Infrared hyperspectral data are obtained from the IASI instrument on board the polar orbiting satellite Metop-A. IASI is measuring within the whole spectral range from 645 to 2760 cm-1 with a spectral sampling of 0.25 cm-1, an apodized effective resolution of 0.25 cm-1 and with a spatial resolution of about 12 km at nadir. One single IASI field of view is analyzed in this study over the Sodankylä observatory, northern Finland (location: 67.368∘ N, 26.633∘ E, 179 m a.s.l.) overpassing the observatory on 17 July 2007 at 08:18 Z. This particular field of view is selected because it is cloud free, making the radiative transfer model calculations simpler. It also has a significant set of accompanying ground-based measurements from the EPS/Metop Sodankylä campaign.

Radiosonde data are from the EPS/Metop Sodankylä campaign, which took place during the time period 4 June to 5 September 2007 (for more details see ). Also, ECMWF analyses have been used either on its own or to complement the radiosonde data. The particular reference temperature and water vapour profiles, which are plotted in Fig. , are obtained from the following sources.

Nearest geo-located ECMWF analysis at 06 Z, which is about 2:30 h before satellite overpass time – This profile will be referred to as “ECMWF”.

It is now worth looking at the different profiles in Fig. . They are generally very similar and consistent except for a few differences. The water vapour concentration for “ECMWF” is clearly much higher than the other ones in the upper troposphere/low stratosphere. The “RS92 Uncorr.” profile is much drier than the others from mid troposphere up. These differences will show up in the observed minus calculated radiances analysis made below (Figs.  and ).

One IASI retrieval is obtained for comparison purposes. The retrieval also constitutes a good starting point to estimate the OE retrieval error, which is essential for the method presented here, but the error could also be calculated from any other realistic atmospheric profile which matches the situation. The IASI retrieval has been calculated following the techniques described in and the fine tuning of . The general description and some particular enhancements and modifications introduced with respect to are briefly summarized below:

Retrievals were obtained using optimal estimation (OE) with physical constraints by prohibiting supersaturation and superadiabaticity.

For illustration purposes the differences of these four profiles against the OE retrieval are plotted in Fig. . It can be seen that the differences depend very strongly on the reference profile used. While most profiles do not deviate significantly from the OE retrieval, the “ECMWF” profile does show comparatively large differences. It is worth noting that all the radiosonde data come from the EPS/Metop Sodankylä campaign and therefore has not been assimilated into any Numerical Weather Prediction (NWP) model.

To get a sense of how well the reference atmospheric profiles are representative of the atmosphere at the IASI field of view, the IASI measured radiances can be compared to the calculated ones using a radiative transfer model. This effectively means that the measured atmospheric profile, the radiative transfer model and the IASI radiances are consistent among themselves within their measurement errors.

The calculated radiances are obtained by applying a radiative transfer model to the measured reference atmospheric profile and its corresponding surface properties. It is important to note here that the atmospheric and surface parameters should come, as much as possible, from measurements or any other sources that are independent from the IASI measurements. In other words, the atmospheric profile and surface properties should ideally not be derived from the IASI measurements, like they would be if a retrieval is performed or some other similar kind of technique is used. The reason behind this is that the final goal of the study is to make an assessment of the reference profile and not of the retrieval. Using data obtained from IASI radiances would artificially increase the agreement between the calculated and measured radiances, thus affecting our assessment method. In the most extreme case, when using atmospheric profiles and quantities that are all derived or retrieved from IASI radiances, it is the retrieval that is assessed and not the reference profiles. It is not always possible to meet this requirement in practice, and it is often the case that some of the parameters needed as input for the radiative transfer model are missing, as typically happens with surface emissivity or surface skin temperature. If this is the case, the number of retrieved parameters should be minimized as much as possible.

In particular, in this paper the calculated radiances are obtained using the following methods.

The temperature and water vapour profiles are used based on radiosonde measurements (“Interpolated”, “RS92 Corr.” and “RS92 Uncorr.”), which are complemented in the upper layers, where the sonde instruments reach their limit, with the “ECMWF” profile. See for more details.

The difference of the observed minus the calculated radiances are shown in Figs. , ,  and . The 3σ IASI noise is plotted in these figures as a black line. Some features are worth noting. The observed minus calculated radiances do not fit well in the ozone band (∼1000 cm-1), indicating that most likely the ozone profile (obtained from ECMWF in all cases) is not very accurate. Radiance differences do not match in IASI band 3 (∼2000 cm-1 and above), which is caused by inadequate modelling of the part of the spectrum that is affected by solar radiation. The “Interpolated” and “RS92 Corr.” profiles (Figs.  and ) fit very well along the rest of the spectrum and mostly lie within the 3σ IASI noise lines. The “ECMWF” profile calculated radiances do not match the IASI observed ones very well (Fig. ), especially in the water vapour band (1400 to 1900 cm-1), caused by the positive deviation in the upper troposphere of the ECMWF water vapour profile as evidenced in Fig. . The “RS92 Uncorr.” profile does not match well in the water vapour band either (Fig. ), showing an opposite sign in the radiance differences with respect to ECMWF, caused by the drier water vapour profile in the upper layers (Fig. ).

From these four observed minus calculated radiance figures (Figs. , ,  and ), it can be concluded that the radiative transfer calculations applied to two of the temperature and humidity profiles,“Interpolated” and “RS92 Corr.”, are consistent with IASI measurements, and the other two, “ECMWF” and “RS92 Uncorr.”, are not. Therefore the former two profiles are suited for validation or calibration of IASI retrievals and the latter two are not. The question that immediately follows is whether an objective criteria can be established to select or reject particular reference atmospheric profiles. This will be developed in the following section.

The natural quantity to set up as a threshold to which the different reference atmospheric profile errors can be compared to is the retrieval error, which arises directly from the OE theory of . If the atmospheric profile errors are much larger than the errors achieved by OE, then the profiles are not suited as reference measurements. If, on the other hand, the atmospheric profile errors are smaller or of the order of the OE retrieval errors, then these profiles can be used as reference measurements. Consequently, the question at this stage is how to convert the observed minus calculated radiance errors into profile errors in the atmospheric state space.

The directly observed minus calculated radiances for one particular IASI field of view (as in Figs. , ,  and ) constitute individual samples of these differences. To estimate the actual errors of these differences it is necessary to estimate their covariances by calculating the standard deviation within a big enough sample. To accomplish this, the values from neighbouring channels are used. This is done by obtaining the square root of the moving average over a spectrum of the square of the observed minus calculated radiances. The length of the window of the moving average which is found to be useful in practice is 500 channels. In doing so, it is implicitly assumed that the statistical probability distribution of the errors of the 500 neighbouring channels are similar. In general this will most likely be the case, but in some circumstances, like particular spectral absorption lines, might not be completely accurate.

The estimation of these standard deviations of the radiances are shown in Fig.  for all four cases. The ozone band is not plotted in this figure because of the big uncertainty shown in this region due to a not well characterized ozone profile. Note the very low standard deviation, below 1σ IASI instrument noise, for some regions of the spectrum for the “Interpolated” and “RS92 Corr.” profiles, as already acknowledged in . Also recall that there is only one parameter retrieved from IASI radiances when obtaining the calculated radiances, which is the surface skin temperature.

The standard deviation of the radiances difference (Fig. ) needs to be translated from radiance space into atmospheric profile space. To do this, the OE theory needs to be recalled by expressing the cost function, J, as J=(y-F(x))TSϵ-1(y-F(x))+(x-xa)TSa-1(x-xa), where y is the hyperspectral measurement, F is the radiative transfer model, Sϵ is the measurement error covariance matrix used in the IASI retrievals, x is the atmospheric profile state, xa is the background state and Sa is the background covariance matrix. This cost function is usually linearised around an atmospheric state close to the final solution, xx, J≈(δy-Kδx)TSϵ-1(δy-Kδx)+(δx-δxa)TSa-1(δx-δxa), where K is the Jacobian of F at the linearization point xx, δx=x-xx, δxa=xa-xx and δy=y-F(xx). To find the most likely atmospheric state or retrieval, x^O, corresponding to a particular IASI observation, y=yO, the derivative of J with respect to δx is set to zero, giving as a final retrieval solution δx^O=(KTSϵ-1K+Sa-1)-1(KTSϵ-1δyO+Sa-1δxa), where δx^O=x^O-xx and δyO=yO-F(xx). It is known that the error or covariance of this retrieval solution is Sx=(KTSϵ-1K+Sa-1)-1, which is a quantity that will be needed later. A similar technique can be applied to obtain the most likely state vector, xC, corresponding to the calculated radiance, yC, obtained from applying a radiative transfer model to any of the reference atmospheric profiles, δx^C=(KTSϵ-1K+Sa-1)-1(KTSϵ-1δyC+Sa-1δxa), where δx^C=x^C-xx and δyC=yC-F(xx). The difference between the two retrieved state vectors, Δx^=x^O-x^C, gives a quantity that measures the error in the state vector when using the calculated radiances, yC, instead of the observed ones, yO. In other words, Δx^ provides a measure of the reference state quality and collocation error plus any errors we might have done in the radiative transfer model assumptions. Solving for Δx^ gives Δx^=(KTSϵ-1K+Sa-1)-1(KTSϵ-1Δy), where Δy=yO-yc. This last equation permits the conversion of the standard deviation radiance difference, Δy, into atmospheric state space, Δx^. The latter will be referred to as collocation and adequacy errors of the reference profiles.

Having all the necessary elements, it is now possible to define a criteria to evaluate whether a given atmospheric profile measurement effectively constitutes a reference profile for IASI. A given atmospheric profile measurement can be classified as a useful reference for IASI if the collocation and adequacy errors in the atmospheric profiles, Δx^ from Eq. (), is below or of the order of the retrieval error, Sx from Eq. (). The results for the four profiles are shown in Fig.  for temperature and water vapour, along with the estimated IASI retrieval error (in black) for comparison. It can be verified that the collocation and adequacy errors of the “Interpolated” and “RS92 Corr.” atmospheric profiles are of the same order of magnitude as the IASI retrieval error. Therefore, these two cases would qualify as reference measurements for the retrievals. The remaining two profiles, “ECMWF” and the “RS92 Uncorr.” show collocation and adequacy errors that are much larger than the retrieval errors and should not be used for validation or calibration purposes.