Bias Correction of the Ratio of Total Column CH₄ to CO₂ Retrieved from GOSAT Spectra

Abstract

The proxy method, using the ratio of total column CH₄ to CO₂ to reduce the effects of common biases, has been used to retrieve column-averaged dry-air mole fraction of CH₄ from satellite data. The present study characterizes the remaining scattering effects in the CH₄/CO₂ ratio component of the Greenhouse gases Observing SATellite (GOSAT) retrieval and uses them for bias correction. The variation of bias between the GOSAT and Total Carbon Column Observing Network (TCCON) ratio component with GOSAT data-derived variables was investigated. Then, it was revealed that the variability of the bias could be reduced by using four variables for the bias correction—namely, airmass, 2 μm band radiance normalized with its noise level, the ratio between the partial column-averaged dry-air mole fraction of CH₄ for the lower atmosphere and that for the upper atmosphere, and the difference in surface albedo between the CH₄ and CO₂ bands. The ratio of partial column CH₄ reduced the dependence of bias on the cloud fraction and the difference between hemispheres. In addition to the reduction of bias (from 0.43% to 0%), the precision (standard deviation of the difference between GOSAT and TCCON) was reduced from 0.61% to 0.55% by the correction. The bias and its temporal variation were reduced for each site: the mean and standard deviation of the mean bias for individual seasons were within 0.2% for most of the sites.

1. Introduction

Atmospheric methane (CH₄) is the most significant anthropogenic greenhouse gas after carbon dioxide (CO₂) and is emitted from both anthropogenic and natural sources. Satellite observation, which can obtain data over wide areas, is effective to elucidate the CH₄ budget over the globe. In the last 15 years, the column-averaged dry-air mole fraction of methane (XCH₄) has been retrieved from the spectra of the backscattered Short-Wavelength InfraRed (SWIR) sunlight measured by sensors onboard satellites [1,2,3,4,5,6]. Satellite-derived XCH₄ data have been applied to the inverse modeling of CH₄ sources and sinks [7,8,9,10,11]. High precision and small bias in spatiotemporal variation are required for the XCH₄ data to be used in inverse modeling [12,13]. It is possible that even a small regional bias (0.5%) in the XCH₄ data can lead to significant errors in regional source and sink estimation [12]. Optical path length modification due to the light scatterings by aerosols and clouds is a large source of error for the satellite-based SWIR retrievals [14,15,16]. The degree of optical path length modification depends on the abundance, optical properties, and vertical distributions of aerosols and clouds and the reflectance of ground surfaces.

Two retrieval methods have been used to reduce systematic biases due to atmospheric scatterings: the full-physics method and the proxy method. In the full-physics method, the existence of aerosols is described in the forward model, and the aerosol-related parameters are simultaneously retrieved with the gas abundance [17,18]. In the proxy method, information on the optical path length modification for the CH₄ absorption band is obtained from that for the adjacent CO₂ absorption band [2] (Equation (1)),

$${\mathrm{XCH}}_4=\frac{{\mathrm{XCH}}_{4,\mathrm{clr}}}{{\mathrm{XCO}}_{2,\mathrm{clr}}}\times {\mathrm{XCO}}_{2,\mathrm{mdl}},$$

(1)

where XCH_4,clr and XCO_2,clr are XCH₄ and XCO₂ retrieved under a clear-sky assumption (no aerosols and clouds are assumed) and XCO_2,mdl is XCO₂ from the numerical model. It is assumed that, in the ratio component (XCH_4,clr/XCO_2,clr), the impacts of aerosol and clouds cancel each other out between XCH_4,clr and XCO_2,clr. It is also assumed that the relative variation of XCO₂ is much smaller than that of XCH₄, and that XCO₂ is well represented by the numerical model. The proxy method is expected to offer a larger amount of useful retrieved data than the full-physics method, since highly cloud- and aerosol-loaded scenes are difficult to handle in the current full-physics algorithms [19,20,21,22].

Both errors in the ratio component and the model XCO₂ lead to errors in the resulting XCH₄. Butz et al. [23] showed that the scattering-related errors are not perfectly canceled out in the ratio component depending on atmospheric and ground surface conditions (i.e., cirrus and aerosol load and surface albedo). Schepers et al. [19] discussed the possibility that the temporal variation of bias in proxy XCH₄ corresponds to that of bias in the ratio component. In the case of inverse modeling, Parker et al. [24] suggested that it is beneficial to use the ratio component with each own XCO₂ model that is consistent with the XCH₄ model used in the inversion. The ratio component can also be directly inverted [25,26,27]. The ratio component derived from the Greenhouse gases Observing SATellite (GOSAT) data has been validated by comparing it with that derived from the Total Carbon Column Observing Network (TCCON) data [19,24,26,28,29]. However, it has not been fully investigated what range of cloud and aerosol load permits the canceling out of scattering-related errors in the ratio component. In general, the criteria for the cloud and aerosol screening have been chosen by the algorithm developer. Scattering-related errors are expected to remain and to cause bias in the resulting XCH₄, especially when relaxing the data-screening criteria, although this increases the data throughput. Bias corrections of the proxy-based XCH₄ have been conducted; however, a simple linear relationship between the bias and the surface albedo [30] and a simple global bias correction [29,31] have been used.

The present study sought to characterize the bias in the GOSAT ratio component and develop a method for correcting the bias while considering the atmospheric scattering effects. GOSAT has been operating for more than 10 years, allowing us to investigate the variation of the bias with time and space and its factors. The ratio component derived from TCCON data was used as the ground truth. In Section 2, the data used and its processing are described. In Section 3, the relationship between the bias and the related variables derived from GOSAT data is investigated. In Section 4, the bias correction is conducted based on the results of Section 3, and the corrected results are evaluated.

2. Materials and Data Processing

2.1. GOSAT Data

GOSAT was launched on 23 January 2009 and is on a sun-synchronous orbit at 666 km altitude with 3-day recurrence and a descending node around 13:00 local time. It is equipped with two instruments: the Thermal And Near-infrared Sensor for carbon Observation–Fourier Transform Spectrometer (TANSO-FTS) and the Cloud and Aerosol Imager (TANSO-CAI). The TANSO-FTS has three bands in the Short-Wavelength InfraRed (SWIR) region (an O₂ A band, a weak CO₂ absorption band, and a strong CO₂ absorption band (Bands 1, 2, and 3) centered at 0.76, 1.6, and 2.0 μm, respectively) and records two orthogonal polarization components (hereafter called P/S components). For the signal processing of the TANSO-FTS, the amplifier gain level can be controlled at different levels, high (H) and medium (M), according to the brightness of the target. Gain M is used over bright surfaces such as the Sahara and central Australia. The instantaneous field of view (IFOV) of the TANSO-FTS is 15.8 mrad, which corresponds to a circular surface footprint of about 10.5 km in diameter at nadir. The TANSO-FTS L1B product (radiance spectral data) version V210.210 was used in the present study. We used spectra acquired from April 2009 to December 2018. The sensitivity degradation of the TANSO-FTS was corrected using a radiometric degradation model that is based on the on-orbit solar calibration data [32]. The P and S polarization components of the observed spectra were synthesized to produce a total intensity spectrum [5]. The TANSO-CAI is a push-broom imager and has four narrow bands in the near-ultraviolet to near-infrared regions centered at 0.38, 0.674, 0.87, and 1.6 μm with spatial resolutions of 0.5, 0.5, 0.5, and 1.5 km, respectively, for nadir pixels. The TANSO-CAI L2 cloud flag product (integrated clear confidence level for each TANSO-CAI pixel) version V02.00 was used in the present study. The integrated clear confidence level expresses the cloudy area with 0, the clear area with 1, and the ambiguous area with a numerical value between 0 and 1 [33].

2.2. Retrieval

The spectral windows of 1.626–1.695 μm and 1.567–1.618 μm within the TANSO-FTS Band 2 were used to retrieve XCH_4,clr and XCO_2,clr under the clear-sky assumption, respectively, using the same retrieval scheme as in the NIES TANSO-FTS L2 SWIR full-physics retrieval [5,21,34]. The atmospheric column was divided into 15 layers from the surface to 0.1 hPa with a constant pressure difference, and the average gas concentration for each layer was retrieved. As an indicator of optical path length modification, the surface pressure (P_srf) under the clear-sky assumption was also retrieved from the TANSO-FTS Band 1 spectra. The state vector for the retrieval of each band also included the surface albedo and the wavenumber dispersion. The surface albedo was retrieved at several wavenumber grid points within each band (CH₄, CO₂, and O₂ A) [5]. The mean value was calculated for each band and was used in the following analysis. Data satisfying all the following criteria were used for the subsequent analysis: (1) several data-quality flags stored in the TANSO-FTS L1B product and spectrum quality check utilizing the out-of-band spectra [34] are set as OK; (2) the solar zenith angle is <70°; (3) the land fraction of the TANSO-FTS footprint is ≥60%; (4) the mean squared value of the residual spectrum of the CO₂ band is ≤4; and (5) the degree of freedom for signals (DFS) is ≥1 for both XCH_4,clr and XCO_2,clr.

2.3. Variables for Explaining the Bias in the Ratio Component

Butz et al. [23] evaluated the accuracy of the ratio component and analyzed the error sources (the reasons why the scattering-related errors were not canceled in the ratio component) using simulated satellite measurements. They used cloud-free aerosol-loaded and cirrus-loaded scenes that were assumed to be the targets of the full-physics method. They showed that the primary sources of error were the difference in surface albedo between the CH₄ band and the CO₂ band and the difference in the retrieval sensitivity to scattering effects at each height level between these bands. The impact of these sources is expected to vary according to the amount and vertical distribution of the scattering materials.

In the studies validating the ratio component derived from the actual GOSAT data [19,24,26,28], the cloud screening was conducted using the cloud fraction within the IFOV of the TANSO-FTS provided by the TANSO-CAI onboard GOSAT. The TANSO-CAI is prone to fail to detect optically thin cirrus clouds [35]. In several studies (e.g., [19]), cirrus-loaded scenes were screened out using the information from the TANSO-FTS 2 μm band. More specifically, if the TANSO-FTS signal level at the strong water vapor absorption channels exceeds the noise level, elevated scattering materials (mainly cirrus cloud) are expected [5,36]. However, it has not been fully addressed how well the cloud fraction and the 2 μm band signal are related to the bias in the ratio component (i.e., the systematic difference between GOSAT and TCCON). Therefore, we investigated the variation of the bias with the cloud fraction and the 2 μm band signal. The cloud fraction (f_c) was defined as the ratio of TANSO-CAI pixels with an integrated clear confidence level lower than 0.33 and all TANSO-CAI pixels within the TANSO-FTS IFOV in this study. The TANSO-CAI tends to identify the pixels over snow and ice surfaces as cloudy pixels. Thus, we calculated the Normalized Difference Snow Index (NDSI = (ρ_O2 − ρ_CH4)/(ρ_O2 + ρ_CH4), where ρ_O2 and ρ_CH4 are the retrieved surface albedo for the O₂ A band and the CH₄ band, respectively), and used data having NDSI ≤ 0.4 for investigating the relationship between the bias and f_c. The threshold value of 0.4 was empirically determined (Figure S1). The radiance at the strong water vapor absorptive channels normalized with its noise level in the TANSO-FTS Band 3 (I_2μm) was calculated in a manner similar to [5,34].

In the bias correction of the proxy method, possible error sources (e.g., those indicated by Butz et al. [23]) have hardly been considered. The correction has been conducted based on the relationship between the bias and the retrieved surface albedo [30] and by a simple global bias correction [29,31]. The bias in the ratio component has also been corrected using the surface albedo [26]. Then, we investigated the relationship between the bias in the ratio component and the related variables while considering f_c and I_2μm. For the related variables, the difference in the surface albedo between the CH₄ and CO₂ bands, the surface albedo, the vertical profile of CH₄ and CO₂, the airmass, and the deviation of the clear-sky surface pressure from its prior value were considered. The details of the variables are described below.

The differences in surface albedo and the vertical profile have been revealed as important error sources [23]. For the difference in surface albedo, the retrieved albedo values (ρ_CH4 and ρ_CO2) were used (Δ_alb = ρ_CH4 − ρ_CO2). Albedo itself (ρ_CH4) was also used, since it has been used to explain the bias of the proxy method [26,30] and the full-physics method [37]. For the vertical profile, the partial column-averaged dry-air mole fractions were calculated for Layers 1–7 (upper atmosphere, 0–0.47P_srf hPa (XCH_4,upper and XCO_2,upper)) and for Layers 12–15 (lower atmosphere, 0.73P_srf–P_srf hPa (XCH_4,lower and XCO_2,lower)). See Section 2.2 for the definition of layers. The range of the calculation (1–7 layers and 12–15 layers) was decided by considering the averaging kernel (Figure S2). It is well-known that the SWIR retrieval has a slight sensitivity to the detailed profile but has a known sensitivity to the lower atmosphere (e.g., [38]); therefore, the ratios (R_CH4 = XCH_4,lower/XCH_4,upper and R_CO2 = XCO_2,lower/XCO_2,upper) were used to represent the characteristics of the vertical profile. Airmass is expected to be related to the impact of optical path length modification on the retrieval of XCH_4,clr and XCO_2,clr. The approximate airmass was calculated as (1/cos(solar zenith angle) + 1/cos(observing zenith angle)), which was similar to the previous studies that conducted bias correction for the full-physics method by considering airmass [37,39]. For the full-physics method, the deviation of the retrieved surface pressure from its prior value was also used for the bias correction [37,39]. In the case of the clear-sky retrieval, the deviation simply indicates the degree of optical path length modification for the O₂ A band and has been used for the cloud screening [40]. The deviation is expected to contain information about the scattering effect by aerosols that can be hardly accounted for by f_c and I_2μm. Then, the deviation of the clear-sky surface pressure from its prior value was calculated as (ΔP_srf = P_srf,retrieve − P_srf,prior).

2.4. TCCON Data and Matching with GOSAT Data

TCCON XCH₄ and XCO₂ data (GGG2014) from 26 sites [41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67] were used as the ground truth to validate the GOSAT ratio component. The map of the sites is shown in Figure A1, and the overview of the sites is shown in

Table A1. Overview of the TCCON sites used.

Site	Country	Latitude (deg.)	Longitude (deg.)	Altitude(km)	Observation Period of the Data Used	Specific Characteristics
Ny Ålesund	Spitzbergen, Norway	78.92N	11.92E	0.02	6 April 2014– 31 December 2018	Useful data are not obtained during winter due to the high solar zenith angle.
Sodankylä	Finland	67.37N	26.63E	0.19	16 May 2009– 31 December 2018	Useful data are not obtained during winter due to the high solar zenith angle.
East Trout Lake	Canada	54.35N	104.99W	0.50	7 October 2016– 31 December 2018
Bialystok	Poland	53.23N	23.03E	0.18	23 April 2009– 1 October 2018
Bremen	Germany	53.10N	8.85E	0.03	22 January 2010– 31 December 2018	The site is in the middle-sized city (population ~550 000).
Karlsruhe	Germany	49.10N	8.44E	0.12	19 April 2010– 31 December 2018	The site is near the middle-sized city (population ~300 000).
Paris	France	48.85N	2.36E	0.06	23 September 2014– 31 December 2018	The site is in the large city (population ~2.15 million).
Orléans	France	47.97N	2.11E	0.13	29 August 2009– 31 December 2018
Garmisch	Germany	47.48N	11.06E	0.74	23 April 2009– 31 December 2018
Park Falls	USA	45.95N	90.27W	0.44	23 April 2009– 31 December 2018
Rikubetsu	Japan	43.46N	143.77E	0.38	16 November 2013– 31 December 2018
Indianapolis	USA	39.86N	86.00W	0.27	23 August 2012– 1 December 2012	The site is in the suburban area of a middle-sized city (population ~880 000).
Four Corners	USA	36.80N	108.48W	1.64	16 March 2013– 4 October 2013	The site is far from the city area but observes plant plumes and methane from mine shafts and fugitive leaks [74,75]. The observed total column peaks in the late morning.
Lamont	USA	36.60N	97.49W	0.32	23 April 2009– 31 December 2018
Anmyeondo	Korea	36.54N	126.33E	0.03	2 February 2015– 18 April 2018	The site is located on the west coast of the Korean Peninsula.
Tsukuba	Japan	36.05N	140.12E	0.03	4 August 2011– 31 December 2018	The site is in the middle-sized city (population ~240 000).
Edwards	USA	34.96N	117.88W	0.70	20 July 2013– 31 December 2018	The site is adjacent to a very bright playa.
JPL	USA	34.20N	118.18W	0.39	19 May 2011– 14 May 2018	The site is near the large city (population ~17 million).
Caltech	USA	34.14N	118.13W	0.23	20 September 2012– 31 December 2018	The site is near the large city (population ~17 million).
Saga	Japan	33.24N	130.29E	0.01	28 July 2011– 31 December 2018	The site is in the middle-sized city (population ~230 000).
Hefei	China	31.91N	117.17E	0.03	18 September 2015– 31 December 2016	The site is near the large city (population ~5 million).
Burgos	Philippines	18.53N	120.65E	0.04	3 March 2017– 31 December 2018	The site is at the northernmost point of Luzon Island in the Philippines.
Manaus	Brazil	3.21S	60.60W	0.05	1 October 2014– 24 June 2015
Darwin	Australia	12.42S	130.89E	0.03	23 April 2009– 31 December 2018
Lauder	New Zealand	45.04S	169.68E	0.37	23 April 2009– 31 December 2018	The site is in the midst of rolling hills.
Wollongong	Australia	34.41S	150.88E	0.03	23 April 2009– 31 December 2018	The site is between the ocean and a sharp escarpment.

. The TCCON XCH₄ and XCO₂ data used in the present study (XCH_4,TCCON and XCO_2,TCCON) represent the mean values measured at each TCCON site within ±30 min of the GOSAT observation time. GOSAT data were selected within a ±2° latitude/longitude box centered at each TCCON site and within the difference in altitude between GOSAT (average within footprint) and TCCON site of 400 m. The ratio component of TCCON was then calculated (XCH_4,TCCON/XCO_2,TCCON). The relative difference (Δ_ratio) was calculated to evaluate the GOSAT ratio component as

Δ_ratio = 100 × (X_ratio,G − X_ratio,T)/X_ratio,T,

(2)

where X_ratio,G and X_ratio,T are the ratio components of GOSAT and TCCON, respectively. Most of the matched GOSAT data were acquired with gain H. Therefore, the data acquired with gain H were used in the following analysis. The data acquired with gain M are briefly addressed in the latter part of the analysis.

3. Investigating the Bias in the Ratio Component

3.1. Comparison Between GOSAT and TCCON Under Cloud-Free Conditions

First, in order to confirm the baseline of the bias, X_ratio,G was compared with X_ratio,T under the conditions in which cloud-free scenes were expected (f_c = 0 and I_2μm ≤ 1). Figure 1 shows the scatterplot of the ratio component and the latitudinal variation of the bias, precision of single scan, and interseasonal bias for each TCCON site. The bias and precision are defined as the mean and standard deviation of Δ_ratio, respectively. This precision value was used with the number of data to calculate the standard error of the mean value. The interseasonal bias is the standard deviation of bias values of the four seasons (DJF, MAM, JJA, SON) regardless of year, which has been used to represent the seasonal variability of bias [68]. The intersite bias is the standard deviation of bias values for individual TCCON sites, which is related to the spatial variability of bias. Only sites having more than nine data points were included in the calculation of intersite bias. The intersite bias of 0.14% might indicate that the spatial variation of bias is sufficiently small; however, the influence of loosening the cloud screening criteria and the temporal variation of bias should be investigated. Previous studies validating the GOSAT ratio component using TCCON data reported that the bias, precision, and intersite bias were about 0.2–0.6%, 0.5–0.7%, and 0.15–0.2%, respectively [19,24,26,28]. Although the retrieval scheme, the version of the TANSO-FTS L1B product, the number of TCCON sites used, the data matching criteria, the cloud screening method, and other details of the data screening differ between the present study and the previous studies, the overall results were comparable.

Table A2. Mean (μ) and standard deviation (SD) of the relative difference in the ratio component between GOSAT and TCCON and the number of matched GOSAT and TCCON data points (N) for each TCCON site. Results for four different matching criteria are shown: GOSAT data within ±2°, ±1°, ±0.5°, and ±0.1° latitude/longitude boxes centered at each TCCON site. Only sites having more than 29 data points are shown. The GOSAT data obtained under conditions where cloud-free scenes were expected (cloud fraction = 0 and normalized 2 μm band radiance ≤ 1) were used. Intersite bias is calculated using the same sites as in the case of matching criteria of ±0.1°.

	±2°			±1°			±0.5°			±0.1°
Site	μ (%)	SD (%)	N	μ (%)	SD (%)	N	μ (%)	SD (%)	N	μ (%)	SD (%)	N
Sodankylä	0.43	0.74	328	0.26	0.85	88
East Trout Lake	0.57	0.68	40
Bialystok	0.50	0.56	263	0.46	0.51	87	0.53	0.45	50
Bremen	0.51	0.54	81
Karlsruhe	0.22	0.62	267	0.19	0.57	102
Paris	0.43	0.52	102	0.50	0.50	59
Orléans	0.35	0.51	518	0.35	0.51	224	0.43	0.52	75
Garmisch	0.55	0.61	286	0.53	0.56	184	0.54	0.52	56
Park Falls	0.61	0.55	1017	0.61	0.55	728	0.59	0.55	575	0.60	0.55	536
Rikubetsu	0.63	0.46	135	0.73	0.44	56
Indianapolis	0.44	0.64	67
Lamont	0.59	0.54	1949	0.59	0.51	855	0.61	0.45	461	0.62	0.45	305
Anmeyondo	0.51	0.45	50	0.52	0.37	33
Tsukuba	0.31	0.61	1407	0.31	0.59	1186	0.28	0.60	675	0.41	0.49	179
Edwards	0.43	0.45	126	0.60	0.45	59
JPL	0.26	0.49	609	0.27	0.43	490	0.24	0.39	438	0.25	0.38	103
Caltech	0.32	0.43	2067	0.32	0.43	1924	0.32	0.43	1412	0.31	0.43	853
Saga	0.59	0.59	438	0.58	0.55	288	0.65	0.53	222	0.72	0.52	66
Darwin	0.37	0.36	555	0.38	0.36	500	0.56	0.36	46	0.48	0.34	30
Wollongong	0.42	0.71	349	0.31	0.58	195	0.34	0.61	100
Lauder	0.36	0.35	124	0.35	0.34	121	0.37	0.31	92	0.36	0.30	85
All sites	0.43	0.55	10846	0.41	0.52	7263	0.40	0.51	4357	0.45	0.49	2249
Intersite bias	0.14			0.13			0.16			0.15

shows that there was no clear variation of bias with tightening of the matching criteria of GOSAT and TCCON, but the precision was improved (there was a decrease in the standard deviation). Then, we assessed the influence of the matching criteria on our analysis and confirmed that the results shown below were hardly affected by the matching criteria (Appendix A). We also assessed the relationship between Δ_ratio and Fractional Variation in Solar Intensity (FVSI). FVSI is stored in TCCON data, and low FVSI values (≤1%) indicate a reasonably clear sky, where larger FVSI values could indicate some cirrus cloud presence. Only TCCON data having small FVSI values (≤5%) were provided to ensure the quality of XCH₄ and XCO₂ data. Figures S3 and S4 show that similar results were obtained between data with FVSI ≤ 1% and that with FVSI > 1%. This suggests that TCCON data can be used to validate the GOSAT ratio component regardless of FVSI values (0–5%).

3.2. Relationship Between Bias and Related Variables

3.2.1. Cloud Fraction and Normalized 2 μm Band Radiance

Figure 2 shows the variation of Δ_ratio with f_c and I_2μm. The data with NDSI ≤ 0.4 were used. Δ_ratio increases with the increase in I_2μm. Δ_ratio decreases with the increase in f_c for the data with small I_2μm. The large Δ_ratio is observed for data with both f_c and I_2μm exceeding certain levels, although the amount of data is small for such cases. To interpret the information from the TANSO-CAI and the TANSO-FTS 2 μm band clearly, we mainly used the data with f_c = 0 and that with I_2μm ≤ 1 in the following analysis. Most of the data fell within these cases (leftmost column and bottom row of Figure 2d). In the case of f_c = 0, I_2μm is related to the optically thin elevated scattering materials (mainly cirrus cloud) that were not identified by the TANSO-CAI. In the case of I_2μm ≤ 1, f_c is related to the middle- or low-altitude clouds with a certain level of optical thickness.

Figure 3a shows the variation of Δ_ratio with I_2μm. Δ_ratio increases with I_2μm. This can be attributed to the light path enhancement, which is greater for the CH₄ band than for the CO₂ band because the surface albedo of the CH₄ band is generally higher than that of the CO₂ band. The difference in vertical profile between CH₄ and CO₂ also seems to contribute to the results. More specifically, the light path enhancement means that the light repeatedly passes the area where the CH₄ concentration is higher than the column average, since the CH₄ concentration significantly decreases in the upper atmosphere. It is considered that the influence of the difference in the albedo and vertical profile becomes large with the increase in I_2μm.

Figure 3b shows the variation of Δ_ratio with f_c. The data with NDSI ≤ 0.4 were used. Δ_ratio is 0.4% to 0.5% for the data with f_c ≤ 0.2 and decreases with increasing f_c. This is because the effect of the difference in the retrieved surface albedo between the CH₄ and CO₂ bands becomes small with the increase in f_c, and the influence of the upper atmosphere where the CH₄ concentration is low becomes large because of the increase in the amount of light passing through a short path (scattered at the upper part of the cloud and reaching the sensor). Although the influence of clouds depends on their height and optical thickness, it is considered that the influence of the ground surface becomes small with the increase in cloud cover. Δ_ratio is almost stable for the data with f_c ≥ 0.4. It seems that the above-mentioned effects of the decreasing Δ_ratio and light path enhancement by clouds (multiple scattering within clouds) are balanced. Note that we obtained GOSAT data having large f_c value, which fell within the matching criteria of GOSAT and TCCON. This means that GOSAT data was obtained under cloudy conditions even when TCCON data was obtained under clear-sky conditions since cloud conditions varied within a ±2° latitude/longitude box.

3.2.2. Surface Albedo, Difference in Surface Albedo, Airmass, and Deviation of Surface Pressure

Figure 4 shows the relationship between Δ_ratio and the related variables (ρ_CH4, Δ_alb, airmass, and ΔP_srf). Section 3.2.1 showed that Δ_ratio was stable for data with f_c ≤ 0.2 and increased with I_2μm continuously; therefore, the results are separately plotted according to the f_c and I_2μm values. Case 1: f_c ≤ 0.2 and I_2μm ≤ 1; Case 2: f_c ≤ 0.2 and I_2μm > 1; Case 3: f_c > 0.2 and I_2μm ≤ 1. The results for Case 1 are discussed in this paragraph. Δ_ratio increases with ρ_CH4, although the variation is gentler than that for the other variables (Figure 4b–d). One possible reason is that the high surface albedo is prone to bring light path enhancement, by which the influence of the difference in the vertical profile between CH₄ and CO₂ becomes large (even if the surface albedo is similar between the CH₄ and CO₂ bands). For the difference in albedo, Δ_ratio clearly increases with the increase in Δ_alb. As Butz et al. [23] indicated in their theoretical study and as discussed in the former section, the difference in albedo causes a difference in optical path length modification between the CH₄ and CO₂ bands, significantly affecting the ratio component. Δ_ratio decreases with an increase in airmass. The influence of optical path length modification seems to be relatively small for the cases with large airmass (the modified light path is relatively short when the geometric path is long). The characteristics of the retrieval (e.g., errors in spectroscopy) might also affect the airmass dependence. The airmass dependence of retrieved XCH₄ and XCO₂ has been corrected empirically for satellite data [37,39] and TCCON data [69,70]. Recently, Mendonca et al. [71] found that using speed-dependent Voigt line shapes for retrieval of the O₂ total column reduces the airmass dependence of TCCON XCO₂. Δ_ratio significantly increases with ΔP_srf, although the number of data with large ΔP_srf is small. Although ΔP_srf is related to the optical path length modification for the O₂ A band (TANSO-FTS Band 1), the large ΔP_srf indicates the possibility that the light path enhancement effect, rather than light path shortening, is dominant for Band 2. More specifically, multiple scattering might occur within the area where the concentration of CH₄ is relatively high compared to the column average. In contrast to the cases with high f_c, the fraction of light passing a short path is expected to be low, and the influence of the ground surface is expected to be large, yielding a positive bias in the ratio component.

For Case 2, Δ_ratio is larger than that for Case 1. Although the dependence of Δ_ratio on Δ_alb is in the same direction between Cases 1 and 2, the increase in Δ_ratio with Δ_alb becomes steep, meaning that the influence of the difference in surface albedo becomes large when elevated scattering materials exist. In contrast, for Case 3, the variation trend of Δ_ratio with ρ_CH4 and Δ_alb differs significantly from that of Cases 1 and 2. This is because clouds affected the retrieved albedo (ρ_CH4 and Δ_alb increased with the increase in f_c).

3.2.3. Vertical Profile of CH₄ and CO₂

Figure 5 shows the variation of Δ_ratio with R_CH4 and R_CO2 (see Section 2.3 for the definition). The variation of Δ_ratio with R_CH4 is small if the possibility of the existence of elevated scattering materials is low (Case 1). In contrast, for Case 2, Δ_ratio increases with the increase in R_CH4. This corresponds to the qualitative discussion of the influence of the CH₄ profile on Δ_ratio in Section 3.2.1. Although the retrieval cannot reproduce the real-world profile in detail, it is considered that the retrieved R_CH4 represents the real-world R_CH4 (${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$) well and can be used to explain Δ_ratio. In contrast to CH₄, Δ_ratio was expected to decrease with an increase in R_CO2 because CO₂ is the denominator of the ratio component. However, no clear relationship between Δ_ratio and R_CO2 is seen in Figure 5. Two possible reasons are considered: (1) the influence of the CO₂ profile on the ratio component is small, since ${\mathrm{R}}_{\mathrm{CO}2}^{\mathrm{act}}$ is smaller than ${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$ in general; (2) the sensitivity of the retrieval to the vertical profile for CO₂ is lower than that for CH₄ (DFS for XCO_2,clr was 1.0–1.5 and that for XCH_4,clr was 1.7–2.3 in the present study). When only the retrieved data having DFS for XCO_2,clr ≥ 1.3 (almost half of all data) were used, the results were not noticeably changed (Figure S5). For Case 3, the range of R_CH4 and R_CO2 differs from that for Cases 1 and 2, since R_CH4 and R_CO2 were affected by clouds. R_CH4 was negatively correlated with f_c, which is considered to contribute to the increase in Δ_ratio with R_CH4. Although a variation of Δ_ratio with R_CO2 was expected for Case 3, since R_CO2 was also negatively correlated with f_c, the variation was small. The correlation between the variables (as mentioned in Section 3.2.2 and Section 3.2.3) was accounted for in the variable selection for the bias correction (Section 4.2).

4. Bias correction

4.1. Method

Linear regression was used as in many previous studies [20,37,39,72] as

$${\mathsf{\Delta }}_{\mathrm{ratio}}^{\mathrm{pred}}={\sum }_{\mathrm{i}=1}^{\mathrm{i}=\mathrm{n}}{\mathrm{C}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}+{\mathrm{C}}_{\mathrm{n}+1},$$

(3)

where ${\mathsf{\Delta }}_{\mathrm{ratio}}^{\mathrm{pred}}$ is the predicted Δ_ratio, n is the number of variables, C₁–C_n+1 are the regression coefficients, and x_i represents the explanatory variable. In the calculation of coefficients (least squares method), each data point (matched GOSAT and TCCON data) was weighted according to the amount of total matched GOSAT and TCCON data of the site to which the data point belonged. More specifically, the weight was given as R_site/N_j and 1/N_j for the data from sites in the northern hemisphere and that from sites in the southern hemisphere, respectively, where N_j is the total number of matched GOSAT data for each site, and R_site is the number of sites in the southern hemisphere divided by that in the northern hemisphere. For each GOSAT data point, the correction was calculated as

$${\mathrm{X}}_{\mathrm{ratio},\mathrm{G}}^{\mathrm{cor}}={\mathrm{X}}_{\mathrm{ratio},\mathrm{G}}/(1+{\mathsf{\Delta }}_{\mathrm{ratio}}^{\mathrm{pred}}/100),$$

(4)

where ${\mathrm{X}}_{\mathrm{ratio},\mathrm{G}}^{\mathrm{cor}}$ is the corrected ratio component.

4.2. Selecting Explanatory Variables

The correlation between the variables and the correlation between Δ_ratio and the variables were evaluated to select the variables for the bias correction (Figure 6). In Figure 6, the data with NDSI ≤ 0.4 were used to calculate the correlation coefficient with respect to f_c. Figure 6a shows that the variables were correlated with each other. In particular, f_c was highly correlated with the other variables, as mentioned in Section 3.2.2 and Section 3.2.3. Therefore, the variation of Δ_ratio was expected to be explained by the use of fewer than the total number of variables. We confirmed that the correlation between Δ_ratio and the variables did not become small by the correction using one variable. Therefore, corrections by multiple linear regression were tested. Figure 6b shows the correlation coefficient between the corrected Δ_ratio and the variables for the corrections using different numbers of variables. First, I_2μm and airmass were used, since Δ_ratio varied significantly with these variables (Figure 3 and Figure 4), and the correlation between them was low (Figure 6a). When three variables including R_CH4 were used, the correlation coefficient became close to zero, except in the case of Δ_alb. This can be attributed to the fact that R_CH4 included information on optical path length modification by scattering by clouds and aerosols. R_CH4 is considered to be a useful variable for correcting Δ_ratio, although the relationship between Δ_ratio and R_CH4 is somewhat empirical, especially when f_c is high.

In addition to the correlation coefficient, the relationship between Δ_ratio and the variables was further evaluated. Figure 7 shows the variation of Δ_ratio with the variables. The results were separately plotted for the different hemispheres and seasons in order to confirm that the spatiotemporal variation of bias was reduced. Data with NDSI ≤ 0.4 were used to obtain the variation of Δ_ratio with f_c. Even when the correction was conducted using I_2μm and one other variable, the difference in variation of the Δ_ratio with I_2μm between the northern and southern hemispheres remained. Although the number of TCCON sites and the number of data points for the southern hemisphere were smaller than those for the northern hemisphere (larger standard error for the southern hemisphere), the difference in variation of the Δ_ratio with I_2μm between hemispheres was larger than the standard error. The cause of this difference is that the degree of influence of elevated scattering materials on Δ_ratio varies according to the vertical profile of CH₄. When R_CH4 was used in the correction, the difference in variation of the Δ_ratio with I_2μm between the hemispheres was significantly reduced. For f_c, the corrected Δ_ratio varies around zero for both hemispheres and both seasons. For other variables, the difference between the hemispheres becomes small. Then, we decided to use the four variables airmass, I_2μm, R_CH4, and Δ_alb for the bias correction.

4.3. Quality Control

As quality control before evaluating the bias-corrected ratio component, cloud screening was investigated. Figure 8 shows the variation of the corrected Δ_ratio by the four variables according to f_c and I_2μm. The data with NDSI ≤ 0.4 were used. Although the data with f_c = 0 and those with I_2μm ≤ 1 were used for the results shown in the previous sections (Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7), all data were used to generate Figure 8 (similar to Figure 2). Although Δ_ratio is close to zero for many cases where f_c is > 0 and I_2μm is > 1 (i.e., data not used for the regression), the large mean and standard deviation of Δ_ratio remains. Therefore, the cloud screening was conducted as follows. We considered a function of f_c as g(f_c) = (af_c + b)/(cf_c + 1), where a, b, and c are coefficients, so that the tolerance range of I_2μm decreases with the increase in f_c. The coefficients were determined to make the criteria be I_2μm ≤ 15 when f_c = 0 and I_2μm ≤ 1 when f_c = 1, and to screen out the data in areas where the mean and/or the standard deviation of Δ_ratio were large in Figure 8. The criteria of I_2μm ≤ 15 when f_c = 0 is based on the result that the difference in Δ_ratio between the hemispheres became large with the increase in I_2μm (Figure 7). Then, we decided to reject the data with I_2μm > g(f_c), where coefficients a, b, and c were 46, 15, and 60, respectively. The criteria are depicted by the white line in Figure 8.

4.4. Evaluating the Corrected Results

To examine the usefulness and applicability of the bias correction, the matched GOSAT and TCCON data acquired in the even-numbered years were used to obtain the regression coefficients, and then the correction was applied to the GOSAT data acquired in the odd-numbered years. The obtained coefficients for airmass, I_2μm, R_CH4, and Δ_alb and the intercept were −0.28, 0.019, 1.06, 17.69, and −0.31, respectively (note that the four variables are dimensionless; see Section 2.3 for the definition of the variables). The cloud screening described in Section 4.3 was conducted. Figure 9 shows the comparison of the bias, precision, and interseasonal bias for each TCCON site between the bias-uncorrected and the bias-corrected ratio component. After the bias correction, the interseasonal bias was reduced, and the variation between sites in the northern hemisphere and the difference between hemispheres became small. The precision and intersite bias were also improved. The reduction of precision value was statistically significant (p < 0.001 from F test). The reduction of intersite bias value was less significant, but the 75% confidence intervals (CI) showed almost no overlap (0.177–0.234% and 0.143–0.179% for before and after the bias correction, respectively). The CI of intersite bias was estimated by the nonparametric bootstrap method. For each site, a bootstrap sample was taken, and a bootstrap estimate of bias (mean Δ_ratio of the sample) was obtained. Then, the intersite bias (standard deviation of the estimated bias values for individual sites) was calculated. This calculation was repeated 2000 times, and the CI was obtained from the 2000 intersite bias values.

Figure 10 shows the temporal variation of the uncorrected and corrected Δ_ratio for each TCCON site. The results for TCCON sites with long-term observation and a large number of data points are shown. For other sites, it was difficult to discuss the temporal variation of Δ_ratio, but no results contradicting the following discussion were obtained. On the whole, seasonality was seen for the uncorrected Δ_ratio, but it was significantly reduced by the correction. Δ_ratio was small even before the correction for the high-latitude site (Sodankylä [73]). Such a general seasonal and latitudinal pattern of Δ_ratio seems to be caused by the airmass dependence of Δ_ratio (Figure 4). In addition to this general pattern, the characteristics of each site were observed as described below. For each site, the temporal variation of Δ_ratio was determined as follows: the mean Δ_ratio was calculated for each season (DJF, MAM, JJA, SON) in each year (four seasons × five years), and then the mean and the standard deviation of the mean Δ_ratio values were calculated (Figure 11). For comparison, results for the corrected Δ_ratio with two and three variables are also shown.

For Sodankylä, the uncorrected Δ_ratio was smaller than that for the other sites owing to the large airmass. The low possibility of elevated scattering materials (I_2μm was small for most of the data) also seems to have contributed to the small Δ_ratio. Δ_ratio was overcorrected by the correction using two variables. f_c tended to be high for the data over this site, and ${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$ seemed to be large according to the model (prior value). Then, the overcorrection was reduced by using four variables. For Orléans, occasional large I_2μm, in addition to the airmass effect, seemed to cause a large standard deviation; however, the deviation decreased after the correction. For Park Falls, the uncorrected Δ_ratio was considered to be affected by many factors. The temporal variation of Δ_alb was large, since this site was covered by snow during winter and by vegetation during summer. Large I_2μm was observed during spring. ${\mathrm{R}}_{\mathrm{CO}2}^{\mathrm{act}}$ is expected to be small during summer due to photosynthesis by vegetation. ${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$ seemed to be large during summer according to the model (prior value). Correction using R_CH4 reduced Δ_ratio, although a relatively large Δ_ratio remained, since the complicated conditions were not perfectly accounted for by the correction. For Lamont, large Δ_alb generally brought large Δ_ratio. The correction using Δ_alb reduced Δ_ratio. A large uncorrected Δ_ratio was occasionally seen in the early months of the year (Figure 10). We found that the large Δ_ratio corresponded to the large I_2μm in February 2013 and 2017. According to Figure 10, these large errors were properly corrected. The use of I_2μm in the correction had only a small effect on the averaged results (Figure 11), since I_2μm was not always large; however, the effect could be confirmed for individual cases. For Tsukuba, a large I_2μm was observed during spring to summer, which enhanced the seasonality of the uncorrected Δ_ratio. Δ_alb of this site was small, and thus the overcorrection was reduced by using Δ_alb in the correction. For Caltech, Δ_alb was small, and the temporal variations of ${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$ and ${\mathrm{R}}_{\mathrm{CO}2}^{\mathrm{act}}$ were small according to the model. The difference between ${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$ and ${\mathrm{R}}_{\mathrm{CO}2}^{\mathrm{act}}$ was also small. Then, the uncorrected Δ_ratio showed small temporal variation, and the corrected Δ_ratio varied around zero with the small temporal variation retained. For Saga, the airmass effect and the large I_2μm during spring to summer enhanced the seasonality, and Δ_ratio was significantly reduced by the correction using two variables. The temporal variation of ${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$ was expected to be large according to the model. Thus, using R_CH4 in the correction improved both the mean and standard deviation (Figure 11). For the sites in the southern hemisphere (Darwin and Wollongong), although ${\mathrm{R}}_{\mathrm{CH}4}^{\mathrm{act}}$ and ${\mathrm{R}}_{\mathrm{CO}2}^{\mathrm{act}}$ were expected to be small, the amplitude of temporal variation of uncorrected Δ_ratio was comparable to that for the sites in the northern hemisphere (Figure 10). For Darwin, the uncorrected Δ_ratio showed large temporal variation, although the variation of airmass was small. For Wollongong, occasional large uncorrected Δ_ratio did not correspond to the large I_2μm. The standard deviation was reduced only slightly by the correction for these sites (Figure 11). Although using R_CH4 in the correction reduced the difference between the northern and southern hemispheres (Figure 7), unaccounted factors might remain. On the whole, the optimal variables differ between sites; but the correction using four variables brought the best result in terms of the balance between sites (the mean of absolute Δ_ratio values for individual sites was close to zero and the variation between sites was small).

We also conducted a bias correction for the data acquired with gain M using the four variables and the above-mentioned coefficients (i.e., the coefficients were obtained using the gain H data). The bias correction functioned properly for the gain M data, although the bias was small even for the uncorrected data (Appendix B). This result supports the applicability of the bias correction.

5. Conclusions

The relationship between the bias in the GOSAT ratio component and the variables derived from GOSAT data was investigated, and the bias correction and its evaluation were performed. The bias between the uncorrected GOSAT ratio component and the TCCON ratio component was 0.43% when the cloud-free condition was expected (normalized 2 μm band radiance (I_2μm) ≤ 1 and cloud fraction (f_c) = 0). The bias increased with the increase in I_2μm and reached 1.5% when I_2μm was 30. The variation of bias with f_c was small when f_c was small or large (the bias was 0.4% to 0.5% for the data with f_c ≤ 0.2 and −0.1% to 0% for the data with f_c ≥ 0.4). The variation of bias according to I_2μm and f_c could be interpreted based on the difference in the detection target between I_2μm and f_c, the difference in surface albedo between the CH₄ and CO₂ bands (Δ_alb), and the vertical profile of CH₄ and CO₂. The relationship between the bias and other related variables was also investigated. We used the retrieved profile and the ratios between the upper and lower atmosphere CH₄ and CO₂ (R_CH4 and R_CO2), in addition to the variables that have been used in the bias correction for the full-physics method (airmass) and in the cloud screening (deviation of the retrieved clear-sky surface pressure from its prior (ΔP_srf)) and that have been revealed to be a large error source for the proxy method (Δ_alb). The bias showed clear variations with the variables except for R_CO2.

Then, airmass, I_2μm, R_CH4, and Δ_alb were selected as explanatory variables for a linear regression of the bias by considering the correlation between the variables and the correlation between the variables and the bias. Using R_CH4 in the correction reduced the dependence of the bias on f_c and ΔP_srf. The difference in bias between the northern and the southern hemispheres was also reduced. These results are attributed to the information on the CH₄ vertical profile and the effect of atmospheric scattering included in R_CH4. Although the relationship between bias and R_CH4 is somewhat empirical, R_CH4 is an important variable for correcting the bias in the ratio component. Before evaluating the corrected results, cloud screening was applied. The criteria were determined as the threshold value of I_2μm decreases with the increase in f_c (I_2μm ≤ 15 when f_c = 0 and I_2μm ≤ 1 when f_c = 1), by investigating the variation of bias in the corrected ratio component with f_c and I_2μm. Although f_c and I_2μm have been used for the cloud screening of the GOSAT proxy retrievals, our results give a quantitative basis for the screening.

Comparison between the corrected ratio component and TCCON showed that the precision (standard deviation of the difference between GOSAT and TCCON) was reduced from 0.61% to 0.55%, and the intersite bias was reduced from 0.20% to 0.15%. The temporal variation of bias was further investigated for the sites having a long-term record and a large amount of data. The uncorrected bias showed a seasonality with a large bias in summer. The difference in monthly mean bias between summer and winter exceeded 1% for several sites. In addition to such seasonality, the months with a large mean bias corresponded to the months with a large mean I_2μm. The temporal variation of bias was significantly reduced by the correction. Although the optimal variables differed between sites, the mean and standard deviation of the mean bias values for individual seasons (each season in each year) were within 0.2% for most of the sites, when the four variables were used for the correction.

The bias-corrected and cloud-screened ratio component data in the present study reduce the concern that the residual errors related to the atmospheric scattering and the property of ground surfaces affect the inverse modeling of CH₄ sources and sinks. In future work, the impact of utilizing the bias-corrected data in the inverse modeling will be investigated. GOSAT has been operating for more than 10 years. GOSAT-2, a successor mission to the GOSAT, was launched on 29 October 2018. Providing long-term, consistent, and high-quality XCH₄ data set by the GOSAT series is expected to contribute to the studies on CH₄ budgets over the globe. To construct such a data set, GOSAT and GOSAT-2 data will be continuously compared with each other and with the data from other satellites and TCCON.