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Journal of Quantitative Spectroscopy &Radiative Transfer

Journal of Quantitative Spectroscopy & Radiative Transfer 125 (2013) 45–50

0022-40http://d

n CorrE-m

pat.mcc

journal homepage: www.elsevier.com/locate/jqsrt

Cloud temperature measurement using rotational Raman lidar

Jia Su a,n, M. Patrick McCormick a,n, Yonghua Wub, Robert B. Lee IIIa, Liqiao Lei a,Zhaoyan Liu c, Kevin R. Leavor a

a Center for Atmospheric Sciences, Department of Atmospheric and Planetary Sciences, Hampton University, Hampton, VA 23668, USAb Optical Remote Sensing Laboratory, the City College of New York, NY 10031, USAc National Institute of Aerospace, Hampton, VA 23666-6147, USA

a r t i c l e i n f o

Article history:Received 5 January 2013Received in revised form11 March 2013Accepted 8 April 2013Available online 17 April 2013

Keywords:Cloud temperatureLidarRotational Raman

73/$ - see front matter & 2013 Elsevier Ltd.x.doi.org/10.1016/j.jqsrt.2013.04.007

esponding author. Tel.: +1 757 728 6867; faail addresses: jia.su@hamptonu.edu, sujia080ormick@hamptonu.edu (M. Patrick McCorm

a b s t r a c t

Insufficient suppression of the elastic-scattering signal in the rotational Raman (RR)detection channels can result in a retrieval error particularly when the temperature of athick cloud is measured using an RR lidar. To solve this problem, a technique is presentedto obtain relative transmission factors for the two RR channels' thereby correcting for theinfluence of residual elastic-signal on the temperature retrieval. The feasibility of thistechnique is demonstrated by applying the algorithm to the Hampton University (HU)lidar measurements. Intercomparisons of these temperature retrievals from both water-phase and cirrus clouds show good agreement with radiosonde measurements.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The study of clouds plays a key role in the understandingof climate change. Reliable measurements of temperature inclouds are important for improving our understanding ofcloud physics, cloud dynamics, and for validating cloud-resolving models [1–5]. Whether from the ground or from asatellite, an instrument that measures the intensity ofinfrared radiation is usually used to measure the tempera-ture of the cloud [6–7]. However, this temperature is biasedby the cloud droplets that are nearest the edge or side ofthe cloud that is being viewed. For instance, the cloudtemperature that is seen by satellite sensors is usually referredto as the temperature of the top of the cloud [8–12]. Radio-sondes sometimes penetrate clouds, as do commercial air-crafts, providing measurements of the interior of clouds[11,12]. Most radiosonde and airborne temperature measure-ments are using “immersion thermometers,” which employ asensor that is immersed into the ambient airstreams. It is

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x: +1 757 727 5090.4@163.com (J. Su),ick).

known that cloud temperature measurement using immer-sion thermometers is limited by two factors: the wetting ofthe sensor by cloud drops and the slowness of response [13–15], which may result in the big error for cloud temperaturemeasurement. Now rotational Raman (RR) lidars have beenproven to be a very useful remote sensing tool to measureatmospheric temperature [16–19]. Generally, conventional RRlidars use a narrow-band interference filter to block theelastic-scattering signal in the RR-channels; this has beenwellverified under the clear sky (only molecular and aerosolelastic-scattering signals) [17,18]. In theory, the capabilitiesof RR technique are extended to the measurement of atmo-spheric temperature even in the presence of cloud. Behrendtand Reichardt have developed the multi-cavity polychromatorallowing temperature measurements independent of thepresence of thin clouds and no influence of particle scatteringon the lidar temperature profile was observed in cloudswhose backscatter ratio is smaller than 45 [20]. However, thiswill become an issue to measure the thick cloud. Becausethick cloud elastic-scattering signals are very strong andRR-wavelengths are so close to the elastic-scatteringwavelength, the narrow-band interference filter in theRR-channel cannot completely suppress the elastic signal,which makes it impossible to retrieve cloud temperature

J. Su et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 125 (2013) 45–5046

without any correction. Herein, we propose a technique thatcan effectively correct this influence on the temperatureretrievals and thus improve the retrieval accuracy of cloudtemperature. This technique is further validated by showinggood agreement between HU RR-lidar and radiosonde mea-surements of cloud temperature.

2. Method

HU lidar can obtain elastic backscatter signals(354.7 nm) and two RR signals (353.35 nm and354.2 nm) excited by 354.7 nm laser beam at the sametime. In general, the elastic backscatter signal in the cloudcan be expressed as

Xeðz; λeÞ ¼Ce

z2βmðz; λeÞ þ βcðz; λeÞ� �

exp −2Z z

0½αmðz0; λeÞ þ αcðz0; λeÞ�dz0

� �:

ð1Þ

Two RR signals in the cloud can be expressed as

Xr1ðz; λr1Þ ¼Cr1

z2βr1ðz; λr1Þexp −

Z z

0½αmðz0; λeÞ þ αcðz0; λeÞ

�

þαmðz0; λr1Þ þ αcðz0; λr1Þ�dz0�

ð2Þ

Xr2ðz; λr2Þ ¼Cr2

z2βr2ðz; λr2Þexp −

Z z

0½αmðz0; λeÞ þ αcðz0; λeÞ

�

þαmðz0; λr2Þ þ αcðz0; λr2Þ�dz0�

ð3Þ

Then atmospheric temperature can be derived fromtwo RR signals and written as [18]

TðzÞ ¼ aIn½ðXr1ðz; λr1ÞÞ=ðXr2ðz; λr2ÞÞ� þ b

ð4Þ

where in Eqs. (1)–(4) C is the lidar constant; β and α are thebackscatter and extinction coefficients; the subscripts ofe, r1 and r2 refer to elastic, and two RR backscatterings;the subscripts of c and m refer to clouds and moleculesrespectively; λ is the wavelength; X is the lidar signal; z isthe altitude; T is the temperature; and a and b are thecalibrated coefficients obtained using balloon-sounding'stemperature.

However, when the laser beam meets thick clouds andthe elastic backscatter signals leak into two RR channels,the total signals from two RR channels will then become asfollows:

XLr1ðz; λr1Þ ¼ Xr1ðz; λr1Þ þ k1Xeðz; λeÞ ð5Þ

XLr2ðz; λr2Þ ¼ Xr2ðz; λr2Þ þ k2Xeðz; λeÞ ð6Þ

where k1Xe(z, λe) and k2Xe(z, λe) are the elastic backscattersignals leaked into two RR channels; k1 and k2 are two RRchannels' transmission for elastic backscatter signals fromHU lidar elastic channel and neutral density filters areused to avoid elastic channel detector damage due tostrong cloud backscatter signals. When k1 and k2 areknown, even if there is insufficient suppression of theelastic backscatter signal in the RR detection channels,

cloud temperature can still be retrieved using the follow-ing expression:

TðzÞ ¼ a

InððXLr1ðz; λr1Þ−k1Xeðz; λeÞÞ=ðXL

r2ðz; λr2Þ−k2Xeðz; λeÞÞÞ þ b

ð7ÞIn this paper, we propose a technique to obtain k1 and

k2 with the following principle. When the cloud elasticbackscatter signal is strong enough and the leaked elasticsignals (k1Xe(z, λe) and k2Xe(z, λe)) are far more thanrotational Raman signals (Xr1(z, λr1) and Xr2(z, λr2)), thenEqs. (5) and (6) can be written as

XLr1ðz; λr1Þ≃k1Xeðz; λeÞ ð8Þ

XLr2ðz; λr2Þ≃k2Xeðz; λeÞ ð9Þ

Thus, k1 and k2 can be obtained using

k1≃XLr1ðz; λr1ÞXeðz; λeÞ

; k2≃XLr2ðz; λr2ÞXeðz; λeÞ

ð10Þ

So the next key step in this technique is to determinewhen clouds are thick enough to satisfy that elastic back-scatter signals leaked into RR detection channels are farmore than RR signals. To this end, we first obtain the ratiosof signals from two RR channels to elastic backscattersignals using Eqs. (5) and (6) respectively dividing Eq. (1)as follows:

R1ðzÞ ¼XLr1ðz; λr1ÞXeðz; λeÞ

¼ Xr1ðz; λr1ÞXeðz; λeÞ

þ k1 ð11Þ

R2ðzÞ ¼XLr2ðz; λr2ÞXeðz; λeÞ

¼ Xr2ðz; λr2ÞXeðz; λeÞ

þ k2 ð12Þ

It can be seen that when the leaked elastic backscattersignals are far more than RR signals at altitudes of z1 and z2(z1 and z2 are adjacent range bins from cloud base to cloudtop), R1(z1) and R1(z2) are equal to k1, and R2(z1) and R2(z2)are equal to k2 according to Eqs. (10) or (11), (12). Thus, thefollowing Eq. (13) can hold.

R1ðz1Þ ¼ R1ðz2ÞR2ðz1Þ ¼ R2ðz2Þ ð13Þ

However, there is another situation; when the follow-ing Eq. (14) is satisfied, Eq. (13) can still hold.

Xr1ðz1; λr1ÞXeðz1; λeÞ

¼ Xr1ðz2; λr1ÞXeðz2; λeÞ

;Xr2ðz1; λr2ÞXeðz1; λeÞ

¼ Xr2ðz2; λr2ÞXeðz2; λeÞ

ð14Þ

Therefore, to ensure that Eq. (13) is only held by the farmore residual elastic scattering than RR signals, we needto exclude the situation that Eq. (14) holds. Below wefurther deduce an expression from Eq. (14) for the opera-tional and practical diagnosis. Because rotational Ramanwavelengths are very close to elastic wavelength, Eq. (14)can be re-written from Eqs. (1)–(3) as below:

Cr1βr1ðz1; λr1ÞCe½βmðz1; λeÞ þ βcðz1; λeÞ�

¼ Cr1βr1ðz2; λr1ÞCe½βmðz2; λeÞ þ βcðz2; λeÞ�

Cr2βr2ðz1; λr2ÞCe½βmðz1; λeÞ þ βcðz1; λeÞ�

¼ Cr2βr2ðz2; λr2ÞCe½βmðz2; λeÞ þ βcðz2; λeÞ�

ð15Þ

J. Su et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 125 (2013) 45–50 47

Then from Eq. (15), the following Eq. (16) can bereduced as

βmðz2; λeÞ þ βcðz2; λeÞβmðz1; λeÞ þ βcðz1; λeÞ

¼ βr1ðz2; λr1Þβr1ðz1; λr1Þ

¼ mðz2Þsr1½Tðz2Þ�mðz1Þsr1½Tðz1Þ�

βmðz2; λeÞ þ βcðz2; λeÞβmðz1; λeÞ þ βcðz1; λeÞ

¼ βr2ðz2; λr2Þβr2ðz1; λr2Þ

¼ mðz2Þsr2½Tðz2Þ�mðz1Þsr2½Tðz1Þ�

ð16Þ

where m is the molecular density, s is the RR backscattercross section and T is the temperature. Then Eq. (17) can becan obtained from Eq. (16).

βmðz2; λeÞ þ βcðz2; λeÞβmðz1; λeÞ þ βcðz1; λeÞ

¼ mðz2Þsr1½Tðz2Þ�mðz1Þsr1½Tðz1Þ�

¼ mðz2Þsr2½Tðz2Þ�mðz1Þsr2½Tðz1Þ�

ð17ÞThen Eq. (18) can be obtained from Eq. (17):

sr1½Tðz2Þ�sr1½Tðz1Þ�

¼ sr2½Tðz2Þ�sr2½Tðz1Þ�

ð18Þ

Below we illustrate that to make Eq. (18) hold, itrequires the temperature at z1 and z2 to be the same, e.g.T(z1)¼T(z2). Fig. 1 gives the Raman-scattering cross sec-tions at two different temperatures and the narrow-bandinterference filters transmittances in two RR channels.

From Fig. 1, we know that 353.35 nm RR backscatter-cross section will increase with increase of temperature;however, 354.2 nm RR backscatter-cross section willdecrease with increase of temperature [18]. Therefore,only when T(z1) is equal to T(z2), Eq. (18) can be tenable.Then with T(z1)¼T(z2), we can get sr1(T(z1))¼sr1(T(z2))and sr2(T(z1))¼sr2(T(z2)). Finally, Eq. (17) can be written as

βmðz2; λeÞ þ βcðz2; λeÞβmðz1; λeÞ þ βcðz1; λeÞ

¼ mðz2Þmðz1Þ

ð19Þ

Rel

ativ

e S

catte

ring

Cro

ssin

g-S

ectio

n, m

-1sr

2

1.2

0.8

0.4

0

Waveleng351.5 352 352.5 353 353

353.35 nm Fi

O2 at 270 kN2 at 270 k353.35 nm Filter Function

O2 at 2N2 at 22353.35

Fig. 1. Calculated atmospheric RR spectr

Further, when the distance of two adjacent range bins znand zn+1 is very small (spaced by 7.5 m for the HU lidar), thedifference of molecular densities at the two bins is verysmall and can be reasonably considered to be the same.Therefore, finally if Eq. (14) holds, then Eq. (19) will be equalto unity, which means the same total backscatterings at z1and z2. In other words, if Eq. (19) is not equal to unity (notsame total backscatterings at z1 and z2), then Eq. (14) cannothold. Under this situation, a holding Eq. (13) indicates thatthe leaked elastic backscatter signals into RR detectionchannels are far more than RR signals as mentioned earlier.

With the above note, here we define a function PXe asthe ratio of elastic signals at two adjacent bins as follows:

PXe ¼ Xeðz2; λeÞXeðz1; λeÞ

−1� �

� 100%

¼ βmðz2; λeÞ þ βcðz2; λeÞβmðz1; λeÞ þ βcðz1; λeÞ

e−2½amðz2 ;λeÞþaaðz2 ;λeÞ�dz−1� �

� 100%

ð20ÞThen with e−2½amðz2 ;λeÞþaaðz2 ;λeÞ�dzo1, the following Eq. (21)

can be obtained. Thus according to Eq. (21), when PXe ismore than zero, the two elastic backscattering signals at z1and z2 are not the same and more than zero, which meansthat Eq. (14) cannot hold.

βmðz2; λeÞ þ βcðz2; λeÞβmðz1; λeÞ þ βcðz1; λeÞ

−1� �

� 100%4PXe ð21Þ

In addition, we define the functions PR1 and PR2,respectively, as follows:

PR1 ¼ absR1ðz2ÞR1ðz1Þ

−1� �

� 100% ð22Þ

PR2 ¼ absR2ðz2ÞR2ðz1Þ

−1� �

� 100% ð23Þ

Filte

r Tra

nsm

issi

on, p

erce

nt

40

30

20

10

0

th, nm.5 354 354.5 355 355.5

lter

354.2 nm Filter

354.7 nm Elastic Beam

20 k0 k

nm Filter Function

um excited by 354.7 nm laser beam.

J. Su et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 125 (2013) 45–5048

According to Eqs. (22) and (23), when PR1 and PR2 areboth equal to zero, Eq. (13) can be satisfied at z1 and z2.Considering noise effects, we set the threshold conditionsPXe410%, PR1o5% and PR2o5%; when all of these con-ditions are satisfied, the leaked elastic backscatter signalsinto RR detection channels can be safely considered to befar more than the RR signals, and k1 and k2 in Eq. (7) can beobtained. The technique can also be used to validate thepurity of RR signals.

3. Errors analysis

In this section, we are taking into account only thestatistical error due to the random noise and fluctuationof detected photons (Raman-scattering signal, sky

Fig. 2. (a) The elastic signal at 354.7 nm and two RR signals (353.35 nm and 35R1, R2, PXe, PR1 and PR2 from 2.3 km to 2.45 km altitude; (c) the two correctetemperature results without (solid line) and with correction (dotted line) usinglidar temperature (K) with correction, and (f) HU lidar range-corrected signals

background and electronic noise). It increases as a functionof the altitude. The systematic errors can be from manysources such as the calibration constant accuracy fromtemperature results of balloon, temperature sensitivity offilters, multiple-scattering and so on which are not con-sidered here. The statistical uncertainties of two RR andelastic channels usually follow the Poisson distribution,hence the statistic uncertainty of temperature retrieval canbe estimated with the law of error propagation to Eq. (7),and it is given by the following formula [21]:

dTdz

¼ dfðaÞ=ðIn½ðXLr1ðz; λr1Þ−k1Xeðz; λeÞÞ=ðXL

r2ðz; λr2Þ−k2Xeðz; λeÞÞ� þ bÞgdz

¼ −a

fIn½ðXLr1ðz; λr1Þ−k1Xeðz; λeÞÞ=ðXL

r2ðz; λr2Þ−k2Xeðz; λeÞÞ� þ bg2

4.2 nm) measured by HU lidar at 22:10 on April 29, 2011; (b) the profiles ofd RR signals using elastic backscatter signal, k1 and k2; and (d) HU lidarEq. (7), and balloon-sounding's results (star). (e) Temporal variation of HUfor a time period of 20:30–22:20 on April 29, 2011.

J. Su et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 125 (2013) 45–50 49

� ðd½XLr1ðz; λr1Þ�=dzÞ−ðdk1=dzÞXeðz; λeÞ−k1ðd½Xeðz; λeÞ�=dzÞ

½XLr1ðz; λr1Þ−k1Xeðz; λeÞ�

(

þðd½XLr2ðz; λr2Þ�=dzÞ−ðdk2=dzÞXeðz; λeÞ−k2ðd½Xeðz; λeÞ�=dzÞ

½XLr2ðz; λr2Þ−k2Xeðz; λeÞ�

)

ð24Þwhere d[XLr1(z, λr1 )], d[XLr2(z, λr2)] and d[Xe(z, λe)] are statisticaluncertainties of two RR and elastic-scattering signals; dk1and dk2 are statistical uncertainties of k1 and k2.

4. Results

The HU lidar system has a bistatic configuration, consistingof transmitter, receiver, and data acquisition subsystems. Thelight source is a Nd:YAG laser (Continuum Powerlite 8020)emitting laser pulses at 20 Hz at the wavelengths of 1064 nm,532 nm and 354.7 nm. The divergence of laser is 0.45mrad.The receiver is built around a Cassegrainian-configured tele-scope whose primary mirror is 48 in. (122 cm) in diameterand focal length is 480 in. (1219 cm). HU lidar can collect threeelastic signals (1064 nm, 532 nm and 354.7 nm) and two RRsignals (354.2 nm and 354.35 nm) at the same time. Aphotomultiplier tube and an avalanche photodiode are usedfor the return signals detection. The FOV of the receiver isadjustable from 0 to 4 mrad. The data acquisition systemconsists of a lidar transient recorder (Licel TR-20-160), whichcan be operated in either an analog mode or a photon

Fig. 3. (a) Elastic signal at 354.7 nm, two RR-channel signals and two corrected Rtime) on October 26, 2011. (b) HU lidar temperature results without (dotted lin(c) Temporal variation of HU lidar temperature with correction. (d) HU lidar ran

counting mode. We present a case measured by HU lidar todemonstrate the technique described above. Fig. 2(a) showsthe 1-min average elastic signal at 354.7 nm and two RR-channel signals (353.35 nm and 354.2 nm) at 22:10 (localtime) on April 29, 2011. The statistic errors are given in theerror bars. According to Fig. 2(a), we focus on the signals from2.3 km to 2.45 km altitude because the cloud backscattersignals are very strong and two RR signals still have goodsignal-to-noise ratio (SNR). Fig. 2(b) shows the profiles of R1,R2, PXe, PR1 and PR2 from 2.3 km to 2.45 km altitude. Thepoints outlined by the black rectangle are satisfied with thecondition (PXe410%, PR1o5% and PR2o5%) andk1¼1.2�10−576.3�10−7 and k2¼3.6�10−477.9�10−6

are obtained using Eq. (10). These selected points are reason-able because they correspond to the positions of strongestelastic-scattering signals of clouds. Fig. 2(c) shows the twocorrected RR signals using elastic backscatter signal, k1 and k2;they become much more reasonable than the raw data byshowing a dramatic decrease in the cloud due to the largecloud attenuation. Presented in Fig. 2(d) are HU lidar tem-perature results without (solid line) and with correction ofelastic-signals (dashed line) using Eq. (7), and balloon-sound-ing's results (star symbol). The error bars represent thestatistical errors caused by the random noise of return signalsand correction constants k1 and k2. It is observed that thedifference of lidar results without correction and balloon-sounding results will be increasing with the increase of cloudbackscattering; however, the lidar results using the corrected

R-channel signals using elastic backscatter signal, k1 and k2 at 22:10 (locale) and with correction (solid line), and balloon-sounding's results (star).ge-corrected signals.

J. Su et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 125 (2013) 45–5050

RR-signals agree well with radiosonde's results. And cloudtemperature without correction is lower than balloon-sound-ing's and cannot show the temperature inversion of cloud. Onthe other hand, the radiosonde data show the low range-solution, so only two data points in the clouds can becompared. There are no temperature results from 2.38 kmto 2.45 km because of low SNR of corrected RR signals in therange. Presented in Fig. 2(e) is the temporal variation of HU-lidar measured temperature with correction using Eq. (7) at20:30–22:20 in the night. Fig. 2(f) shows the temporalvariation of corresponding elastic signals which indicate theclouds at 2–2.5 km altitude after 22:00. From Fig. 2(e), cloudtemperature outlined by a black circle is determined using ourproposed method and it clearly shows cloud temperatureinversion. As the low-level clouds are usually warm andwater-phase clouds, our result illustrates that the tempera-tures are above 274 K for the clouds at 2.0–2.5 km altitude;thus, the temperature retrievals of low clouds in Fig. 2 arereasonable.

Other example for the cumulus cloud is further demon-strated with this technique. Fig. 3(a) shows the 10-minaverage elastic signal at 354.7 nm, raw RR-channel signalsand corrected RR-channel signals at 22:10 (local time) onOctober 26, 2011. Fig. 3(a) shows that the cumulus cloudsappear at 4.0–4.5 km; the corrected RR-channel signalsobtained with above k1 and k2 are more reasonable than theraw ones in the cumulus clouds. Presented in Fig. 3(b) are HUlidar temperature results derived with the raw RR-signals andcorrected RR-signals, and balloon-sounding's results (squaresymbol). Clearly, the lidar-derived cloud temperatures withthe corrected RR-signals agree well with balloon-sounding'sresults, but the difference between lidar results withoutcorrection and balloon-sounding results will be increasingwith the increase of cloud backscattering. Presented in Fig. 3(c) is the temporal variation of HU lidar temperature resultswith correction for a time period of 22:00–06:00 on October26–27, 2011. Fig. 3(d) shows the temporal variation ofcorresponding lidar range-corrected signals which indicatethe clouds between 3.5 and 4.5 km. For this case, the cloudsshow the stable heights, depths and a few hours life-time at22:00–23:10 and 1:30–2:30. As we can see, the corrections onthe retrieved temperature are significant and show goodagreement with the radiosonde measurements (Fig. 3(b)).

5. Conclusion

In conclusion, we proposed a technique to improvecloud temperature retrieval from an RR lidar measurementwhen there is insufficient suppression of the strong elasticbackscatter signal of cloud in the RR-detection channels.A method is advanced to obtain two RR-channels' relativetransmission for elastic backscatter signal, and thereby theresidual elastic backscatter signal recorded by the RR-detection channels can be properly corrected using thetwo relative transmissions and elastic backscatter signal.With the method, cloud temperature can be reasonablyretrieved. We demonstrated this technique by presentingtwo cases analysis from the HU lidar measurements, andthe lidar-derived temperature profiles showed good

agreement with the radiosonde measurements. Theseresults indicated that the technique was feasible.

Acknowledgments

This study was supported by the PIRT project funded bythe US Army Research, Development and EngineeringCommand (AQC) Center (DOD) under HU PIRT Award(No. 551150-211150) and the National Oceanic and Atmo-spheric Administration (NOAA) under the grant—CRESTGrant no. NA06OAR4810162.

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