Atmospheric temperature measurements at altitudes ... - OSA Publishing

Atmospheric temperature measurements at altitudes of 5–30 km with a double-grating-based pure rotational Raman lidar Jingyu Jia1,2 and Fan Yi1,2,* 1 2

School of Electronic Information, Wuhan University, Wuhan 430072, China

State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China *Corresponding author: [email protected] Received 16 April 2014; accepted 5 July 2014; posted 15 July 2014 (Doc. ID 209854); published 12 August 2014

A pure rotational Raman (PRR) lidar based on a second-harmonic generation Nd:YAG laser is built for measuring the atmospheric temperature at altitudes of 5–30 km. A double-grating polychromator is designed to extract the wanted PRR signals and suppress the elastically backscattered light. Measured examples present the overall lidar performance. For the 1-h integrated lidar temperature profiles, the 1σ statistical uncertainty is less than 0.5 K up to ∼17 km, while it does not exceed 2 K at altitudes of 17–26.3 km. Based on 38 nights of high-quality lidar temperature data, the temperature variability is studied. It is found that the variability differs between the nights with inversion layer and those without it. On the nights without inversion layer, the local hour-to-hour temperature variability was mostly less than 1 K at altitudes of 5–17 km. At altitudes of 17–23 km, it grew to 1.2–2.4 K. On the nights with inversion layer, in the middle and upper troposphere, the significant variability was found to occur only at the inversion-layer altitudes. At other tropospheric altitudes off the inversion layer, the variability was generally less than 1 K. The statistical results indicate that the temperature variability mostly was stronger in the presence of inversion layer than in its absence. © 2014 Optical Society of America OCIS codes: (010.0010) Atmospheric and oceanic optics; (010.3640) Lidar; (230.1950) Diffraction gratings; (280.6780) Temperature. http://dx.doi.org/10.1364/AO.53.005330

1. Introduction

Meteorological processes and climate trends are primarily reflected in changes of atmospheric temperature. Since these changes are altitude dependent and sometimes fast and moderate (or weak), accurate and high time/space resolution measurements of atmospheric temperature are required to capture their characteristics as a key hint for identifying the actual physics (cause). Vertical temperature profiles are usually acquired by routinely launched radiosondes (typically twice a day). Although such routine radiosonde temperature profiles have a high 1559-128X/14/245330-14$15.00/0 © 2014 Optical Society of America 5330

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accuracy and good altitude resolution, their low time resolution makes it unlikely to register some fast weather processes. A pure rotational Raman (PRR) lidar with a considerable power–aperture product can readily overcome this drawback to obtain hightime-resolution temperature profiles throughout the troposphere and lower stratosphere with sufficient accuracy. In contrast to the drifting radiosonde, the PRR lidar measures each temperature profile at the same geographical location during the same time interval. Thus, the quality of the individual temperature profiles is greatly improved and local temperature variations can be determined exactly. The methodology of the PRR lidar was first proposed by Cooney [1]. It is based on the fact that, under local thermodynamic equilibrium conditions,

the signal intensity ratio of two individual PRR lines has a temperature dependence defined by the Boltzmann distribution and is independent of atmospheric transmission and altitude. Note that the local thermodynamic equilibrium is generally fulfilled in the atmospheric volume probed by a PRR lidar due to a high molecule collision frequency in the troposphere and lower stratosphere. Taking advantage of a frequency shift between the PRR and elastic signals, the temperature measurement can be made not only in the clear atmosphere, but also in aerosol layers and optically thin clouds [2–5]. In recent years, many PRR temperature lidars have been well developed, with progress in high-performance spectral extraction devices [3–19]. The majority of them extract two small portions from one side (e.g., anti-Stokes) of the PRR spectrum with a polychromator composed of narrowband interference filters [3–8,12,14,16–19]. The filter-based polychromator allows a mechanically stable configuration and a simple optimization adjustment during fabrication. Thus, it is easy to use and can reliably work under severe conditions. The today’s state-of-the-art interference filters allow such filter polychromators to effectively extract two small portions from the PRR spectrum with satisfactory peak transmittances, and sufficiently suppress the elastically backscattered light in the extraction channels. The double-grating polychromator (DGP) provides an alternative to the interference filters [9–11,13,15]. It can optically sum the signals from the Stokes and anti-Stokes branches with the same temperature dependence (i.e., the same rotational quantum number), consequently enhancing the PRR signal intensities. As the large-aperture telescope and high-power laser are employed, the PRR lidar has a high temperature measurement precision and a large measurement range [4,7,17–19]. This is significant for understanding the atmospheric structure and dynamics in the troposphere and lower stratosphere. Considering a fact that only a few of the existing PRR lidars have such a capacity, we have built a doublegrating-based PRR lidar with a 1 m Cassegrain telescope and a powerful injection-seeded Nd:YAG laser (with a pulse energy of ∼900 mJ at 532.085 nm and a pulse repetition rate of 20 Hz). Groundwork for this development has already been laid via our previous work on the spectrally resolved atmospheric water Raman lidar and resonance fluorescence lidars [20,21]. Based on 300 m altitude resolution and 60 min data averaging, the lidar temperature profiles can well extend up to 26 km with statistical error of less than 2.0 K; in particular, the statistical error is less than 0.5 K at altitudes below 17 km. This work is organized as follows: we first revisit the measurement principle starting from the lidar equation in Section 2. The instrument setup, system test, and calibration are given in Sections 3 and 4. The lidar performance and geophysical measurement results are shown in Sections 5 and 6. The summary and conclusion are presented in Section 7.

2. Measurement Principle and Error Analysis

Based on the earlier literature [3,9,22–24], the lidarregistered backscattered photon count of a single PRR line for the gas species i (N2 or O2 ) from distance z at frequency νJ (expressed in cm−1 ) for the transition J → J 2 excited by an emission at a frequency ν0 can be written as Pi νJ ; z P0

KOz HνJ ni zσ i J; Tτν0 τνJ ; z2 (1)

where P0 is the transmitted photon number, K is a frequency-independent system constant, Oz is the overlap factor, HνJ is the filter-function-related transmission of the receiver at the PRR line νJ , ni z is the number density of molecules for the gas species i, and τv0 and τvJ are the atmospheric transmissions for the laser wavelength and the PPR line [note τv0 ≈ τvJ ]. σ i J; T denotes the differential backscatter cross section for a single PRR line νJ at the absolute temperature T, whose expression in SI units is given by [2] σ i J; T

112π 4 hcBi g JXJ 15 2I i 12 kT i γ 2i Ei J ; exp − × ν0 Δνi J4 kT 4πε0 2 (2)

where h is Planck’s constant, c is the velocity of light, Bi is the rotational constant (BN2 1.98957 cm−1 and BO2 1.43768 cm−1 ), I i is the nuclear spin quantum number (I N2 1 and I O2 0), k is the Boltzmann constant, gi J is a statistical weight factor whose value is 6 and 3 respectively for even and odd J N2 lines and 0 and 1 respectively for even and odd J O2 lines. Ei J is the rotational energy in the rotational quantum state J, which takes the form Ei J Bi JJ 1 − Di J 2 J 12 hc; J 0; 1; 2…;

(3)

where Di is the centrifugal distortion constant (DN2 5.76 × 10−6 cm−1 and DO2 4.85 × 10−6 cm−1 ). Δνi J is the Raman shift, which can be calculated with 8 > −B 22J 3 Di 32J 3 2J 33 ; > > < i J 0; 1; 2…Stokes : Δνi J > 22J − 1 − Di 32J − 1 2J − 13 ; B i > > : J 2; 3; 4…anti-Stokes (4) The factor XJ is given by 20 August 2014 / Vol. 53, No. 24 / APPLIED OPTICS

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8 > J 1J 2 > < Stokes 2J 3 : XJ JJ − 1 > > : anti-Stokes 2J − 1

(5)

The combined expression of the anisotropy of the polarizability γ i and the permittivity of vacuum ε0 has the value [24] γ 2i 4πε0 2

0.51 × 10−60 1.27 × 10−60

for γ 2N2 in unit of m6 : for γ 2O2 in unit of m6 (6)

Lidar Eq. (1) actually depicts a system that can extract individual PRR lines. In this case, in terms of Eqs. (1)–(6), the ratio of the system-detected photon counts from two individual PRR lines (e.g., νJ 1 and νJ 2 ) exactly has a simple temperature dependence (given the fact that the atmospheric transmission τνJ is nearly constant within the PRR spectrum)

Pi νJ 2 ; z α exp β ; QT Pi νJ 1 ; z T

(7)

with α

Ei J 1 − Ei J 2 ; k

(8)

β lnHJ 2 XJ 2 − lnHJ 1 XJ 1 :

(9)

In deriving Eqs. (7)–(9), we have set both J 1 and J 2 as even (or odd), and ν0 Δνi J 1 ≈ ν0 Δνi J 2 . Equation (7) gives conceptually the basic principle for measuring atmospheric temperature profiles by a PRR lidar: The distance-dependent atmospheric temperature can be derived from Eq. (7) after the constant parameters α and β are determined via comparison with accompanying local radiosondes. However, because of a limited filter bandwidth, each rotational Raman channel for the existing PRR lidars extract several adjacent PRR lines of both N2 and O2 rather than a single one. Then, the photon count registered in a single PRR channel (channel 1) is expressed as KOzτν0 nz PRR1 z P0 z2 X × H 1 νJ N ηN2 σ N2 J N2 ; TτνJ N 2

J N2

X J O2

H 1 νJ O ηO2 σ O2 J O2 ; TτνJ O 2

2

2

;

(10)

where nz is the total number density of air molecules, and ηN2 and ηO2 are the relative volume abundance of N2 and O2 , respectively. The two summations in brackets are carried out respectively with respect 5332


to N2 PRR lines J N2 and O2 PRR lines J O2 that fall inside the effective (non-null) filter transmission function H 1 νJ for this PRR channel. In order to follow the same scheme of atmospheric temperature profiling as in the case of the individual PRR line extraction, let us examine the ratio of the photon counts from two PRR channels (note that the atmospheric transmissions within the wavelength range of the PRR spectrum are nearly constant), PRR2 z PRR1 z hP J N2 H 2 νJ N2 ηN2 σ N2 J N2 ; T i P J O H 2 νJ O ηO2 σ O2 J O2 ; T 2 2 hP 2 ; J N2 H 1 νJ N2 ηN2 σ N2 J N2 ; T i P J O H 1 νJ O ηO2 σ O2 J O2 ; T

QΣ T

2

2

(11)

1

where H 2 νJ denotes the filter transmission function for the channel 2. In practice, the central wavelengths of the filter transmission functions H 1 νJ and H 2 νJ take the values respectively corresponding to the two N2 PRR lines of J 6 and 12. The indices 1 and 2 on the square brackets signify that the summations in the denominator and numerator are made about N2 and O2 PRR lines, respectively, in the PRR channels 1 and 2. Since both the system parameters (e.g., P0 and K) and explicitly altitude-dependent factors (in the lidar equation) cancel in Eq. (11), we can discuss the temperature dependence of the ratio QΣ T simply in terms of the known characteristic molecular parameters related with the differential backscatter cross sections of N2 and O2 . Considering the typical extraction schemes (the DGP and the interference filters) of the rotational Raman lines in the existing twochannel rotational Raman temperature lidars [11,16], we have calculated the temperature-dependent photon count ratios QΣ T using Eq. (11) and their exponential fits based on the calibration function given by Eq. (7). The calculated results and corresponding approximation errors (e.g., algebraic deviation between the input and retrieved temperatures from the fitted result) are shown in Fig. 1. Different curve colors are used to denote different filter–bandwidth combinations for the two PRR channels. The same filter bandwidths (e.g., 0.50 nm, 0.50 nm given in FWHM) of the two PRR channels typify the DGP scheme, while the different bandwidths (e.g. 0.57 nm, 1.43 nm) typify the interference filter scheme. For comparison, the ratio QT between the two individual N2 PRR lines (J 6 and 12) is also plotted (black diamonds). Note that each channel in the DGP scheme actually collects the summed photon counts from the Stokes and anti-Stokes branches with the same or close temperature dependence [i.e., the same (J S ∕J AS 6∕6 and 12/12) or close (J S ∕J AS 6∕8 and 12/14) N2 rotational quantum numbers]. As seen in Fig. 1, although the theoretically calculated ratio–temperature curves

makes the fitted curves approach perfectly the theoretical results given by Eq. (11), with approximation errors less than 0.07 K in the 180–300 K temperature range (see Fig. 2). Hence the calibration function in Eq. (12) is adopted in this work. This approximation error obviously falls into a category of systematic error. The statistical error for the temperature measurement needs be considered as a measure of measurement precision. Assuming that the background-subtracted photon counts PRR1 z and PRR2 z are statistically independent and follow the Poisson distribution, the statistical error (ΔT, i.e., the statistical uncertainty of the measured temperature induced by the 1 σ uncertainty of the photon counts) is expressed as [2]

(a)

(b)

1 ∂QΣ −1 1 1 1∕2 ΔT QΣ ∂T PRR1 PRR2 1 ∂PRR1 1 ∂PRR2 −1 1 1 1∕2 − : PRR1 ∂T PRR2 ∂T PRR1 PRR2 (13)

The statistical error depends on the two factors 1∕PRR1 1∕PRR2 1∕2 and Q−1 Σ ∂QΣ ∕∂T. The former is related to the photon count levels from the two PRR channels. The latter is designated “system

Fig. 1. (a) Theoretically calculated ratios (diamonds) of the photon counts from two PRR channels as a function of temperature and their exponential fits (solid curves) with an argument of a linear function of 1∕T. The fitting is made in the temperature range of 190–290 K. Different curve colors denote different filter– bandwidth combinations [with the two FWHM values given in Fig. 1(b)] for the two PRR channels centered at the wavelengths of the wanted N2 rotational Raman lines. The ratio for the two individual N2 PRR lines is also plotted versus temperature (black curve). (b) Algebraic deviation between the input temperature and the retrieved temperature from the fitted result as a function of temperature.

(a)

for these typical multiple PRR line extraction schemes differ in shape slightly from that of the two individual N2 PRR lines, all their fits (solid curves) can well represent the behaviors of the corresponding theoretical curves with the approximation errors being less than 2 K in the temperature range between 180 and 300 K. This indicates that the atmospheric temperature can be well derived by sampling two multiple-line portions of the PRR spectrum by available DGP or interference filter technique. Because the approximation errors behave like a second-order polynomial function of temperature [see Fig. 1(b)], a more accurate calibration (fitting) function is proposed as [2] QΣ T exp

γ α β ; T2 T

(b)

(12)

where α, β, and γ are the calibration constants. The application of the calibration function in Eq. (12)

Fig. 2. Same as Fig. 1 but for the calibration (fitting) function [given by Eq. (12)] with an argument of second-order polynomial function of 1∕T. Note that the resulting approximation errors are less than 0.07 K. 20 August 2014 / Vol. 53, No. 24 / APPLIED OPTICS

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sensitivity for temperature measurement” [2,25], which can reduce to an algebraic sum of the temperature sensitivities of the photon counts from the two PRR channels. In terms of Eq. (13), the better temperature measurement precision requires both the higher photon count levels and the higher temperature sensitivities. 3. Lidar Setup Description

The left part of Fig. 3 presents the optical layout of the Wuhan University PRR lidar with the main technical specifications given in Table 1. The lidar transmitter utilizes an injection-seeded second-harmonic generation (SHG) Nd:YAG laser to yield an emission of ∼900 mJ per pulse at 532.085 nm, with a repetition rate of 20 Hz and a pulse width of ∼7 ns. An 8× beam expander is equipped to reduce the radiant flux density and divergence of the output laser beam. The expanded laser beam is guided into the atmosphere zenith-ward by a steerable reflecting mirror (RM). At the receiver side, the atmosphere-backscattered light is collected by a 1 m Cassegrain telescope with a focal length of 8 m. The telescope is followed by an iris and a collimating lens (L3). The light exiting L3 is separated by a dichroic beamsplitter (D) into two parts in accordance with wavelength; one part (wavelength greater than 509 nm) is transmitted into the PRR optical unit via RM, and another (wavelength less than 509 nm) is reflected for other purposes. The transmitted light passes through a bandpass filter (BP) centered at 529 nm with a mean transmittance greater than 90% between 517 and 541 nm. It can prevent spectral overlap in the subsequent PRR optical unit and reduce background noise. After the BP filter, the light is converged on the end face of a fiber (F1) by a coupling lens (L4). The core diameter and numerical aperture (NA) of F1 are 1000 μm and 0.22, respectively. The lidar field of view (FOV) is set as ∼380 μrad by F1 and L4. The light is further

transmitted from F1 to a 600 μm core diameter fiber (F2) via a fiber mode homogenizer (FMH). As an import fiber (equivalent to an entrance slit) for the DGP, F2 has the same NA as F1. The application of FMH expands the lidar FOV and makes the light distribution more homogeneous in the fiber F2, although there is a light loss when a larger core diameter fiber is coupled to a smaller one. As shown in Fig. 3, our DGP is composed of two identical Littrow configuration polychromators, based on 600 gr∕mm gratings blazed at 53° and operated at the fifth diffraction order. Each grating is of an averaged inverse linear dispersion of ∼1.495 nm∕mm. The lens L1 and L2 act as both collimating and imaging. The end faces of the two fiber bundle arrays (FA1 or FA2) are respectively fixed on the focal planes of the two polychromators for light transmitting and collecting. The arrangement diagrams of the fibers on the end faces of FA1 and FA2 are shown on the right part of Fig. 3. The central axis positions (i.e., the fiber arrangement centers) of the two end faces are signified by the “+” (already accurately marked by the manufacturer). The first polychromator unit (FA1, L1, and G1) performs spectrum separation and extraction. L1 converts the signal light exiting fiber F2 to a collimated light that is dispersed further by the grating G1 and then imaged on the FA1 end face. A line of five output fibers along the dispersion direction on the end face extract respectively the elastic component and four portions of the PRR spectrum. The four portions represent respectively two combinations from the Stokes and anti-Stokes branches, with one corresponding to two low-J PRR signals, another to two high-J PRR signals. The center N2 rotational quantum numbers are roughly the same in each combination. The elastic signal is fed into the photomultiplier PMT1 via the fiber F3, while the four PRR spectral portions are delivered to the second polychromator unit (FA2, L2, and G2) by the fiber F4 (four fibers).

Fig. 3. Left part: Optical layout of Wuhan University PRR lidar for atmospheric temperature measurement. D, dichroic mirror; RM, reflecting mirror; BP, bandpass filter; L, lens; FMH, fiber mode homogenizer; F, fiber; FA, fiber bundle array; G, grating; PMT, photomultiplier tube. Right part: Arrangement diagrams of fibers on the end faces of the two fiber bundle arrays (FA1 and FA2). 5334


Table 1.

Main Technical Specifications of Wuhan University PRR Lidar

Lidar Transmitter Nd: YAG laser Pulse energy (mJ) Pulse length (ns) Repetition rate (Hz) Magnification of the beam expander (×) Expanded beam divergence (μrad)

Continuum Powerlite Precision II 9020 ∼900 7–8 20 8 ∼60 Lidar Receiver

Telescope Telescope main mirror diameter/focal length (m) Fiber determined FOV (μrad) Bandpass filter CWL/half-width of 90% transmittance (nm) Diameter/focal length of lens in the DGP (mm) Grating grooves per mm Grating working angle (°) Grating diffraction order @ 532 nm Fiber 1 core diameter (μm)/NA Fiber 2–4 core diameter (μm)/NA Fiber 5–6 core diameter (μm)/NA PMT of the elastic channel PMT of the PRR channel Data acquisition system

Cassegrain 1/8 ∼380 529/24 131/300 600 53 5 1000/0.22 600/0.22 1500/0.26 H10721-20, Hamamatsu H7422P-40, Hamamatsu TR40-160, Licel

CWL, central wavelength; DGP, double-grating polychromator; NA, numerical aperture.

Unlike the case for the first unit, the second polychromator unit (FA2, L2, and G2) implements an optically inverse operation, summation and removal of the remaining elastic signal. Through the inverse inputoutput-fiber collocation, the (low-J or high-J) PRR signals from the Stokes and anti-Stokes branches are summed and the elastic component remaining in the imported PRR signals is further suppressed. The fibers F5 and F6 deliver the low- and high-J summed PRR signals respectively to photomultiplier tubes PMT2 and PMT3. Here the high-quantum-efficiency PMTs (H7422P-40) are employed to improve the temperature measurement precision. In order to prevent the PMT saturation in the elastic channel, a neutral density filter is put in front of the PMT1. The signal at each channel is acquired by a PCcontrolled transient digitizer (TR40-160, manufactured by Licel) with a bin width of 25 ns (equivalent to a range resolution of 3.75 m) and a total bin number of 16384 (corresponding to a maximum detection altitude of 61.44 km). Note that the transient digitizer works simultaneously in two detection modes (photon count and analog). The signal from 1185 laser shots is accumulated to yield a single-sampling signal profile. Thus the raw lidar signal stored to disk has a range resolution of 3.75 m and time resolution of 1 min. Based on a method developed by Newsom et al. [26], the stored photon count and analog data are glued to form a reasonable photon-count profile with a large dynamic range. The range and time resolutions of the glued photon count profiles are respectively 30 m and 1 min. The coarser-resolution signal profiles (e.g., 300 m and 1 h) can be obtained simply by integrating the glued profiles in range and time.

4. DGP Adjustment and System Calibration

The DGP setup requires a fine adjustment. Here, we depict some key steps for this setup. The central axes of the end face of the fiber bundle arrays FA1 and FA2 respectively need to coincide exactly with the optical axes of lens L1 and L2. For this purpose, a 0.55 mm laser beam (from a He–Ne laser) is incident on the convex vertex of the lens (L1 or L2), as shown in Fig. 4(a). A fine adjustment makes the lenstransmitted light pass through the 1 mm diameter central hole of a homemade mechanical component C4 mounted behind the lens, and meanwhile, the lens-convex-reflected light returns to the laser aperture. Note that C4 and the lens are coaxially installed (the outer edge of C4 is a circle with the same diameter as the lens). In this case, the transmitted light visually shows the optical axis of the lens. A homemade mechanical component C1 is then put on a finely adjustable mount as an alternative for the fiber bundle array (FA1 or FA2). It has the same geometrical shape as that of FA1 and FA2. Its central axis is marked with a 1 mm diameter hole (no penetration) on the front end face. The mount is manually adjusted until the transmitted light is incident on the hole, indicating that the central hole is on the optical axis of the lens. After that, two homemade mechanical components (C2 and C3), each having a 1 mm penetration hole, are utilized to register the position of the optical axis together with C4. Following the optical axis determination above, the He–Ne laser is reinstalled behind the mount with C1 removed. From here, the 0.55 mm laser beam is aligned passing through the three 1 mm central holes of C2, C3, and C4, redisplaying the lens optical 20 August 2014 / Vol. 53, No. 24 / APPLIED OPTICS

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(a)

(b)

(c)

Fig. 4. (a) Schematic diagram for determining the optical axis of the lens. C2–C4 are homemade mechanical components, each having a 1 mm diameter central hole (penetration). C4 has a circular outer edge with the same diameter as the lens (131 mm). C1 is also a homemade mechanical component having the same geometrical shape as that of FA1 and FA2, which is a 50 mm long column with a diameter of 22 mm. Its central axis is marked with a 1 mm hole (no penetration) on the front end face. (b) Schematic diagram for making the grating’s normal direction parallel to the lens optical axis. (c) Schematic diagram for making the FA1 (FA2) central axis coincide with the optical axis of the lens. As seen from the left of Fig. 4(c), this happens when the image of the F2 (F5/F6) light spot is located at the symmetrical position with respect to the central axis symbol (+).

axis. The grating (G1 or G2) is then installed on another finely adjustable mount before the lens, as seen from Fig. 4(b). After removing C2, C3, and C4 (shown in dashed line) from their positions, the grating mount is adjusted until the grating-reflected light comes back onto the laser aperture. This indicates that the grating, which operates at the zero diffraction order, has the normal direction (N) parallel to the lens optical axis. Thereafter, as shown in Fig. 4(c), the fiber bundle array FA1 (or FA2) is fixed on the finely adjustable mount, taking the position of C1. The attenuated laser beam from our Nd:YAG laser is fed into FA1 (FA2) via the fiber F2 (fiber F5/F6). Adjusting the FA1 (FA2) via the finely adjustable mount slightly, the mirror image of the F2 (F5/ F6) input light spot is observed to change in position on the FA1 (FA2) end face. When the mirror image is located at the symmetrical position of the input light spot with respect to the central axis symbol (“+”) [see the left of Fig. 4(c)], the FA1 (FA2) central axis is believed to coincide with the optical axis of the lens. The further optical adjustment for the DGP is made in turn from the first polychromator unit (FA1, L1, and G1) to the second (FA2, L2, and G2). After attenuation, the 532.085 nm beam from our Nd:YAG laser is fed into the first polychromator unit 5336


via the fiber F2. The grating G1 is rotated from 0° to about 53°, then it is finely adjusted until the imaging spot from the fifth diffraction order comes forth at the symmetrical position of the F2 light spot [green F3 fiber position, see Fig. 5(a)]. At this point, G1 operates at the fifth diffraction order of the elastic signal. Next, the white light from a plasma lamp (HPLS-30-04, Thorlabs) is fed into the first polychromator unit via F2 instead of the 532.085 nm beam input. Consequently, a dispersive stripe is observed on the end face of FA1 due to the dispersion effect of G1. Thereafter, FA1 is translated along its central axis (optical axis of L1) and finely rotated with respect to the axis until the stripe becomes sharpest and perfectly covers the five fibers in a line F41 ; F42 ; F3; F43 ; F44 [see Fig. 5(b)]. In this situation, the end face of FA1 is on the focal plane of L1 and the straight line composed of the five fiber heads (dispersion direction) is perpendicular to the groove direction of G1, which guarantees a high fiber coupling efficiency and a sufficient out-band rejection for the first polychromator unit. Now the further adjustment turns to the second polychromator unit. The white light is fed into this unit first via four fibers of F4 F41 ; F42 ; F43 ; F44 [denoted as four grey circles on the end face of FA2 in Fig. 5(c)]. When the grating G2 is rotated from 0° to ∼53°, four dispersion stripes (two pairs) are visible on the end face of FA2 due to a dispersive effect of G2. G2 is then finely adjusted, and meanwhile FA2 is rotated and translated with regard to its central axis (the optical axis of L2) until the four stripes merge into two stripes which respectively cover F5 and F6 on the end face of FA2, as shown in Fig. 5(c). This represents that the two straight lines determined by two pairs of symmetrical fibers on the end face of FA2 F41 − F44 ; F42 − F43 are both perpendicular to the groove direction of G2. Translating (a)

(b)

(c)

(d)

Fig. 5. (a) Positions of the input fiber (green F2 circle) and its imaging spot (green F3 circle) on the end face of the fiber bundle array FA1 (22 mm outer diameter) when the grating G1 operates at the fifth diffraction order of the elastic signal (∼53°). The input light is the 532.085 nm beam from a Nd:YAG laser. (b) Schematic position and sharpness of the G1-diffracted light (a dispersive stripe shown as green narrow strip) for white light input via fiber F2 when the end face of FA1 is on the focal plane of L1, and meanwhile the green narrow (straight line) is perpendicular to the groove direction of G1. (c) Schematic position and sharpness of the G2-diffracted light (two dispersive stripes shown as green narrow strip, see text) for white light input via four fibers of F4 F41 ; F42 ; F43 ; F44 when the end face of FA2 (22 mm outer diameter) is on the focal plane of L2, and meanwhile the green narrow strips (two straight lines) are perpendicular to the groove direction of G2. (d) Position and sharpness of the resultant imaging spots (F5 and F6) on the end face of FA2 after the entire DGP adjustment is accomplished (see text). White light is fed into the DGP via the input fiber F2.

FA2, the output intensities of F5 and F6 are monitored respectively by two CCD cameras. When the output intensities arrive simultaneously at their maxima, the end face of FA2 is believed to be on the focal plane of L2. Finally, a joint adjustment of the entire DGP is made. The white light is first fed into the DGP via the input fiber F2. G2 is then finely adjusted, and meanwhile FA2 is translated carefully along its central axis (the optical axis of L2) until the resultant imaging spots on the end face of FA2 become sharpest and fall exactly on the positions of F5 and F6 [see Fig. 5(d)]. This indicates the accomplishment of the entire DGP adjustment. The spectral selection capability of the DGP can be examined by a commercial spectrograph (sp2750i+ PI-MAX II, Princeton Instruments). The white light is fed into the DGP via F2 (see the left part of Fig. 3). After the spectral selection, the DGP’s outputs are in turn guided into the spectrograph via F3, F5, and F6. The spectrograph-measured normalized spectrum intensities (diamonds) and their Gaussian fits (solid curves) are shown in Fig. 6(a). For comparison, the normalized PRR spectrum at 200 K is also shown in Fig. 6(b). The spectral selection parameters are derived from the Gaussian fits, as summarized in Table 2. As seen in Table 2, the center wavelengths of the DGP-extracted signals are close to the theoretical

(a)

Table 2.

Spectral Selection Parameters of DGP Derived from Fig. 6

Channel Elastic Lower quantum number (Stokes) Lower quantum number (anti-Stokes) Higher quantum number (Stokes) Higher quantum number (anti-Stokes)

CWL in Air/Theoretical Value (nm)

FWHM (nm)

532.00/532.08 533.70/533.78

0.55 0.55

530.28/530.40

0.54

535.09/535.14

0.52

529.00/529.06

0.52

values (for the low- and high-quantum-number PRR channels at both the Stokes and anti-Stokes sides), with deviations ranging from 0.05 to 0.12 nm, while their bandwidths (FWHM) are ∼0.5 nm. Considering the fact that the wavelength measurement accuracy for the spectrograph is about 0.1 nm, we believe that the DGP has a perfect spectral extraction that coincides with the theoretical design. The calibration constants α, β, and γ [see Eq. (12)] for the PRR lidar system are determined via comparison with accompanying local radiosondes launched at Wuhan Weather Station (#57494). The station is located ∼23.4 km northwest of our lidar site (30.5°N, 114.4°E). Hence the horizontal inhomogeneity in the atmospheric temperature is ignored. In order to avoid an impact of the overlap factor at lower altitudes and a weak signal-to-noise ratio at high altitudes, the constant calibration is made in an altitude range from 3.8 to 20.6 km. The colorized curves in Fig. 7 present the signal ratio (of the two PRR channels) versus accompanying radiosonde temperature for four different observation nights (at 20:00 LT). Their average is given in the dashed curve. According our calculation,

(b)

Fig. 6. (a) Spectrograph-measured spectrum intensities (diamonds) from the elastic channel (F3) as well as the two PRR channels (F5 and F6) when white light is fed into the DGP via F2. The spectrum intensities (elastic, high- and low-quantum-number channels) are normalized respectively by their maxima. The solid curves represent the Gaussian fits to the spectrum intensity data. The spectral selection parameters are derived from the Gaussian fits, as summarized in Table 2. (b) Normalized PRR spectrum at 200 K, which is from the theoretical calculation by considering the relative volume abundance (N2 , 0.78; O2 , 0.21). The “max value” denotes the maximum line intensity of N2 multiplied by 0.78.

Fig. 7. Signal ratio (of the two PRR channels) versus accompanying local radiosonde temperature from four different observation nights (different colors) at Wuhan. The lidar data were integrated over 80 min and smoothed with a gliding average of a 900 m window length. The constant calibration was made in an altitude range from 3.8 to 20.6 km. The fit function as well as the 1σ standard deviations of the calibration constants are presented. 20 August 2014 / Vol. 53, No. 24 / APPLIED OPTICS

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the 1 σ standard deviations of the three constants (α, β, and γ) are all quite small, indicating the stability of the PRR lidar system. 5. Observations and Lidar Performance

Since our PRR lidar was established in November 2012, it has been operated routinely on the campus of Wuhan University, Wuhan, China (30.5°N, 114.4°E). Up to the end of December 2013, a total of ∼943 h of temperature data were collected from 93 lidar observation nights. Figure 8 exhibits an observational example from the summertime. Figure 8(a) gives the 1-h integrated photon count profiles from the lowand high-quantum-number PRR channels (red and blue curves), respectively, during the 20:02–21:02 LT period on August 7, 2013. Figure 8(b) presents a sequence of the 1-h lidar temperature profiles (bold line) together with their 1σ statistical uncertainties (thin line) during the night of August 7–8, 2013. The profiles have a range resolution of 300 m. Note that the two PRR signals were smoothed at altitudes above 20 km with a sliding average of 900 m. The statistical uncertainties of the 1-h integrated temperature profiles are less than 0.5 K up to an altitude of ∼17.0 km. The corresponding values do not exceed 2 K in the altitude range from ∼17.0 to ∼26.3 km. For comparison, the radiosonde temperature profile (blue curve with diamonds) at 20:00 LT on August 7, 2013 for Wuhan Weather Station is also plotted. The lidar temperature profiles during 20:00–21:00 LT matched the evening radiosonde data well in the 3–13 km altitude range, while their deviations at altitudes above 13 km might arise from radiosonde drift-off. As seen from Fig. 8(b), the lidar temperature profiles are quite smooth at altitudes below the tropopause (∼17 km), while the temperature fluctuations are visible above that altitude. The severe temperature fluctuations at

(a)

altitudes above ∼20 km during 05:00–06:00 LT arose from a low signal to noise ratio due to the sunlight effect in the morning (sunrise at 5:45 LT on August 8, 2013 at Wuhan). Based on the raw lidar data of Fig. 8, we have recalculated the lidar temperature profiles with a 20 min integration time and a range resolution of 240 m. The calculated results, together with their 1 σ statistical uncertainties, are plotted in Fig. 9. The statistical uncertainties of the 20-min lidar temperature profiles are less than 0.5 K up to an altitude of ∼11.5 km. The corresponding values do not exceed 2 K at altitudes of ∼11.5–21.5 km. Obviously, the 1-h temperature profiles in Fig. 8(b) are of smaller statistical uncertainties at altitudes of 5–25 km compared to the 20-min temperature profiles. As seen in Fig. 9, at altitudes of 5–17 km (the middle and upper troposphere), the sequence of the 20-min temperature profiles exhibits stronger small-scale fluctuations compared to the 1-h temperature profiles in Fig. 8(b). The time extent and measurement precision of our PRR lidar observations are variable from night to night because of changeable weather at Wuhan. Note that out of a total of 93 observation nights, 38 nights have at least seven 1-h integrated temperature profiles each, and their statistical uncertainty is less than 2.0 K up to an altitude of ∼20.0 km. The 38 nights with sufficient time coverage and high signal-to-noise ratio are employed in the following investigation on the temperature variability. 6. Local Variability of Temperature

In order to illustrate the hour-to-hour variability in the tropospheric and low stratospheric temperature, Fig. 10(a) presents the nine 1-h lidar temperature profiles (black curves) and their average (red curve)

(b)

Fig. 8. (a) Photon count profiles of the two PRR channels (red and blue curves) measured during 20:02–21:02 LT on August 7, 2013. (b) Sequence of the 1-h lidar temperature profiles (bold line) together with their 1σ statistical uncertainties (thin line) on the night of August 7–8, 2013. The consecutive profiles have an offset of 15 K. The range resolution is 300 m. Note that the two PRR signals were smoothed at altitudes above 20 km with a sliding average of 900 m. The statistical uncertainties of the 1-h integrated temperature profiles are less than 0.5 K up to an altitude of ∼17.0 km. The corresponding values do not exceed 2 K at altitudes of ∼17.0–26.3 km. For comparison, the radiosonde temperature (blue curves with diamonds) obtained at 20:00 LT on August 7 at Wuhan is also plotted. 5338


Fig. 9. Sequence of the 20-min lidar temperature profiles (bold line) together with their 1σ statistical uncertainties (thin line) derived from the same raw lidar data as that plotted in Fig. 8. The consecutive profiles have an offset of 15 K. The range resolution is 240 m. The statistical uncertainties of the 20-min lidar temperature profiles are less than 0.5 K up to an altitude of ∼11.5 km. The corresponding values do not exceed 2 K at altitudes of ∼11.5–21.5 km.

on the night of August 6–7, 2013. For comparison, the conventional radiosonde temperature data from Wuhan Weather Station on this night (blue curve for 20:00 LT and orange for 08:00 LT next morning) are also plotted. Figure 10(b) gives the mean absolute deviation (light blue curve) and maximum absolute deviation (gold curve) of the 1-h lidar temperature profiles from the nightly mean temperature profile as well as the mean profile (dot curve) of the statistical uncertainties for the 1-h lidar temperature measurements. As seen in Fig. 10(a), on this summer night, all the 1-h lidar temperature profiles were very similar in formation at altitudes from ∼5 to

(a)

(b)

17 km, the local hour-to-hour temperature variability being small with the mean deviation less than 1 K (the maximum deviation being ∼0.5–2.0 K). At altitudes of ∼17–28 km, the variability became slightly stronger than that at altitudes below 17 km, the mean deviation having a value of about 1–3 K (the maximum deviation being ∼2–6 K). These features were consistent with that shown by the two radiosonde temperature profiles. The time scale (∼2–9 h) of the hour-to-hour variability falls just inside the period range of atmospheric gravity waves. The small variability between ∼5 and 17 km suggests that the (inertial) gravity wave effect on the atmospheric temperature in the middle and upper troposphere is very weak in the night, but this wave impact might become strong in the low stratosphere. Figure 11(a) gives a comparison between the nightly mean (9-h integrated) lidar temperature profile and the average profile of 15-day Wuhan radiosonde temperature data centered on the lidar

(a)

Fig. 10. (a) 1-h lidar temperature profiles (black curves) and their average (red curve) on the night of August 6–7, 2013. For comparison, the two radiosonde temperature profiles from Wuhan Weather Station are also plotted (blue curve for 20:00 LT on August 6 and orange for 08:00 LT on August 7). (b) Mean absolute deviation (light blue curve) and maximum absolute deviation (gold curve) of the 1-h lidar temperature profiles from the nightly mean temperature profiles as well as the mean profile (dotted curve) of the 1σ statistical uncertainties for the 1-h lidar temperature measurements. Note that on this summer night, the hour-to-hour temperature variability at altitudes of ∼5–19 km was very small, with the mean deviation less than 1 K.

(b)

Fig. 11. (a) Nightly mean lidar temperature profile (solid curve) on August 6–7, 2013 and the average profile (dot curve) of 15-day (30-release) Wuhan radiosonde temperature data centered on the lidar observation night. (b) Their absolute deviation and the 1σ statistical uncertainty for the 1-night lidar temperature measurement. 20 August 2014 / Vol. 53, No. 24 / APPLIED OPTICS

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observation night (August 6–7, 2013). Their absolute deviation, as well as the 1σ statistical temperature uncertainty for the 1-night lidar measurement, are plotted in Fig. 11(b). This absolute deviation roughly reflects the day-to-day variability (with time scale of several days) in temperature. The temperature deviation at altitudes of 5–9.3 km and around ∼17 km was larger than 1 K, indicating that at some altitudes the day-to-day variability in temperature can be stronger than the hour-to-hour variability. As the second example to show the temperature variability, Fig. 12 gives the lidar and radiosonde temperature profiles on the night of March 5–6, 2013 as well as the associated deviations and uncertainty. This night was characterized by a strong inversion layer in the altitude range of ∼10–12 km (the tropopause was at ∼18 km). The temperature difference within the inversion layer was ∼5 K. Such a large temperature difference implies that, on the inversion layer, the atmosphere was highly stable and the convection was suppressed. The hour-to-hour temperature variability on the inversion layer was quite striking, with the mean absolute deviation of 1–1.6 K (the maximum deviation close to 3 K). At those tropospheric altitudes off the inversion layer, the mean absolute deviation for the variability was ∼1 K or less, which was similar to that in the first example without inversion layer (Fig. 10). The same results can be seen from the two radiosonde temperature profiles shown in Fig. 12(a). Interestingly, when the 1-h temperature profiles were plotted together, the inversion layer looked like a “node” [see Fig. 12(a)]. Note that this phenomenon was prevalent in all

(a)

(b)

Fig. 12. (a) 1-h lidar temperature profiles (black curves) and their average (red curve) on the night of March 5–6, 2013. For comparison, the two radiosonde temperature profiles from Wuhan Weather Station are also plotted (blue curve for 20:00 LT on March 5 and orange for 08:00 LT on March 6). (b) Mean absolute deviation (light blue curve) and maximum absolute deviation (gold curve) of the 1-h lidar temperature profiles from the nightly mean temperature profiles as well as the mean profile (dotted curve) of the 1σ statistical uncertainties for the 1-h lidar temperature measurements. This night was characterized by an inversion layer at altitudes of 10–12 km. Note that the hour-to-hour temperature variability at the inversion-layer altitudes was clearly visible with the mean deviation of 1–1.6 K. 5340


the lidar-observed inversion layers mentioned subsequently. The mean deviation had a value from ∼1.5 to 4.7 K in the low stratosphere (18–28 km), which was slightly larger than that in the first example. The vertical temperature gradients at altitudes of 5–17 km are calculated in terms of the 1-h lidar temperature profiles shown in Fig. 12(a). Figure 13 presents the time sequence of the calculated gradient profiles as well as the vertical shear rates for the zonal wind measured by Wuhan radiosondes at 20:00 LT on March 5 and at 08:00 LT on March 6, 2013. As seen in Fig. 13, the inversion layer occurred inside a shear layer associated with the jet-stream-related zonal wind. On this night, the inversion layer moved upward in general, with a mean apparent velocity of ∼0.016 ms−1 [see Fig. 13(a)], while the shear layer appeared to ascend also, with an apparent velocity of ∼0.015 ms−1 [Fig. 13(b)]. The observed facts suggest a connection between the inversion layer formation and the shear layer related to with a strong jet stream. Obviously, the visible hour-to-hour temperature variability observed at fixed altitudes inside the inversion layer resulted partly from the layer’s motion. Plotted in Fig. 14(a) is the nightly mean lidar temperature profile on the night of March 5–6, 2013 as well as the 15-day averaged radiosonde temperature profile over Wuhan (centered on the lidar observation night). Figure 14(b) shows their deviation (absolute value), which is a rough measure of the day-to-day variability. The deviation was significant (∼1–5.5 K) on the inversion layer. In the altitude range from 17 to 28 km, this quantity appeared to be slightly larger than that on the night of August 6–7, 2013 [without inversion layer, see Fig. 11(b)]. For ascertaining the statistical significance of this temperature variability, we have surveyed the 38 lidar observation nights. Out of the 38 total nights, 18 nights had inversion layers present in the middle and upper troposphere. On the remaining 20 nights, no inversion layer existed in this altitude range. The Wuhan radiosonde temperature profiles on the 38 nights confirmed this result (18 nights having inversion layer and 20 nights having no inversion layer). The data amount allows us to statistically characterize the features of the temperature variability in light of the presence and absence of inversion layer. Considering the data feature of the lidar temperature measurements (e.g., noncontinuity due to sunlight and weather interferences), as well as the method used in the aforementioned case study, the hour-to-hour variability is reckoned by taking the mean absolute deviation of the 1-h lidar temperature profiles from their respective nightly mean; the dayto-day variability is estimated by taking the mean absolute deviation of the nightly mean lidar temperature profiles from the corresponding mean of the temperature profiles from 15-day (30) radiosonde measurements centered on lidar observation nights at Wuhan. The estimated results, together with the mean statistical uncertainties of the individual 1-h and individual 1-night temperature profiles, are

(a)

(b)

Fig. 13. (a) Sequence of the temperature gradient profiles derived from the 1-h lidar temperature profiles on the night of March 5–6, 2013 [see Fig. 12(a)]. (b) Vertical shear rate for the zonal wind measured by Wuhan radiosondes at 20:00 LT on March 5 and 08:00 LT on March 6, 2013. Note that on this night, the inversion layer occurred inside a shear layer and both the layers moved upward in similar apparent velocities.

shown in Fig. 15(a) for both the case with inversion layer (red, 18 nights) and without inversion layer (blue, 20 nights). In addition, Fig. 15(b) presents the mean zonal (solid) and meridional (dot) wind shears derived from the Wuhan radiosonde wind measurements for the 18 nights with inversion layer (red) and 20 nights without inversion layer (blue). Compared with the mean statistical uncertainties, the mean absolute deviations were greater at altitudes of ∼5–23 km for the hour-to-hour variability, and also were larger at altitudes of 5–25 km for the dayto-day variability. As seen from Fig. 15(a), in the altitude range of 5–21.5 km, the hour-to-hour variability mostly was slightly larger in the presence of inversion layer compared to the absence of inversion layer. Furthermore, in the altitude range of 5–25 km, the day-to-day variability was also stronger in the presence of inversion layer than in its absence, with the exception of 11–14 km. Interestingly, the dayto-day variability for the nights with inversion layer was larger than 2 K in two separate altitude regions (5–10.5 km and 15–20 km), where the wind shear related with the zonal wind jet stream was very strong (a)

(b)

[see Fig. 15(b)], while it was smaller than that for the nights without inversion layer at the narrow altitude range (11–14 km), where the wind shear became minimal corresponding to the jet maximum. Figure 15(a) shows that the hour-to-hour temperature variability (for both nights with and without inversion layer) was 1.2 K or less in the middle and upper troposphere. At altitudes of 17–23 km, it grew to 1.2–2.4 K. The day-to-day variability was evidently stronger than the hour-to-hour variability at altitudes of 5–19 km. In this altitude range, the dayto-day variability ranged from 1.4 to 3.5 K for the nights with inversion layer, while it varied between 1.1 and 1.9 K for nights without inversion layer. At altitudes above 19 km, this variability decreased to 1.5–2.5 K for the nights with inversion layer, whereas it fell to ∼0.9–1.5 K for nights without inversion layer. Our data statistics show that the 20 nights without inversion layer were from mid-June to mid-October, while the 18 nights with inversion layer were from the remaining months. Based on the conventional radiosonde measurements, the jet stream over Wuhan was relatively strong from late October to early June next year, with the zonal wind velocity greater than 30 ms−1 . According to the present observations, during this period, the inversion layer often arose in a narrow-altitude region that lay just inside the strong shear layer below the jet maximum (∼12 km); meanwhile, the visible temperature variability (day-to-day and hour-to-hour) occurred in the another strong shear region above the jet maximum. 7. Summary and Conclusion

Fig. 14. (a) Nightly mean lidar temperature profile (solid curve) on March 5–6, 2013 and the average profile (dot curve) of 15-day (30-release) Wuhan radiosonde temperature data centered on the lidar observation night. (b) Their absolute deviation and the 1 σ statistical uncertainty for the 1-night lidar temperature measurement.

We have built a PRR lidar for measuring the atmospheric temperature in the 5–30 km range. The transmitter is an injection-seeded SHG Nd:YAG laser with a pulse energy of 900 mJ and pulse repetition rate of 20 Hz. The receiver utilizes a 1 m Cassegrain telescope to collect the backscattered light. A DGP with an average inverse linear dispersion of ∼1.495 nm∕mm is designed to extract the wanted PRR signals with low and high rotational quantum numbers, and to 20 August 2014 / Vol. 53, No. 24 / APPLIED OPTICS

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(a)

(b)

Fig. 15. (a) Mean absolute deviations (solid curves) of the 1-h lidar temperature profiles from their respective nightly mean for 18 observational nights with inversion layer (red) and 20 observational nights without inversion layer (blue). In addition, the mean absolute deviations (dotted curves) of the nightly mean lidar temperature profiles from the corresponding mean of the temperature profiles from 15-day radiosonde measurements centered on lidar observation nights at Wuhan are plotted respectively in terms of the 18 nights with inversion layer (red) and 20 nights without inversion layer (blue). The mean statistical uncertainties of the individual 1-h lidar temperature profiles and individual 1-night lidar temperature profiles are also given respectively in dashed and dashed–dotted curves. (b) Mean zonal (solid) and meridional (dotted) wind shears derived from the Wuhan radiosonde wind measurements for the 18 nights with inversion layer (red) and the 20 nights without inversion layer (blue).

suppress the elastically backscattered light in the PRR channels. We described the procedure making the central axes of the end face of FA1 and FA2 coincide exactly with the optical axes of L1 and L2, respectively, and the optical adjustment of the two units of the DGP. A test by a commercial spectrograph indicates that the central wavelengths of the DGPextracted signals are close to theoretical values, while their bandwidths (FWHM) are ∼0.5 nm. The calculated 1σ standard deviations of the three calibration constants based on four different measurement nights are small, indicating the high stability of our PRR lidar system. The distance-dependent atmospheric temperature is derived by analyzing the ratio of the two extracted PRR signals through the application of a calibration (fitting) function. The application of the calibration function with an argument of second-order polynomial function of reciprocal temperature yields an approximation error less than 0.07 K in the 180–300 K temperature range. This represents the theoretical accuracy of the temperature measurement using the PRR lidar. Since installation, our PRR lidar has been operated routinely at night. Up to the end of December 2013, temperature data from a total of 93 nights was collected. Observational examples revealed the overall lidar performance. For the 1-h integrated lidar temperature profiles, the 1σ statistical uncertainty is less than 0.5 K up to ∼17 km (the tropopause over Wuhan), while it does not exceed 2 K at altitudes of 17–26.3 km. Out of the total 93 nights, 38 nights are of a high data quality where there are at least seven 1-h lidar temperature profiles each, and their 5342


statistical uncertainty is less than 2.0 K up to an altitude of ∼20.0 km. This allows us to investigate the temperature variability. The hour-to-hour variability is reckoned by taking the mean absolute deviation of the 1-h lidar temperature profiles from their respective nightly mean, while the day-to-day variability is estimated by taking the mean absolute deviation of the nightly mean lidar temperature profiles from the corresponding mean of the temperature profiles from 15-day Wuhan radiosonde measurements centered on lidar observation night. Out of the 38 total nights, 18 nights had inversion layers present in the middle and upper troposphere. Of the remaining 20 nights, no inversion layer existed in this altitude range. The variability is found to differ between the nights with inversion layer and those without it. On the nights without inversion layer, all the 1-h lidar temperature profiles were very similar in formation at altitudes from ∼5 to 17 km, the local hour-to-hour temperature variability being small with the mean deviation less than 1.1 K. At altitudes of 17–23 km, it grew to 1.2–2.4 K. The day-to-day variability at altitudes of 5–19 km was evidently stronger than the hour-to-hour one, with the mean deviation from 1.1 to 1.9 K. However, the mean deviation fell to ∼0.9–1.5 K at altitudes above 19 km. As indicated by a case study, on a night with inversion layer, the hour-to-hour temperature variability was found to be significant only at altitudes of the inversion layer (the mean deviation was larger than 1 K). At other tropospheric altitudes off the inversion layer, the mean deviation for the variability was less than 1 K, which was similar to that without inversion

layer. On this night, the inversion layer moved generally upwards, with a mean apparent velocity of ∼1.6 cm s−1 . The visible hour-to-hour temperature variability (“node”) observed at fixed altitudes inside the inversion layer resulted partly from the layer’s motion. Our statistics show that at altitudes of 5–21.5 km, the hour-to-hour variability mostly was slightly larger in the presence of inversion layer compared to its absence. In addition, at altitudes of 5–25 km, the day-to-day variability was also stronger in the presence of inversion layer than in its absence with the exception of 11–14 km. Interestingly, the day-to-day variability in the nights with inversion layer was obviously larger than 2 K in two separate altitude regions (5–10.5 km and 15–20 km) where the wind shear related with the zonal wind jet stream (from radiosonde) was very strong, while it was smaller than that on the nights without inversion layer in the narrow-altitude region (11–14 km) where the wind shear became minimal corresponding to the jet maximum. Our observations suggest a connection between the inversion layer formation and the shear layer related to a strong jet stream. This research is supported by the National Natural Science Foundation of China through Grants 41327801 and 40221003. The authors also thank Changming Yu, Miao Weng, Cheng Wu, and Yunpeng Zhang for their technical assistance and enthusiastic support in collecting lidar data. References 1. J. Cooney, “Measurement of atmospheric temperature profiles by Raman backscatter,” J. Appl. Meteorol. 11, 108–112 (1972). 2. A. Behrendt, “Temperature measurement with lidar,” in Lidar Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 273–305. 3. A. Behrendt and J. Reichardt, “Atmospheric temperature profiling in the presence of clouds with a pure rotational Raman lidar by use of an interference-filter-based polychromator,” Appl. Opt. 39, 1372–1378 (2000). 4. A. Behrendt, “Fernmessung atmosphärischer Temperaturprofile in Wolken mit Rotations-Raman-Lidar,” doctoral dissertation (University of Hamburg, 2000). 5. J. Su, M. P. McCormick, Y. Wu, R. B. Lee III, L. Lei, Z. Liu, and K. R. Leavor, “Cloud temperature measurement using rotational Raman lidar,” J. Quant. Spectrosc. Radiat. Transfer 125, 45–50 (2013). 6. G. Vaughan, D. P. Wareing, S. J. Pepler, L. Thomas, and V. Mitev, “Atmospheric temperature measurements made by rotational Raman scattering,” Appl. Opt. 32, 2758–2764 (1993). 7. A. Behrendt, T. Nakamura, and T. Tsuda, “Combined temperature lidar for measurements in the troposphere, stratosphere, and mesosphere,” Appl. Opt. 43, 2930–2939 (2004). 8. P. D. Girolamo, R. Marchese, D. N. Whiteman, and B. B. Demoz, “Rotational Raman lidar measurements of atmospheric temperature in the UV,” Geophys. Res. Lett. 31, L01106 (2004). 9. Y. F. Arshinov, S. M. Bobrovnikov, V. E. Zuev, and V. M. Mitev, “Atmospheric temperature measurements using a pure rotational Raman lidar,” Appl. Opt. 22, 2984–2990 (1983).

10. A. Ansmann, Y. F. Arshinov, S. Bobrovnikov, I. Mattis, I. Serikov, and U. Wandinger, “Double grating monochromator for a pure rotational Raman-lidar,” Proc. SPIE 3583, 491–497 (1998). 11. I. Balin, I. Serikov, S. Bobrovnikov, V. Simeonov, B. Calpini, Y. Arshinov, and H. V. D. Bergh, “Simultaneous measurement of atmospheric temperature, humidity, and aerosol extinction and backscatter coefficients by a combined vibrational-purerotational Raman lidar,” Appl. Phys. B 79, 775–782 (2004). 12. M. Radlach, A. Behrendt, and V. Wulfmeyer, “Scaning rotational Raman lidar at 355 nm for the measurement of tropospheric temperature fields,” Atmos. Chem. Phys. 8, 159–169 (2008). 13. I. Serikov, H. Linne, F. Jansen, and B. Brugmann, “Combined visible and UV pure rotational Raman lidar channel for air temperature profiling,” in Proceedings of the 25th International Laser Radar Conference, St. Petersburg, Russia, 2010, pp. 27–30. 14. J. Mao, D. Hua, Y. Wang, F. Gao, and L. Wang, “Accurate temperature profiling of the atmospheric boundary layer using an ultraviolet rotational Raman lidar,” Opt. Commun. 282, 3113–3118 (2009). 15. S. Chen, Z. Qiu, Y. Zhang, H. Chen, and Y. Wang, “A pure rotational Raman lidar using double-grating monochromator for temperature profile detection,” J. Quant. Spectrosc. Radiat. Transfer 112, 304–309 (2011). 16. P. Achtert, M. Khaplanov, F. Khosrawi, and J. Gumbel, “Pure rotational-Raman channels of the Esrange lidar for temperature and particle extinction measurements in the troposphere and lower stratosphere,” Atmos. Meas. Tech. 6, 91–98 (2013). 17. A. Behrendt, T. Nakamura, M. Onishi, R. Baumgart, and T. Tsuda, “Combined Raman lidar for the measurement of atmospheric temperature, water vapor, particle extinction coefficient, and particle backscatter coefficient,” Appl. Opt. 41, 7657–7666 (2002). 18. D. Nedeljkovic, A. Hauchecorne, and M. L. Chanin, “Rotational Raman lidar to measure the atmospheric temperature from the ground to 30 km,” IEEE Trans. Geosci. Remote Sens. 31, 90–101 (1993). 19. R. B. Lee III, “Tropospheric temperature measurements using a rotational Raman lidar,” doctoral dissertation (Hampton University, 2013). 20. F. Liu and F. Yi, “Spectrally resolved Raman lidar measurements of gaseous and liquid water in the atmosphere,” Appl. Opt. 52, 6884–6895 (2013). 21. F. Yi, S. Zhang, C. Yu, Y. He, X. Yue, C. Huang, and J. Zhou, “Simultaneous observations of sporadic Fe and Na layers by two closely collocated resonance fluorescence lidars at Wuhan (30.5°N, 114.4°E), China,” J. Geophys. Res. 112, D04304 (2007). 22. C. M. Penney, R. L. St. Peters, and M. Lapp, “Absolute rotational Raman cross sections for N2, O2, and CO2,” J. Opt. Soc. Am. 64, 712–716 (1974). 23. A. Cohen, J. A. Cooney, and K. N. Geller, “Atmospheric temperature profiles from lidar measurements of rotational Raman and elastic scattering,” Appl. Opt. 15, 2896–2901 (1976). 24. U. Wandinger, “Raman lidar,” in Lidar Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 242–271. 25. D. Hua, M. Uchida, and T. Kobayashi, “Ultraviolet highspectral-resolution Rayleigh–Mie lidar with a dual-pass Fabry–Perot etalon for measuring atmospheric temperature profiles of the troposphere,” Opt. Lett. 29, 1063–1065 (2004). 26. R. K. Newsom, D. D. Turner, B. Mielke, M. Clayton, R. Ferrare, and C. Sivaraman, “Simultaneous analog and photon counting detection for Raman lidar,” Appl. Opt. 48, 3903–3914 (2009).

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