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Keywords:

  • data assimilation;
  • error correlations;
  • calibration/validation

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and methods
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References

This article is the second part of a two-part article that uses three methods to estimate observation errors and their correlations for clear-sky sounder radiances used in the European Centre for Medium-Range Weather Forecasts (ECMWF) assimilation system. The analysis is based on covariances derived from pairs of first-guess and analysis departures. The methods used are the so-called Hollingsworth/Lönnberg method, a method based on subtracting a scaled version of mapped assumed background errors from first-guess departure covariances and the Desroziers diagnostic. The present article reports the results for the high-spectral-resolution Atmospheric Infrared Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI).

The findings suggest that mid-tropospheric to stratospheric temperature-sounding channels for AIRS and IASI show little or no interchannel or spatial observation-error correlations, and estimates for the observation error are close to the instrument noise. Channels with stronger sensitivity to the surface show larger observation errors compared with the instrument noise, and some of this error is correlated spatially and between channels. Short-wave temperature-sounding channels also appear more prone to spatial observation-error correlations. The three methods show good consistency for these estimates.

Estimation of observation errors for humidity-sounding channels appears more difficult. A considerable proportion of the observation error for humidity-sounding channels appears to be correlated spatially for short separation distances, as well as between channels. Observation-error estimates for humidity channels are generally considerably larger than the instrument noise.

An analysis of departure statistics and observation-error correlations by scan position and scan-line difference for IASI shows a pattern that correlates with the direction of the movement of IASI's corner cube mirror. The effect is very small and most likely linked to micro-vibrations of IASI's beam-splitter.

The statistics also provide information on the assumed background errors. There are indications that the assumed background errors for tropospheric temperature are inflated (by about 30– 60%), whereas there is little indication for background-error inflation for stratospheric temperatures. Copyright © 2010 Royal Meteorological Society


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and methods
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References

This is the second part of a two-part article in which we estimate and examine observation errors and their correlations for clear-sky radiances used in the European Centre for Medium-Range Weather Forecasts (ECMWF) system. The first part described the methods and summarized the results for instruments of the ATOVS suite (see Bormann and Bauer, 2010, hereinafter BB10). The present article provides the results for advanced high-spectral-resolution infrared sounders.

High-spectral-resolution sounders such as the Atmospheric Infrared Sounder (AIRS) on Aqua and the Infrared Atmospheric Sounding Interferometer (IASI) on the METOP series are the new generation of infrared instruments, providing observations in the 650– 2700 cm−1 range in thousands of channels (Chalon et al., 2001; Aumann et al., 2003). The larger number of channels and the resulting diverse weighting functions mean that the instruments can achieve higher vertical resolution than previous infrared instruments such as the High Resolution Infrared Radiation Sounder (HIRS). For computational reasons, most numerical weather prediction (NWP) applications only use a subset of channels, usually less than 200, primarily located in the long-wave CO2 band. The assimilation of AIRS and IASI observations in NWP has resulted in a substantial positive forecast impact (McNally et al., 2006; Collard and McNally, 2009).

As for all other radiance observations, all current assimilation systems assume that the AIRS or IASI observations do not have spatial or interchannel observation-error correlations. This is even though radiative-transfer errors, apodization (in the case of IASI), representativeness errors and aspects of quality control are likely to introduce some error correlations. Indeed, Garand et al. (2007) found significant interchannel error correlations for AIRS, especially for the water-vapour band, but also for lower tropospheric temperature-sounding and window channels. Neglecting such error correlations is expected to impact the vertical resolution that can be derived from these observations. Ad hoc inflation of observation errors or spatial thinning is usually applied to counteract overfitting of the data. In the case of spatial-error correlations, Liu and Rabier (2003) found in a simulation study that the smallest analysis error was obtained when a thinning scale was used that corresponded to the distance at which the error correlation reaches 0.2. This is for the case when error correlations are neglected in the assimilation system and the diagonal observation errors are not inflated.

In the present study, we provide estimates of observation errors and their spatial and interchannel correlations for AIRS and IASI, using the methods outlined in detail in BB10. The next section briefly recapitulates the methods and the data used in this study. The results are presented next, discussed by groups of channels that share observation-error characteristics. The results are also compared with those provided in Garand et al. (2007). Finally, a discussion and conclusions from both parts of this two-part article are given in the last section.

2. Data and methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and methods
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References

The methods used to estimate the observation errors are the same as in BB10, namely the Hollingsworth/Lönnberg method (Rutherford, 1972; Hollingsworth and Lönnberg, 1986), a method based on subtracting a scaled version of the assumed background error, mapped into radiance space, and the consistency diagnostic provided by Desroziers et al. (2005). All three methods are based on covariances of first-guess (FG) or analysis departures, calculated from a large database of pairs of observations. The radiative-transfer model used in this study is RTTOV, version 9 (Saunders et al., 1999; Bormann et al., 2009). The departures are taken after variational bias correction (Dee, 2004). We only consider fields of view (FOVs) for which all channels currently considered for assimilation are used in the assimilation system, i.e. only FOVs for which all active channels are diagnosed as cloud-free and are not removed by other quality-control procedures. Further details on the methods employed here are given in BB10.

The results presented here are based on data for the 21 day period 22 August– 11 September 2008. The FG and analysis departures were taken from the same assimilation experiment as used in BB10. It employed four-dimensional variational data assimilation (4DVAR) with a 12 hour observation window, a model resolution of T799 (≈ 25 km), an incremental analysis resolution of T255 (≈ 80 km) and 91 levels in the vertical up to 0.01 hPa. The experiment used a thinning scale of 60 km, approximately half the operational thinning scale.

The present article provides observation-error estimates for AIRS and IASI. AIRS is an infrared radiometer on Aqua with 2378 channels, covering the infrared part of the spectrum in three bands, 650.0– 1136.6 cm−1, 1217.0– 1613.9 cm−1 and 2181.5– 2665.2 cm−1 (Aumann et al., 2003). AIRS is flown together with an Advanced Microwave Sounding Unit (AMSU)-A, and 3 × 3 AIRS FOVs are sampled per AMSU-A FOV. At ECMWF, only the warmest FOV within an AMSU-A FOV is considered for assimilation, as it is expected to be clearest. The outermost nine scan positions on either side of the scan are also excluded.

IASI is an interferometer with 8461 channels flown on the METOP series of polar orbiters. It covers the spectral interval from 645– 2760 cm−1 with a spectral sampling of 0.25 cm−1 (Chalon et al., 2001). IASI provides 2 × 2 FOVs within an AMSU-A FOV; only the first of these is considered for assimilation at ECMWF (Collard and McNally, 2009). The scan positions corresponding to the outermost three AMSU-A scan positions on either side of the scan are also excluded.

Up to 119 AIRS and 175 IASI channels are used in the assimilation configuration used in this study; most of these are in the long-wave CO2 band (Figure 1). The use of the water-vapour band is restricted to seven AIRS and 10 IASI channels; experiments with more water-vapour channels have so far resulted in a degraded analysis. Cloud screening for both instruments follows the scheme of McNally and Watts (2003), which aims to identify clear channels based on evaluating FG-departure signatures. The scheme is applied to temperature-sounding channels; for the water-vapour band, the cloud-screening is linked to the results from the temperature-sounding channels. No IASI radiances are used over land, whereas up to 48 stratospheric AIRS channels not sensitive to the surface are assimilated over land.

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Figure 1. (a) Wavenumbers [cm−1] of the AIRS channels used in the ECMWF system as a function of channel index in the list of 119 channels. The top axis gives the values of selected AIRS channel numbers for further orientation. (b) As (a), but for the 175 IASI channels used. (c) Pressure [hPa] of the Jacobian peak for the AIRS channels used in the ECMWF system. (d) As (c), but for the IASI channels.

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The bias-correction models applied to IASI and AIRS data are similar to those employed to other sounder radiances at ECMWF. They consist of a linear model for the airmass bias, with a constant component and four layer thicknesses calculated from the FG as predictors (1000– 300 hPa, 200– 50 hPa, 50– 5 hPa, 10– 1 hPa). Scan biases are modelled through a third-order polynomial in the scan angle. The standard model used in variational bias correction is modified for AIRS channels 1921– 1928 to include a predictor that is zero during night-time and the cosine of the solar zenith angle during daytime (Bormann et al., 2008). Also, no air-mass bias correction is used for window channels (325– 914 for AIRS, 380– 1180 for IASI).

Further information on the initial assimilation of AIRS and IASI data can be found in McNally et al. (2006) and Collard and McNally (2009), respectively.

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and methods
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References

We will now present the results of the observation-error covariance estimates for AIRS and IASI. All statistics shown are for data over sea; for IASI no data are currently assimilated over land, and for AIRS the 48 channels assimilated over land are not sensitive to the surface, so they do not show different characteristics over land.

The channels of each of the instruments can be broadly grouped into six categories that show different behaviour for the observation-error covariance estimates. The groups are summarized in Table I and they will be introduced further below. The table also shows which channel range the groups mostly cover; note that this separation should not be taken too strictly, as the groups overlap for some channels (see also Figure 1(c) and (d) for further orientation).

Table I. Groups of channels showing similar observation-error characteristics for AIRS and IASI.
Group numberDescriptionAIRS channel numbers (wavenumbers [cm−1])IASI channel numbers (wavenumbers [cm−1])
1Long-wave CO2,7– 25116– 249
 upper temperature-sounding(651.05– 721.54)(648.75– 707.00)
2Long-wave CO2,252– 355252– 445
 lower temperature-sounding(721.84– 753.06)(707.75– 756.00)
3Long-wave window channels362– 870457– 921
  (755.36– 948.18)(759.00– 875.00)
4Water-vapour channels1329– 17402889– 3110; 5318, 5399, 5480
  (1251.36– 1513.83)(1367.0– 1422.25; 1990.0, 1994.5, and 2014.75)
5Short-wave window channels1865– 1882Not used
  (2181.5– 2197.0) 
6Short-wave temperature-sounding1897– 1928Not used
   (2210.85– 2240.03)

3.1. Long-wave CO2 channels

The first group of channels is characterized by spatial FG-departure covariances that show a very clear separation between a very small spatially correlated part and a much larger spatially uncorrelated part (see, for example, Figure 2(a)– (c)). Just under half the channels used for each instrument fall into this group; they are the stratospheric to mid-tropospheric long-wave temperature-sounding channels. The estimated observation errors and their correlations show excellent agreement between the three methods. The size of the observation errors is close to the instrument noise, which completely dominates the FG-departure variances (Figures 3 and 4). The channels show virtually no spatial-error correlations right up to the smallest separation bin used (Figures 5 and 6), and small or no interchannel error correlations (Figures 7–12). Similarly to the case of AMSU-A (see BB10), it appears that the radiative-transfer error after bias correction is comparatively small. As in the case of similar AMSU-A channels, the spatial characteristics of the mapped assumed background errors are typically consistent with the FG-departure covariances or somewhat larger.

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Figure 2. First-guess departure covariances (black), Desroziers background-error diagnostics (solid grey) and mapped background-error covariances (dashed grey) as a function of separation distance for a selection of channels from AIRS on Aqua. The number of collocations as a function of separation distance is shown in the last panel. Separation bins with fewer than 5000 observations are not shown. The spatial binning interval is 12.5 km, and the wavenumbers for the selected channels are given in the title of each plot.

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Figure 3. Estimates of observation errors for AIRS channels used in the ECMWF system. The estimates are based on the measured in-flight instrument error (solid grey, converted to brightness-temperature errors using the US Standard Atmosphere), the observation error assumed in ECMWF's assimilation system (dashed grey), the Hollingsworth/Lönnberg method (dotted black, based on subtracting the FG-departure covariances for the 12.5 km separation bin from the FG-departure variances at zero separation), background-error method (dashed black) and the Desroziers diagnostic (solid black). For some channels, results from the background-error method are not shown due to failure of the method (see text for further details). Also shown are the standard deviations of FG departures (dashed grey). The lower x-axis gives the channel numbers for selected channels (linear in the channel index shown in Figure 1), whereas the upper x-axis shows wavenumbers for the corresponding channels.

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Figure 4. As Figure 3, but for the IASI channels used in the ECMWF system. Estimates for the Hollingsworth/Lönnberg method are based on subtracting the FG-departure covariances for the 50 km separation bin from the FG-departure variances at zero separation.

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Figure 5. Estimates of spatial observation-error correlations for AIRS for selected spatial separation-distance bins for the channels used in the ECMWF system. Black lines give estimates from the Desroziers diagnostic, grey lines from the background-error method. Different line styles separate the selected separation distances as provided in the legend. For some channels, results from the background-error method are not shown due to failure of the method (see text for further details).

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Figure 6. As Figure 5, but for METOP-A IASI channels used in the ECMWF system. Note that, in contrast to AIRS, the first populated separation bin for IASI is 50 km, compared with the 12.5 km bin for AIRS.

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Figure 7. Estimates for interchannel error correlations for the AIRS channels used in the ECMWF system, based on the Hollingsworth/Lönnberg method. The lower x-axis and the y-axis give the channel number (linear in the channel index shown in Figure 1), whereas the upper x-axis indicates corresponding wavenumbers.

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Figure 8. As Figure 7, but for estimates of interchannel observation-error correlations for AIRS, based on the background-error method. Channel combinations for which the method produced poor results appear white.

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Figure 9. As Figure 7, but for estimates of interchannel error correlations for AIRS, based on the Desroziers diagnostic.

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Figure 10. As Figure 7, but for estimates of interchannel error correlations for the METOP-A IASI channels used in the ECMWF system, based on the Hollingsworth/Lönnberg method.

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Figure 11. As Figure 7, but for estimates of interchannel error correlations for IASI, based on the background-error method. Channel combinations for which the method produced poor results appear white.

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Figure 12. As Figure 7, but for estimates of interchannel error correlations for IASI, based on the Desroziers diagnostic.

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The second group of channels that share common characteristics in the observation-error covariance estimates are lower-peaking temperature-sounding channels in the long-wave band with weak sensitivity to the surface (surface transmissions of less than 0.2). What distinguishes this group is that the three methods consistently indicate the presence of some interchannel error correlations between channels within this group (Figures 712). The size of these error correlations varies with channel pair, primarily in the range 0.2– 0.6, with the most surface-sensitive channels giving the highest interchannel error correlations. The Hollingsworth/Lönnberg method and the background-error method show remarkable agreement for the interchannel error correlation estimates, whereas the Desroziers diagnostic tends to yield slightly lower values that are still consistently non-zero. The interchannel error correlations for this group tend to be higher for IASI than for AIRS.

The spatial FG-departure covariances for group two show a clear separation into a spatially uncorrelated and a spatially correlated contribution, with the latter being relatively larger than for the first group (see, for example, Figure 2(d)). The mapped assumed background-error covariances appear generally too large when compared with the spatial FG-departure covariance statistics, and a scaling down to around 0.3 is required for the lowest-peaking channels to make the two consistent. Nevertheless, the Desroziers diagnostic and the background-error method give only weak spatial-error correlations that stay below 0.2 even for the shortest separations and tail off rapidly (Figures 5 and 6). Consequently, the three methods employed here give very similar results for the size of the observation errors, which are close to or slightly above the instrument noise (Figures 3 and 4).

3.2. Long-wave window channels

The third group of channels are long-wave window channels with a surface transmission above 0.2. For these channels, FG-departure variances at zero separation are again dominated by a spatially uncorrelated component, as can be seen from the large difference between the values at zero separation and the first non-zero separation bin (see, for example, Figure 2(e)). The mapped assumed background errors are, however, generally considerably too large compared with the FG-departure covariances for non-zero separations, and the functional shape of the mapped background errors is such that no single scaling factor can be found to make the two curves consistent with each other. This is largely because the skin-temperature background error has been modelled as spatially uncorrelated (0.4 K), whereas true background errors in skin temperature are likely to be spatially correlated. The mapped background errors therefore show too sharp a decrease with separation distance for the shortest separation distances. Given the limitations in modelling the spatial skin-temperature error characteristics, the background-error method is not applied for this group of channels. The Desroziers diagnostic is therefore the only method that provides estimates for spatial observation-error correlations for these channels, and it indicates small spatial correlations in the range of 0.2– 0.4 for the 12.5 km separation bin for AIRS, tailing off to below 0.2 by 50– 75 km for both AIRS and IASI. Nevertheless, many channels in this group show rather small but broad and consistently non-zero correlations of around 0.05– 0.1 beyond 500 km (Figure 5). Estimates of the observation error are around 1.5– 3 times the instrument noise, with reasonable agreement between the values from the Hollingsworth/Lönnberg method and the Desroziers diagnostics (Figures 3 and 4).

The most striking characteristic of the channels in group three is the rather strong interchannel error correlations suggested by Hollingsworth/Lönnberg as well as Desroziers (Figures 7–12). For IASI, practically all channels show error correlations between each other, with values between 0.65 and 0.9. Again the Desroziers diagnostic tends towards smaller values in this range, but the block of correlated errors is very consistent with the estimate from Hollingsworth/Lönnberg. For AIRS, the block of interchannel error correlations is less striking, but the group nevertheless exhibits error correlations between channel pairs within this group of 0.35– 0.95. Channels from this group also show error correlations with channels from the second group to varying degree, typically in the range of 0.2– 0.6.

3.3. Water-vapour channels

The fourth group of channels are the water-vapour channels, with seven AIRS channels and 10 IASI channels. These channels show many of the characteristics already noted for the HIRS or Microwave Humidity Sounder (MHS) water-vapour channels (cf. BB10). The spatial FG-departure covariances exhibit no clear separation of the variances at zero separation into a spatially correlated and a spatially uncorrelated part – the transition is fairly smooth (see, for example, Figure 2(f)– (h)). The spatially uncorrelated part of the observation error is less dominant for the FG-departure variances than was the case for the temperature-sounding channels. This is again partly because instrument errors are much smaller compared with background errors for these channels. For IASI, instrument errors are around 0.2 K, and for AIRS they are even smaller, compared with background errors that are of the order of 1 K for mid- and upper-tropospheric water-vapour channels (Figure 2(g) and (h)). Given the steep slope of the FG-departure covariance with separation distance, spatially uncorrelated observation-error contributions of less than 0.4 K would be extremely difficult to detect with the Hollingsworth/Lönnberg method for these channels. As in the case of MHS, the Desroziers diagnostic as well as the background-error method suggests some spatial observation-error correlations for short separations, with values in excess of 0.6 for the 12.5 km separation bin for AIRS (Figures 5 and 6). They fall off fairly sharply to mostly less than 0.2 at 75 km or further. Representativeness issues are likely to be a contributing factor to these apparent spatial observation-error correlations. Consequently, the estimates for the total observation error for the AIRS or IASI water-vapour channels are considerably above the instrument noise, by a factor of 3– 4 (Figures 3 and 4). As seen for MHS or HIRS, the three methods employed here indicate sizeable interchannel error correlations for some of the water-vapour channels, with many values between 0.6 and 0.9 (Figures 712). While the water-vapour channels selected for AIRS and IASI do not match exactly, the findings are overall very similar for the two instruments for this group.

3.4. Short-wave channels

The fifth group are short-wave window channels that are only used from the AIRS instrument, as the equivalent IASI channels have too-large noise characteristics. These channels show similar characteristics to the long-wave window channels in group three, in particular rather strong interchannel error correlations. The Desroziers diagnostic and the Hollingsworth/Lönnberg method consistently estimate these to be frequently above 0.7 between most pairs of channels in this group, and around 0.25– 0.6 between channels from this group and the long-wave window channels (Figures 7 and 9). The method of scaling the mapped assumed background errors again gives unrealistic results, due to poor modelling of the spatial characteristics of the skin-temperature error. The results of this method are therefore not shown.

Group five shows additional observation-error characteristics to the ones in group two, suggesting a spatially correlated radiative-transfer error. Whereas for the long-wave window channels the mapped assumed background-error covariances at larger separation distances were consistently well above the FG-departure covariances, there are many channels in group five for which they are closer to or even well below the FG-departure covariances (see, for example, Figure 2(i) and (j)). In particular, this is the case for channel 1875 (2190.6 cm−1 ). The channel also stands out in the estimates for spatially correlated error from the Desroziers diagnostic (Figure 5), where it exhibits very strong and very broad observation-error correlations that are still above 0.3 at 1000 km separation. Further investigations reveal that the channel is very close to a CO line, and variations of CO are not taken into account in our radiative-transfer model. As CO is not well-mixed, but rather shows strong hemispheric differences that do not project well on to our bias-correction model, this leads to a large and correlated radiative-transfer error. Most channels in this group have some sensitivity to CO, contributing to larger and broader spatial-error correlations as estimated from the Desroziers diagnostic, with many channels still showing error correlations of around 0.2 at 500 km separation. However, it should also be noted that the Desroziers diagnostic for the background error in radiance space is extremely small for channels in this group, and a skin-temperature error well below 0.1 K would be required to achieve this, which appears unrealistic for the sea-surface temperature (SST) analysis used in the ECMWF system. The Desroziers method will be unable to estimate observation or background errors successfully when the scales represented in both are too similar. The indicated spatial correlations in the observation error make it more similar to the situation expected for background-error correlations, so the results from the Desroziers method should also be taken with caution for this group.

The last group are lower-peaking short-wave temperature-sounding channels, again only used for AIRS. These show largely similar characteristics to the lower-peaking long-wave temperature-sounding channels in group two, with observation errors close to or slightly above the instrument noise (Figure 3) and some interchannel error correlations for the three estimation methods used here (Figures 79). Interestingly, error correlations between channels from this group and channels from group two are relatively small, suggesting a different origin for the error correlations. In contrast to the channels in group two, the channels in group six appear to exhibit broader spatial-error correlations, in excess of 0.2 for the shortest separation bin and tailing off only fairly slowly with separation distance (Figure 5). For channels 1897– 1918, spatial-error correlations reach 0.2 only at around 300 km, whereas for the other channels in this group this threshold is reached typically before 50 km. The spatial-error correlations are similar to the behaviour for the HIRS short-wave channels 14 and 15 located in the same spectral region (around 2210.0 and 2235.0 cm−1, respectively; see figure 13 in BB10) and may be due to spectroscopy errors for this spectral region, residual solar effects not included in the radiative transfer or bias correction or other absorbers not allowed to vary in the radiative-transfer calculations.

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Figure 13. Diagnostics for METOP-A IASI channel 360 (734.75 cm−1 ) over sea. (a) FG-departure covariance statistics [K2] as a function of scan position and scan-line difference. The scan position used is the one provided in the disseminated data, with values from 0– 119. The grey-scale has been adjusted to emphasize values for non-zero differences; the FG-departure variance for zero separation is 0.064 K2 and appears white. (b) Background-error covariance estimates from the Desroziers diagnostic [K2] as a function of scan position and scan-line difference. (c) As (b), but for the observation-error correlations. (d) Number of observation pairs used. Note that only one quadrant of each figure has been calculated; the rest is derived from symmetry considerations. Also, the figures show only entries for which more than 5000 observation pairs were available.

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The estimated observation errors for AIRS and IASI are generally lower than the ones currently used in the ECMWF assimilation system for all groups discussed here (with the exception of channels 151– 162 for AIRS; Figures 3 and 4). This is the case for the surface-sensitive and window channels in particular, for which the assumed observation errors are about five times the estimates found in this study. This reflects a cautious approach for these channels, justified due to the smaller atmospheric temperature signal in these channels in clear-sky cases and also due to the interchannel error correlations, which are currently neglected in the ECMWF assimilation system. The step in the assumed observation error from 1.0 K for the stratospheric channels to 0.4 K for the tropospheric channels could be improved, and the setting of observation errors relative to the instrument noise could be harmonized between AIRS and IASI. For most of the mid- to upper-tropospheric channels (151– 299 for AIRS and 191– 366 for IASI), the assumed observation errors are actually fairly close to the observation-error estimates obtained in this study; they are the closest encountered for any of the instruments investigated here.

3.5. IASI-specific results

In the case of IASI, another aspect evident from the estimates of interchannel error correlations is worth mentioning. The three methods consistently estimate non-zero error correlations for the first off-diagonal element in the interchannel error correlation matrix for many channels (Figures 1012). This is due to the apodization used for IASI, which leads to non-zero error correlations for channels that are up to two channels apart and which are strongest for directly neighbouring channels. The effect of this is clearly visible in the statistics: two triplets of channels that are direct neighbours stand out with error correlations of 0.7– 0.75, whereas channels that are one channel apart show error correlations of around 0.25– 0.35 in the absence of further error correlations for other reasons. Neighbouring channels were originally excluded in the IASI channel selection for NWP (Collard, 2007), but the channels in question were later added for monitoring purposes.

Almost all IASI channels exhibit a peculiar pattern in the FG-departure covariances when analyzed as a function of the difference in scan line and scan position. These covariances show a chessboard pattern of lower and higher FG-departure covariances as seen in Figure 13(a) for channel 360, which shows the effect most clearly. Note that the same IASI FOV position within an AMSU-A FOV is always used at ECMWF. Using the IASI scan position numbering from 0– 119 within an AMSU-A scan line (as provided in the disseminated data), the FOVs currently selected at ECMWF are multiples of four. Possible scan-position differences for our analysis are therefore also multiples of four. The feature also shows up as wiggles in the isotropic analysis of FG-departure covariances at short separation distances, such as the ones in Figure 2 (not shown). The magnitude of the feature is dependent on the channel, but practically all channels show at least a hint of this feature (Figure 14). The Desroziers diagnostic attributes the feature to a pattern of alternating positive and negative observation-error correlations (Figure 13(c)). The chessboard feature has also been observed in FG-departure covariances obtained at the Met Office (Cameron, personal communication).

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Figure 14. Strength of the chessboard pattern in the FG-departure covariances as a function of channel number [K2]. The strength has been calculated as the mean difference between the two populations given by the chessboard pattern of high and low FG-departure covariances (excluding the values at zero separation).

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The pattern is very small compared with the instrument noise (as apparent from rather small estimated observation-error correlations), and it is of no concern to the assimilation of the data. The feature appears to correlate with the direction of the movement of the corner-cube mirror of the IASI interferometer (Fiedler, personal communication). The current understanding is that this is the first evidence of the existence of pseudo-noise (‘ghosts’) caused by micro-vibrations of IASI's beam splitter (Blumstein, personal communication). Such effects are expected for instruments like IASI. The beam splitter is fixed on one side to the optical bench and displays a slight periodic variation in position with respect to the corner-cube motion. This leads to slight variations in the spectral characteristics, which appear as pseudo-noise. Consistent with this explanation, investigations at the Met Office found that the chessboard effect is almost zero for those IASI FOVs that project on to the bottom of the beam-splitter where the effect of the vibrations is smaller, as this is where the beam splitter is attached to the optical bench. That is, selecting the third or fourth IASI FOV within the AMSU-A FOV minimizes the chessboard effect. It is remarkable that the monitoring against the FG can detect such small effects, which so far have not been picked up in careful monitoring of the instrument's engineering data. Our investigations also confirm that the effect is as small as expected.

3.6. Comparison with results from Garand et al.

The estimates for observation errors and interchannel error correlations for AIRS can be compared with those obtained by Garand et al. (2007). A stringent comparison is difficult, due to different channel selections. Nevertheless, our results are consistent with Garand et al. (2007) for most channels of group one, both in terms of the size of observation errors and the lack of significant interchannel error correlations. For lower-peaking temperature-sounding or window channels in the long-wave band (groups two and three), Garand et al. (2007) also find significant interchannel observation-error correlations, but their estimates are larger than in the present study, also with larger observation errors. The situation is similar for the water-vapour channels. The reasons for the differences are unclear, but may be due to differences in the approach to bias correction (variational with air-mass predictors versus static with observed brightness temperatures as predictors) or the cloud detection. Undetected cloud contamination may lead to larger observation errors, which appear correlated between channels in the Garand et al. (2007) study, or too strict FG-departure-based cloud detection may give overly optimistic observation errors in the present study. For the short-wave window channels, our estimates of observation errors are again lower than presented in Garand et al. (2007), but the finding of substantial interchannel error correlations is consistent.

3.7. Findings for assumed background errors

While our main focus is the characterization of observation-error covariances for sounder radiances, our analysis also provides information on the assumed background-error covariances. As already mentioned, the spatial-correlation characteristics of the assumed background errors mapped to radiance space appear, on average, consistent with FG-departure covariances, at least for temperature-sounding channels. However, there were also indications that the magnitude of the background errors occasionally appears overestimated. To address this, the background-error method produces channel-specific scaling factors that have been derived by matching spatial FG-departure covariances with assumed background errors mapped into radiance space. The Desroziers diagnostic provides estimates of background-error covariances mapped into radiance space directly. A channel-specific scaling factor can also be derived, which matches the spatial background-error covariance estimates from the Desroziers diagnostic with the assumed background errors mapped into radiance space.

Figure 15 shows an intercomparison of the scaling factors for the background errors for all temperature-sounding channels of the various instruments used in this study as a function of the peak of the weighting function. There is considerable consistency in broad features of these scaling factors between different channels and instruments. Some scatter is to be expected, as the peak of the weighting function is only a crude measure of the sensitivity of the channel in the vertical. Scaling factors are typically around 0.6– 0.8 for the troposphere, indicating an inflation of the assumed background error in this area. In contrast, for most of the stratosphere scaling factors are around 0.9– 1.0, suggesting little or no inflation of the background errors. Not surprisingly, there is also good consistency between the scaling factors from the background-error method and those obtained with the Desroziers diagnostic. The Desroziers diagnostic tends to produce smaller scaling factors, as the assumption on spatially correlated observation errors is more relaxed for this method, so less of the FG-departure covariances is attributed to background error.

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Figure 15. (a) Scaling factors for the background errors for the temperature-sounding channels used in this study, as derived in the background-error method. The scaling factors are plotted as a function of the peak of the temperature Jacobian for the various channels. Different symbols indicate the four temperature-sounding instruments considered in this study (including from BB10), as given in the figure legend. Note that the scaling factors in the background method are restricted to values less than or equal to one. (b) As (a), but for scaling factors for the background errors as derived from the Desroziers diagnostic.

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The agreement for humidity-scaling factors is less good between different instruments, even though the background-error method and the Desroziers-derived scaling factors again agree fairly well. Scaling factors range from around 0.8 for the AIRS water-vapour channels to 1.1– 1.2 and 1.2– 1.6 from the Desroziers diagnostic for the HIRS water-vapour channels and MHS, respectively.

4. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and methods
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References

In the present study we have estimated observation errors and their spatial and interchannel error correlations for clear-sky radiances from AIRS and IASI. The main findings are as follows.

  • Mid-tropospheric to stratospheric temperature-sounding channels from both instruments show little or no interchannel or spatial observation-error correlations, and estimates for the observation error are close to the instrument noise.

  • The finding that observation errors for these channels are comparable to the instrument noise suggests that the radiative-transfer error is small after bias correction.

  • Channels with stronger sensitivity to the surface or clouds show larger observation errors compared with the instrument noise, and some of this error is correlated spatially and between channels. Residual cloud contamination is likely to be a contributing factor to this. Window channels can exhibit very high interchannel error correlations of more than 0.7.

  • Short-wave infrared temperature-sounding channels from AIRS appear more prone to spatial observation-error correlations, probably a result of larger errors in the spectroscopy (e.g. due to more line-mixing effects), residual solar effects or other contaminating gases (CO).

  • As in the case of MHS or HIRS, estimating observation errors for the AIRS and IASI humidity-sounding channels from FG or analysis departures is more difficult, primarily due to the combination of smaller-scale and larger errors in the FG for humidity. A considerable proportion of the observation error for humidity-sounding channels appears correlated spatially for short separation distances, as well as between channels. Representativeness appears to be an important contributor in this respect. Observation-error estimates for humidity channels are generally considerably larger than those provided by the instrument noise.

  • Our statistics suggest that assumed background errors for tropospheric temperature are inflated (by about 30– 60%), whereas there is little indication for background-error inflation for stratospheric temperatures.

Application of the three methods gives some indication about the reliability of the presented estimates, and the findings for AIRS and IASI are consistent with those obtained for the ATOVS instruments. For most temperature-sounding channels the methods show good agreement, as FG errors in radiance space are relatively small and broad. This allows a good distinction between observation and background errors from FG-departure covariances. Estimates for spatial observation-error correlation from the Desroziers diagnostic and the background-error method are very small for these channels, explaining why the Hollingsworth/Lönnberg method gives similar results, even though it neglects such observation-error correlations. As for the ATOVS instruments, the humidity-sounding channels show the worst agreement between the three methods. FG-error correlations are sharper and larger than for temperature-sounding channels, making observation-error contributions less identifiable for any FG-departure-based method.

The results for AIRS and IASI are qualitatively similar for similar channels. A comparison between the two instruments is not entirely straightforward due to the differences in the spectral resolution and channel selection. Nevertheless, similar channels show non-zero interchannel and spatial-error correlations, and estimates for the observation error relative to the instrument noise are also consistent. However, our results also indicate larger interchannel error correlations for surface-sensitive temperature-sounding or window channels for IASI. This is partly explained by lower observation-error estimates for IASI in this spectral region; the difference in terms of interchannel error covariances is smaller than that in terms of interchannel error correlations (not shown). The remaining differences are likely to be related to the specific use of the data in the assimilation system, rather than the instrument itself. For instance, the cloud detection scheme will behave differently for the two instruments due to the different spectral resolution and the larger number of channels available for IASI. Also, the higher spectral resolution of IASI may make the radiative transfer more prone to errors in the spectroscopy.

While our findings for observation errors and their interchannel correlations for AIRS agree qualitatively well with Garand et al. (2007), there are significant differences in the observation-error covariance estimates, with Garand et al. (2007) suggesting larger errors and correlations for some channels. This highlights that the estimates are specific to the use of the radiance data in a given data-assimilation system, and differences in bias correction or quality control will lead to different observation-error covariance estimates for different assimilation systems.

Our anisotropic analysis for IASI showed signatures of ‘ghost’ features, arising from micro-vibrations of the beam-splitter. The highlighted effect appears to be small as expected, but at the same time it is very clear and robust in the statistics presented here. Analyses like these highlight the power of NWP-based instrument monitoring for the characterization of instrument performance.

The findings for the ATOVS instruments as well as the statistics for AIRS and IASI suggest that the spatially correlated error for temperature-sounding channels is small after bias correction. This partly reflects the maturity of the radiative-transfer model, the instrument characterization (e.g. spectral response functions) and the bias correction; a poorer radiative-transfer model, less accurate instrument characterization or a cruder bias correction are expected to lead to different results. The role of the bias correction in removing radiative transfer or instrument-characterization error should be investigated further, in particular as the ability of the bias correction to correct such errors will depend on the chosen bias model. The framework used in this study may provide a means to investigate the adequacy of different bias-correction models.

In this context we found that using a variational bias correction rather than a static one does not significantly change our results regarding the diagnosed observation errors. To investigate this, we produced the same statistics from an experiment that used the same parametric models for bias correction, but in which the coefficients of the bias models were kept static throughout the experiment, instead of the continuous re-estimation otherwise performed by variational bias correction. The results were very similar (not shown), in agreement with the experience that the bias coefficients usually evolve fairly slowly with time. This suggests that the current findings also apply to static bias corrections, provided the bias-correction coefficients are kept adequately up to date by other means.

The current study makes extensive use of the Desroziers diagnostic (Desroziers et al.2005), including the estimation of interchannel and spatial observation-error correlations. It should be noted that the limitations and properties of this method are still an area of active research (Desroziers et al., 2009). For observations with no spatial-error correlations, there is considerable evidence that the method provides reasonable estimates, in agreement with other methods (Chapnik, 2009). For the majority of channels, the Desroziers diagnostic and the background-error method suggest that spatial observation-error correlations are indeed small with small length-scales, so we have good confidence in the results. For channels where the two methods suggest some spatial-error correlations (e.g. water-vapour channels or short-wave infrared temperature-sounding channels) we found that the results still appear reasonable, at least qualitatively. For instance, the method identifies strong spatial observation-error correlations in the case of an AIRS CO channel (1875) as a result of treating CO as fixed in the observation operator, it suggests small-scale error correlations for water-vapour channels for unrepresented scales and it attributes the chessboard pattern in many IASI FG-departure covariances to observation-error correlations. While these findings appear reasonable, at least qualitatively, more work is required to investigate how reliable the estimates are quantitatively when observation errors have spatial-error correlations that are more similar to those for background errors.

The current observation-error covariance estimates will be used to provide guidance for the specification of observation-error covariances and thinning scales used in the ECMWF assimilation system. It is not expected that the estimates given here can be used directly, as other aspects may need to be taken into account, such as uncorrected residual biases (of observations and the forecast model), the performance of quality control (e.g. cloud screening for FOVs that are not totally clear) or limitations in the assumed background-error covariances. Also, the current statistics have been derived as global means; local effects may require further refinements of observation errors. Nevertheless, the present study points to a too-conservative use of some instruments (e.g. AMSU-A) in terms of observation errors and thinning scales, even with diagonal observation errors. For AIRS and IASI, the choice of observation error could be harmonized and artificial steps in the assumed observation error removed. However, the situation for these instruments is otherwise more complex due to the diversity of observation-error characteristics for different channels. While spatial observation-error correlations appear mostly small (except for the AIRS short-wave channels), the presence of interchannel error correlations for some channels may require one to take such error correlations explicitly into account. Experiments are currently under way at ECMWF to use interchannel error correlations in 4DVAR, and we will report on these in the future. For most mid- and upper-tropospheric temperature-sounding channels, the currently assigned observation errors are fairly close to the instrument noise and the observation errors estimated here.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and methods
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References

Mike Fisher, Marco Matricardi, and Tony McNally provided assistance and feedback on various aspects of the study. Discussions with James Cameron and Fiona Hilton (Met Office), Lars Fiedler (EUMETSAT) and Denis Blumstein (CNES) on the IASI chessboard feature are also gratefully acknowledged. Comments from one anonymous reviewer also helped to improve the manuscript.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data and methods
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
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