Full-physics carbon dioxide retrievals from the Orbiting Carbon Observatory-2 (OCO-2) satellite by only using the 2.06 µm band

Passive remote sensing of atmospheric carbon dioxide uses spectroscopic measurements of sunlight backscattered by the Earth's surface and atmosphere. The current state-of-the-art retrieval methods use three different spectral bands, the oxygen A band at 0.76 µm and the weak and strong CO₂ absorption bands at 1.61 and 2.06 µm, respectively, to infer information on light scattering and the carbon dioxide column-averaged dry-air mole fraction XCO₂. In this study, we propose a one-band XCO₂ retrieval technique which uses only the 2.06 µm band measurements from the Orbiting Carbon Observatory-2 (OCO-2) satellite. We examine the data quality by comparing the OCO-2 XCO₂ with collocated ground-based measurements from the Total Carbon Column Observing Network (TCCON). Over land and ocean the OCO-2 one-band retrieval shows differences from TCCON observations with a standard deviation of ∼1.30 ppm and a station-to-station variability of ∼0.50 ppm. Moreover, we compare one-band and three-band retrievals over Europe, the Middle East, and Africa and see high correlation between the two retrievals with a SD of 0.93 ppm. Compared to the three-band retrievals, XCO₂ retrievals using only the 2.06 µm band have similar retrieval accuracy, precision, and data yield.

1 Introduction

Over the past decade, space-based measurements of atmospheric carbon dioxide (CO₂) have been used, along with ground-based measurements, to characterize CO₂ sources and sinks in order to better understand the carbon cycle. The inversion models that calculate the CO₂ fluxes are sensitive to biases in the carbon dioxide dry-air column-averaged mole fraction (XCO₂) as small as 0.5 ppm (see e.g., Miller et al., 2007; Basu et al., 2013). This poses enormous challenges on the instruments, calibration, and retrieval algorithms used to measure XCO₂, and much effort is needed to reduce instrument, calibration, spectroscopy, and other forward model errors. In particular, scattering by aerosol and thin cirrus clouds (thick clouds are screened) can lead to light path modifications causing unacceptable errors in XCO₂ if not accounted for in the radiative transfer calculations (Guerlet et al., 2013; Aben et al., 2007). The currently operational CO₂ satellites, i.e., the Greenhouse Gases Observing Satellite (GOSAT; Kuze et al., 2009) and the Orbiting Carbon Observatory-2 (OCO-2; Crisp et al., 2017), and the corresponding retrieval algorithms (e.g., Butz et al., 2009; Boesch et al., 2011; O'Dell et al., 2012; Buchwitz et al., 2017) apply a three-band approach using three spectral bands around 0.76 (O₂ A band), 1.61 (weak CO₂ band), and 2.06 µm (strong CO₂ band) to simultaneously retrieve XCO₂ and other relevant parameters such as surface albedos and aerosol properties.

It has been proposed by Butz et al. (2009), based on simulated OCO measurements, that retrievals using the 2.06 µm band alone actually show a performance similar to that when using three bands. The reasons would be that one-band retrievals are less dependent on spectral scattering properties than three-band retrievals. We examine whether this claim holds for real OCO-2 measurements by comparing the XCO₂ products for both methods in terms of accuracy and data yield. For the OCO-2 measurements a single-band retrieval is computationally less expensive, which is important considering the huge data amount to be processed. More generally, a single-band retrieval requires a simpler and thus cheaper instrument and may avoid possible complications related to spectral-window-dependent (calibration) errors. For example for OCO-2, there are indications that it is necessary to fit an intensity offset in the weak and strong CO₂ absorption bands to account for potential instrumental errors (Wu et al., 2018).

The paper is organized as follows: we first introduce the data that we used in this work in Sect. 2. The retrieval algorithm and setup for three-band and one-band retrievals are described in Sect. 3. Section 4 evaluates the one-band retrieval performance with the Total Carbon Column Observing Network (TCCON) XCO₂ observations and compares the performance to that of three-band retrievals. Finally we conclude and discuss our findings in Sect. 5.

2 Data

In this paper, we use OCO-2 version 8 L1b data between September 2014 and October 2017. To evaluate the retrieval performance, we only use measurements that are collocated with TCCON measurements. Although some limitations exist as discussed by Kulawik et al. (2016), TCCON measurements are still the most appropriate validation product for space-based XCO₂ retrievals. OCO-2 measurements are considered collocated when they are taken within 2 h and a distance of less than 3^∘ in both latitude and longitude of a TCCON measurement. Here, we do not use TCCON stations located within polluted areas, high-latitude regions, or areas with significant topography. The retrieval algorithm also uses the ECMWF (European Centre for Medium-Range Weather Forecasts) high-resolution analysis data to obtain meteorological information including pressure, temperature, humidity, and surface wind speed. For each OCO-2 measurement, the surface elevation data are obtained from the 90 m digital elevation data of NASA's Shuttle Radar Topography Mission (SRTM) (Farr et al., 2007). Prior information on the carbon dioxide profile is extracted from the CarbonTracker model for the year 2013 with an added annual increase of 2.25 ppm (Peters et al., 2007).

3 Retrieval algorithm and methodology

We use the RemoTeC retrieval algorithm (Hasekamp and Butz, 2008; Butz et al., 2009), which has been extensively used for greenhouse gas retrievals from satellite observations like GOSAT, OCO-2, and S5P measurements (Butz et al., 2011; Schepers et al., 2012; Guerlet et al., 2013; Hu et al., 2016, 2018; Wu et al., 2018). The adaptations and first use for OCO-2 measurements are described in Wu et al. (2018). There we employed the three-band XCO₂ retrievals, which will be used here as a reference to compare against our XCO₂ retrievals from the 2.06 µm band.

Table 1 State vector elements for the three-band and one-band retrievals.

Table 2 Filter variables applied to reject low-quality XCO₂ retrievals over land and ocean in three-band and one-band retrievals. For most variables, ocean glint retrievals have the same filtering criteria as those over land. However, due to ocean glint's unique viewing geometry and different surface properties, aerosol- and surface-related filtering variables have different ranges and are listed separately in brackets. Filter variables not used in the relevant retrieval type are marked with a ∀ sign. The blended albedo can be derived using surface albedos in the O₂ A band (A_0.76) and 2.06 µm band (A_2.06) by 2.4A_0.76–1.13A_2.06 (Wunch et al., 2011). The aerosol ratio parameter is calculated with the three retrieved aerosol parameters by $\mathit{\tau }*z/\mathit{\alpha }$.

The three-band retrieval fits OCO-2 measurements in all three OCO-2 spectral windows. The state vector that is retrieved contains 35 elements as shown in Table 1: a 12-layer vertical profile of CO₂ partial columns, the total columns of H₂O and CH₄, three effective scattering parameters, and, for each channel, three albedo parameters describing the Lambertian albedo up to its 2nd-order spectral dependence, an intensity offset, spectral shifts for the Earth radiance measurement, and the solar reference model. We do not retrieve the dry-air column but compute it using the ECMWF meteorological data. As described in Wu et al. (2018), we use a Lambertian reflection model for land surface reflection properties, and for ocean surfaces we use a wind-speed-driven reflection model of Cox and Munk (1954) combined with an additive wavelength-dependent Lambertian term. The retrieved three aerosol parameters are the total column number density N, the parameter α of a power-law size distribution ($n\left(r\right)\propto r^{-\mathit{\alpha }}$ with the particle radius r), and the central height parameter z of a Gaussian height distribution. The full width at half maximum of the Gaussian height distribution is fixed at 2 km.

Figure 1 XCO₂ retrievals by using only the 2.06 µm band of OCO-2. We evaluate overpass-averaged results over land and ocean separately. In each panel, we include bias (b_a), standard deviation of the difference (σ_a), station-to-station variability (σ_s), number of overpasses (N), Pearson correlation coefficient (r), and one-to-one line. For each overpass, variations in XCO₂ retrievals and TCCON data are presented with error bars.

Figure 2 Bias (a) and standard deviation (b) variation at different TCCON stations for one-band and three-band retrievals over land. To see the bias variation on the same reference level, we directly subtract mean bias b_a of one-band and three-band retrievals accordingly as listed in Table 3. The station-to-station variability (σ_s) is included in the legend of (a). In (b), the number of overpass at each station is listed on the bar. The TCCON stations are ordered by latitude from Southern Hemisphere to Northern Hemisphere. Stations with fewer than five overpasses are excluded.

In the one-band retrieval, we attempt to infer XCO₂ by only using OCO-2 measurements in the spectral range 2042–2081 nm. The state vector is the same as for the three-band retrieval except that the CH₄ column is not included and it only contains surface albedo, intensity offset, and spectral shift parameters for the 2.06 µm band (see Table 1). In the retrieval, we seek the state vector for which a cost function including the difference between the forward model and measurements and a side constraint is minimized. The same Phillips–Tikhonov regularization scheme as employed in the three-band retrieval is used to solve the minimization problem iteratively (Phillips, 1962; Tikhonov, 1963; Hasekamp and Landgraf, 2005; Wu et al., 2018). Like for the three-band retrieval, we choose the regularization parameter such that the degree of freedom for signal (DFS) for the CO₂ profile is in the range 1.0–1.5 (Wu et al., 2018). Clearly, a one-band retrieval using only the 2.06 µm band is only possible if surface pressure information from meteorological reanalysis/forecast is used in the retrieval algorithm. Retrieving this information, as is done by most algorithms, requires the O₂ A band (Yokota et al., 2009; O'Dell et al., 2012).

Figure 3 Same as Fig. 2, but for retrievals over ocean.

Table 3 Overall performance of three-band and one-band retrievals. Here, overall bias and single sounding precision are estimated for single soundings. All other quantities are obtained using overpass-averaged values.

Table 4 Similar to Table 3 but for non-scattering retrievals using the 2.06 µm band. Here, we use the same cases as one-band retrievals in Table 3.

It should be noted that the retrieval algorithm is only applicable to clear-sky scenes, so we must define a suitable cloud filter that preselects the scenes to be processed. Before performing full-physics XCO₂ retrievals, we retrieve the columns of O₂, CO₂, and H₂O independently in the three spectral bands under the assumption of a non-scattering atmosphere. When neglecting cloud or aerosol scattering, the ratio between the CO₂ or H₂O column retrieved from the 1.61 µm band and that retrieved from the 2.06 µm band is a measure of the light path modification because a large deviation can be introduced due to different light path sensitivity. The ratio between the retrieved O₂ column and the one computed from the ECMWF surface pressure can also be used to detect clouds. We consider the following scenes as sufficiently cloud-free:

$$\begin{array}{}\text{(1)}& \begin{array}{rl}\mathrm{0.90}<& {\displaystyle \frac{{\mathrm{O}}_{\mathrm{2}}\left(\mathrm{0.76}\mathrm{\mu }\mathrm{m}\right)}{{\mathrm{O}}_{\mathrm{2}}\left(\mathrm{ecmwf}\right)}}<\mathrm{1.02},\mathrm{0.98}<{\displaystyle \frac{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(\mathrm{1.61}\mathrm{\mu }\mathrm{m}\right)}{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(\mathrm{2.06}\mathrm{\mu }\mathrm{m}\right)}}\\ & <\mathrm{1.05}\mathrm{and}\mathrm{0.98}<{\displaystyle \frac{{\mathrm{CO}}_{\mathrm{2}}\left(\mathrm{1.61}\mathrm{\mu }\mathrm{m}\right)}{{\mathrm{CO}}_{\mathrm{2}}\left(\mathrm{2.06}\mathrm{\mu }\mathrm{m}\right)}}<\mathrm{1.03}\end{array}.\end{array}$$

This classifies around 26 % of all soundings as cloud-free. However, this cloud screening strategy can not work for the one-band retrieval because here we restrict ourselves to using only measurements from the 2.06 µm band.

Here, we propose a new cloud filter based only on the 2.06 µm band to truly investigate the case where the other bands are not available. We first screen by retrieving XCO₂ using the whole 2.06 µm band under the assumption of a non-scattering atmosphere and divide this by the a priori value derived from the CarbonTracker. When this ratio is <0.96 or >1.04, the scene is considered too cloudy for XCO₂ retrieval. Then, we use two sub-spectral windows in the 2.06 µm band: one weak absorption window centered around 2.08 µm in the spectral range 2078–2081 nm and one strong absorption window centered around 2.05 µm in the spectral range 2042–2057 nm. The columns of CO₂ and H₂O are retrieved independently from these two sub-windows under the assumption of a non-scattering atmosphere, and the ratios between the CO₂ and H₂O columns retrieved from those two sub-windows are used for cloud screening. The idea is similar to three-band cloud filtering in that a large deviation can be introduced to CO₂ and H₂O columns retrieved from these two bands due to different light path sensitivity (Taylor et al., 2016). We only use spectra which meet the following criteria:

$$\begin{array}{}\text{(2)}& \begin{array}{rl}\mathrm{0.89}<& {\displaystyle \frac{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(\mathrm{2.08}\mathrm{\mu }\mathrm{m}\right)}{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(\mathrm{2.05}\mathrm{\mu }\mathrm{m}\right)}}<\mathrm{1.05}\mathrm{and}\mathrm{0.98}\\ & <{\displaystyle \frac{{\mathrm{CO}}_{\mathrm{2}}\left(\mathrm{2.08}\mathrm{\mu }\mathrm{m}\right)}{{\mathrm{CO}}_{\mathrm{2}}\left(\mathrm{2.05}\mathrm{\mu }\mathrm{m}\right)}}<\mathrm{1.03}\end{array}.\end{array}$$

After the filtering procedure described above, around 27 % of total soundings are considered cloud-free cases, which is similar to what is found by the three-band cloud filter. The one-band cloud filter and the three-band cloud filter have an overlap of 75 %.

Figure 4 Error on XCO₂ from one-band and three-band OCO-2 land retrievals as a function of aerosol optical thickness (in O₂ A band), size parameter, and layer height as retrieved by three-band retrievals. Shown are the mean bias for each parameter bin along with standard deviation within each bin. Background includes the density map of XCO₂ errors from one-band retrievals.

Figure 5 Histogram of DFS for aerosols, aerosol size parameter, aerosol optical depth, and aerosol layer height in the one-band retrievals.

For cloud-screened soundings, we first run full-physics retrievals and then apply posterior quality filtering based on the criteria shown in Table 2. Those criteria are related to extreme viewing geometry, difficult scattering scenes, challenging surface properties, spectra with larger uncertainties, and poor fit between forward model and measurements. After the quality filtering, the overall throughputs are 17.0 % and 18.0 % for one-band and three-band retrievals, respectively. The two data sets have an overlap of 75 %.

Figure 6 XCO₂ distributions over the EMEA regions from one-band (a) and three-band (b) retrievals in the time period between 8 September and 31 December 2014. In (c) corresponding XCO₂ retrievals from one-band and three-band retrievals are shown with bias (b), standard deviation (σ), and Pearson correlation coefficient (r). Here, a mean bias of 0.88 ppm was subtracted from three-band retrievals.

4 Performance evaluation

Note that in this work, we do not apply a bias correction as it is common practice for CO₂ retrievals from space-based observations (Wunch et al., 2017; Wu et al., 2018; O'Dell et al., 2018), but show the uncorrected results because we want to evaluate the true retrieval capability. Due to the high spatial sampling of OCO-2, we typically obtain several collocations of OCO-2 retrievals with individual TCCON measurements for our collocation criteria in a single overpass. To reduce the impact of random and representation errors in our comparison, we compare overpass averages between OCO-2 and TCCON results and use bias (b_a), standard deviation of the difference (σ_a), and station-to-station variability (σ_s) for performance evaluation (Buchwitz et al., 2017). The station-to-station variability is the standard deviation of all biases between the different TCCON sites and is a measure of regional-scale accuracy, which is crucial for flux inversion.

Figure 1 shows validations of one-band XCO₂ retrievals over land and ocean. We neglect cases where fewer than 10 individual data points are available in OCO-2 retrievals during one overpass. Here, both land and ocean retrievals exhibit high correlation (around 0.94) with TCCON data, and both have a standard deviation (SD) of ∼1.30 ppm.

To evaluate the one-band and three-band retrieval performance in more detail, Figs. 2 and 3 show the bias and SD of the retrievals per TCCON station. One-band and three-band retrievals have similar bias and SD among most individual stations. One-band retrievals have slightly higher overall SD, which is increased by 0.01 ppm for land retrievals and 0.14 ppm for ocean retrievals. Over land, one-band and three-band retrievals have comparable station-to-station variability of 0.44 and 0.42 ppm, respectively. Over ocean, the one-band retrieval has a station-to-station variability of 0.55 ppm, which is about 0.1 ppm higher than that of the three-band retrieval; however, as shown in Fig. 3 this is mainly caused by larger biases from the Lauder and Ascension stations. The causes for large biases over the two sites are still unclear. However, they are unlikely due to aerosols because non-scattering retrievals exhibit similar biases, and over ocean aerosols should lead to underestimation instead of overestimation (Butz et al., 2013).

Table 3 summarizes the overall validation performance of the one-band and three-band retrievals with TCCON measurements. Compared with three-band retrievals, one-band retrievals have similar throughput and similar high correlation coefficients with TCCON. In one-band retrievals, the single sounding precision is 0.16 ppm larger over both land and ocean. In terms of bias, one-band retrievals have a smaller overall bias but a station-to-station variability similar to that of three-band retrievals.

For the general applicability of the one-band retrieval, it is important to know if the performance of the one-band retrievals is more affected by the amount and properties of aerosols than the three-band retrievals. Figure 4 shows one-band and three-band land retrieval differences with respect to TCCON as a function of aerosol optical thickness (AOT) in the O₂ A band, size parameter, and layer height as retrieved by the three-band retrievals. With AOT, one-band retrievals show a positive correlation of 0.17 while three-band retrievals present an anticorrelation of −0.11. In both retrievals, the range of errors between AOT =0.01 and AOT =0.30 is around 1.0 ppm. Scattering errors in both retrievals show similar correlations with aerosol size parameter and layer central height. Thus, compared with three-band retrievals, one-band retrievals exhibit a similar dependence on aerosol properties.

On the other hand, as shown in Fig. 5 the DFS for aerosol parameters in the one-band retrieval is mostly well below 1, while for the three-band retrieval it is around 2 in most cases. Aerosol properties as retrieved by the one-band retrievals vary within a small range around the prior values. This triggers the question of whether a non-scattering retrieval would also provide performance similar to that of the one-band “full-physics” retrieval for the cases considered in this study. To investigate this, we also performed a non-scattering retrieval using the 2.06 µm band only. The results are summarized in Table 4. It can be seen that the non-scattering retrieval has a much larger bias, and the standard deviation of differences with TCCON and the station-to-station bias are somewhat larger than for the one-band (and three-band) retrieval. The improvement of the one-band retrievals compared to the non-scattering retrievals becomes more clear if we consider the Izana TCCON station close to the Sahara, known as a region with difficult aerosol scenes for XCO₂ retrieval. Here, we employ a coarse spatial collocation criteria (16.5< latitude <34.0^∘ and $-\mathrm{16.0}<$ longitude <24.5^∘) for observations made between September 2014 and October 2017, which results in 10⁵ valid retrievals. For this Sahara region, the bias and standard deviation (b, σ) of differences with TCCON for one-band and non-scattering retrievals are (−0.23, 1.49) ppm and (−2.46, 1.93) ppm, respectively.

We conclude that despite the small DFS for aerosol properties in the one-band retrieval, the explicit treatment of aerosols in the one-band retrieval is still important to achieve sufficient accuracy on XCO₂, comparable to the three-band retrievals.

To further investigate the validity of the conclusions based on the OCO-2 vs. TCCON comparison, we performed a comparison between one-band and three-band retrievals over a larger region. Here, we perform one-band and three-band XCO₂ retrievals over Europe, the Middle East, and Africa (EMEA) for all OCO-2 observations made between 8 September and 31 December 2014. In Fig. 6, one-band and three-band retrievals over the EMEA region show similar data coverage and regional XCO₂ variations, for example, low XCO₂ values in eastern Europe and enhancement towards the Middle East. Here, one-band and three-band retrievals are highly correlated (r=0.84) with a SD of 0.93 ppm. This indicates that the conclusions drawn above on the similar performance between the one-band and three-band retrievals are not only valid for regions around TCCON stations.

5 Conclusions

The comparison between the performance of one-band XCO₂ retrievals from OCO-2 using only the 2.06 µm band and the commonly employed three-band retrievals showed that with one band similar accuracy can be achieved as with three bands while the processing time is reduced by 40 %. The most noticeable difference is the slightly increased standard deviation of the differences between OCO-2 and TCCON measurements. We see that leaving out the O₂ A band and weak CO₂ absorption band has little effect on the station-to-station variability in the XCO₂ retrievals. Our results suggest that the O₂ A band adds only limited information on aerosols relevant for XCO₂ retrievals, confirming earlier results (Butz et al., 2009) using simulated OCO measurements. For future missions it may be better to replace the O₂ A band with measurements that have larger information content on aerosols, like a multi-angle polarimeter (MAP) (Mishchenko and Travis, 1997; Hasekamp and Landgraf, 2007; Wu et al., 2015).

In order to evaluate the true retrieval capability of the one-band and three-band retrievals, we have not applied any bias corrections in this study. It should be noted though that in general a bias correction is needed and will improve the validation against TCCON. For example, Wunch et al. (2017) and Kiel et al. (2019) have found it necessary to apply, among others, a swath-dependent bias correction.