An airborne amplitude-modulated 1 . 57 μ m di ff erential laser absorption spectrometry : simultaneous measurement of partial column-averaged dry air mixing ratio of CO 2 and target range

An airborne amplitude-modulated 1.57 μm differential laser absorption spectrometry: simultaneous measurement of partial column-averaged dry air mixing ratio of CO2 and target range D. Sakaizawa, S. Kawakami, M. Nakajima, T. Tanaka, I. Morino, and O. Uchino Japan Aerospace Exploration Agency (JAXA), Tsukuba, Japan National Institute for Environmental Studies, Tsukuba, Japan now at: Japan Aerospace Exploration Agency, Tsukuba, Japan


Introduction
Evaluation of the spatial and temporal distribution of natural carbon fluxes over land and ocean continues to be difficult, hindering improvements in the quantification and understanding of the mechanism of the fluxes (Kawa et al., 2010;Kaminske et al., 2010).Uncertainty in flux evaluations is a major contributor to uncertainty in climate predictions (Randall et al., 2007).However, confirmation of the consistency between the sum of the regional and global budgets of carbon fluxes is expected to provide a unique index of the level of confidence in the outcomes of climate mitigation policies (IPCC, 2007).A global carbon cycle study using higher spatial resolution than an 8 • × 10 • grid is currently required to improve the knowledge of the carbon cycle (Rayner and O'Brien, 2001;Baker et al., 2011).Transport models and observational data sets improve evaluations of regional carbon fluxes (Maksyutov et al., 2008).A sustainable technique for CO 2 remote sensing from space is one of the greatest challenges and necessities for understanding the global carbon cycle, as well as for predicting and validating its evolution under future climate changes.
The Greenhouse gases Observing SATellite (GOSAT) is the first step in dealing with the above-mentioned issue (Kuze et al., 2009;Yoshida et al., 2011;Palmer et al., 2011).The sensors on-board GOSAT are based on a passive remote sensing technique.The GOSAT sensor was developed to derive the column-averaged mixing ratio of CO 2 (XCO 2 ) with a precision better than 1 % for an 8 • × 10 • grid without any biases or with uniform bias (Rayner and O'Brien, 2001;Houweling et al., 2004;Miller et al., 2007;Morino et al., 2011).However, there are unavoidable limitations imposed by the measurement approach: (1) the best performance for CO 2 total column measurements can only be obtained under clear-sky conditions; (2) seasonal dependence, such as in the Published by Copernicus Publications on behalf of the European Geosciences Union.D. Sakaizawa et al.: 1.57 µm differential laser absorption spectrometer case of the Northern Hemisphere in winter, reduces its global coverage; and (3) CO 2 measurements are highly sensitive to unknowns and variations in cloud and aerosol contamination.
In contrast, active optical remote sensing techniques as a differential absorption spectrometer (LAS) are less impacted by the above factors on atmospheric CO 2 measurements.Ground-based differential absorption lidar (DIAL) using a high-energy pulse laser has been developed to measure vertical CO 2 mixing ratios (Amediek et al., 2008;Sakaizawa et al., 2009;Ishii et al., 2010;Gibert et al., 2011).Airborne systems to observe partial column-averaged CO 2 have also been reported in earlier studies (Browell et al., 2011;Abshire et al., 2010;Spiers et al., 2011) to demonstrate technology feasible for future space-borne missions.Although in a pulsed system aerosol or cirrus clouds have less impact on total column measurements, the pulsed-laser wavelength must be stabilized at a seeding laser wavelength with a precision of less than 100 kHz to reduce error due to wavelength stability, which requires large resources.Errors due to variations in the surface reflectivity along the track also increase the impact, unless the transmitter has a double pulse system (Yu et al., 2003).Our fiber-based continuous laser approach to measure the differential absorption optical depth (DAOD = τ ) allows for compact storage of the components, including the electronics and optics.Moreover, the system achieves matching of the optical axes of multi-transmitted laser beams, which can contribute to reducing error due to incompleteness of footprint overlap.In this paper, we evaluated the performance of airborne 1.57 µm amplitude-modulated LAS for obtaining the partial column-averaged mixing ratio of CO 2 with simultaneous range detection.In addition, the impact of integrated aerosol signals on CO 2 measurements is described in an area where aerosol was enhanced (e.g., over urban area).

Partial column-averaged CO 2
A LAS system on an aircraft platform was utilized for measuring the light scattered or reflected by a target (land or sea surface or thick cloud).Our system employed three narrow linewidth lasers, which are based on continuouswave distributed feedback diode lasers and a fiber amplifier (Kameyama et al., 2011a).The system used two laser wavelengths during measurements, and the output of each laser was amplitude modulated by different sinusoidal waves.The details of amplitude modulation, frequencies, and phase shift are described in Sect.3.
One wavelength (offline, λ off ), for which there was weak or no gas absorption, was selected as a reference.The other wavelength (online, λ on ) was selected for strong gas absorption.In this airborne test, the online wavelength could be selected from the center (λ center ) or edge (λ edge ) position of the absorption curve (as shown in Fig. 1).The online laser power was attenuated by CO 2 relative to the offline wave- length in the atmosphere.By taking the ratio of online to offline signals, we could measure τ .
Our system obtained round-trip τ and the range (z) from the height of the aircraft above the target (Sakaizawa et al., 2010;Kameyama et al., 2011a): In Eq. ( 1), P r (λ on ) and P r (λ off ) are the online and offline laser powers received from the surface of the ground, P m (λ on ) and P m (λ off ) the monitored transmitted online and offline laser powers, φ the phase difference between the monitored and the received sinusoidal signals, T the period of a modulated sinusoidal signal, and c the speed of light.
The phase difference between transmitted and received sinusoidal signals corresponds to the range at which a target is acquired.Laser power is amplitude-modulated at 10 kHz for λ on , and at 11 kHz for λ off using LiNbO 3 devices.The phase identification is performed by the fast Fourier transform (FFT).This range of the detection technique is ambiguous at the inverse of the modulation frequency.However, the height of an elevated layer, such as cirrus or water clouds, can be compared with ground returns.In addition, images taken under the moving platform help in filtering signals with cloud returns, especially over complex terrain.The partial column-averaged dry air mixing ratio of CO 2 (XCO 2 (z)) from the ground to the aircraft height can be described by the following equation (Ehret et al., 2008): Here, z ac is the altitude of the aircraft; z grd , the height of the ground surface (mainly z grd = 0); w(r), the weighting function at a specific altitude r; σ , the differential absorption cross section of CO 2 between the online and offline wavelengths; n air , the air molecular number density; and V H 2 O , the water vapor mixing ratio.n air and V H 2 O are calculated from meteorological observation or mesoscale re-analysis data.
The measurement uncertainty is a quadratic summation of the precision and bias factors ((δXCO 2 /XCO 2 ) 2 = precision 2 + bias 2 ).In this paper, we evaluate the precision and bias separately.The precision is evaluated using following equations: (5) where δ τ represents the fluctuation in measured τ , and the second and third term depend on the errors of the range accuracy and the wavelength stability.If mesoscale data reanalysis is employed in Eq. ( 3), the error due to temporal and spatial differences compared with radiosonde measurements (corresponding to (0.16 %) 2 ) is added to Eq. ( 5).Of the total error, the breakdown is as follows: 0.10 % atmospheric temperature (uncertainty of 1 K), 0.12 % atmospheric pressure (uncertainty of 1 hPa), and 0.06 % relative humidity (uncertainty of 20 %).The bias error due to surface pressure is 0.035 % (corresponding to the range measurement accuracy of 5 m).
Considering the sensitivity of near-surface CO 2 and SNR τ , they depend on the stabilized position of the online wavelength (Fig. 1, top panel).As shown in Table 1 and Fig. 1 (top panel), τ taken by the λ center is greater than that taken by the λ edge .Operation at the λ center can mitigate the random error (δ τ ) to decrease the required SNR τ .However, the weighting function of the λ edge indicates a moderate peak less than an altitude of 2 km (Fig. 1, bottom panel), and yields a higher sensitivity at lower altitude.Therefore, in the case of Table 1, the difference of XCO 2 at a boundary-layer enhanced CO 2 profile is +3.9 ppm for the λ edge , +2.2 ppm for the λ center .This implies that the λ edge can more easily indicate a contrast between urban and vegetated areas.For this Table 1.Estimated τ and sensitivity of lower altitude CO 2 for the center and edge wavelength.Atmospheric parameters are based on the AFGL mid-latitude winter.Two CO 2 vertical profiles (boundary-layer enhanced and constant along height) were assumed: for one, the CO 2 mixing ratio was constant at 385 ppm along height; for the other, the mixing ratio was 410 ppm from the ground to 0.5 km, 398 ppm from an altitude of 0.5 to 2 km, and 385 ppm at an altitude above 2 km altitude, respectively.purpose, the wavelength stability on λ edge has to target an absolute precision of less than 1 MHz (1 SD < 300 kHz).The system with targeted wavelength stability at λ edge reduces the error due to the stability of the laser wavelength less than 0.03 %.In addition, use of both edge and wing wavelength (5 GHz offset to the center wavelength) provides better surface constraint and ≥ 50 % improvement in carbon flux evaluations over vegetated land areas at ∼ 500 km resolution for spaceborne measurements (Baker et al., 2011).The bias error is evaluated from the impact of the elevated particulate layer on the measured bias (τ bias ) and the spectroscopic parameter.The bias factor due to spectroscopic parameters is calculated using the Voigt profile function and the uncertainty from earlier studies (Devi et al., 2007;Rothman et al., 2009;Predoi-Cross et al., 2009).Measured τ bias is related to the path-integrated intensity of the aerosol layer or cirrus clouds.A narrow field of view and employment of range detection can allow ground and cloud return signals to be distinguished.Assuming the backscatter coefficients of suburban aerosol data (Sakaizawa et al., 2009), we found that the bias from the integrated backscatter depends on the surface albedo, for example, 0.13 % for a surface albedo of 0.1 sr −1 and 0.05 % for an albedo of 0.3 sr −1 .This evaluation indicates that higher surface albedo (such as for deserts) can suppress the impact of path-integrated aerosol intensity.Mitigation due to amplitude modulation is described in more detail in Kameyama et al. (2011b).

Airborne instruments
We first manufactured an LAS system for ground-based measurements (Kameyama et al., 2011a;Sakaizawa et al., 2009).Figure 2 shows the block diagram of the 1.57 µm prototype LAS system and other instrument settings in the aircraft cabin.The specifications for the instruments are summarized in Table 2.
The online and offline sources were polarizationmaintained, fiber-coupled diode lasers.The other system is based on optical fiber circuits.Laser-1 (as the center of  online wavelength) was stabilized within a root-mean-square (RMS) value of 12 MHz at the peak of the R(12) line in the 30012 ← 00001 absorption band using a gas cell filled with pure CO 2 instead of the reference cavity used in the Pound-Drever-Hall method (Drever et al., 1983).The gas cell was sealed with a gas pressure of 0.1 atm.Laser-2 (as the edge of online wavelength) was stabilized at a position of 2.55 GHz offset from the center position.Laser-1 and Laser-2 were combined using a fiber combiner and detected using a photodiode (InGaAs-PD).The PD generates a heterodyne signal in which the beat signal was controlled at a constant 2.55 GHz.Laser-3 was stabilized at offline wavelength within 48 MHz RMS by controlling its temperature and injection currents.The fiber-coupled outputs were amplitude modulated with LiNbO 3 devices.Each modulation signal had a different sinusoidal frequency.The modulated outputs were combined and amplified using a fiber amplifier.Almost all of the amplified power (99 %) was expanded and transmitted through an anti-reflection coated window.The diameter of the transmitted 1/e 2 beam was 60 mm, and the full angle beam divergence was 0.12 mrad.The total transmitted power at the fiber end was 1.2 W. The residual 1 % was monitored as a reference for received signals.Scattered signals from the ground surface were collected using a receiving telescope with a field of view of 0.2 mrad and a 110 mm active aperture.The receiving and transmitting optics were fixed on a rigid base plate.The signals were focused on a multi-mode fiber with a 200 µm core diameter and detected using a 0.5 mm diameter InGaAs-PIN PD.The received signals were digitized using a high-speed digitizer (60 MS s −1 , 14 bit).The wavelength identification and power evaluation were performed by means of fast Fourier transform (FFT) on a laptop computer.Airborne in situ CO 2 measurements were carried out using a module consisting of a commercial CO 2 analyzer (LI-COR, Inc., Type: LI-840) modified for airborne operation (Machida et al., 2008).In addition, other trace gases, such as carbon monoxide, methane, etc., were also determined by air analysis using flask sampling devices.Both systems collected air from outside the aircraft using stainless steel sampling tubes facing the direction of flight.The flask sampling was only performed during spiral flights.The time resolution of the in situ data was 2 s.The precision of in situ measurements was 0.12 ppm (1 SD) in 2 s data.The end-to-end performance was additionally affected by a change in the instrumental stability.Consequently, highly accurate calibrated gases were used to compensate the instrumental drift.Hence, the total uncertainty of the in situ CO 2 measurement was estimated within ± 0.5 ppm.The measurements in August were taken over Hokkaido prefecture in northern Japan, while those in February were taken over the Tsukuba and Koganei sites.The Tsukuba site is approximately 50 km northeast, and the Koganei site is approximately 10 km west of the center of Tokyo.The LAS system provides the τ and the range from the aircraft to the target.The amplitude modulation frequencies were 10 kHz for the online wavelength and 11 kHz for the offline wavelength in this measurement.The transmitting online wavelength was set to the edge position of absorption in August 2009 (as shown in Fig. 1), and the center position was used as the online wavelength in February 2010.The accumulation time was 2 s during both measurements.An additional 3 s were required for signal processing on the laptop computer.A visible CCD camera (ARTRAY Inc., Model ARTCAM 150pIII) also monitored the landscape under the aircraft every 5 s.These temporal images were capable of detecting cloud cover over both land and sea.

Atmos
To validate the LAS measurements, atmospheric CO 2 was taken from 1500 ft (0.5 km) to 23 500 ft (7 km) using flask sampling and in situ CO 2 devices.Simultaneous radiosonde measurements were carried out by the Japan Weather Agency under a contract with the National Institute for Environmental Studies during the spiral flight measurements over the Moshiri site (Hokkaido) in August and the Tsukuba site in February.Other radiosonde measurements at the Koganei site, corresponding to the path of the aircraft, were also performed by the National Institute of Information Communications Technology.Spiral flight measurements were taken over the Tsukuba (0.5 to 2 km) and Koganei (0.5 to 3 km) sites owing to air traffic control regulations.We employed flask sampling data for validation in August, as the in situ data were unusable owing to a gas leak in the instrument.regardless of observation sites.It is clear that CO 2 differential absorption strength varies according to the position of the online wavelength.

Figure
Figures 5 and 6 show the temporal τ , its fluctuations, and the range from the aircraft to the targets.The graphs at the top of Figs. 5 and 6 depict τ , while the graphs immediately below it (in both figures) depict δ τ .The third graphs from the top depict the optical path length from LAS, the geometrical height from airborne GPS, and the digital elevation model (DEM) from ASTER (Yamaguchi et al., 1998).The graphs at the bottom illustrate the difference between the range obtained from LAS and the geometrical height.The aircraft altitudes from the LAS are corrected according to the information of flight attitude.However, some peaks at τ and aircraft altitude resulted from imperfect correction of the viewing angle.These uncorrected data are excluded when the altitude accuracy and XCO 2 are evaluated.The spiral flight measurements in August 2009 was taken over the Moshiri site (basin in a mountainous area, rough field).Meteorological data from radiosonde were obtained over the Moshiri site.The results in February 2010 also included two sets of spiral measurements over the Tsukuba site.Simultaneous radiosonde measurements were also taken.
The values of SNR τ at an altitude of 2 km were 147 in August and 270 in February.The corresponding errors due to the value of δ τ were 0.68 % (2 τ = 0.18) in August and 0.37 % (2 τ = 0.54) in February.The error at an altitude of 7 km was 0.85 % (2 τ = 0.51, SNR τ = 118) in August.It was found that the SNR τ in February (2 km altitude) was 2.5 times greater than that in August (7 km altitude), despite the fact that τ was nearly unity.This resulted from The upper two panels show the differential absorption optical depth ( τ ) and its fluctuations versus time, and the lower two panels represent the heights and their differences obtained from LAS and airborne GPS and DEM.The LAS measurement was carried out with cloud screening.XCO 2 is calculated from averaged τ indicated by solid line in the top panel.The measured data from the LAS were corrected according to the information flight attitude.However, some peaks at τ and aircraft height resulted from imperfect correction of the viewing angle.attenuated return signal intensities from more distant targets.As illustrated in Fig. 4, the return signals at 7 km altitude in August were smaller than those obtained at a 2 km altitude in February.Furthermore, when τ is small, it is associated with significant online fluctuation at the edge position.The error due to fluctuation of the operating wavelength (∂ w dr/∂λ) was evaluated as being less than 0.58 % at the edge of the online wavelength and 0.05 % at its center.These errors can be reduced by optimizing transmitted laser power, receiving aperture, and detector dark current noise.These improvements result in more precise measurement with more shorter integration time.
To validate LAS altitude, we extracted the geometric height from the on-board GPS and the ASTER-GDEM.Cloud screening was performed in August.The resolution of the DEM was approximately 30 m per pixel, 7-14 m (= 1 SD) vertical precision over a flat field, and 20-30 m over complex terrain, such as mountain slopes (Hirano et al., 2003).The altitude of the aircraft obtained from LAS was consistent with that from GPS-DEM: the difference between the LAS and geometric heights was less than ± 15 m (1 SD = 4.9 m) over a flat field and ± 15-30 m during rotating movements.The Some data points that lie off the validation data resulted from imperfect correction of the viewing angle.These uncorrected data are excluded when the altitude accuracy and XCO 2 are evaluated.
precision of the range measurement and the accuracy of the ground-based measurements were confirmed as 2 and 5 m, respectively (Sakaizawa et al., 2010).The measured phase difference when calculating the target range was based on averaged return signals coming from groups of trees, buildings, and ground surface over a range from 150 to 200 m in these airborne measurements.The probability of detecting elevations from ground surfaces varies because of the presence of trees over the integration range, and the effective optical path also changes during rotating movement, which may be sources of potential bias in measured mean aircraft altitude.The error due to range measurement (∂ w dr/∂z) was 0.12 %.The bias error due to the Voigt profile using the spectroscopic data for the CO 2 R(12) line was estimated to be 0.13 %; the spectroscopic data were taken from recent studies (Devi et al., 2007;Rothman et al., 2009;Predoi-Cross et al., 2009).
τ was compared with validation data ( τ val ) calculated from CO 2 concentrations from 1500 ft (0.5 km) to 23 500 ft (7 km).The values of CO 2 concentrations are collected through the airborne in situ or flask sampling devices shown in Fig. 7. τ val can be evaluated using the following equation: where n CO 2 (r) is the dry air mixing ratio from the flask sampling or in situ n CO 2 data.The CO 2 profiles (n CO 2 (r)) are calculated with a third-order polynomial fitting.The CO 2 concentration from the ground to an altitude of 0.5 km was assumed to be constant, due to a lack of surface CO 2 measurements.Figure 8 indicates the linear relation between XCO 2LAS and XCO 2val over the urban area.Note that XCO 2LAS and XCO 2val are in agreement, as their correlation coefficient (R) is 0.987 for XCO 2 , 0.995 for τ .The difference of XCO 2LAS to XCO 2val is a negative bias of 1.5 ppm with 1 SD = 2.4 ppm.The negative bias between XCO 2LAS and XCO 2val may be attributed to bias sources due to aerosol return signals from nearest area less than 500 m from the aircraft (the overlapping function between fields of view of receiving optics and transmitting laser beam becomes unity after 500 m), the impact of signal averaging over structured terrain (corresponding to range accuracy), and spectroscopic parameters.
The graph on the left in Fig. 9 indicates XCO 2LAS from the ground to various elevations, while the graph on the right indicates the difference between the validation data (in situ and flask sampling) and the measured data.The results indicate a maximum difference of 4 ppm and an averaged difference of 1.5 ppm.XCO 2LAS for the August measurements shows lower CO 2 levels below 2 km than above 2 km, as seen in the in situ data in Fig. 7a.XCO 2LAS for the February measurements shows the boundary-layer enhanced CO 2 (as shown in Fig. 7b-e) and a tendency to decrease monotonically with height.Note that the August measurements were impacted by photosynthesis in the biosphere, while the February measurements were impacted by a high CO 2 mixing ratio.
We evaluated the impact of distributed aerosol on spaceborne CO 2 measurement and found that the bias was less than 0.27 %, as described in Kameyama et al. (2011b).The effect of the other bias factors was evaluated as 0.13 % due to spectroscopic parameters and 0.12 % due to structured terrain (corresponding to range measurement accuracy).The total bias error (τ bias ) is at least 0.52 %, which is reasonable compared with the difference between XCO 2LAS and XCO 2val .In the case of the Tsukuba site, aerosol distributions were measured using a 532-nm ground-based LIDAR.We could not use data analysis of aerosol distribution at other sites, but the atmosphere above Moshiri site is generally clear compared with an urban area such as Tsukuba site.The aerosol optical depth (AOD) from an altitude of 0.4 to 2 km was also evaluated from the LIDAR data.Values of AOD were found to be 0.11 on 14 February, 0.07 on 20 February and 0.12 on 23 February during airborne measurements, for which the corresponding XCO 2LAS and XCO 2val at an altitude of 2 km are summarized in Table 3.The difference of XCO 2LAS to XCO 2val is −1.5 ppm, and evaluated XCO 2LAS is in agreement with XCO 2val within the measurement precision of 2.4 ppm (1 SD); nevertheless, not only CO 2 concentrations but also aerosols are highly distributed in the lower atmosphere.
The global distribution of AOD values, obtained from space-borne measurements by extraction from the 5 km mesh of the CALIPSO level 2 aerosol layer through the year 2008, ranges from 0.02 to 2. The AOD range without any thick clouds indicated that AOD values of less than 0.12 account for 72 % of the total observed data, while AOD values of less than 0.2 account for more than 84 %.The XCO 2LAS measurements listed in Table 3 were observed under the above probability for column-integrated AOD, for which the corresponding AOD at 532 nm is partial column-integrated.In addition, the error is considerably smaller than in the case of the airborne measurement where the modulation frequency is higher than 30 kHz (Kameyama et al., 2011b).

Conclusions
We demonstrated an airborne measurement system for simultaneous detection of the column-averaged dry air mixing ratio of CO 2 (XCO 2 (z)) and target range using a 1.57-µm laser absorption spectrometer.The observed partial columnaveraged dry air mixing ratio and validation data were in good agreement and showed a high correlation coefficient (R) of 0.987.The difference between the value of XCO 2LAS and the validation data XCO 2val had a maximum value of 4 ppm and an average value of 1.5 ppm.In the dense aerosol environment over urban area, the values of XCO 2LAS and XCO 2val were in agreement within the measurement precision of 2.4 ppm, with the corresponding aerosol optical depth in the range 0.07-0.12.In addition, the observed XCO 2 (z) profiles indicated a significant similarity to the validation data.Even though LAS employed a small effective aperture and had a low transmitting laser power, a precision better than 1 % for simultaneous measurements of CO 2 and altitude could be demonstrated.Our prototype LAS, which is engineering designed, will serve as a base for a near-future spaceborne system.

Fig. 3 .
Fig. 3. Flight paths of the aircraft measurements in August 2009 (top panel) and February 2010 (bottom panel).

Fig. 4 .
Figure 4 graphically illustrates the return signal intensity for the August and February measurements.Various return signals were obtained over grassland, urban areas, and the surface of the sea.The return signals were consistent with z −2 .Both offline signals were attenuated by weak CO 2 absorption

Fig. 5 .
Fig. 5. Results of airborne flight measurements taken on 26 August 2009.The upper two panels show the differential absorption optical depth ( τ ) and its fluctuations versus time, and the lower two panels represent the heights and their differences obtained from LAS and airborne GPS and DEM.The LAS measurement was carried out with cloud screening.XCO 2 is calculated from averaged τ indicated by solid line in the top panel.The measured data from the LAS were corrected according to the information flight attitude.However, some peaks at τ and aircraft height resulted from imperfect correction of the viewing angle.

Fig. 6 .
Fig.6.Results of airborne flight measurements taken on 23 February 2010.These data were taken over the Tsukuba site (urban area).Some data points that lie off the validation data resulted from imperfect correction of the viewing angle.These uncorrected data are excluded when the altitude accuracy and XCO 2 are evaluated.

Fig. 9 .
Fig. 9. Evaluated partial column-averaged column CO 2 (XCO 2LAS ) obtained from LAS (left panel) and the difference compared with calculated values (XCO 2val ) from flask and in situ measurements (right panel).

Table 2 .
Specifications for instrumental and spectroscopic data.

Table 3 .
Partial column-averaged CO 2 from the ground to airplane height and aerosol optical depth from the 0.5 to 2 km (February 2010).z is the airplane height.* * 1 SD means measurement precision. *