the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Validation of pure rotational Raman temperature data from the Raman Lidar for Meteorological Observations (RALMO) at Payerne
Giovanni Martucci
Francisco NavasGuzmán
Ludovic Renaud
Gonzague Romanens
S. Mahagammulla Gamage
Maxime Hervo
Pierre Jeannet
Alexander Haefele
The Raman Lidar for Meteorological Observations (RALMO) is operated at the MeteoSwiss station of Payerne (Switzerland) and provides, amongst other products, continuous measurements of temperature since 2010. The temperature profiles are retrieved from the pure rotational Raman (PRR) signals detected around the 355 nm Cabannes line. The transmitter and receiver systems of RALMO are described in detail, and the reception and acquisition units of the PRR channels are thoroughly characterized. The FastCom P7888 card used to acquire the PRR signal, the calculation of the dead time and the desaturation procedure are also presented. The temperature profiles retrieved from RALMO PRR data during the period going from July 2017 to the end of December 2018 have been validated against two reference operational radiosounding systems (ORSs) colocated with RALMO, i.e. the Meteolabor SRSC50 and the Vaisala RS41. The ORSs have also served to perform the calibration of the RALMO temperature during the validation period. The maximum bias (ΔT_{max}), mean bias (μ) and mean standard deviation (σ) of RALMO temperature T_{ral} with respect to the reference ORS, T_{ors}, are used to characterize the accuracy and precision of T_{ral} along the troposphere. The daytime statistics provide information essentially about the lower troposphere due to lower signaltonoise ratio. The ΔT_{max}, μ and σ of the differences $\mathrm{\Delta}T={T}_{\mathrm{ral}}{T}_{\mathrm{ors}}$ are, respectively, 0.28, 0.02±0.1 and 0.62±0.03 K. The nighttime statistics provide information for the entire troposphere and yield ΔT_{max}=0.29 K, $\mathit{\mu}=\mathrm{0.05}\pm \mathrm{0.34}$ K and $\mathit{\sigma}=\mathrm{0.66}\pm \mathrm{0.06}$ K. The small ΔT_{max}, μ and σ values obtained for both daytime and nighttime comparisons indicate the high stability of RALMO that has been calibrated only seven times over 18 months. The retrieval method can correct for the largest sources of correlated and uncorrelated errors, e.g. signal noise, dead time of the acquisition system and solar background. Especially the solar radiation (scattered into the field of view from the zenith angle Φ) affects the quality of PRR signals and represents a source of systematic error for the retrieved temperature. An imperfect subtraction of the background from the daytime PRR profiles induces a bias of up to 2 K at all heights. An empirical correction f(Φ) ranging from 0.99 to 1 has therefore been applied to the mean background of the PRR signals to remove the bias. The correction function f(Φ) has been validated against the numerical weather prediction model COSMO (Consortium for Smallscale Modelling), suggesting that f(Φ) does not introduce any additional source of systematic or random error to T_{ral}. A seasonality study has been performed to help with understanding if the overall daytime and nighttime zero bias hides seasonal nonzero biases that cancel out when combined in the full dataset.
Continuous measurements of tropospheric temperature are essential for numerous meteorological applications and in particular for numerical weather predictions, for satellite calibration and validation applications (Stiller et al., 2012; Wing et al., 2018), and for the understanding of climate change. Colocated temperature and humidity measurements allow us to calculate the relative humidity, a parameter playing a key role in several thermodynamic processes, such as the hygroscopic growth of condensation nuclei, fog and cloud formation. When considering the thermodynamic processes occurring within a stagnant air mass, a strong increase in relative humidity is often a precursor of fog, while the onset of supersaturation is linked to a consolidated radiation fog or a cloud forming at the top of a convective layer. Another important thermodynamic parameter is the convective available potential energy (CAPE); CAPE is directly related to the temperature difference between two layers in the atmosphere. The knowledge of temperature as a function of altitude allows us to monitor the atmospheric thermodynamic stability and to diagnose and forecast the onset and intensity of a thunderstorm. Despite its importance in all these processes, the atmospheric temperature is still undersampled in the lower troposphere where the traditional and wellestablished observing systems (e.g. radiosounding, Aircraft Meteorological DAta Relay (AMDAR), MODES (Selective) EHS (enhanced surveillance), satellites) do not provide continuous measurements. A vertical profile of temperature in the troposphere can be measured efficiently by groundbased remote sensing instrumentation; unlike other technologies, remote sensing is best suited to operate continuously and to satisfy realtime data delivery requirements. Moreover, remote sensing instruments operating continuously for many years ensure long time series of data, which are fundamental for climatology studies.
This study focuses on the measurement of the atmospheric temperature done by a light detection and ranging (lidar) instrument. Best known methodologies to retrieve temperature profiles using a lidar can be split into four groups of techniques: the differential absorption lidar (DIAL), the high spectral resolution lidar (HSRL), the Rayleigh technique and the Raman technique (Wulfmeyer et al., 2015, and references therein). Measurements with DIAL are based on the dependency of the molecular absorption on the atmospheric temperature; namely, oxygen molecules with their constant mixing ratio in the dry atmosphere are used as targets by DIAL to retrieve the temperature profile (Behrendt, 2005; Hua et al., 2005). The HSRL technique uses the Doppler frequency shifts produced when photons are scattered from molecules in random thermal motion; the temperature dependence of the shape of the Cabannes line is used directly for temperature measurements (Theopold and Bösenberg, 1993; Wulfmeyer and Bösenberg, 1998; Bösenberg, 1998). The Rayleigh method is based on the assumption that measured photoncount profiles are proportional to the atmospheric massdensity profile in an atmosphere that behaves like an ideal gas and that is in hydrostatic equilibrium. The massdensity profile is used to determine the absolute temperature profile (Hauchecorne et al., 1991; Alpers et al., 2004; Argall, 2007). The pure rotational Raman (PRR) method relies on the dependence of the rotational spectrum on atmospheric temperature (Cooney, 1972; Vaughan et al., 1993; Balin et al., 2004; Behrendt et al., 2004; Di Girolamo et al., 2004; Achtert et al., 2013; Zuev et al., 2017). A combination of the Rayleigh and Raman methods is also possible and allows us to extend significantly the atmospheric region where the temperature is retrieved (Li et al., 2016; Gerding et al., 2008). The four methods have the common objective to produce a temperature profile as close as possible to the true atmospheric status. In the attempt to do that, a reference must be used to calibrate the lidar temperature and calculate the related uncertainty. Trustworthy references can be provided by colocated radiosondes, satellites or numerical models. A colocated radiosounding system (RS) can act as reference to calibrate and monitor the stability of a lidar system over long periods of time (Newsom et al., 2013). Our study presents a characterization of the RSs in use at Payerne and their validation with respect to the Vaisala RS92 certified by the Global Climate Observing System (GCOS) Reference UpperAir Network (GRUAN). Assimilation experiments using validated Raman lidar temperature profiles have been performed, among others, by Adam et al. (2016) and Leuenberger et al. (2020). Both studies highlight the great potential of Raman lidar to improve numerical weather prediction (NWP) models through data assimilation (DA).
In this study we characterize and validate Raman Lidar for Meteorological Observations (RALMO) temperature profiles and demonstrate the high stability of the system. The paper is organized as follows. In Sect. 2 we establish the quality of the reference radiosonde datasets. The lidar system is described in detail in Sect. 3 followed by a thorough uncertainty budget estimation in Sect. 4. In that section all contributions to the total error are quantified and taken into account (deadtime correction, background correction, photoncounting error, calibration error). In Sects. 5 and 6 we present the statistics of the comparison between lidar and radiosondes. In Sect. 5 we present the statistical analysis of the $\mathrm{\Delta}T={T}_{\mathrm{ral}}{T}_{\mathrm{ors}}$ dataset, and we analyse the possible causes of μ and σ over the period July 2017–December 2018. An additional statistical study has been performed by splitting the ΔT dataset into seasons to investigate the effect of solar background and its correction function f(Φ) on the retrieved temperature profiles in terms of μ and σ (Sect. 6). The maximum (ΔT_{max}) and mean bias (μ) of the difference (ΔT) of the lidar temperature profiles with respect to the temporally and spatially colocated radiosonde profiles represent the systematic uncertainty of the lidar temperature. The standard deviation of all differences ΔT over the entire dataset yields the random uncertainty (σ) of the lidar temperature.
In the framework of the operational radiosonde flight programme, the operational radiosonde is launched twice daily at Payerne at 11:00 and 23:00 UTC (in order to reach 100 hPa by 00:00 and 12:00 UTC) and provides profiles of humidity (q), temperature (T), pressure (P) and wind (u). In addition to the operational programme, MeteoSwiss is part of the Global Climate Observing System (GCOS) Reference UpperAir Network (GRUAN) since 2012 with the Vaisala sonde RS92. In the framework of GRUAN, MeteoSwiss has launched from the aerological station of Payerne more than 300 RS92 sondes between 2012 and 2019, contributing significantly to its characterization (metadata, correction algorithms and uncertainty calculation) and to its GRUAN certification (Dirksen et al., 2014; Bodeker and Kremser, 2015). Before being part of GRUAN and since 2005, MeteoSwiss has used the RS92 sonde as working standard in the framework of the quality assurance programme of the different versions of the Meteolabor Swiss radiosonde (SRS). Different versions of the SRS systems were operated at Payerne since 1990, starting from the analogue SRS400 (from 1990 to 2011) and developing to the digital sondes SRSC34 and C50. Starting from 2012, different versions of the SRSC34 and SRSC50 have been compared to RS92 in the framework of GRUAN. In 2014, the Vaisala RS41 (Dirksen et al., 2020) was added to the GRUAN programme where it performed numerous multipayload flights with RS92 and the SRS carried under the same balloon.
During the studied period, two different operational radiosounding systems (ORSs) have been launched regularly at 11:00 and 23:00 UTC: the SRSC50 (February 2017–March 2018) and the Vaisala RS41 (March–December 2018). Thanks to the multisensor flights performed with the SRSC50, the Vaisala RS41 and the Vaisala RS92, the SRSC50 and RS41 have been validated by the GRUANcertified RS92. Figures 1 and 2 show the statistical biases of RS41 and SRSC50 with respect to the reference RS92 as a function of height for the day and nighttime launches. The differences have been coadded into altitude boxes of 2 km, and the profiles have been sampled every 30 s starting from 15 s after launch. The boxes in the plots have boundaries at the 25th and 75th percentiles and are centred (black dot in each box) in the mean value bias.
The RS41 and SRSC50 show an overall negative bias during both day and night never exceeding −0.1 K along the whole troposphere. Only in the midstratosphere, above 30 km, does the daytime biases reach −0.5 K. In the framework of our study, the region of interest for the temperature profiles measured by RALMO is the troposphere and, more rarely, the UTLS (upper troposphere and lower stratosphere, ∼0–14 km). In this region, as the statistics show, the two ORSs perform very well. For the daytime comparisons (11:00 UTC), the mean bias of RS41 over the region 0–14 km is $\mathrm{0.05}\pm \mathrm{0.03}$ K with a mean standard deviation of 0.15±0.05 K. For the nighttime comparisons (23:00 UTC), the mean bias of RS41 over the region 0–14 km is $\mathrm{0.05}\pm \mathrm{0.02}$ K with a mean standard deviation of 0.11±0.06 K. The statistics of SRSC50 for daytime (11:00 UTC) show a mean bias over the region 0–14 km of $\mathrm{0.08}\pm \mathrm{0.02}$ K and a mean standard deviation of 0.19±0.09 K. For the nighttime comparisons (23:00 UTC), the mean bias of SRSC50 over the region 0–14 km is $\mathrm{0.01}\pm \mathrm{0.02}$ K with a mean standard deviation of 0.13±0.04 K.
The comparisons with RS92 show that for both ORSs the daytime differences undergo a larger variability along the 0–14 km vertical range compared to the nighttime statistics. The main reason for the larger variability is that, during the daytime flights, RS92 and the two ORSs undergo different exposures to the solar radiation, which causes a different response of the thermocouple sensors. The effect on the thermocouple becomes larger with altitude as the solar radiation increases with height. All RSs are corrected by the manufacturer for the effects of solar radiation on the thermocouple sensors. However, different manufacturers use different radiation corrections, which contributes to the statistical broadening of the differences at all levels. The overall (11:00 and 23:00 UTC) performance of the two ORSs in terms of bias with respect to the reference RS92 is summarized in Fig. 3. The distribution and mean value of the differences confirm that in the first 15 km the two ORSs remain well below the −0.1 K bias. The RS41 shows closer values to RS92 than SRSC50 especially in the stratosphere. The better statistics of RS41 should be interpreted also in light of the fact that RS92 and RS41 are both manufactured by Vaisala.
RALMO was designed and built by the École Polytechnique Fédérale de Lausanne (EPFL) in collaboration with MeteoSwiss. After its installation at the MeteoSwiss station of Payerne (46^{∘}48.0^{′} N, 6^{∘}56.0^{′} E; 491 m a.s.l.) in 2007 it has provided profiles of q, T and aerosol backscatter (β) in the troposphere and lower stratosphere almost uninterruptedly since 2008 (Brocard et al., 2013; Dinoev et al., 2013). The T data during the 2008–2010 period are unexploited due to low quality of the analogue channel. RALMO has been designed to achieve a measurement precision better than 10 % for q and 0.5 K for T with a 30 min integration time and to reach at least 5 km during daytime and 7 km during nighttime in clearsky conditions. RALMO uses highenergy emission, narrow field of view of the receiver and a narrowband detection to achieve the required daytime performance. The data acquisition software has been developed to ensure autonomous operation of the system and realtime data availability. RALMO's frequencytripled Nd:YAG laser emits 400 mJ per pulse at 30 Hz and at 355 nm. A beam expander expands the beam's diameter to 14 cm and reduces the beam divergence to 0.09±0.02 mrad. The returned signal is an envelope of the 355 nm elastic and Ramanbackscattered signals, i.e. PRR, water vapour, oxygen, nitrogen and Rayleigh. Next, the Raman lidar equation (RLE) for the PRR signal is presented along with the detailed description of how RALMO selects the high and low quantumshifted wavelengths used in the RLE to retrieve the temperature.
3.1 Pure rotational Raman temperature
Raman lidar measurements of the atmospheric temperature rely on the interaction between the probing electromagnetic signal at wavelength (λ) emitted by the lidar and the molecules of O_{2} and N_{2} encountered along the probing path. In addition to the Rayleigh light backscattered by the aerosols and molecules at the same frequency as the incident light, the O_{2} and N_{2} molecules return a frequencyshifted Raman signal back to the lidar's receiver. The Ramanbackscattered signal is shifted in frequency due to the rotational and vibrational Raman effect. In this study only the purerotational part of the spectrum around the Rayleigh frequency (Cabannes line) is detected by RALMO and analysed (Fig. 4).
The Raman lidar equation, RLE, yields the intensity of the PRR signal S_{PRR}:
The received S_{PRR} signal measured over time t is a function of the altitude z; C is the lidar constant; O(z) is the geometrical overlap between the emitted laser and the receiver's field of view; n(z) is the number density of the air; Γ_{atm}(z) is the atmospheric transmission; τ(J_{i}) is the transmission of the receiver for each PRR line J_{i}; η_{i} is the volume mixing ratio of nitrogen and oxygen; $\left(\frac{\mathrm{d}\mathit{\sigma}}{\mathrm{d}\mathrm{\Omega}}{)}_{\mathrm{\Pi}}^{i}\right({J}_{i})$ is the differential Raman cross section for each PRR line J_{i}; and B is the background of the measured signal. Air mainly contains oxygen and nitrogen (≈99 %) whose ratio remains fairly constant in the first 80 km of atmosphere, so η_{i} can be regarded as a constant in Eq. (1). The lidar constant C depends on the overall efficiency of the transceiver (transmitter and receiver) system including the photomultiplier tube (PMT) efficiency, on the area of the telescope and on the signal's intensity. The full expression of the differential Raman cross section for single lines of the PRR spectrum can be found in the reference book chapter by Behrendt (2005).
3.2 Temperature polychromator of RALMO
The twostage temperature polychromator, hereafter referred to as PRR polychromator, represents the core of the signal selection. The PRR polychromator separates several pure rotational Raman spectral lines and isolates elastic scattering consisting of Rayleigh and Mie lines (Cabannes line).
The PRR signal from the O_{2} and N_{2} atmospheric molecules is collected by four parabolic, highefficiency reflecting mirrors each one with a diameter of 30 cm. The mirrors have a dielectric reflection coating with R>99 % for the vibrational Raman wavelengths and R>96 % for the elastic and pure rotational Raman for both cross and parallelpolarized light. Ninedegreetilted Semrock RazorEdge filters (REFs) are installed just below the focal points of two of the four mirrors (left of Fig. 5). The REFs are longwavelength pass filters and have a cutoff wavelength at 364 nm (right of Fig. 5). The rovibrational Raman scattering from the atmospheric H_{2}O, O_{2} and N_{2} molecules is transmitted by the REF onto the optic fibres placed above the REF at the exact focal distance of the parabolic mirrors. The elastic (Rayleigh and Mie) and PRR scattering are reflected by the tilted REF onto 0.4 mm optic fibres and transmitted to the PRR polychromator.
The two optic fibres transmitting the PRR and the elastic signals enter the temperature polychromator through the first fibre's block shown in Fig. 6. The fibres are fixed into the fibre's block, ensuring no or negligible temperature and mechanicalinduced drifts of the fibre alignment with respect to the other optical elements inside the polychromator (detailed in Fig. 7). The outline of the two fibre block's Cartesian coordinates system in Fig. 6 shows the position of the input, output and intermediate fibres (from stage 1 to stage 2) as a function of their abscissa–ordinate, x–y, positions. At x=21.5 mm, the input fibres, coming from the mirrors, are located at y=20 mm and y=24 mm; the output “elastic” fibres are located at y=18 mm and y=22 mm. The two output elastic signals are then transmitted through the fibres and combined together just before entering the PMT installed outside the polychromator's box (PMT R12421P, Hamamatsu). The two input fibres transmit the PRR and the elastic signals onto an aspheric lens with focal length of 300 mm and diameter of 150 mm. The two signals are then transmitted through the lens onto a reflective holographic diffraction grating with groove density of 600 grooves mm^{−1} oriented at a diffraction angle of 48.15^{∘} with respect to the axis of the lenses in a Littrow configuration. The two input signals (one from each mirror) are diffracted by the grating polychromator and separated into high and low quantum number lines from both Stokes and antiStokes parts of the Ramanshifted spectrum. Two groups of four spectral lines are then diffracted, i.e. ${J}_{\mathrm{high}}^{\mathrm{Stokes}}$, ${J}_{\mathrm{high}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$, ${J}_{\mathrm{low}}^{\mathrm{Stokes}}$ and ${J}_{\mathrm{low}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$.
The theoretical polychromator efficiencies ξ (ξ∈ [0–1]) for the nitrogen and oxygen PRR lines ${J}_{\mathrm{high}}^{\mathrm{Stokes}}$, ${J}_{\mathrm{high}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$, ${J}_{\mathrm{low}}^{\mathrm{Stokes}}$ and ${J}_{\mathrm{low}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$ are shown in Tables 1 and 2, respectively. The low and high quantumnumber signals, J_{low} and J_{high}, Ramanbackscattered by the nitrogen molecules are diffracted by the polychromator most efficiently at lines with quantum number n=6 (${J}_{\mathrm{low}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$, λ=353.97 nm, ${J}_{\mathrm{low}}^{\mathrm{Stokes}}$, λ=355.47 nm) and n=12 (${J}_{\mathrm{high}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$, λ=353.37 nm, ${J}_{\mathrm{high}}^{\mathrm{Stokes}}$, λ=356.07 nm). Similarly to the nitrogen, the PRR signals backscattered by the oxygen molecules are diffracted by the polychromator most efficiently at lines with quantum number n=9 (${J}_{\mathrm{low}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$, λ=353.96 nm, ${J}_{\mathrm{low}}^{\mathrm{Stokes}}$, λ=355.48 nm) and n=17 (${J}_{\mathrm{high}}^{\mathrm{anti}\text{}\mathrm{Stokes}}$, λ=353.38 nm, ${J}_{\mathrm{high}}^{\mathrm{Stokes}}$, λ=356.06 nm).
Signals J_{low} and J_{high} are sums of the respective Stokes and antiStokes lines for nitrogen and oxygen. The eight J signals diffracted by the polychromator are then refocused by the aspheric lens onto the intermediate fibres positioned at the y ordinates y=18 mm and y=22 mm and at the x abscissae x=18.93 mm, x=20.075 mm, x=22.925 mm and x=24.07 mm.
The eight Stokes and antiStokes J signals are transmitted through the intermediate fibres into the second fibre's block (right of Fig. 6) and subsequently transmitted along an optical path almost identical to the one in stage 1. Unlike stage 1, the eight J signals are recombined by the diffraction grating polychromator into two groups of total J signals (J_{high} and J_{low}). The general outline of the twostage PRR polychromator is shown in Fig. 7.
The total J signals are focused by the aspheric lens onto the output fibres positioned in the second fibre's block (right of Fig. 6) at the same x abscissa x=21.5 mm and at the y ordinates y=24.5 mm (J_{high}), y=21.5 mm (J_{high}), y=19 mm (J_{low}) and y=16 mm (J_{low}). The output fibres transmit the four J_{high} and J_{low} signals from the two mirrors to two separate PMT boxes installed outside the polychromator's unit. Inside each PMT box, two J signals are combined by an imaging system made by two lenses focusing onto a common spot. This last recombined signal is then divided by a beam splitter into two signals, one at 10 % and the other at 90 % of the intensity, which are focused onto two independent PMTs. A total of four signals are then obtained at the end of the receiver chain, i.e. ${J}_{\mathrm{high}}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$, ${J}_{\mathrm{high}}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$, ${J}_{\mathrm{low}}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$ and ${J}_{\mathrm{low}}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$.
3.3 PRR channel acquisition system
The acquisition of RALMO's PRR channels were migrated in August 2015 from the Licel acquisition system to the FAST ComTec P7888 (FastCom) system. The P7888 model is one of the fastest commercially available multipleevent time digitizers with four inputs (one for each PRR channel) with very short acquisition system dead time and consequently minimum saturation effects of the photoncounting channels. Compared to the Licel acquisition system, FastCom acquires the PRR channels solely in photoncounting mode, with higher range resolution and with about twice shorter dead time, τ. The FastCom acquisition system acquires two lowtransmission channels (${J}_{\mathrm{high}}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$, ${J}_{\mathrm{low}}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$) and two hightransmission channels (${J}_{\mathrm{high}}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$, ${J}_{\mathrm{low}}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$). Most photoncounting acquisition systems are limited in performance by the dead time τ, i.e. the minimum amount of time in which two input signals may be resolved as separate events. Whenever two consecutive photons impinge on the detector with separation time t<τ, the system counts only one event. Certain types of acquisition systems can be corrected for the underestimation induced by τ; the correction of the PRR signals measured by the FastCom system is presented in the Sect. 4.
The high and lowfrequencyshifted S_{PRR} signals have the expression given in Eq. (1). In order to use them to retrieve the temperature profile, Eq. (1) shall be corrected for the dead time and the background. Once the signals are corrected, their ratio is used to retrieve the temperature from Eq. (3) scaled by two coefficients A and B. The atmospheric temperature is then obtained from the calibration of Eq. (3) with respect to T_{ors} and the determination of A and B. The calibrated temperature is then provided along with its uncertainty. Table 3 summarizes the vertical and temporal resolution of the S_{PRR} signal at different stages of the data processing. The vertical resolution of T_{ral} is not constant with altitude and depends on the calculated total random uncertainty in Eq. (6). A Savitzky–Golay digital filter with polynomial degree K=1 is applied to the T_{ral} profiles to degrade the sampling resolution and reduce the sampling noise. The adopted procedure and the definition of the obtained vertical resolution are compliant with the NDACC (Network for the Detection of Atmospheric Composition Change) recommendations detailed in the work by Leblanc et al. (2016). The initial and highest resolution is δz_{max}=30 m, which is degraded to a minimum δz_{min}=400 m corresponding to the regions where the error is large (normally, the upper troposphere and lower stratosphere). For clearsky measurement, an upper altitude cutoff is set at the altitude where the error exceeds 0.75 K; in the presence of clouds, the upper limit is set by the cloud base detected by a colocated ceilometer. Very often, the clearsky cutoff altitude corresponds to an altitude between 5 and 7 km during daytime measurements.
4.1 Correction of S_{PRR}
The PRR signals are corrected for the systematic underestimation of the true photoncounting signal (dead time) and for the offsets (instrumental and solar). The first correction is then for the acquisition system's dead time τ. The lowtransmission channels ${J}_{\mathrm{high}}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$ and ${J}_{\mathrm{low}}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$ do not become saturated and are used as reference channels to identify the saturation of the hightransmission channels ${J}_{\mathrm{high}}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$ and ${J}_{\mathrm{low}}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$. Assuming that the PMTs and the associated electronics obey the nonparalyzable assumption (Whiteman et al., 1992), we have studied the departure from the constant ratio ${J}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}/{J}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$ as a function of τ. We have applied a method based on the nonparalyzable condition (Newsom et al., 2009) to a year of data and have calculated τ for all the cases when the saturation clearly affected the hightransmission channels J^{90 %}.
As soon as the saturation has its onset, the ratio ${J}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}/{J}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}$ ceases to be constant and the saturated J^{90 %} yields smaller count rates than the true ones. When the J^{90 %} is desaturated using the correct τ, it gives the τcorrected signal ${J}_{\mathrm{desat}}\left(\mathit{\tau}\right)={J}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}/(\mathrm{1}\mathit{\tau}{J}^{\mathrm{90}\phantom{\rule{0.125em}{0ex}}\mathit{\%}})$. Onethousand linear fits J^{10 %}=f(J_{desat}(τ_{i})) are performed with τ_{i} varying within the interval τ_{i}∈ [0–10] ns at steps of 0.01 ns. The linear fits J^{10 %}=f(J_{desat}(τ_{i})) are performed over a temporal interval of 30 min and a vertical range defined by the count rates within the maximum range [0.5–50] MHz: C_{min} and C_{max}, respectively. For each linear fit, we calculate the value e(τ_{i}) that provides the distance in the countrate domain between J^{10 %} and f(J_{desat}(τ_{i})) as a function of τ_{i}. The minimization of e(τ) with respect to τ_{i} determines the value of the acquisition system's dead time ${\mathit{\tau}}_{i}={\mathit{\tau}}_{\mathrm{min}}\in $ [0–10] ns for each channel. The obtained value τ_{min} is used to desaturate J^{90 %} and to reestablish the constant ratio ${J}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}/f\left({J}_{\mathrm{desat}}\right({\mathit{\tau}}_{\mathrm{min}}\left)\right)$, which equals a constant. Figure 8 shows an example calculation of τ_{min} for the hightransmission channel of J_{low}. The curve function e(τ) in the figure's left panel has a minimum at τ_{min}=3 ns. On the right panel, the uncorrected and the τcorrected relations are shown. The uncorrected relation ${J}^{\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathit{\%}}=f\left({J}_{\mathrm{desat}}\right(\mathit{\tau}=\mathrm{0}\left)\right)$ (solid black) departs from the linear relation J^{10 %}=f(J_{desat}(τ_{min})) (dashed green) as soon as the count rates exceed the lower bound C_{min} (dashed red). By applying this method to a year of data and collecting more than 100 cases, we have determined the mean dead times τ_{jh}=1.4 ns and τ_{jl}=3 ns for J_{high} and J_{low}, respectively. The desaturated J_{high} and J_{low} are further corrected for the background and the procedure is described hereafter.
The electronic and solar background must be subtracted from S_{PRR} before retrieving T_{ral}. While the electronic background is stable and does not undergo daily or seasonal cycles, the solar background changes in intensity with the position of the sun Φ (the angle between the zenith and the centre of the sun's disc). We have found that subtracting the mean value of the farrange signal (z∈ [50–60] km) from S_{PRR} (subtraction of term B from Eq. 1) causes a systematic negative bias with respect to T_{ors} of about 1 K at all altitudes z during daytime. A relative change of 1 % in the ratio ${J}_{\mathrm{low}}/{J}_{\mathrm{high}}$ due to an imperfect background subtraction can lead to a variation of up to 2 K in the retrieved temperature T_{ral}. Because the solar background (SB) dominates the total background of S_{PRR}, we focus on the correction of the background B only as a function of the position of the sun. We have developed an empirical correction function f(Φ) applied to the background prior to subtraction from S_{PRR}. The function f(Φ) is applied to the background B and provides the corrected background ${B}_{\mathrm{corr}}=f\left(\mathrm{\Phi}\right)\cdot B$. Through the year's cycle, B is reduced by a maximum amount of 1 % via the action of f(Φ). As Eq. (2) shows, f(Φ) reaches daily minima when $\mathrm{\Phi}={\mathrm{\Phi}}_{\mathrm{min}}^{\mathrm{day}}$ (noon) and returns to 100 % when Φ≥90^{∘} (after sunset and before sunrise). During the daily and annual cycle, f(Φ) then oscillates within the range f(Φ)∈ [99 %–100 %], reducing B by the maximum amount of 1 % (f(Φ)=99 %) at noon on 21 June when $\mathrm{\Phi}={\mathrm{\Phi}}_{\mathrm{min}}^{\mathrm{year}}$.
If uncorrected, the retrieved daytime T_{ral} suffers a bias at all heights with respect to T_{ors}. The bias is largest when $\mathrm{\Phi}={\mathrm{\Phi}}_{\mathrm{min}}^{\mathrm{day}}$. The correction f(Φ) is applied only to the background of J_{high}. The intensity of J_{high} is generally lower than J_{low} at all atmospheric temperatures (see Sect. 4) and so is its signaltonoise ratio (SNR). Even a small error of ≈1 % when subtracting B from J_{high} has a major impact on its SNR; f(Φ) corrects the imperfect subtraction of B from J_{high} and minimizes the daytime bias of T_{ral} with respect to T_{ors} almost perfectly.
4.2 Estimation of total random uncertainty
Once B_{corr} is subtracted from the τcorrected S_{PRR}, the deviation of T_{ral} from T_{ors} depends only on how precisely Eq. (3), derived from the RLE, represents the true atmospheric temperature at the altitude z and time t. The random uncertainty does not account for the error induced by the saturation and the background, which are considered purely systematic. The highfrequencyshifted (J_{high}) and lowfrequencyshifted (J_{low}) signals in the Stokes and antistokes Q branches depend on the temperature of the probed atmospheric volume (Fig. 4). The ratio of the S_{PRR} intensities $Q\left(z\right)={J}_{\mathrm{low}}\left(z\right)/{J}_{\mathrm{high}}\left(z\right)$ is a function of the atmospheric temperature T at the distance z. Based on the calculations shown by Behrendt (2005) and for systems that can detect independent J lines in each channel, the relationship between T and Q would take the form of Eq. (3) with an equals (=) sign. The approximately equal to sign (≈) in Eq. (3) indicates that the detection system detects more than one J line and thus brings an inherent error. The calibration coefficients A and B are a priori undetermined and can be determined by calibration of T_{ral} with respect to T_{ors}.
The coefficients A and B are determined by calibrating T_{ral} with respect to T_{ors}. The coefficient A has units in kelvin as Eq. (3) is not normalized for the standard atmospheric temperature (Behrendt and Reichardt, 2000). The linear relation $y=A/(x+B)$ is used, where x is the ratio Q, and y is the reference temperature T_{ors}. The mean error on T_{ors} for both RS41 and SRSC50 is $\approx \mathrm{0.04}\pm \mathrm{0.15}$ K at 11:00 and 23:00 UTC between 0 and 14 km (Sect. 2). Due to the very small error on T_{ors}, we can calculate the uncertainty U_{fit} of the fitting model only in terms of the fitting parameters' errors σ_{A} and σ_{B} (Eq. 4). As it will be shown in the next section, the covariance σ_{AB} of A and B is very close to zero ($<{\mathrm{10}}^{\mathrm{3}}$); thus, σ_{A} and σ_{B} can be treated as statistically independent and used to calculate U_{fit} from the firstorder Taylor series of propagation of fitting parameter uncertainties.
U_{fit} is not the only error source; a second contribution to the total uncertainty comes from the fact that S_{PRR} is acquired by a photoncounting system and is affected by the measurement's noise that can be calculated using standard Poisson statistics. The error σ_{J} for Poissondistributed data is equal to the square root of the S_{PRR} signals, ${\mathit{\sigma}}_{{J}_{\mathrm{low}}}=\sqrt{{J}_{\mathrm{low}}}$ and ${\mathit{\sigma}}_{{J}_{\mathrm{high}}}=\sqrt{{J}_{\mathrm{high}}}$. In Eq. (5), coefficients A and B can be regarded as independent from the noise on S_{PRR}, as the contribution of it is already included in σ_{A} and σ_{B} in Eq. (4).
The total uncertainty of the calibrated T_{ral} is a typeB uncertainty (JCGM, 2008) and is the sum of the independent error contributions U_{fit} and U_{sig}.
4.3 Calibration of S_{PRR}
For a very stable system like RALMO, calibrations can be performed once every few months to compensate for any occurring drift of the detection system's sensitivity and/or efficiency. Calibrations of RALMO are performed using Eq. (3) in clearsky conditions during nighttime to remove the effect of solar background and have a larger vertical portion of T_{ral} available for calibration (the daytime profiles have normally a lower cutoff altitude). Figure 9 shows a case of RALMO calibration; the greenshaded area represents ±2U_{T} (k=2).
The calibrated T_{ral} results from the integration of 30 τ and Bcorrected S_{PRR} profiles (δt=30 min) into Eq. (3). At a given atmospheric altitude z during the time interval δt, U_{T}(z)_{δt} is made of the single contributions U_{sig}(z,t) and U_{fit}(z,t). U_{sig}(z,t) can be regarded as independent with respect to time; on the other hand, the errors U_{fit}(z,t) depend on the atmospheric processes occurring within the layer [$z\mathit{\delta}z/\mathrm{2},z+\mathit{\delta}z/\mathrm{2}$] during the time interval [$t\mathit{\delta}t/\mathrm{2},t+\mathit{\delta}t/\mathrm{2}$] and are, a priori, not statistically independent. By assuming that all errors in Eq. (6) are statistically independent, we assume that the offdiagonal elements of the variance–covariance matrix are all zero. By doing so, U_{T}(z)_{δt} could be underestimated by an amount equal to the nonzero covariance terms, including the covariance σ_{AB}. A method to assess the exhaustiveness of the theoretical error U_{T} is to calculate how many points in the vector $\mathrm{\Delta}T={T}_{\mathrm{ral}}{T}_{\mathrm{ors}}$ fall within the interval $[k\mathit{\sigma},+k\mathit{\sigma}]$ and check if they are compatible with the Gaussian probability levels 68.3 %, 95.5 % and 99.7 % for $k=\mathrm{1},\mathrm{2}$, and 3, respectively. As it is shown in the right panel of Fig. 9, almost all points along the vector T_{ral}−T_{ors} fall within the interval $[\mathrm{2}\mathit{\sigma},+\mathrm{2}\mathit{\sigma}]$, i.e. the 98.1 % envelope. For k=1, the percentage falls slightly below the expected level for a normal distribution with only 61.2 % of the points within $[\mathit{\sigma},+\mathit{\sigma}]$. Between July 2017 and December 2018, a total of seven calibrations have been performed (three SRSC50 and four Vaisala RS41). The mean percentage of points over all performed calibrations is 65.1 % for k=1; 97.9.1 % for k=2; and 99.98 % for k=3. These values seem to confirm an overall exhaustiveness of U_{T} with a slight underestimation of 3.2 % at k=1. The list of calibrations is shown in Table 4. For each calibration, the table lists the date and end time of the calibration, the calibration coefficients A and B used in the fitting model Eq. (3), the errors σ_{A} and σ_{B}, the covariance σ_{AB}, and the ORS used to calibrate T_{ral}. As to further support the assumption of zero covariance of the coefficients A and B, all covariances σ_{AB} in the table are smaller than $\mathrm{1.71}\times {\mathrm{10}}^{\mathrm{3}}$. Between two consecutive calibrations performed at times t_{i} and t_{i+1}, the coefficients A(t_{i}) and B(t_{i}) are used to calibrate all profiles T_{ral} during the time interval $t\in [{t}_{i},{t}_{i+\mathrm{1}}]$.
More than 450 profiles T_{ral} (245 nighttime, 215 daytime) have been compared to T_{ors} and assessed separately for daytime and nighttime based on the bias and standard deviation (σ) of the differences $\mathrm{\Delta}T={T}_{\mathrm{ral}}{T}_{\mathrm{ors}}$ over the period 1 July 2017–31 December 2018. Two criteria to select the cases for the dataset have been used:
 1.
Only cases with no precipitation and no low clouds or fog are retained.
 2.
Only cases with ΔT<5 K are retained.
Criterion 1 is performed by setting a threshold for minimum cloud base, h_{b}, at 1000 m (a.g.l.), for any values of h_{b}<1000 m that T_{ral} is not retrieved. Whenever h_{b}>1000 m, the cutoff altitude will correspond to h_{b}. Indeed, above h_{b}, the SNR drops abruptly and U_{T}(z)≫1 K. For this reason, especially during winter, when longlasting stratus clouds occur in the altitude range 1–4 km, the nighttime and daytime T_{ral} profiles are limited in range to the altitude h_{b} (or are not calculated if h_{b}<1000 m). Criterion 2 is performed by setting a threshold at 33 % of the number of elements along the profile ΔT exceeding 5 K. If more than 33 % of the elements along ΔT exceed the threshold, the whole of T_{ral} is rejected and not included in the statistics. For any value below the threshold, the outliers are removed from T_{ral}. This is justified by the fact that exceedances counting more than 33 % are caused by temporary misalignment of the transceiver unit. On the other hand, exceedances well below the threshold can always occur (especially in the higher part of the profile) due to low SNR or unfiltered clouds. In Table 5 we present a summary of the statistical parameters characterizing the daytime and nighttime differences ΔT that will be discussed in detail in the following sections. The dataset ΔT is described in terms of maximum mean bias ΔT_{max}, average mean bias μ, standard deviation σ and maximum availability N_{max} of the differences ΔT along the atmospheric range.
Besides a global validation, we also present and discuss the seasonal statistics in order to better characterize the system performance.
5.1 Nighttime temperature statistics
The nighttime ΔT_{max}, μ, σ and N_{max} of ΔT are the metrics to assess the accuracy and precision of T_{ral} with respect to T_{ors}. Figure 10 shows that ΔT_{max}=0.24 K, $\mathit{\mu}=\mathrm{0.05}\pm \mathrm{0.34}$ K, $\mathit{\sigma}=\mathrm{0.66}\pm \mathrm{0.06}$ K and N_{max}=244 over the tropospheric region [0.5–10] km.
In addition to the uncertainty assessment performed in Sect. 4.3, the exhaustiveness of the theoretical total uncertainty U_{T} can be further assessed by comparing U_{T} with σ. The mean value of U_{T} along the troposphere and over the seven nighttime calibrations is ${\stackrel{\mathrm{\u203e}}{U}}_{T}=\mathrm{0.64}$ K; the mean nighttime standard deviation averaged over the tropospheric column in Fig. 10 is $\stackrel{\mathrm{\u203e}}{\mathit{\sigma}}=\mathrm{0.66}$ K. The two 1−k uncertainties are then fully compatible.
The nighttime ΔT data are characterized by values of μ and σ smaller than 1 K, with minimum values in the lower troposphere from [0–5] km. It is indeed in the lower troposphere, where σ is ≈0.6 K, i.e. 0.1 K larger than the 0.5 K requirement for data assimilation into the numerical weather prediction COSMO forecasting system (Fuhrer et al., 2018; Klasa et al., 2018, 2019). In order to achieve a successful assimilation of T_{ral} into COSMO, the overall impact of the assimilation shall correspond to an improvement of the forecasts without increasing the forecast uncertainties. Assimilation of highSNR, wellcalibrated T_{ral} into numerical models leads to the improvement of the forecasts. In the study by Leuenberger et al. (2020), the authors assimilate, amongst other data, temperature and humidity profiles from RALMO, showing the beneficial impact on the precipitation forecast over a wide geographical area.
5.2 Daytime temperature statistics
During daytime, the retrieved temperature profiles are limited in range to about 6 km. The left and right panels of Fig. 11 show the bias ΔT and the standard deviation σ, respectively. The ΔT_{max}, μ, σ and N_{max} of the daytime ΔT over the lower troposphere (0.5–6 km) are 0.25 K, 0.02±0.1 K, 0.62±0.03 K and 212, respectively. The data availability goes rapidly to zero above 5 km.
The daytime T_{ral} profiles have been corrected for the solar background by f(Φ), which proves to be very efficient in removing the noon bias with respect to T_{ors}. To ensure that the correction f(Φ) does not introduce any additional bias during the daily cycle, we have compared T_{ral} with the temperature calculated by the COSMO model. More than 3 months of clearsky 24 h T_{ral}−T_{cos} differences have been collected, yielding a mean daily cycle at the level 1.4–1.7 km a.s.l. The comparison in Fig. 12 shows that RALMO does not suffer any systematic daily Φdependent bias.
In order to study the seasonal effects on μ and σ, the ΔT dataset was divided into seasons. The four seasons are defined as follows: summer from 1 June to 30 August, autumn from 1 September to 30 November, winter from 1 December to 15 March, and spring from 16 March to 31 May. Because of the less favourable conditions in winter due to precipitation and low clouds, only few temperature profiles are available during this period. Additionally, during winter 2018, from January until midMarch, RALMO measurements have been stopped for about 80 % of the time due to maintenance work. The results are summarized in Tables 6 and 7 in terms of μ, σ and maximum availability N_{max} over the lower tropospheric range 0–6 km for daytime and over 0–10 km for nighttime. With the only exception of winter, the other seasons have enough profiles to perform a statistical analysis and to draw quantitative conclusions about the contribution of each season to the overall values μ and σ.
6.1 Seasonal daytime temperature statistics
The seasonal daytime μ and σ profiles are analysed to understand if sources of systematic errors other than SB affect the retrieved T_{ral}. The seasonal profiles are shown in Figs. 13 and 14 and summarized in Table 6. Due to the less favourable weather conditions and the maintenance work, the winter statistics count only eight profiles. The statistical characterization of the winter dataset can then only be qualitative. Summer and spring are the seasons with the minimum values of Φ at noon; during these two seasons, T_{ral} is most affected by SB. If uncorrected for f(Φ), the noon T_{ral} suffers a negative mean bias of about 2 K at all heights (not shown here). Summer counts more than twice the number of cases in the spring dataset; nevertheless, for both seasons the values of μ are compatible with a zero bias within their uncertainties (both σ=0.64 K). Despite the less favourable weather conditions compared to spring and summer, autumn is the season with most cases, and this is because there are two autumn seasons in the dataset. Like spring and summer, autumn also has μ compatible with the zero bias within its uncertainty. Through the four seasons, the mean σ spans from 0.4 to 0.65 K.
Figure 13 suggests that T_{ral} is not affected by any obvious systematic error ($\mathit{\mu}\simeq \mathrm{0}\in [\mathit{\sigma},+\mathit{\sigma}]$) and no seasonal cycle appears in the statistics. From the perspective of the statistical validity of the studied data, any subsample chosen randomly from the total T_{ral} dataset can be described by the same μ and σ that characterizes ΔT.
Unlike Fig. 13, the σ profiles in Fig. 14 show different behaviours in summer–autumn and in winter–spring. The summer and autumn σ profiles in the upperleft and upperright panels undergo a decoupling between the lower and upper part of the profile with inversion point slightly higher in autumn. An increase in σ with height is something expected and can be explained with the decreased data availability and the decreased SNR due to the large distance from the lidar's telescope. However, the abrupt increase in σ at ≈3 km in summer and at ≈4.5 km in autumn is more related to the atmospheric dynamics than to the SNR. In summer, the transition between the boundary layer and the free troposphere is a region of high variability in terms of temperature and humidity. The alternating cold downdraughts and warm updraughts engendered by the overall fair weather conditions and the continuous development of thermals through the boundary layer (Martucci et al., 2010) cause a large variability of T_{ral} at ≈3 km, which translates into large σ values. In autumn, the thermal activity at the top of the boundary layer is less pronounced than in summer; on the other hand, a temperature inversion linked to the formation and dissipation of stratus clouds above Payerne occurs at ≈4.5 km, causing larger discrepancies in the comparison with T_{ors}.
6.2 Seasonal nighttime temperature statistics
At nighttime, f(Φ) has no impact on the temperature retrieval, and the seasonal statistics can reveal sources of systematic error other than the SB causing $\left\mathit{\mu}\right>\mathrm{0}$. The separation into seasons helps with understanding if the overall zero bias shown in Fig. 10 hides seasonal nonzero biases that cancel out when combined in the full dataset. Compared to the daytime cases (215), the availability of the nighttime dataset is higher (245), including the winter dataset, which allows us to perform a statistical analysis for all seasons.
All seasonal μ values are compatible with the zero bias along the troposphere within $[\mathit{\sigma},+\mathit{\sigma}]$. Like the daytime seasonal statistics, the nighttime also does not reveal any obvious source of systematic error. The mean μ and σ in the troposphere are summarized in Table 7.
The nighttime atmosphere undergos different dynamics with respect to daytime. The absence of solar radiation almost entirely removes the convection from the boundary layer and minimizes the variance of the temperature at the top of the nocturnal and residual layers. Consequently, no sharp increase in the σ values is detected at any specific level during the different seasons. The σ profiles increase their value with height in response to the drop of the SNR due to the distance from the emission.
The validated T_{ral} is used to calculate the relative humidity using the humidity profiles also provided by RALMO. The relative humidity product has been validated in a parallel work by NavasGuzmán et al. (2019) that shows that in the first 2 km the RH suffers a mean systematic and random error of $\mathrm{\Delta}\text{RH}=+\mathrm{2}\phantom{\rule{0.125em}{0ex}}\mathit{\%}\pm \mathrm{6}\phantom{\rule{0.125em}{0ex}}\mathit{\%}\text{RH}$. The validated RH can be used to perform, amongst others, studies of supersaturation of water vapour in liquid stratus clouds. As future work, we will investigate the supersaturation corrected for the RH systematic error in a large statistical dataset of liquid clouds above Payerne across different seasons and years. The possibility to study supersaturation is critical to disentangle the microphysics of liquid clouds and better predict the amount of liquid water within the cloud.
More than 450 lidar temperature profiles have been compared to the temperature profiles measured by the reference radiosounding system at Payerne at 11:00 and 23:00 UTC during 1.5 years (July 2017–December 2018). The reference radiosounding systems (SRSC50 and Vaisala RS41) have been validated by the GRUANcertified Vaisala RS92 sonde in the framework of the quality assurance programme carried out at Payerne. A semiempirical modification has been developed and applied to the background correction procedure to reduce the daytime bias. The temperature profiles retrieved from RALMO PRR data show an excellent agreement with the reference radiosounding system during both daytime and nighttime in terms of maximum bias (ΔT_{max}), mean bias (μ) and standard deviation (σ). The ΔT_{max}, μ and σ of the daytime differences $\mathrm{\Delta}T={T}_{\mathrm{ral}}{T}_{\mathrm{ors}}$ over the tropospheric region (0.5–6 km) are 0.28, 0.02±0.1 and 0.62±0.03 K, respectively. The nighttime ΔT dataset is characterized by a mean bias $\mathit{\mu}=\mathrm{0.05}\pm \mathrm{0.34}$ K and $\mathit{\sigma}=\mathrm{0.66}\pm \mathrm{0.06}$ K, while ΔT is smaller than ΔT_{max}=0.29 K at all heights over the tropospheric region (0.5–10 km). We have compared the lidar temperature data against the temperature predicted by the COSMO model and found that there was no dependence of the bias and the standard deviation on the diurnal cycle. This result let us conclude that essentially the same data quality is achieved at day and night. A seasonality study has been performed to help with understanding if the obtained overall daytime and nighttime zero bias hides seasonal nonzero biases that cancel out when combined in the full dataset. The study reveals that all independent seasonal contributions of μ are compatible with the zero bias within their uncertainty. In general, the seasonal datasets confirm the fact that when subsampling the total ΔT dataset the subsamples can still be described by the same μ and σ.
We have shown that the temperature profiles obtained from the PRR RALMO data meet the OSCAR breakthrough uncertainty requirement of 1 K for highresolution NWP (https://www.wmosat.info/oscar/requirements, last access: 1 February 2021). Combined with the water vapour measurements the Raman lidar has a high potential to improve NWP through data assimilation as we have demonstrated recently (Leuenberger et al., 2020), and MeteoSwiss plans to assimilate the Raman lidar in Payerne operationally in the near future.
The code used to analyse the data is a MATLAB code, which is not available on a public repository, e.g. GitHub. The code is property of MeteoSwiss but can be made available in text format upon request to the authors.
The entire dataset used for the analysis shown in this study is available in ASCII format upon request. The dataset is undergoing currently the procedure to obtain a DOI. The dataset includes the following set of data:

the complete radiosounding and temperature datasets over the period July 2017–December 2018,

overall nighttime and daytime bias data (data used to create the left panels of Figs. 10 and 11),

overall nighttime and daytime standard deviation data (data used to create the right panels of Figs. 10 and 11),

seasonal nighttime and daytime bias data (data used to create Figs. 15 and 13),

seasonal nighttime and daytime standard deviation data (data used to create Figs. 16 and 14).
The first author, Giovanni Martucci, has developed the MATLAB code for lidar data processing; he has conducted the statistical analysis of the PRR data and has been the principal writer of the article. Francisco NavasGuzmán has contributed to the statistical validation of the PRR temperature; he has as well provided the full study of validation and uncertainty characterization of the relative humidity retrieved from RALMO humidity and temperature data. Ludovic Renaud has continuously maintained, optimized and improved the performance of RALMO, ensuring the very high data availability and data quality indispensable to perform the statistical analysis. Gonzague Romanens is responsible for the radiosounding data quality and availability. He has largely contributed to the creation of the Vaisala RS92, RS41 and SRSC50 dataset and has therefore made it possible to validate the radiosonde reference and hence the calibration of RALMO. S. Mahagammulla Gamage has provided the calculation of the theoretical polychromator efficiencies. Maxime Hervo has contributed to the validation of the correction function f(Φ) by direct comparison of the PRR temperature data with the temperature from the microwave radiometer. Pierre Jeannet has performed the statistical analysis leading to the validation of the Vaisala RS41 and the Meteolabor SRSC50 with respect to the reference sonde Vaisala RS92. He has as well created Figs. 1–3. Alexander Haefele is the head of the UpperAir division at MeteoSwiss; he has strongly contributed to the statistical analysis leading to the validation of the RALMO temperature, and he has as well supported actively the entire team of coauthors to achieve the results described in this study.
The authors declare that they have no conflict of interest.
This work has been supported entirely by the Federal Office of Meteorology and Climatology, MeteoSwiss, through the Swiss Government. Two projects that have contributed most through the years to improve the quality of the RALMO data are the Global Climate Observing System (GCOS) Reference UpperAir Network (GRUAN) and the Network for the Detection of Atmospheric Composition Change (NDACC). We thank the École Polytechnique Fédérale de Lausanne (EPFL) that codesigned and built RALMO.
This work has been supported by the Swiss National Science Foundation (project no. PZ00P2_168114).
This paper was edited by Vassilis Amiridis and reviewed by four anonymous referees.
Achtert, P., Khaplanov, M., Khosrawi, F., and Gumbel, J.: Pure rotationalRaman channels of the Esrange lidar for temperature and particle extinction measurements in the troposphere and lower stratosphere, Atmos. Meas. Tech., 6, 91–98, https://doi.org/10.5194/amt6912013, 2013. a
Adam, S., Behrendt, A., Schwitalla, T., Hammann, E., and Wulfmeyer, V.: First assimilation of temperature lidar data into an NWP model:impact on the simulation of the temperature field, inversion strength and PBL depth, Q. J. Roy. Meteor. Soc., 142, 2882–2896, https://doi.org/10.1002/qj.2875, 2016. a
Alpers, M., Eixmann, R., FrickeBegemann, C., Gerding, M., and Höffner, J.: Temperature lidar measurements from 1 to 105 km altitude using resonance, Rayleigh, and Rotational Raman scattering, Atmos. Chem. Phys., 4, 793–800, https://doi.org/10.5194/acp47932004, 2004. a
Argall, P. S.: Upper altitude limit for Rayleigh lidar, Ann. Geophys., 25, 19–25, https://doi.org/10.5194/angeo25192007, 2007. a
Balin, I., Serikov, I., Bobrovnikov, S., Simeonov, V., Calpini, B., Arshinov, Y., and van den Bergh, H.: Simultaneous measurement of atmospheric temperature, humidity, and aerosol extinction and backscatter coefficients by a combined vibrational–purerotational Raman lidar, Appl. Phys. BLasers O., 79, 775–782, https://doi.org/10.1007/s0034000416312, 2004. a
Behrendt, A.: Temperature measurements with lidar, in: Lidar, Springer, 273–305, 2005. a, b, c
Behrendt, A. and Reichardt, J.: Atmospheric temperature profiling in the presence of clouds with a pure rotational Raman lidar by use of an interferencefilterbased polychromator, Appl. Optics, 39, 1372–1378, https://doi.org/10.1364/AO.39.001372, 2000. a
Behrendt, A., Nakamura, T., and Tsuda, T.: Combined temperature lidar for measurements in the troposphere, stratosphere, and mesosphere, Appl. Optics, 43, 2930–2939, https://doi.org/10.1364/AO.43.002930, 2004. a
Bodeker, G. E. and Kremser, S.: Techniques for analyses of trends in GRUAN data, Atmos. Meas. Tech., 8, 1673–1684, https://doi.org/10.5194/amt816732015, 2015. a
Bösenberg, J.: Groundbased differential absorption lidar for watervapor and temperature profiling: methodology, Appl. Optics, 37, 3845–3860, https://doi.org/10.1364/AO.37.003845, 1998. a
Brocard, E., Philipona, R., Haefele, A., Romanens, G., Mueller, A., Ruffieux, D., Simeonov, V., and Calpini, B.: Raman Lidar for Meteorological Observations, RALMO – Part 2: Validation of water vapor measurements, Atmos. Meas. Tech., 6, 1347–1358, https://doi.org/10.5194/amt613472013, 2013. a
Cooney, J.: Measurement of Atmospheric Temperature Profiles by Raman Backscatter, J. Appl. Meteorol., 11, 108–112, available at: http://www.jstor.org/stable/26175549 (last access: 15 January 2021), 1972. a
Di Girolamo, P., Marchese, R., Whiteman, D. N., and Demoz, B. B.: Rotational Raman Lidar measurements of atmospheric temperature in the UV, Geophys. Res. Lett., 31, L01106, https://doi.org/10.1029/2003GL018342, 2004. a
Dinoev, T., Simeonov, V., Arshinov, Y., Bobrovnikov, S., Ristori, P., Calpini, B., Parlange, M., and van den Bergh, H.: Raman Lidar for Meteorological Observations, RALMO – Part 1: Instrument description, Atmos. Meas. Tech., 6, 1329–1346, https://doi.org/10.5194/amt613292013, 2013. a
Dirksen, R. J., Sommer, M., Immler, F. J., Hurst, D. F., Kivi, R., and Vömel, H.: Reference quality upperair measurements: GRUAN data processing for the Vaisala RS92 radiosonde, Atmos. Meas. Tech., 7, 4463–4490, https://doi.org/10.5194/amt744632014, 2014. a
Dirksen, R. J., Bodeker, G. E., Thorne, P. W., Merlone, A., Reale, T., Wang, J., Hurst, D. F., Demoz, B. B., Gardiner, T. D., Ingleby, B., Sommer, M., von Rohden, C., and Leblanc, T.: Managing the transition from Vaisala RS92 to RS41 radiosondes within the Global Climate Observing System Reference UpperAir Network (GRUAN): a progress report, Geosci. Instrum. Method. Data Syst., 9, 337–355, https://doi.org/10.5194/gi93372020, 2020. a
JCGM: JCGM 1002008: Evaluation of measurement data (GUM 1995 with minor corrections), JCGM: Joint Committee for Guides in Metrology, available at: http://www.iso.org/sites/JCGM/GUM/JCGM100/C045315ehtml/C045315e.html?csnumber=50461 (last access: 15 January 2021), 2008. a
Fuhrer, O., Chadha, T., Hoefler, T., Kwasniewski, G., Lapillonne, X., Leutwyler, D., Lüthi, D., Osuna, C., Schär, C., Schulthess, T. C., and Vogt, H.: Nearglobal climate simulation at 1 km resolution: establishing a performance baseline on 4888 GPUs with COSMO 5.0, Geosci. Model Dev., 11, 1665–1681, https://doi.org/10.5194/gmd1116652018, 2018. a
Gerding, M., Höffner, J., Lautenbach, J., Rauthe, M., and Lübken, F.J.: Seasonal variation of nocturnal temperatures between 1 and 105 km altitude at 54^{∘} N observed by lidar, Atmos. Chem. Phys., 8, 7465–7482, https://doi.org/10.5194/acp874652008, 2008. a
Hauchecorne, A., Chanin, M.L., and Keckhut, P.: Climatology and trends of the middle atmospheric temperature (33–87 km) as seen by Rayleigh lidar over the south of France, J. Geophys. Res., 96, 15297–15309, https://doi.org/10.1029/91JD01213, 1991. a
Hua, D., Uchida, M., and Kobayashi, T.: Ultraviolet Rayleigh–Mie lidar with Miescattering correction by Fabry–Perot etalons for temperature profiling of the troposphere, Appl. Optics, 44, 1305–1314, https://doi.org/10.1364/AO.44.001305, 2005. a
Klasa, C., Arpagaus, M., Walser, A., and Wernli, H.: An evaluation of the convectionpermitting ensemble COSMOE for three contrasting precipitation events in Switzerland, Q. J. Roy. Meteor. Soc., 144, 744–764, https://doi.org/10.1002/qj.3245, 2018. a
Klasa, C., Arpagaus, M., Walser, A., and Wernli, H.: On the Time Evolution of LimitedArea Ensemble Variance: Case Studies with the ConvectionPermitting Ensemble COSMOE, J. Atmos. Sci., 76, 11–26, https://doi.org/10.1175/JASD180013.1, 2019. a
Leblanc, T., Sica, R. J., van Gijsel, J. A. E., GodinBeekmann, S., Haefele, A., Trickl, T., Payen, G., and Gabarrot, F.: Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms – Part 1: Vertical resolution, Atmos. Meas. Tech., 9, 4029–4049, https://doi.org/10.5194/amt940292016, 2016. a
Leuenberger, D., Haefele, A., Omanovic, N., Fengler, M., Martucci, G., Calpini, B., Fuhrer, O., and Rossa, A.: Improving highimpact numerical weather prediction with lidar and drone observations, B. Am. Meteorol. Soc., 101, E1036–E1051, https://doi.org/10.1175/BAMSD190119.1, 2020. a, b, c
Li, Y., Lin, X., Song, S., Yang, Y., Cheng, X., Chen, Z., Liu, L., Xia, Y., Xiong, J., Gong, S., and Li, F.: A Combined Rotational RamanRayleigh Lidar for Atmospheric Temperature Measurements Over 5–80 km With SelfCalibration, IEEE T. Geosci. Remote, 54, 7055–7065, https://doi.org/10.1109/TGRS.2016.2594828, 2016. a
Martucci, G., Matthey, R., Mitev, V., and Richner, H.: Frequency of BoundaryLayerTop Fluctuations in Convective and Stable Conditions Using Laser Remote Sensing, Bound.Lay. Meteorol., 135, https://doi.org/10.1007/s1054601094743, 2010. a
NavasGuzmáán, F., Martucci, G., Collaud Coen, M., GranadosMuñoz, M. J., Hervo, M., Sicard, M., and Haefele, A.: Characterization of aerosol hygroscopicity using Raman lidar measurements at the EARLINET station of Payerne, Atmos. Chem. Phys., 19, 11651–11668, https://doi.org/10.5194/acp19116512019, 2019. a
Newsom, R. K., Turner, D. D., Mielke, B., Clayton, M., Ferrare, R., and Sivaraman, C.: Simultaneous analog and photon counting detection for Raman lidar, Appl. Optics, 48, 3903–3914, https://doi.org/10.1364/AO.48.003903, 2009. a
Newsom, R. K., Turner, D. D., and Goldsmith, J. E. M.: LongTerm Evaluation of Temperature Profiles Measured by an Operational Raman Lidar, J. Atmos. Ocean. Tech., 30, 1616–1634, https://doi.org/10.1175/JTECHD1200138.1, 2013. a
Stiller, G. P., Kiefer, M., Eckert, E., von Clarmann, T., Kellmann, S., GarcíaComas, M., Funke, B., Leblanc, T., Fetzer, E., Froidevaux, L., Gomez, M., Hall, E., Hurst, D., Jordan, A., Kämpfer, N., Lambert, A., McDermid, I. S., McGee, T., Miloshevich, L., Nedoluha, G., Read, W., Schneider, M., Schwartz, M., Straub, C., Toon, G., Twigg, L. W., Walker, K., and Whiteman, D. N.: Validation of MIPAS IMK/IAA temperature, water vapor, and ozone profiles with MOHAVE2009 campaign measurements, Atmos. Meas. Tech., 5, 289–320, https://doi.org/10.5194/amt52892012, 2012. a
Theopold, F. A. and Bösenberg, J.: Differential Absorption Lidar Measurements of Atmospheric Temperature Profiles: Theory and Experiment, J. Atmos. Ocean. Tech., 10, 165–179, https://doi.org/10.1175/15200426(1993)010<0165:DALMOA>2.0.CO;2, 1993. a
Vaughan, G., Wareing, D. P., Pepler, S. J., Thomas, L., and Mitev, V.: Atmospheric temperature measurements made by rotational Raman scattering, Appl. Optics, 32, 2758–2764, https://doi.org/10.1364/AO.32.002758, 1993. a
Whiteman, D. N., Melfi, S. H., and Ferrare, R. A.: Raman lidar system for the measurement of water vapor and aerosols in the Earth's atmosphere, Appl. Optics, 31, 3068–3082, https://doi.org/10.1364/AO.31.003068, 1992. a
Wing, R., Hauchecorne, A., Keckhut, P., GodinBeekmann, S., Khaykin, S., McCullough, E. M., Mariscal, J.F., and d'Almeida, É.: Lidar temperature series in the middle atmosphere as a reference data set – Part 1: Improved retrievals and a 20year crossvalidation of two colocated French lidars, Atmos. Meas. Tech., 11, 5531–5547, https://doi.org/10.5194/amt1155312018, 2018. a
Wulfmeyer, V. and Bösenberg, J.: Groundbased differential absorption lidar for watervapor profiling: assessment of accuracy, resolution, and meteorological applications, Appl. Optics, 37, 3825–3844, https://doi.org/10.1364/AO.37.003825, 1998. a
Wulfmeyer, V., Hardesty, R. M., Turner, D. D., Behrendt, A., Cadeddu, M. P., Di Girolamo, P., Schlüssel, P., Van Baelen, J., and Zus, F.: A review of the remote sensing of lower tropospheric thermodynamic profiles and its indispensable role for the understanding and the simulation of water and energy cycles, Rev. Geophys., 53, 819–895, https://doi.org/10.1002/2014RG000476, 2015. a
Zuev, V. V., Gerasimov, V. V., Pravdin, V. L., Pavlinskiy, A. V., and Nakhtigalova, D. P.: Tropospheric temperature measurements with the pure rotational Raman lidar technique using nonlinear calibration functions, Atmos. Meas. Tech., 10, 315–332, https://doi.org/10.5194/amt103152017, 2017. a
 Abstract
 Introduction
 Validation of the reference radiosounding systems
 The Raman Lidar for Meteorological Observations – RALMO
 Retrieval of T_{ral} and calculation of the uncertainty
 Validation of PRR temperature
 Seasonality study
 Future applications
 Conclusions
 Code availability
 Data availability
 Author contributions
 Competing interests
 Acknowledgements
 Financial support
 Review statement
 References
 Abstract
 Introduction
 Validation of the reference radiosounding systems
 The Raman Lidar for Meteorological Observations – RALMO
 Retrieval of T_{ral} and calculation of the uncertainty
 Validation of PRR temperature
 Seasonality study
 Future applications
 Conclusions
 Code availability
 Data availability
 Author contributions
 Competing interests
 Acknowledgements
 Financial support
 Review statement
 References