1. Introduction

For a long time, global wind field was mainly measured by the network of radiosondes, wind profiler radars, et al. However, observations of wind over large portions of the Tropics and major oceans are quite incomplete owing to the limits imposed by costs and the geography [1]. The first spaceborne Doppler wind lidar (DWL) mission ADM-Aeolus (Atmospheric Dynamics Mission, ADM) operated by the European Space Agency (ESA) was launched successfully on August 22, 2018 to close the gaps in the global wind observations, and it is expected to improve the accuracy of numerical weather prediction system (NWP) forecasts. The study of Weissmann et al. shows that the forecasts errors of geopotential height, wind, and humidity in the troposphere can be reduced with the high accuracy and spatial resolution wind profiles provided by Aeolus [2]. In the Tropics, only the observed wind can reconstruct the proper atmospheric mass/wind balance [3]. Outside the Tropics, the accurate wind observations appear to be more beneficial than temperature observations in the improvement of NWP forecasts quality [4]. The studies have confirmed the significance of spaceborne DWLs.

However, the observations of spaceborne DWLs do not always improve the NWP forecasts. Experiments in meteorological data assimilation shows that the poor quality observations often fail to have a significant beneficial impact on NWP. According to the accuracy requirement of the ESA for spaceborne DWLs, the uncertainty of the wind observations in the boundary layer, troposphere, and stratosphere should be less than 1, 2, and 3 m s⁻¹, respectively [1], which is the criterion used in this paper to assess the observation accuracy of spaceborne DWLs. The solar background radiation (SBR) is the main source of noise in daytime observations and, thus, have a negative effect on the spaceborne direct detection wind lidars observations. Firstly, the SBR increases the minimum detectability of aerosol/cloud layers for a given atmospheric scene. Secondly, it lowers the signal-to-noise ratio (SNR) and the accuracy of the observed wind speed. The simulation of McGill et al. shows that the uncertainty of the observed wind speed during daytime can be 10%~20% higher than during nighttime [5]. The ESA have tested the effect of the solar background noise (SBN) on the Aeolus wind observations using three SBR scenarios: the nighttime condition, default cases, and worst cases which equals to 154 mW m⁻² sr⁻¹ nm⁻¹. The results show that the largest uncertainty of Rayleigh wind without the impact of SBR is 5 m s⁻¹, whereas it is up to 11 m s⁻¹ in the worst cases on the Rayleigh channel. The experiments show that the SBR has a considerable influence on the accuracy of daytime spaceborne DWLs observations on the Rayleigh channel. In addition, the differences of uncertainty in the Mie channel between nighttime condition and the worst cases are small, which indicates that SBR has a lower impact on the Mie channel [6]. To minimize the impact of SBR on the Rayleigh channel of Aeolus, the dawn-dusk orbit has been selected [7].

Furthermore, the SBR has an impact on other functions of spaceborne lidars, such as the measurement of aerosol, methane, and CO₂. For example, differences in the measurements taken with the cloud–aerosol lidar with orthogonal polarization (CALIOP) and the ground based lidar show that the uncertainty of the attenuated backscatter coefficient in daytime is 14% larger than that in nighttime. Further, the comparisons between CALIOP and airborne high spectral resolution lidar measurements show that the uncertainty of attenuated backscatter coefficients in daytime and nighttime are approximately 20% and 6.3%, respectively, which shows the negative influence of SBR [8]. For spaceborne methane lidars, the SBR at 1645.6 nm is small at a sun-synchronous dawn-dusk polar orbit. However, it would also decrease the SNR of returned signal from methane gas [9,10]. Assuming the spaceborne CO₂ lidar operates on a sun-synchronous orbit with an equator-crossing time of approximately 1:30 a.m./p.m., the uncertainty of the measured CO₂ density caused by SBN is approximately 0.9 ppmv [11].

As is mentioned above, SBR would affect the observations of many kinds of spaceborne lidars. In this study, we assess the impacts of SBR on spaceborne DWLs based on the global distributions of SBR, unlike previous works which assessed it based on the default or worst cases. In the assessment, the orbit parameters and view geometry of the spaceborne DWLs are set according to that of Aeolus. In the future, spaceborne DWLs with different orbit parameters and view geometries will be launched, which, by implementing the method proposed in this paper, will allow engineers to assess the impact of SBR more accurately. The remainder of this paper is organized as follows: in section 2, the methodology to assess the impact of SBR on the wind observations is described; section 3 presents the databases used to derive the global distributions of SBR; section 4 illustrates the global distributions of SBR at 355 nm in summer and winter; in section 5 we describe the implementation of the proposed method with three experiments; and in section 6 we summarize the results.

2. Assessment methodology

2.1. Poisson noise

In spaceborne lidars, photodetectors are used to detect the intensity of the signal backscattered from atmosphere. However, even if the backscatter signal has constant energy, the number of the photoelectrons detected by the photodetectors is inherently uncertain due to the quantum nature of light. Theoretical studies the number of photoelectrons emitted on the detectors follow a Poisson distribution whose variance is equal to the mean, as follows:

The laser signal backscattered from atmosphere would direct toward the telescopes of spaceborne DWLs along with the signal arisen from the SBR. And the SBR would affect the uncertainty of the wind speed observations through Poisson noise [13]. In operation mode, we subtract the photon count caused by SBR (also called SBN in this paper) from the total signal received on the photodetectors [14,15]. In addition, the SBN signal can be obtained by averaging of the signal derived from high altitudes of the atmosphere (generally greater than 65 km). However, due to Poisson noise, the SBR would also affect the accuracy of observed wind speed after the subtraction. Assuming the energy of SBR can excite ${\overline{n}}_p$ photon counts, the detector of the lidar may receive $n_p$ photon counts with uncertainty of $\Delta n_p$. Through the averaged photon counts detected from high altitudes of the atmosphere, we subtract ${\overline{n}}_p$ photon counts from the total photon counts received by detector. Therefore, the SBR adds uncertainty of $\Delta n_p$ to the total backscatter signal from atmosphere, which leads to random error in wind observations.

2.2. Theoretical uncertainty in wind observations on the Rayleigh channel

Several techniques can be used to retrieve the Doppler shift for Rayleigh channel, such as the edge technique and double-edge techniques [16,17]. The latter was used in this paper, similar to the Aeolus [18]. According to the study of Tan et al. [19], the uncertainty of wind observations on Rayleigh channel can be estimated as

The SBR affects the uncertainty in wind speed observations mainly through the response function. In the operation mode, the values of temperature and pressure are obtained from the European Centre for Medium-Range Weather Forecasts (ECWMF) data assimilation system. The scattering ratio can be derived from the intensity of the signal measured by the Rayleigh and Mie channels [20]. In this paper, we assumed that the values of temperature, pressure, and scattering ratio are accurate (no uncertainty). The uncertainty of wind speed observations for Rayleigh channel was calculated as

In Eq. (4), the partial derivate of the ${\nu }_{HLOS}$ with respect to the Rayleigh response $R_{ATM}$ is a function of temperature and pressure, as is shown in Fig. 1.

 

Fig. 1 Lookup table of the partial derivative of HLOS wind component to Rayleigh response, which is determined by temperature and pressure.

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The uncertainty in the response $R_{ATM}$ can be obtained by

Equations (2)-(6) require the useful signals and SBN received by the two Rayleigh channels to assess the impact of SBR on the accuracy of the wind observations. In sections 2.3 and 2.4, the methods used to achieve this are presented.

2.3. Simulation of spaceborne DWLs

To obtain the useful signals $N_A$ and $N_B$, a simulation system of spaceborne DWLs was developed according to the optical structure and instrument parameters of Aeolus, whose optical structure is shown in Fig. 2 and main instrument parameters are shown in Table 1. The instrument parameters in Table 1 mainly obtained from the ADM-Aeolus level 1B algorithm theoretical basis document (ATBD) which was released in 2006 [21]. In the subsequent development process, some parameters may have been improved, so the output of our simulation model may not be completely consistent with the observations of Aeolus. The workflow of our simulation model is described as follows, 1) the laser pulses are sent out via transmitted optics; 2) the signal backscattered from the atmosphere is received by the receiver optics and is directed toward Mie channel through interference filter and polarizing beam splitter. The Fizeau interference of the Mie channel can transmit the central part of the spectrum of the backscattered signals, including the narrow-band backscattered signals from aerosols and part of the wide-band backscattered signals from molecules; 3) the other signal is reflected towards the Rayleigh channel. The Rayleigh channel is composed of two Fabry–Pérot (F-P) interferometers, which acts as spectral filters for the backscattered signals from molecules. The photons of the beam are directed to the F-P A and, subsequently, to the ACCD detection unit. $N_A$ photons are detected by the ACCD. The other photons are reflected to the F-P B and the subsequent ACCD detection unit, and $N_B$ photons are detected.

 

Fig. 2 Optical structure of spaceborne DWLs in the simulation system.

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Table 1. Instrument parameters used for simulations.

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The input parameters of the simulation system include the profiles of temperature, pressure, wind vector, and the extinction and backscatter coefficients of aerosols and clouds. The following steps were implemented to derive the useful signals $N_A$ and $N_B$: 1) the intensity of the signal $S_X(z)$ received by the telescope of the spaceborne DWL was obtained using the lidar equation as is shown in Eq. (7); 2) the spectrum of the signal received by the telescope was simulated according to the Rayleigh spectrum, Mie spectrum, and Doppler shift; 3) the spectrum of transmittance and reflectivity of the Mie channel were simulated, and the spectrum reflected towards the Rayleigh channel was derived; 4) the spectra of transmittance and reflectivity of F-P A, and the spectrum of transmittance of F-P B were simulated. The intensity of signal received by the ACCD on the Rayleigh channel was obtained and converted to photon counts. Through the simulation system, the useful signal in Rayleigh channels A and B can be derived. Further details of the simulations can be found in the ADM-Aeolus level 1B ATBD and the thesis of Praffrath [21–23].

2.4. Conversion from SBR to SBN

According to subsection 2.2, to assess the impact of SBR on the accuracy of wind observations on the Rayleigh channel, $N_{S,A}$ and $N_{S,B}$, which are caused by SBR should be derived. To obtain $N_{S,A}$ and $N_{S,B}$, we should firstly convert the SBR to SBN using Eq. (8).

For spaceborne DWLs operating at 355 nm, the SBR originates mainly from the following contributions: 1) radiation originating from the sun, after propagating through the atmosphere, and scattered into the telescope without reaching the Earth; 2) direct radiation transmitted through the atmosphere without being scattered and reflected by the earth; 3) radiation scattered by the atmosphere onto the Earth and reflected back towards the telescope [25]. Accordingly, SBR is determined by the relative position between the sun and the satellite, the atmospheric optics, and the surface reflectance. The relative position between sun and satellite can be derived through the parameters of the orbit and view geometry of spaceborne DWLs. The global distributions of SBR with a spatial resolution of 1° × 1° were also derived based on the global databases of atmospheric molecules, aerosol optical properties, and surface albedo.

Once the SBN is obtained, its spectrum can be assumed to follow a uniform distribution with $\Delta \lambda$ bandwidth, and its integral energy is equal to the energy of $N_S$ photons. Then, the $N_{S,A}$ and $N_{S,B}$ can be obtained using the simulation system.

3. Databases and processing method

To assess the impact of SBR on the accuracy of wind observations from a global perspective, we derived the distributions of SBR received by spaceborne DWLs in summer and winter. In this section, the databases used to obtain the seasonal global distributions of SBR and their corresponding processing method are present.

3.1. Methodology to derive the global distributions of SBR

The global distributions of SBR under clear skies for spaceborne DWLs in summer and winter at 355 nm was derived using radiative transfer model (RTM) libRadtran [26,27]. The detailed process is illustrated in Fig. 3. First, the longitudes and latitudes of the off-nadir points and their corresponding solar geometries can be derived using satellite orbit simulation software based on the orbit parameters and the view geometry of spaceborne DWLs. Next, the optical properties of aerosols, atmospheric molecules, and surface albedo of the off-nadir points can be obtained through the databases of the lidar climatology of vertical aerosol structure for space-based lidar simulation studies (LIVAS) [28], Global Ozone Monitoring Experiments (GOME) [29], and Ozone Monitoring Instrument (OMI) ozone [30]. Then, the TOA radiance of each off-nadir point can be derived using libRadtran based on its atmospheric and surface optical properties, view geometry, and solar geometry. Finally, we divided the earth into a 1° × 1° grid, each grid would include several off-nadir points, and we picked the maximum TOA radiance as the SBR in one grid.

 

Fig. 3 Process to obtain the global distribution of SBR for spaceborne DWL.

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3.2. LIVAS database

The global optical properties of aerosols were obtained from the LIVAS database [28]. The database provides averaged profiles of aerosol optical properties in a uniform grid of 1° × 1° with high vertical resolution of CALIOP products, including the extinction coefficient (EXT), backscatter coefficient, and aerosol types. The database divides the aerosol into six types according to CALIOP, namely polluted continental, smoke, dust, polluted dust, clean marine, and clean continental, respectively. In each bin of the vertical profiles, the occurrence frequency of each aerosol type is also provided. To calculate the TOA radiance using libRadtran, the profiles of EXT, single scattering albedo (SSA), and asymmetry parameter (ASY) are required. However, the profiles of SSA and ASY were not provided in LIVAS. We obtained the two parameters in the following steps: firstly, the SSA and ASY of each aerosol types at 355 nm were derived based on the bi-lognormal number-based particle size distribution of each aerosol types [31] and their complex refractive indices. The size distribution parameters and SSA and ASY values of each aerosol type were provided in Table 2. Secondly, the weighted vertical profiles of SSA and ASY were obtained based on the vertical profile of aerosol type occurrence frequency using Eqs. (9) and (10).

Table 2. Size distribution parameters and SSA, ASY coefficient of six aerosol types at 355 nm.

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3.3. GOME database

We obtained the global distributions of surface albedo with a spatial resolution of 1° × 1° from the lambert-equivalent reflectivity (LER) of GOME database [29]. The database includes a 1-nm-wide wavelength bins centered at 335 nm, which is used as the surface albedo at 355 nm here. Study shows that the average difference of LER between 335 nm and 355 nm is negligible with a standard deviation within 0.013. The database is made for each month of the year, and the data sets in July and January were defined as the surface albedo in summer and winter, respectively.

3.4. OMI ozone database

As is shown in Fig. 3, the profiles of the atmospheric molecules are needed to derive the SBR for spaceborne DWLs. Considering that the ozone shows absorption bands in the ultraviolet region, the global database of ozone was taken into account in deriving SBR. The database was obtained from the OMI ozone database, which consists of temperature, pressure, and ozone profiles by binning ozonesonde and satellite data over 12 months in 18 latitude (each 10° wide) bins [30]. The molecular density profiles can be derived from temperature and pressure.

4. Global distributions of SBR at 355 nm

To assess the impact of SBR on the accuracy of wind observations for spaceborne DWLs of which the orbit parameters and view geometry were set according to Table 1, the global distributions of SBR at 355 nm under clear skies in summer and winter were derived using the method mentioned in subsection 3.1 and are shown in Fig. 4.

 

Fig. 4 Global distributions of SBR at 355 nm received by the spaceborne DWLs of which the orbit and view geometry were set according to Table 1. The isolines of SBR are related to the percentiles of 50%, 60%, 70%, 80%, 90%, and 100%, respectively. (a) summer, (b) winter.

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Figure 4 illustrates that: 1) the SBR of most regions in the southern and northern hemispheres are equal to zero in summer and winter, respectively, which indicates that approximately half of the total wind observations is free from SBN; 2) in summer, the maximum SBR, up to 169.03 mW m⁻² sr⁻¹ nm⁻¹, can be found in the northern pole. In winter, the maximum SBR, up to 90.98 mW m⁻² sr⁻¹ nm⁻¹, can be found in the southern pole; 3) the SBR in the Pole regions is greater than that in other surface types, mainly due to the large surface albedo in the polar regions. According to Koelemeijer et al, the surface albedo on snow/ice land is much larger than other land cover types [29]. The differences of SBR on other regions are also small, probably due to approximately the same amount of surface albedo on other land cover types, which illustrates that the surface albedo has a great impact on the SBR under clear skies.

We also derived the frequency of SBR, as is shown in Fig. 5. The frequency of zero SBR values is nearly 50% (not shown in Figs. 5(a) and 5(b)). As is illustrated in Fig. 5, the SBR in summer is larger than that in winter. The mean SBR is 46.85 mW m⁻² sr⁻¹ nm⁻¹ with a standard deviation of 26.09 mW m⁻² sr⁻¹ nm⁻¹ in the northern hemisphere in summer, and the mean SBR is 33.65 mW m⁻² sr⁻¹ nm⁻¹ with a standard deviation of 21.84 mW m⁻² sr⁻¹ nm⁻¹ in the southern hemisphere in winter. The quantile statistics of SBR is presented in Table 3. The SBR is equal to zero when the quantiles are lower than 50%. The isolines in Fig. 4 and Table 3 illustrate that the values SBR range from ~0 to 60 mW m⁻² sr⁻¹ nm⁻¹ in greater than 90% regions of Earth. And the SBR is extremely large only in the polar regions.

 

Fig. 5 Frequency of SBR values. The frequency of zero SBR was not shown which is nearly 50%. (a) summer, (b) winter.

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Table 3. Quantile SBR statistics from the Aeolus telescope.

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5. Impact of SBR on the accuracy of wind observations

The accuracy of wind observations on the Rayleigh channel is mainly affected by atmospheric constituents, parameters of optical structure, and the SBR. In this section, we designed three experiments to assess the impact of SBR on the accuracy of wind speed observations on the Rayleigh channel for spaceborne DWLs.

5.1. Sensitivity of the uncertainty in the wind observations on atmospheric constituents

We assessed the performance of wind observations on six atmospheric climatological constituents, which were obtained from the Air Force Geophysical Laboratory (AFGL) atmospheric constituents profiles, including midlatitude summer, midlatitude winter, subarctic summer, subarctic winter, tropical, and the US76 model [32]. The aerosol model was set to continental clean, which was derived from the optical properties of aerosols and clouds (OPAC) data sets [33]. Two levels of SBR were used, including no SBR and the worst case SBR, which is equal to 169.03 mW m⁻² sr⁻¹ nm⁻¹, as is illustrated in Fig. 6. The red bold lines indicates the accuracy expectations for the wind observations of spaceborne DWLs from the ESA. The main findings derived from Fig. 6 are listed as follows:

 

Fig. 6 The profiles of wind observation uncertainty under various atmospheric constitutes. The red solid lines illustrate the accuracy requirement of the ESA for spaceborne DWLs. (a) No SBR; (b) The value of SBR equals to 169.03 mW m⁻² sr⁻¹ nm⁻¹.

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5.2. Sensitivity of the uncertainty in wind observations on SBR

In this subsection, the sensitivity of the uncertainty in the wind observations on SBR was tested. In the experiment, the atmospheric constituent was set to the US76 model, and the aerosol model was set as continental clean. The values of SBR ranged from 0 to 100 mW m⁻² sr⁻¹ nm⁻¹, with 20 mW m⁻² sr⁻¹ nm⁻¹ steps. The profiles of the uncertainty in wind observations under different levels of SBR are shown in Fig. 7. According to the global distributions of SBR illustrated in Fig. 4, the corresponding quantiles of the SBR are labelled in the legend of Fig. 7. The mean uncertainty in the wind observations on the Rayleigh channel in the troposphere and the stratosphere under different levels of SBR is given in Table 4. We can draw the following conclusions from Fig. 7 and Table 4:

 

Fig. 7 Sensitivity of the uncertainty in wind observations on SBR. The label on the brackets denotes the corresponding quantiles of the global distribution of SBR on summer shown in Fig. 4(a).

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Table 4. Mean of uncertainty in wind observations on Rayleigh channel under different levels of SBR.

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From Fig. 7 and Table 4, we can conclude that the uncertainty in the wind observations for spaceborne DWLs is sensitive to the level of SBR. Therefore, the impact of SBR cannot be neglected in the design of the spaceborne DWLs.

5.3. Wind observations uncertainty profiles under various amounts of SBR

In section 4, we obtained the global distributions of SBR and derived its quantiles statistics. In this subsection, the wind observations uncertainty profiles under different amounts of SBR are calculated, setting the atmospheric constituent and aerosol model were set as in subsection 5.2. Because the value of SBR is equal to zero when the percentiles are lower than 50%, the uncertainty in wind speed observations corresponding to the percentiles of SBR ranging from 50% to 100% with 5 percentile increments were derived and are illustrated in Fig. 8. The following findings can be obtained:

 

Fig. 8 Profiles uncertainty in wind observations on the Rayleigh channel under different quantiles of SBR ranges from 50% to 100%, here the 100% percentile of SBR means the maximum value of SBR, and it’s related values of SBR are labelled in the top of the figures. The white contour illustrates the accuracy requirement for spaceborne DWLs of the ESA. (a) summer, (b)winter.

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6. Summary and conclusions

The SBR is the major source of noise on wind observations of spaceborne DWLs during daytime. To eliminate its negative effects, engineers detect and subtract the SBN from the total signal. However, the SBR still affects the accuracy of the observations due to Poisson noise. In this study, we assessed the impact of SBR on the accuracy of wind observations for spaceborne DWLs simulated based on the orbit parameters and optical structure of Aeolus. According to previous studies, the SBR has little influence on the observations in the Mie channel for Aeolus; hence, only the observations in the Rayleigh channel were considered in this study.

To assess the impact of SBR on the accuracy of wind observations from a global perspective, a simulation system of spaceborne DWLs was developed and the SBR was converted into SBN according to the instrument parameters. The global distributions of SBR at 355 nm in summer and winter were derived using the LIVAS, GOME, and OMI ozone databases. According to the distributions, we assessed the uncertainty in the wind speed observations under various amounts of SBR. The main findings are listed as following:

In summary, the SBR has a considerable impact on the accuracy of spaceborne DWLs, especially when the values of SBR are larger than a threshold value, which indicates that the impact of SBR cannot be negligible while designing spaceborne DWLs mission. When the spaceborne DWLs operate on the sun-synchronous, dawn-dusk orbit, nearly the observations in one hemisphere are always free of SBR. For the other hemisphere, only the values of SBR in the regions close to the Pole are large, where the SBR will have significant impact on the uncertainty in wind speed observations compared with the accuracy requirement of the ESA. In the future, several spaceborne DWLs will be launched in different orbits for different purposes. For example, wind has clear diurnal variation characteristics and spaceborne DWLs that operates on orbits with different local times of ascending node may be needed. Furthermore, the corresponding global distributions of SBR would increase compared with the sun-synchronous, dawn-dusk orbit. We can assess the impact of SBR on different orbit parameters using the method mentioned in this paper, and improve the instrument parameters to compensate for the increased uncertainty in the wind speed observations caused by the increase of SBR.

Appendix

The descriptions and units of the variables used in the equations of this manuscript were listed in Table 5.

Table 5. The descriptions and units of the variables used in this paper.

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Funding

National Natural Science Foundation of China (NSFC) (41575020).

Acknowledgments

Thanks for the helpful discussions provided by Dr. Karsten Schmidt from DLR, Dr. Gert-Jan Marseille and Dr. Ad Stoffelen from Royal Netherlands Meteorological Institute. Thanks for the suggestions provided by Dr. Claudia Emde in running the libRadtran. The LIVAS database was provided by Dr. V. Amiridis from Institude for space applications and remote sensing, National observatory of Athens. The GOME databases was provided by R. B. A. Koelemeijer from Royal Netherlands Meteorological Institute. We also thank the anonymous reviewers for the great help in the improvement of this paper.

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