The first nadir retrievals of NH3, obtained using a prototype retrieval with data from the TES instrument (Beer et al., 2008), exploited the NH3 ν2 vibrational band between 960 and 970 cm-1 to demonstrate that TES could measure the variability in NH3 along a transect in China. Shephard et al. (2011) implemented a full optimal estimation (OE) approach (Rodgers, 2000), which sought to reduce the difference between the measured CrIS radiances in the ν2 band and the calculated radiances from a radiative transfer model (Moncet et al., 2008). Before the OE algorithm was run, an a priori profile was chosen from one of three possible profiles (Fig. S1 in the Supplement), representing background, moderate and enhanced NH3 concentrations. These profiles were derived by binning global distributions of NH3 (Shephard et al., 2011) from the chemical transport model GEOS-Chem (Zhu et al., 2013). The profile is selected by applying an online/offline brightness temperature (BT) difference test centered around the 967 cm-1 line. The OE algorithm is then run as a refinement step, in which the a priori and the initial guess profiles are identical except for the background profile, for which the moderate profile is chosen as the initial guess, in order to provide Jacobians with some sensitivity.

The algorithm developed for the TES NH3 retrievals has since been adapted with minor changes for CrIS (Shephard and Cady-Pereira, 2015; Shephard et al., 2020) and AIRS (this paper). The spectral retrieval window and the frequencies for the online/offline BT test were slightly modified for the CrIS and AIRS spectral resolutions, and a preliminary retrieval step to adjust the surface temperature and emissivity was introduced. This algorithm forms the core of the NH3 component of the MUSES software used here and also of the CrIS Fast Physical Retrieval (CFPR) code, whose product has been used in a number of previous studies (e.g., Shephard and Cady-Pereira, 2015; Dammers et al., 2017; Shephard et al., 2020; Cao et al., 2022; Marais et al., 2021). The two products have much in common (the same spectral microwindows, a priori selection, constraint matrices and forward model), but obtain temperature and water profiles and surface properties from different sources and use different software to carry out the optimal estimation (Table S2 in the Supplement). Preliminary comparisons have shown good agreement on average between the two algorithms (Fig. S2), but a full comparison is beyond the scope of this paper, as the objective here is the validation of the MUSES AIRS and CrIS NH3 retrievals.

The MUSES algorithm is an end-to-end optimal estimation process that provides a complete characterization of the parameters involved in the radiative transfer processes in the infrared region, using a multi-step approach. Before the NH3 retrieval step is reached, the atmosphere has been well characterized by the previous retrieval steps: temperature and water vapor profiles, surface properties and cloud absorption are thus known and can be accounted for in the NH3 retrieval, significantly reducing errors from radiatively interfering species. Other species, such as carbon monoxide and ozone, are also retrieved in separate steps. This ensures that the atmospheric state is derived using the same forward model and radiance data that are used in the NH3 retrieval, reducing possible sources of error. Since cloud optical depth is retrieved, cloud-clearing algorithms (Susskind et al., 2003) are not needed and retrievals can be performed on every pixel, or field of view (FOV), rather than on the 9-pixel field of regard (FOR). This allows for retrievals from AIRS with a 15 km rather than 45 km minimum footprint, which was the resolution for the earlier NH3 retrievals from AIRS obtained by Warner et al. (2016) using cloud-cleared radiances.

MUSES uses the optimal spectral sampling (OSS) model (Moncet et al., 2008) as its forward model; OSS is a fast and accurate radiative transfer method designed specifically for the modeling of radiances measured by sounding radiometers in the infrared, although it is applicable throughout the microwave, visible, and ultraviolet regions.

Since the retrieval is non-linear, an a priori constraint is used for estimating the true state (Bowman et al., 2006). If the estimated (retrieved) state is close to the actual state, then the estimated state can be expressed in terms of the actual state through the linear retrieval (Rodgers, 2000): 1x^=xa+Ax-xa+Gn+GKbb-ba, where x^ , xa, and x are the retrieved, a priori, and the “true” state vectors, respectively, G is the gain matrix, b is the vector that contains parameters not retrieved in the current step and ba the a priori values for these parameters if they are retrieved in another step.

The averaging kernel, A, describes the sensitivity of the retrieval to the true state: 2A=∂x^∂x=KTSn-1K+Sa-1-1KTSn-1K=GK, where Sn is the instrument noise covariance matrix, and Sa is the a priori covariance matrix for the retrieval. The Jacobian, K, is the sensitivity of the forward model radiances to the true state vector, K=∂L/∂x. The rows of A are functions with a finite width corresponding to the vertical resolution of the retrieved parameter. The sum of each row of A provides a measure of retrieval information that comes from the measurement (Rodgers, 2000) at the corresponding altitude, provided that the retrieval is quasi-linear. The trace of the averaging kernel matrix gives the number of degrees of freedom for signal (DOFS) from the retrieval.

The total a posteriori error covariance matrix Sx for a given retrieved parameter x^ is given by 3Sx=A-ISaA-IT+GSnGT+GKbSbGKbT, where Sb is the expected covariance of the non-retrieved parameters. The total error (or uncertainty) for a retrieved profile is expressed as the sum of: (i) the smoothing errors (first term on the right-hand side), i.e., the uncertainty due to unresolved fine vertical structure in the profile; (ii) the measurement errors (second term) originating from random noise in the spectrum; and (iii) the systematic errors (last term) due to uncertainties in the forward model parameters not retrieved in the NH3 step, some of which are constant and some of which change from retrieval to retrieval (Worden et al., 2006). The MUSES NH3 retrieval step includes the estimated errors in water vapor and temperature in the systematic errors. For the retrieved profiles used in this study the measurement error ranged from 3 % to 23 %, the systematic errors mainly from 1 % to 60 %, and the smoothing errors from 24 % to 130 %. Example retrieved profiles and corresponding errors are shown in Fig. S3. By providing the expected error covariance and the averaging kernels, this approach facilitates the use of the retrieved profiles in inverse modeling efforts, since both terms are used to weight the information coming from the retrieval. The error covariance gives users an uncertainty estimate for each retrieved profile, which can be utilized to screen the data or be included in a statistical analysis. Furthermore, the estimated uncertainty derived from the error covariance can be compared with measured uncertainties, obtained by calculating the spread of the differences between satellite and in situ data, as will be shown in Sects. 4.1 and 4.2; this analysis can indicate whether there are error terms missing from the optimal estimation formulation. Note that the estimated error cannot account for sampling errors, i.e., differences between the air masses sampled by the satellite and by the in situ instruments, or for sub-pixel variability.

Rodgers and Connor (2003) presented a method for comparing satellite profiles of trace gases with limited vertical resolution with in situ profiles obtained on a much finer grid. This approach is often described as “applying the instrument operator” or “applying the averaging kernel”. It attempts to estimate how the space-based instrument would “see” an in situ profile by applying the equation below to the in situ data: 4X=Xapriori+AXaircraft-Xapriori. The estimated profile X has been smoothed by the operator, simulating the smoothing due to the coarser resolution of the satellite observation. When X is compared with the satellite observations it is assumed that the smoothing error has been accounted for and can be ignored, which is not the case when satellite observations are compared directly with measured profiles; the remaining errors will be due to instrument noise and temporal and spatial sampling differences; the latter can be especially large for NH3, due to its large variability, as was discussed earlier. We will follow the Rodgers and Connor (2003) approach as described earlier, as it is the optimal method for taking into account the sensitivity of the instruments; however, as a way of introducing the data while also demonstrating the pitfalls of not considering the different vertical resolution of the satellite and aircraft data, we will also show simple differences between the aircraft and satellite data.

A note on applying the operator: AIRS and CrIS profiles extend to the top of the atmosphere, while the aircraft profiles used here rarely go above 700 hPa in California and 500 hPa in Colorado. We have extended the aircraft profiles by blending in the MUSES a priori profile above the top of the aircraft profile, then applied the instrument operator to these extended profiles.

The NASA DISCOVER-AQ (Crawford and Pickering, 2014) campaigns were designed to validate collocated satellite observations of atmospheric pollutants over four regions in the United States: (Maryland/Washington DC, California, Texas and Colorado), but NH3 was only measured in California and Colorado. Vertical profiles of NH3 were obtained by the PTR-MS instrument (Müller et al., 2014) deployed aboard the NASA P3B aircraft during the California campaign in January and February 2013 and in Colorado in July and August 2014. The P3B flight pattern was specifically designed for satellite validation: the aircraft flew repeated upward and downward spirals, typically 5 km wide connected by transects. An example trajectory, overlaid on the locations of CrIS NH3 retrievals, is shown in Fig. 1: the aircraft altitude is indicated by the colors, and the locations of the spirals are marked with letters. Note that the PTR-MS instrument samples the atmosphere at 1 Hz but the data in Fig. 1 were binned over 100 m to improve visibility. The estimated instrument uncertainty is 35 % (Müller et al., 2014). However, the PTR-MS NH3 data were a side product of the PTR-MS measurements during DISCOVER-AQ, which were designed to obtain data on volatile organic compounds (VOCs). NH3 is sticky and accumulates in the instrument inlet, slowing the instrument response. This effect leads to biases if the NH3 amounts are changing rapidly (Sun et al., 2015); when the aircraft is leaving the boundary layer on upward spirals, the instrument does not respond quickly enough to the sharp decrease in NH3 and overestimates the NH3 concentration; similarly, when entering the boundary layer on downward spirals, the response to the increase in NH3 is slow, and NH3 is underestimated (see Fig. 9 in Guo2021). Furthermore, the detection limits for NH3 were much higher than for the VOCs that were the primary target of the PTR-MS measurements: 7.0 ppbv in California and 3.0 ppbv in Colorado (Armin Wisthaler, personal communication, 2023). These limits imply that any aircraft observations below these values are effectively noise.

The USDA-ARS Northwest Irrigation and Soils Research Laboratory established a regional NH3 monitoring network in the Magic Valley region of south-central Idaho, USA, utilizing the NADP AMoN (Puchalski et al., 2015) network technology and protocols, but with much greater spatial density. The network measured ambient NH3 concentrations along two transects of the Magic Valley (north–south and west–east) utilizing passive diffusive NH3 samplers collected on a bi-weekly basis from February 2018 through December 2020. The objective of the project was to determine the spatial variability of ambient NH3 concentrations across the region, which is dominated by agricultural production and high-density dairy operations, to better understand the potential for NH3 transport within and downwind of the region.

DISCOVER-AQ in California took place during January and February 2013. The Central Valley is one of the strongest NH3 source regions in North America (e.g., Clarisse et al., 2009; Shephard et al., 2020), and this was reflected in the aircraft data, which registered near-surface amounts as high as 100 ppbv (Fig. 2a). There were thermal inversions over the entire period (Fig. 2b), which led to increased uncertainties in the retrieval, as they effectively created an emission layer above the surface, i.e., a layer that is warmer than the surface and therefore emits more than it absorbs. Inversions also limit the vertical extent of the boundary layer, with consequently lower NH3 concentrations at altitudes where the retrieval has greater sensitivity. Nevertheless, evaluating the AIRS and CrIS NH3 profiles against the aircraft data is a useful exercise, as the combination of inversions and strong sources is not a rare occurrence, and this analysis demonstrates both the capabilities and limitations of retrievals under these conditions.

A total of 43 AIRS and 58 CrIS profiles met the aforementioned co-location criteria. Before applying the instrument operator as described in Sect. 2.1, we directly compare the satellite data against the aircraft profiles (Fig. 3a and b). This is done to introduce the satellite data, and to demonstrate to users unfamiliar with the instrument operator the importance of accounting for the different vertical resolution of the remote and in situ instruments through the use of the operator. Both instruments showed large negative biases near the surface, as low as -80 ppbv for AIRS and -100 ppbv for CrIS, while the average bias at this level was ∼ -38 ppbv for AIRS and ∼ -44 ppbv for CrIS, with a spread of ∼ 24 and 38 ppbv, respectively (see Table 1). This large negative bias is likely due to a combination of sub-pixel heterogeneity (Sun et al., 2015; Kille et al., 2019), the inherent difficulties of carrying out retrievals over thermal inversions, and systematic and smoothing errors (due to the different vertical resolution). Note that the mean CrIS value at the surface (∼ 16 ppbv) is 60 % greater than the AIRS value (∼ 10 ppbv), while the reverse is true at 908 hPa (7.6 ppbv vs. 9.7 ppbv). This difference can be attributed to the greater number (24 out of 43) of moderate (green curves) or background (blue curves) a priori profiles selected by the MUSES algorithm for the AIRS retrievals, when compared with CrIS (4 out of 58). The moderate and background a priori profiles and constraints drive the retrieval to distribute NH3 more uniformly over the vertical range, rather than concentrating it near the surface. For either instrument the surface mean value is much lower than the PTR-MS mean (∼ 37 ppbv), consistent with the large biases noted earlier, although the CrIS mean value (∼ 16 ppbv) is just within the standard deviation of the PTR-MS data. Clouds are accounted for in the MUSES retrieval (Kulawik et al., 2006) and thus cloudy conditions should not significantly impact the NH3 retrievals. Both the bias and the spread drop significantly with increasing altitude, as do the measured concentrations; while the biases decrease, they become positive and are not insignificant at 825 hPa (∼ 30 % at 825 hPa), and the spread is quite large (∼ 100 %). However, at this level, which is above the mixed layer height (MLH) for all flight days, many of the aircraft observations are below the detection limit of the PTR-MS (see Fig. S5) and are thus highly uncertain.

Therefore it become impossible to make any quantitative statements about the differences between the satellite and aircraft data at these higher altitudes.

The sum of the rows of the averaging kernels (SRAK) (Fig. 4), which provides an estimate of the retrieved information at each level originating from the measurement rather than from the a priori, shows for both AIRS and CrIS that while the information from the radiance data peaks just below 700 hPa, it also significantly contributes to the retrieved surface values. This is driven by the structure of the covariance matrix (Sa). As noted in the introduction of the DISCOVER-AQ section, the DOFS for AIRS and CRIS NH3 ranged mostly between 0.8 and 1.0, signifying the retrieval provides only one piece of information, basically a column amount. By building off-diagonal correlations in a priori covariance matrix between the surface level and a few levels above, this information is vertically distributed in such a way that it restricts unphysical oscillations in the retrieved profile and deviations in the a priori profile shape. Each of the three a priori profiles is associated with a different covariance matrix. The enhanced a priori retrieval tends to load the profiles at the surface, while the moderate and background profiles push NH3 to the free troposphere. The maximum SRAK (∼ 1.2–1.3) is similar for both sensors, as is the mean SRAK at the surface (∼ 0.6). However, there is much greater variability in the AIRS SRAK, possibly due to higher instrument noise.

Applying the instrument operators following Eq. (4) (Fig. 5a and b, red and black curves) eliminates the smoothing error, which reduces the bias at all levels to close to or less than 1.0 ppbv (Table 1, top section), corresponding to roughly 1 % to 12 % at the surface, and increasing to 13 % to 25 % at 825 hPa, indicating that the large differences seen in the direct comparison are due mainly to the inability of the satellite instruments to resolve the fine vertical structure of the profile. The standard deviation is also reduced, especially at the lower levels, but is not eliminated, which suggests that other error sources are present. If instead the a priori profiles are compared with the aircraft data, we see a large negative bias near the surface (∼ -9 ppbv for AIRS and ∼ -18 ppbv for CrIS). This result demonstrates that the retrieval process adds significant information and reduces the a priori error.

A great benefit of the optimal estimation approach is that is provides both retrieved profiles and estimated errors. If these errors are lower than the error relative to the in situ or model data, they indicate that some error sources have not been accounted for in the retrieval. Here we compare the sum of the measurement and systematic errors from Eq. (3) (Fig. 6a and b, red and blue curves) against the measured uncertainties (the fractional standard deviation derived from the standard deviations of the differences in the “Satellite-Aircraft with AK” column in Table 1) (Fig. 6a and b, black curve), which have the smoothing error removed by the application of the averaging kernel, A. Since the measurement error is usually quite low (see Fig. S3 for examples) the estimated uncertainties are nearly equivalent to the systematic errors, and thus represent the estimate of the error in NH3 due to errors in temperature and water vapor. The average estimated uncertainties are below the measured uncertainties for both AIRS and CrIS, confirming that some error sources are not accounted for in the optimal estimation process.

A possible candidate is the sampling difference: AIRS and CrIS sampled three-dimensional columns, 15–50 km wide, while aircraft instruments sampled in two dimensions, vertically and along a spiral line with a 5 km width. Sub-pixel variability likely also contributes to these errors. The estimated uncertainties range in general from 5 % to 50 % at the surface, although five cases had significantly larger errors. At 850 hPa the variability in the uncertainties is much larger, ranging from 10 % to 250 %, strengthening the argument that it is not possible to carry out a meaningful comparison at this altitude or higher with this dataset.

Much of the work on validating NH3 from space-based infrared sensors has been done using IASI data, which provide total columns rather than profiles (e.g., van Damme et al., 2015a; Dammers et al., 2017; Guo2021), although Dammers et al. (2017) estimated IASI profiles by using two fixed vertical profiles to convert column amounts to profiles and thus to also obtain surface values. Guo2021 explored four approaches (see Fig. 5 in Guo2021) to account for the NH3 amount above the mixed layer height (MLH) and obtained the best agreement with IASI data by assuming zero NH3 above the MLH (R=0.57 and slope =1.0). This is a fairly reasonable assumption, since NH3 has a short lifetime (on the order of hours or days), and is rarely transported to the middle or upper troposphere, except during strong fires; it has been measured above the mixed layer, but at low levels (less than 1 ppbv; e.g., Höpfner et al., 2019; Nowak et al., 2010). Here we compare AIRS and CrIS total columns with aircraft total columns calculated following two approaches. First we used the zero NH3 above the MLH approach adopted by Guo2021. In this procedure the in situ NH3 total column is estimated by integrating the aircraft NH3 profile to the top of the mixed layer; above this level, NH3 amounts are assumed to be zero.

The MUSES total columns are compared against the integrated aircraft columns, using orthogonal linear regression (Fig. 7a and b), again colored by the choice of the a priori profile; the intercept has been allowed to vary, as both AIRS and CrIS have detection limits, (∼ 1.0 ppbv, for thermal contrast above 5 K), as does IASI (3.0×1015 molec. cm-2, for thermal contrast above 5 K). Note that in this approach the instrument operators have not been applied to the aircraft column data. The correlation coefficients are 0.58 for AIRS and 0.62 for CrIS, within the range of results from previous studies (e.g., Dammers et al., 2017), found correlations ranging from 0.28 to 0.81 when comparing surface FTIR and CrIS columns. However, the slopes are very much greater than 1 (1.9 for AIRS and 1.6 for CrIS), which was not the case in the IASI evaluation of Guo2021. If this assumption of zero amounts of NH3 above the mixed layer is no longer valid at the later (13:30 LST) CrIS and AIRS overpass times, the aircraft columns would be biased low with respect to CrIS and AIRS; the profile differences shown in Table 1 also suggest that AIRS and CrIS are measuring more NH3 above 910 hPa. Given the uncertainty in the aircraft measurements at these higher altitudes, it is not possible to currently determine the true NH3 amounts above the mixed layer.

In the second approach (Fig. 8) we calculate partial AIRS/CrIS columns by integrating the profiles to the MLH only. The results are interesting: the AIRS correlation (Fig. 8a) decreases (from 0.58 to 0.46), and the slope drops from 1.9 to 1.4. These changes occur because many of the columns decrease substantially (note large group of values below 1.0×1016 molec. cm-2). We found that these observations derive from profiles for which the retrieval selected a background or moderate prior. When a background or moderate prior is chosen, the retrieval distributes the NH3 differently than if the enhanced prior is used (see Fig. S3, two rightmost panels): in the moderate case the retrieval creates a profile that peaks around 900 hPa, while in the polluted case the peak is at the surface. By limiting the integration to the top of the MLH, a substantial fraction of the retrieved column from the AIRS observations is excluded for the profiles derived from the moderate prior. The slope of the CrIS comparison drops dramatically from 1.6 to 0.6, but the correlation actually increases slightly from 0.61 to 0.64. Visual inspection suggests that truncating the CrIS integration had a large impact on a few outliers but overall reduced most columns only slightly, since the bulk of the NH3 is below the MLH, and thus did not substantially affect the correlation. Both the AIRS and CrIS results demonstrate that the retrievals are showing a non-negligible amount of NH3 above the mixed layer, more so for AIRS than for CrIS, but at present it is not possible to determine whether these values are real, given the uncertainties in the aircraft data at these altitudes, or whether they are the result of redistribution of NH3 to higher altitudes driven by the a priori profile shape and error covariance.

DISCOVER-AQ Colorado took place during July and August 2014, in the Colorado Front Range. While this is also a region with strong NH3 sources, the aircraft data showed lower values than in the California Central Valley (Fig. 2c); maximum values are on the order of 20 ppbv, with most near-surface values ranging from 5 to 10 ppbv, above the uncertainty in the aircraft data, which was ∼ 3ppbv in the Colorado campaign. In contrast to the Central Valley there were no thermal inversions during this period (Fig. 2d) and the MLH was much higher, about 3 km (∼ 700 hPa) on average. Applying the co-location criteria yielded 46 AIRS profiles but only 34 CrIS profiles, in part due to some poor quality CrIS retrievals. Direct comparisons of the AIRS and CrIS profiles with aircraft data (Fig. 3c and d) show both AIRS and CrIS biased high by 3.8 ppbv (AIRS) and 3.4 ppbv (CrIS) near the surface (∼ 844 hPa) and by 2.2 ppbv (AIRS) and 1.9 ppbv (CrIS) at 825 hPa, but the bias is close to zero at 750 hPa. Note that this is in direct contrast to the California results, which showed both AIRS and CrIS NH3 biased very low at and near the surface and biased slightly high at greater altitudes. However, here too the mean AIRS (10.3 ppbv) and CrIS (9.8) surface values are within the standard deviation of the aircraft data.

The sum of the rows of the averaging kernel plots (Fig. 4c and d) present similar maximum and surface values as in California, and again applying the instrument operator reduced the bias to below 1.0 ppbv (∼ 10 %), but did not reduce the spread in the satellite–aircraft differences dramatically (Fig. 5a and b), while the large bias at the surface seen against the a priori profiles (∼ -12 ppbv for AIRS and ∼ -10 ppbv for CrIS) is removed by the retrieval, confirming again that the retrieval process provides information content beyond the a priori.

The uncertainty analysis (Fig. 6a and b) shows that in the region where both the satellite and aircraft observations are reasonably robust, the estimated uncertainty is quite close to the measured uncertainty below 700 hPa. Finally, the total column comparisons also indicate that the AIRS and CrIS NH3 (Fig. 7c and d) columns are correlated with the aircraft values (with correlation coefficients of 0.56 for AIRS and 0.42 for CrIS), but are biased high, most notably for CrIS, for which the regression presents a slope of 2.3. The AIRS total columns (Fig. 7c) and partial columns (Fig. 8c) are very similar, indicating the most of the retrieved NH3 is below the MLH; since all AIRS retrievals used the enhanced prior, which concentrates NH3 in the surface layer, this is to be expected. The CrIS partial columns (Fig. 8d) show marked reductions in the smaller column values, which increase the slope from 2.3 to 3.5, and reduce the correlation to 0.31. These smaller columns correspond to retrievals that used background or moderate a priori profiles, and, as was described in the California section, push NH3 higher up in the column, and are thus more sensitive to truncation. The fact the columns from the satellite instruments are much higher than the aircraft columns is possibly due to NH3 produced by fires and lofted above the MLH, which were not measured by the PTR-MS but would be detected by AIRS/CrIS and redistributed downward by the retrieval, leading to the high biases seen in the surface values before applying the instrument operator.

The USDA-ARS established and maintained an NH3 monitoring network along two transects (north–south and west–east) across the Magic Valley region of south-central Idaho during the period February 2018–December 2020 (Fig. 9). The Magic Valley region is heavily dominated by irrigated agriculture and is one of the most concentrated dairy production regions in the United States. Research in this region has reported that NH3 emissions from agricultural and dairy production contribute approximately 44 000 MT N yr-1 to the atmosphere (Leytem et al., 2021) and that NH3 emissions fluctuate by season following trends in temperature (Leytem et al., 2011, 2013). The network was established to gain a better understanding of the spatial variability of ambient NH3 concentrations and transport within the region. The network consisted of eight sampling locations (seven until 2020, when an additional site was added), and also utilized data from the NADP AMoN site located to the north of the region at Craters of the Moon National Monument. NH3 concentrations were measured with passive diffusive NH3 samplers (Radiello), which were deployed bi-weekly, and generated 2-week mean surface NH3 concentrations. Radiello samplers have been shown to be approximately 9 % biased low (Puchalski et al., 2015). These data provided a unique opportunity to evaluate the seasonal signals measured by CrIS NH3, as well as its capability to capture small-scale (on the order of a few kilometers) spatial variability.

CrIS SNPP NH3 data are available for most of the 2018–2020 period, with a gap in the spring of 2019 due to an instrument malfunction. Surface CrIS data within 15 km of each site were compared with the ground data at that site. Profiles with RMSE greater than 5.0 were excluded from the time series, as were clouds with COD greater than 1.0. Only the CrIS observations at ∼ 13:30 LST were analyzed. The NH3 retrievals at 01:30 LST have weaker signals (due to lower thermal contrast), and would add uncertainty to the results. While there are strong diurnal cycles in the NH3 emitted from the dairy facilities (Leytem et al., 2011, 2013) the average daily emissions and temperatures, which strongly control the emissions, are close to the early afternoon values. Ideally one would use measurements of the daily cycle in NH3 concentrations, to estimate the ratio between the concentration at 13:30 LST and daily mean concentrations, as was done by Pinder et al. (2011), but such data are not available for the Magic Valley site. Figure 10 shows the individual CrIS observations (small red triangles), the 2-week averages of the CrIS data (large red triangles connected with a red line) and the ground data (blue triangles) at each site.

The time series in Fig. 10 are sorted by the peak values of the ground data. At every site, CrIS clearly captures the seasonal cycle, although winter values are usually underestimated: this can be attributed to weak radiative signals due to low temperatures and low thermal contrast. The CrIS level of detectability is normally cited as ∼ 1.0 ppbv (Shephard and Cady-Pereira, 2015), but at low thermal contrast this level increases significantly. A few strong warm season peaks in the ground data are also not captured. At Craters of the Moon, a national monument, and at Rogerson, in land administered by the Bureau of Land Management, CrIS returns consistently higher values than the ground site during the warmer months (May to October). At present we have no definitive explanation for this high bias. At the next four sites (Glenns Ferry, Richfield, Lake Walcott and Kimberly), which are in areas of mixed agricultural activity, CrIS and the ground data are in good agreement during the warmer months, although CrIS underestimates the June 2018 maximum at the Kimberly site. At all four sites there is a peak in the ground data in November 2019 that is either matched in the CrIS data (Glenns Ferry) or at least visible (Richfield, Kimberly, Lake Walcott). This peak is also evident in the data from Paul and possibly Wendell, although the variability at this latter site makes it difficult to confirm. This suggests an area-wide change in meteorological conditions, such as an inversion, that led to increased NH3 near the surface: however, there is no evidence in the meteorological data for such an inversion. The last three sites (Paul, Jerome and Wendell) are close to and/or downwind of multiple dairies, which likely leads to greater sub-pixel inhomogeneity. CrIS underestimates the warm season maximum, and does not capture many of the peaks in the ground data, most notably at the Wendell site, where CrIS did not observe the peaks over 80 ppbv in 2018 and 2019.

Analyzing these data in aggregate, first spatially then temporally, provides some useful insights. Plotting the CrIS 2-week averages against all the ground data values (Fig. 11), and excluding CrIS data with cloud OD greater than 2.0, along with the data from the Wendell site, which are extreme outliers, shows a correlation of 0.6, at the high end of the values reported in the literature (e.g., see van Damme et al., 2015b, as noted in Introduction) and a slope of 0.66, indicating that CrIS NH3 is biased low overall. This result is in line with the low biases found in the surface values of the AIRS and CrIS California data, although here not necessarily caused by thermal inversions, and with the low biases in the CFPR results at high NH3 FTIR values seen by Dammers et al. (2017). It provides a quantitative measure of the agreement seen in the seasonal cycles shown in Fig. 10.

Three years of fairly dense data over a region with many sources with fixed locations are an excellent candidate for spatial oversampling algorithms, which trade temporal resolution for greater information on spatial variability. Here we applied the physics-based oversampling algorithm developed by Sun et al. (2018), which uses the instrument spatial response function to weight the contributions of each satellite observation to a fine grid (here 0.002∘), to each of the 3 years of CrIS data taken over the Magic Valley region (Fig. 12). The in situ data are overlaid on the CrIS maps; note that the Wendell values are shown in the upper-right corner of the maps, as otherwise they would distort the color scale; note also that the Jerome data are blank in 2018 and 2019, when this site was not operational.

The location of the CrIS NH3 “hotspots” and the gradients in NH3 are very consistent from year to year, although NH3 concentrations are lower in 2019, possibly due to the CrIS data gap between March and June. There is good qualitative agreement with the in situ data, with the exception of the Wendell site, which was discussed earlier. Moreover, the hotspots are very well correlated with the areas of high dairy density (Fig. 11, upper right). These maps illustrate the power of the CrIS data to provide context to in situ measurements and far more information on the spatial variability in NH3 than is normally available from emissions databases in the United States, which are frequently at county level. Data from these gridded maps could be used to constrain emission inventories over much larger areas and at more frequent intervals than is currently possible. This oversampling analysis demonstrates the utility of providing users with Level 2 products, since they then choose the sampling periods and resolution that are most appropriate for their purposes and are best suited to the times and regions under investigation. For example, a user might want to study the variability of NH3 over only the urban area of Mexico City (e.g., Herrera et al., 2022). Level 3 products provide no such flexibility.