the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Shipborne Wind Measurement and Motion-induced Error Correction of a Coherent Doppler Lidar over the Yellow Sea in 2014

### Xiaochun Zhai

### Songhua Wu

### Bingyi Liu

### Xiaoquan Song

### Jiaping Yin

Shipborne wind observations by a coherent Doppler lidar (CDL) have been
conducted to study the structure of the marine atmospheric boundary layer
(MABL) during the 2014 Yellow Sea campaign. This paper evaluates
uncertainties associated with the ship motion and presents the correction
methodology regarding lidar velocity measurement based on modified 4-Doppler
beam swing (DBS) solution. The errors of calibrated measurement, both for the
anchored and the cruising shipborne observations, are comparable to those of
ground-based measurements. The comparison between the lidar and radiosonde
results in a bias of −0.23 ms^{−1} and a standard deviation of 0.87 ms^{−1} for the wind speed measurement,
and 2.48, 8.84^{∘} for the wind direction. The biases of horizontal wind speed and random
errors of vertical velocity are also estimated using the error propagation
theory and frequency spectrum analysis, respectively. The results show that
the biases are mainly related to the measuring error of the ship velocity and
lidar pointing error, and the random errors are mainly determined by the
signal-to-noise ratio (SNR) of the lidar backscattering spectrum signal. It
allows for the retrieval of vertical wind, based on one measurement, with
random error below 0.15 ms^{−1} for an appropriate SNR threshold and bias
below 0.02 ms^{−1}. The combination of the CDL attitude correction system
and the accurate motion correction process has the potential of continuous
long-term high temporal and spatial resolution measurement for the MABL
thermodynamic and turbulence process.

The vertical structure of atmospheric variables in the marine atmospheric boundary layer (MABL) plays an important role in the earth's climate system, governing exchanges of energy, sensible heat, water vapour, and momentum between the ocean and the overlying atmosphere (Rocers et al., 1995; Wulfmeyer and Janjic, 2005). The turbulence characteristics are significant for understanding the driving and coupling mechanisms and for parameterizing the ocean–atmosphere interaction process. There are a number of studies on the turbulent fluxes measurement over the sea surface. Various motion sensing techniques on the moving platform have been developed in the field of airborne (Axford, 1968), space-borne (Hawley et al., 1993), and shipborne observations (Fujitani, 1992; Song et al., 1996; Edson et al., 1998; Miller et al., 2008; Tucker et al., 2009). Many shipborne field experiments have been widely carried out over Pacific Ocean (Mitsuta and Fujitani, 1974; Bradley et al., 1991; Shao, 1995; Tsukamoto et al., 1995; Tucker et al., 2009). One of the most common direct techniques for measuring surface fluxes is eddy correlation, which utilizes the covariance of mixing ratios and vertical wind velocity (Lenschow et al., 1981; Anctil et al., 1994; Fairaill et al., 2000), but wind velocity retrieval is complicated by contamination due to platform motion, representing a major source of uncertainty in measurement of turbulence and air–sea interaction. Several techniques have been used to correct the wind vector measured at sea for the influence of platform motion (Fujitani, 1992; Dunckel et al., 1974; Song et al., 1996; Edson et al., 1998; Schulz et al., 2005). Fujitani (1985) used a stable platform System (SPS) consisting of a vertical, gyro-stabilized system and three accelerometers to measure the turbulent flux on the ship, and concluded that this system was applicable to measurement under rough sea surface conditions. A similar method was also used on a buoy (Anctil et al., 1994). This gyro-stabilized system can provide roll, pitch and yaw angles describing the ship's orientation in a fixed frame, which can be used directly in the total rotational coordinate transformation matrix. Song et al. (1996) used a strapped-down system (SDS), consisting of six accelerometers, to measure the air–sea fluxes in the western tropical Pacific and estimated that the system appeared to be relatively robust for use at sea for extended periods. In SDS, the attitude angles are calculated indirectly from the strapped-down angular rate sensors. Edson (1998) also used the SDS consisting of three orthogonal angle rate sensors and three orthogonal linear accelerometers to compute direct covariance fluxes from anemometers mounted on a moving platform at sea, and found that the results were in good agreement with fluxes derived using the bulk aerodynamic method. Miller et al. (2008) modified the procedure of Edson (1998) to explicitly account for misalignment between anemometers and motion sensors.

The coherent Doppler lidar (CDL) has proven to be a powerful tool with high temporal and spatial resolution, providing nearly continuous particle backscatter and wind profile observation in the cloud-free atmosphere, which is vital for the vertical structure of turbulent characteristics measurement in MABL. Unlike the conventional in situ wind measuring methods, CDL can only detect the line of sight (LOS) velocity, which is the projection of the horizontal and vertical velocity along the laser beam direction, thus it is necessary to conduct measurement of three or more different directions of the probing beam to retrieve the wind vector (Werner, 2005; Cheong et al., 2008). More complicated attitude corrections need to be considered when CDL is carried out on a moving platform such as a ship or aircraft, since the orientation of the transmitting laser beam is not fixed and the speed of the ship itself and ocean wave will be stacked to the LOS velocity. This has a more serious detrimental effect on vertical velocity. Several studies have been carried out to investigate the CDL platform motion correction either by actively stabilizing the instrument based on a robust mechanical compensation system or by accurately measuring platform motion and correcting for this in post-processing. Wolfe et al. (2007) and Pichugina et al. (2012) deployed the NOAA high resolution Doppler lidar (HRDL) along with the first use of a motion compensation system at sea in 2004. The HRDL control computer can drive the scanner to actively stabilize the pointing of the scanner and modified velocity azimuth display (VAD) technique are used in the mean-profile calculation. Hill et al. (2005, 2008) used the NOAA HRDL with a SDS to compensate for the orientation of the lidar's scanning unit for the ship's motion and concluded that the attitude correction depends on the velocity of the shipping container and on the motion of the hemispheric scanner relative to the shipping container. Wulfmeyer et al. (2005) corrected the vertical velocity using LOS velocity in zenith stare mode and horizontal wind derived from VAD mode using NOAA HRDL. Lacking real-time control of the scanning head orientation, Achtert et al. (2015) placed a CDL instrument on a motion-stabilization platform to remove the effect of ship motion, and the five-point geometrical wind solution and the four-point sinusoidal fit method were used to obtain wind profiles, showing that motion stabilization was successful for high wind speed in open water and the resulting wave condition. Reitebuch et al. (2001) presented the instrumental correction required for horizontal wind retrieval from an airborne CDL, using conical scanning pattern measurement and recalculation of the lidar mounting angle, based on the ground return speed and distance. It can be seen that an active, mechanical compensation system is used in most of these studies. Especially with the improvements in technology along with decreasing costs robust correction process is increasingly needed. In order to simplify the mechanical structure and to ease installation of the CDL on the ship platform, an algorithm-based attitude correction method was developed for relaxing the requirements for mechanical stability and active compensation mechanisms. This method did not use any active stabilization method. Instead, only a relatively simple but robust algorithm was used to achieve the motion correction in post-processing, which is very easy to use in limited space under the conditions of the shipborne measurements.

The experimental investigation was undertaken by *Dongfanghong-2* research vessel affiliated
with the Ocean University of China in 2014 over the Yellow Sea. The Yellow Sea,
a marginal sea of the Pacific Ocean, is the northern part of the East China
Sea. It is located between mainland China and the Korean Peninsula. There is
seldom study on boundary layer dynamics based on CDL in this region.
In order to achieve one of the main objectives of the study, the CDL was deployed on the ship on this
campaign to demonstrate the feasibility of the algorithm-based attitude
correction method. The obtained accurate three-dimensional wind information
can provide significant preparation for further studies on characteristics
of dynamics and thermodynamics in the MABL and turbulence flux exchange over the sea surface.
In addition to CDL, as another important part of this campaign,
a high spectral resolution lidar (HSRL) and a Vaisala CL31 ceilometer were
also deployed on the ship platform in order to detect the spatial-temporal
evolution of the MABL height and to retrieve the aerosol and cloud optical
characteristics, such as extinction coefficient and backscatter ratio.
It will help us to understand the complex behaviour of MABL and the
aerosol cloud forcing characteristics over sea regions and its impact on
climate change. This paper focuses on CDL performance and gives a thorough
analysis of the attitude correction for lidar velocity measurement. To
illustrate the effect of ship motion on Doppler measurement, we focus on
horizontal and vertical wind profile analysis. In Sect. 2, the
specifications of CDL and especially its attitude correction system are
described in detail, and the velocity correction method is discussed in Sect. 2. In
Sect. 3, the corrected results of horizontal wind are analysed and compared
with simultaneous radiosonde data. A case study is presented to analyse the
effect of the ship velocity and horizontal wind on vertical velocity.
Furthermore, the errors of horizontal and vertical velocity are analysed in
Sect. 3. Finally, Sect. 4 provides a summary and concluding remark.

The CDL system WindPrint S4000, manufactured by Seaglet Environmental Technology, is based on all-fibre laser technology and the heterodyne detection technology. Wu et al. (2016a) and Zhai et al. (2017) provide a comprehensive description of the CDL including a figure of the optical setup. The lidar has a semi-conductor single frequency seed laser that provides both the local oscillator reference beam for heterodyne detection as well as the transmitted beam. The laser operates at a wavelength of 1.55 µm with a linewidth (full width at half maximum of a Lorentzian function) of 1.6 kHz. Using the acoustic optic modulator (AOM) and master oscillator power-amplifier (MOPA) configuration, the achieved pulsed energy is approximately 150 µJ and the pulse repetition frequency is 10 kHz. The number of laser shots used for each spectrum accumulation is 5000. The pulse width produced by the modulation, which is also the width of the time window for obtaining the lidar signal power spectrum, is adjustable from 100 to 400 ns, thus the spatial resolution can be varied from 15 to 60 m. We typically operate the CDL with a pulse width of 200 ns for this study. The transmitted beam is directed into the atmosphere using the 3-D scanner that contains an azimuth and elevation mirror. The scanner allows the lidar beam to probe the hemisphere above the container by means of the “azimuth rotation” and “elevation rotation”. The detection range of 4000 m (maximum 6000 m for high aerosol concentration) enables the system to monitor the complete MABL structure most of the time. A fibre optical circulator and a telescope are used as the optical transceiver. The atmospheric return beam passes through the 3-D hemispheric scanner and the optical transceiver, and is combined with the local oscillator reference beam at the balanced detector. Using heterodyne detection, the frequency difference between the atmospheric return beam and the local oscillator reference beam is detected, which is the measured Doppler shift caused by the relative motion of atmospheric scatters and the lidar system. The real-time analysis based on fast Fourier transform (FFT) is used with a field programmable gate array (FPGA) signal processer. Table 1 lists the general specifications of CDL.

Figure 1 shows the CDL setup on *Dongfanghong-2* research vessel during the
MABL field project over the Yellow Sea in 2014. It is located at the back of
the upper deck and is around 8 m from the sea surface. The CDL scanner is
mounted on the roof of the cabinet container with two fixed global
navigation satellite system (GNSS) antennas. Double antennas are used for
determining the exact heading angle with an accuracy of 0.1^{∘} when the
ship is anchored. The attitude correction system uses XW-GI5651
micro-electromechanical systems (MEMS) inertial–satellite integrated
navigation system. It is equipped with MEMS gyroscope, accelerometer, and
multi-mode and multi-frequency GNSS receiver. It can realize single antenna
dynamic alignment or double antenna auxiliary fast and high-precision
orientation. The specifications are listed in Table 2. Generally, the
attitude correction system uses GNSS to define the Earth coordinate system
(ECS), where the ship speed, heading angle and earth location, including the
longitude and latitude in ECS can be obtained. Another important part of
attitude correction system is the inertial navigation system (INS). The INS
is rigidly mounted on the base of the scanner within the cabinet container,
instead of the deck of the ship, to keep constant relative angles with
reference to the lidar coordinate system. It records the lidar motion angles
in real time including pitch, roll, laser beam azimuth and elevation even
when the GNSS is sheltered or disturbed, and the recorded information is the
exact lidar itself attitude in lidar coordinate system. After installation,
a hard target calibration is performed to determine the misalignment
between the ship and laser beam axes. Specifically, the buildings near the
wharf where there is no occlusion issue between the CDL and the candidate
buildings can be chosen as the hard target. The distance between hard target
and lidar is about 300 m in this experiment. As shown in Fig. 2, the ECS,
ship coordinate system (SCS) and lidar coordinate system (LCS) are marked
with black, red and green arrowed lines, respectively. When the laser beam
direction points to the hard target, the azimuth angle *φ*_{lidar}
in LCS is recorded, meanwhile the azimuth angle *φ*_{g} in ECS can
be obtained using the Google Earth software if the exact longitude and
latitude of hard target is determined. According to the ship heading angle
*ψ*, we can get the azimuth angle ${\mathit{\phi}}_{\mathrm{s}}={\mathit{\phi}}_{\mathrm{g}}-\mathit{\psi}$ between ship heading and the hard target in SCS. So far, the
misalignment angle between the ship and laser beam axes $\mathrm{\Delta}\mathit{\phi}={\mathit{\phi}}_{\mathrm{s}}-{\mathit{\phi}}_{\mathrm{Lidar}}$ can be corrected using the geometrical
relationship between these three angles. Then the standard ship attitude
definition can be determined based on the relationship between lidar and
ship coordinate system, which will be used in the following ship motion
correction process. The laser direction error determined
by misalignment between the ship and Lidar is negligible since the Lidar is
considered to be relatively static compared with the ship during the field
experiment. Ship motion turns out to be an important error source for the
determination of turbulence variables using shipborne CDL (Wulfmeyer and
Janjic, 2005). To study boundary layer dynamics, the atmospheric wind
velocity in ECS is required, so the compensation for the pointing error and
along-beam platform velocity due to ship motion need to be determined using
the attitude correction system. Figure 2 shows the specific definition of
the parameters in SCS (${X}_{\mathrm{s}},{Y}_{\mathrm{s}},{Z}_{\mathrm{s}})$, ECS (${X}_{\mathrm{g}},{Y}_{\mathrm{g}},{Z}_{\mathrm{g}})$
and LCS (${X}_{\mathrm{Lidar}},{Y}_{\mathrm{Lidar}},{Z}_{\mathrm{Lidar}})$, respectively. Details on the
motion-correction algorithm are given in Appendix A.

For a shipborne CDL, the recorded velocity corresponds to the relative velocity along the laser beam direction between the ship and the atmospheric target, where the ship platform motion will add to the measured LOS velocity in SCS. Therefore, the first step in the wind retrieval process is the removal of the along-beam platform velocity due to ship motion ${\overrightarrow{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{ship}}$. It is noted that wave induced velocity perturbations would add to the ship's mean velocity when underway, which needs no correction independently in the correction procedure. During the experiment, the speed of the ship ${\overrightarrow{V}}_{\mathrm{ship}}$ is acquired by GNSS with temporal resolution of 0.5 s, and is recorded as the horizontal component ${\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{horizontal}}$ and vertical component ${\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{vertical}}$, respectively, thus the ${\overrightarrow{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{ship}}$ can be calculated as follows:

The LOS velocity ${\overrightarrow{V}}_{\mathrm{LOS}}$ in ECS is the vector sum of the LOS velocity measured by CDL in SCS ${\overrightarrow{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{measure}}$ and the ${\overrightarrow{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{ship}}$, that is,

and

where $\overrightarrow{V}=[u,v,\mathrm{0}]$ and $\overrightarrow{W}=[\mathrm{0},\mathrm{0},w]$ are the
horizontal and vertical component of the wind speed respectively, *u* *v*
and *w* are the north-south, east-west and vertical velocity in ECS,
respectively. The CDL measured LOS velocity has the same temporal resolution
of 0.5 s as the ${\overrightarrow{V}}_{\mathrm{ship}}$ parameters acquired by GNSS.

Profiles of the wind vector can be retrieved by scanning the lidar beam or
stepping the lidar beam through a sequence of different angles or
perspectives (Reitebuch et al., 2001; Frehlich, 2001a; Werner, 2005). For the
ground-based CDL, the profile of horizontal wind velocity can be retrieved
using 4-Doppler beam swing (DBS) mode which is faster and simpler both in
the hardware and in the data evaluation algorithm (Werner, 2005; Weitkamp,
2005; Wang et al., 2010). Specifically, the wind vector components at target
altitude can be derived by measuring the LOS wind velocities in four
directions (normally east, west, south and north) under the assumption of
homogenous flow with little turbulence. However, the shipborne platform, the
elevation *θ*_{g} in four directions (north, south, west and east in
ship coordination system) may have a slight difference (see Eq. A5) due to
ship rotation and movement during the time period of measuring different LOS
directions. A conversion of ${\overrightarrow{V}}_{\mathrm{LOS}}$ from real elevation
*θ*_{g} to the expected elevation *θ*_{0} is firstly
processed, that is,

In this study ${\mathit{\theta}}_{\mathrm{0}}=\mathrm{60}{}^{\circ}$ is set for horizontal wind profile retrieval. During the experiment, each radial direction will take 5 s to obtain 10 measured LOS velocity for accumulation and the average. In this sense, the highest temporal resolution of horizontal wind velocity using 4-DBS mode is 20 s. The recorded ship condition information has the same update rate of 0.5 s as radial velocities, which can be averaged to remove the platform motion effect on radial velocity.

Furthermore, since the laser beam azimuth angle in ECS need to be determined
using Eq. (A4), the conventional DBS formula where four directions at an
interval of azimuth-angle of 90^{∘} are detected need to be modified.
Except for the extremely rough sea condition, the LOS velocity component
from vertical velocity in different directions is assumed to be identical.
Then the *u*, *v* can be calculated using a modified 4-DBS formula:

where ${a}_{\mathrm{1}}=\mathrm{cos}{\mathit{\phi}}_{\mathrm{N}}-\mathrm{cos}{\mathit{\phi}}_{\mathrm{S}}$, ${a}_{\mathrm{2}}=\mathrm{sin}{\mathit{\phi}}_{\mathrm{N}}-\mathrm{sin}{\mathit{\phi}}_{\mathrm{S}}$, ${a}_{\mathrm{3}}=\mathrm{cos}{\mathit{\phi}}_{\mathrm{E}}-\mathrm{cos}{\mathit{\phi}}_{\mathrm{W}}$, ${a}_{\mathrm{4}}=\mathrm{sin}{\mathit{\phi}}_{\mathrm{E}}-\mathrm{sin}{\mathit{\phi}}_{\mathrm{W}}$, ${b}_{\mathrm{1}}=({\overrightarrow{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{N}}{}^{\prime}-{\overrightarrow{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{S}}{}^{\prime})/\mathrm{cos}{\mathit{\theta}}_{\mathrm{0}}$, and the subscript N, S, E, and W represent the north, south, east and west in SCS, respectively. It is noted that under extremely rough sea conditions, the difference of elevation angle in different directions is significant, and the contribution of vertical velocity to LOS velocity needs to be treated carefully. In this case, the height interpolation of radial velocity can be used, and if three or more radial velocities at the same height are obtained, the horizontal and vertical velocity can be retrieved. But if the elevation angle in one direction is too small, the detectable height will be limited.

For the case of vertical wind measurement, small deviations from vertical
pointing due to ship motion induces a projection of the horizontal wind in
the laser beam direction. To correct this effect, estimations of the
horizontal wind using Eqs. (5), (6) and (7) are used and then the vertical
velocity *w* can be obtained using Eq. (3), where in this formula
${\overrightarrow{V}}_{\mathrm{LOS}}$ is the measurement in zenith stare mode in ship
coordination system.

The sampling rate in our study is *f*=1 GHz, corresponding to the sampling
interval of *T*_{s}=1 ns. By applying the discrete Fourier
transform to *M*=256 samples, the spectrum estimate has a frequency
resolution of $\mathrm{\Delta}f=({\mathrm{MT}}_{\mathrm{s}}{)}^{-\mathrm{1}}=\mathrm{3.906}$ MHz and a velocity resolution
of $\mathrm{\Delta}V=(\mathit{\lambda}/\mathrm{2})\mathrm{\Delta}f=\mathrm{3.027}$ ms^{−1}, where
*λ*=1.55 µm is the wavelength. In order to obtain
the spectrum with better resolution, the interpolation method of adding 768
zeros to the 256 selected samples of the backscatter signal is used, thus
the final frequency resolution is Δ*f*≈0.98 MHz and the
corresponding velocity resolution is Δ*V*=0.76 ms^{−1}.

Based on the heterodyne detection, the frequency of the local oscillator
*f*_{0} is optically mixed with the backscatter signal ${f}_{\mathrm{0}}+{f}_{\mathrm{IF}}+\mathrm{\Delta}{f}_{\mathrm{D}}$, where *f*_{IF} is the intermediate
frequency and Δ*f*_{D} is the Doppler shift from atmospheric
movement. Thus the beat signal of *f*_{IF}+Δ*f*_{D} is obtained
in a detectable range *B* of MHz. Figure 3 shows the array of the FFT
spectrum *S*(lΔ*f*;*k*Δ*R*) after zero padding
interpolation obtained from the raw data measured with PCDL, where
$l=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{\dots},L-\mathrm{1}$ is the spectral channel number and *L*=100 and
$k=\mathrm{1},\mathrm{2},\mathrm{3}\mathrm{\dots},K$ is the range bin number and *K*=104. It is noted that the 100
spectral channel is symmetrically selected near the intermediate frequency
with ${B}_{\mathrm{100}}=(L-\mathrm{1})\mathrm{\Delta}f=\mathrm{97.68}$ and corresponding radial
velocity measurement range of ±37.5 ms^{−1}.

The scattering particles in the sensing volume have a certain velocity distribution. It is easy to estimate the mean radial velocity from the FFT spectrum estimate with high SNR. However, evaluation of the maximal velocity with acceptable accuracy is not possible because of the strong fluctuation of the signal and noise components in the spectrum estimate. In order to reduce these fluctuations, spectrum accumulation is used. In our study the pulse repetition rate is 10 kHz and the accumulation shot is 5000 for each radial velocity measurement.

The SNR in this study is defined as the ratio of the peak value of FFT spectrum signal in each range bin to the Root-Mean-Square (RMS) of background noise signal. Figure 3a shows the last 10 range bins' raw array of spectrum in green line. We estimate the averaged background noise spectrum,

by subtracting the background noise spectrum ${\stackrel{\mathrm{\u203e}}{S}}_{\mathrm{N}}\left(l\mathrm{\Delta}f\right)$
from the raw spectrum array *S*(lΔ*f*;*k*Δ*R*), the unnoisy
array of spectrum $\widehat{S}(l\mathrm{\Delta}f;k\mathrm{\Delta}R)$ can be obtained and
shown in the red line in Fig. 3. The peak value index *l*_{peak} from the
$\widehat{S}(l\mathrm{\Delta}f;k\mathrm{\Delta}R)$ can be obtained and thus the
absolute signal power *P*_{s}(*k*Δ*R*) at various range *k*Δ*R* can
be represented as follows:

Replacing integration by summation and taking into account that the zero
velocity point in one channel is *l*_{zero}=50, we estimate the noise power
*P*_{N} as:

Finally, we obtain the range profile of the SNR(*k*Δ*R*) using the
equation as follows:

It is noted that unlike the definition of SNR in previous studies (Banakh and Smalikho, 2013) where the SNR is defined as the ratio of the average heterodyne signal power to the averaged detector noise power in a 50 MHz bandwidth, the SNR in this study is simpler and also indicates the CDL detection capability, data accuracy and atmospheric tracer particle relative intensity. In this sense, the SNR threshold value in this study is higher than the one in previous studies (Banakh and Smalikho, 2013; Achtert et al., 2015) for the same signal power spectrum.

Figure 4 shows the flowchart of shipborne CDL data processing. Specifically, the LOS velocity and SNR can be determined using lidar data and FFT analysis. After the data pre-processing, including the quality control based on SNR threshold, the attitude transformation is then used to obtain the azimuth and elevation in each LOS velocity in ECS with temporal resolution of 0.5 s. The LOS velocity detected by the lidar is the atmosphere motion relative to SCS, thus the removal of the along-beam platform velocity due to ship motion is needed. In this study, the horizontal wind profile with 2 min temporal resolution will be retrieved for vertical velocity correction. Basically, the LOS velocities from north, south, east, and west direction after SNR quality control during the chosen 2 min interval are collected firstly. Then the procedure of filtration of reliable estimates of each radial velocity based on SNR threshold is used to obtain “good” speed estimates. The selected radial velocities and corresponding ship condition information in each radial direction are averaged and the averaged ship condition will be used for the removal of platform velocity effect. Finally, the horizontal velocity with 2 min temporal resolution can be retrieved using modified 4-DBS mode. The vertical wind measurement has a temporal resolution of 0.5 s, the horizontal wind that has the retrieved time closest to vertical wind measured time will be used for vertical velocity correction.

## 3.1 Horizontal wind evaluation

The modified 4-DBS method for horizontal wind profile retrieval is illustrated in Fig. 4. Two examples of the comparison between uncorrected and corrected horizontal wind profiles are shown in Fig. 5 for anchored measurement and Fig. 6 for cruising observation, respectively. The temporal resolution of radial velocity is 0.5 s and the lidar results (black curves) averaged over at least 10 min after the launch of the radiosonde are compared with the radiosonde data (red curves). The type of radiosonde is Model GTS1 digital radiosonde with the basic parameters listed in Table 3 (Song et al., 2017).

Figure 5 shows the horizontal wind profile during anchored measurement (mean
ship speed equals to 0.27 ms^{−1}) during 15:52–16:02 local time
(LT) on 9 May 2014 at 37.00^{∘} N, 122.86^{∘} E. The black line
in Fig. 5b–e indicates the mean measurement by CDL during the
10 min period, and the red line shows the result from simultaneous
radiosonde data. The blue bars represent the standard deviation of CDL wind
measurement from the 2 min temporal resolution results during the chosen
analysis period, which can effectively represent the atmospheric
fluctuations. It can be seen that the wind is approximately southerly
through the measurement altitude, but slightly southeasterly below 1.6 km,
and then shifts to southwesterly above 1.6 km. The wind speed gradually
decreases with height up to 1.6 km and then increases above. The standard
deviation of wind speed and direction below 1.4 km are less than 0.5 ms^{−1} and 5^{∘}, respectively, showing that the atmospheric
condition is relative stable below 1.4 km. While there are higher
fluctuations in the height of 1.4–1.6 km. The higher SNR in the layer
of 1.4–1.6 km shown in Fig. 5a implies the existence of a cloud or
aerosol layer, more active and complex atmospheric movement in this layer
may result in higher fluctuations. The specific ship condition
parameters are listed in Table 4. The time series of ship horizontal speed,
pitch and roll angles are shown in Fig. 7a and b, respectively. It can be
seen that the mean pitch and roll are −0.17 and 0.63^{∘}
with a standard deviation 0.06 and 0.11^{∘}, respectively,
thus the swing of the ship is not obvious. It is noted that the standard
deviation of the angles is determined from the variability during the 10 min
period using *N*= 1200 raw data with a temporal resolution of 0.5 s, which is
shown in Fig. 7b. Since lower SNR makes the data invalid, data quality
control based on SNR threshold is used to remove the spikes higher than 2.4 km. The SNR threshold in this study is 8 dB and the reason will be
analysed in Sect. 3.3. The root mean square error (RMSE) in speed between
lidar and radiosonde below 2 km is 0.49 ms^{−1} for the uncorrected
measurement, and 0.45 ms^{−1} for the corrected measurements, both
consistent with the radiosonde wind speed. It is reasonable, as the effect
of ship motion speed on LOS velocity is less obvious in anchored
measurement. Moreover, the variation of lidar elevation and azimuth in ECS
is small, and in this case, when the lidar points to the bow with an
elevation of 60^{∘} in SCS. If the ship's pitch, roll and heading are
−0.17, 0.63, 5.28^{∘}, respectively. According to
Eqs. (A4) and (A5), the lidar azimuth and elevation in Earth coordinates are
${\mathit{\phi}}_{\mathrm{s}}=\mathrm{6.37}{}^{\circ}$ and ${\mathit{\theta}}_{\mathrm{s}}=\mathrm{59.82}{}^{\circ}$,
respectively. Similarly, when the lidar points to starboard, stern, and port,
the corresponding azimuth are 94.99, 184.18, and
275.58^{∘}, and the elevations are 59.37, 60.16
and 60.63^{∘}, respectively, resulting in less difference of
horizontal wind speed retrieved from the SCS and ECS . However, the RMSE in
wind direction between lidar and radiosonde is 84.43^{∘} for
uncorrected measurement and 5.27^{∘} for corrected measurement. The
obvious difference in the wind direction results from two aspects. The first
is the definition in different coordinate systems, where the heading has
an important effect on lidar azimuth. The second is that because of
the experimental field limitation, the direction of GNSS master antenna is
perpendicular to the ship bow, meaning that the “real” heading is the
recorded heading plus 90^{∘}, and this angle offset due to placement
problem is fixed and calibrated using hard target detection before the
campaign. Generally, attitude correction is necessary, especially for the
wind direction retrieval even though the ship is anchored with slight shake.

Figure 6 shows the results of the cruising observation from 07:44 to 07:54 LT on 13 May 2014 when the mean ship speed is 4.84 ms^{−1} with standard
deviation of 0.03 ms^{−1}. It can be seen that the wind is constantly
southwesterly through the available measurement altitude, and there is a
low-level-jet at around 0.3 km where the wind speed exceeds 25 ms^{−1}.
Additionally, the fluctuation in wind speed and direction above 1 km is more
severe than the result below 1 km. The specific ship condition parameters
are also listed in Table 4. The time series of ship horizontal speed, pitch
and roll angles are shown in Fig. 7c and d, respectively. It can be seen
that the mean pitch and roll are −0.43 and 2.06^{∘} with
standard deviation 0.05 and 0.87^{∘}, respectively.
Generally, the ship roll has a more effect on the lidar elevation when it
points to the port or starboard, conversely, the lidar elevation in bow
or stern direction is more sensitive to ship pitch. In this case, the lidar
mean elevation in bow, starboard, stern, and port direction after attitude
transformation are 59.51, 57.8, 60.30, and
62.49^{∘}, respectively, and the mean heading is 75.86 with
standard deviation 1.22^{∘} where the ship sails downwind. In this
condition, the horizontal wind speed without motion correction will be
underestimated compared with the radiosonde result. The RMSE in speed
between lidar and radiosonde data below 1.0 km are 4.42 ms^{−1} for
uncorrected measurement and 0.88 ms^{−1} for corrected measurements, and
the corresponding RMSE in wind direction are 48.71 and
9.52^{∘}, respectively. Therefore, the attitude correction algorithm
has obviously improved the wind profile result when the ship is in cruising
observation. The difference in mean wind speed and direction between
radiosonde and CDL above 1 km is about 3.4 ms^{−1} and 15.2^{∘},
respectively, showing significant discrepancy. On the one hand, the random
error of the corrected CDL estimation of the wind due to the low SNR shown
in Fig. 6a contributes to this discrepancy. On the other hand, according to
the recorded information, the mean heading angle and cruising speed of the
ship is 75.86^{∘} and 4.84 ms^{−1}, respectively, and the
mean wind speed and direction above 1 km is 255^{∘} and 18.4 ms^{−1}, respectively. Since the drift of radiosonde is affected by
atmospheric wind and turbulence perturbation, and the CDL detection volume
is changing during cruising observation, the result discrepancy between
radiosonde and CDL caused by different observation location, also called the
multipath effect, is larger with increasing height. In order to assess the
accuracy of the shipborne lidar wind measurement, a comparison of the lidar
measurement and 11-radiosonde dataset during the experiment is made. It is
noted that the radial range resolution of lidar in this study is 30 m, and
the corresponding vertical range resolution with elevation angle of
60^{∘} is about 26 m. The vertical resolution of radiosonde is 10 m.
During the comparison, the wind profile of radiosonde is interpolated into
the common height grid with finer resolution of 2 m firstly, and then the
data point closest to height point of lidar will be chosen for comparison.
Figure 8 shows a scatter plot of wind speed and direction for radiosonde and
lidar measurement based on modified 4-DBS solution. The radial measurement
range in this study is between 150 and 3240 m (corresponding to the 104th
range bin), thus the altitude range between 130 and 2806 m with elevation
angle of 60^{∘} are used for the statistical comparison shown in the
Fig. 8. The red trend line plotted through these points represents an
ordinary linear least square regression for the data excluding $\left|y\mathrm{data}-x\mathrm{data}\right|>\mathrm{2}\times $ SD, where *y*data and *x*data is the lidar and
corresponding radiosonde data, respectively, and SD represents the standard
deviation of the difference of *y*data–*x*data. According to the distribution
of difference of *y*data–*x*data and fitted Gaussian distribution, the
criteria of excluding data with 2× SD is reasonable for gross
outliers. The excluded data-pair number and proportion is 62 and 6 % for
wind speed, respectively, 56 and 5.9 % for wind direction, respectively.
The wind speed linear regression shows a correlation coefficient of 0.982,
SD of 0.87 ms^{−1} and RMSE of 0.90 ms^{−1}. The wind direction linear
regression shows the correlation coefficient of 0.995, SD of 8.84^{∘}
and RMSE of 9.50^{∘}. The bias of wind speed and direction is −0.23 ms^{−1} and 2.48^{∘}, respectively, demonstrating the feasibility
and reliability of the modified 4-DBS solution.

Table 5 lists a height-resolved view (from 0.2 to 1.6 km) of the
linear fit parameters between lidar and radiosonde. The correlation
coefficient *R* for wind direction is approximately 0.99 and almost constant
with altitude up to 1.6 km. The correlation coefficient for wind speed is
minimum at the lowest altitudes, and improves with height to values
comparable to those for wind direction, the trends of which compare well
with the results from Achtert et al. (2015). An obvious feature in SD, RMSE,
normalized RMSE for wind speed and direction is found at the lowest levels
where the discrepancies between lidar and radiosonde data are larger than
the higher levels. On the one hand, the relative height between CDL and the
highest building on the ship is about 15 m, as shown in Fig. 1b. When strong
wind blows from the ship bow, the building and experimental setups on ship
have an important effect on CDL lower-level detection volume where the
induced-turbulence may be unable to meet the assumption of homogeneous isotropic
atmosphere for 4-DBS retrieval. On the other hand, the blind area of the CDL
is 150 m and corresponds to the height of 129.9 m when laser beam elevation
angle is 60^{∘}, meaning that less data points are available below
200 m with effective comparison. Whether the flow distortion around the ship
is the main reason for the discrepancies in the lower part measurement or
not is yet unclear. Further study, especially focused on the computational
fluid dynamics (CFD) model, needs to be used to the assess the potential effects on
turbulent flow and wind field analysis (Achtert et al., 2015). It is also
significant for assessing turbulence fluxes exchange from sea-air interface.
Furthermore, SD, RMSE, normalized RMSE for wind speed and direction increase
with altitude from 0.4 km, which are mainly caused by the lower SNR and
increasing spatial separation because of the multipath effect mentioned
above.

## 3.2 Vertical wind evaluation

The motion correction of vertical velocity, which is more challenging
compared with the horizontal wind component, has been specifically described
in Sect. 2. A typical measurement case study on 14 May 2014 is presented in
Fig. 9. Figure 9a shows the whole series of time-height cross sections of the
SNR. According to the Vaisala CL31 ceilometer recorded result, an aerosol
layer is presented at around 2.1 km during 07:33–08:40 LT. The MABL
height has been retrieved and compared using different instruments such as
the CDL, radiosonde, and Vaisala CL31 ceilometer during this campaign (Wang
et al., 2015). Many papers have discussed the use of the backscatter signal of
Lidar for mixing height estimation, assuming that the boundary layer has
higher aerosol concentrations than the free troposphere above. In this
study, the SNR, representing the relative aerosol backscatter profiles, were
used and two common methods includes thresholding SNR to determine MABL
height (Melfi et al., 1985) and finding the height of the first strong
negative gradient (White et al., 1999; Hennemuth and Lammert, 2006) in SNR.
The temporal and spatial variation of MABL height from threshold and
gradient methods can be seen in Fig. 9a marked with black and red solid
circles, respectively. The radiosonde data during 12:00 LT on 14 May 2014
and corresponding MABL height using the gradient of potential temperature
and relative humidity are also shown in Fig. 10. It can be seen that diurnal
variation of MABL height is less obvious within 1.0–1.5 km, consistent
with the mixing layer height retrieved from the radiosonde potential
temperature and relative humidity profile. The corrected vertical velocity
wind speed is presented in Fig. 9b. It is noted that the data analysis below
0.15 km is not reliable because of the lidar blind area, and the data
above 1.5 km is also removed since the SNR is less than its threshold
value. The red and blue colours indicate positive (upward) and negative
(downward) movement of the atmosphere parcels along the laser beam,
respectively. It can be seen that the vertical velocity has a significant
diurnal variation. Specifically, the downdraft dominants mixing layer in the
morning amounted to about 0.5 ms^{−1}, and small-scale convective
activity can be observed at the top of mixing layer. As the solar radiation
strengthens, the atmospheric convection becomes more active and extends to
the whole mixing layer, the strengths of updrafts and downdrafts are weakly
stronger than before and the atmospheric vertical alternation becomes more
frequent. The mixing layer recovers to descending motions over a continuous
and long period after 13:11 LT.

Figure 11a shows the time series of ship heading, CDL laser beam azimuth and
elevation, and horizontal wind direction at 0.4 km. Figure 11b shows the time series of elevation angles in zenith stare mode from SCS
and ECS. It can be seen that the hemispherical scanner
maintains the pointing of the lidar beam to zenith stare mode with an
averaged elevation of $\mathrm{88.6}{}^{\circ}\pm \mathrm{0.35}{}^{\circ}$ because of the ship
motion. During the zenith stare mode, the mean angle between ship heading
and the laser azimuth is 66^{∘} with standard deviation of 7^{∘}, thus the projection of ship velocity on vertical velocity is always
positive, the results of which are shown in Fig. 12a. Furthermore, the
estimation of the horizontal wind speed and direction (black line in Fig. 11a) from modified 4-DBS solution is used to remove the horizontal wind
speed projection $\overrightarrow{{r}_{\mathrm{g}}}\cdot \overrightarrow{V}$ from
the relative speed measured by CDL. In this case, the $\overrightarrow{{r}_{\mathrm{g}}}\cdot \overrightarrow{V}$ is positive and negative in downwind and
headwind, respectively, causing the overestimate and underestimate of the
vertical velocity, the effect of which is shown in Fig. 12b. The difference
between the corrected and uncorrected vertical velocity shown in Fig. 12c, obviously showing the temporal and spatial variation of the
contribution of the ship motion and horizontal wind on the vertical
velocity.

## 3.3 Measurement uncertainty and error analysis

Error analysis is useful in assessing the accuracy and precision of the lidar wind measurements (Wang et al., 2010). They also shed light on the potential improvements of this CDL. According to the definition of error for measurement of a random wind field, the measured velocity is represented as (Frehlich, 2001a):

where *V*_{truth} is the desired or true wind measurement, *e*_{V} is
the random error with zero mean, representing the precision of wind
measurements, and bias_{V} is the systematic error, representing the
accuracy of the wind measurements.

As for radial velocity, for instance, the north radial velocity
${\widehat{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{N}}$ with azimuth angle *φ*_{N} and elevation angle *θ*_{N}, the measurement can be
represented as follows:

where $\stackrel{\mathrm{\u203e}}{h}=[\stackrel{\mathrm{\u203e}}{u},\stackrel{\mathrm{\u203e}}{v}]$ and $\stackrel{\mathrm{\u203e}}{w}$ are the
spatially averaged horizontal and vertical velocity, respectively, and *c*_{1}=cos *φ*_{N}cos *θ*_{N}, *c*_{2}=sin *φ*_{N}cos *θ*_{N},
*c*_{3}=sin *θ*_{N}, *e*_{N} and bias_{N} are the random
error and bias of the north radial velocity measurements.

For shipborne measurement, the ship platform velocity ${\overrightarrow{V}}_{\mathrm{ship}}$ produces a large contribution
${\overrightarrow{V}}_{\mathrm{LOS}\mathit{\_}\mathrm{ship}}$ to the total radial velocity (see Eq. 1). The bias
in the radial velocity measurement comes from errors in the knowledge of
${\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{horizontal}}$, ${\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{vertical}}$,
*ψ*_{N}, *φ*_{N}, and *θ*_{N},

where $\mathrm{\Delta}{\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{horizontal}}$, $\mathrm{\Delta}{\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{vertical}}$, and Δ*ψ*_{N} are
the errors in the determination of the ship speed and direction, and equal
to 0.1 ms^{−1}, 0.1 ms^{−1}, 0.1^{∘}, respectively. Δ*θ*_{N}, Δ*φ*_{N} are the pointing angle knowledge
errors of the north direction lidar beam. In this case, Δ*φ* and Δ*θ* are related to the servo system, and the scanner
pointing accuracy is 0.1^{∘}, thus $\mathrm{\Delta}\mathit{\phi}=\mathrm{\Delta}\mathit{\theta}=\mathrm{0.1}{}^{\circ}$ in all directions. It is noted that the knowledge error of
the ship velocity and lidar pointing angle mentioned above are systematic
part and it is assumed that the random error of these quantities is zero,
which is reasonable and robust for horizontal wind retrieval. Similarly, to
derive the ${\overrightarrow{V}}_{\mathrm{LOS}}{}^{\prime}$ bias, we take the derivatives of
Eq. (4),

Because of the requirement for a small bias in the radial velocity
measurements, the error in the laser beam direction must be very small and
one can assume perfect knowledge of the coefficient *a*_{i} (Frehlich,
2001a), so the biases of *u* and *v* from the radial velocity estimation can
be described as follows:

It can be seen that the dominant source of bias of the horizontal velocity
estimates come from the biases of the radial velocity estimates (bias_{N}, bias_{S}, bias_{E} and bias_{W}),
which are determined by the
error in the ship velocity ${\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{horizontal}}$, ${\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{vertical}}$ and
heading angle *ψ* and lidar pointing knowledge errors Δ*φ*
and Δ*θ* (see Eq. 13).

Various methods of estimating the magnitude of the random error of Doppler
lidar velocity measurements have been introduced (Frehlich, 2001b). A method
based on the frequency spectrum of the retrieved velocity has been used to
determine the random error of vertical wind measurements. A 50 % window
overlap factor, a Hamming window is used in order to reduce leakage in the
spectra (Chouza et al., 2016). A zero-padding of the missing values were
applied to each window for each spectrum calculation to improve the
frequency resolution. The constant high-frequency region of vertical
velocity spectrum higher than 0.2 Hz, shown in Fig. 13 at a height of 1495 m,
represents uncorrelated random error contribution, which is departing from
the Kolmogorov's $-\mathrm{5}/\mathrm{3}$ law. The random error of vertical velocity is
estimated as the standard deviation of the measured signal after high-pass
filter. Figure 14 shows the error analysis of horizontal and vertical wind
during 15:52–16:02 LT on 9 May 2014. The observed SNR is illustrated in
Fig. 14a, and there is an aerosol layer at around 1.5 km, consistent with
the higher value in SNR. The random errors of vertical velocity from the
standard deviation of the random noise signal, shown in Fig. 14b, are less
than 0.1 ms^{−1} below 1 km with SNR < 8 dB, and a peak value
appears at around 1.3 km and decreases with altitude until around 1.5 km. Then the random errors increase with altitude as the SNR decrease, and
reach about 1.2 ms^{−1} at 2.3 km. It is clear that the random error is
mainly determined by the SNR. Figure 14c shows the bias_{u}, bias_{v},
and corresponding bias of horizontal wind velocity bias_{h}. The
bias_{h} is less than 0.02 ms^{−1} below 2.5 km, which is negligible
and consistent with the result shown in Sect. 4.1. According to Eqs. (16) and (17), the dominant source of bias of horizontal wind velocity is mainly
from the ship velocity and lidar pointing errors in different directions. In
this case, ${\overrightarrow{V}}_{\mathrm{ship}\mathit{\_}\mathrm{horizontal}}$ provides
the highest contribution on the bias of the radial velocity. The observed
random error of the vertical velocity as a function of SNR is presented in
Fig. 15, which is retrieved from the frequency spectrum of the retrieved
vertical velocity during 07:33 to 15:29 LT on 14 May 2014. It can be seen
that in the high SNR region above 8 dB, a constant random error range
between 0.03 and 0.15 ms^{−1} is found because of the effect of the
speckle-induced phase noise (Frehlich, 1997, 2001b), which is much
smaller than the standard deviation between the mean wind speed derived from
lidar and radiosonde of 0.75 ms^{−1} (see Sect. 3.1). At reduced values of
the SNR, the errors increase as a result of increasing signal noise, rising
to approximately 4 ms^{−1} at an SNR = 0 dB. It is confirmed that the
choice of a conservative SNR threshold of 8 dB is robust for the data quality
control process.

Shipborne wind observations by a CDL during the 2014 Yellow Sea campaign were carried out to study the structure of the MABL. An algorithm to compensate for error of wind measurement due to the motion of the ship is presented in this paper. The algorithm-based attitude and velocity correction methods greatly relax the requirements for mechanical stability and compensation mechanisms. The attitude correction system of the CDL consists of GNSS and INS to directly measure the speed and the attitude of the ship. According to the transformation matrix from the product of roll, pitch and heading rotation matrix, the azimuth and elevation of the LOS velocity in the ECS can be firstly determined. Then the removal of the along-beam platform velocity due to ship motion is needed to obtain the “real” LOS velocity in the ECS. The horizontal wind profiles can be retrieved by a modified 4-DBS method. For the case of vertical velocity, small deviations from vertical pointing due to ship motion induces a projection of the horizontal wind on the LOS vector, thus estimation of the horizontal wind speed contribution are used to correct the vertical velocity.

In order to assess the accuracy of the shipborne lidar wind measurement, a comparison of the lidar measurement and 11-radiosonde dataset from 9 to 19 May 2014 was made. The total number of the wind speed and direction datasets for comparison are 1321 and 1275, respectively. The comparison of the CDL and radiosonde shows that attitude correction is essential for the wind retrieval in cruising measurement. The correlation coefficients of wind speed and direction are 0.982, 0.995, respectively, both of which show negligible bias and demonstrate the feasibility and reliability of the modified 4-DBS method. A case study of an 8 h time series observation on 14 May 2014 is presented to compare uncorrected and corrected vertical velocity, additionally showing the specific temporal and spatial variation of the contributions of ship motion and horizontal wind on vertical velocity.

The bias of horizontal wind velocity is estimated using error propagation
analysis and concluded that the dominant source comes from the radial
velocity estimates, which are determined by the error in the ship velocity
and lidar pointing errors. The random error is estimated based on the
frequency spectrum of the retrieved velocity. A case study during 15:52 to
16:02 LT on 9 May 2014 is presented. The radial measurement range is from
0.15 to 3.105 km, where the blind area of CDL is less than 0.15 km and the
maximum detectable range is 3.105 km. It is found that the random error of
vertical velocity is between 0.03 and 1.2 ms^{−1} and is mainly
determined by the SNR, while the bias was less than 0.02 ms^{−1}, which is
negligible and consistent with the result of comparison between lidar and
radiosonde data. The fundamental random error of the lidar vertical wind
obtained from 07:33 to 15:29 LT on 14 May 2014 in all height ranges is found
to be in the range of 0.03 to 0.15 ms^{−1} for SNR above 8 dB, which is
much smaller than the standard deviation between the mean wind speed derived
from lidar and radiosonde of 0.75 ms^{−1}. The choice of a conservative
SNR threshold of 8 dB is also confirmed by the error analysis results of
vertical velocity. Overall, combining a CDL with an attitude correction system
and accurate motion correction process as presented here forms a reliable
and autonomous set-up that could be placed on a mobile platform to provide
more detailed, higher spatial and temporal resolution view of
three-dimensional wind field information. It will be further validated and
improved under different sea conditions using CFD model simulation in
further field campaigns. More specific studies are being carried out or
prepared, including atmospheric turbulence characteristic statistics and
multi-scale wind field observations in MABL, wind turbine wake and
atmospheric turbulence interaction over offshore wind power field (Wu et
al., 2016a; Zhai et al., 2017), mass transport and flux analysis in MABL with
combination of CDL, and multi-wavelength polarization Raman lidar (Wu et al.,
2016b).

All the data presented in this study are available from the authors upon request.

As can be seen in Fig. 2, the SCS (${X}_{\mathrm{s}},{Y}_{\mathrm{s}},{Z}_{\mathrm{s}})$ is defined as
*X*_{s} axis along the centre line of the ship, positive toward bow, *Y*_{s} axis
is perpendicular to *X*_{s}, and positive toward starboard, *Z*_{s} axis
is positive toward the bottom. The attitude of the ship can be expressed by
roll *φ*, pitch *θ*, and heading angles *ψ*. The *φ*,
*θ* and *ψ* refer to rotations about *X*_{s}, *Y*_{s}, and
*Z*_{s} axes, respectively. Specifically, positive *φ* is defined
as when the port is up, and positive *θ* is defined when the bow is up.
The *ψ* is defined 0^{∘} when the bow points to north in ECS. The
ECS (${X}_{\mathrm{g}},{Y}_{\mathrm{g}},{Z}_{\mathrm{g}})$ is defined as *X*_{g} axis along north-south
direction, positive toward to north, *Y*_{g} axis is along east-west
direction, and positive toward to east, *Z*_{g} axis is positive toward the
bottom.

In the SCS, the recorded azimuth and elevation of the transmitting laser are
*φ*_{s} and *θ*_{s}, respectively. *φ*_{s} is defined
as the angle between the projection of transmitting laser path on *X*_{s}−*Y*_{s} plane and the positive
*X*_{s} axis. From the top view, *φ*_{s} increases in a clockwise direction during 4-DBS mode operation.
*θ*_{s} is defined as the angle between the laser beam direction and
the *X*_{s}−*Y*_{s} plane. Therefore, the direction of the transmitting
laser in the SCS can be expressed by a unit vector $\overrightarrow{{r}_{\mathrm{s}}}$ as (Hill, 2005; Liu et al., 2010).

A coordinate transformation from the SCS to that of the ECS is needed. According to the transformation matrix from the product of the three rotation matrixes shown in Eq. (A2), the unit vector $\overrightarrow{{r}_{\mathrm{g}}}$ of transmitting laser direction in ECS can be expressed as Eq. (A3):

where *H*_{1}, *H*_{2}, *H*_{3} are the rotation matrices of roll, pitch,
and heading, respectively (Hill, 2005).

Once the unit vector $\overrightarrow{{r}_{\mathrm{g}}}$ is calculated from Eqs. (A2) and (A3), the
azimuth *φ*_{g} and elevation *θ*_{g} of
LOS observation in ECS can be calculated as follows:

The authors declare that they have no conflict of interest.

We thank very much the reviewers for their time and efforts, thoughtful and
very useful comments. This work was partly supported by the National Key
Research and Development Program of China under grant 2016YFC1400904, the
National Natural Science Foundation of China under grant 41375016 and
41471309, and the National High Technology Research and Development Program
of China under grant 2014AA09A511.

Edited by: Murray Hamilton

Reviewed by: three anonymous referees

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