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A comparative study of Rayleigh lidar performance

G. P. Gobbi_{(∗) and L. Reali}

Istituto di Scienze dell’Atmosfera e del Clima, CNR - Roma, Italy

(ricevuto l’8 Maggio 2000; revisionato il 13 Settembre 2001; approvato il 18 Settembre 2001)

Summary. — Two co-located Rayleigh lidarshave been operated together to as-sess the quality of the middle-atmosphere temperature profiles obtained by this technique. Telescopes of the two systems have a 5 m2 and a 1.2 m2 collecting area, respectively. The smaller receiver has been implemented to replace the larger one in long-term observations of the middle-atmosphere temperature. A procedure to determine systems dead time is presented and characteristics of the dead-time correction are discussed. Temperature retrievals were performed at night with typ-ical integration time of 2 hoursand verttyp-ical resolution of 2.7 km. Comparative results reveal a systematic temperature difference between the two instruments of approximately 0.1 K. Fluctuationsin temperature differenceswell follow a Poisso-nian statistics at levels above 45 km. Below that altitude the temperature differences do not decrease with the same law but remain quasi-constant, at a level of about 0.7 K. We show that the systematic part of these differences is attributable to the dead-time correction of the larger receiver, the balance being caused by shot-noise in the smaller receiver. Therefore, the error of the new system is at most of 0.5 K be-low these levels. These results stress the importance of determining accurate signal corrections in Rayleigh lidar observations.

PACS 92.60.Ry – Climatology.

PACS 94.10.Dy – Atmospheric structure, pressure, density, and temperature (strato-sphere, meso(strato-sphere, thermo(strato-sphere, exosphere).

1. – Introduction

Rayleigh lidars exploit the proportionality existing between the elastic backscatter (li-dar signal) and the molecular density of a particle-free atmosphere to retrieve atmospheric temperature proﬁles [1].Such a retrieval is performed under the well-posed assumption of thermodynamic equilibrium and perfect gas behavior of the atmosphere [2].In this way, the temperature of the region above the stratospheric aerosol layer (30–35 km) can be easily retrieved up to an altitude of approximately 80–100 km.

(∗) E-mail: g.gobbi@isac.cnr.it

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Table_{I. – Technical speciﬁcations of the two Rayleigh lidar systems.}

Emitter Receivers

36-Mirror 6-Mirror

Nd-YAG laser Range 35–90 km Range 20–80 km

Wavelength 532 nm Telescope: 36-mirror mosaic, Telescope: 6× 50 cm mirror, Pulse energy 0.25–0.35 J 5 m2 surface area 1.2 m2 surface area

Pulse length 13 ns Bandwidth: 1nm interference Bandwidth: 2 nm interference

ﬁlter ﬁlter

Repetition rate 10 Hz 24000 rpm shutter Fiber optic link Beam diameter 4 cm Photon counting Photon counting Beam divergence 0.3 mrad Vertical resolution: 300 m Vertical resolution: 300 m

Cross validations of lidar and satellite-retrieved temperatures have already appeared in the literature [3,4].First long-term analyses of lidar-measured middle-atmosphere tem-perature [5] clearly demonstrate the importance of such a technique for climatological studies.In fact, climate models indicate that the stratopause temperature is more sensi-tive to greenhouse eﬀects than the troposphere and that a cooling of 8–10 K is expected for a doubling in the tropospheric CO₂ concentration from pre-industrial levels [6, 7].

A Rayleigh lidar for the night-time observation of middle-atmosphere temperature has been operated by the Institute of Atmospheric Physics CNR at Frascati, Italy (42◦ N-13◦E) between 1989 and 1997.Main aim of this project is to collect a record long enough to provide some insight into possible greenhouse-induced middle-atmosphere temperature changes [8].A first analysis of the Frascati record showed that the stratopause at 45– 55 km is the region in the middle atmosphere the less affected by natural temperature variability [8].This region appears then to be well suited for the detection of possible greenhouse-induced effects.However, length of the observational record and quality of the data play a crucial role in detecting long-term trends.The necessity to move the lidar facility to new laboratories in late 1997 and the impossibility to displace the large 36-mirror telescope, determined the need to build a second Rayleigh receiver.This new system became operational in May 1996.Temporary availability of two Rayleigh lidars at the same site then provided the opportunity to make intercomparisons and evaluate factors as the performance of the new system, relative errors and reliability of the Rayleigh lidar temperature technique.This paper will present the results obtained during four intercomparison tests carried out at Frascati in the period May 1996 - February 1997.

2. – The lidar systems

Table I summarizes the characteristics of the two Rayleigh lidars operated at Fras-cati in 1996-97.A single Nd:YAG laser emitting 300 mJ, 532 nm pulses at 10 Hz was used as a common source for the two lidars.The old receiver was based on a Newto-nian, 36-mirror telescope, with 8 m focal length and total surface area of 5 m2.The photomultiplier detector was placed at the focal plane of the telescope [8].Conversely, the new collector consists of six 50-cm parabolic mirrors with 150 cm focal length and total surface area of 1.2 m2.Each mirror focuses onto a 1-mm diameter optical ﬁber, which both determines the system ﬁeld of view (1/1500 rad) and conveys the received

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radiation onto a photomultiplier, common to the six mirrors.For both receivers, signal detection is performed in a photon counting mode, i.e. single-photon light pulses are discriminated, gated and counted.PC-based multi-channel counters are employed for integrating the signal.Typical acquisitions last 2 hours, divided into eight 15-minute records and have a vertical resolution of 300 m, determined by the 2 µs gating time of the counter.Nine-point running averages are applied to the signals, then reducing the actual vertical resolution of temperature proﬁles to 2700 m.

Temperature proﬁles T (z) are obtained by means of the inversion method developed by Hauchecorne and Chanin [8],i.e. at each height z, we have

T (z) = [M × g × dz]/[R × d ln(p(z))] ,

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where M , g and R are the air mean molecular weight, the acceleration of gravity and the universal gas constant, respectively.The change in pressure logarithm across the altitude interval dz (centered at the heigth z) is computed from the pressure profile p(z) obtained by integrating the lidar-derived air-density profile upward of the calibration point, chosen at 36 km [8].Both values of air-density at 36 km and pressure at the upper end of the profile [8] are obtained by the CIRA 86 model atmosphere [9].It is useful to note that an error of 1% in the lidar-derived air density (i.e. signal) corresponds to a temperature error of approximately 1%,i.e. of the order of 2.5 K at 45 km.

During the comparative measurements the new 6-mirror receiver was located in a cabin next to the 36-mirror telescope building, approximately 7 m apart from the laser beam.Such separation allowed for full superposition of the laser beam and telescope ﬁeld of view only upward of 18 km, thus eliminating the saturation and hysteresis problems generated by intense returns from the lower atmosphere.Conversely, being located next to the laser beam, the 36-mirror receiver always employed a mechanical shutter rotating at 24000 rpm to avoid laser returns from below 20 km altitude and the resulting hysteresis.

3. – Determination of the lidar receiver dead time

When approaching their limiting frequency all counters are subject to dead-time losses.In photon counting techniques, the dead time (τ ) is the typical time lag be-tween successive photons at which counting losses become signiﬁcant.In our systems, when returning photons start to get close and pile-up, the counter ﬁrst misses pulses, then gets saturated when the signal reaches constantly above the discriminator threshold level.For this kind of counters it has been shown [10] that the actual input signal rate

S_i is linked to the measured signal rate S₀ by the relationship

S_i = S₀exp[S_iτ] . (2)

To determine the dead time τ of lidar receivers a simple technique has been imple-mented: the signal is first recorded in normal conditions,i.e. reaching non-linear response in the low-altitude range.The signal is then attenuated by a factor of approximately 30 by placing a neutral density filter (ND = 1.5) in front of the photomultiplier and recorded again.Thanks to its lower photon rate, this latter trace extends its linearity down to lower altitudes.This procedure is iterated at least twice to smooth out possible signal fluctuations during the 15-minute acquisition averages.The attenuated trace is then normalized to the non-attenuated one (S₀) and used as a reference,i.e. it is assumed to

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Fig. 1. – Lidar signals recorded to deﬁne the dead time of the 6-mirror receiver: the attenuated and non-attenuated signals are plotted by dashed lines with full square and full triangle symbols, respectively. The attenuated signal after normalization in the 35–45 km region is plotted by a solid line with open squares. The non-attenuated signal after 8 ns dead-time correction is plotted by a solid line with open triangles.

represent Si.The system dead time is then determined as the best ﬁt to the various τ obtained by solving eq.(2) at diﬀerent signal rates,i.e. altitudes.

The two traces recorded to define the dead time of the 6-mirror receiver, τ6, are reported in fig.1. Here the attenuated and non-attenuated signals are represented by dashed lines with full square and full triangle symbols, respectively.After normalization in the 35–45 km region, the attenuated signal is then plotted by the open square solid line.Comparison of the normalized attenuated and non-attenuated signal shows that the latter starts missing counts in the region below approximately 27 km, i.e. at rates higher than 10 MHz.We then employ eq.(2) at each measurement point to determine the value of τ which equals the non-attenuated signal (S0) to the attenuated one (Si). The plot of the resulting values of τ vs.signal rate for the 6-mirror receiver is reported in fig.2. This plot shows that the estimated values of τ are not perfectly constant over the comparison range.In fact, at rates below 5 MHz the higher noise in the attenuated signal S_i leads to an increase in the variability of the derived τ .Conversely, values of τ are quite regular at higher frequencies.

Naturally, dead-time corrections are possible only before the non-attenuated channel gets saturated.Our measurements showed this to happen at count rates of approximately

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Fig. 2. – Plot of computed dead timeτ at various signal rates for the 6-mirror system (solid line with dots). The linear ﬁt in the region 1–25 MHz is shown as a dashed line.

30 MHz.Therefore, the linear fit to evaluate the average value of τ from the plot in fig.2 has been computed in the interval 1–25 MHz.This fit reveals a typical dead time of

τ₆ = 8 ns for the 6-mirror system.The slightly positive slope of the fit visible in fig.2 also indicates that, in the attempt to correct for saturation effects, τ tends to increase at higher frequencies and therefore the dead-time correction should be intended as a first-order correction.

The non-attenuated signal after dead-time correction is reported in ﬁg.1 by a full line with open triangles.This trace presents a good agreement (within 1%) with S_i up to approximately 14 MHz (25 km), while being undercorrected at higher rates.This shows that even after dead-time correction, discrepancies with respect to the attenuated signal sharply increase for corrections larger than 12%.Use of the 8 ns dead time leads to signal corrections of approximately 22% at 25 MHz rates, 10% at 12 MHz and 5% at 6 MHz (approximately 29 km).A correction of 5% is then the maximum one accepted in our lidar analysis.With respect to the 1% correction region (1.24 MHz, corresponding to approximately 37 km altitude), the altitude gain achieved by the use of the dead-time correction is of approximately 11 km, when accepting up to a 10% correction and 8 km for a 5% correction.

The dead time of the 36-mirror receiver, evaluated by means of the same technique, is τ36= 7.7 ns.However, due to the larger telescope collecting area the signal is in this case rather stronger and the correction is of the order of 1% at 45 km, 2.5% at 40 km, 6.6% at 35 km and 17% at 31 km.

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Fig. 3. – Temperature proﬁles (solid lines) obtained by the two receivers on June 27, 1996. Dashed lines represent the measurement statistical error. Below 32 km each proﬁle is comple-mented by a radio sounding taken approximately 30 km West of Frascati.

4. – Co-located lidar observations

The expected random error in lidar temperature proﬁles is usually expressed as the statistical ﬂuctuation of the detected signal, which is assumed to be Poissonian [11]. This error does not include possible dead-time losses of the signal, i.e. it is assumed that, if applied, the dead-time correction does not introduce any error.In the case of the 36-mirror telescope, at the 2.7 km vertical resolution and 2-hour integration time em-ployed here, the statistical error is of the order of 0.3 K at 45 km and 1.3 K at 65 km [8]. Because of the lack in independent accurate temperature observations at altitudes above radio-sounding levels, systematic errors are harder to evaluate.In this respect, comparisons made between a one-year temperature record as obtained by several lidars and by the NOAA-NMC satellites have shown the latter retrievals to be on average 2 K warmer than lidar ones at 10 hPa (approximately 32 km), and 2 K colder between 5 and 1 hPa (37–47 km) [4].In that study, the Frascati lidar typically detected temperatures 3 K colder than satellite at 10 hPa and 3.5 K warmer between 5 and 1 hPa. Availability at Frascati of a second lidar receiver also allows to cross-check the quality of these previous measurements.

The series of four lidar intercomparison observations was carried out in the period May 1996-February 1997.Overall, these measurements show a good agreement between old and new receiver results.As an example, in fig.3 are reported temperature profiles obtained on June 27, 1996.Below 32 km, lidar-retrieved temperatures are complemented by data from radio-soundings taken approximately 30 km South-West of Frascati.These profiles show that the 6-mirror system maximum altitude was of approximately 80 km,i.e. some 6 km lower than the 36-mirror receiver (maximum altitude is determined here by the signal descending below two standard deviations of the background noise).This result is consistent with the large telescope signal being about 4 times the smaller telescope one.As previously mentioned, the statistical error of the lidar linear measurement is

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Fig. 4. – Diﬀerencesbetween the temperature measured by the 6-mirror and the 36-mirror lidar systems (∆T = T₆− T₃₆) as a function of the 6-mirror telescope count rate. Diﬀerent symbols represent the measurement date: 30 May 1996 (open triangles), 31 May 1996 (full diamonds), 27 June 1996 (full squares), 7 February 1997 (full stars). Solid lines show the average sum of the statistical errors of the two measurements.

proportional to the signal square root.In this respect, the new system is characterized by an error approximately two times larger than the 36-mirror receiver one.This error is of the order of 0.5 K at 45 km, the level best-suited for the detection of greenhouse-induced changes [8].

In fig.4 are shown the temperature differences (∆T = T₆− T₃₆) measured by the two systems as a function of the 6-mirror telescope count rate.In the same figure the average sum of the expected statistical errors of the two measurements is also plotted.Up to 60 km,i.e. the region where calibration errors start to influence the temperature retrieval, the average value of temperature differences reported in fig.4 is ∆T = +0.10 K.In this respect, the two independent retrievals show little systematic shift and are very consistent one with another.In the region 35–45 km, the new system detects temperatures 0.2 K warmer than the old one.Since comparisons with satellite retrievals [4] showed a ten-dency of the 36-mirror system to measure temperatures warmer than NOAA satellites, this result acts in support of the quality of the lidar profiles employed in those compar-isons.Therefore, we can confirm a tendency of the NOAA-NMC to underestimating the atmospheric temperature at the stratopause.

Above approximately 45 km, the scatter of ∆T values well agrees with the hypothesis that errors follow a Poissonian statistical distribution (errors proportional to the signal square root).In fact most of the data points fall within the sum of the two statistical error bars plotted in ﬁg.4. However, below 45 km, i.e. for count rates larger than 100 kHz, the expected statistical error curve tends to decrease with a slope steeper than

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actual temperature diﬀerences do.In this region, ∆T values stay within a quasi-constant variability range of approximately±1.5 K, with typical standard deviation σ_∆T = 0.73 K. We explain the increasing discrepancy at altitudes below 45 km as due to increasing eﬀects of the dead-time correction on the large telescope signal and to shot noise in the smaller telescope one.In fact, from the points mentioned in sect.3, the dead-time correction of the 36-mirror signal is of the order of 6.6% at 35 km and 1% at 45 km,

i.e. it is likely that this signal is increasingly underestimated for decreasing altitudes.

We would then expect a larger rate of density (i.e. pressure) change between 35 and 45 km in the 36 mirror signal with respect to the 6-mirror one.According to eq.(1) this would lead, as observed, to systematically lower temperatures measured by the larger lidar system at these levels.We then expect this effect to be responsible for both the systematic difference observed between the two lidar profiles above 45 km (0.1 K) and of its increase (from 0.1 to 0.2 K) below 45 km.

Conversely, oscillating differences appearing in fig.4 are attributed to random noise observed in the 6-mirror signal.This was possibly generated by the long transmission line employed in these observations and contribute for the balance 0.5 K to the total temper-ature differences reported above.These results indicate that at altitudes below 45 km, the 6-mirror Rayleigh lidar temperature profiles discussed here are characterized by a typical error of at most 0.5 K. Nevertheless, due to the larger receiver dead-time effects, comparisons below the 45 km level should not be used in the reciprocal characterization of the systems.

5. – Conclusions

Two Rayleigh lidars, one employing a 36-mirror, 5 m2receiver, the second a 6-mirror, 1.2 m2 receiver, have been operated together to characterize lidar-derived atmospheric temperature profiles.Measurements were taken at night, with vertical resolution of 2.7 km (9-point running averages of signal digitized every 300 m) and with a 2-hour in-tegration time.Results show very good consistency of the two instruments, with slightly warmer temperatures (0.1 K) systematically observed by the new, 6-mirror system. Mea-surement errors, defined by differences between temperatures retrieved by the two sys-tems, closely fall within the expected statistical Poissonian distribution down to altitudes of approximately 45 km.Below that level measurements are characterized by a quasi-constant variability range of ±0.73 K and a systematic difference of about 0.2 K. This behavior is explained as generated by dead-time correction effects in the larger telescope signal summed to shot noise in the smaller system signal.For the new 6-mirror receiver, these results convert into a typical error of at most±0.5 K below the stratopause.

A method for the definition of the Rayleigh lidar dead time presented here led to the finding of a typical dead time of τ₆ = 8 ns for the 6-mirror receiver and τ₃₆ = 7.7 ns, for the 36-mirror one.Use of the dead-time correction in the saturating lidar signal also showed that corrections of at most 10% of the measured signal still result in acceptable temperature profiles.Since maximum corrections of 5% were accepted in our inversion procedure, this result confirms the reliability of lidar profiles commonly retrieved by our new system down to approximately 25 km.Finally, the Rayleigh lidar intercomparisons presented here showed that the new 6-mirror receiver designed to operate at the ISAC laboratories in Rome provides observations consistent with the old 36-mirror system, allowing then for a reliable continuation of the temperature observations collected at Frascati in the period 1989-1997.

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