2.1.

Ground-Based Validation of the AIRS ${\mathsf{CO}}_{\mathsf{2}}$ Product

The AIRS instrument has been orbiting the earth on NASA’s Aqua satellite in a sun-synchronous near-polar orbit since 2002. For the first time, it affords us the ability to retrieve ${\mathrm{CO}}_2$ concentrations globally over land, ocean, and polar regions during the daytime and nighttime, even in the presence of clouds. The accuracy is better than 2 ppmv (i.e., $<0.5\%$), without relying on a priori or background information.⁸ An earlier study⁸ compared the monthly seasonal variations of the AIRS retrievals to those of airborne measurements¹⁷ for the period between September 2002 and March 2004. This comparison showed an agreement of $0.43\pm 1.20\mathrm{ppmv}$. Further comparisons have been performed with collocated in situ observations available for the period from September 2002 to July 2011.⁷

The satellite data for this article come from NASA’s official AIRS mid-troposphere ${\mathrm{CO}}_2$ product site ( http://airs.jpl.nasa.gov/AIRS_CO2_Data/). Hyperspectral data of low instrument noise from the AIRS have been used to produce global profiles of temperature and water vapor as well as carbon dioxide and other trace gases. The tropospheric ${\mathrm{CO}}_2$ products are derived by binning the Level 2 standard retrievals in a grid that is 2 deg in latitude by 2.5 deg in longitude over daily, 8-day, and monthly time spans.⁷

Ground-based measurements can provide the ${\mathrm{CO}}_2$ concentration with high precision. The World Meteorological Organization (WMO), the U.S. National Oceanic and Atmospheric Administration (NOAA), the Meteorological Service of Canada (MSC), and the Japanese National Institute for Environmental Studies (NIES) have built numerous ground-based ${\mathrm{CO}}_2$ observation stations throughout the world^18,19 to obtain information about variations in ${\mathrm{CO}}_2$. Data from ground-based and aerial ${\mathrm{CO}}_2$ measurements are available at the WMO World Data Centre for Greenhouse Gases (WMO WDCGG) web site ( http://gaw.kishou.go.jp/wdcgg/wdcgg.html).¹⁸

The above-mentioned agencies provide measurements from a total of $\sim 201$ baseline observatories, fixed sites, and tall towers, complemented by measurements from ships and aircraft. Although the in situ measurements are highly accurate, the distribution in space and time is necessarily somewhat limited for global process studies.¹⁵

In this article, 123 in situ data are selected to validate the quality of the AIRS ${\mathrm{CO}}_2$ product. These data cover the period from September 2002 to July 2011, which is the same period as covered by the AIRS data. Figure 1 compares the AIRS ${\mathrm{CO}}_2$ products with the in situ observations for September 2002 to July 2011. This comparison shows that the AIRS results are consistent with the ground-based observations. Figure 1 provides the average bias, standard deviation, and correlation coefficients for both the ground-based and satellite observations over the years. The correlation coefficients are higher than 0.8 for most stations from 60°S to 30°N. Further, the bias is lower than 3 ppmv, and the monthly average standard deviation is $<3\mathrm{ppmv}$.

Fig. 1

Error comparisons between atmospheric infrared sounder (AIRS) products and in situ observations.

The correlation coefficient is lower than 0.5 for the areas from 30°N to 90°N. That is, the northern hemisphere shows a lower correlation than the southern hemisphere, because the concentration of human activities is higher in the northern hemisphere than in the vast sparsely populated areas of the southern hemisphere. The bias is $\sim 5\mathrm{ppmv}$, and the monthly average standard deviation is generally within 6 ppmv (though some individual sites have large deviations).

The validation results show that the AIRS mid-troposphere ${\mathrm{CO}}_2$ product is consistent with ground-based and aerial measurements at various latitudes. The error is mainly for northern latitudes from 30°N to 60°N, followed by the Arctic.

2.2.

Sensitivity of AIRS ${\mathsf{CO}}_{\mathsf{2}}$ Retrieval

2.2.2.

Sensitivity of ${\mathsf{CO}}_{\mathsf{2}}$ concentration retrieval

Radiance measurements from the space in a ${\mathrm{CO}}_2$ absorption band can reflect the total ${\mathrm{CO}}_2$ column. Variations in the vertical temperature profile, the water vapor profile, and the distribution of interfering gases as the satellite instrument moves will add uncertainties to the ${\mathrm{CO}}_2$ measurements.¹ To study the effects of these variations on the retrieval of ${\mathrm{CO}}_2$ columns, the AIRS measurements are simulated in the spectral range 690 to $725\mathrm{c}{\mathrm{m}}^{-1}$. The strong ${\mathrm{CO}}_2$ emission band at 15 μm is used to derive atmospheric temperature profiles, with the assumption that the ${\mathrm{CO}}_2$ concentration throughout the atmosphere is fixed. The sensitivity of space-observed radiance to emission temperature in this band is much greater than the sensitivity to the ${\mathrm{CO}}_2$ concentration. In addition, water vapor and the ${\mathrm{O}}_3$ column cause significant interference within this band.

The radiative transfer model used for atmospheric absorption in this study is called the line-by-line radiative transfer model (LBLRTM).²¹ The LBLRTM is an accurate, efficient, and well-established line-by-line algorithm that is widely used in studies of atmospheric radiation and remote sensing to validate band models, generate fast-forward models in retrieval processes, and simulate radiance for high-spectral-resolution sensor designs. The high-resolution transmission molecular absorption database is used as input to the LBLRTM.²² The Voigt profile is used for absorption line shapes to include both collisional- and Doppler-broadening processes throughout the column of the atmosphere.

Models of five standard atmospheres are used for atmospheric profiles with extensions to 100 km.²³ The atmospheric radiance in the spectral range 690 to $725\mathrm{c}{\mathrm{m}}^{-1}$ is shown in Fig. 2(a). The baseline atmospheric ${\mathrm{CO}}_2$ mixing ratio is set to 380 ppmv, and the satellite view is set to nadir.

Fig. 2

Radiance at different spectral resolutions under five different standard atmospheric models: (a) all standard atmospheric models, (b) tropical, (c) midlatitude summer, (d) midlatitude winter, (e) subarctic summer, and (f) subarctic winter.

According to the accuracies of the AIRS products, the temperature profiles have an accuracy of 1 K for every 1-km layer, the atmospheric water vapor profile has an accuracy of 20% in 2-km layers, and there are 10% errors in the ${\mathrm{O}}_3$ column. Based on the error quantification presented here, the change produced in the measured radiance by these errors is compared with the change in the ${\mathrm{CO}}_2$ concentration. Then the maximum uncertainty in the retrieved ${\mathrm{CO}}_2$ concentration is produced by these errors under the five standard atmospheric models.

3.1.

Spectral Resolution

A scanning function is used, which can simulate the slit function of a grating spectrometer to convolve the monochromatic radiances calculated line-by-line. The radiance measurement of the reflected IR wavelength at high spectral resolution results in a high sensitivity to atmospheric ${\mathrm{CO}}_2$ change. Thus, a balance in the spectral resolution and the radiance sensitivity is required of instrumentation for ${\mathrm{CO}}_2$ measurements.

The effects of spectral resolution on radiance and radiance sensitivity are presented in Figs. 2(b)–2(f), from the highest possible resolution of the model ($\sim 0.00015\mathrm{c}{\mathrm{m}}^{-1}$, black lines) to the spectral resolution of AIRS ($\lambda /\mathrm{\Delta }\lambda =1200$, colored lines). The results show that the AIRS resolution, unlike the model resolution, is adequate for ${\mathrm{CO}}_2$ spectral features, can maintain a moderate radiance level, and has good radiance sensitivity.

3.2.

Radiance Sensitivity for ${\mathsf{CO}}_{\mathsf{2}}$ Change

Altitude has an important effect on the ${\mathrm{C}\mathrm{O}}_2$ absorption linewidth through pressure broadening.¹⁵ Figure 3 shows the change produced in the measured radiance by a 1 ppmv increase in the ${\mathrm{C}\mathrm{O}}_2$ concentration in each 1-km layer of the atmosphere. The measured radiance decreases with a 1-ppmv increase in the ${\mathrm{C}\mathrm{O}}_2$ concentration because the transmittance decreases as the ${\mathrm{C}\mathrm{O}}_2$ concentration increases. Furthermore, the vertical sensitivity calculated for a 1-ppmv ${\mathrm{C}\mathrm{O}}_2$ increase in each 1-km layer is shown in Fig. 4 for the 13 AIRS channels used in the NOAA retrievals under the five different standard atmospheric models. The AIRS mid-troposphere ${\mathrm{C}\mathrm{O}}_2$ is well mixed, because the channels used for retrieval are sensitive to altitudes of $\sim 10\mathrm{km}$, which provide the strongest contributions to the measured radiance. The changes in radiance are mainly caused by the variations in atmospheric ${\mathrm{C}\mathrm{O}}_2$ concentration at altitudes of 20 km or less.

Fig. 3

$\mathrm{C}{\mathrm{O}}_2$ Jacobians for a 1-ppmv layer perturbation under five different standard atmospheric models: (a) tropical, (b) midlatitude summer, (c) midlatitude winter, (d) subarctic summer, and (e) subarctic winter.

Fig. 4

$\mathrm{C}{\mathrm{O}}_2$ Jacobians for a 1-ppmv layer perturbation for the 13 AIRS channels used in the National Oceanic and Atmospheric Administration (NOAA) retrievals under five different standard atmospherics models: (a) tropical, (b) midlatitude summer, (c) midlatitude winter, (d) subarctic summer, and (e) subarctic winter.

Moreover, the AIRS weighting functions have a tail that extends into the stratosphere, especially in the polar regions, where the tropopause is lower. The stratospheric air is colder than that of the troposphere by an amount that varies with latitude.^24–28 As can be observed in Fig. 4, an increase in latitude produces a negative change in radiance sensitivity. Additionally, the radiance sensitivity is greater in summer than in winter. Overall, greater radiance sensitivity leads to a more precise retrieval of the ${\mathrm{C}\mathrm{O}}_2$ concentration data.

The change in the measured radiance was also calculated for a 1-ppmv increase in the ${\mathrm{C}\mathrm{O}}_2$ column for the 13 AIRS channels used in the NOAA retrievals under the five different standard atmospheric models. The results include the variance and sensitivity of the upwelling radiance at the top of the atmosphere, as shown in Table 2. The band at $711.005\mathrm{c}{\mathrm{m}}^{-1}$ is particularly sensitive in all five standard atmospheric models, and the maximum value of the radiance sensitivity is 0.078%. Comparing the values of radiance sensitivity under the five standard atmospheric models, it can be seen that an increase in latitude corresponds to a decrease in radiance sensitivity, whereas the radiance sensitivity is greater in summer than in winter.

Table 2

Variations and sensitivities of measured radiance for a 1-ppmv CO2 change in five different standard atmospheres.

3.3.

Temperature Dependence

Temperature greatly affects the ${\mathrm{CO}}_2$ absorption coefficient in terms of line strength, line shape, and even line position. Thus, the amount of back-to-space radiance in the IR greatly depends on the atmospheric temperature, even though the dependence is much weaker than in the bands for temperature profile retrieval.¹⁵

The AIRS/AMSU/HSB instrument suite is able to measure atmospheric temperature profiles to an accuracy of 1 K for every 1-km layer in the troposphere and 1 K for every 4-km layer in the stratosphere up to an altitude of 40 km. In this study, a 1-K temperature deviation was added to each layer of the five standard atmospheric models. Such a deviation is likely for temperature profile retrieval errors when matching the observed radiances with computed radiances. Figure 5 shows the radiance changes in percent for the 13 AIRS channels used in the NOAA retrievals after the 1-K temperature error was introduced into the temperature profile under the five standard atmospheric models. The overall influence of the temperature retrieval error is $<0.2\%$, which is significantly smaller than the change due to a 1% ${\mathrm{C}\mathrm{O}}_2$ change.

Fig. 5

Temperature Jacobians for a 1-K layer perturbation for the 13 AIRS channels used in the NOAA retrievals under five different standard atmospheric models: (a) tropical, (b) midlatitude summer, (c) midlatitude winter, (d) subarctic summer, and (e) subarctic winter.

The channels used for retrieval are sensitive to altitudes of $\sim 10\mathrm{km}$, which provide the strongest contributions to the measured radiance. These altitudes are similar to those of the ${\mathrm{C}\mathrm{O}}_2$ radiance sensitivity, resulting in a greater interference for ${\mathrm{C}\mathrm{O}}_2$ concentration retrieval. The $706.137\text{-}\mathrm{c}{\mathrm{m}}^{-1}$ band is the most sensitive, but the change produced in the measured radiance by a temperature increase of 1 K is negligible above 40 km in the atmosphere. Furthermore, the tropical and subarctic regions have greater radiance sensitivity than the midlatitude areas, while the radiance sensitivity at each latitude is greater in winter than in summer because of the seasonal dependence, especially in the subarctic region.

Figure 6 shows the variations in measured radiance caused by temperature errors (top curve) and the change in ${\mathrm{C}\mathrm{O}}_2$ concentration (bottom curve) under the five standard atmospheric models. It can be observed that the change in the measured radiance is a function of the 1-K increase in each 1-km layer of the atmosphere. In the troposphere, the measured radiance is more sensitive to temperature changes. As observed in Fig. 6, the maximum sensitivity to a 1-K change in each 1-km layer of the atmosphere is approximately three times the sensitivity to a 1-ppmv change in ${\mathrm{C}\mathrm{O}}_2$. If the curves in Fig. 6 are integrated and compared with the ${\mathrm{C}\mathrm{O}}_2$ column sensitivities (Table 2), a 1-K decrease in the atmospheric temperature over the entire profile is found to produce a change in measured radiance comparable with that produced by a 1% increase in the ${\mathrm{C}\mathrm{O}}_2$ concentration (listed in Table 3 for all channels).

Fig. 6

Variations in radiance caused by measured temperature errors (top curve) and the change in $\mathrm{C}{\mathrm{O}}_2$ concentration (bottom curve) under five different standard atmospheric models: (a) tropical, (b) midlatitude summer, (c) midlatitude winter, (d) subarctic summer, and (e) subarctic winter.

Table 3

Uncertainty in CO2 retrieval caused by temperature, water vapor, and O3 errors under five different standard atmospheres.

In summary, an analysis of the sources of uncertainty in the proposed ${\mathrm{C}\mathrm{O}}_2$ radiometer was performed. The analysis shows that the most important potential source of error is uncertainty in the temperature profile. The maximum sensitivity to temperature, at 3.82 ppmv, is found in the $704.436\text{-}\mathrm{c}{\mathrm{m}}^{-1}$ band. This value is at least 1-ppmv higher than those in other bands. Moreover, higher latitude leads to more serious temperature interference. The effect that temperature error has on the ${\mathrm{C}\mathrm{O}}_2$ retrieval is less in summer than in winter at the same latitude. Therefore, a good knowledge of the atmospheric temperature profile is required as ancillary data in ${\mathrm{C}\mathrm{O}}_2$ retrieval.

3.4.

Water Vapor Interference

Water vapor has only slight absorption in the band 690 to $725\mathrm{c}{\mathrm{m}}^{-1}$, which requires attention when channels are selected for ${\mathrm{C}\mathrm{O}}_2$ retrieval. Fortunately, most of the water vapor line centers in this band are not aligned with the ${\mathrm{C}\mathrm{O}}_2$ line centers. The calculated difference in ${\mathrm{C}\mathrm{O}}_2$ sensitivity between atmospheres with and without water vapor is negligible for most lines. However, atmospheric water vapor can significantly modify air density, reinforcing the abovementioned requirement for dry-air surface pressure measurements. However, for some wet-summer areas, such as the tropics and midlatitudes, major interference from highly variable atmospheric water vapor is a great concern for this IR band.

Figure 7 shows that the lowest layers of the atmosphere provide the strongest contributions to the measured radiance. The $714.773\text{-}\mathrm{c}{\mathrm{m}}^{-1}$ band is the most sensitive, and most of the change in radiance is contributed by the variation in the water vapor concentration of the atmosphere below 15 km.

Fig. 7

Water vapor Jacobians for a 20% layer perturbation for the 13 AIRS channels used in the NOAA retrievals under five different standard atmospheric models: (a) tropical, (b) midlatitude summer, (c) midlatitude winter, (d) subarctic summer, and (e) subarctic winter.

Although this spectral interval was chosen partly to reduce the interference of water vapor in the measured radiances, such interference remains a significant factor in the retrieval of ${\mathrm{CO}}_2$ concentrations. The proposed measurement of atmospheric water vapor has an accuracy of 20% every 2-km layers. Figure 8 shows the fractional change in the measured radiance as a function of a 20% relative humidity decrease in each 2-km layer of the atmosphere, with respect to a standard relative humidity profile. The fractional changes in the measured radiance are $<0.01\%$ for the midlatitude winter and the subarctic region. Given this level of sensitivity to water vapor, the maximum errors for a ${\mathrm{CO}}_2$ measurement precision of 0.5% are $\sim 2.58$, 2.63, 0.85, 1.36, and 0.12 ppmv for the tropics, midlatitude summer, midlatitude winter, subarctic summer, and subarctic winter, respectively (see Table 3). In relative terms, lower latitude areas have greater uncertainty than higher latitude areas, and summer has greater uncertainty than winter for a given latitude.

Fig. 8

Variations caused by water vapor errors from observation under five standard atmospheric models: (a) tropical (b) midlatitude summer, (c) midlatitude winter, (d) subarctic summer, and (e) subarctic winter.

For water vapor, the column sensitivity is greatly determined by seasonal dependence, which is mostly a result of higher densities because of the greater amounts of water vapor in the atmosphere. However, the uncertainty for ${\mathrm{CO}}_2$ concentration retrieval is generally $<2\mathrm{ppmv}$ in summer and $<1\mathrm{ppmv}$ in winter.

3.5.

${\mathrm{O}}_3$ Interference

Interference in the measured radiance due to ${\mathrm{O}}_3$ is a significant factor in the process of ${\mathrm{CO}}_2$ retrieval. The radiance measured for the reflected IR wavelength results in a high sensitivity to ${\mathrm{O}}_3$ change. Comparisons with ${\mathrm{O}}_3$ radiosonde data have shown for the AIRS observations that such interference leads to errors as sizeable as $-10\%$ in the ${\mathrm{O}}_3$ column of the stratosphere and yields an accuracy of 20% to 70% for the troposphere. The ${\mathrm{O}}_3$ product of the AIRS has a bias of $-11\%$ to $+3\%$ compared with that of the total ozone mapping spectrometer.^29–31 The sensitivity of the measured radiance to the ${\mathrm{O}}_3$ profile is presented in Fig. 9.

Fig. 9

${\mathrm{O}}_3$ Jacobians for a 10% layer perturbation for the 13 AIRS channels used in the NOAA retrieval under five different standard atmospheric models: (a) tropical, (b) midlatitude summer, (c) midlatitude winter, (d) subarctic summer, and (e) subarctic winter.

The channels used for retrieval are sensitive to stratospheric altitudes of $\sim 20$ to 30 km, which provide the strongest contributions to the measured radiance. These altitudes are much greater than those of the ${\mathrm{CO}}_2$ radiance sensitivity, but the measured radiance produces fractional change by a 10% decrease of ${\mathrm{O}}_3$ in each 1-km layer of the atmosphere above 60 km. Tropical areas have greater radiance sensitivity than higher latitude areas, and the radiance sensitivity at each latitude is greater in winter than in summer because of the seasonal dependence, especially in the subarctic region.

In these IR channels, the sensitivity of measured radiance exhibits a 0.016% change by $-10\%$ variation of ${\mathrm{O}}_3$ concentration (a reasonable level of variation in ${\mathrm{O}}_3$ over the globe). Given this level of sensitivity, the maximum errors in ${\mathrm{O}}_3$ concentration for ${\mathrm{CO}}_2$ measurements are $\sim 1.69$, 2.20, 3.01, 1.98, and 3.17 ppmv, respectively (see Table 3).

Another source of error is spectral interference from ${\mathrm{O}}_3$ in the $709.279\text{-}\mathrm{c}{\mathrm{m}}^{-1}$ band. This interference has a minimal value of 1.69 ppmv in the tropics, and then increases to 3.17 ppmv when coupled with higher latitude areas and seasonal dependence. The value of the uncertainty is 1-ppmv higher in winter than in summer at the same latitude.

In summary, the three factors of temperature, ${\mathrm{O}}_3$, and water vapor have great influences on the sensitivity of atmospheric ${\mathrm{CO}}_2$ retrieval from the AIRS observations. In particular, the most important factor in the tropics is water vapor, while temperature represents major interference for midlatitude and subarctic regions. Moreover, the maximum error in ${\mathrm{CO}}_2$ retrieval occurs for mid latitude regions under summer conditions.