Operational carbon monoxide retrieval algorithm and selected results for the MOPITT instrument



[1] Measurements of Pollution in the Troposphere (MOPITT) is a new remote sensing instrument aboard the Earth Observing System (EOS) “Terra” satellite which exploits gas correlation radiometry principles to quantify tropospheric concentrations of carbon monoxide (CO) and methane (CH4). The MOPITT CO retrieval algorithm employs a nonlinear optimal estimation method to iteratively solve for the CO profile which is statistically most consistent with both the satellite-measured radiances and a priori information. The algorithm's theoretical basis is described in terms of the observed radiances and their weighting functions, the a priori information, and the retrieval averaging kernels. Examples of actual CO retrievals over scenes with contrasting pollution conditions are demonstrated, and interpreted in the context of the retrieval averaging kernels and a priori.

1. Introduction

[2] The MOPITT remote sensing instrument, which was developed to quantify and track the movement of pollution in the troposphere, was launched aboard the EOS Terra satellite in December 1999. MOPITT includes nadir-viewing channels for monitoring both carbon monoxide and methane and became operational in March 2000. At nadir, the MOPITT instantaneous field of view (or “pixel size”) is 22 by 22 km. Although similar in some respects to a space shuttle-based instrument known as “Measurements of Air Pollution from Space” (or MAPS) [Reichle et al., 1999], MOPITT was designed to perform with much greater spatial and temporal coverage than was possible from the shuttle platform. Also, unlike MAPS, MOPITT includes multiple spectrally distinct channels which permit retrieval of the carbon monoxide vertical distribution. This paper describes the current method used to retrieve the carbon monoxide profile from the calibrated MOPITT radiances in detail and provides several examples of actual retrieval results.

1.1. Principles of the MOPITT Instrument

[3] The physical basis of MOPITT's ability to detect tropospheric CO and CH4 lies in the principles of gas correlation radiometry. Modulation cells containing each of the target gases act as high-spectral resolution optical filters. The filtering characteristics of the cells vary dynamically by modulation of either (1) the cell pressure [Taylor, 1983] (as in a pressure-modulated cell or “PMC”) or (2) the optical path length through the absorbing gas [Tolton and Drummond, 1997] (as in a length-modulated cell or “LMC”). In both types of cells, the applied modulation has the effect of varying the spectral absorption (and emission) only in the vicinity of the absorption lines of the gas contained in the cell. Measurements of the transmitted optical intensity in the modulation cell states of minimum and maximum cell absorption are combined to form two synthetic signals. The average signals (or “A-signals”) and difference signals (“D-signals”) are calculated, respectively, by taking the mean and the difference of the measured radiances in the cell states of minimum and maximum absorption. The equivalent spectral response functions of these synthesized signals are described by the A- and D-signal response functions [Pan et al., 1995]. The A-signal response is dominated by the spectral regions between the target gas absorption lines, where the mean response is typically high. In these spectral regions, surface temperature dominates as the source of radiance variability. In contrast, the D-signal response is highest very close to the absorption lines. These signals are relatively much more sensitive to atmospheric target gas concentrations than the A-signals. The spectral position of the maximum of the D-signal response function will depend on the particular type and operating parameters of the modulation cell. For example, increasing the absorption for both the minimum and maximum cell absorption states (for example, by increasing the absorbing path length in the cell) will tend to push the D-signal response function maxima farther into the line wings and away from the line center.

1.2. Mathematical Formulation of the MOPITT CO Retrieval Algorithm

[4] A nonlinear optimal estimation algorithm [Rodgers, 2000; Pan et al., 1998] and a fast radiative transfer model [Edwards et al., 1999] are used to invert the measured A- and D-signals to determine the tropospheric trace gas concentrations. Retrievals of CO may involve up to six channels (12 measured signals) in two distinct bands: two channels in a solar reflectance band near 2.3 microns (channels 2 and 6), and four channels in a thermal emission band near 4.7 microns. As described in Table 1, the thermal band channels include two LMC channels (channels 1 and 5) and two PMC channels (channels 3 and 7). The eight thermal band signals are sensitive to thermal emission from the Earth's surface as well as atmospheric absorption and emission. The solar band signals are sensitive to atmospheric CO through absorption processes only. It is implicitly assumed in the following that only clear-sky radiances (i.e., radiances uncontaminated by clouds) are fed to the retrieval algorithm. A detailed description of the MOPITT cloud-detection algorithm has recently been published [Warner et al., 2001].

Table 1. Thermal-Channel Modulator Characterististicsa
ChannelModulator TypeCell Pressure, mbarEnabled Signals
  • a

    Last column identifies signals from each channel actually used in current operational retrievals.

7pressure25–50A, D

[5] The general concepts underlying the MOPITT CO retrieval algorithm have been discussed in detail previously [Pan et al., 1998]. Recently, however, significant changes have been made to the MOPITT CO retrieval algorithm in order to improve the quality of the retrieval products and make them more useful to potential data users. In addition, after MOPITT became operational, the retrieval algorithm was reconfigured in response to observed noise and bias characteristics of the operational (in-orbit) MOPITT radiances. The purpose of this paper is to describe the current operational retrieval algorithm used to process the MOPITT radiance data in detail, describe the MOPITT CO retrieval products (with reference to the retrieval averaging kernels), and finally present some selected actual retrieval results which demonstrate the capabilities of this new tool for global atmospheric chemistry studies.

[6] In atmospheric remote sensing, the common problem of inverting a set of measured radiances to determine aspects of the atmospheric state (temperature profile, trace gas mixing ratio profiles, etc.) is often ill-conditioned, meaning that no unique solution exists. Thus additional information of some type is usually required to constrain the retrieval to fall within physically reasonable limits. The CO retrieval algorithm used for MOPITT exploits the maximum a posteriori (“MAP”) solution which is a specific type of optimal estimation technique [Rodgers, 2000]. The general strategy of such techniques is to seek the solution most statistically consistent with both the measured radiances and the typical observed patterns of CO vertical profiles as represented by the a priori. The methodology for generating the a priori (i.e., both the a priori mean profile and the a priori covariance matrix) is described in detail in section 2.

[7] The equation relating the true atmospheric state and the measured radiances can be written as

equation image

where y is the measurement vector (i.e., the observed MOPITT radiances), x is the state vector (i.e., all the desired retrieved variables), b represents all other forward model parameters (i.e., all parameters needed to calculate the MOPITT radiances not explicitly included in the state vector), F(x, b) represents the forward radiative transfer model [Edwards et al., 1999], and Nϵ is the radiance error vector. The goal of the retrieval algorithm is to estimate the true state vector x from the measured radiances y and the associated measurement errors.

[8] In the MOPITT CO retrieval algorithm, the measurement vector y is formed solely from the calibrated satellite radiances (also called the “Level 1 Product”). For the thermal band signals, SiA and SiD are used to represent the A and D signals for the ith radiometer and are included in the measurement vector y directly. A different strategy is employed for the solar band channels. For these channels, the ratio SD/SA is employed because it greatly reduces the effect of the generally unknown and highly variable surface reflectivity. This ratio is still a valid indicator for CO, however, because of the much greater sensitivity to CO exhibited by the solar D channel than by the solar A channel. Forward model studies also indicate that the contaminating effects of gas species other than CO are reduced in the ratio SiR = SiD/SiA [Pan et al., 1995]. For these reasons, the solar band channels are represented in the measurement vector only through the solar ratio signal SiR.

[9] The thermal band signals depend not only on the atmospheric CO distribution but also on various other atmospheric quantities (such as the atmospheric temperature and water vapor mixing ratio profiles) and surface parameters (surface temperature Tsfc and longwave emissivity ϵsfc). Accurate values for all of these geophysical parameters must be obtained to produce accurate retrievals. Atmospheric temperature and water vapor profiles are obtained by spatially and temporally interpolating reanalysis profiles from NCEP to the location and time of each MOPITT pixel. However, sources of geophysical data such as NCEP are unable to provide accurate values of surface temperature and emissivity (both of which are highly variable) at the temporal and spatial resolution demanded by the MOPITT retrievals. Fortunately, information contained in the MOPITT thermal band signals allows retrieval of the surface temperature and emissivity along with the CO profile, and makes external data sources for these quantities necessary only for providing a priori and initial guess values.

[10] Thus, rather than assuming fixed values for Tsfc and ϵsfc, both parameters are included in the retrieval state vector x along with the elements of the CO profile. (A detailed inspection of the radiative roles of Tsfc and ϵsfc reveals that their effects on the thermal-band signals are often nearly indistinguishable. Therefore MOPITT radiances do not always contain sufficient information to retrieve both parameters independently. Both parameters are included in the retrieval state vector because (1) they represent physically different sources of radiance variability and (2) assuming fixed values for either parameter would unnecessarily constrain the CO retrieval.)

[11] Using these notations, the most general measurement and state vectors for a given pixel can be written, respectively, as

equation image
equation image

where qi represents the CO mixing ratio at the ith pressure level of the predefined retrieval grid. The seven levels in the current operational retrieval grid include the surface, 850, 700, 500, 350, 250, and 150 mbar.

[12] The MAP solution combines two independent estimates of the same vector quantity (i.e., the state vector determined solely from the measurement vector y and the “virtual” measurement represented by the a priori state vector xa) inversely weighted by their respective covariances. The MAP solution equation image for this problem is written

equation image

where Ca is the a priori covariance matrix (described below), K is the weighting function matrix defined by

equation image

which thus describes the model-calculated sensitivity of the each of the measurement vector elements to each of the elements of the state vector (described further below), KT is its transpose, and Cϵ is the radiance error covariance matrix. Cϵ can be used to represent errors from sources including (but not limited to) instrumental noise, forward model error, and ancillary error (e.g., errors in the assumed temperature and water vapor profiles) [Rodgers, 2000]. The corresponding covariance for the MAP solution is

equation image

and describes the uncertainty in the retrieved state vector equation image.

[13] However, equation (4) for the maximum a posteriori solution cannot be used directly to retrieve the CO profile because the weighting function matrix K is itself a function of equation image. Rather, an iterative form of the MAP solution is needed. The method of Newtonian iteration is therefore used, in which

equation image

where n is the order of iteration, and Fn is the theoretical radiance vector based on equation imagen as calculated by the forward model. The initial guess state vector equation image0 need not equal the a priori state vector xa. For example, during processing of a swath of MOPITT radiances, the initial guess CO profile for a particular pixel might be efficiently generated from the retrieval of a nearby, previously processed pixel. (In current operational processing, however, CO initial guess profiles are provided by monthly-mean output from the chemical transport model known as “Model for OZone And Related Tracers,” or MOZART [Hauglustaine et al., 1998].) In any case, the a priori state vector xa always represents the “best guess” CO profile and surface parameters excluding any analysis of the MOPITT radiances. The calculation and implementation of the a priori is discussed in section 2.3 below. After each iteration of the maximum a posteriori solution, the solution is checked for convergence. Currently, the convergence test is based on the fractional change in the CO profile relative to the previous iteration. By definition, convergence occurs when the root-mean-square (RMS) value of the fractional change in the seven levels of the CO profile decreases to 5% or less. Retrievals typically converge in three or four iterations. Increasing the number of retrieval iterations (i.e., decreasing the convergence threshold) produces a negligible effect on the retrieval results.

[14] Retrievals of the CO profile consist of a “floating” surface-level retrieval (tied to the pixel-dependent surface pressure value) and retrievals at up to six fixed pressure levels including 850, 700, 500, 350, 250, and 150 mbar. (In elevated areas where one or more of the fixed pressure level values exceed the actual local surface pressure, that part of the retrieved state vector is filled with the missing-value identifier.) As demonstrated in section 3, the retrieval grid resolution is typically finer than the vertical resolution of the actual retrieved CO profile. We expect that many users of MOPITT CO retrievals will attempt to compare MOPITT CO profiles with products (either from chemical transport models or from other observations) with higher intrinsic vertical resolution. The pressure grid on which the retrieval results are reported was selected to facilitate these comparisons by minimizing errors caused by interpolating or extrapolating MOPITT results. Moreover, future schemes for processing MOPITT radiances will likely incorporate more signals and exhibit finer vertical resolution than the current scheme. The current retrieval grid will be capable of accommodating the additional information contained in these retrievals.

[15] The retrieved CO total column equation image is simply the total column value obtained by integrating the retrieved profile from the surface to the top of the atmosphere. The uncertainty in the total column is obtained through the relation

equation image

where equation image is the total column error covariance and g is the total column linear operator which relates the profile equation image and the total column value equation image [Rodgers and Connor, 2003].

[16] The MOPITT CO “Level 2 Product” consists of retrieved values and estimated uncertainties of the CO profile, CO total column, surface temperature, and surface emissivity. For the CO profile, the retrieved error covariance matrix is also provided. Although this covariance matrix may be useful in and of itself, it is also a necessary element of averaging kernel calculations (as described below).

2. Operational CO Retrievals

[17] For several reasons, operational MOPITT radiances may not be perfectly modeled by the operational forward model (which is perhaps the most critical component of the retrieval algorithm). Such errors, which may be manifested as either excessive random radiance errors or systematic radiance biases, can produce significant degradation of the retrieval product. For example, early operational MOPITT A-signal radiances exhibited a systematic bias which was found to be caused by relative spectral shifts in the initial assumed (pre-launch) and operational (post-launch) optical bandpass filter profiles [Deeter et al., 2002]. This particular source of radiance bias has since been eliminated, though it is possible that other more subtle sources of radiance error still exist.

[18] Rather than initially attempting to “force” the CO retrieval algorithm to incorporate all available radiances, we have taken a more conservative approach. Specifically, we have chosen to base the retrievals on the minimum number of radiances necessary for a useful CO profile retrieval. The radiances actually used for the retrievals described throughout the rest of this paper include the A signal for channel 7, and the D signals for channels 1, 3, and 7. The channel 5 D signal was excluded because of an apparent radiance bias which greatly degraded the retrievals. A-signal radiances for channels 1, 3, and 5 were excluded because of the high redundancy of the information contained in these signals with the information contained in the 7A signal (signals 1A, 3A, 5A, and 7A are all primarily sensitive to surface temperature and emissivity rather than atmospheric CO). The solar CO channels 2 and 6 were excluded from the retrievals because of low observed signal-to-noise ratios. (Techniques for reducing the apparent noise in these channels are under development.)

[19] Although the MOPITT CO retrieval results reported here are based on only four of the available signals, no “ad-hoc” correction factors have been applied either to the radiances or retrieval results. Similarly, the forward model has not been revised to force the retrieval results to behave in any particular way. Signals currently excluded from the retrievals will be incorporated into future versions of the retrieval algorithm after issues of signal-to-noise ratio and radiance bias are resolved.

2.1. Mopitt Level 1 Radiances

[20] As defined in equation (5), the weighting function matrix K defines the sensitivity of the MOPITT CO radiances (contained in the measurement vector y) to the elements of the state vector x (surface temperature Tsfc, surface longwave emissivity ϵsfc, and discretized CO profile). Numerically, K is calculated by a finite difference algorithm using the operational forward model to calculate the change in each of the MOPITT radiances per unit change in the values of each of the state vector elements. The sensitivities of the MOPITT radiances to surface temperature and emissivity have been described previously [Pan et al., 1998]. Generally, the thermal-channel “A” radiances (only one of which is used in current operational retrievals) are much less sensitive to changes in the CO profile than are the thermal-channel “D” radiances. Thus the information in the four thermal channel A signals is highly redundant. Typical weighting functions for the three D signals actually used in the operational retrievals are shown in Figure 1. The weighting functions shown were calculated for the a priori CO profile. Significant variability of the weighting functions is associated with variability of the atmospheric temperature profile, “true” CO profile, and surface temperature. Thus geographic and seasonal variability of the weighting functions results in significant variability in the vertical sensitivity of the retrievals (see section 3).

Figure 1.

Typical weighting functions for thermal band D signals used in operational retrievals.

2.2. Radiance Errors

[21] The radiance error covariance matrix Cϵ describes the statistical uncertainties and error correlations of all elements of the measurement vector y. For MOPITT CO retrievals, Cϵ includes components representing two independent sources of radiance error: instrumental noise and forward model error. Thus,

equation image

where Cy is the instrument noise covariance matrix and Cf is the forward model error covariance matrix.

[22] Cy is formed with non-zero elements on the matrix diagonal only, which is equivalent to assuming that only uncorrelated noise processes act on the various MOPITT channels. Instrument noise measurements are performed approximately every 2 min from data acquired during periodic space-view intervals. Observations of the space-view background provide a zero-radiance reference which is useful for both radiance calibration and instrument noise characterization. For each signal and for each of the four elements of the detector array [Drummond, 1992], the instrument noise is calculated as the product of the standard deviation of the uncalibrated instrument data (in digital “counts”) acquired during these space views and an appropriate gain factor which converts the value into radiance units. Finally, for each signal and each of the four detector array elements, all instrument noise values for each day are averaged to produce a single daily noise value.

[23] The operational forward radiative transfer model MOPFAS [Edwards et al., 1999] was designed for both accuracy and computational efficiency, and therefore lacks the precision of a line-by-line model. MOPFAS is a parameterization of another radiative transfer model known as MOPABS, which is itself a derivative of the line-by-line radiative transfer model GENLN2 [Edwards, 1992]. To characterize the forward-model error, a statistical analysis was made of the radiance errors between MOPFAS and MOPABS for all profiles used in the development of the a priori (described below). Radiance error vectors were formed for each profile by regarding the MOPABS radiances yabs as “truth” and subtracting those values from the corresponding MOPFAS values y. Thus this analysis does not account for errors in MOPABS itself which, for example, might be due to errors in the HITRAN spectroscopic database. The forward model radiance error covariance matrix was then calculated by computing the expectation value E of the vector (yyabs), i.e.,

equation image

Mathematically, Cf is calculated by forming a matrix of the vector quantity (yyabs) calculated for all profiles used in the development of the a priori, multiplying this matrix by its transpose, and then normalizing by the number of profiles. Calculated this way, fractional radiance errors for the MOPITT CO channels vary from approximately 0.1 to 0.5% and exhibit substantial correlations with each other (i.e., diagonal and off-diagonal elements of Cf are generally of the same order of magnitude). A typical radiance error covariance matrix Cϵ (used in the actual CO retrievals for March 19, 2000) is listed in Table 2. Elements of Cy (which are non-zero only on the matrix diagonal) are indicated by values in parentheses. Forward model error dominates instrument noise in Cϵ except for the variance values (diagonal elements) for signals 3D and 7D.

Table 2. Typical Radiance Error Covariance Matrix Cϵa
  • a

    Contributions to diagonal elements from Cy are indicated by values in parentheses. (Elements below matrix diagonal are not shown, since Cϵ is symmetric.) All values are expressed in units of (W/(m2 sr))2.

7A9.89 × 10−9 (1.03 × 10−11)5.09 × 10−103.93 × 10−111.37 × 10−11
1D 8.2 × 10−11 (1.30 × 10−11)3.04 × 10−111.04 × 10−11
3D  2.59 × 10−10 (2.34 × 10−10)1.10 × 10−10
7D   7.77 × 10−11 (7.17 × 10−11)

2.3. A Priori Development

[24] In principle, the a priori represents the expected statistical behavior (both in terms of the mean state and variability) of the state vector. For CO, seasonal and geographic patterns are well documented [Hauglustaine et al., 1998]. Therefore it might be reasonable to incorporate some degree of spatial and/or temporal dependence into the a priori. At the current stage of MOPITT operational processing, however, we have chosen to use a fixed “global” a priori (described below) for all CO retrievals. There are at least three motivations for this choice. First, use of a spatially-varying a priori would produce corresponding spatial features in the retrieved profiles which would not be associated with any information in the actual satellite-observed radiances. Similarly, as the a priori becomes more specific (either spatially or temporally), the a priori variances and covariances would be expected to decrease. In the maximum a posteriori technique, this will tend to decrease the relative weight of the radiances in the CO retrieval (and thereby increase the relative weight of the a priori mean profile). Neither of these effects seems desirable at present, as they both would complicate interpretation of the retrieval results. Finally, as a practical matter, use of a fixed a priori covariance matrix simplifies averaging kernel calculations, as described below.

[25] The a priori, consisting of both the covariance matrix Ca and the mean state vector xa, describes the statistical behavior of the CO profile, surface temperature, and emissivity. Currently, MOPITT employs a global CO a priori generated from a master set of 525 in situ profiles measured from aircraft during eight atmospheric chemistry field campaigns (TROPOZ-II [Boissard et al., 1996], STRATOZ-III [Gerhardt et al., 1989], TRACE-A [Fishman et al., 1996], PEMWEST-A [Newell et al., 1996], PEMWEST-B [Talbot et al., 1997], PEMTROP-A [Hoell et al., 1999], ABLE-3A [Harriss et al., 1992], and ABLE-3B [Harriss et al., 1994]) and at two fixed sites (Carr, Colorado, [Bakwin et al., 1994] and Cape Grim, Australia [Pak et al., 1996]). Typically, these in situ profiles extend from the surface to approximately 400 mbar (the aircraft maximum flight altitude). At higher levels, in situ data were extended vertically with monthly climatology values from the chemical transport model “MOZART” [Hauglustaine et al., 1998]. As shown in Figure 2, all profiles were initially interpolated to a common standard pressure grid of 32 levels between 1000 and 0.1 mbar. (The six fixed levels in the MOPITT retrieved CO profile are all elements of this high-resolution grid.)

Figure 2.

In situ CO profile set used to construct a priori. In each plot, vertical axis is pressure in mbar, and horizontal axis is CO volume mixing ratio in ppbv.

[26] Geographically, the master set of in situ profiles are not distributed uniformly. For example, tropical and mid-latitudes are represented much better than are polar regions, and the Northern Hemisphere is better represented than the Southern Hemisphere. Ignoring this point in the development of Ca and xa (by simply using all profiles in the master set) would produce an a priori which was not globally balanced. Thus a strategy for developing a global a priori was developed in which the master set of profiles was first divided into four zonal subsets separated by boundaries at 30°S, the equator, and 30°N. By definition, each zone covers one fourth of the Earth's surface. These boundaries also seemed appropriate because of their approximate correspondence to boundaries between tropical and extratropical atmospheric states, and the ITCZ, all of which may influence CO distribution patterns [Gregory et al., 1999]. After generation of the four zonal subsets, multiple global subsets were formed by grouping Nz randomly drawn distinct profiles from each zonal subset. (In practice, Nz was set to 89, which was observed to be the number of profiles in the least-populated zone.) Thus each global subset of 4Nz profiles represented the four equal-area zones defined above equally. Global a priori mean profiles and covariance matrices were then generated for each randomly drawn global subset.

[27] For the ith randomly drawn global subset of CO profiles, both an a priori mean profile xai and a corresponding a priori covariance matrix Cai were generated. The CO component of xai was taken as the mean of all 4Nz CO profiles in the subset. The CO component of Cai was then generated by subtracting the CO component of xai from each profile in the global subset (producing a M by 4Nz profile deviation matrix, where M is the number of standard levels in the CO profile) and then calculating the corresponding covariance matrix (by multiplying the profile-difference matrix by its transpose and dividing by 4Nz) according to

equation image

The a priori value of surface temperature in xai is interpolated from NCEP reanalysis at each pixel. The component of xai related to the longwave surface emissivity is obtained from a surface-emissivity database [Wilber et al., 1999] coupled to a geographical database of surface types [Belward and Loveland, 1996]. Off-diagonal elements of the rows and columns of Cai related to the surface temperature and emissivity are set to 0, since there is no apparent reason to assume any correlation between these parameters and the CO profile or between themselves (surface emissivity is typically fixed for a specific spectral band and surface material, whereas surface temperature is often highly variable). Fixed variance values (i.e., diagonal covariance matrix elements) for the surface temperature and emissivity of 25.0 K2 and 0.025 were selected as reasonable upper limits for the expected global variability in these a priori values. Finally, the operational a priori state vector xa and covariance matrix Ca were generated by averaging the profiles and covariance matrices for all global subsets, i.e.,

equation image
equation image

where Nsub was the number of randomly drawn global subsets. Nsub was set to a value of 20, since this value was more than sufficient to produce converged values of xa and Ca. The resulting a priori mean profile is shown in Figure 3. Error bars at each level indicate the a priori standard deviations (i.e., square roots of the diagonal elements of Ca). The operational covariance matrix for a surface pressure of 1000 mbar is tabulated in Table 3.

Figure 3.

“Global” CO a priori profile and associated standard deviation values (from diagonal elements of a priori covariance matrix). Current retrievals exploit mean profile and covariance matrix values only at seven levels (surface, 850, 700, 500, 350, 250, and 150 mbar).

Table 3. Operational Covariance Matrix Ca for Surface Pressure Value of 1000 mbara
 Surface850 mbar700 mbar500 mbar350 mbar250 mbar150 mbar
  • a

    Elements below matrix diagonal are not shown, since Ca is symmetric. All values are expressed in units of ppbv2.

850 mbar 431925301126836725521
700 mbar  2312889675521306
500 mbar   919623378193
350 mbar    659437259
250 mbar     481344
150 mbar      379

3. Averaging Kernel Analysis

[28] The concept of the retrieval averaging kernel [Rodgers, 2000] is fundamental to understanding the physical significance of the retrieved MOPITT CO profile. The averaging kernel A describes the dependence of the retrieved state vector equation image on the “true” state vector x through the relation

equation image

For the MAP retrieval algorithm employed for MOPITT retrievals, the retrieved state vector equation image can be expressed as a weighted average of the “true” state vector x and a priori state vector xa through the relation

equation image

where I is the identity matrix. In the ideal case, A would equal I, and any perturbation to the true state vector would produce identical changes in the retrieved state vector. Generally, however, changes to any particular element of the true state vector result in finite changes to all elements of the retrieved state vector. Analysis of the retrieval averaging kernels thus permits analysis of the vertical resolution and sensitivity of the retrieved profiles and the degree to which the a priori influences the retrieval.

[29] Each row of A describes how all of the elements in the true state vector contribute to a particular element of the retrieved state vector and constitutes the averaging kernel for that element of the retrieved state vector. Computed mean averaging kernels (produced by averaging all averaging kernels for actual MOPITT CO retrievals within a 20°-wide latitude by 30°-wide longitude box) for a tropical ocean scene are shown in Figure 4. For example, the averaging kernel identified as “Surface” shows how changes to the true CO mixing ratio at all seven retrieval levels would theoretically each contribute to a change in the retrieved value at the surface. Averaging kernels for each level in the retrieved profile do not necessarily peak at the corresponding pressure level of the true profile. Thus, for the case shown, the surface-level CO retrieval is in fact mainly sensitive to CO between 350 and 850 mb. Averaging kernels for successively higher (lower pressure) retrieved levels do, however, systematically shift towards higher levels. Thus the averaging kernel for 250 mbar indicates highest sensitivity between 150 and 500 mbar.

Figure 4.

Mean averaging kernels obtained by averaging all nighttime averaging kernels in the box defined by 10°S, 10°N, 180°W, and 150°W (in the central Pacific Ocean) on March 14, 2000.

[30] The averaging kernels' shapes describe the vertical resolution of the retrieved profile. Clearly, Figure 4 shows that the kernels are rather broad and exhibit a significant degree of overlap. Mathematically, this indicates that the retrievals at the seven levels that form the retrieval grid for this specific case are not generally independent. This is partially a result of the fact that the number of levels in the retrieved profile exceeds the number of CO-sensitive signals used in the retrievals. For example, the strong similarity of the averaging kernels at the surface and at 850 mbar indicates a very high correlation for the retrieved values at these levels. Physically, this correlation can be traced to the very low relative sensitivity of all three thermal-channel D-signals to CO in the boundary layer (as demonstrated in Figure 1). Thus the retrieved CO values at 1000 and 850 mbar are both heavily influenced by CO at higher levels, and by the a priori correlations between CO in the boundary layer and CO at higher levels.

[31] Like the weighting functions described above, operational MOPITT CO averaging kernels exhibit significant variability. Generally, all variables which are required as inputs to the forward radiative transfer model influence A. In particular, though, variability of the atmospheric temperature profile, surface pressure and temperature, and actual CO profile are responsible for most of the variability in the averaging kernels. The observed variability in the averaging kernels for actual MOPITT retrievals indicates that it would not be possible to use “fixed” averaging kernels when analyzing MOPITT data.

[32] Mean averaging kernels for daytime and nighttime retrievals over western Australia for November 1, 2000, are presented separately in Figures 5 and 6. These figures demonstrate the considerable effect diurnal variations of surface temperature can have for retrievals over land. Daytime retrievals over land (based on observations near 1030 local time) are generally characterized by higher surface temperatures compared to nighttime retrievals (based on observations near 2230 local time). For the selected region, retrieved daytime surface temperatures mostly fall in the range of 305 to 320 K whereas retrieved nighttime surface temperatures fall in the range of 280 to 295 K. For the same atmospheric temperature profile, increasing the surface temperature has the effect of shifting the peak of the thermal-channel D-signal weighting functions closer to the surface. Thus the CO near the surface becomes more detectable and the lower-level averaging kernels (e.g., for the surface and 850 mbar retrievals) shift downward. Conversely, lower surface temperatures over land at night produce an upward shift in the averaging kernels. The diurnal variability of the averaging kernels should be maximum over dry, sparsely vegetated regions such as deserts where diurnal variability of surface temperature is largest. In contrast, averaging kernels over the oceans exhibits much smaller diurnal variability due to the much smaller diurnal variability of sea-surface temperature.

Figure 5.

Mean averaging kernels obtained by averaging all daytime averaging kernels in the box defined by 30°S, 15°S, 120°E, and 140°E (western Australia) on November 1, 2000.

Figure 6.

Mean averaging kernels obtained by averaging all nighttime averaging kernels in the box defined by 30°S, 15°S, 120°E, and 140°E (western Australia) on November 1, 2000.

[33] In both midlatitude and polar regions, seasonal and geographic variability of the atmospheric temperature profile also influences the retrieval averaging kernels. Mean averaging kernels obtained for retrievals over the Canadian Plains on November 2, 2000, are presented in Figure 7. Here, both the weaker gradient in the temperature profile and the lower surface temperatures (compared to the previous cases) cause the averaging kernels to become less distinct. Thus, at these higher latitudes, the vertical resolution of MOPITT CO retrievals will generally be lower over the winter hemisphere than the summer hemisphere (particularly over land).

Figure 7.

Mean averaging kernels obtained by averaging all daytime averaging kernels in the box defined by 55°N, 65°N, 120°W, and 100°W (northwestern Canada) on November 2, 2000.

[34] For each MOPITT CO retrieval, there exists a unique averaging kernel matrix. The averaging kernels are not, however, explicitly included in the MOPITT Level 2 Product. Instead, the averaging kernel matrix for any MOPITT retrieval may be calculated from the retrieved error covariance matrix Cx (which is part of the standard Level 2 Product) and the fixed a priori covariance matrix Ca (available from the MOPITT website) through the relation

equation image

Details of this technique are described in a publicly available document which may be obtained either from the internet (at www.eos.ucar.edu/mopitt/data) or by directly contacting one of the authors.

4. Selected Retrieval Results

[35] Retrieval results for three selected tropical oceanic scenes have been analyzed to demonstrate MOPITT's performance under varying pollution conditions. (Results of validation studies in which MOPITT retrievals are compared with colocated in situ CO profiles will be published separately.) The first scene consists of MOPITT CO retrievals obtained within the central Pacific Ocean region bounded by 10°S, the equator, 180°W, and 140°W on September 15, 2000. During this season, this region is characterized by very low tropospheric CO mixing ratio values [Gregory et al., 1999]. The second scene includes retrievals obtained within the eastern Indian Ocean region bounded by 20°S, 15°S, 115°E, and 125°E, also on September 15, 2000. This scene lies off the northwestern coast of Australia, which often experiences large biomass burning events during this particular season. The final scene includes MOPITT CO retrievals obtained off the northeastern coast of South America in the region bounded by 5°S, the equator, 40°W, and 30°W on September 16, 2000. This region within the western Atlantic Ocean is affected by biomass burning both in Africa and South America [Gregory et al., 1996]. Retrieval results for the three scenes are compared in Figure 8. For each scene, both the mean retrieved profile and standard deviation values at each level are indicated.

Figure 8.

MOPITT CO retrieval statistics (mean profiles with standard deviations at each level indicated by error bars) for three tropical oceanic scenes from September 2000. Specific dates and geographical boundaries of scenes are defined in text.

[36] At all tropospheric levels, CO concentrations are lowest in the central Pacific scene. CO concentrations in this area are generally very low during this season because of pollution barriers created by the Inter-Tropical Convergence Zone and the South Pacific Convergence Zone [Gregory et al., 1999]. In contrast, retrieved CO concentrations in the western Atlantic scene are nearly twice as large as values at corresponding levels in the central Pacific scene. In this region, high CO concentrations have been observed throughout the troposphere due to sources in both Africa and South America [Gregory et al., 1996]. In contrast to both the Pacific and Atlantic scenes, MOPITT CO retrievals for the eastern Indian Ocean scene indicate a highly polluted lower troposphere coupled with a relatively clean upper troposphere. During September 2000, extensive fires throughout northern Australia were detected by the TRMM satellite [Giglio et al., 2000]. NCEP reanalysis data for the same period indicate prevailing low-level easterly winds from northern Australia into the eastern Indian Ocean. Thus the observed strong vertical gradient in the MOPITT retrieved profiles over the eastern Indian Ocean suggests the advection of burning-related CO from northern Australia by prevailing easterly low-level winds with weak vertical mixing.

5. Conclusion

[37] Validation of the MOPITT CO retrieval products is well underway. Three types of retrieval errors are to be expected. First, random (unbiased) retrieval errors corresponding to random radiance errors are inevitable but can be reduced by averaging techniques. Second, retrieval biases arising from inadequate a priori are more likely to be a regional problem than a global problem (since the current a priori is specifically intended to describe global CO variability). Finally, retrieval errors due to biases in either the calibrated radiances or the forward model can also produce significant retrieval biases. For this reason, validation of the calibrated radiances and forward model is being conducted as an activity completely separate from retrieval validation.

[38] The initial operational MOPITT retrieval algorithm for tropospheric CO has been described in detail. Four MOPITT thermal-channel signals are currently used as the basis of the CO retrievals. The channel 7A signal is primarily sensitive only to surface temperature and emissivity. D-signals for channels 1, 3, and 7 provide the information from which the CO vertical distribution and total column are retrieved. The a priori CO profile and covariance matrix needed for the maximum a posteriori retrieval algorithm are generated from a globally-distributed set of 525 in situ CO profiles acquired during eight field campaigns and at two fixed sites.

[39] Mean operational retrieval averaging kernels for both oceanic and terrestrial scenes were presented to demonstrate the effects of geophysical variability (e.g., surface temperature variability) on the MOPITT retrieval sensitivity. For tropical oceanic scenes, the averaging kernels indicate that upper levels in the retrieved CO profile (i.e., 150, 250, and 350 mbar) are primarily sensitive to upper tropospheric CO (p < 500 mbar), whereas the lower levels in the retrieved profile (i.e., surface, 850, and 700 mbar) are primarily sensitive to CO in the layer between 300 and 800 mbar. Finally, retrieval results for three contrasting tropical oceanic scenes were compared to demonstrate the observed variability in the actual MOPITT retrievals. These results generally agree with previously observed or expected trends in tropospheric CO in the selected regions.


[40] The University of Toronto MOPITT team would like to acknowledge the Canadian Space Agency (CSA) for the instrument finance, the Natural Sciences and Engineering Research Council (NSERC) and Meteorological Service of Canada (MSC) for help with the data processing, COMDEV (the prime contractor), ABB BOMEM, and the University of Toronto. The NCAR MOPITT project is supported by the National Aeronautics and Space Administration (NASA) Earth Observing System (EOS) Program. The National Center for Atmospheric Research (NCAR) is sponsored by the National Science Foundation.