

where $h_{max}$ is the height at the top of the box, m.

3. Results

The parameters used in the methane release rate calculation are shown in Table S1. The methane concentration contours of the oil field well sites are presented in Figure 3, and the calculated results of the methane release rate for all sample points are presented in

Table 1. Quantification results for methane release rate.

Series No.	Name	Flight Date	Calculated Release Rate of CH4 by ODM (g/h)	Calculated Release Rate of CH4 by TERRA (g/h)	Relative Error (%)
1	JD-R1	13/06/2023	13.118	19.2	46.4
2	JD-T1	15/06/2023	833.3	841.7	1.0
3	JD-R2	15/06/2023	527.5	586.1	11.1
4	JD-712	12/07/2023	1.207	−1.8	/
5	JD-713	13/07/2023	8.432	−3	/
6	JD-715	15/07/2023	23.738	21.55	−9.2
7	JD-716-1	16/07/2023	17.976	21.9	21.8
8	JD-716-2	16/07/2023	3.727	−45.1	/
9	LH-1142	16/09/2023	151.661	135.54	−10.6
10	LH-1529	16/09/2023	359.006	−250.1	/
11	LH-1743	16/09/2023	557.592	690.1	23.8
12	LH-1606	17/09/2023	36.023	28.15	−21.9
13	LH-1024	19/09/2023	613.613	771.06	25.7
14	LH-1244	19/09/2023	655.206	−1018.5	/
15	LH-1526	19/09/2023	736.931	651.4	−11.6
16	CQ-R1630	11/10/2023	3000	2380.6	−20.6
17	CQ-R1654	11/10/2023	4832	−3709.7	/
18	CQ-R0934	10/12/2023	2754	−1440.65	/
19	CQ-R1120	10/12/2023	2754	−834.6	/

Notes: JD—Jidong oil field; LH—Liaohe oil field; CQ—Changqing oil field; ODM—Onsite Direct Measurement; TERRA—top–down emission rate retrieval algorithm.

. The release rates were also calculated using Onsite Direct Measurement (ODM). Emission sources were first identified during a comprehensive site survey using a handheld laser methane detector. Facility-level emissions estimates were then performed using a high-flow sampler (Hi Flow^®) to measure methane emissions from each identified point source.

There were 19 flight measurements with eight negative emissions numbers that indicated measurements below the detection limit or upwind sources of a chemical species were present and not fully captured during the measurement [19]. The absolute value of the relative error between the methane release rate calculated via TERRA and ODM is between 1% and 46.4%, and the average value is 18.5%.

Table S2 contains the related parameters used for uncertainty calculation. The results of the uncertainty analysis are shown in

Table 2. Uncertainty analysis results of methane emission quantification.

Name	Uncertainty by Wind Speed and Direction (g/h)	Percentage (%)	Uncertainty by CH4 Concentration (g/h)	Percentage (%)	Uncertainty by Background CH4	Percentage (%)	Uncertainty by CH4 Plume (g/h)	Percentage (%)	Total Percentage (%)
JD-R1	12.66	65.93	3.71	19.27	7.37	38.39	0	0	78.69
JD-T1	367.4	43.65	94.05	11.17	173.95	20.67	0	0	49.57
JD-R2	170.17	29.03	148.42	25.32	216.11	36.88	0	0	53.33
JD-715	13.11	60.82	6.14	28.49	10.92	50.67	0	0	84.13
JD-716-1	8.25	37.62	3.09	14.08	6.13	27.94	0	0	48.93
NH-1142	43.89	32.38	35.76	26.38	66.22	48.86	55.53	40.97	76.22
NH-1743	162..17	23.50	88.19	12.78	202.67	29.37	0	0	39.73
NH-1606	17.30	61.47	7.69	27.31	10.97	38.97	5.1	18.1	79.82
NH-1024	206.68	26.80	77.63	10.07	168.08	21.8	424.39	55.04	65.76
NH-1526	200.16	30.72	99.11	15.21	196.62	30.18	0.2	0.03	45.67
CQ-R1630	515.81	21.67	314.98	13.23	484.63	20.36	104.27	4.38	32.84
Average	155.54	39.42	79.89	18.48	140.33	33.10	53.59	10.80	55.75

Notes: JD—Jidong oil field; LH—Liaohe oil field; CQ—Changqing oil field.

. The average total uncertainty accounts for 32.84–84.13%, an average of 55.75% of the calculated value. The factors causing uncertainty are ranked from large to small as wind speed and direction > background CH₄ concentration > measurement of CH₄ concentration > incomplete CH₄ plume, accounting for 39.42%, 33.10%, 18.48%, and 10.80%, respectively.

4. Discussion

4.1. Accuracy and Uncertainty of the Method

When compared to similar research results, which had a measurement accuracy ranging from 5% to 28% [7,11,14], this study’s accuracy of 18.5% places it in a significant position. This suggests that the methane monitoring system, sampling pattern, and quantification method developed in this study are highly suitable for assessing the release rate of small source strengths (methane release rate < 1 kg/h).

The TERRA method used for small sources is versatile as it can adapt to different source intensities. The critical variables contributing to its uncertainty include the uncertainty of wind speed and direction, determining the background CH₄ concentration, measurement of CH₄ concentration and wind speed, and the appropriate flight altitude to include the complete CH₄ downwind plume. The most significant difference lies in the flight height when comparing the quantification of large and small source intensities using the same method. In this study, the flight height ranges from 5 to 100 m for small sources, while the flight height for large sources ranges from 200 to 1200 m. In the former case, whether the flight height includes the entire downward plume needs to be considered, and the latter requires ground extrapolation of methane concentration and a wind speed between 0 and 200 m.

While most surface emissions noted in the previous literature were as high as >500 kg/h [12,14,19], the total uncertainty of large source strengths was estimated to be less than 30% [12,14]. The mixing ratio of ground extrapolation from the lowest airborne sampling altitude to the ground emerged as the dominant source of uncertainty. When the plume is clearly elevated and fully contained in the flight range, the uncertainty is insignificant. When the bulk of the mixing ratio is closer to the surface (as with CH₄), the uncertainty is very large (approaching 30%). As the surface source strengths further decreased to <1 kg/h, the uncertainty can be estimated to increase further in the case of more unstable meteorological conditions near the source, resulting in confusion between low concentrations and background concentrations. For this reason, though the uncertainty of this study is larger, 55.75%, it is acceptable.

The sources of uncertainty in this study mainly come from wind speed and direction, as well as the background concentration of methane, which is different from that of large surface sources. When quantifying large sources, flight patterns, such as minimum flight altitude and fight altitude intervals, are the primary sources of uncertainty. The measuring and temporal variation errors of variables were insignificant items in large source measuring. The different sources of uncertainty for small pollution sources can be explained from three aspects: Firstly, local wind turbulence and emission variations at small scales will result in a less uniform and more changeable CH₄ plume. It is hard to model correctly as the measured concentrations have larger variations in the atmosphere. Secondly, the surface source strength is minimal, requiring higher methane measurement accuracy. At the same time, the plume diffusion concentration is deficient, which makes it difficult to distinguish from the background concentration and increases the uncertainty caused by the background value. Thirdly, the measurement error of the methane measuring instrument is 5% of the estimated value, and the measurement error is relatively large.

4.2. The Explanation of Monitoring Failure

Of the nineteen measurements, we obtained a negative value eight times, a measurement failure. The causes of measurement failure have been interpreted as “storage-and-release events” [7]. The mass-balance approach based on the divergence theorem can accurately equate the source emission rate to the net integrated flux leaving the box through the enclosing surfaces under the condition that the storage term equals zero ($E_{CS}=0$). However, non-steady state conditions, including meteorological fields (e.g., atmospheric stability, wind) and chemical fields (e.g., temporal changes in source emission rate or significant incoming upwind emissions) during the retrieval time, can result in mass balance failures. Three factors are involved: atmospheric stability, variations in the direction of transport, and the upwind-to-downwind concentration ratio [7]. To accurately discuss the effect of “storage and release events” on measurement, it is necessary to know the monitored or simulated values of the concentration and density and the timely changes in the volume during the measurement period. We only discuss meteorological and concentration conditions where severe events lead to negative values.

When conditions (e.g., meteorology, emissions) deviate from steady-state and/or localized inhomogeneity, they affect the accuracy of the estimates based on the mass balance approach. For example, temporal changes in source emission rate or significant incoming upwind emissions also contribute to monitoring failure.

Horizontal and vertical turbulent fluxes will increase closer to the source location. As a result, the negative upwind turbulent flux accounts for 15–20% of the total flux [11]. This means that the variance of measured values of wind speed, wind direction, and methane concentration increases, leading to more disadvantageous events, such as upwind release and storage release, violating the assumption of a steady-state and/or homogeneity of meteorological conditions and pollution sources. At last, it increases the uncertainty of the proposed method. However, compared to high-altitude sampling, the quantitative results of low-altitude sampling under the same conditions have greater uncertainty.

Choosing an appropriate sampling distance from the pollution source may mitigate these disadvantages. It requires a distance far enough to maintain the horizontal homogeneity assumption but also close enough so that plume crossings are easily observable against the background variability and instrument noise. The proportion of horizontal turbulent flux decreases with distance from the source. According to [12], the ratio of the horizontal turbulent flux ($E_{C,HT}$) to horizontal advection ($E_{C,H}$) can be simplified to the following:

$${\displaystyle \frac{E_{C,HT}}{E_{C,H}}}=2K_x/x_{\perp }U,$$

(14)

where $K_x$ is the diffusion constant, $x_{\perp }$ is the distance downwind of the source, and $U$ is the mean wind speed. As $x_{\perp }$ = 4 km, giving a ratio of ${\displaystyle \frac{E_{C,HT}}{E_{C,H}}}$∼0.03% [12], if a 3% error is tolerated, the downwind distance will be reduced to 40 m. As the downwind distance increases, the plume’s vertical spread will be enlarged, increasing the risk of not capturing the full plume. According to [25,26], a minimum threshold wind speed of 2.3 m·s⁻¹ and wind direction variability no greater than 33.1°, while additionally restricting the measurements to a maximum downwind distance of 75 m will quantify emissions (0.5–2 kg/h) with an accuracy of better than 50%. Combined with this study, when the distance between the monitoring section and the source center is between 35 and 78 m, we are sure that 75 m is a suitable distance that is neither too far nor too close in terms of balancing the two factors.

Due to the offset of the surface flux, the TERRA method does not require the subtraction of background concentration values. However, according to our observations, subtracting background values can reduce the effect of storage and release events. This can be explained when the mass entering and exiting is not balanced. The background value can significantly reduce the number of grids involved in balancing, thereby reducing the error caused by a mass imbalance. This also can be related to the decrease in the upwind-to-downwind concentration ratio when subtracting background concentration, meaning relatively low upwind emissions.

4.3. The Influence of Wind Speed and Direction on Measurement

Figure 4 shows the relationship between the mean and standard deviation of normal wind speed ($V_i$), the wind direction, and the quantified methane release rates.

Average V_i and Sted (WD) and the calculated methane release rate showed positive and negative correlations, respectively. The coefficient of determination (R²) is 0.199 and 0.163, with the p-value of the F test being 0.056 and 0.087, respectively. This implies that the measurement results are favorable at higher wind speeds with a stable direction. However, there is no correlation between Std (V_i) and the calculated methane release rate, whose p-value obtained in the F test is 0.909, as shown in Figure 4b. This means the calculated methane release rate will increase with the V_i increase and Sted (WD) decrease. As shown in Figure 4a, the calculated methane release rates of all sample points, except for a single sample point, will have positive values when the average V_i value is greater than zero. In this case, the occurrence of upwind is relatively small, and the overall wind direction is downwind, with fewer storage and release events. As shown in Figure 4c, the calculated methane release rates of all sample points, except for a single sample point, will have negative values when the Sted (WD) value is greater than 30°. Previous research results have shown that, when the standard deviation of the wind direction is greater than 33.1°, the error in retrieval results will significantly increase [25,26].

4.4. The Influence of Flight Hight and Source Strength on Measurement

As the source strength increases and the maximum flight height decreases, the error caused by the incomplete coverage of the plume by the sampling screen increases. Assuming that the methane divergence rate follows a normal distribution along the height, the average emission rate of each sampling layer can be fitted using a normal probability density function. The fitting results are shown in

Table 3. The fitted normal probability density function for the vertical methane divergence.

Sampling Point	Fitted Normal Probability Density Function of CH4 Divergence (g/m·s)	Curve Type	Maximum Flight Altitude (m)	Uncertainty by CH4 Plume (%)
JD-R1	$\mathrm{y}=0.00004+\left({\displaystyle \frac{0.001018}{15.8144\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-26.0898}{15.8144}}\right)}^2)$	III	95	0
JD-T1	$\mathrm{y}=0.00327+\left({\displaystyle \frac{0.03109}{15.59\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-39.2225}{15.59}}\right)}^2)$	II	80	0
JD-R2	$\mathrm{y}=0.00146+\left({\displaystyle \frac{0.08323}{10.48\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x+1.94}{10.48}}\right)}^2)$	III	45	0
JD-715	$\mathrm{y}=0.00015+\left({\displaystyle \frac{0.000646}{5.073\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-20.442}{5.073}}\right)}^2)$	II	35	0
JD-716-1	$\mathrm{y}=0.00006+\left({\displaystyle \frac{0.00147}{7.846\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-5.555}{7.846}}\right)}^2)$	II	30	0
NH-1142	$\mathrm{y}=-0.04312+\left({\displaystyle \frac{7.082}{125.819\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-20.626}{125.819}}\right)}^2)$	I	35	40.97
NH-1743	$\mathrm{y}=0.0035+\left({\displaystyle \frac{0.0139}{10.422\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-19.293}{10.422}}\right)}^2)$	III	45	0
NH-1606	$\mathrm{y}=0.00012+\left({\displaystyle \frac{0.0021}{16.716\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-37.379}{16.716}}\right)}^2)$	I	45	18.10
NH-1024	$\mathrm{y}=0.00213+\left({\displaystyle \frac{0.06633}{15.8035\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-36}{15.8035}}\right)}^2)$	I	35	55.04
NH-1526	$\mathrm{y}=0.00137+\left({\displaystyle \frac{0.112}{17.498\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-4.724}{17.498}}\right)}^2)$	III	35	0.03
CQ-R1630	$\mathrm{y}=0.00203+\left({\displaystyle \frac{1.105}{86.55\sqrt{\frac{\pi }{2}}}}\right)\ast exp(-2\ast {\left({\displaystyle \frac{x-26.065}{86.55}}\right)}^2)$	III	100	4.38

Notes: JD—Jidong oil field; LH—Liaohe oil field; CQ—Changqing oil field.

. The shapes of the fitted probability density functions can be categorized into three types, as illustrated in Figure 5. The only type I has a large divergence error among the three types due to insufficient sampling height. Types II and III contain the entire plume, with small errors noted. Based on the normal probability density function shown in Table 3, we can calculate the probability (P > X). In the three type I sample points, if the maximum error does not exceed 5%, the maximum flight height of samples NH-1606 and NH-1024 should be no less than 51 and 49 m, respectively. If the maximum error does not exceed 10%, the maximum flight height of NH-1142 should be no less than 100 m. The flight height of NH-1142 exceeds the best sample height due to the large variance of the normal distribution. Therefore, we believe that a sampling height of no less than 50 m can avoid most of the problems of extrapolating a low altitude to a high altitude.

From Table 1, only one (CQ-R1630) of the eleven valid measurements had a methane release rate greater than 1 kg/h. The shape of the normal distribution function belongs to type III, but there is up to 4.38% uncertainty in the diffusion of the plume, and the uncertainty of other pollution sources with the same shape type is almost zero. The main reason for this phenomenon is that its source is more substantial; moreover, its vertical diffusion range is more extensive. Its sampling height is already 100 m (Table 3), and the uncertainty of plume diffusion cannot be reduced by increasing the flight height. Therefore, it is recommended that the source strength not exceed 1 kg/h.

4.5. Optimization of Experimental Design

It is essential to further refine the methodology via the optimization of the experimental design. Based on the research results, we suggest the following improvements to the method: (1) subtract the background CH₄ concentration when calculating the surface flux and carefully determine the background concentrations from the edges of the unfolded transects or upwind monitoring; (2) choose favorable weather conditions to start the monitoring, such as selecting a downwind-dominant period with moderate wind speeds or wind direction changes of less than 30 degrees; (3) restrict the maximum downwind distance to 75 m and minimum flight height to 50 m; (4) improve the accuracy of the methane measurements. The latest reported measurement accuracy of off-axis integrated cavity output spectroscopy is up to 2 ppb [1].

The above improvements are based on case study experiences and can provide general guidance for other monitoring procedures, as well as paths and directions for accuracy improvements. However, it is still necessary to optimize relevant monitoring parameters through trial sampling when confronting a new pollution source. Low and high-altitude sampling methods are complementary. The advantages of one process are the disadvantages of another, and vice versa. This provides a way to integrate the two methods to improve accuracy and reduce uncertainty when quantifying different levels of pollution sources without limits.

5. Conclusions

Most TERRA methods measure the methane release rates of much larger sources, requiring high performance in terms of the flight platform used, and thus, increased monitoring costs. The near-field sampling of minor methane sources does not require flights above the boundary layer. This paper studied methane release in some oil fields in China based on the Sniffer4D multi-gas detection system of the Soarability Corporation. The absolute value of the relative error between the methane release rate calculated using TERRA and ODM is between 1% and 46.4%, and the average value is 18.5%. This suggests that the methane monitoring system, sampling pattern, and quantification method developed in this study are suitable for assessing the release rates of small sources.

However, the atmospheric stability of low-altitude sampling is poor, which may be caused by the effects of horizontal and vertical turbulence interference, together with a not well-mixed plume, indicating that the spatio-temporal variability of wind direction and speed are generally large compared to typical high-altitude sampling in the far region. Moreover, the poor resolution of the methane concentration emitted from small sources will result in more monitoring failures. Specifically, temporal variability and the measuring errors of wind speed and direction, background CH₄ concentration determination, measuring errors relating to CH₄ concentration, and flight height uncertainties mainly account for measurement accuracy failures.

Carefully designed flight patterns can alleviate this situation. Some steps that may reduce measurement errors include monitoring the background value and using a concentration increment during the calculation process; selecting favorable meteorological conditions during monitoring, such as a period of downwind dominant with moderate wind speed or a wind direction change of less than 30 degrees; adopting a well-designed sampling pattern with a maximum downwind distance of 75 m and a minimum flight of height 50 m; improving the accuracy of the measuring instruments.