Chino (34.02∘ N, -117.69∘ W) is located in the eastern part SoCAB, called the Inland Empire, and has historically been a major center for dairy production. With a growing population and expanding housing demand, the agricultural industry has shrunk in this region and grown in the San Joaquin Valley (California Central Valley). The number of dairies decreased from ∼ 400 in the 1980s to 95 in 2013 (red area of Fig. 1a–c). Nevertheless, in 2013 ∼ 90 % of the southern California dairy cow population (California Agricultural Statistics, 2013) remained within the Chino area of ∼ 6 × 9 km (Fig. 1). These feedlots are a major point source of CH4 in the Los Angeles Basin (Peischl et al., 2013).

Atmospheric column-averaged dry-air mole fractions of CH4 and CO2 (denoted XCH4 and XCO2; Wunch at al., 2011) have been measured using four ground-based mobile Fourier transform spectrometers (FTS). The mobile instruments were developed by Bruker Optics and are all EM27/SUN models. The four FTS (two owned by Harvard University, denoted Harvard 1 and 2, one owned by Los Alamos National Laboratory, denoted LANL, and one owned by the California Institute of Technology, denoted Caltech) were initially gathered at the California Institute of Technology in Pasadena, California in order to compare them against the existing Total Carbon Column Observing Network (TCCON, Wunch et al., 2011) station and to each other, over several full days of observation. The instruments were then deployed to Chino to develop a methodology to estimate greenhouses gas emissions and improve the uncertainties on flux estimates from this major local source. Descriptions of the capacities and limitations of the mobile EM27/SUN instruments have been published in Chen et al. (2016) and Hedelius et al. (2016). Using Allan analysis, it has been found out that the precision of the differential column measurements ranges between 0.1 and 0.2 ppb with a 10 min averaging time (Chen et al., 2016). For this analysis, we need to ensure that all the data from the EM27/SUN instruments are on the same scale. Here, we reference all instruments to the Harvard2 instrument. Standardized approaches (retrieval consistency, calibrations between the instruments) are needed to monitor small atmospheric gradients using total column measurements from the EM27/SUN. Indeed we ensured all retrievals used the same algorithm, calibrated pressure sensors, and scaled retrievals according to observed, small systematic differences to reduce instrumental biases (Hedelius et al., 2016).

These modest-resolution (0.5 cm-1) spectrometers are equipped with solar trackers (Gisi et al., 2011) and measure throughout the day. To retrieve atmospheric total column abundances of CH4, CO2, and oxygen (O2) from these near-infrared (NIR) solar absorption spectra, we used the GGG software suite, version GGG2014 (Wunch et al., 2015). Column measurements at Chino were obtained on 5 days: 15, 16, 22 and 24 January, and the 13 August 2015. Of these days, 15, 16, and 24 January are sufficiently cloud-free for analysis. These days have different meteorological conditions (i.e., various air temperatures, pressures, wind speeds and directions), improving the representativeness of the flux estimates at Chino.

Figure 1 shows measurements made on 15, 16, and 24 January. Wind speeds and directions, shown in the bottom panels of Fig. 1, are measured at the two local airports inside the domain (the Chino airport indicated on Fig. 1d–f and the Ontario airport Fig. 1g–i). Wind measurements from these two airports, located at less than 10 km apart, are made at an altitude of 10 m above the surface. The exact locations of the four EM27/SUN spectrometers (colored symbols in Fig. 1a–c) were chosen each morning of the field campaign to optimize the chance of measuring upwind and downwind of the plume. On 15 and 16 January, the wind speed was low with a maximum of 3 ms-1 and in a highly variable direction all day (Fig. 1d, e, and g, h); therefore the four EM27/SUN spectrometers were placed at each corner of the source area to ensure that the plume was detected by at least one of the instruments throughout the day. On the contrary, the wind on 24 January was in a constant direction from the northeast and was a relatively strong 8–10 ms-1 (Fig. 1f and i), so the instruments were located such that one spectrometer (Harvard2) was always upwind (blue symbols in Fig. 1) and the others are downwind of the plume and at different distances from the sources (black, green, and red symbols in Fig. 1).

The EM27/SUN column measurements are supplemented by ground-based in situ measurement using a commercial Picarro instruments during the January campaign. The Picarro instruments use a cavity ring-down spectroscopy (CRDS) technique that employs a wavelength monitor and attenuation to characterize species abundance.

In situ 12CH4, CO2, and 13CH4 measurements were performed on 15, 16, and 22 January, and 13 August 2015 at roughly 2 m away from the LANL EM27/SUN (Fig. 1a–c) with a Picarro G2132-I instrument (Arata et al., 2016, http://www.picarro.com/products_solutions/isotope_analyzers/). This Picarro, owned by LANL, utilize a 1/4′′ synflex inlet tube placed approximately 3 m a.g.l. (above ground level) to sample air using a small vacuum pump. Precisions on 12CH4, CO2, and 13CH4 measurements are 6 ppb, 2 ppm, and 0.6 ‰, respectively.

To locate the major CH4 sources in the dairy farms area, a second Picarro G2401 instrument (http://www.picarro.com/products_solutions/trace_gas_analyzers/) from the Jet Propulsion Laboratory (JPL, Hopkins et al., 2016) was deployed on 15 January 2015. Precision on CH4 measurements is ∼ 1 ppb.

The Weather Research and Forecasting (WRF) model (Skamarock et al., 2008) is an atmospheric dynamics model used for both operational weather forecasting and scientific research throughout the global community. Two key modules that supplement the baseline WRF system are used here. First, the chemistry module WRF-Chem (Grell et al., 2005) adds the capability of simulating atmospheric chemistry among various suites of gaseous and aerosol species. In this study, CH4 is modeled as a passive tracer because of its long lifetime relative to the advection time at local scales. The longest travel time from the emission source region to the instrument locations is less than 1 h, which is extremely short compared to the lifetime of CH4 in the troposphere (∼ 9 years). Therefore, no specific chemistry module is required. The version of WRF-Chem used here (Lauvaux et al., 2012) allowed for the offline coupling between the surface emissions, prescribed prior to the simulation, and their associated atmospheric tracers. Second, we make use of the large-eddy simulation (LES) version of WRF (Moeng et al., 2007) on a high-resolution model grid with 111 m horizontal grid spacing. A key feature of the simulation is the explicit representation of the largest turbulent eddies of the planetary boundary layer (PBL) in a realistic manner. The more typical configuration of WRF (and other atmospheric models) is to be run at a somewhat coarser resolution that is incapable of resolving PBL eddies. An advantage in this study is that the effect of the most important PBL eddies to vertical turbulent transport (i.e., the largest eddies) are not parameterized. By having a configuration with the combination of CH4 tracers and PBL eddies, we can realistically predict the evolution of released material at scales of the order of the PBL depth or smaller. The WRF-LES mode has been evaluated over Indianapolis, IN and compared to the commonly used mesoscale mode of WRF (Gaudet et al., 2017). The representation of plume structures in the horizontal and in the vertical is significantly improved at short distances (< 8 km) compared to mesoscale simulations at 1 km resolution, while the meteorological performance of WRF-LES remains similar to coarser domains due to the importance of boundary nudging in the nested-domain configuration. Thus, the representation of the CH4 plumes in this study should be significantly improved with the LES mode configuration by Gaudet et al. (2017).

In this real case experiment, the model configuration consists of a series of four one-way nested grids, shown in Fig. 2 and described further in Supplement S1. Each domain contains 201 × 201 mass points in the horizontal, with 59 levels from the surface to 50 hPa, and the horizontal grid spacings are 3 km, 1 km, 333 m, and 111 m. All four domains use the WRF-Chem configuration. The model 3 km, 1 km, and 333 m grids are run in the conventional mesoscale configuration with a PBL parameterization, whereas the 111 m grid physics is LES. The initial conditions for the cases are derived from the National Centers for Environmental Prediction (NCEP) 0.25∘ Global Forecast System (GFS) analysis fields (i.e., 0 h forecast) at 6 h intervals. The simulations are performed from 12:00 to 00:00 UTC (04:00 to 16:00 LT) only, which corresponds to daylight hours when solar heating of the surface is present and measurements are made.

Data assimilation to optimize meteorological fields is performed using four-dimensional data assimilation (FDDA; Deng et al., 2009) for the 3 km and 1 km domains. The assimilation improves the model performance significantly (Rogers et al., 2013; Deng et al., 2017) without interfering with mass conservation and the continuity of the airflow. Surface wind and temperature measurements, including from the Ontario (KONT) and Chino (KCNO) airport stations, and upper-air measurements were assimilated within the coarser grids using the WRF-FDDA system. However, no observations of any kind were assimilated within the 333 and 111 m domains; therefore, the influence of observations can only come into these two domains through the boundary between the 333 m and 1 km grids. Wind measurements at fine scale begin to resolve the turbulent perturbations, which would require additional prefiltering. These measurements are used to evaluate the WRF model performances at high resolutions.

Based on the terrain elevation in the LES domain (Fig. 2), target emissions are located in a triangular-shaped valley with the elevation decreasing gradually towards the south. However, hills nearly surround the valley along the southern perimeter. Meanwhile, the foothills of the San Gabriel Mountains begin just off the 111 m domain boundary to the north. As a result, the wind fields in the valley are strongly modified by local topography and can be quite different near the surface than at higher levels.

Figure 3 shows the 1 min average time series of XCH4 (Fig. 3a–c) and XCO2 (Fig. 3d–f) derived from the four EM27/SUN. For days with slow wind (∼ 3 m s-1), i.e., on 15 and 16 January (Fig. 1d, e, and g, h), the maximum gradients observed between the instruments are 17 and 22 ppb (parts per billion), and 2 and 3 ppm (parts per million), for XCH4 and XCO2, respectively. Assuming that the observed Xgas changes are confined to the PBL, gradients in this layer are about 10 times larger. Gradients observed on 15  and 16 January are higher than those of XCH4 and XCO2 of 2 ppb and 0.7 ppm observed on a windy day, the 24 January. The XCH4 and XCO2 variabilities captured by the instruments are due to changes in wind speed and direction, i.e., with high XCH4 signals when the wind blows from the dairies to the instruments. Thus, the EM27/SUN are clearly able to detect variability of greenhouses gases at local scales (temporal is less than 5  min, and spatial is less than 10 km) indicating that these mobile column measurements have the potential to provide estimates of local source emissions.

Total column measurements are directly linked to total emissions (McKain et al., 2012) and are sensitive to surface fluxes (Keppel-Aleks et al., 2012). To derive the total emissions of trace gases released in the atmosphere from a source region, the ”mass balance” approach is often used. In its simplest form, the XCH4 fluxes can be written as in Eq. (2), but this requires making assumptions on the homogeneity of the sources and wind shear in the PBL. FXCH4=ΔXCH4V(z)m(θ)SCair(z), where FXCH4 is the flux (molecules s-1 m-2), ΔXCH4 is the XCH4 enhancement between the upwind and the downwind region (ppb), V is the average wind speed (ms-1) from both airports, m is the distance in meters that air crosses over the dairies calculated as a function of the wind direction θ, and SCair(z) is the vertical column density of air (molecules m-2). The distances that air masses cross over the dairies (m) before reaching a receptor (EM27/SUN) are computed for each day, each wind direction, and each instrument (see complementary information Sect. S3).

Equation (2) can be reformulated as ΔXCH4=ΔtFXCH4SCair(z), where Δt = m(θ)V(z) is the residence time of air over the dairies (in seconds).

A modified version of this mass balance approach has been used by Chen et al. (2016) to verify that the XCH4 gradients measured by the EM27/SUN are comparable to the expected values measured at Chino during the CalNex aircraft campaign (Peischl et al., 2013). In Chen et al. (2016), XCH4 enhancements measured between upwind and two of the downwind sites on 24 January (day of constant wind direction; Fig. 1f and i) are compared to the expected value derived from Peischl's emission numbers, which were determined using the bottom-up method and aircraft measurements. They found that the measured XCH4 gradient of ∼ 2 ppb, agrees within the low range of the 2010 value. However, this differential approach, using upwind and downwind measurements, reduces the flux estimates to only 1 day (24 January), since the wind speed and direction were not constant during the other days of field measurements.

In this study, we extend the analysis of the Chino data set using the mass balance approach on steady-wind day (on 24 January) for all the FTS instruments (i.e., three downwind sites), as well as employing the other two days of measurements (15 and 16 January) in conjunction the WRF-LES model to derive a flux of XCH4 from the dairy farms. We exclude measurements from 22 January and 13 August because of the presence of cirrus clouds during those days, which greatly reduce the precision of the column measurements. Our XCH4 signal measured by the FTS can be decomposed as the sum of the background concentration and the enhancements due to the local sources: XCH4,measured=XCH4,background+ΔXCH4. Gradients of XCH4(ΔXCH4) are calculated relative to one instrument for the 3 days. The XCH4 means (and standard deviations) over the 3 days of measurements at Chino are 1.824 (±0.003), 1.833 (±0.007), 1.823 (±0.003), and 1.835 (±0.010) ppm for the Caltech, Harvard1, Harvard2, and LANL instruments, respectively. The Harvard2 XCH4 mean and standard deviation are the lowest of all the observations; therefore these measurements are used as background measurements. This background site is consistent with wind directions for almost all observations, except for small periods of time on 16 January, which highlights the limitation of our method. Gradients of XCH4(ΔXCH4) for an instrument i (i.e., Caltech, Harvard1, or LANL) are the differences between each 10 min average XCH4 measured by i and the simultaneous 10 min average XCH4 measured by the Harvard2 instrument. Details on the residence time calculation can be found in Sect. S3. Time series of anomalies for individual measurement days are presented in Fig. 4.

Assuming the background levels XCH4 are similar at all the instrument sites within 10 km distance and steady state wind fields, Eq. (3) can be written as XCH4,i-XCH4,Harvard2∝ti-tHarvard2⋅FXCH4. A graphical representation of Eq. (5) is shown in Fig. 5 in which ΔXCH4, the measured gradients by the four FTS during 24 January, are plotted as a function of Δt, so that the slope corresponds to a flux in ppb s-1 or ppt s-1 (parts per trillion). In this figure the slope of the blue lines (dark and light ones) represents the flux measured at Chino in previous studies (Peischl et al., 2013). These studies estimating CH4 fluxes at Chino in 2010 reported a bottom-up value of 28 Gg yr-1 with a range of top-down measurements from 24 to 74 Gg yr-1 (Table 1). To compare these values (in Gg yr-1) to the fluxes derived from column average (in ppt s-1), we used Eq. (6): Fcol=F×109a⋅Y⋅SCair(z)⋅mgNa1012, where Fcol is the column average flux in ppt s-1, F the flux in Gg yr-1, a the area of Chino (m2) , Y the number of seconds in a year, SCair(z) the vertical column density of air (molecules m-2), mg the molar mass of CH4 (g mol-1), and Na the Avogadro constant (mol-1).

On 24 January, when the wind speed is higher than on the other days (Fig. 1f and i), the residence time over the dairies (Δt) is reduced by a factor of 30. The mean Δt from the closest to the furthest instruments to the upwind site are 4 min for Caltech (black square, Fig. 5), 13 min for Harvard2 (green square, Fig. 5), and 16 min for LANL (red square, Fig. 5). The XCH4 fluxes estimated using the mean states (mass balance approach) are 4.8, 1.6, and 1.4 ppt s-1 for the Caltech, LANL, and Harvard2 downwind instruments. For that day, the high wind speed causes a reduction of the methane plume width across the feedlot, which may increase uncertainties on the mass-balance approach since the FTS measurements may only detect a small portion of the total plume. Overall, the FTS network infers XCH4 emissions at Chino, which are at the low end of previous top-down estimates reported by Peischl et al. (2013), consistent with the decrease in cows and farms in the Chino area over the past several years.

However, the flux estimated using the closest instrument/shortest residence time (i.e., Caltech) exceeds the value from previous studies by almost a factor of 2. The other values from LANL and Harvard2, on the other hand, are lower than previous published values. This analysis demonstrates that, even with the day of steady-state winds and the simple geometry, the mass balance still has weaknesses, since it does not properly explain the differences seen at the three downwind sites. The close-in site exhibits the highest apparent emission rate possibly due to the proximity of a large CH4 source. This exhibits delusive approximations implied by this method (i.e., spatial inhomogeneity of XCH4 sources completely averaged out and conservative transport in the domain) even on the “golden day” of strong steady-state wind pattern. Therefore, when investigating emissions at local scales these assumptions can be dubious and lead to errors in the flux estimates.

Analysis of the spatial sources at Chino is developed in this section using the WRF-LES model and in Sect. 4.4 with in situ Picarro measurements.

To map the sources of CH4 at Chino with the model, we focus on the 2 days of measurements during which the wind changed direction regularly (i.e., 15 and 16 January; Fig. 1d, e, and g, h). This provides the model with information on the spatial distribution of CH4 emissions.

During the field campaign in January 2015, in situ measurements of CH4, CO2, as well as δ13C are collected simultaneously with a Picarro instrument at the same site as the LANL EM27/SUN. Fossil-related CH4 sources, such as power plants, traffic, and natural gas, emit CH4 with an isotopic depletion δ13C ranging from -30 to -45 ‰, whereas biogenic methane sources, such as those from enteric fermentation and wet and dry manure management in dairies and feedlots emit in the range of -65 to -45 ‰ (Townsend-Small et al., 2012). During the January 2015 campaign, the δ13C at Chino ranged from -35 to -50 ‰, indicating a mixture of fossil and biogenic sources, respectively. Most of the air sampled included a mixture of both sources. However, the measurements with the highest CH4 concentrations had the lowest δ13C signatures, suggesting that the major CH4 enhancements measured by the Picarro instrument can be attributed to the dairy farms and not the surrounding urban sources.

On 16 and 22 January, the Picarro and the LANL EM27/SUN were installed at the southwestern side of the largest dairies in Chino (red pin, Fig. 1b), near a wet lagoon that is used for manure management (, 150 m away). For these days, the Picarro measured enhancements of CH4 up to 20 ppm above background concentrations, demonstrating that the lagoon is a large source of CH4 emissions in the Chino area. The location of the lagoon was identified and verified by satellite imagery, visual inspection, and also with measurements from the second Picarro instrument deployed in the field on 15 January 2015. With this instrument, CH4 spikes up to 23 ppm were observed near the wet manure lagoon. The measurements from both Picarros and the LANL EM27/SUN instrument near the lagoon suggested that this is a significant local source of CH4 emissions in the Chino area.

As opposed to column measurements, Picarro measurements are very sensitive to the dilution effect of gases in the PBL. With a low boundary layer, atmospheric constituents are concentrated near the surface, and the atmospheric signal detected by the in situ surface measurements is enhanced relative to the daytime, when the PBL is fully developed. For this reason, additional Picarro measurements were made at night on 13 August 2015, when the PBL height is minimal. Between 04:00 and 07:00 LT, we performed Picarro measurements at different locations in Chino to map the different sources of CH4 and verify that the large sources observed in January, such as the lagoon, are still emitting in summer. Figure 11 shows the scatter plot of 1 min-average anomalies of CH4(ΔCH4) vs. CO2(ΔCO2), colored by the δ13C values, measured by the Picarro on the night of 13 August 2015. During that night, the isotopic range of δ13C in sampled methane ranged from -45 to -65 ‰. These low δ13C values are consistent with the expectation that the sources of CH4 in the Chino area are dominated by biogenic emissions from dairy cows. In the feedlots (side triangles, Fig. 11), ΔCH4 and ΔCO2 are well correlated (r2 = 0.90), because cows emit both gases (Kinsman et al., 1995). The observed ΔCH4 / ΔCO2 emission ratio, 48 ± 1.5 ppb ppm-1, is in good agreement with a previous study measuring this ratio from cows' breath (Lassen et al., 2012). Measurements obtained at less than 1 m away from cows (circles, Fig. 11) had the lowest the δ13C observed, ∼ -65 ‰, and these points scale well with the linear correlation observed during the survey. This confirms that the emission ratio derived by surveying the feedlots is representative of biogenic emissions related to enteric fermentation. For, measurements obtained next to the lagoon (diamond marks, Fig. 11), the 12CH4 concentrations were enhanced by up to 40 ppm above background levels observed that night, while the relative enhancement of CO2 was much smaller. This extremely large CH4 enhancement relative to CO2 indicates a signature of CH4 emissions from wet manure management (lagoon), confirming that there is significant heterogeneity in the CH4 sources within the Chino dairy area.