1. Introduction

Water vapor (H₂O) is widely acknowledged as an important atmospheric molecule that plays an essential role in many meteorological processes associated with meteorology, climate, and the global water cycle [1]. Accurate measurements of the spatial and temporal variabilities of H₂O are very important for weather analysis and forecasting. The Japan Meteorological Agency (JMA) has identified the accurate initial state for H₂O and wind fields to improve the accuracy of prediction for phenomena such as heavy rain associated with typhoons, fronts, and stationary linear mesoscale convection systems [2]. In particular, the variability of H₂O distributions in the lower troposphere is essential for the prediction of thunderstorm initiation and severe weather events [3,4]. In addition to the H₂O distributions, the data of low-level airflows (i.e., wind fields in the atmospheric boundary layer or lower troposphere) are important for forecasting mesoscale convective systems because they improve the accuracy of the simulated water vapor flux [5].

Ground-based active and passive remote sensing techniques for H₂O profiling offer higher spatial and temporal coverage than in situ sensors such as radiosondes. Passive remote sensing techniques include the global navigation satellite system (GNSS) [6], multichannel microwave radiometers (MWRs) [7], and Fourier transform infrared spectrometry (FTIR) [8]. GNSS receivers provide column-integrated precipitable water vapor without range-resolved information. Although MWR and FTIR provide spectrally resolved measurements of downwelling radiance at the surface, their height profile of H₂O is retrieved under some pertinent assumptions.

Compared with radiosondes and passive remote sensing instruments for H₂O profiling, lidar-based active remote sensing techniques have the advantage of providing higher temporal and vertical resolution observations continuously. The two primary lidar techniques for H₂O profiling are Raman lidar and differential absorption lidar (DIAL). Raman lidars, which use weak inelastic scattering (Raman scattering), have proven to be capable of measuring accurate H₂O profiles with good temporal and vertical resolutions [9–11]. Although the advantage of the Raman lidar is its simple optical configuration, it requires powerful (usually non-eye-safe) laser transmitters and large receiver apertures to detect the weak Raman backscattered signals. Because solar background light reduces the signal-to-noise ratio (SNR) of the signals, the observational range is limited during the daytime. The other disadvantage of the Raman lidar that it requires independent ancillary observations for calibration, for example, from a radiosonde or MWR [12].

DIALs provide range-resolved measurements of trace gas (including H₂O) concentrations from the difference in attenuation observed between two closely spaced (in the spectral sense) laser lines. DIALs can be categorized into two main types: incoherent and coherent. A number of incoherent DIAL systems have been developed to measure the H₂O profile, taking advantage of technological developments in lasers, such as ruby lasers [13], CO₂ lasers [14], ruby- and Nd:YAG-pumped dye lasers [15,16], alexandrite lasers [17], and Ti:sapphire lasers [18,19]. Although these lasers were useful as high-power transmitters, these high-power systems were not designed to run operationally under an unattended condition. Moreover, these lasers were not operated within eye-safety limits (except CO₂ lasers). Recently, an eye-safe, low-power, and diode-laser-based incoherent DIAL has been developed [20,21]. Although narrow-band filters are used to filter solar backgrounds to allow daytime measurements, incoherent DIALs are dominated by solar background error. The incoherent DIALs can measure radial wind velocity as an incoherent Doppler lidar using narrow-band spectral filters, which convert a Doppler-shifted frequency change to a spectral intensity change due to the atmospheric molecule (Rayleigh-Brillouin) scattering [22,23]. Since the molecular backscattered signal is the main source for the incoherent Doppler lidar, it is not suitable for observing wind in areas with higher aerosol loadings, i.e., the atmospheric boundary layer and lower troposphere.

The coherent DIALs have the advantage of high receiving sensitivity gained by the use of heterodyne detection. The dominant source of the noise is the shot noise generated by the local oscillator, and the near-quantum-limited detection of the backscattered signal can be achieved by the coherent DIAL systems. The solar background is not an issue owing to the narrow-band detection. Since the detector current in a coherent DIAL contains information on the phase of the backscattered signal, the coherent DIAL can measure the radial wind velocity with high accuracy. The first coherent DIAL for range-resolved measurements of the H₂O profile was developed using a CO₂ laser technology operated at 10.6-µm wavelength [24,25]. Hardesty [24] also presented the feasibility of simultaneous profiling of H₂O and radial wind measurements. Because of the evolution of eye-safe solid-state lasers based on holmium or thulium and operating at wavelengths around 2 µm, short-range results have been published on measurements of H₂O and CO₂ in both a DIAL instrument and a differential optical absorption spectroscopy instrument [26,27]. Although a coherent lidar with a Tm,Ho:YLF laser has also been demonstrated for DIAL measurements of H₂O amounts with a capability for simultaneous H₂O and radial wind profiling [28], the lidar was not operated under an unattended condition and the performance evaluation for the DIAL measurements of H₂O amounts was not done enough.

Because of the evolution of optical fibers for operation at wavelengths around 1.5 µm, there has been considerable research and development on coherent lidars for wind measurements since the 2000s [29–32]. Since the absorption of laser light by H₂O is too weak within the gain wavelength band around 1.5 µm of the fiber amplifier (i.e., erbium-doped fiber amplifier), it was difficult to measure the H₂O profile using 1.5-µm coherent DIALs. Recently the performance of fiber amplifiers has been improved, and a capability for simultaneous H₂O and radial wind profiling was demonstrated using a 1.53-µm coherent DIAL with an erbium-doped fiber amplifier [33].

The National Institute of Information and Communication Technology (NICT) started the development of a coherent 2-µm differential absorption and wind lidar (Co2DiaWiL; [34]) with a high-power Q-switched Tm,Ho:YLF laser [35,36] to measure CO₂ concentration and radial wind velocity from 2006. The capability of the Co2DiaWiL to measure CO₂ column-averaged dry-air mixing ratios with respect to the laser frequency offset locking was demonstrated in field experiments [37]. The accuracy and precision in radial velocity measurements of the Co2DiaWiL have also been verified in field experiments [38]. Although high repetition rate is appropriate for speckle averaging, the Tm,Ho:YLF laser is difficult to efficiently operate in high repetition rate due to high thermal loads. Direct in-band Tm:fiber-laser-pumped Ho:YLF laser has higher efficiency than the Tm,Ho:YLF laser and the ability to operate in high repetition rate (usually hundreds Hz to a few kHz) [39–41]. We have developed a Tm:fiber-laser-pumped Ho:YLF laser of a ring resonator oscillator and amplifier and used it for Doppler wind lidar measurements [42].

The peak power of the fiber laser system used in 1.5-µm coherent lidars is limited by the stimulated Brillouin scattering. The peak power in the fiber laser system is much lower value than in solid-state laser system such as Ho:YLF laser. Furthermore, for coherent detection, the effect of refractive turbulence is smaller on lidars with longer wavelength laser. Therefore, the development of a coherent 2-µm DIAL using solid-state lasers appears desirable in the perspective of a ground-based lidar system for simultaneously measuring H₂O and radial wind velocity.

Our final goal is to develop a coherent 2-µm DIAL for a future ground-based network of H₂O and wind measuring instruments required for the improvement of heavy rainfall forecasts. Recently, as the first step of our goal, making use of the ability to measure the H₂O profile, we have developed a dual-wavelength locking technique using sideband frequencies generated with the electro-optic modulator (EOM) to simply and easily tune the laser wavelength [43]. In this study, as the second step of our goal, we evaluate the performance of a prototype H₂O-DIAL system using the wavelength locking instrument and the Tm,Ho:YLF laser. We show the experimental demonstration for DIAL measurements of H₂O amounts with a capability for simultaneous H₂O and radial wind measurement. An overview of the H₂O-DIAL system is presented in Sec. 2. The theoretical background and error analysis of the DIAL measurements of H₂O is described in Sec. 3. The results of an intercomparison with the radiosondes and surface meteorological sensors are presented in Sec. 4. We also show the example of the simultaneous measurement of H₂O and wind velocity along the observation direction. Conclusions are given in Sec. 5.

2. Instrument descriptions

The H₂O-DIAL system is based on the Co2DiaWiL [34] for measuring CO₂ concentration and radial wind velocity. For measuring H₂O, we developed the dual-wavelength locking technique [43], which was used to lock and stabilize the on-line laser. The H₂O-DIAL system was housed in a container installed on the rooftop of a building at the NICT headquarters (35.71°N, 139.49°E, height 75 m above mean sea level), 20 m above ground level. Radiosondes and surface meteorological sensors were used for H₂O comparisons. An ultrasonic anemometer was used for radial wind comparisons.

2.1 H₂O-DIAL system

Similarly to the Co2DiaWiL, the H₂O-DIAL system used a 2-µm conductively cooled, laser-diode-pumped single-frequency Q-switched Tm,Ho:YLF laser [35,36] as a pulse laser transmitter. This pulse laser has an operating wavelength of 2.05 µm, an output energy of 50 mJ, a pulse duration of 200 ns, and a pulse repetition frequency of 30 Hz. Three 2-µm, fiber-coupled, single-longitudinal-mode, continuous-wave Tm,Ho:YLF lasers were used as seed lasers, referred to as the λ-center, on-line, and off-line lasers, respectively [43]. A block diagram of the H₂O-DIAL system is shown in Fig. 1, and the main instrument parameters of the H₂O-DIAL system are listed in Table 1.

 

Fig. 1. Block diagram of H₂O-DIAL system. Abbreviations are defined in the inset.

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Table 1. Specifications of H₂O-DIAL system

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Figure 2 shows the absorption cross sections of H₂O and CO₂ in the wavelength range from 2050.4 to 2051.3 nm at the ground surface and at an altitude of 4 km. The absorption cross sections are calculated using the High-Resolution Transmission Molecular Absorption Database (HITRAN; [44,45]), assuming the Lorentz profile at two altitudes. The atmospheric temperature and pressure at two altitudes used in the calculation are obtained from the tropical atmospheric model [46]. The wavelength of the λ-center laser is set at 2050.967 nm, corresponding to the R30 absorption line center of CO₂. The CO₂ R30 absorption line is compatible with Tm,Ho:YLF technology. The λ-center laser is locked and stabilized to the CO₂ R30 absorption line by a wavelength-locking instrument, which is a modification of a previously developed locking instrument [37]. The sideband frequency of the λ-center laser is used as a reference to lock the on-line laser. Optimized wavelengths for the on-line and off-line lasers are selected such that CO₂ interference and the effect of the CO₂ absorption are minimized as far as possible for the H₂O measurement, as indicated in Fig. 2. Moreover, the value of the differential absorption cross section for H₂O is to be maximized and the effect of temperature and pressure variation for the on-line wavelength is to be minimized to improve the precision of DIAL measurements. Five criteria of the on-line and off-line wavelength selection have been well described in our previous study [43]. In accordance with the criteria, 2050.550 and 2051.103 nm are selected as the on-line and off-line wavelengths for H₂O-DIAL measurement, respectively. Interference from other molecules, such as ozone (O₃) and nitrous oxide (N₂O), is negligible owing to the weaker absorption strength around the 2 µm wavelength and lower abundance.

 

Fig. 2. Absorption cross-section spectra of H₂O (blue) and CO₂ (red) at ground surface (solid lines) and at an altitude of 4 km (dashed lines) using the tropical atmospheric model. Vertical dashed lines mark the CO₂ R30 absorption line and on-line and off-line wavelengths.

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In this system, the on-line wavelength is controlled by the wavelength-locking instrument, which is composed of the Pound–Drever–Hall [47,48] and optical phase-locked loop units [43]. The wavelength stability of the on-line laser of <0.2 pm, which corresponds to 14 MHz, was achieved for more than 48 hours [43]. The off-line wavelength is controlled by adjusting the resonator temperature and the piezoelectric movement of the output coupler element. Its wavelength fluctuation is smaller than 7 pm and has little impact on a systematic error in H₂O measurement (see Appendix B). The on-line and off-line lasers are alternately switched by a fiber optic switch every one shot. The switching interval of the fiber optic switch is controlled by a personal computer (PC).

Portions of the outputs of the on-line and off-line lasers are diffracted by an acousto-optic modulator (AOM). The AOM upshifts the frequency of the on-line and off-line laser outputs by 105 MHz to create an intermediate frequency. The upshifted outputs are injected into the acousto-optic Q-switched (AO Q-sw) pulse laser in a ring-configuration resonator. Single-frequency Q-switched laser pulses are obtained by the injection seeding of each upshifted laser beam to which the resonator is matched by the ramp-and-fire technique [49].

The pulsed laser beams are transmitted to the atmosphere by a 100-mm-diameter off-axis telescope. After being expanded by the telescope, the pulsed laser beam is pointed and scanned with a two-axis scanner mounted on the container roof. The scanner is capable of full hemispherical coverage and is controlled by the PC.

The signals backscattered by moving aerosol particles in the atmosphere are mixed with a small optical sample of the on-line and off-line laser outputs on an InGaAs-PIN photodiode (DET2). A small optical sample of the pulsed laser beams is also mixed with on-line and off-line laser outputs on an InGaAs-PIN photodiode (DET1) to monitor the frequency properties of the transmitted laser pulses. DET1 and DET2 convert the frequencies of the laser pulse and backscattered signals into intermediate frequencies for heterodyne detection. The outputs of DET1 and DET2 are passed through a preamplifier and bandpass filter.

The outputs of DET1 and DET2 are analog-to-digital (A/D) converted and digitized on 14 bits at a 400 MHz sampling frequency starting from a 30-Hz trigger. In this experiment, 65536 samples for the DET2 output (called backscattered signals hereafter) and 4096 samples for the DET1 output (called the monitor pulse hereafter) are digitized. The 65536 samples of backscattered signal correspond to a data system-limited range of 24.6 km. The 65536 samples of backscattered signals are divided into 256 segments of 256 samples (corresponding to 95.93 m lengths), and the segments are called range gates. The monitor pulse is available as a reference for subsequent signal processing steps to calculate ranges and correct pulse-by-pulse frequencies. An algorithm proposed by Frehlich et al. [50] is used to produce the spectrum of noise-corrected and frequency-corrected backscattered signals at each range gate. A maximum likelihood discrete spectral peak estimator [51,52] is used for estimating the spectral peak, spectral width, and wideband SNR [38].

2.2 Radiosondes and in situ measurements

The Vaisala RS41-SGP radiosondes were launched about 300 m north-northwest of the H₂O-DIAL system. The observed data were transmitted every 2 s to a Vaisala DigiCORA sounding system MW41 and processed by the system. The measurement uncertainty of relative humidity by the RS41-SGP radiosonde is 4%. The measurement uncertainty of temperature is 0.15 °C at 100 hPa or more. Table S1 in Supplement 1 summarizes launch times of radiosondes used for comparison.

Gill MaxiMet 500, deployed at the radiosonde launch site, is an in-situ surface meteorological sensor for measuring pressure, temperature, and relative humidity. The observed data were recorded every 1 minute and used as a ground-based reference for the radiosondes. Surface meteorological information obtained by Gill MaxiMet 500 is listed in Supplement 1, Table S1.

Vaisala WXT-530, mounted on a tower at a height of 56 m above ground level (AGL), is an in-situ surface meteorological sensor for measuring pressure, temperature, and relative humidity. The location of WXT-530 was about 120 m south of the H₂O-DIAL system. The observed data were recorded every 1 minute. The temperature and relative humidity data were used for the comparison with volumetric humidity derived from the H₂O-DIAL system.

SONIC SAT-600, mounted on the tower at a height of 59 m AGL, is a three-axis ultrasonic anemometer for measuring the three components of wind at a rate of 10 Hz. The observed data were used for the comparison with radial wind derived from the H₂O-DIAL system.

3. Theoretical considerations

3.1 Power estimation

The lidar equation for coherent detection that gives the return signal power [53] can be written as

The carrier-to-noise ratio (CNR) is defined as [57]

The theoretical SNR for the squarer estimator described by Rye and Hardesty [58] and Gibert et al. [59] is given by

3.2 Local optical depth and H₂O measurement

Because the on-line and off-line wavelengths are close, we can neglect the wavelength dependence of the lidar system’s efficiency, the aerosol backscattering coefficient, the extinction coefficient due to the atmospheric molecules but excluding H₂O, and the extinction coefficient due to the aerosol. Thus, the ratio of on-line to off-line measured return signal power is given by

3.3 Error analysis on H₂O measurement

Wulfmeyer et al. [1] stated requirements of H₂O profiling in lower troposphere for data assimilation. The temporal resolution should be 5–10 min, and the minimum requirement of temporal resolution is 60 min for resolving the diurnal cycle and for reaching the nowcasting range. The vertical resolution in the convective mixed layer should be 100–300 m. The noise error (random error) and bias (systematic error) should be <10% and <5%, respectively. To determine the range resolution and accumulation time of the H₂O-DIAL system, we calculated the random error using a simulation under summer daytime conditions in Japan (Appendix A). For the 60 min average and range resolution of 100 m, H₂O retrieval with 10% random error is feasible in the altitude range up to 1 km under the condition that on-line and off-line SNRs exceed 25 dB. Assuming that the values of atmospheric parameters are uniform horizontally at the ground level, H₂O retrieval with 10% relative error is feasible in the horizontal range up to 2 km with a range resolution of 100 m for 60 min signal averaging. In accordance with the atmospheric and instrument systematic error analysis (Appendix B), the systematic error is <3% in vertical and horizontal measurement. The systematic error is dominated by temperature deviation, and the effect of the wavelength jitter and linewidth of the on-line and off-line laser is small on the systematic error. From the results of the local optical depth sensitivity analysis shown in Appendix A and B, the error in the H₂O retrievals is dominated by the receiver random error.

4. Atmospheric measurement results

4.1 Comparison with radiosonde measurements

To provide error estimates from the H₂O-DIAL system and characterize its performance, radiosonde measurements for the validation of the H₂O-DIAL system were made from 24 June to 28 July 2020 at the NICT headquarters. We validated H₂O-DIAL-derived volumetric humidity values by comparing them with collocated and coincident radiosonde data. We compared the vertical profile of volumetric humidity obtained with the H₂O-DIAL system with that obtained by the radiosonde launched at 16:28 Japan standard time (JST) on 20 July 2020 (Fig. 3(a)). The H₂O-DIAL data were accumulated from 30 min before to 30 min after the radiosonde launch. Both the range bin size and DIAL measurement resolution were 95.9 m. Since the nearest range was 239.8 m, the first center range in the DIAL measurement was 287.8 m. The agreement in the figure is generally good, although there is an underestimated value at the lower limit altitude for the H₂O-DIAL system. The maximum height of H₂O-DIAL measurements with an uncertainty of less than 50% was 1.2 km. Figure 3(b) shows height profiles of on-line and off-line SNRs. The off-line SNR gradually decreased with height, and the on-line SNR was below 20 dB above 800 m. Since the mixing ratio in this case was larger than that of the tropical atmospheric model (radiosonde No. 16 shown in Fig. 7(c)), the absorption of laser light by H₂O was strong and the on-line signal rapidly decreased with height.

 

Fig. 3. (a) Vertical profile of the volumetric humidity obtained with the H₂O-DIAL system (black circles and bars) and radiosonde (dashed line; radiosonde No. 16 listed in Supplement 1, Table S1) at 16:28 JST on 20 July 2020. The H₂O-DIAL data with uncertainty of less than 50% are plotted. (b) Vertical profile of the off-line (solid line) and on-line (dashed line) SNRs.

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Figure 4 shows the scatterplot of the volumetric humidity measured using the H₂O-DIAL system and the radiosondes. The maximum height of H₂O-DIAL measurements with uncertainty of less than 50% was 1.3 km. For this comparison, the radiosonde data were averaged to the range bins of the H₂O-DIAL system. The H₂O-DIAL-derived volumetric humidity values agreed with the radiosonde-derived values over the range from 11 to 20 g/m³ with a correlation coefficient of 0.81 and a root-mean-square difference of 1.46 g/m³. We found no significant bias (0.14 g/m³) in the difference between H₂O-DIAL and radiosondes measurements. This result is consistent with a small systematic error derived in the error analysis (see Appendix B). A linear regression analysis yielded a slope of 1.10 and an intercept of –1.24 g/m³.

 

Fig. 4. Scatterplot of the volumetric humidity measured using the H₂O-DIAL system and radiosondes. Circles show the means and vertical lines show the random error of the volumetric humidity measured using the H₂O-DIAL system. Colors correspond to the radiosonde No. listed in Supplement 1, Table S1. The H₂O-DIAL data with random error of less than 50% are plotted. The x = y line is represented by the dashed line. In the legend, N is the number of points included, R is the correlation coefficient, RMSD is the root-mean-square difference between the H₂O-DIAL system and radiosondes, and the slope and intercept are for the least-squares-fit line.

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4.2 Comparison with surface meteorological sensors

The time series of the horizontal profile of volumetric humidity and radial velocity were simultaneously measured using the H₂O-DIAL system from 00 to 24 JST on 16 September 2020. The laser beam of the H₂O-DIAL system was oriented along an azimuth of 50.99° and an elevation angle of 3.68°. The H₂O-DIAL data were accumulated every hour. Since the range data of 527.6 and 623.6 m for the horizontal path was used in the DIAL measurement, the range resolution was 95.9 m and the center range was 575.6 m. The height of the center range was 56.9 m AGL. Figure 5 shows the time series of the volumetric humidity measured using the H₂O-DIAL system and WXT-530. The random errors of the volumetric humidity measured using the H₂O-DIAL system were within a range of 7.6 to 15.6%. The volumetric humidity measured using the H₂O-DIAL system was slightly higher than that from the WXT-530. The difference might be caused by the different sampling volumes. The H₂O-DIAL system sensed the lower atmosphere with higher water vapor density using the oblique laser beam. The WXT-530-measured volumetric humidity increased from 15 to 17 g/m³ at about 19:50 JST. The rainfall had started about 4 km east of the H₂O-DIAL system at about 19:30 JST. The increase corresponds to the outflow of cool and moist air associated with the precipitation.

 

Fig. 5. Time series of the volumetric humidity measured using the H₂O-DIAL system and WXT-530 on 16 September 2020. Circles show the means and vertical lines show the random error of the volumetric humidity measured using the H₂O-DIAL system.

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Figure 6(a) shows 1-s-averaged radial wind velocity in the range–time format for off-line wavelength observed using the H₂O-DIAL system. Positive values (warm colors) for these data indicate motion away from the H₂O-DIAL system. At about 09 JST, the maximum horizontal measurement range was about 9 km. Weak northerly to northeasterly surface winds were observed by ambient air pollution monitoring stations (not shown) near the H₂O-DIAL observation range from 00 to 12 JST. The surface wind gradually shifted to the east from 12 to 18 JST. Then, the surface wind turned southeasterly at 18 JST. The H₂O-DIAL system well captured the wind field changes. Figure 6(b) shows a time series of 1-s-averaged radial wind velocity from the H₂O-DIAL and SAT-600. Since the range data of 623.6 m from the H₂O-DIAL system was used, the height of the center range was 60 m AGL. The three wind components observed by the SAT-600 were projected onto the direction of the radial wind velocity measured using the H₂O-DIAL system. The radial wind velocities are generally in good agreement with wind fluctuations, although there are greater differences in measured wind speeds for rapid fluctuations. Possible reasons for the discrepancy are the different observation positions (about 700 m apart) and the different sampling volume.

 

Fig. 6. (a) Range-time display of quasi-horizontal radial velocity for off-line wavelength observed using the H₂O-DIAL system on 16 September 2020. Positive (negative) velocities, represented in red and yellow (blue), indicate flow away from (toward) H₂O-DIAL. (b) Time series of 1-s-averaged radial velocities from H₂O-DIAL (blue) and SAT-600 (red).

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5. Conclusions

We developed a prototype coherent 2-µm H₂O-DIAL system using the novel wavelength locking technique for simultaneously measuring H₂O profiles and radial wind velocity. Similarly to our previous system (Co2DiaWiL), the H₂O-DIAL system used a 2-µm conductively cooled, laser-diode-pumped single-frequency Q-switched Tm,Ho:YLF laser with an operating wavelength of 2.05 µm, output energy of 50 mJ, and a pulse repetition frequency of 30 Hz.

In field validation experiments conducted in Tokyo, Japan, we demonstrated the performance of the H₂O-DIAL under summer daytime conditions. The H₂O-DIAL data were accumulated for 60 min with a range resolution of 95.9 m. The comparison of the H₂O-DIAL-derived volumetric humidity values with those obtained with collocated radiosondes showed that they agreed over the range from 11 to 20 g/m³ with a correlation coefficient of 0.81 and a root-mean-square difference of 1.46 g/m³. The small bias (0.14 g/m³) in the difference between H₂O-DIAL and radiosonde measurements is consistent with the small systematic error derived in the error analysis. A comparison of volumetric humidity measured using the H₂O-DIAL system with those from a surface meteorological sensor demonstrated good agreement between them. At the same time, the comparison of the H₂O-DIAL-derived radial velocities with those obtained with a sonic anemometer showed that they are generally in good agreement for wind fluctuations, although there are greater differences in measured wind speeds for rapid fluctuations. We confirmed the capability of the H₂O-DIAL system to simultaneously measure the H₂O profile and radial wind velocity.

The measurement altitude of the prototype H₂O-DIAL system is limited to 1.3 km and the data accumulation time is long (60 min). The performance of the prototype H₂O-DIAL system is not sufficient to use of data from the system for forecasting mesoscale convective systems and atmospheric studies. For higher altitude profiling with a shorter accumulation time, a laser transmitter with higher power and repetition rate is needed. We have been developing a coherent 2-µm H₂O-DIAL with a Tm:fiber-laser-pumped Ho:YLF laser for this purpose. A laser system of a ring resonator oscillator and amplifier will operate at pulse repetition rates of hundreds Hz and output energies of tens mJ. We expect that the SNR is improved by a factor of 5 compared with the prototype H₂O-DIAL system and have started demonstrations of the performance of the H₂O-DIAL system using this laser.

Appendix A: Random error analysis

The performance of the H₂O-DIAL system was modeled to demonstrate the H₂O measurement capability and to evaluate the random errors using a simulation under summer daytime conditions in Japan. The simulation needs input parameters that describe the H₂O-DIAL system and the atmospheric model. The input parameters on the H₂O-DIAL system are listed in Table 1. Figure 7 shows the atmospheric profiles of (a) pressure, (b) temperature, (c) water vapor mixing ratio, (d) aerosol extinction coefficient, (e) aerosol backscattering coefficient, and (f) refractive index structure constant used for the simulation. Their profiles were interpolated to 100 m vertical resolution from the original vertical resolution of 1 km.

The atmospheric extinction coefficient comprises molecular absorption and scattering, and aerosol absorption and scattering. We calculated the height profiles of molecular absorption by using the HITRAN database [44] and the tropical atmospheric model [46,60]. The tropical atmospheric model provides height profiles of pressure, temperature, air density, water vapor density, and 27 other molecular densities. Here, the height profile of the CO₂ dry-air mixing ratio was scaled to a current typical surface value of 410 ppm. For this study, only the most abundant isotope of each molecule was considered, and Lorentzian line shapes were assumed at all altitudes. Molecular scattering and aerosol absorption and scattering were interpolated versus height and wavelength from the clear air table of McClatchey et al. [60]. Height profiles of pressure, temperature, and water vapor mixing ratio obtained from radiosondes listed in Table S1 are superposed in Figs. 7(a)-(c). These profiles generally agree with those of the tropical atmospheric model. Since backscatter datasets at 2 µm do not exist, we referred to the height profile of the aerosol backscattering coefficient at 1.064 µm, which is taken from Spinhirne et al. [61]. Then, a conversion function was used to convert the backscatter dataset to 2 µm (Fig. 7(e)) [62]. We used a version of the submarine laser communications daytime model altitude profile for the refractive index structure constant (Fig. 7(f)) [63].

 

Fig. 7. Height profile of atmospheric parameters for error analysis: (a) pressure, (b) temperature, (c) water vapor mixing ratio, (d) aerosol extinction coefficient, (e) aerosol backscattering coefficient, and (f) refractive index structure constant. Height profiles of pressure, temperature, and water vapor mixing ratio obtained from radiosondes listed in Table S1 are superposed in Figs. 7(a)-(c). Colors correspond to the radiosonde No. listed in Supplement 1, Table S1.

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Using Eqs. (10) and (11), the random errors on local optical depth and volumetric humidity are found to be equal. Consequently, minimizing the random error on the estimate of volumetric humidity is tantamount to minimizing the random error on the local optical depth. According to Eq. (9), the random error on the local optical depth between two ranges R₁ and R₂ can be expressed as [37]

(12)$$\frac{{\sigma ({\delta \tau ({{R_1},{R_2}} )} )}}{{\delta \tau ({{R_1},{R_2}} )}} \cong \frac{1}{{2\delta \tau ({{R_1},{R_2}} )}}\sqrt {\frac{1}{{\textrm{SNR}_{\textrm{on}}^2({{R_1}} )}} + \frac{1}{{\textrm{SNR}_{\textrm{off}}^2({{R_1}} )}} + \frac{1}{{\textrm{SNR}_{\textrm{on}}^2({{R_2}} )}} + \frac{1}{{\textrm{SNR}_{\textrm{off}}^2({{R_2}} )}}},$$

where SNR_on and SNR_off are the SNRs of the on-line and off-line return signals, respectively. This equation implies the necessity of producing high SNR for the DIAL signals for highly precise H₂O measurements. Since the on-line return signals exhibit lower SNR owing to higher H₂O absorption, the dominant source of the random errors is the on-line return signals.

Figures 8(a) and 8(b) show the height profiles of the random error on the local optical depth and SNR with a range resolution of 100 m, respectively. The blue, green, and red lines indicate the profiles obtained with accumulation times of 10, 30, and 60 min, respectively. At short range the random error on the local optical depth is small. The longer accumulation time provides a high SNR and highly precise H₂O measurements. For the 60 min average, H₂O retrieval with 10% random error is feasible in the altitude range up to 1 km under the condition that on-line and off-line SNRs exceed 25 dB. Figures 8(c) and 8(d) show the height profiles of the random error on local optical depth and SNR with different range resolutions and an accumulation time of 60 min, respectively. The coarser range resolution provides a high SNR and highly precise H₂O measurements. If the range resolution, equal to the range gate duration $\delta {t_R}$, is coarser, the number of coherent cells M_t is larger. Thus, the coarser range resolution results in a higher SNR in accordance with Eq. (6).

 

Fig. 8. Height profiles of (a,c) random errors on local optical depth and (b,d) off-line (solid line) and on-line (dashed line) SNRs. (a,b) The red, green, and blue lines correspond to the data accumulation time of 10, 30, and 60 min with a range resolution of 100 m, respectively. (c,d) The red, green, and blue lines show results for the range resolutions of 100, 200, and 300 m with an accumulation time of 60 min, respectively.

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We evaluate the performance of the H₂O-DIAL system in horizontal measurement using a simulation under summer daytime conditions in Japan. Input parameters of the simulation are the same as those used in vertical measurement, provided that the values of atmospheric parameters at ground level are used. Furthermore, it is assumed that the values of atmospheric parameters are uniform horizontally. Figures 9(a) and 9(c) shows the resulting horizontal profiles of the SNR and random error on the local optical depth, plotted with a range resolution of 100 m. The blue, green, and red lines indicate the profiles obtained with 10, 30, and 60 min data accumulation times, respectively. At short range, the random error on the local optical depth is small. For the 60 min average, H₂O retrieval with 10% relative error is feasible in the horizontal range up to 2 km under the condition that on-line and off-line SNRs exceed 25 dB. Figures 9(b) and 9(d) show the height profiles of the random error on the local optical depth and SNR with different range resolutions and an accumulation time of 60 min, respectively. As with the vertical H₂O measurement, the coarser range resolution provides a high SNR and highly precise H₂O measurements.

 

Fig. 9. Horizontal profiles of (a,b) random errors on local optical depth and (c,d) off-line (solid line) and on-line (dashed line) SNRs. (a,c) The red, green, and blue lines show results for the data accumulation times of 10, 30, and 60 min with a range resolution of 100 m, respectively. (b,d) The red, green, and blue lines correspond to the range resolutions of 100, 200, and 300 m with an accumulation time of 60 min, respectively.

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Appendix B: Systematic error analysis

The systematic errors in the H₂O retrievals are dominated by the atmospheric and instrument systematic errors ${\varepsilon _A}$ and ${\varepsilon _T}$ [64–66]. The atmospheric systematic error ${\varepsilon _A}$ results from the sensitivity dependence on temperature, pressure, and the interference from CO₂, according to [65,66]

(13)$${\varepsilon _A} = \sqrt {\varepsilon _{A,t}^2 + \varepsilon _{A,p}^2 + \varepsilon _{A,\textrm{CO2}}^2},$$

where ${\varepsilon _{A,t}}$, ${\varepsilon _{A,p}}$, and ${\varepsilon _{A,\textrm{CO}2}}$ are the systematic errors due to temperature deviation, pressure deviation, and interference from CO₂, respectively. The systematic error due to temperature deviation (${\varepsilon _{A,t}}$) is calculated as the local optical depth sensitivity to atmospheric temperature deviation $\Delta T ={\pm} 5\circ{C}$ from the tropical atmospheric model (see Fig. 7(b)) and is given by

(14)$${\varepsilon _{A,t}} = \max \left\{ {\frac{{|{\delta \tau (T )- \delta \tau ({T + \Delta T} )} |}}{{\delta \tau (T )}}} \right\}.$$

Equation (14) is applicable to the systematic error due to pressure (${\varepsilon _{A,p}}$) with atmospheric pressure deviation $\Delta P ={\pm} 10\; \textrm{hPa}$ from the tropical atmospheric model. The systematic error due to interference from CO₂ (${\varepsilon _{A,\textrm{CO}2}}$) is calculated as the ratio of the local optical depth of CO₂ ($\delta {\tau _{\textrm{CO}2}}$) to the local optical depth of H₂O at the sensing wavelength and is given by

(15)$${\varepsilon _{A,\textrm{CO2}}} = \frac{{\delta {\tau _{\textrm{CO2}}}}}{{\delta \tau }}.$$

Figure 10(a) shows the results of atmospheric systematic error analysis for the tropical atmospheric model. The atmospheric systematic error is dominated by temperature deviation. The low CO₂ interference on H₂O measurement is a result of the selection of appropriate on-line and off-line wavelengths (see Sec. 2.1).

 

Fig. 10. (a) Local optical depth sensitivity analysis due to the total atmospheric uncertainties ${\varepsilon _A}$, temperature, ${\varepsilon _{A,t}}$, pressure ${\varepsilon _{A,p}}$, and CO₂ ${\varepsilon _{A,\textrm{CO}2}}$. (b) Local optical depth sensitivity analysis due to the total laser transmitter uncertainties ${\varepsilon _T}$, on-line and off-line laser line jitter, ${\varepsilon _{j,\textrm{on}/\textrm{off}}}$, and on-line and off-line laser linewidth ${\varepsilon _{p,\textrm{on}/\textrm{off}}}$.

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The instrument systematic error ${\varepsilon _T}$ results from the sensitivity dependence on the wavelength jitter and linewidth of the on-line and off-line laser lines and is given by [65,66]

(16)$${\varepsilon _T} = \sqrt {\varepsilon _{j,\textrm{on}}^2 + \varepsilon _{j,\textrm{off}}^2 + \varepsilon _{p,\textrm{on}}^2 + \varepsilon _{p,\textrm{off}}^2},$$

where ${\varepsilon _{j,\textrm{on}}}$ and ${\varepsilon _{j,\textrm{off}}}$ are the errors due to on-line and off-line laser line jitter, and ${\varepsilon _{p,\textrm{on}}}$ and ${\varepsilon _{p,\textrm{off}}}$ are the errors due to on-line and off-line laser linewidths, respectively. The on-line and off-line laser line jitter errors are calculated as the local optical depth sensitivity to the laser line wavelength position variances of $\Delta {\lambda _{\textrm{on}}} ={\pm} 0.2\; \textrm{pm}$ and $\Delta {\lambda _{\textrm{off}}} ={\pm} 3.5\; \textrm{pm}$ (see Sec. 2.1). These errors are calculated by applying Eq. (14). The on-line and off-line laser linewidth errors are estimated by computing the effective local optical depth using the effective absorption cross section of H₂O, ${\tilde{\sigma }_{\textrm{eff},\textrm{on}/\textrm{off}}}$, defined by [67]

(17)$${\tilde{\sigma }_{\textrm{eff},\textrm{on/off}}} = \frac{{\int {G({\nu ,r} )\cdot {{\tilde{\sigma }}_{\textrm{on/off}}}({\nu ,r} )\cdot \textrm{d}\nu } }}{{\int {G({\nu ,r} )\cdot \textrm{d}\nu } }},$$

where G is the laser spectral intensity profile, which is assumed to be an altitude-independent Gaussian function, r is the distance between the lidar system and the scattering volume, $\nu $ is the wavenumber [1/cm], and ${\tilde{\sigma }_{\textrm{on}/\textrm{off}}}({\nu ,r} )$ is the on/off-line absorption cross section profile of H₂O. Assuming diffraction-limited operation, the full width at half maximum (FWHM) correlates to the laser pulse duration ${T_c}$ and is defined as $\textrm{FWHM} = {{2 \cdot \ln (2 )} / {{T_c}}} \cdot \pi$. The FWHM results in a worst case of ±1.1 MHz for 200 ns pulse duration (Table 1). Thus, the on-line and off-line laser linewidth errors are given by

(18)$${\varepsilon _{p,\textrm{on/off}}} = \frac{{|{\delta \tau ({{{\tilde{\sigma }}_{\textrm{on/off}}}} )- \delta \tau ({{{\tilde{\sigma }}_{\textrm{eff},\textrm{on/off}}}} )} |}}{{\delta \tau ({{{\tilde{\sigma }}_{\textrm{on/off}}}} )}},$$

Figure 10(b) shows the results of instrument systematic error analysis for the tropical atmospheric model. It is evident that the instrument systematic error is dominated by on-line laser line jitter. Since the wavelength stability of the on-line laser is <0.2 pm, the error due to on-line laser line jitter is small. Although the wavelength fluctuation of the off-line laser is larger than that of the on-line laser, its effect on the systematic error is small. The effects of laser linewidth are small compared with the errors due to laser line jitter.

Assuming that the values of atmospheric parameters are uniform horizontally, the value of the systematic error is the same as that calculated at ground level and constant regardless of the distance between the lidar system and the scattering volume. The atmospheric and instrument systematic errors are 2.8% and 0.47%, respectively.

Funding

Japan Society for the Promotion of Science (JP19K15471, JP22K04978).

Acknowledgments

The authors thank Professor S. Ishii of Tokyo Metropolitan University, Drs. T. Itabe and K. Mizutani of NICT, and H. Fukuoka of Hamamatsu Photonics K.K. for their advice.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request, after the permission in the affiliations of the authors based on their data delivering policy.

Supplemental document

See Supplement 1 for supporting content.

References

1. V. Wulfmeyer, R. M. Hardesty, D. D. Turner, A. Behrendt, M. P. Cadeddu, P. Di Girolamo, P. Schlüssel, J. Van Baelen, and F. Zus, “A review of the remote sensing of lower tropospheric thermodynamic profiles and its indispensable role for the understanding and the simulation of water and energy cycles,” Rev. Geophys. 53(3), 819–895 (2015). [CrossRef]  

2. Japan Meteorological Agency (JMA), “JMA's NWP strategic plan toward 2030,” (2018), https://www.jma.go.jp/jma/en/Publications/JMA_NWP_Strategic_Plan_Toward_2030.pdf.

3. N. A. Crook, “Sensitivity of moist convection forced by boundary layer processes to low-level thermodynamic fields,” Mon. Wea. Rev. 124(8), 1767–1785 (1996). [CrossRef]  

4. T. M. Weckwerth, J. W. Wilson, and R. M. Wakimoto, “Thermodynamic variability within the convective boundary layer due to horizontal convective rolls,” Mon. Wea. Rev. 124(5), 769–784 (1996). [CrossRef]  

5. T. Kawabata, H. Iwai, H. Seko, Y. Shoji, K. Saito, S. Ishii, and K. Mizutani, “Cloud-resolving 4D-var assimilation of Doppler wind lidar data on a meso-gamma-scale convective system,” Mon. Wea. Rev. 142(12), 4484–4498 (2014). [CrossRef]  

6. M. Bevis, S. Businger, T. A. Herring, C. Rocken, R. A. Anthes, and R. H. Ware, “GPS meteorology: remote sensing of atmospheric water vapor using the global positioning system,” J. Geophys. Res. 97(D14), 15787–15801 (1992). [CrossRef]  

7. D. C. Hogg, F. O. Guiraud, J. B. Snider, M. T. Decker, and E. R. Westwater, “A steerable dual-channel microwave radiometer for measurement of water vapor and liquid in the troposphere,” J. Climate Appl. Meteorol. 22(5), 789–806 (1983). [CrossRef]  

8. P. Griffiths and J. De Haseth, Fourier Transform Infrared Spectrometry, 2nd Edition (Wiley, 2007).

9. S. H. Melfi, “Remote measurements of the atmosphere using Raman scattering,” Appl. Opt. 11(7), 1605–1610 (1972). [CrossRef]  

10. D. N. Whiteman, “Examination of the traditional Raman lidar technique. II. Evaluating the ratios for water vapor and aerosols,” Appl. Opt. 42(15), 2593–2608 (2003). [CrossRef]  

11. T. Sakai, T. Nagai, T. Izumi, S. Yoshida, and Y. Shoji, “Automated compact mobile Raman lidar for water vapor measurement: instrument description and validation by comparison with radiosonde, GNSS, and high-resolution objective analysis,” Atmos. Meas. Tech. 12(1), 313–326 (2019). [CrossRef]  

12. D. N. Whiteman, S. H. Melfi, and R. A. Ferrare, “Raman lidar system for the measurement of water vapor and aerosols in the Earth’s atmosphere,” Appl. Opt. 31(16), 3068–3082 (1992). [CrossRef]  

13. R. M. Schotland, “Some observations of the vertical profile of water vapor by means of a ground based optical radar,” in Proceedings of the Fourth Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1966), pp. 273–283.

14. E. R. Murray, R. D. Hake Jr, J. E. van der Laan, and J. G. Hawley, “Atmospheric water vapor measurements with an infrared (10-µm) differential-absorption lidar system,” Appl. Phys. Lett. 28(9), 542–543 (1976). [CrossRef]  

15. E. V. Browell, T. D. Wilkerson, and T. J. McIlrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18(20), 3474–3482 (1979). [CrossRef]  

16. C. Cahen, G. Mégie, and P. Flamant, “Lidar monitoring of the water vapor cycle in the troposphere,” J. Appl. Meteorol. 21(10), 1506–1515 (1982). [CrossRef]  

17. D. Bruneau, H. Cazeneuve, C. Loth, and J. Pelon, “Double-pulse dual-wavelength alexandrite laser for atmospheric water vapor measurement,” Appl. Opt. 30(27), 3930–3937 (1991). [CrossRef]  

18. V. Wulfmeyer, “Ground-based differential absorption lidar for water-vapor and temperature profiling: development and specifications of a high-performance laser transmitter,” Appl. Opt. 37(18), 3804–3824 (1998). [CrossRef]  

19. V. Wulfmeyer and J. Bosenberg, “Ground-based differential absorption lidar for water-vapor profiling: assessment of accuracy, resolution, and meteorological applications,” Appl. Opt. 37(18), 3825–3844 (1998). [CrossRef]  

20. S. M. Spuler, K. S. Repasky, B. Morley, D. Moen, M. Hayman, and A. R. Nehrir, “Field-deployable diode-laser-based differential absorption lidar (DIAL) for profiling water vapor,” Atmos. Meas. Tech. 8(3), 1073–1087 (2015). [CrossRef]  

21. R. K. Newsom, D. D. Turner, R. Lehtinen, C. Münkel, J. Kallio, and R. Roininen, “Evaluation of a compact broadband differential absorption lidar for routine water vapor profiling in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 37(1), 47–65 (2020). [CrossRef]  

22. C. L. Korb, B. M. Gentry, and C. Y. Weng, “Edge technique: theory and application to the lidar measurement of atmospheric wind,” Appl. Opt. 31(21), 4202–4213 (1992). [CrossRef]  

23. C. L. Korb, B. M. Gentry, S. X. Li, and C. Flesia, “Theory of the double-edge technique for Doppler lidar wind measurement,” Appl. Opt. 37(15), 3097–3104 (1998). [CrossRef]  

24. R. M. Hardesty, “Coherent DIAL measurement of range-resolved water vapor concentration,” Appl. Opt. 23(15), 2545–2554 (1984). [CrossRef]  

25. W. B. Grant, J. S. Margolis, A. M. Brothers, and D. M. Tratt, “CO₂ DIAL measurements of water vapor,” Appl. Opt. 26(15), 3033–3042 (1987). [CrossRef]  

26. S. Cha, K. P. Chan, and D. K. Killinger, “Tunable 2.1-μm Ho lidar for simultaneous range-resolved measurements of atmospheric water vapor and aerosol backscatter profiles,” Appl. Opt. 30(27), 3938–3943 (1991). [CrossRef]  

27. T. M. Taczak and D. K. Killinger, “Development of a tunable, narrow-linewidth, cw 2.066-µm Ho:YLF laser for remote sensing of atmospheric CO₂ and H₂O,” Appl. Opt. 37(36), 8460–8476 (1998). [CrossRef]  

28. G. J. Koch, R. E. Davis, A. N. Dharamsi, M. Petros, and J. C. McCarthy, “Differential absorption measurements of atmospheric water vapor with a coherent lidar at 2050.532 nm,” in Tenth Biennial Coherent Laser Radar Technology and Applications Conference (Universities Space Research Association, Huntsville, Ala., 1999), pp. 68–71.

29. C. J. Karlsson, F. Å. A. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous wave coherent laser radar at 1.55 μm for range, speed, vibration, and wind measurement,” Appl. Opt. 39(21), 3716–3726 (2000). [CrossRef]  

30. G. N. Pearson, R. J. Roberts, J. R. Eacock, and M. Harris, “Analysis of the performance of a coherent pulsed fiber lidar for aerosol backscatter applications,” Appl. Opt. 41(30), 6442–6450 (2002). [CrossRef]  

31. J. P. Cariou, B. Augere, and M. Valla, “Laser source requirements for coherent lidars based on fiber technology,” Comptes Rendus Physique 7(2), 213–223 (2006). [CrossRef]  

32. S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46(11), 1953–1962 (2007). [CrossRef]  

33. M. Imaki, H. Tanaka, K. Hirosawa, T. Yanagisawa, and S. Kameyama, “Demonstration of the 1.53-μm coherent DIAL for simultaneous profiling of water vapor density and wind speed,” Opt. Express 28(18), 27078–27096 (2020). [CrossRef]  

34. S. Ishii, K. Mizutani, H. Fukuoka, T. Ishikawa, B. Philippe, H. Iwai, T. Aoki, T. Itabe, A. Sato, and K. Asai, “Coherent 2 μm differential absorption and wind lidar with conductively cooled laser and two-axis scanning device,” Appl. Opt. 49(10), 1809–1817 (2010). [CrossRef]  

35. K. Mizutani, T. Itabe, S. Ishii, T. Aoki, K. Asai, A. Sato, H. Fukuoka, and T. Ishikawa, “Conductive-cooled 2 micron laser for CO₂ and wind observations,” Proc. SPIE 7153, 71530J (2008). [CrossRef]  

36. K. Mizutani, T. Itabe, S. Ishii, M. Aoki, K. Asai, A. Sato, H. Fukuoka, T. Ishikawa, and K. Noda, “Diode-pumped 2-μm pulse laser with noncomposite Tm,Ho:YLF rod conduction-cooled down to −80°C,” Appl. Opt. 54(26), 7865–7869 (2015). [CrossRef]  

37. S. Ishii, K. Mizutani, B. Philippe, H. Iwai, R. Oda, T. Itabe, H. Fukuoka, T. Ishikawa, M. Koyama, T. Tanaka, I. Morino, O. Uchino, A. Sato, and K. Asai, “Partial CO₂ column-averaged dry-air mixing ratio from measurements by coherent 2-μm differential absorption and wind lidar with laser frequency offset locking,” J. Atmos. Oceanic Technol. 29(9), 1169–1181 (2012). [CrossRef]  

38. H. Iwai, S. Ishii, R. Oda, K. Mizutani, S. Sekizawa, and Y. Murayama, “Performance and technique of coherent 2-μm differential absorption and wind lidar for wind measurement,” J. Atmos. Oceanic Technol. 30(3), 429–449 (2013). [CrossRef]  

39. F. Gibert, D. Edouart, C. Cénac, and F. Le Mounier, “2-μm high-power multiple-frequency single-mode Q-switched Ho:YLF laser for DIAL application,” Appl. Phys. B 116(4), 967–976 (2014). [CrossRef]  

40. F. Gibert, D. Edouart, C. Cénac, F. Le Mounier, and A. Dumas, “2-μm Ho emitter-based coherent DIAL for CO₂ profiling in the atmosphere,” Opt. Lett. 40(13), 3093–3096 (2015). [CrossRef]  

41. F. Gibert, J. Pellegrino, D. Edouart, C. Cénac, L. Lombard, J. Le Gouët, T. Nuns, A. Cosentino, P. Spano, and G. Di Nepi, “2-μm double-pulse single-frequency Tm:fiber laser pumped Ho:YLF laser for a space-borne CO₂ lidar,” Appl. Opt. 57(36), 10370–10379 (2018). [CrossRef]  

42. K. Mizutani, S. Ishii, M. Aoki, H. Iwai, R. Otsuka, H. Fukuoka, T. Ishikawa, and A. Sato, “2 μm Doppler wind lidar with a Tm:fiber-laser-pumped Ho:YLF laser,” Opt. Lett. 43(2), 202–205 (2018). [CrossRef]  

43. M. Aoki and H. Iwai, “Dual-wavelength locking technique for coherent 2-μm differential absorption lidar applications,” Appl. Opt. 60(14), 4259–4265 (2021). [CrossRef]  

44. I. E. Gordon, L. S. Rothman, C. Hill, et al., “The HITRAN2016 Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer 203, 3–69 (2017). [CrossRef]  

45. R. V. Kochanov, I. E. Gordon, L. S. Rothman, P. Wcislo, C. Hill, and J. S. Wilzewski, “HITRAN Application Programming Interface (HAPI): A comprehensive approach to working with spectroscopic data,” J. Quant. Spectrosc. Radiat. Transfer 177, 15–30 (2016). [CrossRef]  

46. G. Anderson, S. Clough, F. Kneizys, J. Chetwynd, and E. Shettle, “AFGL atmospheric constituent profiles (0–120 km),” Air Force Geophys. Lab. AFGL-TR-86-0110, 954 (1986).

47. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983). [CrossRef]  

48. E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001). [CrossRef]  

49. S. W. Henderson, E. Y. Yuen, and E. S. Fry, “Fast resonance detection technique for single-frequency operation of injection seeded Nd:YAG lasers,” Opt. Lett. 11(11), 715–717 (1986). [CrossRef]  

50. R. G. Frehlich, S. M. Hannon, and S. W. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36(15), 3491–3499 (1997). [CrossRef]  

51. M. J. Levin, “Power spectrum parameter estimation,” IEEE Trans. Inf. Theory 11(1), 100–107 (1965). [CrossRef]  

52. B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31(1), 16–27 (1993). [CrossRef]  

53. R. G. Frehlich and M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30(36), 5325–5352 (1991). [CrossRef]  

54. M. J. Kavaya, S. W. Henderson, E. C. Russell, R. M. Huffaker, and R. G. Frehlich, “Monte Carlo computer simulations of ground-based and space-based coherent DIAL water vapor profiling,” Appl. Opt. 28(5), 840–851 (1989). [CrossRef]  

55. R. Targ, M. J. Kavaya, R. M. Huffaker, and R. L. Bowles, “Coherent lidar airborne windshear sensor: performance evaluation,” Appl. Opt. 30(15), 2013–2026 (1991). [CrossRef]  

56. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26(5), 627–644 (1979). [CrossRef]  

57. F. Gibert, P. H. Flamant, D. Bruneau, and C. Loth, “Two-micrometer heterodyne differential absorption lidar measurements of the atmospheric CO₂ mixing ratio in the boundary layer,” Appl. Opt. 45(18), 4448–4458 (2006). [CrossRef]  

58. B. J. Rye and R. M. Hardesty, “Estimate optimization parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 36(36), 9425–9436 (1997). [CrossRef]  

59. F. Gibert, P. H. Flamant, J. Cuesta, and D. Bruneau, “Vertical 2-μm heterodyne differential absorption lidar measurements of mean CO₂ mixing ratio in the troposphere,” J. Atmos. Ocean. Technol. 25(9), 1477–1497 (2008). [CrossRef]  

60. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, “Optical properties of the atmosphere (Third edition),” Air Force Cambridge Research Laboratories, No. AFCRL-72-0497 (1972).

61. J. D. Spinhirne, S. Chudamani, J. F. Cavanaugh, and J. L. Bufton, “Aerosol and cloud backscatter at 1.06, 1.54, and 0.53 µm by air-borne hard-target-calibrated Nd:YAG/methane Raman lidar,” Appl. Opt. 36(15), 3475–3490 (1997). [CrossRef]  

62. V. Srivastava, J. Rothermel, A. Clarke, J. Spinhirne, R. Menzies, D. Cutten, M. Jarzembski, D. Bowdle, and E. McCaul, “Wavelength dependence of backscatter by use of aerosol microphysics and lidar data sets: application to 2.1-μm wavelength for space-based and air-borne lidars,” Appl. Opt. 40(27), 4759–4769 (2001). [CrossRef]  

63. R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, and E. M. Dewan, “Atmospheric models of optical turbulence,” Proc. SPIE 0928, 165–186 (1988). [CrossRef]  

64. G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and S. Houweling, “Space-borne remote sensing of CO₂, CH₄, and N₂O by integrated path differential absorption lidar: a sensitivity analysis,” Appl. Phys. B 90(3-4), 593–608 (2008). [CrossRef]  

65. T. F. Refaat, U. N. Singh, J. Yu, M. Petros, S. Ismail, M. J. Kavaya, and K. J. Davis, “Evaluation of an airborne triple-pulsed 2 μm IPDA lidar for simultaneous and independent atmospheric water vapor and carbon dioxide measurements,” Appl. Opt. 54(6), 1387–1398 (2015). [CrossRef]  

66. U. N. Singh, T. F. Refaat, S. Ismail, K. J. Davis, S. R. Kawa, R. T. Menzies, and M. Petros, “Feasibility study of a space-based high pulse energy 2 μm CO₂ IPDA lidar,” Appl. Opt. 56(23), 6531–6547 (2017). [CrossRef]  

67. S. Ismail and E. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28(17), 3603–3615 (1989). [CrossRef]