Among lidar techniques, the pure rotational Raman (PRR) technique is the
best suited for tropospheric and lower stratospheric temperature
measurements. Calibration functions are required for the PRR technique to
retrieve temperature profiles from lidar remote sensing data. Both
temperature retrieval accuracy and number of calibration coefficients depend
on the selected function. The commonly used calibration function (linear in
reciprocal temperature

The pure rotational Raman (PRR) technique is known to be the best suited for
lower atmosphere temperature measurements (Wulfmeyer et al., 2015). The
retrieval algorithm of vertical temperature profiles of the troposphere and
lower stratosphere from PRR lidar raw signals consists of four main steps:

PRR lidar raw data averaging to improve the signal-to-noise ratio and decrease the statistical uncertainties;

lidar calibration, i.e., determination of the lidar calibration function coefficients by applying, for example, the least square method to the reference radiosonde (or model) data and previously averaged lidar data;

temperature profile retrieval by using the temperature retrieval function derived from the selected calibration function;

estimation of the absolute and relative uncertainties of the temperature retrieval and calculation of the difference between the reference temperature (radiosonde, model) and temperature retrieved from lidar data.

Equidistant PRR spectra of N

In practice, diffraction gratings (DGs) or interference filters (IFs)
extract several adjacent PRR lines in the lidar temperature channels from
backscattered light. IFs extract PRR lines from the anti-Stokes branches of
N

Assuming that each PRR line profile represents the Dirac function, the
general calibration function can be written in a natural logarithm form as
follows (Gerasimov and Zuev, 2016):

IMCES lidar optical layout (see also Table 1): PC & DAS indicates personal computer and data acquisition system; PhC is the photon counter; PMT1–PMT3 are photomultiplier tubes; F0–F3 are optical fibers; FB is the four fiber bundle, connecting two monochromator blocks; DGM is the double-grating monochromator; L1 and L2 are lenses; DG1 and DG2 are diffraction gratings; BE is the beam expander with expansion factor of 10; M is the mirror; SM is the stepping motor.

IMCES lidar data taken between 03:45 and 05:15 LT on 1
April 2015 (31 March, 21:45–23:15 UTC).

In order to take into account the atmospheric extinction of backscattered
signals and their losses in the lidar transmitting and receiving optics, one
should consider the lidar equation (Measures, 1984)

In our recent Optic Express paper, we considered the physics of our approach,
derived mathematically the general calibration function that takes into
account the collisional broadening of all N

Temperature profiles from radiosondes launched on 1 April 2015 at 06:00 LT (00:00 UTC) in Novosibirsk (station 29634) and Kolpashevo (station 29231) as well as temperature points over Tomsk retrieved from constant pressure altitude charts (CPACs).

(1 April 2015) Temperature profile retrieved using the
temperature retrieval function (Eq. 11) derived from the standard linear
calibration function (Eq. 10, Arshinov et al., 1983). The absolute and
relative uncertainties

(1 April 2015) Temperature profile retrieved using the
temperature retrieval function (Eq. 13) derived from the standard calibration
function suggested by Behrendt and Reichardt (2000). The uncertainties

(1 April 2015) Temperature profile retrieved using the
temperature retrieval function (Eq. 15) derived from the calibration function
suggested by Gerasimov and Zuev (2016). The uncertainties

(1 April 2015) Temperature profile retrieved using the
temperature retrieval function (Eq. 18) derived from the calibration function
suggested by Lee III (2013). The uncertainties

The general calibration function expressed by Eq. (8) represents an infinite
series and, hence, the temperature retrieval function

The frequently used calibration function linear in

The most used nonlinear calibration function (Behrendt and Reichardt, 2000),
containing the term quadratic in

(1 April 2015) Temperature profile retrieved using the
temperature retrieval function (Eq. 20) derived from the calibration function
suggested by Gerasimov and Zuev (2016). The uncertainties

There exists another way to represent collisional PRR lines broadening (and,
therefore, nonlinear effects). Adding a term hyperbolic in

The IMCES PRR lidar was developed in the Institute of Monitoring of Climatic
and Ecological Systems of the Siberian Branch of the Russian Academy of
Sciences (IMCES SB RAS) for nighttime tropospheric temperature measurements.
A frequency-tripled Nd:YAG laser operating at a wavelength of 354.67 nm with
105mJ pulse energy at a pulse repetition rate of 20 Hz is used as the lidar
transmitter. The backscattered signals (photons) are collected by a
prime-focus receiving telescope with a mirror diameter of 0.5 m. The IMCES
lidar optical layout is shown in Fig. 2. The selection of spectrum bands
containing PRR lines with

Main technical parameters of the IMCES lidar transmitting, receiving, and data acquisition systems.

Spectral selection parameters of the DGM channels (central wavelength (CWL) and full width at half maximum (FWHM)).

(1 April 2015) Comparative analysis of the absolute temperature uncertainties yielded by using Eqs. (A27), (A33), (A40), and (A47) and of the difference in modulus between temperature values retrieved from the CPACs and IMCES lidar data.

IMCES lidar data taken between 20:21 and 21:21 LT on 2 October 2014
(13:21–14:21 UTC).

In this section we consider an example of nighttime tropospheric temperature
measurements performed with the IMCES lidar on 1 April 2015 in Tomsk
(56.48

(2 October 2014) Temperature profile retrieved using
Eq. (11). The absolute and relative uncertainties

(2 October 2014) Temperature profiles retrieved using Eqs. (13) and (18).

In order to improve the signal-to-noise ratio, raw lidar data
(background-subtracted photocounts

(2 October 2014) Temperature profiles retrieved using Eqs. (15) and (20).

(2 October 2014) Comparative analysis of the absolute temperature uncertainties yielded by using Eqs. (A27), (A33), (A40), and (A47) and of the difference in modulus between temperature values retrieved from the CPACs and IMCES lidar data.

One of the problems we face during temperature measurements is as follows.
Unfortunately, we do not have our own radiosondes and, therefore, we have no
possibility to launch a radiosonde simultaneously with lidar remote sensing
at the lidar site. The two nearest to Tomsk meteorological stations launching
radiosondes twice a day are situated in Novosibirsk (55.02

Here we compare nighttime temperature profiles retrieved using five
calibration functions considered in Sect. 2 from the altitude where the
laser-beam receiver-field-of-view overlap is complete (

Comparing all five profiles among themselves, one can see that, despite the
lowest values of both the statistical uncertainties in the 3–12 km altitude
region (

Let us consider another example of nighttime tropospheric temperature measurements performed with the IMCES PRR lidar on 2 October 2014 in Tomsk. The lidar data were taken from 20:21 to 21:21 LT (13:21–14:21 UTC), i.e., within 60 min integration time (72 000 laser shots). The raw and averaged IMCES lidar signals together with raw and averaged signal ratios are presented in Fig. 11. Here also we compare five temperature profiles retrieved using Eqs. (11), (13), (15), (18), and (20). The temperature retrieval algorithm is the same as was applied to the IMCES lidar data dated 1 April 2015. For the lidar calibration, we retrieved temperature points over Tomsk using the corresponding CPACs. Two temperature profiles from radiosondes, launched on 2 October 2014 at 19:00 LT (12:00 UTC) in Novosibirsk and Kolpashevo, are also given for comparison.

Figure 12 shows a temperature profile retrieved using Eq. (11). For this
profile in the 3–12 km altitude region we have

The calibration coefficients of all the calibration functions used in both the temperature measurement examples can be found in the Supplement.

We have considered and used the linear and four nonlinear (three-coefficient)
in

For the case of the IMCES PRR lidar system, the comparative analysis of three
parameters

the nonlinear functions expressed by Eqs. (13), (15), (18), and (20) retrieve the tropospheric temperature much better compared to the linear function (Eq. 11);

Eqs. (18) and (20) give the almost equally best-suited functions for the tropospheric temperature retrievals (although Eq. (20) is slightly better than Eq. 18);

the function given by Eq. (18) is the best from both practical (real lidar data) and theoretical (simulation) points of view (Gerasimov and Zuev, 2016).

The radiosonde data are available on the web page

Each value

There are two ways to average previously averaged PRR lidar data. The first
way is to average the ratio

Let

The weighting coefficients can be determined from Eq. (A14) of the following
form:

Let

The corresponding weighting coefficients are determined similar to case (1).

Let

The weighting coefficients are determined similar to cases (1) and (2). The
vertical resolution of the double-averaged data series

As we applied the first way of the second-order averaging of the IMCES lidar raw data (see Appendix A and Sect. 4.1), we use Eqs. (A9) and (A10) to derive the absolute and relative uncertainties in an analytical form. In case of the first-order averaging of lidar raw data, one can use Eqs. (A5) and (A6), respectively.

In order to obtain both the uncertainties for the linear calibration
function, let us differentiate the temperature retrieval function derived
from Eq. (10), i.e. (see Sect. 2)

Substituting Eq. (A19) into Eq. (A9), for the absolute uncertainty we get

The temperature retrieval function derived from Eq. (12) is written as (see
Sect. 2)

The first-order derivative of the function is

After substitution of Eqs. (A25) into Eq. (A24), we can write instead of
Eq. (A24)

The temperature retrieval function in the general form derived from Eq. (14)
represents (see Sect. 2)

The derivative of the temperature retrieval function is

The first-order derivative of the temperature retrieval function, obtained
from Eq. (16) (see Sect. 2)

Tropospheric temperature profiles are mentioned in Sect. 2 can also be
retrieved via the function

We thank S. M. Bobrovnikov for helpful discussions. This study was conducted in the framework of the Federal Targeted Programme “R&D in Priority Fields of S&T Complex of Russia for 2014–2020” in the priority field “Rational use of natural resources” (contract no. 14.607.21.0030, unique identifier ASR RFMEFI60714X0030).Edited by: R. Sica Reviewed by: A. Hauchecorne and one anonymous referee