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

Haruki Oshio, Yukio Yoshida, Tsuneo Matsunaga, Nicholas Deutscher, Manvendra Dubey, David Griffith, Frank Hase, Laura Iraci, Rigel Kivi, Cheng Liu, et al.

► To cite this version:

Haruki Oshio, Yukio Yoshida, Tsuneo Matsunaga, Nicholas Deutscher, Manvendra Dubey, et al. Bias Correction of the Ratio of Total Column CH4 to CO2 Retrieved from GOSAT Spectra. Remote Sensing, 2020, 12 (19), pp.3155. 10.3390/rs12193155. hal-03958622

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Article

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

Haruki Oshio ¹,* , Yukio Yoshida ¹, Tsuneo Matsunaga ¹, Nicholas M. Deutscher ², Manvendra Dubey ³, David W. T. Griffith ², Frank Hase ⁴, Laura T. Iraci ⁵, Rigel Kivi ⁶, Cheng Liu ⁷,⁸, Isamu Morino ¹, Justus Notholt ⁹, Young-Suk Oh ¹⁰, Hirofumi Ohyama ¹, Christof Petri ⁹, David F. Pollard ¹¹, Coleen Roehl ¹², Kei Shiomi ¹³, Ralf Sussmann ¹⁴, Yao Té ¹⁵, Voltaire A. Velazco ², Thorsten Warneke ⁹ and Debra Wunch ¹⁶

¹ Center for Global Environmental Research, National Institute for Environmental Studies, Tsukuba, Ibaraki 305-8506, Japan; yoshida.yukio@nies.go.jp (Y.Y.); matsunag@nies.go.jp (T.M.); morino@nies.go.jp (I.M.); oyama.hirofumi@nies.go.jp (H.O.)

² Centre for Atmospheric Chemistry, School of Earth, Atmospheric and Life Sciences, Faculty of Science, Medicine and Health, University of Wollongong, Wollongong 2522, Australia; ndeutsch@uow.edu.au (N.M.D.); griffith@uow.edu.au (D.W.T.G.); voltaire@uow.edu.au (V.A.V.)

³ Los Alamos National Laboratory, Los Alamos, NM 87545, USA; dubey@lanl.gov

⁴ Institute of Meteorology and Climate Research IMK-ASF, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany; frank.hase@kit.edu

⁵ Atmospheric Science Branch, NASA Ames Research Center, Moffett Field, CA 94035, USA; laura.t.iraci@nasa.gov

⁶ Space and Earth Observation Centre, Finnish Meteorological Institute, 99600 Sodankylä, Finland; rigel.kivi@fmi.fi

⁷ Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China; Chliu81@ustc.edu.cn

⁸ Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China

⁹ Institute of Environmental Physics, University of Bremen, 28359 Bremen, Germany; jnotholt@iup.physik.uni-bremen.de (J.N.); christof_p@iup.physik.uni-bremen.de (C.P.); warneke@iup.physik.uni-bremen.de (T.W.)

¹⁰ Climate Research Division, National Institute of Meteorological Sciences, Seogwipo, Jeju-do 63568, Korea; ysoh306@korea.kr

¹¹ National Institute of Water and Atmospheric Research, Lauder, Omakau 9352, New Zealand; dave.pollard@niwa.co.nz

¹² Division of Geology and Planetary Science, California Institute of Technology, Pasadena, CA 91125, USA; coleen@caltech.edu

¹³ Japan Aerospace Exploration Agency (JAXA), Tsukuba, Ibaraki 305-8505, Japan; shiomi.kei@jaxa.jp

¹⁴ Institute of Meteorology and Climate Research—Atmospheric Environmental Research (IMK-IFU), Karlsruhe Institute of Technology, 82467 Garmisch-Partenkirchen, Germany; ralf.sussmann@kit.edu

¹⁵ Laboratoire d'Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères (LERMA-IPSL), Sorbonne Université, CNRS, Observatoire de Paris, PSL Université, 75005 Paris, France; yao-veng.te@upmc.fr

¹⁶ Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada; dwunch@atmosp.physics.utoronto.ca

Received: 21 August 2020; Accepted: 24 September 2020; Published: 25 September 2020

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**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)

<footnote>* Correspondence: oshio.haruki@nies.go.jp; Tel.: +81-29-850-2416</footnote>
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 CH$_4$ for the lower atmosphere and that for the upper atmosphere, and the difference in surface albedo between the CH$_4$ and CO$_2$ bands. The ratio of partial column CH$_4$ 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.

**Keywords:** methane; proxy method; GOSAT; TCCON

# 1. Introduction

Atmospheric methane (CH$_4$) is the most significant anthropogenic greenhouse gas after carbon dioxide (CO$_2$) and is emitted from both anthropogenic and natural sources. Satellite observation, which can obtain data over wide areas, is effective to elucidate the CH$_4$ budget over the globe. In the last 15 years, the column-averaged dry-air mole fraction of methane (XCH$_4$) has been retrieved from the spectra of the backscattered Short-Wavelength InfraRed (SWIR) sunlight measured by sensors onboard satellites [1–6]. Satellite-derived XCH$_4$ data have been applied to the inverse modeling of CH$_4$ sources and sinks [7–11]. High precision and small bias in spatiotemporal variation are required for the XCH$_4$ data to be used in inverse modeling [12,13]. It is possible that even a small regional bias (0.5%) in the XCH$_4$ 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 [14–16]. 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 CH$_4$ absorption band is obtained from that for the adjacent CO$_2$ absorption band [2] (Equation (1)),

$$XCH_4 = \frac{XCH_{4,clr}}{XCO_{2,clr}} \times XCO_{2,mdl}, \quad (1)$$

where XCH$_4$$_{,clr}$ and XCO$_2$$_{,clr}$ are XCH$_4$ and XCO$_2$ retrieved under a clear-sky assumption (no aerosols and clouds are assumed) and XCO$_2$$_{,mdl}$ is XCO$_2$ from the numerical model. It is assumed that, in the ratio component (XCH$_4$$_{,clr}$/XCO$_2$$_{,clr}$), the impacts of aerosol and clouds cancel each other out between XCH$_4$$_{,clr}$ and XCO$_2$$_{,clr}$. It is also assumed that the relative variation of XCO$_2$ is much smaller than that of XCH$_4$, and that XCO$_2$ 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 [19–22].

Both errors in the ratio component and the model XCO$_2$ lead to errors in the resulting XCH$_4$. 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 XCH$_4$ 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 XCO$_2$
model that is consistent with the XCH₄ model used in the inversion. The ratio component can also be
directly inverted [25–27]. 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 XCH₄,clr and XCO₂,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 XCH4,clr and XCO2,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<sub>srf</sub> hPa (XCH<sub>4,upper</sub> and XCO<sub>2,upper</sub>) and for Layers 12–15 (lower atmosphere, 0.73P<sub>srf</sub>–P<sub>srf</sub> hPa (XCH<sub>4,lower</sub> and XCO<sub>2,lower</sub>)). 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<sub>CH4</sub> = XCH<sub>4,lower</sub>/XCH<sub>4,upper</sub> and R<sub>CO2</sub> = XCO<sub>2,lower</sub>/XCO<sub>2,upper</sub>) 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<sub>4,clr</sub> and XCO<sub>2,clr</sub>. 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 O<sub>2</sub> 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<sub>c</sub> and I<sub>2µm</sub>. Then, the deviation of the clear-sky surface pressure from its prior value was calculated as (ΔP<sub>srf</sub> = P<sub>srf,retrieve</sub> – P<sub>srf,prior</sub>).

## 2.4. TCCON Data and Matching with GOSAT Data

TCCON XCH<sub>4</sub> and XCO<sub>2</sub> data (GGG2014) from 26 sites [41–67] 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. The TCCON XCH<sub>4</sub> and XCO<sub>2</sub> data used in the present study (XCH<sub>4,TCCON</sub> and XCO<sub>2,TCCON</sub>) 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<sub>4,TCCON</sub>/XCO<sub>2,TCCON</sub>). The relative difference (Δ<sub>ratio</sub>) was calculated to evaluate the GOSAT ratio component as

$$ \Delta_{\text{ratio}} = 100 \times (X_{\text{ratio,G}} - X_{\text{ratio,T}})/X_{\text{ratio,T}}, \quad (2) $$

where X<sub>ratio,G</sub> and X<sub>ratio,T</sub> 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<sub>ratio,G</sub> was compared with X<sub>ratio,T</sub> under the conditions in which cloud-free scenes were expected (f<sub>c</sub> = 0 and I<sub>2µm</sub> ≤ 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<sub>ratio</sub>, 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.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Comparison of the ratio component between Greenhouse gases Observing SATellite (GOSAT) and Total Carbon Column Observing Network (TCCON): (a) Scatter plot of individual data; (b) result for each site. GOSAT data obtained under conditions where cloud-free scenes were expected (cloud fraction = 0 and normalized 2 µm band radiance ≤1) were used. In (a), the correlation coefficient (R), the slope and intercept of the linear regression, and the number of data points (N) are also shown. In (b), the latitudinal variations of the bias, precision, and interseasonal bias for TCCON sites having more than nine data points are presented.</figcaption></figure>

Table A2 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 $\Delta_{ratio}$ 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 XCH$_4$ and XCO$_2$ 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 $\Delta_{ratio}$ with $f_c$ and $I_{2\mu m}$. The data with NDSI ≤ 0.4 were used. $\Delta_{ratio}$ increases with the increase in $I_{2\mu m}$. $\Delta_{ratio}$ decreases with the increase in $f_c$ for the data with small $I_{2\mu m}$. The large $\Delta_{ratio}$ is observed for data with both $f_c$ and $I_{2\mu m}$ 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 $I_{2\mu m}$ ≤ 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, $I_{2\mu m}$ is related to the optically thin elevated scattering materials
(mainly cirrus cloud) that were not identified by the TANSO-CAI. In the case of $I_{2\mu m} \le 1$, $f_c$ is related to the middle- or low-altitude clouds with a certain level of optical thickness.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Variation of the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) according to the cloud fraction ($f_c$) and the normalized 2 µm band radiance ($I_{2\mu m}$). Data with $I_{2\mu m} < f_c \le 1$ were divided into 10 bins (horizontal axis), and data with $-1 \le I_{2\mu m} \le 35$ were divided into 18 bins (vertical axis). The mean $\Delta_{ratio}$, standard error (SE) calculated by the precision of single data (a,b)), standard deviation (SD) of $\Delta_{ratio}$ (c), and number of data points (d) for each bin are presented. Data with Normalized Difference Snow Index (NDSI) $\le 0.4$ were used. Only bins having more than two data points are colored except in panel (d). The white line indicates the cloud screening criterion (Section 4.3).</figcaption></figure>

Figure 3a shows the variation of $\Delta_{ratio}$ with $I_{2\mu m}$. $\Delta_{ratio}$ increases with $I_{2\mu m}$. This can be attributed to the light path enhancement, which is greater for the CH$_4$ band than for the CO$_2$ band because the surface albedo of the CH$_4$ band is generally higher than that of the CO$_2$ band. The difference in vertical profile between CH$_4$ and CO$_2$ also seems to contribute to the results. More specifically, the light path enhancement means that the light repeatedly passes the area where the CH$_4$ concentration is higher than the column average, since the CH$_4$ 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 $I_{2\mu m}$.

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Variation of the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) according to (a) the normalized 2 µm band radiance ($I_{2\mu m}$) and (b) the cloud fraction ($f_c$). Only data with $f_c = 0$ were used for (a), and only data with $I_{2\mu m} \le 1$ and NDSI $\le 0.4$ were used for (b).</figcaption></figure>

Figure 3b shows the variation of $\Delta_{ratio}$ with $f_c$. The data with NDSI $\le 0.4$ were used. $\Delta_{ratio}$ is 0.4% to 0.5% for the data with $f_c \le 0.2$ and decreases with increasing $f_c$. This is because the effect of the difference in the retrieved surface albedo between the CH$_4$ and CO$_2$ bands becomes small with
the increase in $f_c$, and the influence of the upper atmosphere where the CH$_4$ 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. $\Delta_{ratio}$ is almost stable for the data with $f_c \ge 0.4$. It seems that the above-mentioned effects of the decreasing $\Delta_{ratio}$ 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 $\pm 2^\circ$ latitude/longitude box.

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

Figure 4 shows the relationship between $\Delta_{ratio}$ and the related variables ($\rho_{CH_4}$, $\Delta_{alb}$, airmass, and $\Delta P_{srf}$). Section 3.2.1 showed that $\Delta_{ratio}$ was stable for data with $f_c \le 0.2$ and increased with $I_{2\mu m}$ continuously; therefore, the results are separately plotted according to the $f_c$ and $I_{2\mu m}$ values. Case 1: $f_c \le 0.2$ and $I_{2\mu m} \le 1$; Case 2: $f_c \le 0.2$ and $I_{2\mu m} > 1$; Case 3: $f_c > 0.2$ and $I_{2\mu m} \le 1$. The results for Case 1 are discussed in this paragraph. $\Delta_{ratio}$ increases with $\rho_{CH_4}$, 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 CH$_4$ and CO$_2$ becomes large (even if the surface albedo is similar between the CH$_4$ and CO$_2$ bands). For the difference in albedo, $\Delta_{ratio}$ clearly increases with the increase in $\Delta_{alb}$. 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 CH$_4$ and CO$_2$ bands, significantly affecting the ratio component. $\Delta_{ratio}$ 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 XCH$_4$ and XCO$_2$ 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 O$_2$ total column reduces the airmass dependence of TCCON XCO$_2$. $\Delta_{ratio}$ significantly increases with $\Delta P_{srf}$, although the number of data with large $\Delta P_{srf}$ is small. Although $\Delta P_{srf}$ is related to the optical path length modification for the O$_2$ A band (TANSO-FTS Band 1), the large $\Delta P_{srf}$ 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 CH$_4$ 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.
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Variation of the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) according to the related variables: (a) retrieved surface albedo of the CH$_4$ band ($\rho_{CH4}$); (b) difference in the retrieved surface albedo (CH$_4$ band minus CO$_2$ band, $\Delta_{alb}$); (c) airmass; (d) deviation of the retrieved clear-sky surface pressure from its prior ($\Delta P_{srf}$). In each panel, the mean and standard deviation (SD) of $\Delta_{ratio}$ and the number of data points (N) for each bin are presented. The results are separately plotted according to the cloud fraction ($f_c$) and the normalized 2 µm band radiance ($I_{2\mu m}$).</figcaption></figure>

For Case 2, $\Delta_{ratio}$ is larger than that for Case 1. Although the dependence of $\Delta_{ratio}$ on $\Delta_{alb}$ is in the same direction between Cases 1 and 2, the increase in $\Delta_{ratio}$ with $\Delta_{alb}$ 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 $\Delta_{ratio}$ with $\rho_{CH4}$ and $\Delta_{alb}$ differs significantly from that of Cases 1 and 2. This is because clouds affected the retrieved albedo ($\rho_{CH4}$ and $\Delta_{alb}$ increased with the increase in $f_c$).

### 3.2.3. Vertical Profile of CH$_4$ and CO$_2$

Figure 5 shows the variation of $\Delta_{ratio}$ with $R_{CH4}$ and $R_{CO2}$ (see Section 2.3 for the definition). The variation of $\Delta_{ratio}$ with $R_{CH4}$ is small if the possibility of the existence of elevated scattering materials is low (Case 1). In contrast, for Case 2, $\Delta_{ratio}$ increases with the increase in $R_{CH4}$. This corresponds to the qualitative discussion of the influence of the CH$_4$ profile on $\Delta_{ratio}$ 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 $R_{CH4}$ ($R_{CH4}^{act}$) well and can be used to explain $\Delta_{ratio}$. In contrast to CH$_4$, $\Delta_{ratio}$ was expected to decrease with an increase in $R_{CO2}$ because CO$_2$ is the denominator of the ratio component. However, no clear relationship between $\Delta_{ratio}$ and $R_{CO2}$ is seen in Figure 5. Two possible reasons are considered: (1) the influence of the CO$_2$ profile on the ratio component is small, since $R_{CO2}^{act}$ is smaller than $R_{CH4}^{act}$ in general; (2) the sensitivity of the retrieval to the vertical profile for CO$_2$ is lower than that for CH$_4$ (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} \ge 1.3$ (almost half of all data) were
used, the results were not noticeably changed (Figure S5). For Case 3, the range of R<sub>CH4</sub> and R<sub>CO2</sub> differs from that for Cases 1 and 2, since R<sub>CH4</sub> and R<sub>CO2</sub> were affected by clouds. R<sub>CH4</sub> was negatively correlated with f<sub>c</sub>, which is considered to contribute to the increase in Δ<sub>ratio</sub> with R<sub>CH4</sub>. Although a variation of Δ<sub>ratio</sub> with R<sub>CO2</sub> was expected for Case 3, since R<sub>CO2</sub> was also negatively correlated with f<sub>c</sub>, the variation was small. The correlation between the variables (as mentioned in Sections 3.2.2 and 3.2.3) was accounted for in the variable selection for the bias correction (Section 4.2).

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Variation of the relative difference in the ratio component between GOSAT and TCCON (Δ<sub>ratio</sub>) according to the ratio between the partial column-averaged dry-air mole fractions for the lower atmosphere and that for the upper atmosphere (R<sub>CH4</sub> and R<sub>CO2</sub>): (a) Case 1 (the cloud fraction (f<sub>c</sub>) ≤ 0.2 and the normalized 2 µm band radiance (I<sub>2µm</sub>) ≤ 1); (b) Case 2 (f<sub>c</sub> ≤ 0.2 and I<sub>2µm</sub> > 1); (c) Case 3 (f<sub>c</sub> > 0.2 and I<sub>2µm</sub> ≤ 1).</figcaption></figure>

# 4. Bias correction

## 4.1. Method

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

$$ \Delta_{\text{ratio}}^{\text{pred}} = \sum_{i=1}^{i=n} C_i x_i + C_{n+1}, \qquad (3) $$

where Δ<sub>ratio</sub><sup>pred</sup> is the predicted Δ<sub>ratio</sub>, n is the number of variables, C<sub>1</sub>–C<sub>n+1</sub> are the regression coefficients, and x<sub>i</sub> 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<sub>site</sub>/N<sub>j</sub> and 1/N<sub>j</sub> for the data from sites in the northern hemisphere and that from sites in the southern hemisphere, respectively, where N<sub>j</sub> is the total number of matched GOSAT data for each site, and R<sub>site</sub> 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

$$ \chi_{\text{ratio,G}}^{\text{cor}} = \chi_{\text{ratio,G}} / (1 + \Delta_{\text{ratio}}^{\text{pred}} / 100), \qquad (4) $$

where χ<sub>ratio,G</sub><sup>cor</sup> is the corrected ratio component.

## 4.2. Selecting Explanatory Variables

The correlation between the variables and the correlation between Δ<sub>ratio</sub> 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<sub>c</sub>. Figure 6a shows that the variables were correlated with each other. In particular, f<sub>c</sub> was highly correlated with the other variables, as mentioned in Sections 3.2.2 and 3.2.3. Therefore, the variation of Δ<sub>ratio</sub> was expected to be explained by the use of fewer than the total number of variables. We confirmed that the correlation between Δ<sub>ratio</sub> 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 $\Delta_{ratio}$ and the variables for the corrections using different numbers of variables. First, $I_{2\mu m}$ and airmass were used, since $\Delta_{ratio}$ varied significantly with these variables (Figures 3 and 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 $\Delta_{alb}$. 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 $\Delta_{ratio}$, although the relationship between $\Delta_{ratio}$ and $R_{CH4}$ is somewhat empirical, especially when $f_c$ is high.

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Correlation coefficient (a) between variables and (b) between the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) and variables. The color in the figure corresponds to the coefficient value (blue: large negative coefficient; white: zero; red: large positive coefficient). The meaningless pixels are filled by gray. Eight variables were used: the normalized 2 µm band radiance ($I_{2\mu m}$), cloud fraction ($f_c$), retrieved surface albedo of CH$_4$ band ($\rho_{CH4}$), difference in the retrieved surface albedo (CH$_4$ band minus CO$_2$ band, $\Delta_{alb}$), airmass ($A_m$), deviation of the retrieved clear-sky surface pressure from its prior ($\Delta P_{srf}$), and ratio between the partial column-averaged dry-air mole fractions for the lower atmosphere and that for the upper atmosphere ($R_{CH4}$ and $R_{CO2}$). In (b), results for bias-uncorrected $\Delta_{ratio}$ and bias-corrected $\Delta_{ratio}$ (corrections using two, three, and four variables) are shown. Data with $f_c = 0$ and that with $I_{2\mu m} \le 1$ were used. Only data with NDSI $\le 0.4$ were used to calculate the correlation coefficient for $f_c$.</figcaption></figure>

In addition to the correlation coefficient, the relationship between $\Delta_{ratio}$ and the variables was further evaluated. Figure 7 shows the variation of $\Delta_{ratio}$ 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 $\le 0.4$ were used to obtain the variation of $\Delta_{ratio}$ with $f_c$. Even when the correction was conducted using $I_{2\mu m}$ and one other variable, the difference in variation of the $\Delta_{ratio}$ with $I_{2\mu m}$ 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 $\Delta_{ratio}$ with $I_{2\mu m}$ between hemispheres was larger than the standard error. The cause of this difference is that the degree of influence of elevated scattering materials on $\Delta_{ratio}$ varies according to the vertical profile of CH$_4$. When $R_{CH4}$ was used in the correction, the difference in variation of the $\Delta_{ratio}$ with $I_{2\mu m}$ between the hemispheres was significantly reduced. For $f_c$, the corrected $\Delta_{ratio}$ 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, $I_{2\mu m}$, $R_{CH4}$, and $\Delta_{alb}$ for the bias correction.
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Variation of the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{\text{ratio}}$) according to the explanatory variables: normalized 2 µm band radiance ($I_{2\mu m}$); cloud fraction</figcaption></figure>
(f_c); retrieved surface albedo of CH4 band (ρ_CH4); difference in the retrieved surface albedo (CH4 band minus CO2 band, Δ_alb); airmass (A_m); deviation of the retrieved clear-sky surface pressure from its prior (ΔP_srf); and ratio between the partial column-averaged dry-air mole fractions for the lower atmosphere and that for the upper atmosphere (R_CH4 and R_CO2). Results for (a) bias-uncorrected Δ_ratio and bias-corrected Δ_ratio (corrections using (b) two, (c) three, and (d) four variables) are presented. Results for the winter (January to April) northern hemisphere, the summer (July to October) northern hemisphere, and the southern hemisphere are plotted with different colors. Data with f_c = 0 and that with I_2_μm ≤ 1 were used. Only data with NDSI ≤ 0.4 were used to obtain the variation of Δ_ratio with f_c.

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<sub>ratio</sub> by the four variables according to f<sub>c</sub> and I<sub>2μm</sub>. The data with NDSI ≤ 0.4 were used. Although the data with f<sub>c</sub> = 0 and those with I<sub>2μm</sub> ≤ 1 were used for the results shown in the previous sections (Figures 3–7), all data were used to generate Figure 8 (similar to Figure 2). Although Δ<sub>ratio</sub> is close to zero for many cases where f<sub>c</sub> is > 0 and I<sub>2μm</sub> is > 1 (i.e., data not used for the regression), the large mean and standard deviation of Δ<sub>ratio</sub> remains. Therefore, the cloud screening was conducted as follows. We considered a function of f<sub>c</sub> as g(f<sub>c</sub>) = (af<sub>c</sub> + b)/(cf<sub>c</sub> + 1), where a, b, and c are coefficients, so that the tolerance range of I<sub>2μm</sub> decreases with the increase in f<sub>c</sub>. The coefficients were determined to make the criteria be I<sub>2μm</sub> ≤ 15 when f<sub>c</sub> = 0 and I<sub>2μm</sub> ≤ 1 when f<sub>c</sub> = 1, and to screen out the data in areas where the mean and/or the standard deviation of Δ<sub>ratio</sub> were large in Figure 8. The criteria of I<sub>2μm</sub> ≤ 15 when f<sub>c</sub> = 0 is based on the result that the difference in Δ<sub>ratio</sub> between the hemispheres became large with the increase in I<sub>2μm</sub> (Figure 7). Then, we decided to reject the data with I<sub>2μm</sub> > g(f<sub>c</sub>), where coefficients a, b, and c were 46, 15, and 60, respectively. The criteria are depicted by the white line in Figure 8.

<figure><img src="image_11.png" /><figcaption>**Figure 8.** Similar to Figure 2, but for the bias-corrected ratio component: (a) mean relative difference in the ratio component between GOSAT and TCCON (Δ<sub>ratio</sub>); (b) standard error (SE); (c) standard deviation (SD) of Δ<sub>ratio</sub>; (d) number of data points. The white line indicates the cloud screening criterion.</figcaption></figure>

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, I2µm, RCH4, and Δalb 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 $\Delta_{ratio}$ 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><img src="image_12.png" /><figcaption>**Figure 9.** Latitudinal plot of (a) the bias, (b) precision, and (c) interseasonal bias of the uncorrected and the bias-corrected GOSAT ratio component for each TCCON site. Only sites having more than nine data points are shown. The bias, precision, correlation coefficient (R), and the slope and intercept of the linear regression calculated using all data (in a manner similar to Figure 1a) are presented below the graphs.</figcaption></figure>

Figure 10 shows the temporal variation of the uncorrected and corrected $\Delta_{ratio}$ 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 $\Delta_{ratio}$, but no results contradicting the following discussion were obtained. On the whole, seasonality was seen for the uncorrected $\Delta_{ratio}$, but it was significantly reduced by the correction. $\Delta_{ratio}$ was small even before the correction for the high-latitude site (Sodankylä [73]). Such a general seasonal and latitudinal pattern of $\Delta_{ratio}$ seems to be caused by the airmass dependence of $\Delta_{ratio}$ (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 $\Delta_{ratio}$ was determined as follows: the mean $\Delta_{ratio}$ 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 $\Delta_{ratio}$ values were calculated (Figure 11). For comparison, results for the corrected $\Delta_{ratio}$ with two and three variables are also shown.
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Temporal variation of the relative difference in the ratio component between GOSAT (bias-uncorrected and bias-corrected) and TCCON ($\Delta_{ratio}$) for each TCCON site: (a) Sodankylä; (b) Orléans; (c) Park Falls; (d) Lamont; (e) Tsukuba; (f) Caltech; (g) Saga; (h) Darwin; (i) Wollongong. Individual data and monthly mean are plotted. Results for the data acquired in the odd-numbered years are shown to assess the applicability of the bias correction using the independent data (coefficients for the correction were obtained using the data acquired in the even-numbered years).</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 11.** (a) Mean and (b) standard deviation (SD) of the mean values of relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) calculated for individual seasons (each season in each year) for each TCCON site. Results for the bias-uncorrected and bias-corrected ratio component (corrections using two, three, and four variables) are presented. The color in the figure corresponds to the $\Delta_{ratio}$ value (blue: large negative value; white: zero; red: large positive value) and the SD value (blue: zero; red: large value) for the mean and SD, respectively.</figcaption></figure>
For Sodankylä, the uncorrected Δ<sub>ratio</sub> was smaller than that for the other sites owing to the large airmass. The low possibility of elevated scattering materials (I<sub>2µm</sub> was small for most of the data) also seems to have contributed to the small Δ<sub>ratio</sub>. Δ<sub>ratio</sub> was overcorrected by the correction using two variables. f<sub>c</sub> tended to be high for the data over this site, and R<sup>act</sup><sub>CH4</sub> seemed to be large according to the model (prior value). Then, the overcorrection was reduced by using four variables. For Orléans, occasional large I<sub>2µm</sub>, 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<sub>ratio</sub> was considered to be affected by many factors. The temporal variation of Δ<sub>alb</sub> was large, since this site was covered by snow during winter and by vegetation during summer. Large I<sub>2µm</sub> was observed during spring. R<sup>act</sup><sub>CO2</sub> is expected to be small during summer due to photosynthesis by vegetation. R<sup>act</sup><sub>CH4</sub> seemed to be large during summer according to the model (prior value). Correction using R<sub>CH4</sub> reduced Δ<sub>ratio</sub>, although a relatively large Δ<sub>ratio</sub> remained, since the complicated conditions were not perfectly accounted for by the correction. For Lamont, large Δ<sub>alb</sub> generally brought large Δ<sub>ratio</sub>. The correction using Δ<sub>alb</sub> reduced Δ<sub>ratio</sub>. A large uncorrected Δ<sub>ratio</sub> was occasionally seen in the early months of the year (Figure 10). We found that the large Δ<sub>ratio</sub> corresponded to the large I<sub>2µm</sub> in February 2013 and 2017. According to Figure 10, these large errors were properly corrected. The use of I<sub>2µm</sub> in the correction had only a small effect on the averaged results (Figure 11), since I<sub>2µm</sub> was not always large; however, the effect could be confirmed for individual cases. For Tsukuba, a large I<sub>2µm</sub> was observed during spring to summer, which enhanced the seasonality of the uncorrected Δ<sub>ratio</sub>. Δ<sub>alb</sub> of this site was small, and thus the overcorrection was reduced by using Δ<sub>alb</sub> in the correction. For Caltech, Δ<sub>alb</sub> was small, and the temporal variations of R<sup>act</sup><sub>CH4</sub> and R<sup>act</sup><sub>CO2</sub> were small according to the model. The difference between R<sup>act</sup><sub>CH4</sub> and R<sup>act</sup><sub>CO2</sub> was also small. Then, the uncorrected Δ<sub>ratio</sub> showed small temporal variation, and the corrected Δ<sub>ratio</sub> varied around zero with the small temporal variation retained. For Saga, the airmass effect and the large I<sub>2µm</sub> during spring to summer enhanced the seasonality, and Δ<sub>ratio</sub> was significantly reduced by the correction using two variables. The temporal variation of R<sup>act</sup><sub>CH4</sub> was expected to be large according to the model. Thus, using R<sub>CH4</sub> in the correction improved both the mean and standard deviation (Figure 11). For the sites in the southern hemisphere (Darwin and Wollongong), although R<sup>act</sup><sub>CH4</sub> and R<sup>act</sup><sub>CO2</sub> were expected to be small, the amplitude of temporal variation of uncorrected Δ<sub>ratio</sub> was comparable to that for the sites in the northern hemisphere (Figure 10). For Darwin, the uncorrected Δ<sub>ratio</sub> showed large temporal variation, although the variation of airmass was small. For Wollongong, occasional large uncorrected Δ<sub>ratio</sub> did not correspond to the large I<sub>2µm</sub>. The standard deviation was reduced only slightly by the correction for these sites (Figure 11). Although using R<sub>CH4</sub> 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<sub>ratio</sub> 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<sub>2µm</sub>) ≤ 1 and cloud fraction (f<sub>c</sub>) = 0). The bias increased with the increase in I<sub>2µm</sub> and reached 1.5% when I<sub>2µm</sub> was 30. The variation of bias with f<sub>c</sub> was small when f<sub>c</sub> was small or large (the bias was 0.4% to 0.5% for the data with f<sub>c</sub> ≤ 0.2 and -0.1% to 0% for the data with f<sub>c</sub> ≥ 0.4). The variation of bias according to I<sub>2µm</sub> and f<sub>c</sub>
could be interpreted based on the difference in the detection target between I2µm and fc, the difference in surface albedo between the CH4 and CO2 bands (Δalb), 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 (RCH4 and RCO2), 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 (ΔPsf)) and that have been revealed to be a large error source for the proxy method (Δalb). The bias showed clear variations with the variables except for RCO2.

Then, airmass, I<sub>2µm</sub>, R<sub>CH4</sub>, and Δ<sub>alb</sub> 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<sub>CH4</sub> in the correction reduced the dependence of the bias on f<sub>c</sub> and ΔP<sub>sf</sub>. The difference in bias between the northern and the southern hemispheres was also reduced. These results are attributed to the information on the CH<sub>4</sub> vertical profile and the effect of atmospheric scattering included in R<sub>CH4</sub>. Although the relationship between bias and R<sub>CH4</sub> is somewhat empirical, R<sub>CH4</sub> 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<sub>2µm</sub> decreases with the increase in f<sub>c</sub> (I<sub>2µm</sub> ≤ 15 when f<sub>c</sub> = 0 and I<sub>2µm</sub> ≤ 1 when f<sub>c</sub> = 1), by investigating the variation of bias in the corrected ratio component with f<sub>c</sub> and I<sub>2µm</sub>. Although f<sub>c</sub> and I<sub>2µm</sub> 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 I2µm. 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.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2072-4292/12/19/3155/s1, Figure S1: Relationship among the Normalized Difference Snow Index (NDSI), relative difference in the ratio component between GOSAT and TCCON (Δ<sub>ratio</sub>), and month of observation. Figure S2: Averaging kernel of the GOSAT clear-sky retrieval for (a) XCH<sub>4</sub> and (b) XCO<sub>2</sub> (monthly mean values of GOSAT data matched the TCCON data). Figure S3: Similar to Figure 1, but for the data with TCCON Fractional Variation in Solar Intensity (FVSI) ≤ 1% and the data with FVSI > 1%. Figure S4: Relationship between the relative difference in the ratio component between GOSAT and TCCON (Δ<sub>ratio</sub>) and the TCCON Fractional Variation in Solar Intensity (FVSI). Figure S5: Similar to Figure 5, but using GOSAT data with DFS for XCO<sub>2</sub> ≥ 1.3.

**Author Contributions:** Conceptualization, Y.Y.; methodology, H.O. (Haruki Oshio) and Y.Y.; software, H.O. (Haruki Oshio) and Y.Y.; validation, H.O. (Haruki Oshio); formal analysis, H.O. (Haruki Oshio) and Y.Y.; investigation, H.O. (Haruki Oshio); resources, T.M., N.M.D., M.D., D.W.T.G., F.H., L.T.I., R.K., C.L., I.M., J.N., Y.-S.O., H.O. (Hirofumi Ohyama), C.P., D.F.P., C.R., K.S., R.S., Y.T., V.A.V., T.W., and D.W.; data curation, Y.Y. and T.M.; writing—original draft preparation, H.O. (Haruki Oshio); writing—review and editing, all; visualization,
H.O. (Haruki Oshio); supervision, Y.Y.; project administration, T.M.; funding acquisition, T.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** The Garmisch TCCON station has been supported by the European Space Agency (ESA) under grant 4000120088/17/I-EF and by the German Bundesministerium für Wirtschaft und Energie (BMWi) via the Deutsche Zentrum für Luft- und Raumfahrt (DLR) under grant 50EE1711D. TCCON stations at Tsukuba, Rikubetsu and Burgos are supported in part by the GOSAT series project. Burgos is also partially supported by the Energy Development Corp, Philippines. Darwin and Wollongong TCCON sites and NMD are supported by Australian Research Council funding via FT180100327, DP160101598, DP140101552, DP110103118, DP0879468 and LE0668470 and NASA grants NAG5-12247 and NNG05-GD07G and the University of Wollongong. The Paris TCCON site has received funding from Sorbonne Université, the French research center CNRS, the French space agency CNES, and Région Île-de-France.

**Acknowledgments:** GOSAT clear-sky retrieval in the present study was conducted at the GOSAT-2 Research Computation Facility.

**Conflicts of Interest:** The authors declare no conflict of interest.

## Appendix A. TCCON Sites and the Influence of the Matching Criteria of GOSAT and TCCON

We used TCCON data from 26 sites [41–67]. Figure A1 shows the map of TCCON sites, and Table A1 shows an overview of the sites. Basically, the sites are located in areas with relatively uniform surface properties and are reasonably far from anthropogenic sources. However, several sites are in areas with nonflat topography or are located near or in urban areas. Such characteristics are summarized in the rightmost column of Table A1.

In the main text, GOSAT data within a ±2° latitude/longitude box centered at each TCCON site were used for the comparison. The influence of the matching criteria on the analysis was assessed. Table A2 shows the mean and standard deviation of Δratio for each TCCON site. Results for the different matching criteria are tabulated. The mean value showed almost no clear trend, but the deviation value decreased as the matching criteria were tightened. Figure A2 shows the relationship between Δratio and the related variables for the matching criteria of ±2° and that of ±0.5°. Although more deviated values are seen for the matching criteria of ±2°, the regression lines were similar between the criteria. The mean Δratio values for the bins also show similar trends between the criteria (Figure A3). The skewness around 0 indicates the small asymmetry for the distribution of Δratio values for each bin. Large negative kurtosis values were hardly seen, meaning there was no high frequency for either side (large and small Δratio).

<figure><img src="image_15.png" /><figcaption>Figure A1. Map of the TCCON sites used.</figcaption></figure>
<table><caption>**Table A1.** Overview of the TCCON sites used.</caption><thead><tr><th>Site</th><th>Country</th><th>Latitude (deg.)</th><th>Longitude (deg.)</th><th>Altitude(km)</th><th>Observation Period of the Data Used</th><th>Specific Characteristics</th></tr></thead><tbody><tr><td>Ny Ålesund</td><td>Spitzbergen, Norway</td><td>78.92N</td><td>11.92E</td><td>0.02</td><td>6 April 2014–31 December 2018</td><td>Useful data are not obtained during winter due to the high solar zenith angle. Useful data are not obtained during winter due to the high solar zenith angle.</td></tr><tr><td>Sodankylä</td><td>Finland</td><td>67.37N</td><td>26.63E</td><td>0.19</td><td>16 May 2009–31 December 2018</td><td></td></tr><tr><td>East Trout Lake</td><td>Canada</td><td>54.35N</td><td>104.99W</td><td>0.50</td><td>7 October 2016–31 December 2018</td><td></td></tr><tr><td>Bialystok</td><td>Poland</td><td>53.23N</td><td>23.03E</td><td>0.18</td><td>23 April 2009–1 October 2018</td><td></td></tr><tr><td>Bremen</td><td>Germany</td><td>53.10N</td><td>8.85E</td><td>0.03</td><td>22 January 2010–31 December 2018</td><td>The site is in the middle-sized city (population ~550 000). The site is near the middle-sized city (population ~300 000). The site is in the large city (population ~2.15 million).</td></tr><tr><td>Karlsruhe</td><td>Germany</td><td>49.10N</td><td>8.44E</td><td>0.12</td><td>19 April 2010–31 December 2018</td><td></td></tr><tr><td>Paris</td><td>France</td><td>48.85N</td><td>2.36E</td><td>0.06</td><td>23 September 2014–31 December 2018</td><td></td></tr><tr><td>Orléans</td><td>France</td><td>47.97N</td><td>2.11E</td><td>0.13</td><td>29 August 2009–31 December 2018</td><td></td></tr><tr><td>Garmisch-Park Falls</td><td>Germany</td><td>47.48N</td><td>11.06E</td><td>0.74</td><td>23 April 2009–31 December 2018</td><td></td></tr><tr><td>Rikubetsu</td><td>Japan</td><td>45.95N</td><td>90.27W</td><td>0.44</td><td>23 April 2009–31 December 2018</td><td></td></tr><tr><td></td><td></td><td>43.46N</td><td>143.77E</td><td>0.38</td><td>16 November 2013–31 December 2018</td><td></td></tr><tr><td>Indianapolis</td><td>USA</td><td>39.86N</td><td>86.00W</td><td>0.27</td><td>23 August 2012–1 December 2012</td><td>The site is in the suburban area of a middle-sized city (population ~880 000). 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.</td></tr><tr><td>Four Corners</td><td>USA</td><td>36.80N</td><td>108.48W</td><td>1.64</td><td>16 March 2013–4 October 2013</td><td></td></tr><tr><td>Lamont</td><td>USA</td><td>36.60N</td><td>97.49W</td><td>0.32</td><td>23 April 2009–31 December 2018</td><td></td></tr><tr><td>Anmyeondo</td><td>Korea</td><td>36.54N</td><td>126.33E</td><td>0.03</td><td>2 February 2015–18 April 2018</td><td>The site is located on the west coast of the Korean Peninsula. The site is in the middle-sized city (population ~240 000).</td></tr><tr><td>Tsukuba</td><td>Japan</td><td>36.05N</td><td>140.12E</td><td>0.03</td><td>4 August 2011–31 December 2018</td><td>The site is adjacent to a very bright playa. The site is near the large city (population ~17 million).</td></tr><tr><td>Edwards</td><td>USA</td><td>34.96N</td><td>117.88W</td><td>0.70</td><td>20 July 2013–31 December 2018</td><td></td></tr><tr><td>JPL</td><td>USA</td><td>34.20N</td><td>118.18W</td><td>0.39</td><td>19 May 2011–14 May 2018</td><td></td></tr><tr><td>Caltech</td><td>USA</td><td>34.14N</td><td>118.13W</td><td>0.23</td><td>20 September 2012–31 December 2018</td><td>The site is near the large city (population ~17 million).</td></tr></tbody></table>
<table><caption>Table A1. *Cont.*</caption><thead><tr><th>Site</th><th>Country</th><th>Latitude (deg.)</th><th>Longitude (deg.)</th><th>Altitude(km)</th><th>Observation Period of the Data Used</th><th>Specific Characteristics</th></tr></thead><tbody><tr><td>Saga</td><td>Japan</td><td>33.24N</td><td>130.29E</td><td>0.01</td><td>28 July 2011–31 December 2018</td><td>The site is in the middle-sized city (population ~230 000).</td></tr><tr><td>Hefei</td><td>China</td><td>31.91N</td><td>117.17E</td><td>0.03</td><td>18 September 2015–31 December 2016</td><td>The site is near the large city (population ~5 million).</td></tr><tr><td>Burgos</td><td>Philippines</td><td>18.53N</td><td>120.65E</td><td>0.04</td><td>3 March 2017–31 December 2018</td><td>The site is at the northernmost point of Luzon Island in the Philippines.</td></tr><tr><td>Manaus</td><td>Brazil</td><td>3.21S</td><td>60.60W</td><td>0.05</td><td>1 October 2014–24 June 2015</td><td></td></tr><tr><td>Darwin</td><td>Australia</td><td>12.42S</td><td>130.89E</td><td>0.03</td><td>23 April 2009–31 December 2018</td><td></td></tr><tr><td>Lauder</td><td>New Zealand</td><td>45.04S</td><td>169.68E</td><td>0.37</td><td>23 April 2009–31 December 2018</td><td>The site is in the midst of rolling hills.</td></tr><tr><td>Wollongong</td><td>Australia</td><td>34.41S</td><td>150.88E</td><td>0.03</td><td>23 April 2009–31 December 2018</td><td>The site is between the ocean and a sharp escarpment.</td></tr></tbody></table>

<table><caption>**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°.</caption><thead><tr><th rowspan="2">Site</th><th colspan="3">±2°</th><th colspan="3">±1°</th><th colspan="3">±0.5°</th><th colspan="3">±0.1°</th></tr><tr><th>μ (%)</th><th>SD (%)</th><th>N</th><th>μ (%)</th><th>SD (%)</th><th>N</th><th>μ (%)</th><th>SD (%)</th><th>N</th><th>μ (%)</th><th>SD (%)</th><th>N</th></tr></thead><tbody><tr><td>Sodankylä</td><td>0.43</td><td>0.74</td><td>328</td><td>0.26</td><td>0.85</td><td>88</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>East Trout Lake</td><td>0.57</td><td>0.68</td><td>40</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Bialystok</td><td>0.50</td><td>0.56</td><td>263</td><td>0.46</td><td>0.51</td><td>87</td><td>0.53</td><td>0.45</td><td>50</td><td></td><td></td><td></td></tr><tr><td>Bremen</td><td>0.51</td><td>0.54</td><td>81</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Karlsruhe</td><td>0.22</td><td>0.62</td><td>267</td><td>0.19</td><td>0.57</td><td>102</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Paris</td><td>0.43</td><td>0.52</td><td>102</td><td>0.50</td><td>0.50</td><td>59</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Orléans</td><td>0.35</td><td>0.51</td><td>518</td><td>0.35</td><td>0.51</td><td>224</td><td>0.43</td><td>0.52</td><td>75</td><td></td><td></td><td></td></tr><tr><td>Garmisch</td><td>0.55</td><td>0.61</td><td>286</td><td>0.53</td><td>0.56</td><td>184</td><td>0.54</td><td>0.52</td><td>56</td><td></td><td></td><td></td></tr><tr><td>Park Falls</td><td>0.61</td><td>0.55</td><td>1017</td><td>0.61</td><td>0.55</td><td>728</td><td>0.59</td><td>0.55</td><td>575</td><td>0.60</td><td>0.55</td><td>536</td></tr><tr><td>Rikubetsu</td><td>0.63</td><td>0.46</td><td>135</td><td>0.73</td><td>0.44</td><td>56</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Indianapolis</td><td>0.44</td><td>0.64</td><td>67</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Lamont</td><td>0.59</td><td>0.54</td><td>1949</td><td>0.59</td><td>0.51</td><td>855</td><td>0.61</td><td>0.45</td><td>461</td><td>0.62</td><td>0.45</td><td>305</td></tr><tr><td>Anmeyondo</td><td>0.51</td><td>0.45</td><td>50</td><td>0.52</td><td>0.37</td><td>33</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Tsukuba</td><td>0.31</td><td>0.61</td><td>1407</td><td>0.31</td><td>0.59</td><td>1186</td><td>0.28</td><td>0.60</td><td>675</td><td>0.41</td><td>0.49</td><td>179</td></tr><tr><td>Edwards</td><td>0.43</td><td>0.45</td><td>126</td><td>0.60</td><td>0.45</td><td>59</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>JPL</td><td>0.26</td><td>0.49</td><td>609</td><td>0.27</td><td>0.43</td><td>490</td><td>0.24</td><td>0.39</td><td>438</td><td>0.25</td><td>0.38</td><td>103</td></tr><tr><td>Caltech</td><td>0.32</td><td>0.43</td><td>2067</td><td>0.32</td><td>0.43</td><td>1924</td><td>0.32</td><td>0.43</td><td>1412</td><td>0.31</td><td>0.43</td><td>853</td></tr><tr><td>Saga</td><td>0.59</td><td>0.59</td><td>438</td><td>0.58</td><td>0.55</td><td>288</td><td>0.65</td><td>0.53</td><td>222</td><td>0.72</td><td>0.52</td><td>66</td></tr><tr><td>Darwin</td><td>0.37</td><td>0.36</td><td>555</td><td>0.38</td><td>0.36</td><td>500</td><td>0.56</td><td>0.36</td><td>46</td><td>0.48</td><td>0.34</td><td>30</td></tr><tr><td>Wollongong</td><td>0.42</td><td>0.71</td><td>349</td><td>0.31</td><td>0.58</td><td>195</td><td>0.34</td><td>0.61</td><td>100</td><td></td><td></td><td></td></tr><tr><td>Lauder</td><td>0.36</td><td>0.35</td><td>124</td><td>0.35</td><td>0.34</td><td>121</td><td>0.37</td><td>0.31</td><td>92</td><td>0.36</td><td>0.30</td><td>85</td></tr><tr><td>All sites</td><td>0.43</td><td>0.55</td><td>10846</td><td>0.41</td><td>0.52</td><td>7263</td><td>0.40</td><td>0.51</td><td>4357</td><td>0.45</td><td>0.49</td><td>2249</td></tr><tr><td>Intersite bias</td><td>0.14</td><td></td><td></td><td>0.13</td><td></td><td></td><td>0.16</td><td></td><td></td><td>0.15</td><td></td><td></td></tr></tbody></table>
<figure><img src="image_16.png" /></figure>

**Figure A2.** Relationship between the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) and the related variable: (a) normalized 2µm band radiance ($I_{2\mu m}$); (b) difference in retrieved surface albedo (CH$_4$ band minus CO$_2$ band, $\Delta_{alb}$); (c) airmass; (d) ratio between the partial column-averaged dry-air mole fractions for the lower atmosphere and that for the upper atmosphere ($R_{CH4}$). Results for the different matching criteria are plotted (GOSAT data within ±2° and ±0.5° latitude/longitude boxes centered at each TCCON site). Linear regressions are depicted by solid lines. For $I_{2\mu m}$ and $R_{CH4}$, the data with cloud fraction = 0 were used. For $\Delta_{alb}$ and airmass, the data with cloud fraction = 0 and $I_{2\mu m} \le 1$ were used.
<figure><img src="image_17.png" /><figcaption>**Figure A3.** Relationship between the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) and the related variables. The variables (a–d) are similar to those in Figure A2, but in each panel, the mean and standard deviation (SD) of $\Delta_{ratio}$, number of data points (N), skewness, and kurtosis for each bin are shown. Results for the different matching criteria are plotted (GOSAT data within ±2° and ±0.5° latitude/longitude boxes centered at each TCCON site). For $I_{2\mu m}$ and $R_{CH_4}$, the data with cloud fraction = 0 were used. For $\Delta_{alb}$ and airmass, the data with cloud fraction = 0 and $I_{2\mu m} \le 1$ were used.</figcaption></figure>

## Appendix B. Bias Correction for the Data Acquired by Gain M

The different gain settings of the TANSO-FTS (H and M) only affect the spectral radiance of the Band 1 [76]. Therefore, the ratio component should show similar characteristics between the data acquired with gain H and that acquired with gain M. Then, the bias correction equation established using the gain H data (four variables with the coefficients shown in Section 4.4) was applied to the gain M data. Figure A4 shows the scatterplot of the ratio component derived from GOSAT gain M data and that derived from TCCON. The results for each site are shown in Table A3. The bias-uncorrected and bias-corrected results are presented in the left and right sides in Figure A4 and Table A3, respectively. Figure A5 shows the dependence of $\Delta_{ratio}$ on the related variables for the uncorrected and the corrected data. The matching criteria were similar to those in the main text. Only GOSAT data over the areas east of 118°W were used to reject the data over Bakersfield where there are oil fields. According to
Figure A4, the bias was smaller than that for the gain H data for the uncorrected data, and the bias was slightly overcorrected. Table A3 shows that the overcorrection was seen for the data of JPL and Caltech. This is reasonable for the following reasons. Almost all the GOSAT data acquired with gain M in this region were located around the Edwards site. For the time period during which TCCON observation was not being performed at the Edwards site, the GOSAT data were matched with the TCCON data at JPL or Caltech. The Edwards site is located in the north of San Gabriel Mountains, while the other two sites are located in the south of the mountains. Therefore, it was possible that the air at the other two sites was occasionally different from the air at the Edwards site. Then, the results for the Edwards site (bias of -0.07% after the correction) indicate that the GOSAT data can be used for the proxy retrieval without exercising caution with respect to the gain settings and support the applicability of the bias correction.

<figure><img src="image_18.png" /><figcaption>(b) Bias corrected</figcaption></figure>

<figure><img src="image_19.png" /></figure>

**Figure A4.** Similar to Figure 1a but for GOSAT data acquired with gain M: (a) bias-uncorrected; (b) bias-corrected.

**Table A3.** The relative difference in the ratio component between GOSAT (gain M) and TCCON ($\Delta_{ratio}$) for each site: mean ($\mu$), standard deviation (SD), and interseasonal bias ($S_{SD}$) of $\Delta_{ratio}$ and the number of matched GOSAT and TCCON data points (N) are shown.

<table><thead><tr><th rowspan="2">Site</th><th rowspan="2">μ (%)</th><th colspan="2">Uncorrected</th><th rowspan="2">N</th><th rowspan="2">μ (%)</th><th colspan="2">Bias-Corrected</th><th rowspan="2">N</th></tr><tr><th>SD (%)</th><th>S<sub>SD</sub> (%)</th><th>SD (%)</th><th>S<sub>SD</sub> (%)</th></tr></thead><tbody><tr><td>Edwards</td><td>0.35</td><td>0.41</td><td>0.11</td><td>766</td><td>-0.07</td><td>0.39</td><td>0.04</td><td>766</td></tr><tr><td>JPL</td><td>0.01</td><td>0.50</td><td>0.11</td><td>214</td><td>-0.39</td><td>0.46</td><td>0.09</td><td>214</td></tr><tr><td>Caltech</td><td>0.04</td><td>0.35</td><td></td><td>15</td><td>-0.40</td><td>0.34</td><td></td><td>15</td></tr></tbody></table>
<figure><img src="image_20.png" /><figcaption>**Figure A5.** Relationship between the relative difference in the ratio component between GOSAT and TCCON ($\Delta_{ratio}$) and the related variables for the GOSAT data acquired with gain M: (a) normalized 2 µm band radiance ($I_{2\mu m}$); (b) cloud fraction ($f_c$); (c) retrieved surface albedo of CH$_4$ band ($\rho_{CH4}$); (d) difference in the retrieved surface albedo (CH$_4$ band minus CO$_2$ band, $\Delta_{alb}$); (e) airmass ($A_m$); (f) deviation of the retrieved clear-sky surface pressure from its prior ($\Delta P_{srf}$); (g,h) ratio between the partial column-averaged dry-air mole fractions for the lower atmosphere and that for the upper atmosphere ($R_{CH4}$ and $R_{CO2}$). Mean $\Delta_{ratio}$ for each bin is plotted for the bias-uncorrected and bias-corrected data.</figcaption></figure>

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