1. Introduction
In recent years, the growth in the volume of satellite data made available to numerical weather prediction (NWP) centers has been phenomenal. A major component of that growth is due to the advent of the Atmospheric Infrared Radiance Sounder (AIRS) hyperspectral infrared instrument launched in 2002, which provides 2378 channels for swaths 1650 km wide (Aumann et al. 2003). Soon, data from a similar instrument, the Infrared Atmospheric Sounding Interferometer (IASI; 8461 channels), will become available. For such hyperspectral data, NWP centers have considered for possible assimilation subsets on the order of 300 channels. Apart from the problem of handling such a high volume of data and meeting operational time constraints, the main challenges leading to operational assimilation include the identification of clear radiances (i.e., not affected by clouds), radiance bias correction, and quantification of the observation error.
An NWP analysis consists of combining in a statistically optimum way the observations and a background field, which is typically a short-term forecast. This process requires good a priori knowledge of both the background and observational error statistics. In the case of radiance measurements, the observation error includes various components: instrument noise, radiative transfer modeling errors, and representativeness errors induced by unresolved spatial scales or the mismatch in time and space between the observations and the background. Because of the latter two factors, there is a possibility that the observation error is spectrally correlated—in particular, for neighboring channels with similar sensitivity to atmospheric gases and temperature. The object of this paper is twofold. First, a means to separate the background and observation errors is presented. Second, by extending this technique to interchannel covariances, the interchannel observation error correlation (IOEC) is derived. Up to now, the IOEC has not been considered in data assimilation. Instead, the best estimate of the observation error variance is inflated to compensate for effects such as IOEC, possible horizontal correlation of errors, and unresolved scales. The assimilation of AIRS radiances has been successfully implemented at several NWP centers, including the National Centers for Environmental Prediction (Le Marshall et al. 2006), the European Centre for Medium-Range Weather Forecasts (ECMWF; McNally et al. 2006), and the Met Office. Proper consideration of the IOEC should lead in principle to an improved analysis system.
The error contribution originating from imperfect radiative transfer modeling was studied by Sherlock et al. (2003) using simulated AIRS radiances. Significant error correlations were found for channels within the window region and within the 6.7-μm water (H2O) absorption band. To our knowledge, studies of the IOEC based on real radiance observations have not been published yet. It is fortunate that the nature of AIRS data, including the close horizontal spacing between fields of view, lends itself to a relatively straightforward evaluation of the IOEC, provided that some basic hypotheses, to be discussed later, are valid.
The paper is organized as follows. Section 2 briefly describes the AIRS processing steps that lead to a coherent dataset of radiances that are not affected by clouds. Observed-minus-calculated radiance statistics are then computed. The separation procedure of the total error into its observation and background components is described, and the results are presented in terms of the interchannel error correlation matrix for a subset of 123 AIRS channels. In section 3, the impact of the IOEC is evaluated in data assimilation from 1D variational experiments. Section 4 concludes the article.
2. Estimation of the error covariances
a. AIRS processing
Goldberg et al. (2003) provide a description of the AIRS near-real-time products. As of the writing of this article, the AIRS team maintains a comprehensive Internet site (http://airs.jpl.nasa.gov/). AIRS data are received at the Meteorological Service of Canada (MSC) from the National Environmental Satellite, Data, and Information Service (NESDIS) in the form of a subset of 281 channels out of 2378. MSC organizes the data in files representing 6-h periods centered at the four synoptic times of 0000, 0600, 1200, and 1800 UTC. Each file contains 81 000 locations and represents four orbits. The whole globe is well covered in a period of 24 h. The field of view (FOV) at nadir is 13.5 km. Only one FOV out of three in each direction is received, which implies a horizontal spacing of about 40 km at nadir. This study is based on a period of 1 week of AIRS observations obtained in February of 2004.
MSC has developed a processing system for AIRS identifying clear pixels or, to be more general, channels that are not sensitive to clouds. Details are provided in the appendix. A simple bias correction scheme was developed for the observations that is linear with the observed brightness temperature itself. The same type of bias correction is applied to Geostationary Operational Environmental Satellite radiances (Garand 2003). The bias correction procedure is based on the commonly used assumption that the forecast model equivalent radiances are not climatologically biased. For this work, cloud-free bias-corrected observations are used. Figure 1a shows the correspondence between wavelength and AIRS channel numbers. MSC is currently considering 123 of the available 281 channels for assimilation. Figure 1b shows the correspondence between wavelength and these 123 channels. Results presented in this paper refer to this subset of 123 channels. Channels that are not used include those with a response above the forecast model top at 10 hPa, channels sensitive to ozone (O3), channels with large modeling errors, and highly redundant surface-sensitive channels in the 3.7–4.1-μm region.
The method to derive the observation error statistics is based on the calculation of observed (O) minus “predicted” (P) or calculated radiances from a 6-h forecast referred to as the background state. The match in time is therefore ±3 h. The current resolution of the global forecast model is 100 km. The background is interpolated to each observation location to obtain the variables needed for radiance calculations: temperature and humidity profiles, surface pressure, and surface skin temperature. The radiance calculation is made with the fast radiative transfer model known as Radiative Transfer for Television and Infrared Observation Satellite Operational Vertical Sounder (RTTOV)-8 (Matricardi et al. 2004). The accuracy of RTTOV-8 is estimated to be better than 0.2 K in units of brightness temperature for most AIRS channels. Surface emissivity over oceans is based on Masuda et al. (1988). Surface-sensitive channels are not used over land.
b. Fitting procedure
The method to separate the observation and background error components from (O − P) statistics is well established and has been used extensively at NWP centers to characterize both forecast and observation error covariances (e.g., Rutherford 1972; Hollingsworth and Lönnberg 1986; Daley 1993). The method is here applied for the first time, we believe, to radiance data. The method is based on two basic assumptions: first, that background and observation errors are uncorrelated and, second, that the background errors are correlated in the horizontal plane while the observation errors are not. Because AIRS data are not yet assimilated, the background error has no connection with the observations, implying that the first assumption is valid. The validity of the second assumption is studied further. If that hypothesis is also valid, the fit of an appropriately chosen function for the (O − P) covariance as a function of the distance allows one to separate the O and P error components, as shown below.
The bias component associated with radiative transfer calculations is, it is hoped, minimized by the radiance bias correction procedure. It is possible that, in opposition to the working hypothesis, some portion of the spatially correlated part of the error is due to the observation error. From collocation with radiosondes, Bormann et al. (2003) found significant horizontal error correlation associated with satellite wind retrievals. This correlation was attributed to the use of model temperature information for cloud-height assignment and horizontal-consistency quality-control procedures. Here, the correlation study is facilitated by the short distance between measurements (40 km) as opposed to ∼200 km for radiosondes and by the large amount of collocations with forecasts obtained from a limited time period.
The (O − P) covariances are computed for all possible channel pairs and as a function of horizontal separation in 25-km bins. The first bin is at distance 0; the other bins are centered at 50, 75, 100 km, and so on up to 500 km (the 25-km bin is empty). Covariances are typically low beyond that distance for water vapor channels and surface-sensitive channels. For other channels, the 18 bin values are sufficient to derive a reliable fit of the short-range correlations because of the high spatial density of the data. The search is facilitated by the MSC processing in groups of 120 locations. Because locations within a group are contiguous, only the pairs within a group are examined. Statistics were cumulated for two different periods of 3.5 days. Differences between the two IOEC resulting matrices confirm that the sample size is sufficient, with values differing by less than 5%. The largest uncertainty occurs for low correlations (<40%) between water vapor channels and surface-sensitive channels. Results presented in this study are based on the combined period representing 7 days. For channel pairs involving at least one surface-sensitive channel (requiring a clear-sky situation), the number of collocations in each bin is on the order of 140 000. For channels that are only sensitive to the upper atmosphere and therefore are less often affected by clouds, the number of collocations is on the order of 1.35 million. Only data between 60°N and 60°S were retained because the cloud analysis is more reliable at these latitudes.
No attempt is made to fit negative correlations. Some negative covariances do exist, with values of T(i, j) up to −0.20 K2, mostly between upper-tropospheric-temperature-sensitive channels (14.4–15.4 μm) and water vapor channels (6.3–7.5 μm). It is assumed here that these are entirely due to background errors, which is supported by the observation that V(i, j; 50 km) is close to T(i, j) in these situations. Furthermore, there are cases in which interchannel covariances (again, weak values) seem to increase with distance. This is detected from a linear fit using values of V for bins 50–500 km (with negative values set to zero). If the correlation from that linear fit is between 0.0 and −0.2, V(i, j; 0) is set to the intercept. When the correlation is positive, V(i, j; 0) is set to the mean value of V. Last, lower and upper limits of 0 and T(i, j) are imposed on the values of V.
c. Results from the fitting procedure
Figure 2 shows examples of the fitting procedure pertaining to AIRS channel pairs 174–174, 174–175, 1652–1652, and 1652–1669. Channels 174–175 (indices 29–30; main sensitivity between 100 and 400 hPa) are neighboring temperature sounding channels centered at 14.297 and 14.291 μm, respectively, and 1652 and 1669 (indices 82–83; main sensitivity between 400 and 700 hPa) are water vapor–sensitive channels centered at 6.935 and 6.808 μm, respectively. The chosen function provides a satisfactory fit. The covariances are normalized by division with T(i, j), and that value is noted on the top-left corner. The separation procedure yields an observation error variance of 0.17 K2 for channel 174 and 0.81 K2 for channel 1652. In comparison, the derived observation error covariance is low for the pair 174–175 (0.02 K2) while remaining large for the pair 1652–1669 (0.73 K2). As will be seen from the complete results, low IOEC values characterize the 13–15-μm carbon dioxide (CO2) absorption band and high IOEC values characterize the 6.7–7.0-μm H2O absorption band.
The complete 123 × 123 observation error correlation matrix obtained by the fitting procedure is shown in Fig. 3. The striking characteristics that are immediately apparent are the four distinct blocks. These blocks are defined in Table 1 in terms of channel number, spectral ranges, and dominant channel sensitivity. The first block, in the lower-left corner of Fig. 3, is characterized by very low IOEC (<15%). The second block may be divided in two subgroups. The second subgroup (2-B) is more sensitive to the surface than the first one (2-A) and has higher values of IOEC. The third block represents the water vapor–sensitive channels. The IOEC is large within that block but tends to be negligible where it involves channels from other blocks. The fourth block is split between the nitrous oxide (N2O) and CO2 sounding channels. The IOEC is large among members of block 4 and often exceeds 50% between members of blocks 2 and 4, both of which are characterized by a significant sensitivity to surface skin temperature. The causes leading to high correlations in various spectral regions are not obvious. Detector characteristics could be a factor, because a different type of detector is used in block 1 (photoconductive, indices 1–47) while photovoltaic detectors are used for the remaining part of the spectrum (http://airs.jpl.nasa.gov/technology/airs_desc.html). The AIRS calibration team did identify noise correlation at the level of 20%–50% in several spectral areas located in blocks 3 and 4 and essentially no such correlation in blocks 1 and 2 (M. Weiler 2006, personal communication). However, the noise level itself, on the order of 0.15 K in blocks 3–4 (shown below), is too low in comparison with the inferred observation error to explain the high correlations seen in Fig. 3. Undetected clouds may play a nonnegligible role because clouds would affect most channels in a similar fashion (cold bias). Other causes, which likely dominate, are unresolved vertical and horizontal scales and radiative transfer modeling errors. The effect of unresolved scales is expected to be more important in channels that are strongly sensitive to water vapor (block 3) and in channels that are sensitive to the lower troposphere (blocks 2 and 4) than in upper-tropospheric-temperature channels (block 1).
The separation of the total error variance into its background and observation components is shown in Fig. 5 for the 123 channels. The total error standard deviation is largest in the 6.2–7.1-μm water vapor channels, with most of that error attributed to the background. The observation error is typically in the range 0.35–1.1-K, with similar values found within each block of channels. Figure 5 suggests that the largest radiative transfer errors are present in the water vapor channels (block 3). Unresolved spatial scales for the moisture variable likely play a significant role in increasing that error. In comparing Figs. 4 and 5, we see that the observation error is always larger, as it should be, than the noise level. However, for indices 1–4, the estimated noise level is only ∼0.1 K below the observation error.
d. Other estimation of the background error
Figure 6 compares values of diagonal elements 𝗘1/2b with the background error standard deviations obtained from the fitting procedure [as in Fig. 5; V(i, j; 0)1/2]. The horizontal axis represents wavelength, allowing direct comparison with those presented by McNally and Watts (2003), which are derived from the 𝗕 matrix used at ECMWF. These two estimates agree within 0.2 K, except in the region of water vapor channels: 6.2–7.7 μm. ECMWF values in that spectral region are in the range 1.0–1.7 K, as compared with 1.4–2.4 K in Fig. 6. This is the consequence of significantly larger humidity errors in the MSC 𝗕 matrix. At another NWP center (the Met Office), the error std dev of ln(q) are everywhere set to values not exceeding 0.46 (English 1999).
Figure 6 shows that the separation method and 𝗘1/2b are largely similar in channels only sensitive to atmospheric temperature (channel indices 1–40). This gives confidence that errors associated with temperature are realistic. It also gives confidence that the separation technique works well. Higher values of 𝗘1/2b seen in surface-sensitive channels in the near-infrared region (channel index > 98) may indicate a too-high estimate of the skin temperature error variance in 𝗕. The same is likely true for the assumed humidity errors in the midtroposphere, as discussed previously, creating differences of ∼0.3 K in the water vapor channels (6.2–7.8 μm). For the remaining portion of the spectrum (7.9–12.5 μm), both Ts and ln(q) background errors make 𝗘1/2b significantly larger than the values obtained by the separation technique. In fact, the 𝗘1/2b estimates in that part of the spectrum are often larger than the total error, which is a clear indication that they are overestimated. Consistency among total, observation, and background error covariances is currently the object of active research (Buehner et al. 2005; Chapnik et al. 2004). The results shown in Fig. 6 do not confirm the working hypothesis that the observation errors are not spatially correlated. However, if that spatial error correlation was found to be significant, and values of the background errors were corrected accordingly, then the difference between the two estimates shown in Fig. 6 would increase further. Thus, the argument here is that the working hypothesis holds to first order, that is, the correlated part of the (O − P) statistics is dominated by background errors. Collocation of observations with radiosondes could, in principle, help to resolve the issue. However, a significant difficulty there is that the radiosonde profiles must be transformed into radiances. Therefore, errors associated with the radiative transfer model, including possible spatial correlation, are transferred to the radiosonde-derived radiance. Other difficulties include the need for very large datasets (on the order of 1 yr of collocations), the absence of observed surface skin temperature and emissivity, and the fact that radiosondes are often incomplete (stopping at ∼100 hPa). In addition, for water vapor channels (e.g., Fig. 2c) and surface-sensitive channels, the lack of radiosonde data pairs for distances of less than ∼200 km creates a substantial uncertainty for the extrapolated value at D = 0.
3. Impact of the IOEC in 1D variational data assimilation
a. Assimilation setup
It is necessary that the 𝗥 matrix be positive definite, otherwise serious convergence problems may occur as well as unrealistic results. Each element of 𝗥 in Fig. 3 was derived separately from all others. This empirical procedure allows some level of inconsistency between the individual estimates, resulting in a non-positive-definite matrix. A new matrix was constructed after eliminating the near-zero and negative eigenvalues. Here 85 of the 123 eigenvalues were retained, using a threshold of 0.5 times the lowest eigenvalue of the diagonal matrix. The net effect was to reduce slightly (<10%) some of the correlations related to blocks 2 and 4. The reconstructed matrix is rank deficient and thus requires the use of a pseudoinverse (Strang 1998) in Eq. (6). Other methods were attempted (e.g., Wothke 1993), leading to a true inverse, such as augmenting the covariances on the diagonal or imposing a minimum positive eigenvalue. However, these alternative methods had the disadvantage of modifying more significantly the original matrix. To evaluate the impact of the IOEC, the 𝗥 matrix is either complete (FULL) or diagonal (DIAG). The 1D-var tests were made from an ensemble of 381 locations using all 123 channels.
b. Assimilation results
Figure 7 compares the standard deviations of the temperature and ln(q) increments (analysis minus background, referred to as A − P) from the FULL and DIAG assimilations. It is seen that the std dev of the difference in temperature increments (FULL − DIAG) is on the order of 0.20–0.35 K, and the magnitude of the increments themselves is on the order of 0.5–0.6 K. Thus, the IOEC impact is significant. The corresponding std dev of increment differences for ln(q) is on the order of 0.10 as compared with increment std dev, which is in the range 0.25–0.35 K between 150 and 800 hPa, the main region of sensitivity to moisture for AIRS observations. Again, the effect is not negligible. For individual profiles, temperature differences exceeding 1 K and ln(q) differences reaching 0.5 are possible. Another interesting result is the fact that the rate of convergence is on average 2 times as fast for FULL (typically 15–25 iterations) as for DIAG (typically 30–50 iterations). The IOEC matrix better constrains the assimilation process and the equivalent BTs are not required to fit as closely the observed BTs in the FULL experiment in comparison with the DIAG experiment. The bottom panel of Fig. 7 shows the corresponding (A − P) BT statistics for each channel. It is clear that more weight is given to the AIRS data in the DIAG experiment as compared with the FULL experiment, with larger BT increments by about 0.3 K in water vapor channels (indices 75–97) and 0.1 K for indices 98–123. It is noted that the DIAG increment magnitude curve (A − P) is nearly a copy of the total error curve (O − P) presented in Fig. 5. Thus, the DIAG assimilation fits the observations very closely.
In the same manner as Fig. 7, Fig. 8 provides a specific example of the increment differences in the terms temperature, ln(q), and BT. The BT spectrum (Fig. 8c) illustrates the rich information content of AIRS data. A major feature of Fig. 8b is the humidity increment in the 300–600-hPa layer, which is higher for the DIAG assimilation. This translates into a closer fit to BT observations for indices 75–85 and 95–97 (the latter are AIRS 1826, 1843, and 1852). These channels have a peak sensitivity near 500–550 hPa, whereas indices 86–94 have a peak sensitivity near 350–400 hPa. The (O − P) forcing is significantly less strong for the latter channels because the observations indicate that the atmosphere is warmer than the first guess in the 200–400-hPa layer, resulting in a strong temperature increment (maximum of 0.9 K). That warming feature is linked to the positive (O − P) for indices 25–40. Another significant difference is the stronger DIAG temperature increment in the 600–850-hPa layer. That feature is linked to the stronger DIAG assimilation of near-infrared radiances (indices 99–123) relative to the FULL assimilation.
It is also noted that the BT increments (A − P) tend to be spectrally smooth as compared with (O − P) forcing, which in part reflects the noise level present in the observations. The assimilation process filters the noise due to correlations between the background errors when transformed into observation space. The noise level seems to be large for channel indices 1–18, resulting in systematically flat increments (noted also in Fig. 7). It was shown previously (Fig. 4) that the noise level increases in that spectral region. In addition, it was found that these channels have a nonnegligible contribution above the forecast model top at 10 hPa. As a consequence, channels beyond 14.5 μm will not be used in operations until the forecast model top is raised.
c. Consistency test
4. Conclusions
A standard technique was used to separate the observation and background error from (O − P) statistics. By extending the application of this technique to interchannel covariances, the IOEC was determined. The 1D-var experiments showed that the impact of the IOEC is significant for AIRS, with typical increment differences (DIAG − FULL) on the order of 0.25 K for temperature and 0.1 for ln(q). The IOEC reduces the relative weight of the observations with respect to the background. The impact is limited by the fact that the IOEC is nearly negligible in the 13.2–15.4-μm spectral region, which plays an important role in the retrieval of temperature in the middle and upper atmosphere.
The working hypothesis that only the background errors are spatially correlated may not be satisfied for all channel pairs. Cross validation, involving the mapping of the MSC 𝗕 matrix in radiance space, suggests that the correlated part of the total error is indeed dominated by background errors. If it is not the case, then the observation error will be underestimated. To compensate for factors such as the IOEC and cloud contamination, AIRS errors were set to values exceeding the total error in all channels at ECMWF (McNally et al. 2006). Inflating the observation error to compensate for the IOEC seems to be a practical solution, but it will not provide an optimum weight of the observations with respect to the background. It was verified that to approach the observation weight in a global sense of experiments with IOEC (i.e., Fig. 7c) the observation error would need to be inflated to values significantly above the total error in the water vapor and surface-sensitive channels.
The next step to complete this study is to test the impact of the IOEC on analyses and forecasts from 3D or 4D assimilation cycles. A difficulty related to such experiments is that unless only clear-sky observations are used, the number of channels available for assimilation varies with location, depending on the height of the clouds. As a consequence, the inverse of 𝗥 has to be calculated separately for each point. More studies are also needed to understand better the nature of the IOEC—notably, to explain why it is so high for some channel pairs. In the near future, it will be interesting to evaluate the IOEC between IASI channels. While the AIRS instrument is an array-grating spectrometer, IASI is based on Fourier-transform interferometry. The IOEC impact will potentially be larger for IASI because of the different nature of the measurements and the use of apodization in particular (Aires et al. 2002).
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APPENDIX
Determination of Clear Radiances
The inference of cloud cover and cloud-free radiances is done through various tests. Cloud cover is first determined using the Garand and Nadon (1998) cloud algorithm. That algorithm uses window channel 787 (10.9 μm) in combination with the guess temperature profile. The logic considers possible surface-inversion cases. The same channel is used to infer the surface skin temperature Ts by inversion of the radiative transfer equation, assuming the guess profile as perfect. A difference of more than 2 K (4 K) over ocean (land) between the retrieved and guess Ts is indicative of possible cloud contamination. NESDIS provides an estimate of cloud fraction in daytime based on a high-resolution visible channel. A pixel is considered to be cloudy if that estimate exceeds 3%. Next, our implementation of the CO2-slicing technique (Garand and Beaulne 2004) is used for those pixels assumed to be cloudy to infer the cloud-top height and emissivity. Twelve estimates are made from as many pairs of AIRS channels, using channel 870 (10.5 μm) as reference channel. Data are not assimilated where the method fails or where the variance among the various estimates is in excess of 50 hPa for the effective cloud top. The level-to-top transmittance from the radiative transfer model is used to infer the local response function. Radiances are considered as not affected by clouds if the cloud top is lower then the lowest level at which the response function becomes significant, plus a security margin. That margin is the greater of 50 hPa or 2 times the std dev among the CO2-slicing cloud-top estimates. Last, a background check is applied: |O − P| in excess of 3 std dev of the ensemble value are rejected.
Wavelength vs AIRS (top) channel number and (bottom) channel index for the 123-channel subset used is this study.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Normalized covariance fit vs horizontal separation (km) for AIRS channel pairs indicated in the upper-right corner. Covariance (K2) at zero separation distance is shown in upper-left corner. Derived observation errors for channels 174 and 1652 are 0.41 and 0.90 K, respectively. Values of L (km) and b are (a) 243 and 0.584, (b) 357 and 0.675, (c) 115 and 0.806, and (d) 111 and 0.780.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Interchannel error correlation (%) associated with the 123-channel AIRS subset. Channel index boundaries of the blocks (noted as B1–B4, where B stands for block) described in Table 1 are indicated on the horizontal axis.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Instrument noise (NEDT) at 250 K (solid line) and that estimated at the mean observed brightness temperature (plus signs) for each channel.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Separation of the total error std dev (K; solid line) into its background (B symbols) and observation (O symbols) error components for each channel.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Background error std dev (K) as a function of wavelength (μm) obtained from the separation technique (B symbols) and that obtained from 𝗘b defined in Eq. (5) (solid line).
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Std dev of (top) temperature and (middle) ln(q) analysis increments (A − P) derived from 381 FULL and DIAG 1D-var assimilation experiments using 123 channels in clear-sky situations. (bottom) Corresponding (A − P) BT std dev (K). The std dev of the FULL − DIAG differences (DIFF) is shown in each panel.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Example of (top) temperature and (middle) ln(q) analysis increments (A − P) associated with FULL and DIAG retrievals. Increment differences FULL − DIAG (DIFF) is also shown. (bottom) Corresponding (A − P) BT difference (K), as well as (O − P) BT difference.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Std dev of the BT observation error (K) vs channel index associated with matrix 𝗥 (OBS) and estimated from 〈(O − P) × (O − A)〉 based on 381 FULL and DIAG retrievals.
Citation: Journal of Applied Meteorology and Climatology 46, 6; 10.1175/JAM2496.1
Definition of channel groups (blocks) seen in Fig. 3 in terms of AIRS channel number or index, spectral range, and atmospheric or surface sensitivity (strongest first); Ts designates surface temperature.
