The authors present an analysis of the global midtropospheric CO2 retrieved for all-sky (clear and cloudy) conditions from measurements by the Atmospheric Infrared Radiation Sounder on board the Aqua satellite in 2003–09. The global data coverage allows the identification of the set of CO2 spatial patterns and their time variability by applying principal component analysis and empirical mode decomposition. The first, dominant pattern represents 93% of the variability and exhibits the linear trend of 2 ± 0.2 ppm yr−1, as well as annual and interannual dependencies. The single-site record of CO2 at Mauna Loa compares well with variability of this pattern. The first principal component is phase shifted relative to the Southern Oscillation, indicating a causative relationship between the atmospheric CO2 and ENSO. The higher-order patterns show regional details of CO2 distribution and display the semiannual oscillation. The CO2 distributions are compared with the distribution of two major characteristics of air transport: the vertical velocity and potential temperature surfaces at the same height. In agreement with modeling, CO2 concentration closely traces the potential temperature surfaces (isentropes) in middle and high latitudes. However, its vertical transport in the tropics, where these surfaces are mostly horizontal, is suppressed. The results are in agreement with the previous results on annual and interannual CO2 time variability obtained by using the network flask data. This knowledge of the global CO2 spatial patterns can be useful in climate analyses and potentially in the challenging task of connecting CO2 sources and sinks with its distribution in the atmosphere.
Carbon dioxide (CO2), a critical component of climate change, is a long-lived gas in the earth’s atmosphere; hence its distribution is fully determined by the sources and sinks at the earth’s surface and by the transport in the atmosphere. The classic work by Keeling (1960) based on his single-site Mauna Loa measurements resulted in the discovery of a long-term trend driven by the burning of fossil fuels and a seasonal cycle, which arises from the seasonal growth and decay of land plants in the Northern Hemisphere. Since that time, substantial progress has been made in measurement and data analysis techniques and in modeling codes used for the CO2 studies. The Mauna Loa single-site measurements have been expanded to a global network of ground-based flask observations (GLOBALVIEW-CO2; http://www.esrl.noaa.gov/gmd/ccgg/) to infer surface CO2 flux estimates as input to modeling of the CO2 transport. There are also atmospheric column measurements of CO2 from the ground using high-resolution solar absorption spectra in near-IR (Yang et al. 2002) and aircraft measurements of vertical atmospheric distributions of CO2 (Stephens et al. 2007) at several different locations around the globe. Recently the High-Performance Instrumented Airborne Platform for Environmental Research (HIAPER) Pole-to-Pole Observational (HIPPO) program has accomplished its first three aircraft transects of the Pacific from 85°N to 67°S, providing fine vertical profiles of CO2 every 2.2° latitude (Wofsy et al. 2011). These aircraft measurements allow the resolution of sharp gradients of CO2, which exist at air mass boundaries or are caused by plumes of concentration emanating from some ground sources, thus overcoming one of the shortcomings of modeling and smoothed datasets. Comparison of modeling with the ground-based, aircraft, and satellite data can be found in a recent paper by Feng et al. (2011).
There are ongoing efforts to use satellite measurements, which offer advantages of global spatial and continuous coverage of greenhouse gases. The designated remote sensing measurements, such as from the Greenhouse Gases Observing Satellite (GOSAT; Yokota et al. 2009) and Orbiting Carbon Observatory-2 (OCO-2; Crisp et al. 2004), provide and will provide the column CO2 to constrain the exchange of CO2 between the atmosphere and the surface in cloud-free regions (Chevallier et al. 2007) and have the potential for the ground flux reconstructions in a modeling framework (Engelen et al. 2004; Tiwari et al. 2006). Work has been done on the CO2 retrieval from the measurements carried out by the Atmospheric Infrared Radiation Sounder (AIRS) and the Advanced Microwave Sound Unit (AMSU) on board Aqua (see Strow and Hannon 2008, and references therein). These retrievals used cloud-clear regions and the values of other parameters (e.g., temperature) from the European Centers for Medium-Range Weather Forecasts (ECMWF). In contrast, Chahine et al. (2005, 2008) using the AIRS level-2 (L2) product carried out retrievals that provide the global CO2 data at specific atmospheric heights without limitation to cloud-free regions, thus substantially expanding the global coverage.
Substantial progress has also been made in understanding time and spatial variability of the atmospheric CO2 on synoptic (Fung et al. 1983) and interannual time scales (Dargaville et al. 2000; Dettinger and Ghil 1998; Lintner 2002; Taguchi et al. 2003). The interannual variability in atmospheric CO2 has been attributed mostly to the effect of the El Niño–Southern Oscillation (ENSO) based on singular spectrum analysis of the Mauna Loa and South Pole data (Dettinger and Ghil 1998) and on the principal component analysis (PCA) of the rate of CO2 growth derived from 89 stations in the GLOBALVIEW-CO2 dataset (Lintner 2002). Important studies have been made on understanding the origin of the interhemispheric gradient of CO2. It has been shown that the gradient is caused not only by the interhemispheric differences in fossil-fuel emission but also by seasonal exchange of the terrestrial biota (Tans et al. 1990; Denning et al. 1995). The mechanisms of interhemispheric transport of passive tracers, such as CO2, are discussed in Lintner et al. (2004).
Here we use the global all-sky satellite CO2 data in the midtroposphere retrieved from the AIRS measurements for a prolonged 7-yr period to identify for the first time the set of global spatial patterns formed by the observed CO2 and to investigate their long-term time variability from seasonal changes to trends. In section 2, we describe the data used for our study. In section 3, as a prelude and demonstration of why the search for patterns is necessary, we calculate the distributions of means, standard deviations, linear trends, and the time evolution of zonal averages under the assumption that spatial grid points are independent of each other. In section 4, we describe the methods we use to take into account the correlations between the spatial grid points in order to identify the global patterns of CO2. Section 5 presents the major patterns. In section 6, we compare the time variability of the dominant pattern with the well established a single-site standard record of CO2 at Mauna Loa. Section 7 concludes the paper by a brief discussion of the possible origin of the patterns related to transport of CO2 in the troposphere.
2. AIRS CO2 data
The previous work on satellite retrievals (see Chédin et al. 2003; Crevoisier et al. 2003; Engelen et al. 2004; Tiwari et al. 2006), which used measurements in limited time intervals and for only clear-sky regions, showed the feasibility of obtaining successful CO2 datasets and indicated some outstanding problems. Strow and Hannon (2008) gave a comprehensive review of the previous work on the atmospheric CO2 retrievals from AIRS measurements. They used clear-sky radiances over the ocean in frequency channels sensitive to 550 hPa. For the CO2 retrievals, 4 yr of AIRS measurements were combined with the nearest matching ECMWF forecast and analysis fields. These works showed a seasonal pattern in global CO2 distribution.
What distinguishes our work is the use of CO2 for all-sky conditions and for a period of time (7 yr) longer than previously done. This allows us to identify the spatial patterns and long-term variability of CO2. We use the CO2 retrieved from the measured and modeled AIRS spectra at a set of frequencies in the 15-μm band of the CO2 absorption line. The maximum sensitivity in this band is at 450 hPa (about 6.3 km); that is, the data cover an atmospheric layer in the midtroposphere. The retrievals produce daily, 8-day, and monthly averaged data with 90 × 90 km2 spatial resolution at nadir. The AIRS instrument (Aumann et al. 2003) has excellent stability (better than 10 mK yr−1) so that the trends determined in this paper cannot be caused by instrument drift.
Although the retrieval process is described in Chahine et al. (2005), we briefly repeat the description emphasizing some aspects of the retrieval that are essential for understanding the quality and accuracy of the AIRS CO2 data we use in this study. The retrieval process is based on minimizing the sum of squares of the difference F between the measured radiances RM(ν) and radiances RC(ν) calculated using the previously retrieved variables from the AIRS L2 product: basically, temperature, water vapor, and ozone. The AIRS level-2 retrieved variables on 50 × 50 km2 footprints are available online (at http://disc.sci.gscf.nasa.gov). The CO2 retrieval was done at the pressure level of 450 hPa and includes secondary fine retrievals of temperature, water vapor, and ozone. At each step n, one variable—say the temperature T(p)—is slightly perturbed: T → T(1 + α), α ≪ 1 (i.e., the minimization is univariant). Then a line is fitted to the function F(n−1)(ν, α) = a(ν) + αb(ν), where a and b are expressed via RM(ν) and RC(ν), at a selected set of frequencies using the standard least squares method. The sets of frequencies are carefully selected for each of the four variables to minimize the temperature dependence on CO2 variations and CO2 dependence on ozone and water vapor. Specifically, it has been found that the 690–725 cm−1 band is most suitable for CO2 and the two sets for temperature and ozone retrievals, while the 1370–1610 cm−1 band is the best suited for water vapor retrievals. Additional regularization is imposed as follows: After each iteration step, all variables except CO2 are returned back to the initial (prior) values to be sure that the iterative values of CO2 drive changes in T, q, and O3 and not vice versa. The described minimization and regularization procedure does not involve the error-measurement variance and the prior covariance and thus does not automatically provide retrieval errors. It also does not account for potential influence of optically thin cirrus clouds missed in the AIRS L2 product. To circumvent potentially unaccounted errors, minimize and estimate the errors Chahine et al. (2005) made two steps: 1) The AIRS retrievals were grouped in four cells and the cells that contain less than three successful AIRS retrievals and those that do not converge to a minimum during the iteration process were excluded. 2) The retrieved CO2 were compared with aircraft flask measurements to find the monthly standard deviation of AIRS data to be 1.4 ppmv: that is, small compared with the annual variation of CO2.
Here, we use monthly-mean data retrieved during 2003–09. We exclude the regions around the South Pole (90°–60°S), which are poorly covered by the retrievals or have large retrieval errors. To have a sufficiently large sampling we box the data onto a 1° × 1° latitudinal–longitudinal grid. The size of the 1° × 1° grid box is close to the size of the retrieval box. Each grid box includes about 30 retrieved data points, and this number is almost uniformly distributed along the latitude. There is not a substantial difference between the number of successful retrievals in the ocean and land areas for monthly data. The selected dataset consists of 84 (the number of months in the 7-yr period 2003–09) maps of the size 140 × 360 in latitude–longitude dimension. The data gaps, which are still present in the monthly averages, are removed by 2D interpolation for each map. For this interpolation we use the “inpaintn” algorithm (Garcia 2010). The algorithm, based on the discrete cosine transform and a penalized least squares method, allows fast smoothing of data in two dimensions. An iteratively weighted robust version of the algorithm takes care of missing and outlying values.
3. On the mean, standard deviation, and trend
It is instructive to look first at the distributions of the mean, standard deviation, and linear trend distributions of the global CO2 calculated over the whole period of time independently in each grid point (Fig. 1). We see that the mean is not uniformly distributed: for example, there are enhanced concentrations of the CO2 in the Northern Hemisphere and near 40°S in the Southern Hemisphere. The interhemispheric (north–south) asymmetry of the CO2 distributions is well known from the studies with ground network data (see, e.g., Lintner 2002; Lintner et al. 2004). We see elevated standard deviations in the Northern Hemisphere. However, the standard deviation taken independently at each grid point is not sufficient for characterization of the actual variance of the spatiotemporal distribution because it does not take into account the correlations between the spatial grid points. It also gives no information about time variability. The multiplicity of trends is also puzzling. This is why we need to apply a method of pattern analysis that takes into account the correlations between spatial grid points (i.e., includes the CO2 transport effects). We will see that there is a unique trend associated with the major pattern.
Figure 2 shows the time evolution of zonally averaged CO2 data as the standard Hovmoeller diagram for zonal-mean anomalies. To plot the diagram, we take out the mean and the trend using the least squares linear fit to the time series of CO2 at each grid point. We see that the zonal means evolve with seasons. We also see a reduced CO2 in the tropics and several large enhancements near the northern polar region. They may be related to CO2 transported up and north because of buildups of fossil fuels and biomass burning in winter.
4. Methods of analysis
The availability of the global data coverage allows us to confidently apply the methods of pattern identification, which take into account the correlations between the grid points. Here, we apply the PCA (cf. Preisendorfer and Mobley 1988) to identify the major spatial patterns of the CO2 and their time variability in the midtroposphere. Because we are looking for spatially robust structures (analogs of eigenfunctions) varying on seasonal and longer time scales, the use of monthly data will not seriously affect the results. The major patterns, which are represented by the first few empirical orthogonal functions (EOFs) and the corresponding PCs, are not affected by data noise. We also apply to the data an adaptive filtering method described below, which allows us to split the principal components into modes characterized by progressive time scales. To identify these modes in the principal components we use the empirical mode decomposition (EMD) method (for a review, see Huang and Wu 2008), which allows us to adaptively filter and display the oscillating modes and the trend. The EMD method has been subjected to rigorous mathematical scrutiny and now successfully used in many applications. The method is specially designed to deal with nonstationary, nonlinear time series such as seen in the CO2 variations. The EMD represents the data as a sum of a small number of quasi-orthogonal empirical modes that have time-variable amplitudes and frequencies. Each mode is equivalent to an adaptively filtered signal in an empirically determined frequency band. The mean period of a mode can be determined by counting the number of maxima in the mode’s amplitude time series. We employ the ensemble approach to avoid the mixing of modes with different periods. An ensemble of a large number of data realizations (NE > 100) is created by adding a small-amplitude white noise to the original data. Each realization is subjected to the EMD process. Since the added white noise occupies the entire time–frequency domain, the signal is automatically projected onto the scales of reference established by the white noise, thus eliminating mode mixing. The resulting NE time series for each mode are then averaged. The averaging removes the noise contribution producing unmixed modes. More exactly, the noise contribution decreases as , where σ is the standard deviation of the noise added to the signal. In our calculations, we use NE = 150 and 0.1–0.2 for the ratio of the standard deviation of the added noise to that of signal. The results are robust to changing NE (e.g., to 100 or 50).
5. The CO2 patterns
To take into account the spatial correlations and their time variability (including the full latitude–longitude dependence), we decomposed the data into EOFs, which define the spatial patterns, and the accompanying PCs characterizing the time behavior of these patterns. The EOFs, the percent of the variance they explain λ, and the PCs are determined here using the singular value decomposition code available in Matlab. It is equivalent but faster than the direct calculation of the eigenvectors and eigenvalues of the correlation matrix. The code generates a diagonal matrix of eigenvalues Λ of the same dimension as the 2D data matrix, with nonnegative diagonal elements in decreasing order, and unitary matrices and so that data = ′. The matrix gives the EOFs and their projections on the data matrix (the product Λ × ) generates the PCs, which we normalized to unity. Prior to applying the code, we remove the 7-yr mean from each grid point so that the calculated EOFs refer to the deviation from the mean (anomalies).
Table 1 displays the percent of the variance λ accounted for by the first six principal components. The first and dominant EOF shown on the top panel in Fig. 3 explains 93.2% of the variance. The pattern is strongly asymmetric across the equator. Its PC (Fig. 3, bottom) has a trend, which is modulated by the annual and interannual variability (detailed in Fig. 5). The second EOF is shown in the left panel in Fig. 4. The corresponding PC displays a semiannual variability in addition the annual cycle. The semiannual variability is more pronounced in the third EOF (Fig. 4, right). The third PC displays the semiannual variation and annual variability phase shifted by about 90° relative to the second PC. The fourth EOF complements the structure seen in the second EOF in the Southern Hemisphere and shows some enhancements of CO2 in about five regions of the Northern Hemisphere. The higher EOFs, such as EOF 5 shown in the Fig. 4 (bottom), account for very small variances and are not statistically significant. We check the statistical significance using the well-known North criteria (North et al. 1982) based on the comparison of values of neighboring λs: δλi = λi(2/N)1/2, δEOFi = (δλi/λi) × EOFi, where N is the number of samples and i = 1, 2, 3, … . The application of this test shows that the 1, 2, and 3 EOFs are statistically significant, the fourth EOF is marginally significant, and the higher EOFs can be delegated to noise.
6. Comparison with the Mauna Loa record
We compare the first PC determined from the global satellite data with the well-known single-point monthly record of the CO2 at Mauna Loa (MLO). We select the Mauna Loa site because the station is located at 603 hPa (4169 m): that is, within the heights covered by the weighting function of the AIRS CO2 data under consideration.
The top panel in Fig. 5 displays both time series, which are normalized to unity for better comparison. We apply the EMD method described in section 3 to both time series to separate the noise, natural variability, and trend components. The panels in Fig. 5 positioned below the data show the EMD modes and the residual (trend). The first EMD mode characterizes a high-frequency noise and is omitted from the display. The second mode displays annual cycle in the AIRS CO2 PC1, which is phase shifted relative to the MLO annual mode in the last two cycles. Since the global pattern includes both hemispheres (i.e., opposite seasons) and Mauna Loa is located in the Northern Hemisphere, the amplitude of the PC1 is lower than the amplitude of the MLO annual cycle, and the phase shift may be caused by an increasing influence of the low-frequency third and fourth modes related to the ENSO and the Southern Oscillation. The third mode is a nonlinear interannual oscillation with a mean period of about 2.7–3 yr: that is, in the ENSO range of time scale. We compare the fourth mode with period 6–7 yr with the Southern Oscillation index (SOI; Fig. 6). The plot of the corresponding 6–7-yr EMD mode for the SOI shows a similar oscillation, which is phase shifted by one year against the corresponding AIRS CO2 EMD mode. The sign of the phase shift points to a reasonable relationship: that is, that the increase of El Niño episodes (SOI < 0) leads to increase of CO2 rather than other way around.
The statistical significance of the modes has been evaluated using the method suggested by Huang and Wu (2008). The trend error is evaluated as a standard deviation of trends obtained for each realization of the EMD ensemble. All modes, except the first one, which represents the noise, are statistically significant at 95% level of significance. The trends in both (MLO and AIRS) residuals are close to 2 ppmv yr−1 within 0.2 ppmv yr−1 error bars.
The global distribution of the atmospheric CO2 provided by satellite measurements opens an opportunity to identify the major spatial patterns that take into account the correlations between spatial points. This complements and expands the studies of atmospheric CO2 carried out using the flask network data. Using the data retrieved from the AIRS measurements, we have found the major pattern of CO2 variability, the strength of which grows almost linearly in time and oscillates with annual and interannual periodicities in general accord with the flask data analyses and modeling. The dominant pattern, which accounts for 93% of the midtropospheric CO2 variability, has a pronounced north–south asymmetry with an interhemispheric gradient on the order of 3 ppm. It is similar to the interhemispheric gradient found from the flask data (Tans et al. 1990; Denning et al. 1995), although the AIRS CO2 data are limited to the 60°S–90°N range of latitudes. The principal component corresponding to the dominant pattern displays the interannual variability, which has a time scale typical for the ENSO. The phase shift between this PC and the Southern Oscillation index indicates a reasonable causal relationship between the ENSO and CO2 variability and deserves a further study.
The second, third, and fourth patterns displayed in Fig. 4, which account for less than 7% of the CO2 variability, show regional details in the CO2 distribution and display an additional, semiannual cycle. These details may be important for interpretation of CO2 long-term concentrations in particular regions in the Northern and Southern Hemispheres. Thus, Chahine et al. (2008), using the data for July 2003, emphasized an enhancement of the CO2 concentration in the Southern Hemisphere (25°–35°S). The EOFs in Fig. 4 indicate some enhanced concentrations of CO2 in the Southern Hemisphere and the corresponding PCs indicate the seasonal character of these enhancements. Aircraft HIPPO measurements along the Pacific show that CO2 concentration was enhanced above the surface from 45° to 70°S in January 2009 but emphasized that the structure of the CO2 distribution is rather complex, with probable contributions from multiple processes including fires in Australia and the uptake of CO2 at the ocean surface (Wofsy et al. 2011). Further investigations are needed to test the origin of these enhancements in the Southern Hemisphere.
Understanding the origin of the atmospheric CO2 patterns requires comparison with 3D transport models, which is beyond limits of this paper. As a final note, we would like to only briefly touch a general transport aspect of this problem. It had been pointed out earlier (Mahlman 1997) that the CO2 is expected to be uplifted by rising motions in the tropical areas and to move along the surfaces of constant potential temperatures (isentropes) in the free midlatitude (and high-latitude) troposphere because the air motion there is adiabatic in the first approximation. The modeling confirmed that CO2 transport approximately follows dry isentropes slanted toward the poles in midlatitudes but is less sensitive to tropical convection (Tiwari et al. 2006). Synoptic events in the midlatitude atmosphere apparently have a tendency to drive CO2 along the surfaces of moist isentropes (Parazoo et al. 2011).
To test how a 2D slice of the midtropospheric CO2 found from the AIRS data fits into these general transport concepts, we compare the CO2 spatiotemporal distribution with the spatiotemporal distribution of the vertical velocity at 500 hPa and of the potential temperature at the same height and for the same time period 2003–09. For this purpose, we employ the data for the vertical velocity and the potential temperature on 2.5° × 2.5° grid from National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (http://www.esrl.noaa.gov/psd/data/). If the CO2 in the tropics were indeed uplifted by convection, we would expect it to be correlated with the vertical velocity there, but in agreement with the modeling results by Tiwari et al. (2006) we were not able to find any substantial correlation between the vertical velocity and the AIRS CO2. However, we believe that the relationship between the atmospheric CO2 and the vertical velocity in the tropics deserves a more detailed study including the investigation of the role of El Niño–La Niña variability. In contrast, the midlatitude and high-latitude contours of the potential temperature (Fig. 7) provide a visual indication of possible relationship between the potential temperature and the CO2, at least in the Northern Hemisphere. The transport in the tropics, where isentropes are mostly horizontal, is clearly suppressed. [The CO2 distribution is more complicated in the jet stream regions where air parcels are mixed across isentropes, and perhaps a better fit would be seen with the moist isentropes as advocated by Parazoo et al. (2011).] A more quantitative analysis of this relationship is presented in Fig. 8, which shows the covariance between the potential temperature and CO2 in the Northern Hemisphere. Further and more detailed analysis of the relationship between the CO2 distribution and dynamics will provide a better understanding of the origin of the CO2 patterns in the midtroposphere.
This work could not have been done without the support of Mous Chahine, who initiated and passionately forwarded the retrievals of the AIRS CO2 data until the last day of his life. We thank Ed Olson, Steve Licata, and Luc Chen for their help with the AIRS data. We are grateful to the reviewers for their helpful critical comments. This work was supported in part by the Jet Propulsion Laboratory of the California Institute of Technology, under a contract with the National Aeronautics and Space Administration.