We report the first continuous measurements of chlorine nitrate (ClONO2) in high-latitude regions taken by the Improved Limb Atmospheric Spectrometer (ILAS) on board the Advanced Earth Observing Satellite (ADEOS) and processed using the latest data retrieval algorithm (version 6.1). Performance of the measurements, validation with three balloon-borne sensors, and seasonal variation of ClONO2 in the Arctic and Antarctic stratosphere are presented, as well as a brief description of the version 6.1 algorithm and data characteristics for both the Arctic and Antarctic. Although the ILAS-measured ClONO2 data show, on average, ∼30% lower values than the validation data, they agree with validation data within the combined total error (∼20–40%) of the ClONO2 measurements at ∼15- to 32-km altitudes. In the Arctic, enhancement of ClONO2 amounts was observed in spring 1997 after the appearance of polar stratospheric clouds (PSCs) inside the polar vortex. This is the result of preference for ClONO2 formation rather than HCl after the activation of ClOx in this Arctic spring of 1997. In the Antarctic, ClONO2 amounts showed strong local time/latitudinal dependence around the austral fall equinox in 1997.
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 Chlorine nitrate (ClONO2) plays an important role in stratospheric ozone-related chemistry. It acts as a reservoir of active chlorine species (ClOx) such as Cl or ClO, which destroy ozone catalytically. In the cold polar winter, ClONO2 is converted to more active forms through the following heterogeneous reactions on the surface of polar stratospheric clouds [e.g., Solomon, 1999]:
At the same time, another important chlorine reservoir, hydrogen chloride (HCl), is also converted to more active forms. As a result, a large amount of reactive chlorine (Cl) or ClOx exists when Cl2 is photolyzed to yield Cl or ClOx if sunlight is available in the polar winter stratosphere. These radicals effectively destroy ozone, resulting in ozone depletion. When there are enough nitrogen oxides (NOx = NO + NO2) in the atmosphere, which is usually the case in Arctic spring, chlorine radicals are converted to ClONO2 through the following reaction:
Consequently, a large fraction of the total chlorine species (Cly = Cl + Cl2 + ClO + Cl2O2 + HCl + ClONO2 + HOCl) exists in the form of ClONO2 in the late springtime polar stratosphere [Michelsen et al., 1999]. Conversion of active chlorine into ClONO2 was measured by Oelhaf et al.  in the Arctic vortex.
 However, when denitrification leads to insufficient nitrogen oxides, as is usually the case in the Antarctic polar spring, chlorine radicals are more likely to be converted into HCl:
Conversion of active chlorine into HCl was measured by CLAES [Douglass et al., 1995] and HALOE [Grooss et al., 1997] in the Antarctic. The partitioning of Cly species gradually recovers to normal partitioning ratios in late spring, when polar vortex breakup leads to mixed midlatitude air and photochemical equilibrium of Cly species resumes [Michelsen et al., 1999]. Therefore measurements of ClONO2 can supply indispensable information for understanding polar stratospheric processes including ozone destruction. Santee et al.  analyzed the conversion of active chlorine species into ClONO2 or HCl for both hemispheric polar regions using data from the Microwave Limb Sounder (MLS), Cryogenic Limb Array Etalon Spectrometer (CLAES), and Halogen Occultation Experiment (HALOE) on board the Upper Atmospheric Research Satellite (UARS). Douglass and Kawa  compared partitioning of Arctic Cly species in 1992 and 1997 using HCl data from HALOE and ClONO2 data from CLAES, both on board the UARS, and discussed differences in Cly partitioning between these two years by comparison to three-dimensional model outputs. Information on diurnal variation of ClONO2 was obtained from space shuttle observations by the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) [Riese et al., 2000].
 So far, there have been few continuous ClONO2 measurements from satellite-borne sensors. The CLAES sensor measured ClONO2 from October 1991 to May 1993 [Roche et al., 1993a, 1993b; Mergenthaler et al., 1996]. However, measurements of CLAES over both hemispheres were only possible at approximately monthly intervals because of the attitude change (yaw maneuver) of the satellite.
 The Improved Limb Atmospheric Spectrometer (ILAS) is a solar occultation satellite sensor developed by the Ministry of the Environment (MOE) of Japan to monitor the stratospheric ozone layer [Sasano et al., 1999; Sasano, 2002]. ILAS was the first space-borne instrument that measured ClONO2 continuously in high-latitude regions. ILAS was on board the Advanced Earth Observing Satellite (ADEOS), which was launched on 17 August 1996. The characteristics of the ILAS instrument are described by Nakajima et al. . Because of the measurement principle and the orbit of the satellite, the latitudinal coverage of ILAS measurements was from 56 to 70° in the Northern Hemisphere and 63–88° in the Southern Hemisphere. The latitudinal coverage was affected by seasonal changes in the configuration between the orbital plane of ADEOS and the rotation axis of the Earth [Sasano et al., 1999]. After the initial checkout of ADEOS, ILAS started normal operation on 30 October 1996. For 8 months, ILAS functioned successfully and gathered data with approximately 6700 occultation measurements before ADEOS stopped working on 30 June 1997. Vertical profiles of atmospheric minor species, such as ozone (O3), nitric acid (HNO3), nitrogen dioxide (NO2), nitrous oxide (N2O), methane (CH4), and water vapor (H2O), in addition to aerosol extinction coefficients (AEC) at 780 nm were retrieved with the version 5.2 retrieval algorithm [Yokota et al., 2002]. ClONO2 and N2O5 are added as new data products of ILAS with the version 6.1 retrieval algorithm.
 After the continuous measurement of ClONO2 from ILAS, there have been several satellite-borne sensors that measured ClONO2 from space. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on board the Envisat satellite has also been measuring stratospheric ClONO2 and other minor constituents with vertical resolutions of 3 to 7 km (depending on altitude) since September 2002 using the limb emission technique [Fischer and Oelhaf, 1996; Höpfner et al., 2004]. Furthermore, the Atmospheric Chemistry Experiment–Fourier transform spectrometer (ACE–FTS) solar occultation sensor on board the Canadian satellite SCISAT-1 has successfully measured ClONO2 [Bernath et al., 2005; Mahieu et al., 2005].
 This paper introduces a new ClONO2 data product measured by the ILAS and processed with the latest data retrieval algorithm, version 6.1. The retrieval procedure, data quality, and overall data characteristics of the ILAS ClONO2 product are described.
2. ILAS Version 6.1 Retrieval Algorithm
 ILAS measured atmospheric trace molecules using an infrared grating spectrometer, which covered 6.21–11.77 μm (1610–850 cm−1) with a 44-element pyroelectric detector (spectral resolution of 0.13 μm) [Nakajima et al., 2002]. The gas retrieval procedure with the version 5.2 algorithm is described in detail by Yokota et al. . In this version, the standard gas products were O3, HNO3, NO2, N2O, CH4, and H2O. In addition, three gases, CFC-11 (CCl3F), CFC-12 (CCl2F2), and carbonyl fluoride (COF2), were simultaneously retrieved as research products. The AECs at 780 nm and at four infrared spectral elements were also produced as standard and research products, respectively. The quality of version 5.2 ILAS data was validated by Sugita et al.  for O3, Irie et al.  for HNO3 and NO2, Kanzawa et al.  for H2O, Kanzawa et al.  for CH4 and N2O, and Saitoh et al.  for the AEC at 780 nm, respectively. Also, the quality of CFC-12 by the more recent data processing algorithm version 6.0 was validated by Khosrawi et al. .
 In the latest 6.0 and 6.1 version algorithms, ClONO2 and N2O5 were newly assigned as retrieval targets; COF2 was excluded as a retrieval target. The only difference between versions 6.0 and 6.1 is in the error bars. The systematic biases that were included in the internal error calculations for version 6.0 or version 5.2 were removed for calculating the version 6.1 internal errors [Yokota et al., 2002; Sugita et al., 2005]. Appendix A provides details of the method used to remove the systematic biases. The derivation of ClONO2 and N2O5 became possible after refining the calculation procedure of ClONO2 and N2O5 absorption coefficients in the forward model of the retrieval procedure. The refined calculation procedure uses the pseudoline data set provided by G. C. Toon (unpublished data, 2000) based on laboratory measurements by [Wagner and Birk, 2003], which were used for the MkIV [e.g., Toon et al., 2002] and Atmospheric Trace Molecule Spectroscopy (ATMOS) retrievals [Irion et al., 2002]. The retrieval of ClONO2 by the version 6.1 algorithm uses the ν2 absorption band of ClONO2 centered at 7.73 μm (1293 cm−1). In addition, the version 6.1 algorithm includes several updates of molecular spectroscopic data from the High-resolution Transmission Molecular Absorption (HITRAN) 2000 database [Rothman et al., 2003], including spectroscopic data from the oxygen A band for altitude registration [Sugita et al., 2005]. Temperature and pressure profiles in the upper stratosphere were created from United Kingdom Meteorological Office (UKMO) data [Swinbank and O'Neill, 1994] below 40–45 km and mean profiles from the version 19 HALOE, version 5 Microwave Limb Sounder (MLS), or Global Positioning System/Meteorology Project (GPS/MET) data for altitudes between 50 and 60 km; these data were then connected to Cospar International Reference Atmosphere-86 (CIRA-86) profiles for higher altitudes to use in the forward model calculation.
 Data quality assessment of the version 6.1 standard products showed that changes in the products from version 5.2 to version 6.1 depended on species and altitudes. Overall, version 6.1 products showed better or equal agreement with the validation data (HALOE, Stratospheric Aerosol and Gas Experiment [SAGE] II, or balloon-borne data) than version 5.2 products. Details of the version 6.1 algorithm and the validation results for the standard products (O3, HNO3, NO2, N2O, CH4, H2O, and the aerosol extinction coefficient at 780 nm) can be found elsewhere [Sugita et al., 2005] and also in the README file for ILAS version 6.1, which will be open to public access at http://www-ilas.nies.go.jp/.
3. ILAS ClONO2 Error Analysis
 First, we show the precision of the ClONO2 measurements in terms of measurement repeatability and the supplied official internal and total errors. According to the International Bureau of Weights and Measures [International Organization for Standardization, 1993, p. 33], the repeatability of measurement results is defined as the “closeness of the agreement between the results of successive measurements of the same measure, which means a particular quantity subject to measurement, carried out under the same conditions of measurement.” Hence the repeatability of ILAS measurements was approximated empirically using the following procedure.
 Repeatability was evaluated from the relative standard deviation, computed from one sigma standard deviation (around the mean) divided by the mean value, over the possible geophysically quiescent period chosen. We calculated the ClONO2 repeatability for each of 100 consecutive occultation measurements for the entire ILAS measurement period for both the Northern and Southern hemispheres. Figure 1 shows the lowest relative standard deviation (repeatability) profiles of the ILAS version 6.1 ClONO2 measurement for the Northern Hemisphere (Figure 1a) and the Southern Hemisphere (Figure 1b). For comparison, the official internal error and total error (root-sum-square of internal and external errors) in the retrieval of ILAS ClONO2 is also shown [Yokota et al., 2002]. Internal errors in the ILAS version 6.1 algorithm were calculated by subtracting the systematic residuals from the measured spectra, which may have arisen from imperfect instrument function of each element in the infrared spectrometer [Nakajima et al., 2002]. As noted above, Appendix A details the removal of the systematic biases. As a result, internal errors in version 6.1 products became much smaller than those in version 6.0 for most species. However, results showed that the measurement repeatability still had smaller values than the official total error for the entire altitude range, especially in the Southern Hemisphere, indicating that the total error evaluated from the present retrieval algorithm was still overestimated and was larger than the actual random error. Note that the error we discuss in this paper is ∼20–40% between the altitudes of ∼15 and 35 km.
 Derived gas products using the ILAS data retrieval algorithm are also considered to have possible bias errors when large numbers of aerosols and/or polar stratospheric clouds (PSCs) are present [Yokota et al., 2002]. This phenomenon is called the “nongaseous contribution correction” and occurs by the simple linear interpolation among the four window spectral elements, in which absorption by gases is small [Yokota et al., 2002]. Figure 2 shows the bias error caused by nongaseous contribution correction for the ILAS version 6.1 ClONO2 product calculated using the method described by Yokota et al. . Bias errors were calculated using the refractive indices of various aerosols and PSCs as inputs for Mie-scattering calculation of nongaseous contribution, and are expressed in gas number density (cm−3) as a function of the extinction coefficient at 780 nm. Curves S(75) and S(50) represent the calculated bias errors by sulfuric acid aerosols (H2SO4/H2O binary solutions) with sulfuric acid weight percentages of 75% at 230 K and 50% at 200 K, respectively [Biermann et al., 2000]. Similarly, calculated bias errors for supercooled ternary solution (STS) with four combinations of weight percentages, STS(a): 5 wt% H2SO4/37wt% HNO3/H2O; STS(b): 33 wt% H2SO4/15wt% HNO3/H2O; STS(c): 47 wt% H2SO4/3 wt% HNO3/H2O; STS(d): 60 wt% H2SO4/0.5 wt% HNO3/H2O [see Yokota et al., 2002, Table 3], are shown by four lines: STS(a), STS(b), STS(c), and STS(d). These lines correspond to temperatures of 188, 192, 194, and 200 K, respectively, under the assumption of 10 ppbv nitric acid and 5 ppmv water vapor [Carslaw et al., 1995]. Bias errors by nitric acid trihydrate (NAT) and water ice (ICE) were also calculated using the refractive indices of Richwine et al.  and Clapp et al. , respectively. The assumed mode radii of H2SO4/H2O, STS, NAT, and ICE were 0.075, 0.5, 0.5, and 10 μm, respectively.
 When calculating bias errors for PSC conditions, the extinction profiles were assumed to consist of background aerosols and PSCs. For the background aerosols, the extinction coefficients at 780 nm for sulfuric acid aerosols were assumed to be 1 × 10−7 km−1 at 40 km and 1 × 10−4 km−1 at 10 km, and linearly interpolated between these values on a logarithmic scale. A PSC layer with a Gaussian shape, a peak at 15 km, and a width of 3 km was added to this background aerosol layer. The extinction coefficient at the peak was such that the total extinction coefficient was 0.5, 1.0, or 2.0 × 10−3 km−1, generating three different conditions. Other PSC layers with peaks at 20 and 25 km were also simulated with total extinction coefficients of 0.5, 1.0, and 2.0 × 10−3 km−1. In total, nine cases were simulated with gas profiles corresponding to February and June in the Northern Hemisphere. The differences in ClONO2 number density between profiles derived in this manner and those initially assumed (i.e., regarded as true) as a function of the extinction coefficient at 780 nm are shown in Figure 2. Lines in Figure 2 show a linear least squares fit of individual points on a logarithmic scale.
 The scales of the volume mixing ratios (ppmv) for altitudes of 15, 20, and 25 km are also shown on the right side of Figure 2. Figure 2 indicates that the effects of nongaseous contribution correction due to aerosols and/or PSCs are comparatively smaller in ILAS ClONO2 data products than in other gas products. Nevertheless, there might be relatively large (>0.5 ppbv at 25 km) negative ILAS ClONO2 biases in the presence of dense (>1.0 × 10−3) STS- or NAT-type PSCs.
4. Comparison to Balloon Measurements
 During the operational period of ILAS, three coordinated balloon flights were made that included ClONO2 measurements. These three measurements were made by the Michelson Interferometer for Passive Atmospheric Sounding-Balloon-borne version 2 (MIPAS-B2) [Wetzel et al., 2002; Friedl-Vallon et al., 2004], Far–Infrared Spectrometer-2 (FIRS-2) [Johnson et al., 1995], and Jet Propulsion Laboratory (JPL) MkIV solar occultation FTS [Toon, 1991]. The MIPAS-B2 and MkIV used the ν4 ClONO2 absorption band centered at 12.8 μm (780 cm−1), while FIRS-2 used the ν4 and ν5 bands centered at 17.8 μm (563 cm−1) [Johnson et al., 1996]. All these methods used the ClONO2 absorption coefficients by Wagner and Birk  for data retrievals. Table 1 summarizes these correlative balloon-borne measurements.
Table 1. List of Correlative Balloon-Borne Experiments
Location at 20 km
Time Difference, hours
24 March 1997
30 April 1997
8 May 1997
 Because ClONO2 has a diurnal variation, a photochemical box model was used to correct balloon-measured ClONO2 values to ILAS measurement local times (local sunset). The three-dimensional Karlsruhe Simulation Model of the Middle Atmosphere (KASIMA) [Ruhnke et al., 1999] was used to convert the nighttime ClONO2 values to those of local sunset at the ILAS measurement point by multiplying the MIPAS ClONO2 values with the ratio of the model ClONO2 values for the time and location of the ILAS and MIPAS-B2 measurements. Another photochemical model [Osterman et al., 1999, and references therein] was used to convert ClONO2 values at the MkIV measurement location and time to those of the ILAS. The model was constrained by temperature, pressure, O3, H2O, CH4, CO, NOy, and Cly inferred from MkIV measurements. For both of these model corrections, the magnitudes of correction were within 0.2 ppbv (∼15% at ∼25 km) between 10 and 27 km (MIPAS-B2) or between 8 and 38 km (MkIV). Although no model correction was applied to FIRS-2 data, diurnal variation of ClONO2 during daytime below 30 km is considered to be small [Brasseur and Solomon, 2005].
Figures 3a, 3b, and 3c present comparisons of the results of these balloon-borne measurements and the nearest ILAS ClONO2 profile for MIPAS-B2, FIRS-2, and MkIV, respectively. Differences in ClONO2 mixing ratios at each altitude are defined as (ILAS − balloon)/balloon × 100 (%). In all cases, ILAS ClONO2 values are systematically lower by ∼30% between altitudes of 15 and 32 km, as seen in Figure 3. Figure 3d shows the averages of the ClONO2 differences calculated for the three comparisons. This type of error is referred to as the accuracy of the measurements. The cause of this negative systematic (∼30%) bias in version 6.1 ILAS ClONO2 data can be explained by the effect of the nongaseous contribution correction [Oshchepkov et al., 2005].
 In summary, the systematic and random errors for the ILAS ClONO2 data are ∼−30% and ∼20–40%, respectively, for altitudes of 15 to 32 km.
5. ClONO2 Data Characteristics
 Within these levels of uncertainty in the ILAS ClONO2 measurements, it is worthwhile to examine seasonal variations in the data. Figures 4 and 5 show ClONO2 profiles for the Arctic and Antarctic stratosphere, respectively, for the period between November 1996 and June 1997. The ClONO2 profiles were sorted for those inside and outside the polar vortex as defined by the method of Nash et al.  using the UKMO stratospheric analysis data. When the polar vortex was nonexistent, data were sorted as “outside the polar vortex.” The ClONO2 mixing ratio is shown in color, while the black dots in Figures 4d and 5d indicate the appearance of PSCs defined by the version 5.2 ILAS aerosol extinction coefficient at 780 nm [Saitoh et al., 2002]. Note that there could be a ∼30% negative offset of the ClONO2 mixing ratio at altitudes between 15 and 32 km, as previously shown. The ILAS measurement latitudes are shown in Figures 4a and 5a, while the local time at measurement locations is shown in Figures 4b and 5b.
Figures 4e and 5e show the Arctic and Antarctic minimum temperatures taken from the UKMO assimilation data. Temperatures above 205 and 200 K are shown in black for the Arctic and Antarctic, respectively. The area surrounded by white dots in Figures 4e and 5e represents temperatures below the NAT saturation temperature (<∼196 K) calculated by assuming averaged ILAS version 6.1 HNO3 and H2O profiles inside the polar vortex for the period 1–10 February 1997 for the Arctic and 21–31 May 1997 for the Antarctic [Hanson and Mauersberger, 1988]. The black broken curves in Figures 4d and 4e show the vortex-averaged diabatic descent of air in the Arctic [Knudsen et al., 1998].
5.1. Northern Hemisphere Characteristics
 The ClONO2 measurement characteristics in the Arctic are shown in Figure 4. In the Arctic winter of 1996/1997, PSCs frequently occurred inside the polar vortex from January to March 1997 on days 5, 12–23, 25, 39–45, 47–48, 52–58, 62, and 65–70, as seen in Figure 4d. The occurrence of these PSCs exactly coincides with the period when Arctic minimum temperatures were well below NAT saturation temperatures [Hayashida et al., 2000]. Also, the altitude for the PSCs descended following the diabatic descent of the air mass in the polar vortex, as shown in Figures 4d and 4e. After the occurrence of PSCs in February, substantially increased ClONO2 was observed inside the Arctic polar vortex, but not outside the polar vortex, as seen in Figures 4d and 4c. The increase of ClONO2 inside the polar vortex can be explained by the occurrence of reaction (4) rather than reaction (5) in the Arctic winter, as suggested by Michelsen et al. .
 The region of ClONO2 increase descended following a diabatic descent curve, as shown in Figure 4d. At the end of March (day number ∼90), the enhancement of ClONO2 gradually diminished at higher altitudes when there was again sufficient sunlight to photochemically destroy excess ClONO2. The Arctic polar vortex persisted until April 1997, when it started to collapse from higher altitudes; this occurred later than in normal years [Coy et al., 1997; Manney et al., 1997]. After the collapse, ClONO2 values remained almost constant, although the peak altitude gradually ascended as illustrated in Figure 4c because of the change in photochemical conditions.
5.2. Southern Hemisphere Characteristics
 ClONO2 measurement characteristics for the Antarctic are shown in Figure 5. Since measurements by ILAS started in austral late spring (November) and ended in early winter (June), observations of the Antarctic polar vortex period were limited. However, there were some measurements within the polar vortex in early November 1996 and from late May to June 1997, as shown in Figure 5d. The characteristics of ClONO2 variation outside the polar vortex shown in Figure 5c are as follows. First, the peak altitude of the ClONO2 mixing ratio was located at around 25 km and showed gradual descent from spring (November) to summer (January). This contrasts with the increase in peak altitude in the case of Arctic spring (April) to summer (June). Also, the peak mixing ratio of ClONO2 showed a decrease from spring to fall (March). Rapid decrease of ClONO2 was observed just before the fall equinox (around day number 70–80), when the occultation measurement latitude was highest (most poleward). This can be explained by the ClONO2 being mostly photolyzed and thus unable to exist in the totally sunlit summer stratosphere:
After the fall equinox, the ILAS measurement local time rapidly changed from evening (2100–2200 LT) to morning (1000–1100 LT). Also, sunlight disappeared at higher latitudes from fall to winter. This explains the rapid increase in ClONO2 mixing ratios after the fall equinox, as shown in Figure 5c. A small decrease in ClONO2 mixing ratios was observed at 23 to 26 km on ∼85 and 100 total days. This may have been due to the intrusion of ClONO2-poor air from lower latitudes, as suggested by backward trajectory analysis (data not shown).
 A rapid decrease in ClONO2 mixing ratios was observed at altitudes ∼20 km inside the polar vortex in June (days 150–180), as shown in Figure 5d. This can be explained by the occurrence of heterogeneous reactions (1) and (2) on the surface of PSCs. Also, ClONO2 mixing ratios showed very low values below 20 km in November (days −60 to −40) inside the polar vortex. Denitrification inside the Antarctic polar vortex during the previous winter may explain this pattern.
 This report is the first to provide continuous measurements of chlorine nitrate (ClONO2) at high-latitude regions made by the Improved Limb Atmospheric Spectrometer (ILAS) on board the Advanced Earth Observing Satellite (ADEOS) and processed with the latest data retrieval algorithm, version 6.1. The performance of the measurements, validation using three balloon-borne sensors, and the seasonal variation of ClONO2 in both the Arctic and Antarctic stratosphere are presented. Although the ILAS-measured ClONO2 data show, on average, ∼30% lower values than the validation data, they agree with validation data within the combined total error (∼20–40%) of the ClONO2 measurements at altitudes of ∼15 to 35 km. Seasonal variations in ClONO2 in the Arctic show enhanced amounts of ClONO2 after the occurrence of PSCs in the polar vortex in boreal early spring 1997. This suggests that during this Arctic winter, activated chlorine species were converted into ClONO2 rather than HCl. Seasonal changes in ClONO2 in the Antarctic late spring to early winter were observed continuously for the first time with high (∼2 km) vertical resolution by the ILAS. Variations in ClONO2 at Antarctic high latitudes were shown to be highly dependent on measurement latitude, local time, and season. ILAS ClONO2 data can be used to further improve our understanding of the partitioning of NOy and Cly species in the polar stratosphere.
Appendix A:: Updated Error Evaluations for the Version 6.1
 It has been noted that the internal errors released for the versions 5.2 and 6 ILAS data products may involve systematic errors inherent in the calculated and/or measured spectra. Basically, internal errors have been estimated on the basis of the assumption that spectral residuals are due to random errors and that the spectral residuals are evenly provided for respective gas species. Recently, however, an in-depth study of spectral residuals has revealed that systematic spectral residuals of nonnegligible magnitude exist in common in the respective measurement events obtained by the ILAS. In principle, this type of systematic deviation of spectra represents the biases of retrieved gas concentrations and so should not be considered internal errors (random errors). As a result, the internal errors estimated for version 6 (as well as for version 5.2) have caused dramatically large relative errors, particularly for minor gas species.
 With this in mind, the error calculation method has been updated as the version 6.1 data product. For the ILAS version 6 product, the systematic structure has been recognized in the residual spectra:
If a residual sum of squares including systematic residuals (part of the diagonal of the matrix, i.e., diag( ), on the right side of equation (A1)) were used in computing internal errors, the errors would be overestimated. (Because diag( ) is a scalar quantity, i.e., a constant value, the retrieval error for each gas increases at the same rate.)
 An improved method is as follows. Systematic residuals are assumed to originate from unknown external error factors. Consequently, in calculating internal errors, components of estimated systematic residuals are subtracted from the squared sum of spectral residuals. However, the components of the estimated systematic residuals are added to the term in the external errors.
 In order to separate systematic residuals from internal error bars, the following procedure was taken. As the first approximation of the systematic residuals, averaged values for each of the Northern and Southern hemispheres, and for each tangent height, ave(Δτs(h)), ave(Δτr(h)), are calculated from the residuals after retrieving data for the entire period. The internal errors excluding the systematic residuals are calculated from the following equation (A2):
Then the estimated value, caused by the systematic residuals, would be newly added to the external errors resulting from the climatological data, as follows:
Here, ext.original represents the errors resulting from the climatological data used in the nongaseous correction; these errors are the same as the conventional external errors of version 6. Furthermore, ext.unknown indicates the errors resulting from unknown external factors caused by estimated systematic residuals of the spectra; these errors are calculated by equation (A4) as follows:
where J′ is the mean Jacobian value for each hemisphere (Northern and Southern) and for each tangent height.
 Note that the evaluation equation for ext.unknown should only be used when the observed value for each detector element originally has a random error of almost the same order as ave(Δτ*(h)).
 Systematic residuals of spectra, which are caused by the unknown factors, are the rest of the fitted spectra that cannot be explained by the bias of the gas retrieved value from the true value (the so-called bias error of the gas retrieved values).
 The component of the systematic spectral residuals explained by the gas retrieval bias is actually unknown; however, here we assumed that the primary approximation may be almost the same as the estimated systematic residuals of the spectra. Hence we newly added this value to the external error.
 We thank the Japan Aerospace Exploration Agency (JAXA) for their cooperation with the ILAS project and their successful launch and operation of the ADEOS satellite. We are grateful for helpful comments and advice from S. Hayashida of Nara Women's University. The contents of this paper were much improved by the useful comments of three anonymous reviewers. The authors also acknowledge M. Kaji and Y. Itou of Fujitsu FIP Co. for developing the ILAS data retrieval algorithms. ILAS data were processed at the ILAS Data Handling Facility (ILAS-DHF) of the National Institute for Environmental Studies, Japan. A part of this work was performed at the Jet Propulsion Laboratory under contract with NASA. Another part of this work was supported by the Global Environment Research Fund provided by the Ministry of the Environment of Japan (MOE). The ILAS project was also funded by the MOE.