1. Introduction

2. Description of the OMPS Instrument and Validation Data

3. Description of the Temperature Inversion Method

3.2. Onion Peel Method

As mentioned above, the OMPS team provides an integrated radiance profile with 1-km vertical resolution, i.e. the radiance measured on the line of sight is affected by the upper layers. In order to correct for the contribution of the other layers, we apply the so-called ‘onion peel’ technique, which allows us to obtain the radiance value of each layer by ‘removing’ the layers above it:

$${\mathrm{newprofil}}_i={\mathrm{profil}}_i-{\mathrm{profil}}_j\times \left(\sqrt{j-i+1}-\sqrt{j-i}\right)$$

$$\mathrm{with}\mathrm{j}=\mathrm{i}+1$$

$$\left(\sqrt{j-i+1}-\sqrt{j-i}\right)\mathrm{representing}\mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{layers}\mathrm{j}\mathrm{in}\mathrm{layer}\mathrm{i},\mathrm{proportional}\mathrm{to}\mathrm{the}\mathrm{length}$$

$$\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{of}\mathrm{sight}\mathrm{i}\mathrm{in}\mathrm{the}\mathrm{j}\mathrm{layer}.$$

This method assumes that the atmospheric layers are homogeneous over the viewing distance. It gives excellent vertical resolution (of the order of a km) but does not provide information on horizontal variability better than a few 100 km as a function of altitude (Figure 10).

Figure 2. As indicated in Section 2.1, the green part of the profile is unused, the red part is the profile measured by OMPS and the violet part is simulated using an inverse exponential thanks to the red part. The initialisation altitude marks the ‘boundary’ between these 2 parts.

Figure 2. As indicated in Section 2.1, the green part of the profile is unused, the red part is the profile measured by OMPS and the violet part is simulated using an inverse exponential thanks to the red part. The initialisation altitude marks the ‘boundary’ between these 2 parts.

3.3. Observation Geometry for OMPS Layers

Sunlight entering the instrument is attenuated by the absorption of constituents. In the UV/Visible spectral range, it is mainly O3 and NO2 that cause a reduction in the radiance of the layers observed, particularly around areas where the constituent is in high concentration, in our case the stratosphere. Similarly, molecular scattering (known as Rayleigh scattering) diffuses photons via the molecules encountered, thus reducing the signal received, particularly towards the lowest layers where the density of the air increases. It is therefore necessary to evaluate the distance of each path in order to apply a reduction corresponding to the concentration of the component in the layer under consideration.

$${\mathrm{D}}_{c-Sati}=\sqrt{Rcouch{e}_i^2-Rcouch{e}_{i-1}^2}$$

$${\mathrm{D}}_{c-Sati}\mathrm{corresponding}\mathrm{to}\mathrm{the}\mathrm{distance}\mathrm{covered}\mathrm{in}\mathrm{layer}\mathrm{i}\mathrm{by}\mathrm{the}\mathrm{radiance}\mathrm{to}\mathrm{reach}\mathrm{the}\mathrm{satellite}$$

$${\mathrm{R}}_{couchei}\mathrm{corresponding}\mathrm{to}\mathrm{the}\mathrm{terrestrial}\mathrm{radius}\mathrm{at}\mathrm{layer}\mathrm{i}$$

By performing the calculation for the highest layer, it is possible to estimate the signal reduction for the layer below, and thus to obtain the calculation for the entire vertical profile. This method assumes that the layers are homogeneous in their composition.

Figure 3. This diagram illustrates the path taken by the radiance in each layer observed by OMPS. At each layer, the radiance is scattered by air molecules and absorbed by ozone and nitrogen dioxide molecules. $R_{{\mathrm{Couche}}_i}$ represents the radius from the Earth to the given layer, and $D_{{\mathrm{c}-\mathrm{Sat}}_i}$ represents the distance that the radiance in layer i crosses to reach the satellite. Similarly, $D_{{\mathrm{sol}-\mathrm{c}}_i}$ represents the distance traveled by the radiance arriving from the sun to the layer.

Figure 3. This diagram illustrates the path taken by the radiance in each layer observed by OMPS. At each layer, the radiance is scattered by air molecules and absorbed by ozone and nitrogen dioxide molecules. $R_{{\mathrm{Couche}}_i}$ represents the radius from the Earth to the given layer, and $D_{{\mathrm{c}-\mathrm{Sat}}_i}$ represents the distance that the radiance in layer i crosses to reach the satellite. Similarly, $D_{{\mathrm{sol}-\mathrm{c}}_i}$ represents the distance traveled by the radiance arriving from the sun to the layer.

Once the distance matrix has been obtained and using modelled density profiles, modelled NO2 profiles and O3 profile measurements, we can measure all the radiance loss that applies to each observation path. The first thing we notice is that between km 45 and km 30 the total correction that must be applied to the profile to correct it is almost multiplied by 10, whatever the wavelength (Figure 4).

Next comes the wavelength correction difference. From around 330 nm to 420 nm, the total attenuation of the signal decreases to a minimum as we leave the Huggins absorption band for O3 and Rayleigh scattering also decreases. From 420 nm onwards, despite the fact that Rayleigh scattering continues to fall, we see an increase in the total attenuation of the signal. This is due to the fact that we are entering the Chappuis absorption band for O3. The NO2 correction remains more or less constant throughout the spectrum of the study, with a slight increase up to around 400 nm and then a slight constant decrease. Once again, depending on the wavelengths chosen, the total correction of the profile required is almost multiplied by 10 when taken at the same layer (Figure 4).

3.4. Diffusion and Absorption of the Various Constituents of the Middle Atmosphere

3.4.1. Rayleigh Scattering

Since our initial hypothesis assumes Rayleigh scattering of the atmosphere above 30 km, we can use the molar mass of the air to find the number of ‘Rayleigh’ $\left(N_{\mathrm{i}-\mathrm{Rayleigh}}\right)$ molecules in each layer of the atmosphere:

$$N_{i-\mathrm{Rayleigh}}={\displaystyle \frac{{\rho }_i\times N_A}{M_{\mathrm{air}}}}$$

with :

$${\rho }_i\mathrm{the}\mathrm{density}\mathrm{of}\mathrm{the}\mathrm{layer}\mathrm{in}{\mathrm{cm}}^{-3}$$

$$N_A=6.022\times {10}^{-23}{\mathrm{mol}}^{-1}\mathrm{Avogadro}\text{’}\mathrm{s}\mathrm{number}$$

$$M_{\mathrm{air}}=28.965\mathrm{g}/\mathrm{mol}\mathrm{the}\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{air}$$

The Rayleigh scattering per molecule is given by the formula below (Bucholtz, 1995):

$${\sigma }_{\lambda -\mathrm{Rayleigh}}={\displaystyle \frac{24\times {\pi }^3\times {(n_s^2-1)}^2}{{\lambda }^4\times N_s^2\times {(n_s^2+2)}^2}}\times {\displaystyle \frac{6+3\times {\rho }_n}{6-7\times {\rho }_n}}$$

$${\sigma }_{\lambda -\mathrm{Rayleigh}}\mathrm{the}\mathrm{wavelength}\mathrm{in}\mathrm{cm}\lambda$$

$$n_s\mathrm{the}\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{the}\mathrm{air}\mathrm{at}\lambda \left(\mathrm{unitless}\right)$$

$$N_s\mathrm{the}\mathrm{numerical}\mathrm{molecular}\mathrm{density}\mathrm{of}\mathrm{air}$$

$${\rho }_n\mathrm{the}\mathrm{depolarising}\mathrm{factor}\mathrm{at}\lambda \left(\mathrm{unitless}\right)$$

${\sigma }_{\lambda -\mathrm{Rayleight}}$ and $N_{i-\mathrm{Rayleight}}$ allow us to find the total Rayleigh scattering of a layer :

$${\beta }_{\lambda \mathrm{i}-\mathrm{Rayleight}}={\sigma }_{\lambda -\mathrm{Rayleight}}\times N_{i-\mathrm{Rayleight}}$$

From around 330 to 380 nm, the Rayleight correction’s contribution to total signal attenuation increases to almost 100%, and at these wavelengths it is the greatest source of error. After 380 nm its share gradually decreases, giving way to O3 and NO2 absorption (Figure 5).

3.4.2. Ozone Absorption

O3 absorption is measured in the laboratory for a given wavelength and temperature (${\sigma }_{{\lambda }_{\mathrm{T}-{\mathrm{O}}_3}}$) (Serdyuchenko et al., 2014). The number of $O_3$ molecules is measured by the same instrument that measures OMPS radiance profiles (Kramarova et al., 2018). With these 2 values, we obtain the ozone absorption for each layer measured by OMPS:

$${\beta }_{{\lambda }_{\mathrm{T}-{\mathrm{O}}_3}}={\sigma }_{{\lambda }_{\mathrm{T}-{\mathrm{O}}_3}}\times N_{{\mathrm{i}-\mathrm{O}}_3}$$

For O3, the effects of the Huggins-Chappuis absorption bands can be seen in the total attenuation of the signal. In the Huggins absorption band, the O3 absorption accounts for a large part of the correction (up to 40%) but as Rayleigh scattering is also very strong at these wavelengths, it is not the most important part of the correction. The proportion then decreases to almost 0% between the 2 absorption bands. Once the start of the Chappuis band is reached, it increases again until it reaches 80%, becoming the largest source of error. It should be noted that the Huggins and Chappuis absorption bands are extremely similar in absorption values, the difference being that Rayleigh scattering is much weaker in the Chappuis band (Figure 7).

3.4.3. Nitrogen Dioxide Absorption

NO2 absorption is also measured in the laboratory for a given wavelength and temperature (${\sigma }_{\lambda -{\mathrm{NO}}_2}$) (Bogumil et al., 2003). Variations in NO2 concentration are given by the WACCM model (Whole Atmosphere Community Climate Model (Kyrölä et al., 2018)) which is a climate modelling software package developed to study and simulate the complex large-scale interactions between different components of the Earth’s atmosphere, The profiles given are monthly profiles. With these 2 values, we obtain the absorption of Nitrogen Dioxide for each layer modelled by WACCM :

$${\beta }_{{\lambda }_{\mathrm{Ti}-{\mathrm{NO}}_2}}={\sigma }_{{\lambda }_{\mathrm{T}-{\mathrm{NO}}_2}}\times N_{{\mathrm{i}-\mathrm{NO}}_2}$$

Figure 8. Example of a NO2 profile in the middle atmosphere

Figure 8. Example of a NO2 profile in the middle atmosphere

NO2 absorption varies little compared with O3 absorption and Rayleigh scattering in our study area, so the main cause of variation in its share of total signal attenuation comes from the variation in O3 absorption and Rayleigh scattering (Figure 9).

3.5. Correcting the Attenuation of Radiance Profiles

The total attenuation of the sign as seen in part 3.4, coupled with the light paths calculated in part 3.3, enables the radiance profile to be corrected:

$${\mathrm{newprofil}2}_i={\mathrm{newprofil}}_i\times e^{D_{\mathrm{c}-\mathrm{si}}\times ({\beta }_{{\lambda }_{i-\mathrm{Rayleigh}}}+{\beta }_{{\lambda }_{\mathrm{T}-{\mathrm{O}}_3}}+{\beta }_{{\lambda }_{\mathrm{T}-{\mathrm{NO}}_2}})}$$

Now that we have corrected for the loss of radiance caused by Rayleigh scattering, O3 and NO2 absorption during the layer-to-satellite ‘path’, we need to correct for the same loss caused during the sun-to-layer ‘path’. First we calculate the Rayleigh phase function (Chandrasekhar , 1950) at our scattering angle :

$$P_{\mathrm{ray}\theta }={\displaystyle \frac{3}{4(1+2\gamma )}}\left[(1+3\gamma )+(1-\gamma ){cos}^2\theta \right]$$

with :

$$\gamma ={\displaystyle \frac{{\rho }_n}{2-{\rho }_n}}$$

$$\theta =\widehat{z}+{90}^{\circ }$$

$$\widehat{z}\mathrm{measured}\mathrm{zenith}\mathrm{angle}$$

We then calculate the angular volume diffusion coefficient :

$${\beta }_{\theta {\lambda }_i}={\displaystyle \frac{{\beta }_{{\lambda }_i-\mathrm{Rayleigh}}}{4\pi }}\times P_{\mathrm{ray}\theta }$$

New radiance profile :

$${\mathrm{newprofil}3}_i={\displaystyle \frac{{\mathrm{newprofil}2}_{2i}}{{\beta }_{\theta {\lambda }_i}}}$$

(Note that variations in the zenith angle are negligible, so we will keep the z measured throughout the profile).

As with the layer-satellite ‘path’, the sun-layer ‘path’ also generates radiance losses caused by the combination of the observation geometry and Rayleigh scattering, O3 and NO2 absorption. According to al-Kashi’s theorem, we can write :

$$D_{\mathrm{c}-\mathrm{sol}i}^2-2\times R_{\mathrm{couche}i}\times cos\alpha \times D_{\mathrm{c}-\mathrm{sol}i}+R_{\mathrm{couche}i}^2-R_{\mathrm{couche}i+1}^2=0$$

with :

$$\alpha ={180}^{\circ }-z$$

As with the layer-satellite path, this matrix continues until the last layer where the treatment is applied, allowing the profile to be corrected.

$${\mathrm{newprofil}4}_i={\mathrm{newprofil}3}_i\times e^{D_{\mathrm{c}-\mathrm{si}}·({\beta }_{{\lambda }_i-\mathrm{Rayleigh}}+{\beta }_{{\lambda }_{\mathrm{T}-{\mathrm{O}}_3}}+{\beta }_{{\lambda }_{\mathrm{T}-{\mathrm{NO}}_2}})}$$

The newprofil4 and newprofil3 are the radiance profiles received by each layer, but we want the radiance profile that should have been measured by the satellite, so we need to make this last calculation:

$${\mathrm{newprofil}5}_i=({\mathrm{newprofil}4}_i-{\mathrm{newprofil}3}_i)\times {\beta }_{\theta {\lambda }_i}$$

Calculating these 2 paths gives us the horizontal resolution of the instrument. This resolution changes with altitude, but always reaches a maximum at around 110 km, as shown in the figure below:

Figure 10. Representation of the horizontal resolution for three tangent heights, each point represents a layer measured by OMPS

Figure 10. Representation of the horizontal resolution for three tangent heights, each point represents a layer measured by OMPS

Figure 11. (a) Temperature profile obtained without correction of the radiance profile, (b) the same temperature profile after correction of the radiance profile.

Figure 11. (a) Temperature profile obtained without correction of the radiance profile, (b) the same temperature profile after correction of the radiance profile.

This resolution, combined with the effects of Rayleigh dispersion and O3 and NO2 absorption, results in a variation in the radiance profile obtained, which must be corrected. Below is an example of O3 and NO2 profiles and a curve showing the percentage correction for each of these effects :

Figure 12. Kelvin correction at different wavelengths (raw profile - corrected profile)

Figure 12. Kelvin correction at different wavelengths (raw profile - corrected profile)

4. Comparisons of Temperature Profiles Obtained with the OMPS Instrument with Lidars from the NDACC Network

4.2. Wavelength Analysis

We analysed the different temperature profile inversions obtained for the different wavelengths available with the OMPS spectrometer with a step of 1 nm over the spectral range from 330 to 562 nm. The signal received is a combination of the scattering efficiency of solar radiation and attenuation. The solar spectrum follows Planck’s law (Meftah et al., 2023) with a maximum around 550 nm. In our study range, which is between 230-1020 nm, the power per square metre received by the atmosphere can vary by up to a factor of 4 depending on the wavelength chosen. Molecular scattering efficiency depends on Rayleigh’s law (Bucholtz, 1995) and gives a maximum scattering efficiency for short wavelengths; in our study range, scattering varies by up to a factor of 100. As described in the previous chapters, total attenuation due to atmospheric composition modulates the signal by a factor of 10 and must also be taken into account. The combination of all these factors is illustrated in Figure 13. It appears that the wavelength range around 450 nm is ideal, but for wavelengths shorter than 330 nm the conditions for obtaining good temperature profiles are no longer met due to attenuation.

Since scattering is optimal at short wavelengths, we stopped this sensitivity study at 562 nm. On the other hand, due to instrumental problems, the spectral range between 360 and 380 nm is not available. For reference purposes, we carried out this analysis over 4 lidar sites for 2015. In particular, we observed similar behaviour for the comparison with all 4 sites. The differences are radically different for wavelengths between 399.15 and 450.63 in the mesosphere between 50 and 70 km, as can be seen for example for the Réunion site (Figure 14).

The comparisons show 2 groups of wavelengths, one that will give positive temperature variations (1-3 K) for wavelengths between 380 and 439 nm and another of negative differences for short (<359 nm) and long wavelengths (> 450 nm).

Figure 15. The effect of aerosols on temperature profiles can be seen between 20 and 30 km. As the wavelength increases, aerosol scattering takes precedence over molecular scattering. Lidars do not provide temperature data below 30 km, so we show this phenomenon using MSIS differences.

Figure 15. The effect of aerosols on temperature profiles can be seen between 20 and 30 km. As the wavelength increases, aerosol scattering takes precedence over molecular scattering. Lidars do not provide temperature data below 30 km, so we show this phenomenon using MSIS differences.

Analysis at lower altitudes towards the middle stratosphere shows discrepancies that are probably due to the presence of aerosols. The comparison with lidars, which are also sensitive to the presence of aerosols, is not relevant for validating the OMPS inversions in this altitude range. On the other hand, comparison with the MSIS climatological model shows that the differences increase logically with the wavelength, confirming the reason for these differences. As this contribution is difficult to correct, it seems more appropriate to select short wavelengths, thereby minimising this effect. On the other hand, it is also the shortest wavelengths that are least affected by noise in the upper mesosphere, as we showed in part 3.1 Figure 1. For all these reasons, we have chosen to select wavelengths from 335 to 345 nm for this study and to add them together in order to reduce the measurement noise due to the entire acquisition chain, from the optics to the detector.

The standard deviation between these different profiles calculated for each wavelength makes it possible to estimate the intrinsic error linked to our inversion method applied to the observations of the OMPS instrument. In a perfect case, all the wavelengths are supposed to give the same results, since they are all looking at the same scene. The temperature variations between the signals from the different wavelengths are therefore due to the uncertainty in the radiance measurement. The corresponding error is less than 1 K.

Figure 16. Point cloud and its mean standard deviation of temperature inversions obtained with each wavelength as a function of altitude.

Figure 16. Point cloud and its mean standard deviation of temperature inversions obtained with each wavelength as a function of altitude.

4.3. Results of Temperature Analyses for Each Site

As mentioned in Section 4.1, we compared the results obtained via OMPS with 4 lidars from the NDACC network, the 2 MSIS and ERA5 models and the MLS satellite instrument. Here is the list of the number of comparisons for each position:

• OHP : 1685 comparisons for MLS, MSIS and ERA5 and 777 comparisons against lidar between 2015 and 2020.
• MLO : 990 comparisons for MLS, MSIS and ERA5 and 493 comparisons with lidar between 2015 and July 2018.
• RUN : 1207 comparisons for MLS, MSIS and ERA5 and 257 comparisons against lidar between 2015 and 2020, there are no comparisons for the year 2016.
• HOH : 597 comparisons for MLS, MSIS and ERA5 and 263 comparisons against lidar for the 2 years 2015 and 2016.

Figure 17. Comparisons of OMPS temperature profiles with MLS, ERA5, MSIS 2.0 and HOH. On the left are the differences between OMPS and the various sources compared, in the centre the standard deviation and on the right the uncertainty on the standard deviation. In order from first to last line, the study sites are : OHP, RUN, MLO and HOH.

Figure 17. Comparisons of OMPS temperature profiles with MLS, ERA5, MSIS 2.0 and HOH. On the left are the differences between OMPS and the various sources compared, in the centre the standard deviation and on the right the uncertainty on the standard deviation. In order from first to last line, the study sites are : OHP, RUN, MLO and HOH.

The temperature differences between OMPS, MSIS and the lidars show very similar results, never exceeding 5 K except for the HOH lidar at high altitude and the MLO lidar below 35 km. For the HOH lidar, this is probably due to the fact that the statistical error associated with this lidar is smaller than that of other lidars and that its range rarely exceeds 75 km. At this altitude, the lidar’s temperature error exceeds 20 K, so the results for this high-altitude site should be treated with caution. For the MLO lidar, we believe that it is the effect of aerosols, the effects of which we have not taken into account, that is responsible for this variation. In fact, we observe a slight increase in the standard variation compared with all the lidars below 35 km and it is known that stratospheric aerosols begin to be observable at these altitudes (Khaykin et al., 2017). This altitude zone is therefore subject to uncertainties, although in view of the proportions and results available to us, this uncertainty remains more or less low depending on the sites.

The differences with MLS are a little greater, sometimes reaching 10 K as in the case of the OHP site, and finally we have the case of ERA5 where the differences are very small below 50 km but increase sharply after that, sometimes reaching more than 10 K.

At higher altitudes, the standard deviation increases gradually in the mesosphere, due to gravity waves and instrumental errors in the Lidar and OMPS signals. The systematic deviations observed in the mesosphere may be induced by atmospheric tides, as the measurements are not obtained at the same time. We note that for HOH and OHP the standard deviation drops suddenly at very high altitudes. This is only due to the fact that the temperature profiles of these lidars generally stop earlier than MLO and RUN, so there are very few values to compare at very high altitudes and the standard deviation is therefore not significant. As can be seen, the uncertainty on these standard deviations is very low except for the last kilometre, where there is a sharp increase. The reason for this is that at this altitude there are far fewer comparisons due to the variable initialisation altitude. It is important to understand that these variations are not ‘errors’ but rather expected results, as illustrated in the diagram below :

Figure 18. The red zone represents the calculated expected differences. The blue and yellow curves represent the temperature differences between OMPS and OHP at 2 and 3 std.

Figure 18. The red zone represents the calculated expected differences. The blue and yellow curves represent the temperature differences between OMPS and OHP at 2 and 3 std.

Using an internal procedure, we can calculate the variations due to gravity waves, atmospheric tides and errors in the measurements of the expected lidar caused by the temporal spatial differences between OMPS and the OHP lidar. We then compare the average of the variations calculated throughout the study with the variation in the measurements obtained, and we can see that the calculated variations are between 2 and 3 std of the measured variations.

5. Application to a Miniaturised Instrument

6. Conclusions

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