The AUX_MET auxiliary file provides profiles of several meteorological variables such as temperature, pressure, specific and relative humidities, and wind (as well as information on cloud cover and cloud liquid/ice water content) along the Aeolus orbit. The AUX_MET data are available for nadir (laser is pointing perpendicular towards the earth surface) and off-nadir (laser is tilted 35∘ off nadir). Currently, the L2/Met PF provides meteorological quantities as vertical profiles interpolated spatially and temporarily from a short-term IFS forecast having a validity from 6 to 30 h and produced twice per day. Representation of a slanted off-nadir data with a vertical profile has been found to be an acceptable simplification e.g.. Indeed, the maximal difference in terms of geolocation between the model vertical profile and the Aeolus orbit is about 21 km at 30 km altitude, which is not significant given the effective resolution of the model that cannot resolve scales below around 100 km e.g.. This operational auxiliary meteorological file is denoted hereafter as AUX_METecmwf.

The production of auxiliary meteorological data at Météo-France (named AUX_METmf) is an offline procedure. In that respect the production of meteorological auxiliary files did not follow exactly the production at L2/Met PF, but it has been instead simplified allowing for minimal adaptation of existing operational ARPEGE routines at the time of the study.

A flowchart of the working processing chain is shown in Fig. . It is important to notice that a production of AUX_METmf is done every 6 h, which is consistent with the ARPEGE data assimilation system (Fig. b). For the purpose of explaining the behaviour of the chain, a production at 06:00 UTC is discussed next.

At Météo-France the L1B measurement geolocation is used to provide information on the Aeolus orbit needed for production of AUX_MET data. In particular, L1B output files store the geolocation for each measurement, which is ideally available every ∼3 km, being a baseline for the sampling distance of vertical profiles in the AUX_METmf. Similarly, as in AUX_METecmwf, AUX_METmf vertical profiles are provided both for the nadir and off-nadir. The geolocations are gathered from all available L1B data over the time period of 03:00 to 09:00 UTC (typically of about 5–6 L1B files). This is the main input dataset for the production of auxiliary meteorological files.

In the following stage, the extracted geolocation is first reformatted (pre-processing stage in Fig. a) in a way that is compatible with the ARPEGE data assimilation system through BUFR (Binary Universal Format for the Representation of meteorological data) files. Then, for each geolocation, model vertical profiles of several variables are extracted during the data assimilation window. These ARPEGE outputs in ODB (Observation Data Base) format are finally reformatted (in the post-processing stage in Fig. ) into a single AUX_METmf file ready to be used in L2Bp. The chosen ARPEGE model configuration corresponds to the operational one (CY43T2). This spectral model has a stretched and tilted horizontal grid with the highest horizontal resolution over France (∼5 km) and the lowest (∼20 km) on the opposite pole (New Zealand). The model consists of 105 vertical levels defined in between 10 m and 0.1 hPa following a hybrid vertical coordinate. The model profiles are extracted from the ARPEGE model background trajectory in the so-called screening task. This is a part of the 4D-Var system where the model is run forward and compared to observations within 30 min time slots.

On top of various error sources affecting this sensitivity study (as discussed in Sect. ), additional errors arise due to the specific configuration displayed in Fig. . In particular, AUX_METmf data represent a so-called first guess (a very short-term forecast of 3–9 h), whereas AUX_METecmwf data represent a longer-range forecast (6–30 h). Thus, the statistics of their differences are affected by differences in forecast lead times. Furthermore, since the two datasets are produced from two different operational data assimilation system implementations, their differences will further increase the complex interplay of various error sources and therefore the estimate of the uncertainty in temperature and pressure fields. These statements support the initial proposal to perform the analysis of the spatially and temporally averaged differences in model forecast temperature and pressure fields that will reduce some of these effects on the HLOS sensitivity.

In addition, one side effect of the configuration presented in Fig.  is that AUX_METmf files are not partly overlapping in time as is the case for the AUX_METecmwf files. Indeed, the validity of AUX_METmf files is exactly 6 h, which are produced four times per day, whereas AUX_METecmwf represents 6–30 h IFS forecast, the files which are produced twice per day. Therefore, when using AUX_METmf files in the L2Bp, a specific approach must be used in the case the L1B input file spans a time period in between two data assimilation windows of the ARPEGE system (i.e. two AUX_METmf files). In such a case the L2Bp must be run twice for each AUX_METmf file, and finally data from both L2B runs must be merged into one single L2B output.

From two distinct auxiliary meteorological data (AUX_METecmwf and AUX_METmf), covering the same Aeolus orbit section, it is possible to analyse differences induced by the two associated L2B HLOS retrievals. The necessary processing chain for performing such a study is displayed in Fig. . The part enclosed in the dashed lined box corresponds to the simplified operational L2B processing chain performed by the PDGS which essentially consists of running the L2Bp with all necessary input files and a configuration file. A similar chain of processes has been replicated locally at Météo-France, using the same L2Bp version, the same configuration file and the same input files, except for the AUX_METmf input file which is produced as described in Sect. . The statistical evaluation of the difference between the two HLOS wind products, to be explained in more details in Sect. , is shown in Fig.  by the two black arrows pointing towards the “statistical evaluation” box.

Another evaluation approach is used as is depicted by the three red arrows in Fig. . In this particular case the L2Bp is not used, but instead all the necessary information is directly extracted from the AUX_METecmwf and AUX_METmf files and the operational L2B product. As described in Sect. , given the small model differences in terms of temperature and pressure with respect to reference values (from IFS), it is possible to express the HLOS difference (Eq. ) by a Taylor expansion. It is first assumed that the third term in Eq. () can be neglected, i.e. Δρ=0. Then, the computation of temperature and pressure differences (i.e. ΔT and Δp in Eq. ) is done by comparing the two AUX_MET files. This has been possible by closely replicating the L2Bp algorithm that first interpolates temperature and pressure (the nearest profile from the AUX_MET) onto the HLOS measurement geolocation. Note that HLOS measurement is representative of ∼2.8 km, whereas HLOS observation represents the accumulation (i.e. average) of up to about 30 (for Rayleigh clear) measurements. The same averaging approach applies for temperature and pressure information representative of a particular HLOS observation. Finally, using the sensitivity values (∂THLOS and ∂pHLOS) available in the operational L2B output the HLOS difference has been computed.

As Aeolus is an explorer mission the retrieval of HLOS winds from raw satellite data is continuously adapting and improving. The choice of selected dataset is therefore an important factor that should be taken into a consideration. For this particular study the dataset is part of the reprocessed one available for a period of July–December 2019 (i.e. baseline 2B10). This is an official reprocessing from PDGS and contains a number of improvements of several deficiencies closely examined by ESA and DISC. This is an improved treatment for removing spurious outliers induced by dark current signals (hot pixels) . A dark current signal is measured when no laser pulse is emitted. Moreover, orbit variable systematic errors have been removed by an innovative method based on a linear relation of the satellite primary mirror temperature gradient and the model estimated HLOS systematic error . In addition, since 1 August 2019 the Rayleigh–Brillouin correction has been affected by calibration update, having a direct impact on the properties studied in this paper. As a consequence, the dataset selected for this study is valid for the period of 1 August up to 31 December 2019. This dataset is used for the study, concerning the methodology of a second approach of the sensitivity validation (without using the L2Bp) as described in Sect. . On the other hand, data from the first Aeolus laser period (so-called FM-A period) are used for the experiment using L2Bp. In this case the dataset consists of 464 orbits from the period of 30 November 2018 to 13 January 2019. As this particular dataset has not yet been officially corrected, it can impact results presented afterwards. However, as will be discussed later this effect is expected to be small.

The L2Bp used here is of version 3.01. The configuration file of the processor (AUX_PAR) is of version 8 (used during baseline 2B02), which consists of a scattering ratio threshold of 1.5–1.6 for Rayleigh classification on clear and cloudy scenarios and a Rayleigh-clear accumulation length (i.e. the distance along the orbit for which the observation is representative) of 86.4 km.

From L2B outputs only Rayleigh-clear information is used after applying a basic quality control. It consists of rejecting all observations identified as invalid (information available in the L2B output) or for which the L2B estimated observation error is larger than 10 ms-1 (similar to a range of values typically used in the quality control of several NWP centres assimilating Aeolus data). In addition, a quality check against the ARPEGE background is performed such that HLOS observations that differ significantly from ARPEGE-derived HLOS winds are discarded. This approach allows the study of the sensitivity properties only for data that would be considered for data assimilation in NWP models.

Main properties of ΔHLOS, ΔT and Δp are examined by using typical robust statistical metrics. Such are median (50th percentile of the distribution) and median absolute difference (mad) evaluated spatially and/or temporally, along with several other distribution percentiles. Median absolute difference is a robust measure of dispersion computed as a median of absolute difference of the original distribution with respect to its median chap. 3.1.2. These quantities are especially useful in case of outliers in the distribution. The so-called madn=1.48mad is used instead of mad since it agrees with the standard deviation when the sample distribution is Gaussian. The same approach is chosen to describe the statistical properties of the HLOS sensitivity terms, e.g. ∂THLOS.

Main properties of the sensitivity (i.e. ∂THLOS and ∂pHLOS) valid for the period from 1 August up to 31 December 2019 are shown in Fig. . Statistics as a function of HLOS wind velocity are displayed in Fig. a and b. These are computed by grouping available data in to 10 ms-1 HLOS wind velocity bins. In addition to the average sensitivity, measured by the median, the percentiles of 0.5 and 99.5 (as well as 25 and 75 for the sensitivity against pressure) are also computed to give an estimate of its variability for a particular range of HLOS wind velocities.

One property of the HLOS sensitivity to temperature is its approximate linear dependency with HLOS wind velocity. The slope of the median curve is ∼0.002 K-1, which is in good agreement with the value for the standard atmosphere given by . The variability shown by the two percentiles is mostly induced by the fact that inside each bin HLOS wind velocity varies by 10 ms-1 and is less effected by the fact that atmospheric conditions, i.e. temperature and pressure, vary significantly over the same range bin. The variability is rather consistent over the whole range of HLOS wind velocity.

As discussed in Sect. , by using properties of the sensitivity presented in Fig. a it is possible to approximately estimate the random error contribution since temperature information is not known exactly (i.e. based on Eq. ). Typically, for a random error of 1 K in temperature the random error in HLOS would increase by only of about 0.2 ms-1 for a 100 ms-1 HLOS wind. However, for temperature differences of about 10 K, an increase of up to about 2 ms-1 in HLOS (for 100 ms-1 HLOS wind) is expected, i.e. a relative error of 2 %. As a consequence, outliers in the model temperature distribution are going to produce significant differences in HLOS retrievals.

Moreover, sensitivity varies in the vertical, as shown in Fig. c, as a function of pressure (i.e. altitude) but only for positive HLOS winds since it is symmetric for negative HLOS. The largest values are expected near the upper troposphere–lower stratosphere (UTLS), both of which are associated on average with globally stronger winds. Similarly, the sensitivity increases with altitude in the stratosphere due to the positive temperature gradient in this region.

On the other hand, the HLOS sensitivity to pressure is significantly less, given the small uncertainties in model pressure information. In particular, the sensitivity shown in Fig. b and d indicates a median value (over all positive HLOS) of about -0.002 ms-1hPa-1, which is in the range of expected values (e.g. 0.003 ms-1hPa-1 for the standard atmosphere as shown by ). The variability of the sensitivity (Fig. b) becomes stronger with larger absolute HLOS winds, which is induced by the effect of variable temperature and pressure conditions in a given HLOS bin. Therefore, a significant slope (especially for percentile 0.5) of the sensitivity with altitude is shown in Fig. d. With a 10 hPa (a typical root-mean-squared error of 24 h global model mean-sea-level forecast against analysis, https://apps.ecmwf.int/wmolcdnv/scores/mean/msl, last access: 17 May 2021) error in pressure, the random error in HLOS would increase by about 0.1 %, whereas a 100 hPa random error would increase the HLOS error by 1 %. The effect of the pressure sensitivity is thus expected to be at least 1 order of magnitude smaller compared to the temperature sensitivity when the NWP model pressure is provided in AUX_MET.

Overall the statistics shown in Fig.  are very consistent over the chosen time period of 5 months – i.e. no significant variations have been observed when shorter time periods have been analysed separately (not shown). The bulk analysis of the sensitivity, as presented above, is therefore sufficient.

The comparison of the AUX_METecmwf and AUX_METmf files allows estimating uncertainties in model pressure and temperature with their effects on HLOS sensitivities. For that purpose a second approach described in Sect.  has been proposed. The temperature and pressure differences between ARPEGE and IFS (i.e. ΔT and Δp) have been computed from AUX_MET by mimicking the accumulation algorithm in L2Bp.

The average difference is less than about 0.5 K in temperature and 0.25 hPa in pressure below 30 km altitude (Fig. ), showing an overall good consistency among the two model atmospheric temperature and pressure averaged globally and in time. Nonetheless, the small differences also reflect the fact that the two models share several design features, i.e. the underestimation of actual errors due to a likely correlation of forecast errors of temperature fields. The difference in temperature is on average the largest over a pressure layer of 100–300 hPa, mainly over both poles (see Fig. c). In the tropics the mean difference is the largest above and below the tropical stratosphere near the minimum temperature core (see Fig. a) and higher in the stratosphere. A larger average difference is also noticed near the surface in polar regions. For this particular dataset the IFS zonal mean temperature and its variability are shown in Fig. a and b. These are broadly consistent with available reanalysis statistics i.e., taking into account the rather short period of the current dataset (5 months). Namely, the largest temperatures are found in the tropical troposphere and the lowest temperatures are observed in UTLS. The amount of data used for statistics (Fig. e) becomes reduced especially above about 10–15 hPa, where they become unreliable. The largest temperature zonal variability (Fig. b) over the 5-month period is found over the South Pole, which coincides with the lowest zonal mean temperature (Fig. a) area in the stratosphere. This is a typical feature of the Southern Hemisphere winter period e.g.. The ARPEGE model has a higher polar tropopause and a slightly reduced temperature gradient in tropical stratosphere, when compared to the IFS model.

A good consistency between model temperature fields is not only observed for the mean distribution. For 50 % of the distribution the differences remain below 1 K and 0.5 hPa almost everywhere below 30 km altitude (Fig. ). For temperature this uncertainty is rather similar at all altitudes, although it is slightly larger in the stratosphere. A noticeable variability in temperature difference exists in the tropical stratosphere as shown in Fig. d. The largest amplitude in temperature difference, although spatially very localized, is observed near the ground over the two poles (Fig. d). Given that the chosen dataset describes primarily the Southern Hemisphere winter months, slightly increased variability is also observed to be high in the stratosphere over the South Pole (Fig. d). This is consistent with the largest variability in IFS model temperature observed over that area as shown in Fig. b. These regions, therefore, represent the most sensitive (in respect of temperature) areas for the HLOS retrieval in the studied period.

A scenario displayed in Fig. c presents the difference between two model temperature fields. Here data (each coloured box represents a valid observation) are extracted from a section of the Aeolus orbit crossing the regions of South Indian Ocean, tropical Indian Ocean and Southeast Asia. As shown in Fig. b several deep cloud systems exist on the path of Aeolus, increasing the lidar signal attenuation, as denoted by increased scattering ratio. In such situations temperature differences are found fairly consistent with the overall statistics shown in Fig. c; there is an overall positive ΔT along with vertical layers where ΔT becomes negative (e.g. especially above the tropical troposphere). Only few events of |ΔT| larger than 1–2 K are observed.

The largest deviations between the two NWP models can be further identified by analysing outliers of the difference probability density function (PDF) better shown in Fig. . Tails of the PDF are presented by the percentiles 0.5 and 99.5, which includes 99 % of data. It can be seen that model temperature difference will exceed about 2 K in the mid-troposphere and 3–4 K near the ground and in higher layers of troposphere and stratosphere for only 1 % of the distribution. For pressure this goes to about 1.5 hPa near the ground and decreases with altitude. In less than 1 % of cases, differences are even larger, although the overall summary of the results shown in Fig.  is that differences in temperature and pressure between the models are overall small.

The initial hypothesis assuming that statistical properties of the difference between two model forecasts can be used as a proxy of forecast errors is evaluated by a comparison against the ensemble spread of the ECMWF Ensemble of Data Assimilation (EDA) . Even though EDA does not provide information on long forecast range errors, the spatial patterns of the temporally averaged temperature forecast differences (Fig. ) are relatively similar to those represented by the EDA temperature spread in Fig. 5a of , supporting the experimental approach used in this paper. This qualitative comparison also shows that the EDA temperature spread in Fig. 5a of is typically twice as large as the median absolute difference of temperature differences reported in Fig. d with peak values around 2 K in the stratosphere. This factor is expected to be even larger since the EDA only describes short-range forecast errors.

Properties of the forecast differences displayed in Figs. – and sensitivities shown in Fig.  can be combined to estimate the largest expected HLOS variations due to the Rayleigh–Brillouin effect. The largest variations in HLOS are expected for temperature particularly in the stratosphere, due to larger HLOS sensitivity, but also near the ground, due to significant temperature differences between the two models. For an HLOS value of about 100 ms-1 the HLOS variations could exceed 0.6 ms-1 in less than 1 % of the situations. On the other hand the maximum expected variation of HLOS due to differences in pressure fields could be about 0.015 ms-1 at HLOS of 100 ms-1 but only near the ground (which is very unlikely) in less than 1 % of the cases. Therefore, the pressure component has no significant impact on the HLOS sensitivity and will not be analysed further.

By combining the HLOS sensitivity of the Rayleigh interferometer for Aeolus (Sect. ) with temperature differences between ARPEGE and IFS models (Sect. ), the HLOS correction (ΔHLOS as defined in Eq. ) can be evaluated next.

Similar statistics as for ΔT are computed for ΔHLOS (Fig. ). The spatial and temporal statistics lead to a symmetric PDF as shown in Fig. a, with madn larger than about 0.2 ms-1 above 30 hPa. The curve for the madn almost overlaps with the 75th percentile curve, which along with the 25th percentile presents 50 % of the distribution. Since a sensitivity ∂THLOS strongly depends on HLOS wind amplitude (Fig. ), statistics for ΔHLOS should display this dependency. This is confirmed by Fig. a. Here the median is slightly larger only for HLOS winds larger than about 100 ms-1. On the other hand, several outliers with significantly larger values (up to more than 5 ms-1 – not shown) of ΔHLOS are observed. However, these outliers have no significant effect on the statistical properties of the ΔHLOS; in particular, 99.9 % of the distribution is still confined within the 1 % HLOS slope.

The largest difference (i.e. 1 % of the PDF) in Fig. a exceeds 0.1 ms-1 below about 30 hPa and increases to about 0.4 ms-1 above. Although temperature differences are 99 % of the time smaller than about 4 K (Fig. a), the remaining 1 % of the distribution introduces differences of about several tens of kelvins. To better distinguish such outliers from the remaining distribution, statistics are re-evaluated for events with a temperature difference lower than 4 K (Fig. b). This simple filter efficiently removes all situations for which a relative difference ΔHLOS/HLOS>1 %. The comparison between Fig. a and b reveals that the largest differences in HLOS are associated with the outliers of the temperature difference ΔT distribution. Figure b shows that over the whole range of HLOS values the difference ΔHLOS is well confined below a 1 % slope of HLOS and that in 99 % of situations it is well confined below a 0.7 % slope (i.e. ESA mission requirements).

The remaining question concerns the main characteristics of situations with ΔT>4 K. This can be discussed first by examining where such cases typically take place. Figure f displays the percentage of such cases relative to the total number of cases found in each latitude–pressure bin (i.e. Fig. e). The percentage shown in Fig. f is closely related to the madn of the ΔT shown in Fig. d. The largest contribution of the outliers (up to 10 % locally) is thus observed near the ground on both poles. A relatively large contribution is also noticeable in the tropical stratosphere, South Pole stratosphere (above ∼50 hPa) and around 200 hPa at latitudes 30–40∘ N/S. The latter is closely correlated with the position of the subtropical jet stream as can be confirmed by the median of IFS HLOS in Fig. c.

The largest values of ΔHLOS are produced by two mechanisms as is revealed by the outliers of the distribution displayed in Fig. b. First, the difference in HLOS is larger for in absolute larger HLOS winds, as is a consequence of the linear relation of ∂THLOS presented in Fig. a. This effect is confirmed by comparing it with the average HLOS shown in Fig. c. Thus, the largest differences in HLOS are expected near the location of subtropical jet streams. Due to the Southern Hemisphere winter months prevailing in the dataset, the stratosphere polar night jet is clearly evident over the South Pole (Fig. c). The second effect producing large values comes from the largest temperature differences (i.e. Fig. f). This contribution is the strongest near the ground over both poles, but it also contributes to increased HLOS differences in the tropical stratosphere and over the subtropical jet streams. Overall the largest relative differences ΔHLOS/HLOS are expected near the ground over both poles where the HLOS is on average small in absolute values.

The effect of, mainly, the first mechanism is well observed in the scenario displayed in Fig. d, taking into account associated temperature differences (Fig. c) and HLOS amplitude (Fig. a). The largest increments ΔHLOS are observed over the subtropical jet-stream regions (especially in the Southern Hemisphere) as well as in the tropical UTLS. In particular situation the largest differences in HLOS are found near the active deep cloud systems.

The advantage of running L2Bp is that it allows the cross-validation of Eq. () and thus the estimation of the relative importance of the Mie contamination sensitivity term (i.e. in Eq. ). To examine this contribution a second dataset is used (the FM-A period) to first produce the AUX_METecmwf and AUX_METmf files, and then L2Bp is run to generate HLOSecmwf and HLOSmf as described in Sect. , respectively. In addition, HLOSmf,estimate=HLOSecmwf+ΔHLOS=HLOSecmwf+ΔT∂THLOS|ecmwf+Δp∂pHLOS|ecmwf is computed using Eq. (), with metadata provided from the L2B output of HLOSecmwf and ΔT, Δp from the two AUX_MET files. Taking into account Eqs. ()–() and vLOS=-νdλ0/2, the following equation can be derived. 4HLOSmf,estimate-HLOSmf≈-(1-ρ)∂ρHLOS|mf-∂ρHLOS|ecmwf=-Δ, where subscripts mf and ecmwf essentially define conditions of T, p, ρ and RR for which derivatives are computed. So, the difference between the methodology of Eq. () and L2Bp allows estimating properties of the contribution of the Mie contamination due to uncertain temperature and pressure information that affects the HLOS scattering ratio sensitivity term.

Since the FM-A dataset used here has not yet been officially reprocessed, it was first necessary to evaluate the sensitivity ∂THLOS|ecmwf. Its properties have been found (not shown) very similar and consistent with the one from the FM-B dataset (i.e. Fig. a). In particular the slope of ∼0.002 K-1 is evident, although overall the sensitivity in FM-A dataset is for a value of about 0.05 ms-1K-1 smaller, which has been found small enough to be not significant for the rest of the study.

The Δ value has been found overall small as expected. Its PDF distribution is symmetric with values smaller than 0.05 ms-1 for 99 % of cases in absolute value for the dataset of interest. This suggests that the computation of correction using Eq. () compares well with the direct use of L2Bp in the particular case with the two AUX_MET files. This result suggests that in practice it is preferable to compute the HLOS correction using Eq. () when small differences in model temperature and pressure are expected, since it is faster and technically less demanding than rerunning the L2Bp using a different AUX_MET file. On the other hand, a portion of the distribution of Δ (i.e. 1 %) has been found having values of 0.4 ms-1 in absolute terms. These differences are a consequence of differences that arise in the HLOS sensitivity to scattering ratio evaluated with different atmospheric situations (i.e. temperature and pressure) as reflected by Eq. ().

The Δ values are on average smaller than the HLOS differences due to temperature and pressure (i.e. ΔHLOS estimated by Eq. ) as shown in Fig. . On average the HLOS sensitivity to scattering ratio brings an additional 10 %–20 % to HLOS correction when ΔHLOS>0.2 ms-1. The larger the value of ΔHLOS is, the smaller the relative contribution becomes. However, for large values of ΔHLOS, the amount of data used in the statistics becomes small (green line in figure), so the estimation is not significant, but this decreasing trend with increasing ΔHLOS is apparent. When ΔHLOS is small a value of Δ can increase up to about 70 % for the distribution median or even more than 100 % in about 1 % of cases. However, for small ΔHLOS values the overall correction to the HLOS correction is not of significant practical importance. Overall the sensitivity to scattering ratio is of less importance, even for the relatively large scatter ratio threshold of 1.6 used in the L2Bp, compared to the sensitivity to temperature.