Dairy Methane Emissions in California's San Joaquin Valley Inferred With Ground‐Based Remote Sensing Observations in the Summer and Winter

The dairy industry in the San Joaquin Valley (SJV) is one of California’s largest methane (CH4) sources. Reducing dairy emissions is a priority for the state’s climate change plans. Observations of current dairy CH4 emissions are key to monitoring actions taken toward this goal. To help support this, we present new ground‐based measurements of atmospheric column‐averaged CH4 mixing ratio (XCH4) gradients across a group of 600 dairies in the central SJV using EM27/SUN solar spectrometers. We used measurements from the 2019 summer and 2020 winter seasons for a top‐down emission inversion based on the WRF‐STILT model. Our top‐down estimates of the region’s dairy emissions range from 90% to 183% of the current CALGEM inventory’s emissions of 277 Gg/yr. In contrast to the strong temperature dependence found by earlier dairy CH4 emission studies, we also find that our top‐down emissions during the winter measurement days are comparable to the summer measurement days, possibly due to seasonal changes in dairy management practices and meteorological conditions. Furthermore, we find significant interday variability in our measurements and find that our emission estimates overlap with earlier top‐down studies and bottom‐up inventories in this region. Our study demonstrates how analysis of ground‐based remotely sensed CH4 gradient observations can help improve our understanding of CH4 sources at scales relevant to mitigation policy. It also reflects the need for long‐term monitoring of CH4 emissions in the region and at individual facilities to better understand their emissions.

Despite the magnitude of dairy CH 4 emissions, different methodologies for estimating emissions disagree on their size and little is known about their variability in time and space. Bottom-up methods use process-based emission factors with data on CH 4 emitting activities in a region to estimate emissions. Uncertainty is introduced in these methods by uncertainties in the emission factors and activity data used to calculate them, particularly at regional scales (Marklein et al., 2020). California currently uses bottom-up methods to track its total emissions (CARB, 2019). In contrast, top-down approaches are based on measurements of atmospheric CH 4 and modeling the transport of CH 4 emissions in the atmosphere. In California, several top-down studies have found that bottom-up CH 4 inventories may underestimate emissions from the statewide dairy sector and in the SJV region specifically Jeong et al., 2016;Miller et al., 2013;Trousdell et al., 2016;Turner et al., 2015;Wecht, Jacob, Sulprizio, et al., 2014). This discrepancy has important implications for developing baseline estimates against which the state's emission reduction policies are bench-marked, underscoring the need for research to improve our understanding of the dairy sector's emissions as a function of season and management practices.
Dairy CH 4 emissions are also thought to be seasonally variable. Temperature is known to act as a strong control of emissions from dairy farms' manure systems because of its effect on microbial productivity (Arndt et al., 2018;Husted, 1994). This is the only seasonal effect that is included in the US-wide bottom-up inventory of monthly dairy emissions created by Maasakkers et al. (2016), which is presently the only published US-wide, sub-annual CH 4 inventory. However, there is evidence that other factors could significantly contribute to seasonality in dairy CH 4 emissions. During periods of high soil moisture, dairy cows are kept inside longer, which increases the amount of waste entering liquid manure systems where it can be converted to CH 4 (Meyer et al., 2019). The size of this effect is uncertain as it depends on the management choices at individual dairies as well as precipitation. Previous studies have also found that the build-up of waste in liquid waste systems during unfavorable CH 4 production conditions and management choices on individual dairy farms can dramatically impact their emissions (Leytem et al., 2017;VanderZaag et al., 2014). Other factors that cause agitation of the liquid waste systems such as wind, rainfall, or mechanical pumping have also been found to impact individual dairy farms' emissions (Leytem et al., 2017). Studies attempting to quantify the amplitude of the seasonal variability of SJV dairy emissions are limited and have shown conflicting results. Jeong et al. (2016) did not find significant seasonality in the statewide dairy source using ground-based in-situ measurements while Arndt et al. (2018) reported that emissions at two Californian dairy farms were lower in the winter than in the summer due to a temperature effect. Seasonality in the region, therefore, remains an important gap in our understanding of dairy methane emissions.
Atmospheric CH 4 enhancements from a region of interest can be measured by remote sensing. Ground or satellite based remote sensing instruments can use the absorption of sunlight through the atmosphere by a particular gas to derive its average mixing ratio over the entire atmospheric column (Xgas). Xgas measurements are less sensitive to errors in difficult-to-model phenomena such as small-scale turbulence and vertical mixing compared to in-situ measurements taken in the atmospheric boundary layer (McKain et al., 2012). Because they measure the entire atmospheric column, they are also more sensitive to fluxes at regional scales compared to in-situ measurement techniques (Keppel-Aleks et al., 2011;Lauvaux & Davis, 2014). Several studies have demonstrated the usefulness of both ground and satellite-based Xgas measurements to provide top-down estimates of emissions at regional scales (km to 10s of km scales) such as urban regions (Hase et al., 2015;Hedelius et al., 2018;Jones et al., 2021;Makarova et al., 2021;Schwandner et al., 2017;Vogel et al., 2019;Wu et al., 2018Wu et al., , 2020Wunch et al., 2009Wunch et al., , 2019Ye et al., 2020;Zhao et al., 2019), fossil fuel-producing basins (Kort et al., 2014;Luther et al., 2019;Zhang et al., 2020), agricultural regions Kille et al., 2019;Viatte et al., 2017) and in state and country-level domains (Shekhar et al., 2020;Turner et al., 2015;Wecht, Jacob, Frankenberg, et al., 2014). This makes Xgas measurements a good complement to other previously used techniques like aircraft and tower-based in-situ measurements for inferring dairy CH 4 emissions in the SJV. To date, however, groundbased remote sensing measurements have not been used to measure CH 4 emissions in the SJV.
Our study aimed to measure emissions from a large grouping of dairies in the central part of the SJV (about 600 dairy farms over approximately 9 × 10 3 km 2 ) using a network of ground-based remote sensing instruments, the EM27/SUN, during three field measurement periods in the region (July 2019, September 2019, and January-February 2020). Emissions in this part of the SJV are weakly constrained by past measurements and measuring them 10.1029/2021JD034785 3 of 17 is considered a priority for understanding California's emissions because of the high concentration of agricultural sources in the area (Cui et al., 2019). We used these EM27/SUN measurements with the Lagrangian atmospheric transport model, STILT , to create top-down estimates of emissions in the region. We used these estimates to assess variability in the SJV's dairy CH 4 emissions during our measurement days and compared them to published bottom-up and top-down estimates of emissions in the region. This analysis gives new independent constraints on CH 4 emissions in the SJV and demonstrates how ground-based remote sensing data can be used to infer regional greenhouse gas emissions.

Central San Joaquin Valley Study Area
We made our measurements in the SJV, illustrated in Figure 1. The SJV is a flat region bounded by mountains on its eastern, western, and southern sides. In the north, the SJV merges with the Sacramento Valley. Air typically enters the SJV from the northwest near the San Joaquin Delta and remains confined in the SJV for long periods (San Joaquin Valley United Air Quality District, 2004). This containment mixes and traps air pollutants and greenhouse gases in the SJV.
As an a-priori map of emissions in the area, we used the non-dairy emission inventory from CALGEM (Fischer, 2017;Jeong et al., 2016) along with a new dairy CH 4 inventory (Marklein et al., 2020). CALGEM is a high resolution (0.1°) disaggregation of California's regulatory CH 4 inventory that uses detailed spatial information to distribute emissions from the regulatory inventory. Its total emissions are scaled to match the regulatory inventory' total statewide CH 4 emissions. For the dairy sector, we used a facility level inventory of annual dairy emissions created by Marklein et al. (2020) gridded at a 0.1° resolution. Their inventory draws on farm level permitting information and regionally specific manure management practices to estimate and localize dairy emissions at a higher accuracy than CALGEM's dairy inventory.
Our EM27/SUN measurements were focused on capturing emissions from a large grouping of dairies in Tulare and Kings counties in the central part of the SJV. In the a-priori inventory used in this study, these counties emit 362 Gg CH 4 /year with most emissions (89%) from the dairy sector. The next largest CH 4 source in this region is natural gas transmission and distribution emissions concentrated in urban areas. South of the area, in Kern County, there is also significant oil and natural gas extraction and processing related CH 4 emissions, but these sources are typically downwind and unsensed by our instruments.
On all measurement days, one instrument was located to the northwest of the dairy grouping at Cantua Creek (36.445°N, −120.248°E, 86 m above sea level (a.s.l.)) and one instrument was located to the southeast of the diaries at Terra Bella (35.931°N, −119.036°E,153 m a.s.l.). Prevailing winds in the SJV are from the northwest so these instruments typically captured background air upwind of the dairies and polluted air downwind of them. On measurement days when we had three instruments, the third instrument was located at either a site south of the dairy grouping at Helm's Corner (36.084°N, −119.644°E, 53 m a.s.l.) or at a site to the east of the dairies at Visalia (36.308°N, −119.194°E, 110 m a.s.l.). The specific location of the third instrument site was determined by the forecast winds on each measurement day. The distance between the instruments was on the order of 10s of kilometers which was similar to the size of the Xgas measurement networks used in Hedelius et al. (2018) and Vogel et al. (2019).

EM27/SUN XCH 4 Measurements
The EM27/SUN is a compact field deployable solar tracking Fourier transform spectrometer further described in Gisi et al. (2012). The instrument uses direct solar absorption spectroscopy to retrieve total column abundances of CH 4 , CO 2 , CO, H 2 O, and O 2 along an atmospheric path from the instrument to the sun over a 9-11 s measurement period. The abundances are converted to dry air mixing ratios by dividing by the retrieved oxygen column and using the known column average concentration of O 2 . The EM27's XCH 4 measurements have a precision of 0.06% at a 10 min integration time and can be reliably tied to the World Meteorological Organization (WMO) trace gas scale Hase et al., 2015;Hedelius et al., 2016).
We deployed three EM27's owned by Los Alamos National Lab (LANL), NASA's Jet Propulsion Lab (JPL) and Harvard University to the SJV for 2 days during the 2019 summer (July 22 and September 12) and for 4 days in the 2020 winter (January 22, 27, 30, and February 3). The LANL and JPL instruments were used during both seasons and the Harvard instrument was used only in the winter. The LANL and JPL instruments were co-located with Zeno weather stations and the Harvard instrument was co-located with a Digital Instruments MHB-382SD weather station. These stations were used to provide accurate surface pressure values for the EM27 retrievals. Additionally, we used temperature, pressure and humidity profiles from the NCEP/NCAR reanalysis product (available at https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html) interpolated to each measurement station for the retrievals. This was done instead of using a common meteorological profile because of the large distance between the sites, following Hedelius et al. (2016). XCH 4 measurements were retrieved from unaveraged double-sided interferograms using the GGG and i2s software distributions (Wunch et al., 2015) and the EGI tool suite (Hedelius & Wennberg, 2019). We used the absorption windows described by Hedelius et al. (2016) for our retrievals. Within 1-2 weeks of our field measurements, we calibrated our instruments by making measurements with the EM27/SUN's at the NASA Armstrong Total Carbon Column Observing Network (TCCON) site (July campaign) or the Californian Institute of Technology TCCON site (September 2019 and January 2020). The TCCON is a network of high resolution solar Fourier transform spectrometers which are tied to the WMO trace gas scale using aircraft measurements of vertical concentration profiles (data available at https://tccondata.org/). We calculated multiplicative offsets for the EM27 XCH 4 retrieval relative to the TCCON observations following the methodology outlined by Hedelius et al. (2016), tying our retrievals to the WMO scale. This calibration also ensured that any systematic offsets between the EM27/SUN's were removed, allowing for accurate measurements of XCH 4 gradients for our top-down inversions. The correlation plots between the EM27's and the TCCON are shown in Figure S1 in Supporting Information S1. The XCH 4 measurements collected by the EM27/SUN's on all the measurement days are shown in Figure 2.

STILT: Modeling Emissions Transport
To simulate the atmospheric transport of emissions to our instruments, we used a modified version of the Stochastic Time Inverted Lagrangian Transport model (STILT; Fasoli et al., 2018;Lin, 2003). STILT uses a 4D meteorological field to calculate back trajectories from a receptor location and then analyzes these trajectories to determine a sensitivity footprint. This footprint represents how sensitive a measurement at the receptor is to emissions from different areas and times. The modified STILT version models the Xgas measurements made by the EM27/SUN by creating a slant profile of receptors oriented from the instrument location to the sun (Jones et al., 2021). This creates a profile of emission sensitivity footprints along the measurement columns of the EM27s, F(z, t), representing the sensitivity of CH 4 mixing ratios at different heights to surface emissions, E. Convolving F(z, t) and E create a mixing ratio enhancement profile reflecting the effect of surface emission along the slant EM27 measurement profile at the measurement location and time.
We ran STILT using meteorological fields generated using the WRF model (V 3.9.1) (Skamarock et al., 2008). These fields were run in a nested 36, 12, and 4 km resolution domain centered over western North America with 50 vertical levels from the surface to a pressure height of 100 mb. Boundary conditions for the WRF fields came from the North American Regional Reanalysis forecast product. The model was configured with the MYNN boundary layer parametrization and other options were based on previous work by Jeong et al. (2016) and Bagley et al. (2017) using WRF in the SJV. We used only the MYNN model rather than changing boundary layer para- metrization in the winter as done in these other studies because we found that the MYNN model showed a better fit with our XCH 4 measurements (Text S3 in Supporting Information S1).
STILT was run using the vertical profile spacing (100 m spacing in the first 3 km of the atmosphere and 500 m spacing above 6 km) and particle release numbers (200 at each vertical level) suggested by Wu et al. (2018) for modeling Xgas signals. For other model control parameters, we used the default STILT parameters described by Lin (2003) and Fasoli et al. (2018). We also ran STILT backwards in time for 7 days as we found that this was sufficient time for the particles to leave the SJV, ensuring that we captured the full influence of the region's emissions.

Calculating Background CH 4
Aside from the influence of emissions, XCH 4 measurements can vary due to differences in the influence of the far-field CH 4 mixing ratios and differences in the atmospheric column caused by elevation differences . Neglecting these effects can introduce spurious XCH 4 gradients which propagate into emission estimates derived with these measurements.
We generated a background XCH 4 time series for each of our instruments to account for these effects. We did this using the Copernicus Atmosphere Monitoring Service near realtime model (CAMS-NRT) model which provides forecast fields for greenhouse gas mixing ratios and atmospheric variables at a 6-hr and 0.4° grid (Inness et al., 2019). In the first 6 km of the slant model profile, we followed STILT back trajectories from our measurement locations at each measurement time to their endpoints after 7 days. These endpoints were typically over the Pacific. The CAMS model was interpolated to these endpoints to set a dry air CH 4 mixing ratio for each back trajectory. The average of these concentrations was taken as the background concentration for a specific height in the model profile for each measurement location and time. Above our maximum STILT release height of 6 km, we used the CAM-NRT model to directly set concentrations in the profile up to a pressure height of 1 hPa. Together this generated a set of background profiles for each measurement location and time, reflecting both the effects of far-field concentrations and topographic effects on the XCH 4 measurements. We refer to these profiles as B(z, t).
In addition to the CAMS-derived background described above, we also implemented a background estimation method that estimated a spatially constant background XCH 4 time series for air entering the SJV (Jones et al., 2021) and created emissions estimates using the minimum observed XCH 4 value as a constant background. These two methodologies gave similar top-down emission results as the CAMS background method and are described fully in Text S2 in Supporting Information S1.

Model XCH 4
Adding the modeled emission enhancements from STILT, F(z, t) × E, and the background signals from the CAMS-NRT analysis, B(z, t), gives a model estimate of the CH 4 slant mixing ratio profile at a given measurement location and time. We call this mixing ratio profile x sim (z, t). To create an XCH 4 model estimate, XCH 4,sim , for comparison with our measurements, we integrated x sim (z, t) vertically. The integration uses a vector of pressure weights, h, to capture the contribution of each profile level to XCH 4,sim (t) as well as an averaging kernel vector, a, that accounts for the sensitivity of the XCH 4 measurement to changes from the a-priori profile, x ap , used in the EM27/SUN retrieval (Wu et al., 2018). The relation between these variables is shown in Equation 1: h is calculated by creating density and water profiles for our measurements using the WRF meteorological fields below 6 km and the CAMS-NRT model above 6 km. These profiles were converted to weights for the CH 4 profile using the weighting function from the GGG-2014 retrieval software (Wunch et al., 2015). The a vector is based on a look-up table from Hedelius and Wennberg (2019) and was interpolated to the solar zenith and pressure profile used for each measurement. x ap was calculated from the a-priori profile calculated by GGG-2014 for the measurements, with the profiles rescaled to match the surface pressure observed at each measurement.

Top-Down Emission Estimates
We used the hourly average XCH 4 differences (ΔXCH 4 ) between our instruments on each measurement day as an observational constraint to create top-down estimates of dairy and non-dairy emissions. Using a difference has advantages over XCH 4 data as measurement and modeling errors that are common to two instruments cancel out in differences and interfering effects due to emissions outside our target region and due to variations in background CH 4 concentrations should be reduced in size Hedelius et al., 2018;Vogel et al., 2019;Zhao et al., 2019). Hourly averaged ΔXCH 4 observations (ΔXCH 4,obs ) were calculated from the EM27/SUN measurements with the Cantua Creek measurements used as the reference on most measurement days except on January 22nd where Terra Bella was used as the reference instrument. This was done because on this day Terra Bella showed the lowest XCH 4 values.
Plots of sample STILT trajectories on each measurement day show that on most measurement days air at each instrument enters the SJV at similar locations and times from the Pacific (see Figures S2-S7 in Supporting Information S1), suggesting that background differences between them should be small. An exception to this was on January 22nd where air from the three instruments appear to follow different paths out of the SJV which may indicate that there are larger background differences on this day. We note that these interfering effects are still modeled in our framework through the modeling of emissions throughout California and through the use and optimization of the CAMS model gradient.
These gradient observations are used in a Bayesian inversion to find multiplicative scaling factors (λ p ) on the modeled gradient signals from dairy and non-dairy emissions in the a-priori inventory and from the background (ΔXCH 4,sim,d , ΔXCH 4,sim,nd , and ΔXCH 4,sim,b , respectively). Because emissions are linearly related to the ΔXCH 4 model signals, λ p gives the optimal amount that the emissions and background gradients should be changed from the a-priori to match our observations given the uncertainties in our observations, model, and in the a-priori emissions. Under the assumption that the model gradient is linearly related to the measured gradient and that all uncertainties are normally distributed, λ p and its error covariance matrix, S, are given by the equation from Rodgers (2000) where λ ap represents the a-priori scaling factors on the model signals, S ap represents the covariance matrix of the a-priori scaling factor and S e represents the covariance matrix of the model-measurement mismatch.
S ap is taken to be a diagonal matrix, meaning we assume there is no correlation between errors in the dairy, nondairy, and background scaling factors. The diagonal elements were calculated using a 36% standard deviation for the dairy scaling based on the uncertainty in statewide dairy emissions given in Marklein et al. (2020), a 70% standard deviation for non-dairy emissions based on estimates of CALGEM's uncertainty in the SJV by Jeong et al. (2013) and a 100% standard deviation for the background gradients, representing minimal constraints on changes to the background gradient.
S e is also taken as a diagonal matrix with elements taken as the sum in quadrature of the model gradient uncertainty and measured gradient uncertainty. The model gradient uncertainty is dominated by transport uncertainty that can be divided into two parts: uncertainty due to horizontal transport and uncertainty due to vertical turbulence. We estimated the effect of horizontal transport uncertainty on our STILT XCH 4 enhancements by calculating the additional variance in the enhancements introduced by a stochastic wind component parameterized to model the uncertainty in our WRF wind fields in the SJV (Lin, 2005). Our full methodology is outlined in Text S1 in Supporting Information S1. The average horizontal error for the measurement days ranges from 2.5 to 3.6 ppb. We 10.1029/2021JD034785 8 of 17 assessed the vertical mixing error following the methodology outlined by Wu et al. (2018). In their technique, the STILT boundary layer is uniformly rescaled by 20% during the first 24 h of the model run time and the difference in the enhancements of this perturbed model run and the unperturbed run is taken as the vertical mixing error. This error term ranges from 0.8 to 2.9 ppb over the measurement days. We note that the 20% perturbation used by this method may not be directly applicable to our SJV WRF fields. However, as XCH 4 measurements are less sensitive to boundary layer errors we did not attempt to further characterize boundary layer errors specific to our modeling setup. The measurement error is taken as the hourly standard deviation of the EM27/SUN's ΔXCH 4 measurements. The average measurement error over the measurement days ranges from 2 to 3.6 ppb. This standard deviation represents atmospheric variability in the measured XCH 4 over the hour-long averaging time. Because of the large number of measurements used to create the average, the instruments' retrieval uncertainty is relatively small. We additionally note that although we have taken S ϵ to be diagonal, there are likely covariances in the model errors that affect the fit and neglecting these may act to make our inversion errors too conservative.

Observed Meteorology
Meteorological conditions in the SJV were recorded on all our measurement days by 15 surface weather stations in the ASOS network (retrieved from https://mesonet.agron.iastate.edu/request/download.phtml). A map of these stations is shown in Figure S8 in Supporting Information S1. We aggregated data from these stations to estimate average meteorological conditions and their variability over the SJV during the time periods on and preceding our measurement days. These variables are shown in Table 1 and are used to help interpret the EM27/SUN measurements. Wind direction and speed at 10 m are reported as an SJV wide average over the night before the measurement day, defined as beginning at 20:00 local time, and the end of the measurement day at 17:00 local time. This period was based on Figure 7 which shows that most of the XCH 4 enhancements measured by the instruments are released over this period. Temperature, humidity and rainfall statistics are reported as SJV wide averages over the 7 days prior to and including the measurement days. This was based on the assumption that changes to dairy emissions due to these variables should occur on the order of days as they should affect conditions within the liquid manure systems.
As expected, temperature in the SJV is highest during the summer (July and September measurement days) and declines on the winter measurement days. Humidity and rainfall, in contrast, are highest on the winter measurement days and. Wind speed is low on all measurement days except on February 3rd when average wind speeds are 5 m/s. The average wind direction is from the northwest on all days except on January 22nd and 30th when it is on average from the east. All the meteorological variables fall within 1σ of the 30 day SJV-wide average centered around each measurement day except for the wind speed in February which is 2.8σ higher than the average winds.
Because the accuracy of the model wind fields is important for determining the accuracy of a transport simulation, we also compared our WRF fields to the 10m wind measurements from the ASOS network in the SJV. This allows us to assess the quality of the STILT model on each measurement day. The comparison is shown in Figure 3. On most of the measurement days, there is a good correlation between the WRF and ASOS winds and Note. Two meters temperature and relative humidity statistics are aggregated over the 7 days prior to and on the measurement day. Accumulated rainfall is reported as a sum averaged across ASOS stations in the SJV for the 7 days prior to the measurement day. 10m wind speed and direction statistics are aggregated on each measurement day.

Table 1 Meteorological Conditions Observed by ASOS Weather Stations in the SJV During the Measurement Days
biases are typically small. The exceptions to this are the high bias in both wind components observed on January 27th and the low correlation with the ASOS network on January 30th. The deficiency in the wind fields may indicate problems in the model signals on these days but our meterological uncertainty analysis should model the effect of the higher random error on January 30th.

STILT Model Results
Comparisons between the optimized model ΔXCH 4 signals and the measured EM27/SUN signals are shown in Figure 4 for each of the 6 sampling days. We find that on all measurement days except January 30th, there is a good fit between our model results and the measurements as measured by the reduction in uncertainty in the a-posteriori dairy emission scaling factors. Notably, our top-down inversion reduces the uncertainty on the emissions by a factor of 2 or more compared to the a-priori uncertainty (0.36) on most days, showing that the observations can constrain the emissions. The RMSE between the optimized model and the measurements varies over the measurement days and is smallest on the July, September, and February days. This indicates a better model fit and stronger constraints on emissions on these days. On January 30th, the fit was much worse by both metrics, with the model failing to capture the enhancements observed at the Helm's Corner site in the morning. We attribute this to errors in the WRF model, evidenced by the poor correlation between the WRF 10 m winds and weather station observations in the SJV on this day (see Figure 3).
The a-priori non-dairy emissions were not significantly changed on any of the measurement days and there is minimal reduction in these emissions' uncertainty compared to the a-priori. This indicates that non-dairy emissions are not constrained by our measurements and this is expected given the small amount of non-dairy emissions in the study area. Finally, the a-priori background gradient is not significantly changed on the July 22, September 12 (summer), and February 3 (winter) measurement days indicating that the background gradient does not have a strong effect on the inversion on these days. In contrast, on January 22, 27, and 30, the inversion significantly changes the background gradient between the instruments indicating that the CAMS model background gradient needs to be altered to match the measurements on these days. The adjustment to the model background gradient is especially large on January 22 for the Cantua Creek and Terra Bella gradient and is on the order of 500%. This may reflect a difficulty in CAMS-NRT modeling the differences in background XCH 4 caused by the more distinct paths air arriving at each instrument takes entering the SJV on this day ( Figure S4 in Supporting Information S1).

Emission Sensitivity Area
Our top-down analysis gives single top-down scaling factors for dairy and non-dairy emissions but does not give information on the spatial region they apply to. Because of this, it is necessary to determine which locations in the a-priori inventory contribute to the ΔXCH 4 signals before inter-comparing our results or comparing it to other emission estimates. We did this by creating contribution maps showing how much ΔXCH 4 each grid cell in the a-priori emissions contributed to the STILT model signals as shown in Figure 5. They show that on all the measurement days a large proportion of the modeled ΔXCH 4 comes from emissions from dairy farms in Tulare and Kings counties. This was the area that we targeted with our measurement network and the maps suggest that the scaling factors on these days apply to roughly the same area. We explicitly define this area by selecting grid cells in the a-priori inventory that on average contribute at least 0.1 ppb to the modeled ΔXCH 4 signal over the measurement days.
This sensitivity area is outlined in Figure 5. It contains 585 dairy farms out of 1,317 in the SJV and covers approximately 3 × 10 3 km 2 . Liquid manure management in waste ponds is the predominant manure management method among these dairy farms and they contain a mix of freestall and dry lot animal housing (Marklein et al., 2020;Meyer et al., 2011). At least 60% of the modeled signal on each of these days comes from this area and at least 90% of its total emissions are from the dairy sector. The a-posteriori scaling factors derived from the inversion are applied only to a-priori emissions in this area giving top-down emission estimates for each day. These are shown in Figure 6. This restriction ensures that the scaling factors are applied only to areas that our measurements are sensitive to.

Temporal Sensitivity to Emissions
Similar to the above spatial analysis, we can use our STILT footprints to estimate the time period when the CH 4 emissions we measure were released. Determining the sensitivity time of our top-down emissions is useful as work by Wood et al. (2013) on dairy manure emissions and Vaughn et al. (2018) on fossil fuel emissions suggest that differences in the time period different methods estimate emissions for can create discrepancies between them. Figure 7 shows the contribution of emissions released at different times to the modeled absolute ΔXCH 4 averaged over each measurement day. This plot suggests that our XCH 4 measurements have a broad temporal sensitivity spanning several hours and that their peak sensitivity ranges from 02:00 on the night before the measurement day to 07:00 on the morning of the measurement day. Although our measurements were mostly taken in the afternoon, this result is not unexpected. Because of the large size of our sensitivity area (10s of km) and the low wind speeds and ventilation rates present in the SJV, it takes several hours from entering the SJV for air to flow to the downwind sites. This allows the instruments to measure emissions released overnight and in the morning. Interestingly, Wood et al. (2013) found that the lowest deviation from diurnally averaged emission rates in dairy manure lagoons is realized when the top-down emissions are sensitive to emissions released between 18:00 and 08:00. This suggests that our measurements may have minimal bias due to diurnal variations in the dairy farms'  emissions. However, the broad temporal sensitivity also means that it is difficult to assess if there is coherent diurnal variability in the SJV's emissions from our measurements.

Discussion
Our analysis finds that the dairy emissions on the winter measurement days (January 22nd 371 ± 54 Gg/yr, January 27th 237 ± 52 Gg/yr, January 30th 281 ± 81 Gg/yr, and February 3rd 491 ± 43 Gg/yr) are comparable to or higher than dairy emissions on the 2 summer measurement days (July 22nd 291 ± 47 Gg/yr and September 12th 292 ± 38 Gg/yr). Although temperature is an important driver of dairy CH 4 emissions and would be expected to reduce dairies' manure emissions in the winter, this finding suggests that other factors act to increase dairy emissions in our study area over the winter measurement days.
We can estimate the expected effect of temperature on manure dairy emissions over the measurement days using an Arrhenius temperature relationship (Safley & Westerman, 1988) driven by 7 day averaged SJV surface temperatures from the ASOS stations. The change in manure emissions can then be converted to the relative change in total dairy emissions using the ratio of manure emissions to total dairy emissions in the a-priori inventory (47%). This analysis predicts that temperature changes should cause emissions on the winter days to be approximately 60% of emissions on July 22nd or 174 Gg/yr. None of our top-down emission estimates on the winter measurements days overlap with this value within the 1σ uncertainty and the emissions on January 22nd, February 3rd are higher than this value within their 2σ uncertainty. This difference from the decline in emissions predicted from temperature changes suggests that other factors act to control seasonality in the SJV's dairy CH 4 emissions. Additionally, dairy emissions on the second summer day (September 12) should be 89% of emissions on the first summer day due to the temperature effects and this overlaps within the 1σ error with the ratio of topdown emission we measured (100 ± 20%).
This result in the central SJV on our measurement days is in accord with other studies which showed no significant seasonality in California's statewide dairy emissions  and which showed increases in winter emissions in the northern SJV relative to other seasons (Johnson et al., 2016). Additionally, a study by Leytem et al. (2017) at a group of US dairy farms found that non-temperature factors could act to mask seasonal temperature effects on emissions. We note that aside from temperature changes, there are dramatic changes in precipitation patterns in the SJV between the summer and winter (see Table 1). Rainfall could act to increase the SJV's dairy emissions by altering the input of manure to anaerobic liquid waste storage systems through management decisions (Meyer et al., 2019). Also, rainfall has been shown to increase individual dairy farms' CH 4 emissions by enhancing the agitation of liquid manure ponds (Leytem et al., 2017) and could also increase emissions by expanding the emitting area of the manure ponds (Petersen, 2018). With our time-limited campaign data set, we can not directly attribute the higher than expected winter emissions to any one factor. However, the result suggests a need for measurements at regional scales like ours as well as on individual dairy facilities to constrain the seasonally varying effects of temperature, moisture, and dairy management on the SJV's dairy emissions.
During the winter, the SJV's natural gas consumption is about 3.5 times higher than in the summer (Pacific Gas & Electric, 2019). Higher winter natural gas emissions could contribute to total emissions in the SJV being higher than expected rather than dairy emissions. To assess this explanation, we ran a sensitivity test by artificially increasing the size of natural gas emissions in the a-priori inventory by a factor of 5. The scaling factors recovered for this perturbed a-priori overlap within 1σ error with the scaling factors calculated with our unperturbed a-priori emissions and do not show a decline in dairy emissions in the winter. This suggests that natural gas emissions do not contribute to our observation of relatively high winter emissions.
Interestingly, our measurements also show evidence of interday variability in emissions. Top-down emissions on February 3rd are higher than emissions on all the other measurement days at the 2σ uncertainty level except on January 22nd where it is higher at the 1σ uncertainty level. This may be related to the anomalously high wind speed measured across the SJV on the night before and during February 3rd (see Table 1). Leytem et al. (2017) and Grant et al. (2015) both reported strong correlations between manure methane emissions and wind speed at individual facilities that they attributed to enhanced agitation and release of CH 4 from the liquid manure ponds. This effect could be driving a coherent increase in emissions over all the dairy farms in our sensitivity area causing the higher top-down emissions. Given that we are restricted to 6 measurement days, it is difficult to fully assess the importance of intermittent emission events on longer term emissions or to unambiguously attribute the higher emissions to wind speed. Work by Duren et al. (2019) in the SJV also found that emissions at individual dairies in the region were intermittent in time. This along with our regional finding suggests a need for reanalysis of existing long term data sets, such as the GOSAT and TROPOMI satellite XCH 4 record and the CARB in-situ tower record as well as new long term sampling in the SJV to further investigate the drivers of interday variability and to determine its importance to emissions in the region.
Our top-down emissions in the sensitivity area all overlap with the bottom-up emissions in the a-priori inventory within their respective 1σ uncertainties. Since the a-priori was constructed with annual bottom-up emissions this means that both the variability in our days' top-down estimates and their difference from the a-priori fall within the overall uncertainty of the annual bottom-up emissions. Our top-down emissions also overlap with the emissions from the CALGEM inventory within an assumed 70% 1σ error on CALGEM's total emissions. Other bottom-up inventories in the region such as the EPA inventory (Maasakkers et al., 2016) have known issues in localizing emissions in the SJV (Marklein et al., 2020) that preclude them from comparison to emission in our sensitivity area.
We also compared our EM27/SUN XCH 4 based emissions to three other studies that estimated top-down emissions in the SJV using different measurement techniques: an aircraft-based estimate by Cui et al. (2017), an in-situ tower-based estimate by Jeong et al. (2016), and a satellite XCH 4 -based estimate by Turner et al. (2015). Cui et al. (2017) created emission estimates in the southern SJV (encompassing our sensitivity area) based on boundary layer CH 4 mixing ratio data collected on four aircraft flights during the spring and early summer of 2010. Jeong et al. (2016) used near-surface mixing ratio measurements from CARB's regional tower network from June 2013 to May 2014 to make an estimate of the entire SJV's annual emissions. For these studies, we applied the average ratio between their top-down emissions and CALGEM to CALGEM's emissions in our sensitivity area. We also assumed that the uncertainty they reported for these larger regions applied to the downscaled emissions. Turner et al. (2015) reported annual emissions across North America at a 0.5° × 0.667° resolution using XCH 4 soundings from the GOSAT satellite from 2009 to 2011. We summed emissions in grid cells in their top-down emission map that overlapped with our sensitivity area for comparison with our emissions and assumed that the uncertainty they reported for California-wide emissions applied to this area.
We note that there are difficulties inherent in these comparisons, particularly in downscaling emissions, in the multi-year difference in when these measurements were collected, and in the differences in the timescales and time periods the top-down estimates apply to. Despite this, an error-weighted average of emissions across our measurement days overlaps within 1σ error with the other top-down estimates as shown in Figure 8. On individual days, emissions all overlap within their respective 95% CIs with the other estimates. However, emissions on the summer days and January 27th fall below the 1σ uncertainty band of Cui et al. (2017) results and emissions on February 3rd fall above the 1σ uncertainty band of Turner et al. (2015) results. Despite this, the overall consistency of our results suggests that our EM27/SUN methodology is able to retrieve emissions correctly and suggests that emissions in the central SJV region we were sensitive to are similar to emissions in the wider SJV.

Conclusions
We reported EM27/SUN ΔXCH 4 across the SJV during the summer and winter and used them to constrain dairy CH 4 emissions using WRF-STILT inversions. We find that our measurements capture the influence of CH 4 emissions from a large grouping of dairies in the central SJV, a region with low constraints on emissions, on all of our measurement days and are sensitive to relatively similar times of day. Our measurements also span the summer and winter and we find that CH 4 emissions in the SJV are much higher during the winter measurement days than would be expected from the temperature effects used in the current national scale CH 4 inventories of dairy emissions. We also observe significant interday variability in our measurements. These results suggest that seasonal management changes in the dairies, wind agitation of manure ponds, and other biogeochemical responses in the region could be important factors controlling emissions. They also demonstrate a need for more long-term measurements to constrain the size and causes of variability in the SJV and to determine its importance on long-term emissions. On average we find top-down emissions of 347 ± 46 Gg/yr in our sensitivity area in the central SJV, representing a scaling factor of 125 ± 17% on CALGEM's emissions in the area. These average emissions were also found to fall within the uncertainty ranges of previous top-down and bottom-up inferences.
Given the importance of the SJV region for statewide CH 4 emissions, our study underscores the need for longer term and more varied measurements of CH 4 emissions in the SJV to fully characterize the factors controlling its emissions. In particular, reanalysis of existing long-term measurements such as the decade long XCH 4 record from the GOSAT satellite and the CARB in-situ tower network could provide further insight into controls on emissions in the SJV. Further analysis at the individual dairy facility scale would also be useful for resolving questions about controls on emissions. Our analysis also demonstrates that the EM27/SUN instruments can constrain regional emissions to a relatively good accuracy compared to other techniques and suggest that they can play a role in further studies of CH 4 emissions in the SJV.

Data Availability Statement
The EM27/SUN retrievals used in this study and the STILT footprints are available at https://osf.io/gnfb4/.