Evaluation of single-footprint AIRS CH4 Profile Retrieval Uncertainties Using Aircraft Profile Measurements

We evaluate the uncertainties of methane optimal estimation retrievals from single footprint thermal infrared observations from the Atmospheric Infrared Sounder (AIRS). These retrievals are primarily sensitive to atmospheric methane in the mid-troposphere through the lower stratosphere (~2 to ~17 km). We compare to in situ observations made from aircraft during the Hiaper Pole to Pole Observations (HIPPO), the NASA Atmospheric Tomography Mission (ATom) campaigns, and 20 from the NOAA ESRL aircraft network, between the surface and 5-13 km, across a range of years, latitudes between 60 S to 80 N, and over land and ocean. After a global, pressure dependent bias correction, we find that the land and ocean have similar biases and that the reported observation error (combined measurement and interference errors) of ~27 ppb is consistent with the standard deviation between aircraft and individual AIRS observations. A single measurement has measurement (noise related) uncertainty of ~17 ppb, a ~20 ppb uncertainty from radiative interferences (e.g. from water, temperature, etc.), and ~ 25 30 ppb due to “smoothing error”, which is partially removed when making comparisons to in situ measurements or models in a way that account for this regularization. We estimate a 16 ppb validation error because the aircraft typically did not measure methane at altitudes where the AIRS measurements have some sensitivity, e.g. the stratosphere. Daily averaged AIRS measurements of at least 9 observations over spatio-temporal domains of < 1 degree and 1 hour have a standard deviation of ~17 ppb versus aircraft, likely because the observation errors from temperature and water vapor (for example) are only partly 30 reduced through averaging. Seasonal averages can reduce this ~17 ppb uncertainty further to ~10 ppb, as determined through comparison with NOAA aircraft, likely because uncertainties related to radiative effects of temperature and water vapor can be reduced when averaged over a season. https://doi.org/10.5194/amt-2020-145 Preprint. Discussion started: 8 May 2020 c © Author(s) 2020. CC BY 4.0 License.

396 QCLS CH4 profiles from the HIPPO campaigns. Using coincidence criteria of ±9 hours, ±50 km,22,271 AIRS observations were processed, of which 5537 passed quality flags. The latitude of the matches ranges from 57S to 81N.
We compare AIRS to observations from the ATom aircraft campaigns 1-4 (Wofsy et al., 2018). This comparison provides 100 validatation ~7 years after HIPPO, between 2016 and 2018. Similar to HIPPO, these observations include observations in the Pacific Ocean, but ATom also includes observations in the Atlantic (as seen in Table A.1 and Fig. 1). ATom methane data are reported on the WMO X2004A scale. We used 289 profiles from the ATom campaigns from the NOAA Picarro instrument (Karion et al., 2013).  Figure 1 shows the locations of all the aircraft data used for the comparisons described in this paper. Most of the ocean measurements are from the HIPPO and ATom campaigns that spans a range of latitudes, whereas most of the land 120 measurements are taken over North America.. compare them to models and independent data sets, while accounting for the regularization used for the retrieval. We follow the OE approach for the Aura TES instrument (e.g. Bowman et al., 2006;Worden et al., 2006Worden et al., , 2012 but with some differences. 130 First, methane retrievals using the TES radiances are obtained using only the 8 micron band, because of slight calibration differences between the detectors that measure the 12 and 8 micron bands (e.g. Shephard et al., 2008;Connor et al., 2011).
For the AIRS retrievals, we use both the 8 and 12 micron bands in order to better constrain temperature in the troposphere and stratosphere. Secondly, the TES based retrieval uses the ratio of a jointly-retrieved N2O profile to the CH4 profile in order to help correct biases related to temperature variations in the (UTLS) upper-troposphere lower-stratosphere (Worden et al., 2012). 135 However, the N2O correction is not used for the AIRS retrievals because we can jointly estimate temperature in the UTLS region using the 12 micron band. We use similar quality flags as the TES retrievals such as checks on the 2, residual signal, and cloud optical depth as discussed in Kulawik et al. (2006aKulawik et al. ( , 2006b, except that we screen out cloudy and low-sensitivity cases, resulting in about 1/4 of the data passing screening. The specific flags used for AIRS CH4 are as follows: 140 Good quality and sensitivity flagging for AIRS CH4: Radiance residual rms < 1.5. This screens off the standard deviation of the radiance residual (the difference between the observed and fit radiance normalized by the NESR). |Radiance residual mean| < 0.15. This screens off the mean difference of the radiance residual. |KdotdL| < 0.23. This screens off the dot product of the Jacobians and the radiance residual and indicates that there 145 is little remaining information relative to the noise level about the surface and atmosphere in the retrieval TSUR < near-surface atmospheric temperature value + 30K. This ensures that the thermal gradient is less than 30K.
Cloudtop pressure > 90 hPa. This ensures that the retrieved cloudtop is not above 90 hPa.
Cloud OD < 0.3. This ensures that the cloud is not opaque and there is sensitivity below the cloud.
Cloud variability versus wavenumber < 1.5 * cloud OD. This ensures that the cloud optical depth does not vary too 150 much with wavenumber.
Degrees of freedom > 1.1. This ensures a minimum sensitivity.
Tropospheric degrees of freedom > 0.7. This ensures a minimum Tropospheric sensitivity.
Stratospheric degrees of freedom < 0.5. This ensures that there is not too much sensitivity in the stratosphere.
Predicted error on the column above 750 hPa < 53 ppb. This ensures that the predicted error is not too large. 155

Retrieval Error Characteristics
Detailed descriptions of the use of optimal estimation (OE) to infer trace gas profiles from remote sensing radiance measurements retrieval is included in numerous publications (e.g. Rodgers, 2000;Worden et al., 2006;Bowman et al., 2006). However, we present a partial description here as it is relevant for comparing the AIRS methane retrievals and aircraft profile measurements. As discussed in Rodgers (2000), the estimate for a trace gas profile inferred (or inverted) from a radiance 160 spectrum is described by the following linear equation: https://doi.org/10.5194/amt-2020-145 Preprint. Discussion started: 8 May 2020 c Author(s) 2020. CC BY 4.0 License.
where x _is the estimate of Log(VMR), 〖x_ 〗_a^ is the log of the a priori concentration profile used to regularize the 165 inversion. We split x into [x,y], where x is the quantity of interest, the methane profile, and y are the jointly estimated quantities (such as temperature, water vapor, clouds, and surface properties), which results in the cross-state error (Worden et al., 2004;Connor et al., 2008).
For the AIRS (and TES) OE methane retrievals, xa comes from the MOZART atmosphere chemistry model (e.g. Brasseur et al., 1998). The vector x is the "true state", or in this case the (log) concentration profile. The matrix A is the averaging kernel matrix or =̂ and describes the vertical sensitivity of the measurement. The matrix G relates changes in the radiance (L) to perturbations in x, = . The vector n is the noise vector, the matrix K is the sensitivity of the radiance to changes in observed radiances. The true state, noise vector, and interference errors as described here are the "true" values and are therefore not actually known but are represented in this form so that we can calculate how their uncertainties affect the estimate ̂. An example averaging kernel matrix is shown in Figure 2 and shows that AIRS based estimates of methane are most sensitive to methane in the free-troposphere and lower-stratosphere as demonstrated previously for AIRS and other TIR based estimates of tropospheric methane (e.g. Xiong et al., 2016;de Lange and Landgraf, 2018). 180 Finally, we look at the quantity of interest, ̂ = hx. The vector h combines all the necessary operations that maps the (log) concentration profiles to whatever quantity is needed such as selecting one particular pressure level (e.g. h= [0,0,0,1,0,0,0, …], selecting a column average, (h = pressure weighting function)see Connor et al., 2008) or selecting the VMR mean (e.g. h=1/m, where m is the number of pressure levels to average). 185 In Eq. 3a, the vector ̂ (denoted in bold) is converted to the scalar of interest, ̂ (non-bold, italic). In our validation 190 comparisons, h is used to select 1) a specific pressure level that is measured by the aircraft, 2) the partial column average over the pressure levels measured by the aircraft, and 3) the partial column above 750 hPa.

Approach for Comparing AIRS measurements to aircraft profiles
A challenge in comparing the satellite-based AIRS measurements to aircraft data is that the aircraft will typically measure only a section of the atmosphere (e.g. the troposphere), whereas the AIRS measurements are sensitive, to varying degrees (see Fig.  195 2), to the entire atmosphere. To account for these differences, we divide the atmosphere into two parts x = [xc,xs]: where xc is the part measured by the aircraft (denoted c for airCraft), and xs is the part not measured by the aircraft (denoted s for Stratospheric): where the term Acs is the cross-term in the averaging kernel that describes the partial derivatives of the aircraft-measured levels (e.g. the troposphere) to the un-measured levels (e.g. the stratosphere).
One issue is that we do not actually have aircraft observations in the "s" part of the atmosphere, , which is used in the second term of Eq. 5a. We have aircraft observations in the "c" part of the atmosphere only, so we apply the Averaging 215 Kernel to this part of the atmosphere only: Equation 5a accounts for the AIRS smoothing error, whereas Equation 5b (the equation used in this work) only accounts for 220 the smoothing error from the part of the atmosphere measured by the aircraft profile. The difference from Eqs. 5a and 5b is discussed in Section 3.3. https://doi.org/10.5194/amt-2020-145 Preprint. Discussion started: 8 May 2020 c Author(s) 2020. CC BY 4.0 License.
The expected difference between ̂ (the measured AIRS value) and ̂ (the aircraft value with the AIRS Averaging kernel applied) is calculated from Eqs. 4 and 5b: 225 The matrix Sa term describes the a priori uncertainty of methane, interferents, or systematic parameters, which propagate into the error in the first 3 terms: (1) describes systematic error, e.g. due to spectroscopy and calibration; these likely 230 impart biases into the AIRS measurement which are characterized during validation, (2) describes the "cross-state error", the effect of jointly retrieved parameters like temperature onto methane, (3) describes the impact of the part of the atmosphere not covered by the aircraft on the measured section: this must be included because the AIRS measurement sees a combination of both parts of the atmosphere and cannot completely disentangle them. The final term, , is the measurement error, which is the propagation of radiance error into the retrieved parameters, and is , where is the 235 gain matrix and is the covariance of the radiance error, in our case, a diagonal matrix. The error covariances all represent fractional errors, in log(VMR). The error in ppb is approximately the fractional error times the methane value in ppb.
For the purpose of evaluating the AIRS methane measurement uncertainties and comparing the AIRS methane to aircraft in situ measurements we refer to the four terms on the right side of Eq. 6 as: 240   1) is the systematic error due to terms that are not accounted for in the retrieval state vector, such as spectroscopy and calibration; these terms are estimated by comparisons with the aircraft data. A pressure-dependent bias correction, described in Section 3.4, of approximately -60 ppb is used to correct this systematic bias.
2) , the "cross-state", which is included in the MUSES-AIRS methane estimate product files, and is the 245 propagation of temperature, water vapor, and cloud errors into AIRS. The errors in the retrieved temperature and water vapor at nearby location are correlated over short spatio-temporal scales, as described in Section 4, and so this error does not reduce with averaging nearby observations. However, monthly or seasonal averages reduces crossstate error, because systematic errors from temperature / water / cloud can be assumed to vary pseudo-randomly over larger time scales. We estimate this error as ~21 ppb (see next paragraph). 250

3)
is the "validation uncertainty" due to knowledge uncertainty of the stratosphere although this may also contain other levels that are also not measured by the aircraft. This is the smoothing error which cannot be removed from the comparisons because the aircraft does not make measurements at the "n" (not measured) levels. We estimate this validation error as ~16 ppb (see next section).

4)
, the "measurement" error, which is included in the AIRS methane estimate product files. The measurement 255 error is random and is expected to reduce as the inverse square root of the number of observations averaged. We estimate this error as ~18 ppb (see next paragraph) Figure 3 shows the predicted errors for the AIRS partial column matching the aircraft measurements. The measurement error (light green) is 18 ppb, the cross-state error is 21 ppb (red minus green in quadrature), and the total error for a single observation 260 (including smoothing error) is 41 ppb. The errors not shown in this plot are the validation error, estimated in the next section, and systematic error, which we remove with a bias correction in Section 3.4. ocean and land data; these differences show that model/model differences in the stratosphere can contribute significantly to the differences between AIRS and aircraft validation.

Estimating validation error due to aircraft not measuring the stratosphere
These differences provide an estimate for how knowledge error in the stratosphere projects to uncertainties in our methane retrievals. For example, this uncertainty varies with latitude, similar to the residual bias between the AIRS estimate and aircraft 280 (next section). Furthermore, the variability over small latitudinal ranges of 10 degrees or less suggests that the random part of the stratospheric error is smaller than this latitudinal variability. Our 16 ppb estimate for this error is similar to the 10 ppb estimate for the impact of stratospheric uncertainty on column estimates from aircraft profiles (Wunch et al., 2010). Appendix A shows further analysis of mean differences of AIRS minus aircraft for different profile extension choices.

Bias Correction 285
AIRS CH4 shows a persistent high bias of 25 to 90 ppb versus aircraft observations in Fig. 6. Previous studies using remotely sensed measurements suggest that a bias correction to the AIRS methane profile measurement must account for the vertical sensitivity (e.g. Worden et al., 2011). For example, in the limit where the AIRS measurement is perfectly sensitive to the vertical distribution of methane, the bias correction could be a simple scaling factor. However, in the limit where the AIRS measurement is completely insensitive (e.g. DOFS = 0.0) then the bias correction is zero. We therefore use the bias correction 290 approach described in Worden et al. (2011), which passes a bias correction through the averaging kernel to account for the AIRS sensitivity.
We use HIPPO-4 observations to set a bias correction which we then evaluate with the other HIPPO campaigns and NOAA aircraft network data. To set the bias, we use Eq. 5 to estimate the aircraft observation as seen by AIRS, then compare this to 295 AIRS observations. The result (by pressure level) is shown in Table 1. Then a bias was applied to AIRS using Eq. 7, with the bias term in the form of Eq. 8. 300 Where ln() is the natural log, because the retrieved quantity is ln(VMR). We fit a single bias function for all AIRS measurements by minimizing the difference between the AIRS and HIPPO-4 with δ_bias constrained to have a slope with pressure, and two pressure domains. We specify that δ_bias cannot jump more than 0.05 (5%) between the two domains.
= + (P > Po) 305 where P is pressure in hPa. The optimized bias correction parameters were: c = 0.0; d = -6.1e-5; Po=400 hPa; e=-0.09; f=0.00018. This bias correction results are shown for HIPPO-4; HIPPO-1,2,3,5; and NOAA observations in Table 1. The remainder of the paper, unless specified, uses data bias-corrected by Eqs. 7 and 8. 310 Figure 5 shows the effect of bias correction on the average of all HIPPO 1,2,3,5 AIRS profiles. The bias correction improves the mean AIRS / aircraft difference and improves the pressure-dependent skew in the bias (Table 1). The HIPPO data is shown before and after the AIRS averaging kernel is applied (using Eq. 5), which has the effect of bringing the HIPPO observations towards the AIRS prior. This is to match the imperfect sensitivity of satellite-based observations, which are 315 similarly influenced by the prior.  Figure 6 shows a comparison between all AIRS measurements within 50 km and 9h of an aircraft measurement for the partial column measured by the aircraft. There is a mean bias of 57 ppb overall, ~56 ppb for ocean and ~64 ppb for the land. The 320 RMS difference is ~27 ppb. Furthermore, there appears to be latitudinal variations in the bias. For example, the mean difference between the AIRS and aircraft over the ocean for latitudes less than 20 S is ~74 ppb and for latitudes between 20 S and 20 N this bias is ~ 56 ppb. Figure 7 shows the same comparisons as Fig. 6 after bias correction (described in Section 3.4). The mean bias is 1 ppb, and 325 the RMS difference is 24 ppb. The overall land bias is 13 ppb, and the overall ocean bias is 1 ppb (shown in Table A.1). Note that the HIPPO land observations are primarily in Australia, New Zealand, and North America, whereas the ocean comparisons are in the mid-Pacific, as seen in Fig. 1. We expect the RMS difference to be similar to the observation error, as the terms that make up the observation error are the primary source of variability in the observations (e.g. Worden et al., 2017b). The predicted observation error from Fig. 3, is 27 ppb, and is consistent with the RMS difference seen here, 24 ppb. However, 330 knowledge of the stratosphere / validation error is potentially a large component of the latitudinal variability in the difference seen in the bottom panel of Fig. 7.
We also compare to NOAA aircraft network and ATom observations and find similar results as HIPPO. Figure 8, discussed in Section 4.2, shows ATom results, and Figure 9, discussed in Section 4.2, shows comparisons to a NOAA aircraft time series. 335 The biases for different pressure ranges, campaigns, and surfaces is shown in

Errors in averaged AIRS data
Satellite data are typically averaged in order to improve the precision of a comparison between data and model. However, as shown in the previous figure, these data contain errors that vary with latitude. For example, knowledge error of the true profile 340 in the stratosphere as well as errors in the jointly retrieved AIRS temperature and water vapor retrievals have both a random and a bias component, both of which vary with latitude. The bias component is approximately the same for all AIRS methane measurements taken at roughly the same location and time as we do not expect large variations in temperature and water vapor errors over these scales. To quantify the component of the accuracy that cannot be reduced by averaging, we compare averages of AIRS measurements to HIPPO and ATom measurements. We average the daily matches, which contain at least 9 AIRS 345 observations matching a single HIPPO or ATom measurement, within +-50 km of the measurement. The number of AIRS observations averaged ranges from 9 to 53 and averages 20. We specify that there needs to be at least 9 AIRS observations for each comparison so that the systematic error, and not the precision (or measurement error) , is the dominant term. Figure 8 https://doi.org/10.5194/amt-2020-145 Preprint. Discussion started: 8 May 2020 c Author(s) 2020. CC BY 4.0 License.
shows the average predicted error, assuming that the error is random, e.g. if 20 observations were averaged, this would equal 24 / √20 ppb or ~ 5 ppb. The standard deviation between the averaged AIRS and HIPPO or ATom data is ~17 ppb. Note that 350 same-colored adjacent points (i.e. adjacent observations from the same campaign) often show similar biases. Because this RMS difference is much larger than what is expected if the errors were purely random, this shows the presence of systematic errors, either in the AIRS data or in the validation error. We therefore report 17 ppb as the limiting error when averaging AIRS data within one-degree grids and 1 day for the purpose of comparing to models or other methane profiles.

355
On the other hand, averaging AIRS data seasonally can reduce the error further because geophysical errors from as temperature and water vapor vary over longer time scales. We demonstrate this aspect of the AIRS uncertainties by comparing averaged AIRS data to the NOAA aircraft methane profiles taken off the coast near Corpus Christi, Texas (27.7N, 96.9W, site TGC).
We screen for at least 3 observations per day, less than the 9 observations/day used for HIPPO / ATom daily averages in order to get enough daily averages to explore how the errors reduce with monthly and seasonal averages, since the aircraft make 1-360 2 measurements per month. Figure 9 shows daily, monthly, 90-day, and seasonal averages of the partial column matching the aircraft measured column at TGC. The seasonal averages are created by converting all AIRS/aircraft matched pairs to 2012 by adding 5.4 ppb per year multiplied by (year minus 2012), then averaging all values within each month. Similarly to the findings for HIPPO and ATom, the daily error is much larger than predicted from the observation error with the assumption of randomness. The standard deviation of AIRS minus aircraft at TGC is 24 ppb (for single AIRS observation, not shown), 365 11.5 ppb (for daily AIRS average, (Figure 9a)). The predicted error with the assumption that the error is random, is 6.0 ppb. Therefore, similarly to the ATom and HIPPO findings, the errors within small geophysical region are correlated and do not average as the square root of the number of observations. However, next, we try averaging multiple days within 1 month, and find a standard deviation of for monthly averages of at least 2 days of 8.2 ppb (Figure 9b), and the standard deviation of 3month averages containing at least 3 days, 6.2 ppb (Figure 9c). These agree with the predicted errors of 8.0 and 6.0 ppb, 370 respectively, by taking the daily standard deviation (11.5 ppb) and dividing by the square root of the number of days averaged.
The seasonal cycle average, which is a monthly average of all matched pairs from any year, has a standard deviation of 5.9 ppb, whereas the predicted error, from the daily average divided by the square root of number of observations, is 4.2 ppb.
Appendix A, Table A.3 shows the standard deviation for all NOAA ESRL stations, for ocean and land AIRS observations. 375 The ocean vs. land observations show similar values, with land and ocean standard deviations within 2 ppb. A single land observation has a standard deviation versus aircraft observations of 23 ppb for the partial column, in agreement with predicted observation error of 23 ppb. The standard deviation for daily observations is 15.2 ppb, whereas the predicted error, using 23 ppb divided by the square root of the number of observations averaged, is 5.9 ppb, indicated correlated errors when averaging nearby observations. The monthly standard deviation is 10.9, in reasonable agreement with the predicted of 9.4 ppb, from the 380 daily average standard deviation divided by the number of observations averaged. The seasonal cycle average, which is a monthly average of all matched pairs from all years, has a standard deviation of 7.7 ppb, which is similar to the predicted error https://doi.org/10.5194/amt-2020-145 Preprint. Discussion started: 8 May 2020 c Author(s) 2020. CC BY 4.0 License. of 6.9 ppb, from the daily average divided by the square root of number of observations. We find that estimating the error as the daily standard deviation divided by the square root of the number of days averaged is a reasonable estimate of the actual error. 385

Discussion and Conclusions
We validate single-footprint AIRS methane by comparing 27,000 AIRS methane retrievals to 396 aircraft profiles from the HIPPO campaign, 719 profiles from the NOAA ESRL aircraft network, and 289 aircraft profiles from the ATom campaign, taken across a range of latitudes, longitudes, and times. The AIRS methane retrievals are derived using the MUSES optimal estimation algorithm that has previously been applied to Aura TES radiances (e.g. Fu et al., 2013). After adjusting the aircraft 390 profile to account for the AIRS sensitivity (using the averaging kernel and a priori profile), we compare the mean methane value over the aircraft profile to the mean methane from the AIRS profile over the same altitude (or pressure) range. We use a subset of validation data to derive a pressure-dependent bias correction on the order of -60 ppb, and test this on an independent set of validation data. After the bias correction, we report a bias of 0 +/-10 ppb. The bias between AIRS and aircraft varies with pressure and location, as seen in Appendix A. 395 After applying the bias correction, from Eq. 7 and 8, the RMS difference between the AIRS and aircraft data of the partial column matching the aircraft of ~22 ppb is consistent with the mean observation error, composed of random error from noise and the cross-state errors from jointly retrieved temperature, water vapor, clouds, and surface parameters that are projected onto the AIRS methane retrieval. The extent to which the aircraft profiles used here can be utilized as "truth" for the purposes 400 of validation is limited by knowledge of the methane profile above the aircraft profile (referred to here as "validation error", which limits our knowledge of "truth" to within about 16 ppb. This uncertainty is consistent with the location-dependent bias in the satellite/aircraft comparisons which can vary by ~10 ppb. We quantify the AIRS minus validation standard deviation for single observations, daily averages (within 50 km of the 405 validation location), monthly averages, and seasonal averages for data bias corrected using Eqs. 7 and 8. The AIRS minus validation standard deviations are: 24 ppb (single AIRS footprint), 17 ppb (daily AIRS averages within 1 degree latitude and longitude), 10 ppb ("monthly" AIRS averages), 9 ppb (3-month AIRS average), and 7 ppb (seasonal cycle average). The errors on averaged AIRS data are likely an upper bound on the AIRS error, due to the uncertainty in the validation. The singlefootprint and daily average standard deviations for different pressure ranges and surface types are shown in Appendix A. We 410 recommend using the standard deviations in this paragraph as the error budget for the specified averaged quantities.

Appendix A: Biases and standard deviations for different stations, campaigns, pressures, and surface types
We characterize the bias versus validation data by station, campaign, and pressure level. Table A.1 shows biases versus validation data, after bias correction with Eq. 7. In the HIPPO comparisons, the biases are generally smaller than about 10 420 ppb. There is no overall pattern in the bias by season. The land data is biased higher than ocean for HIPPO comparisons (about +20 ppb). However, note that the land observations versus HIPPO are primarily in Australia and New Zealand, whereas the ocean comparisons are in the mid-Pacific.
The NOAA aircraft network comparisons are sorted by site. Many NOAA aircraft locations are at land/ocean interfaces, 425 allowing a more direct comparison of the land/ocean biases. On average, the AIRS land observations are 0-5 ppb higher than AIRS ocean observations at the different pressures and pressure ranges. The overall bias of AIRS versus NOAA aircraft is +7.1 ppb, whereas AIRS versus HIPPO is 4.4 ppb for the partial column matching the aircraft observations. This is consistent with AIRS land having a high bias versus ocean of 0-5 ppb.
The standard deviation of the bias for the different campaigns is a useful quantity as it is an indication of systematic error. The 430 standard deviation of the bias varies from 4 ppb to 9 ppb for the different pressures and campaigns. error for the daily average is the observation error divided by the square root of the number of observations, and is much smaller than the actual standard deviation, indicating correlated errors. The predicted error for the monthly, 3-month, and seasonal cycle averages is the daily standard deviation divided by the square root of the number of days averaged and ~agrees with the actual standard deviation for the partial column. The location-dependent biases are subtracted from AIRS prior to calculating the standard deviation in all but the last two rows. The last two rows shows the standard deviations without subtracting the location-dependent biases, which increases the partial column standard deviation from about 8 ppb to about 9 ppb.
Author contributions: SSK and JRW are responsible for the study design, data analysis, and manuscript writing; VHP was responsible for data analysis and manuscript editing; DF was responsible for implementing AIRS into the MUSES retrieval 450 system; SCW and BCD were responsible for HIPPO Picarro CH4 data; KM and CS were responsible for the ATom Picarro