On the relationship between wind observation accuracy and the ascending node of sun-synchronous orbit for the Aeolus-type spaceborne Doppler wind lidar

The launch and operation of first spaceborne Doppler wind lidar (DWL) Aeolus is of great significance in observing global wind field. Aeolus operates on the sun-synchronous dawn-dusk orbit to minimize the negative impact of solar background radiation (SBR) on wind observation accuracy. For that the future spaceborne DWLs may not operate on sun10 synchronous dawn-dusk orbits due to their observation purposes, the impact of the local time of ascending node (LTAN) crossing of sun-synchronous orbits on the wind observation accuracy was studied in this paper by proposing two added Aeolustype spaceborne DWLs operated on the sun-synchronous orbits with LTANs of 15:00 and 12:00 combined with Aeolus. On the two new orbits, the increments of averaged SBR received by the new spaceborne DWLs range from 39 to 56 mW⋅m⋅sr⋅nm under clear cloud-free skies near summer and winter solstices, which will lead to the increment of averaged 15 Rayleigh channel wind observation uncertainties of from 0.3 to 0.4 m/s in the troposphere and from 0.9 to 1.4 m/s in the stratosphere0.19 m/s for 15:00 orbit and 0.27 m/s for 12:00 orbit when the instrument parameters of new spaceborne DWLs are the same with those of Aeolus with 30 measurements per observation with 20 laser pulses per measurement. Increasing laser pulse energy of the new spaceborne DWLs is used to lower the wind observation uncertainties. Furthermore, a method to quantitatively design the laser pulse energy according to specific accuracy requirements is given in this paper based on the 20 relationship between the signal noise ratio and the uncertaintyy of response function of Rayleigh channel of Aeolus-type spaceborne DWLs. The laser pulse energiesy of the two new spaceborne DWLs is are set to 80 70 mJ based on the statistical results according to the method, meanwhile other instrument parameters are the same as those of Aeolus. Based on the parameter proposal, the accuracy of above 85%about 77.19% and 74.71% of the bins of the two new spaceborne DWLs would meet the accuracy requirements of European Space Agency (ESA) for Aeolus, of which values are closely equivalent 25 to the percentage of 76.46% when Aeolus are free of the impact of SBRwhich would improve the forecast results of Numerical Weather Prediction. And the averaged uncertainties of the two new spaceborne DWLs in free troposphere and stratosphere are 2.62 and 2.69 m/s respectively, which perform better than that of Aeolus (2.77 m/s)And the averaged observation uncertainties show the consistence in observation accuracy of the three spaceborne DWLs, which can be used for joint observations.


Introduction 30
The first spaceborne Doppler wind lidar (DWL) mission ADM-Aeolus (ADM, Atmospheric Dynamics Mission) designed by European Space Agency (ESA) was launched successfully on 22 August 2018, which improves people's knowledge on global wind field. Aeolus carries a spaceborne DWL, Atmospheric Laser Doppler Instrument (ALADIN), has been used to make preliminary observations of global wind field since the launch. And the first Numerical Weather Prediction (NWP) experiments show that the assimilated wind observations have significant positive impact in on the forecast of wind, humidity and 35 temperature at short-range, especially in the tropical troposphere and south hemisphere (Straume et al., 2019). Furthermore, scientists have also designed several possible observation scenarios of future spaceborne DWLs. Considering Aeolus can only realize the observations of single horizontal line-of-sight (LOS) wind components, Ma et al., (2015) and Masutani et al., (2010) proposed a spaceborne DWL concept with two pairs of telescopes (azimuth angles from one pair is 45° and 315°, the other pair is 135° and 225°) using both coherent-detection and direct-detection technology, and ISHII et al., (2017) proposed the 40 spaceborne coherent DWL concept with one pair of telescopes (azimuth angles of 45° and 315°), both of the two observation scenarios can provide the horizontal vector wind. In addition, Marseille et al. (2008) demonstrated that larger observation coverage is more beneficial in the improvement of NWP results in global scale compared to the measurement of horizontal vector wind by proposing several multi-satellites joint observation scenarios with Aeolus-type instruments. However, the measurementobservations of horizontal vector wind perform better for NWP results in the region close to the satellite tracks. 45 In short, Aeolus is a demonstration mission which primarily aims to improve NWP and medium-range weather forecast, and there will be more observation scenarios of spaceborne DWLs with different observation purposes launched in the future.
The future spaceborne DWLs may operate on different orbits which should be related to their observation purposes.
Aeolus operates on the sun-synchronous, dawn-dusk orbit to minimize the impact of solar background radiation (SBR) on the accuracy of wind observations (Heliere et al., 2002, Baars et al., 2019. The SBR is defined as the top-of-atmosphere (TOA) 50 received signal. In this paper, increasing laser pulse energy was used to lower the uncertainty. The remainder of this paper is organized as follows. The details of the orbits of the three spaceborne DWLs and the Aeolus-type spaceborne DWL simulation system are presented in Sect. 2. Section 3 gives a method to quantitatively design the laser pulse energy of spaceborne DWLs based on specific accuracy requirements. Before that, the relationship between the signal noise ratio (SNR) and the uncertainty 95 of response function of Rayleigh channel is also discussed. In Sect. 4, the preliminary proposal of laser pulse energy of the two new spaceborne DWLs is given using the method mentioned in Sect. 3 based on the global distributions of SBR and wind observation uncertainties, as well as the accuracy requirements for spaceborne DWLs. Sect. 5 presents the summary and conclusions.

The sun-synchronous orbits and simulation system of spaceborne DWLs 100
In general, for sun-synchronous orbits, the spaceborne DWL runnings on the dawn-dusk orbit (LTAN of 18:00) would receive minimum SBR, and the spaceborne DWL runs running on the noon-midnight orbit (LTAN of 12:00) would receive maximum SBR. In order to study the impact of orbit selection on the wind observation accuracy, the spaceborne DWLs runs operating on three sun-synchronous orbits with LTANs of 18:00, 15:00, and 12:00 respectively were proposed. And the simulation system used to calculate the uncertainty of wind observations was also described. 105

The sun-synchronous orbits
The three sun-synchronous orbits with LTANs of 18:00, 15:00, and 12:00 are are illustrated in Fig.1 (a). Aeolus operates operating in on the sun-synchronous, dawn-dusk orbit with height of 320 km is marked in blue. The spaceborne DWL is equipped with a single-perspective telescope, which scanning at 90° with respect to the satellite track, under a slant angle of 35° versus nadir, measuring profiles of HLOS wind components. The other two spaceborne DWLs running in on the sun-110 synchronous orbit with LTANs of 15:00 and 12:00 which are marked in yellow and red lines respectively. The intersection points between laser beam and earth surface are called off-nadir points of which lines are illustrate in Fig. 1(b). The received SBR of spaceborne DWLs is related to their optical architecture and instrument parameters. The two new spaceborne DWLs are assumed to be Aeolus-type instruments whose instrument parameters the same as those of Aeolus except higher different laser pulse energiesy which aims to improve wind observation accuracy. When demonstrating the instrument parameters of spaceborne DWLs, people also pay attention to the observation accuracy under worst cases. Solar zenith angle 120 is the dominant factor for SBR received by spaceborne DWL. The variations of solar zenith angles of the off-nadir points on the three orbits within one-year range are illustrated in Fig. 2, which indicates that received SBR would reach maximum values near summer solstice and reach maximal values near winter solstice. For the off-nadir points in the north hemisphere, SBR will reach maximum near summer solstice. And SBR will reach maximum near winter solstice for the off-nadir points in the south hemisphere. In this paper, the global distributions of maximum SBR in 1°×1° grid near the summer solstice which range 125 from June 14 to 28 and near the winter solstice which ranges from December 15 to 30 are used for the investigations of the worst cases with maximum Rayleigh channel wind observation uncertainties due to SBR. Furthermore, the annual variation characteristics of solar zenith angles are less obvious on the two new orbits compared to that of Aeolus as shown in Fig  According to the characteristics of sun-synchronous orbits, the local observation time of the spaceborne DWLs focus mostly on about 06:00/18:00, 03:00/15:00, and 00:00/12:00. The shadow area of Fig. 1(b) illustrates the observations in nighttime. Figure 1 (b) shows that the solar zenith angle of the observation points of the two new Aeolus-type instruments is low compared to that of Aeolus, and thus lead to larger SBR. The phenomenon also indicates that the sun-synchronous dawn-140 dusk orbit is the orbit which would receive the minimum SBR compared to the others. Figure 1. The orbits of the spaceborne DWLs operate on the sun-synchronous orbits with LTAN of 18:00, 15:00, and 12:00, which are marked in blue, yellow, and red respectively. (a) 3D graphics; (b) 2D graphics.

Spaceborne DWL simulation system 145
An Aeolus-type spaceborne DWL simulation system considering the impact of SBR on wind observation uncertainties was was developedused to retrieve HLOS wind components and calculate observation uncertainties. The simulation system was was built according to the optical structure of Aeolus, which were consists of laser transmitter, the telescope and front optics, Mie spectrometer, Rayleigh spectrometer, and detection front units Stoffelen, 2003 andPaffrath, 2006).
Considering that SBR mainly affect the observation accuracy of Rayleigh channel, we focused on the simulation of the wind 150 retrieved method on Rayleigh channel, and assumed that the cross-talk effect between Mie channel and Rayleigh channel is negligible. The details of the working principle and instrument parameters of Aeolus used in the simulation system are were set according to the ADM-Aeolus Algorithm Theoretical Basis Document (ATBD): ADM-Aeolus Level1B products (Reitebuch et al., 20062018), expect the mean altitude of satellite which is set to 320 km, the laser pulse energy which is set to 60 mJ, which was consist with the laser pulse energy of onboard Aeolus, and the repetition rate of the laser transmitter is 155 set to 50 Hz. In addition, in the simulation system, one observation consistsed of 50 30 accumulations (also called as measurements) of 14 20 shots,. resulting in a horizontal averaging length of about 90km per observation Combined with the ground speed of Aeolus of 7.2 km/s, the horizontal resolution of about 100.8 km per observation. Detection chain noise of 4.7 e -/pixel on Rayleigh channel for each measurement was also taken into account. The vertical resolutions of retrieved wind are were 500 m in the PBL, 1 km in the troposphere, and 2 km in the stratosphere (Marseille et al., 2008). 160 The input parameters of simulation system includedd u-and v-components wind, temperature, pressure, aerosol optical properties, and TOA radiance. In this paper, the impacts of SBR on the wind observation accuracy of spaceborne DWLs under cloudy atmosphere were were not considered. The first five components are were derived from the pseudo-truth global atmospheric condition dataset, which consisteds of the Ozone Monitoring Instrument (OMI) database (McPeters et al., 2008), including the latitude-averaged profiles of temperature, pressure, and density of ozone, and the lidar climatology of vertical 165 aerosol structure for spaceborne lidar simulation studies (LIVAS) database (Amiridis et al., 2015), which was was used to describe aerosol optical properties.. Only aerosols in the PBL were considered here. The details to derive the global distributions of SBR received by Aeolus-type spaceborne DWLs couldan refer to (Zhang et al., (2019), which were were briefly introduced here. First, the satellite orbit simulation software was required to obtain the positions of the off-nadir points of the spaceborne DWLs were obtained using satellite orbit simulation software. Atmospheric conditions were were retrieved 170 from the pseudo-truth databases and spatially interpolated to the off-nadir points. The surface albedo was was also needed to generate the TOA radiance, which were was derived from the database of lambert-equivalent reflectivity (LER) (Koelemeijer et al., 2003). Then the SBR of off-nadir points was was generated by radiative transfer model (RTM) libRadtran with the input of temperature, pressure, aerosol optical propertiesatmospheric optical properties, and surface albedo (Emde et al., 2016).
Finally, the earth was divided into 1°×1° grid, and the maximum SBR in each grid is picked out as the worst cases of Rayleigh 175 channel wind observation uncertainties due to SBR. Once the atmospheric conditions and SBR were were input to the simulation system, the HLOS winds and their corresponding uncertainties in the grids could could be figured out.

Methodology
Method of iIncreasing the laser pulse energiesy of Aeolus-type spaceborne DWLs was used to lower wind observation uncertainties in this paper. To assess the performance of spaceborne DWLs under worst cases of Rayleigh channel, and 180 quantitatively design the laser pulse energiesy of two new spaceborne DWLs as mentioned in SubsectSect. 2.1, the steps are as follows: 1) the global distributions of maximum SBR received by the spaceborne DWLs on the three orbits are were figured out to compare the SBR received by the two new spaceborne DWLs with that of Aeolus. In this paper, the global distributions of SBR near the summer solstice which range from June 14 to 28 are derived as the SBR in summer and near the winter solstice which ranges from December 15 to 30 are derived as the SBR in winter; 2) the uncertainties of wind observations on Rayleigh 185 channel of the three spaceborne DWLs are were derived and the uncertainty increments of the two new spaceborne DWLs compared to that of Aeolus are were figured out; 3) the relationship between wind observation uncertainty and laser pulse energy is was established; 4) the values of laser pulse energiesy which would lower the uncertainties to required accuracy level is were derived based on the relationship established in the step 3).

Uncertainty of wind observation on Rayleigh channel 190
The double-edge technique was is used to retrieve the HLOS wind components on Rayleigh channel for Aeolus (Flesia andKorb, 1999, Zhang et al., 2014). The study of Tan et al., (2008) shows that the uncertainty on Rayleigh channel is determined by response function, temperature, and pressure, and scattering ratio. Lookup table between wind speed and response function, temperature, pressure, scattering ratio was is established prior to the launch of Aeolus. In operation mode, the profiles of temperature and pressure are obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) data 195 assimilation system. The scattering ratio can be derived from the intensity of the signal received by Rayleigh channel and Mie channel (Flamant et al., 2008), which are assumed to be accurate (no uncertainty) in this paper. Once the response function of Rayleigh channel was is detected by spaceborne DWL, wind speed would will be figured out. The uncertainty of wind observation is estimated as
means the HLOS wind component. means response function of Rayleigh channel which is defined as where and are the useful signal detected by Rayleigh channel.
The ⁄ is a function of temperature and pressure, which ranges from 420 to 520 m/s upon most occasions, 205 as shown in Fig. 1 of Zhang et al., (2019). The uncertainty of response function is derived from where and denote the uncertaintiesy of and . Here, and can be obtained using the simulation system of spaceborne DWLs. Taking the SBR and the dark currentnoise of spaceborne DWL detectors into account, according to the feature of Poisson noise, the uncertaintiesy in and can be estimated as 210 where the , and , are the photon counts which are excited by SBR on Rayleigh channel. denote the dark current of Accumulation Charge Coupled Device (ACCD)noise of detection unit on Rayleigh channel.
, and , can be derived using the following method: the SBR can beis viewed as the spectrum which followings the uniform distribution, of which energy can be obtained using Eq. (5) of (Nakajima et al., (1999), and the bandwidth equals 215 to that of the interference filter of the Rayleigh channel.
, and , can be obtained from the simulation system with the input of the spectrum.
where denotes the energy of SBR, denotes the number of the accumulated laser shots, and denote the quantum efficiency of the detector on Rayleigh channel (Reitebuch et al., 2018), denotes the TOA radiance of the off-220 nadir point. As to the instrument parameters, denotes the field of view; denotes the diameter of the telescope; Δλ denotes the bandwidth of the interference filter. Δ denotes the laser detection time which was dependent on the vertical resolution.

Relationship between uncertainty and laser pulse energy
The laser pulse energy of laser transmitter has an important influence on the uncertainty of wind observation. Provided that 225 the atmospheric conditions remain unchanged, the higher the laser energy, the backscattered signal received by the telescope of Aeolus-type instrument will become stronger, and the influence of corresponding Poisson noise will be smaller, which will lower the uncertainty of wind observation finally. However, due to that the wind observation uncertainty is affected by various factors such as the atmospheric conditions and instrument parameters, the quantitative relationship between laser pulse energy and wind observation uncertainty is not yet derived due to the fact that the wind observation uncertainties are affected by 230 various factors such as the atmospheric conditions and instrument parameters. In this paper, the method for quantitative derivation of the laser pulse energy according to specific accuracy requirement of wind observation was is proposed through establishing the relationship between SNR of Rayleigh channel and uncertainty of response function of Rayleigh channel.
According to the characteristics of Poisson noise, Marseille and Stoffelen, (2003) defined the SNR of Rayleigh channel.
For the Rayleigh channel of spaceborne DWL, difference between and is not large, especially when the wind speed is close to zero, ≈ . Based on the assumption that ≈ and, , ≈ , , we derived the relationship between the SNR and uncertainty of response function of the Rayleigh channel.
The details of the derivations and proofs are shown in Appendix. Then the uncertainty of wind observation on Rayleigh 240 channel can be estimated as While increasing the laser pulse energy, the value of + will proportional increase; similarly, , + , will proportional increase with the increase of SBR, which can be written as According to Eqs. (6) and (8), setting = + , which is in proportion to the energy of laser pulse ; = , + , , which is in proportion to the energy of SBR , and = , ( , ) = / , = 2 2 , where denotes temperature and denotes pressure, the relationship between , , and can be expressed as Equation (10) can be solved as 250 Equation (10) illustrates that the uncertainty is determined by temperature, pressure, variable , the SBR, and dark noise of the detector. The value of can be estimated using Eq. (11). Knowing the value of , the value of laser energy cannot be figured out for that the variable is dependent on the laser energy and wind speed. However, when the wind speed keeps unchanged, the variable would be in proportion to the energy of laser pulse . That is to say, if the laser energy 255 increases by several times, the corresponding value of variable will increase by the same multiples when the HLOS wind speed keeps unchanged. Then the required value of laser energy can be obtained based on the proportional relationship between and .

Derivation of laser pulse energy
In SubsectSect. 3.2 and Appendix, the relationship between laser pulse energy and wind observation uncertainty was 260 established based on some assumption and simplifications. The following methods was used to solve the problem that how much the laser energy could be set to increase the accuracy of the observation of new spaceborne DWLs to the meet specific accuracy requirements.
Firstly, the laser pulse energiesy of the two new spaceborne DWLs wereas assumed to be 60 mJ of which parameters are the same as thoseat of Aeolus, the profiles of uncertaintiesy were derived using simulation system based on the global 265 distributions of maximum SBR on the three orbits; secondly, the profiles of variable at each bin (layer, the concept can refer to Fig. 5 in Tan et al., (2008)) were figured out using Eq. (11), which were set as 1. Provided that the accuracy requirements of the two new spaceborne DWLs are to reach the accuracy level of Aeolus, then, the uncertaintiesy of the new spaceborne DWLs were replaced with the uncertaintiesy of Aeolus at the same bins, and the variables of ( , ), , and kept unchanged, the variables were figured out using Eq. (11), which were set as 2; finally, according to the proportional 270 relationship between and laser energy, ≈ 2 1 ⁄ ⁄ , the required laser pulse energy at each bin could be derived.
Therefore, we could determine the laser energyies of the two new spaceborne DWLs according to the statistical results.
In the same way, if the accuracy requirements of the two new spaceborne DWLs were to meet the accuracy requirements of ESA, we needed to replace the wind observation uncertaintiesy which were calculated when the laser energy is was 60 mJ with the accuracy requirements of ESA when calculating the value of 2, and the other steps were the same as above. 275

Results and discussions
A The preliminary results for to determining determine the laser pulse energiesy of two new spaceborne DWLs wereas presented in this section. To obtain the laser pulse energiesy, the global distributions of maximum SBR on the three orbits and the corresponding wind observation uncertaintiesy caused by SBR were calculated, firstly. Then the distributions of required laser energiesy were obtained according to accuracy requirements based on the method mentioned in Subsect. 3.3. Finally, 280 based on the results, a the proposal of determining the laser pulse energyies of two new spaceborne DWLs was presented. And the global distributions of wind observation uncertainties of the three spaceborne DWLs were figured out according to the instrument parameter proposal. The details were shown in the following subsections.

Global distributions of maximum SBR on the three orbits
The SBR received by spaceborne DWLs is mainly determined by instrument parameters and orbits. Global distributions of the 285 maximum SBR received by the spaceborne DWLs running on the three orbits in summer and winter are shown in Fig. 2 3 based on the instrument parameters of Aeolus and the three orbits mentioned in Subsect. 2.1Sect. 2.
The contours in Fig. 3 denote the differences between SBR of two new orbits and sun-synchronous dawn-dusk orbit, which demonstrates that the dawn-dusk orbit is an effective solution to minimize received SBR for spaceborne DWL operating on sun-synchronous orbits. While operating on the sun-synchronous dawn-dusk orbit, the maximum SBR of the off-nadir 290 points located in the southern hemisphere is nearly equal to zero in summer, and the maximum SBR of the off-nadir points located in the northern hemisphere is nearly equal to zero in winter. For the two new orbits, almost the wind observations of few areas are not affected by SBR, which are mainly located in the regions near the Antarctic and Arctic circles. According to the contours, the ascending order of the values of maximum SBR on the three orbits is dawn-dusk orbit, the orbits with LTAN of 15:00, and that of 12:00 respectively. The closer the LTANs of the orbits to noon, the values and the affected area of SBR 295 will become larger. Statistics illustrate that the averaged SBR illustrated in Fig. 3 are 20.99, 60.68, and 76.36 mW⋅m −2 ⋅sr −1 ⋅nm −1 respectively near the summer and winter solstice periods. The averaged increments of SBR received by new spaceborne DWLs are 60.68-20.99=39.69 mW· m −2 · sr −1 ·n m −1 and 76.36-20.99=55.37 mW· m −2 · sr −1 · nm −1 compared to that of Aeolus.  (c, d) and (e, f) present the sun-synchronous orbits with LTAN of 18:00, 15:00, and 12:00 respectively, and the upper panels denote the SBR in summer, and the lower panels denote the SBR in winter.
The contours in Fig. 2 demonstrate that the dawn-dusk orbit is an effective solution to minimize SBR received by 305 spaceborne DWL operated on sun-synchronous orbits. While operating on the sun-synchronous dawn-dusk orbit, the SBR of the off-nadir points located in the southern hemisphere is nearly equal to zero in summer, and the SBR of the off-nadir points located in the northern hemisphere is nearly equal to zero in winter. For the two new orbits, there are fewer areas with SBR of zero, mainly located in the regions near the Antarctic and Arctic circles. According to the contours, the ascending order of the values of SBR in the three orbits is dawn-dusk orbit, the orbits with LTAN of 15:00, and that of 12:00 respectively. The closer 310 the LTANs of the orbits to noon, the values and the affected area of SBR will become larger. The differences of SBR received by the three spaceborne DWLs mainly focus on the equatorial region.
As is mentioned in Introduction, Zhang et al., (2019) illustrate that the uncertainty of wind observations would increases of about 0.18 and 0.69 m/s in the troposphere and the stratosphere respectively as 20 mW⋅m −2 ⋅sr −1 ⋅nm −1 of SBR increases.
Statistics illustrate that the averaged SBR of the three spaceborne DWLs are 20.99, 60.68, and 76.36 mW⋅m −2 ⋅sr −1 ⋅nm −1 315 respectively. The quantile statistics of SBR is presented in Table 1, which means that the corresponding percentages of the grids (the earth is divided into 1°×1° grid) of which the SBR will be smaller than the values listed in the first line of Table 1.   Table 1 indicate that the spaceborne DWLs operate on the two new orbits would receive larger SBR compared with the sun-synchronous dawn-dusk orbit, which would lead to larger uncertainty of wind observations as 320 is shown in the following subsection.  relatively low, which basically cannot meet the requirements of ESA. In fact, the Mie channel is mostly used for wind observations due to the widespread presence of aerosols in PBL. Therefore, the accuracy of the Rayleigh channel in the PBL is not considered in the following of this paper. Statistics show that the averaged uncertainties without impact of SBR are all about 2.61 m/s in summer and winter, and about 76.46% of the bins would meet the accuracy requirements of ESA overall.

Uncertainties of wind observations based on the instrument parameters of Aeolus
2) Without the impact of SBR, the wind observation uncertainties have little differences among different latitudes. 335 3) The wind observation uncertainties increase with atmospheric altitudes when the heights of range gates are unchanged. This is mainly due to the fact that molecular number density is proportional to pressure. Near the height of 16 km, the uncertainties decrease first and then increase with the increases in altitude, which attributes to the change in thickness of bins from 1 km to 2 km. 4) Compared with other regions, uncertainties in the equatorial region are higher at the bottom of the troposphere, and 340 lower in the stratosphere. The trend of temperature profile in the equatorial region is the main reason for this phenomenon, which is consist with the trend of uncertainties. Number density of molecules is inversely proportional to temperature. Low molecular number density leads to weak return signal of spaceborne DWLs, which leads to higher wind observation uncertainties. Assuming the instrument parameters of the two new spaceborne DWLs were set to be the same as those of Aeolus,Based on the global distributions of maximum SBR of the three orbits illustrated in Fig. 3, the worst cases of Rayleigh channel with maximum wind observation uncertainties due to SBR were also derived as shown in Fig. 5. Considering that the distributions of maximum SBR were nearly horizontal to latitudes, and to simplify the calculation, Fig. 5the profiles of wind observation 350 uncertainties were derived as is shown in Fig. 3, which was obtained from the spaceborne DWLs simulation system using the 10 ° latitude-averaged SBR and atmospheric conditionsshown in Fig. 2, for whose contour lines illustrated that the distributions of SBR were nearly horizontal to latitude. Each subgraph in Fig. 3 was obtained based on 18 wind uncertainty profiles.
Comparisons between Fig. 4 and Fig. 5 illustrate that wind observation uncertainties become larger with the impact of 355 SBR. And the uncertainties show obvious characteristics of latitudinal variation, which is mainly attributed to the latitudinal variation of maximum SBR shown in Fig. 3. Figure 3 illustrates that the wind observation accuracy can meet the accuracy (a) (ab requirements of ESA in most bins of most latitudes in the troposphere and stratosphere even when the instrument parameters of the three spaceborne DWLs are the same as those of Aeolus. The bins of which uncertainty are beyond the requirements of ESA mostly located in the upper layer of troposphere and stratosphere. In addition, the accuracy of wind observations in the 360 PBL is relatively low, which basically cannot meet the requirements of ESA. In fact, the Mie channel is mostly used for wind observations in the PBL, which are of higher accuracy. It is meaningless to study the wind observation accuracy of the Rayleigh channel in the PBL, the accuracy of the Rayleigh channel in the PBL is not considered in the following of this paper. As the

Distributions of required laser pulse energy
In order to make the accuracy of two new spaceborne DWLs to reach the specific accuracy level under worst cases of Rayleigh 385 channel, the required laser pulse energiesy wereas obtained using the method mentioned in SubsectSect. 3.3. According to Eq.
(11), the required energy is determined by temperature, pressure, wind uncertaintiesy, and SBR, and noise of instrument, thus the required laser pulse energy is different in different bins. Therefore, the laser pulse energiesy of the new spaceborne DWLs should be determined by the statistics of the profiles of required energy. Statistics reveal that the averaged values of required laser pulse energies in Fig. 6 is 64.80 mJ for the 15:00 orbit, and 66.59 mJ for the 12:00 orbit respectively. The quantiles of the required energy of the two spaceborne DWLs are shown in Table 1, which means that the corresponding percentages of the bins whose accuracy will reach the accuracy level of Aeolus 400 once the laser pulse energies equal to the specific values. For example, 90% of the bins will reach or exceed the accuracy level of Aeolus when the laser energy is 70.37 mJ for the spaceborne DWL operating on the 15:00 orbit. As we can see from Table   1, when the instrument parameters of two new spaceborne DWLs are the same as Aeolus, of which the laser pulse energies are equal to 60 mJ, only the accuracy of about 20% of the bins can reach the accuracy level of Aeolus near summer and winter solstices. However, as long as the laser energy is slightly increased, the percentages of bins will greatly increase. When the 405 laser pulse energies reach 70 mJ, the accuracy of about 90% of bins could reach or exceed the accuracy level of Aeolus on the orbit 15:00, and the percentage is about 80% on the orbit 12:00.  Table 3 which means that the corresponding percentages of the bins whose accuracy will reach the accuracy level of Aeolus once the laser pulse energy 415 equals to the specific values.   Table 42. The statistics and Table 4 illustrate that not too larger laser energy is required to meet ESA's accuracy requirements for wind observations. Even if the instrument parameters of the spaceborne DWLs are consistent with that of Aeolus, the wind observation accuracy of above 60% of bins can basically meet the accuracy requirements of ESA.The statistics of Table 2 illustrate that the percentages of bins which can 440 meet the accuracy requirements of ESA increase by 10% even if the laser pulse energy is not increased much when quantile is between 40% to 90%. The averaged increment of laser pulse energy is 6.75 mJ which can increase the quantiles by 10% considering the three orbits as a whole. When the laser pulse energies are set to 67.89, 73.71, and 75.98 mJ, the quantiles will be up to be 80%, which exceeds the percentage of bins (76.46%) for Aeolus without the impact of SBR.

Uncertainties of wind observations resulting from an increased laser pulse energyUncertainties of wind observations 450 based on new instrument parameter proposal
In SubsectSect. 4.3, the zonal profiles distributions of required laser pulse energiesy were derived for different purposes. In order to offer a feasible proposal for the laser pulse energiesy of the new spaceborne DWLs, the percentages of bins that can meet the specific accuracy requirements when the laser energyies reachesd a certain values were figured out, as is shown in Table 53. 455 Table 5 illustrates that the percentages of bins that meet the specific accuracy requirements will become larger with higher laser pulse energy. Considering the accuracy requirements of ESA and accuracy level of Aeolus, while taking the existing technical level into account, the laser energies of the two new spaceborne DWLs are set to 70 mJ in this paper. In fact, the laser energy of 80 mJ has been already required by ESA in ATBD (Reitebuch et al., 2018)However, assuming the laser energy increases by the same amount each time, the increments of the percentages decrease. According to the current technology, the 460 technical difficulty will increase a lot for each small increment in the laser energy of spaceborne DWLs. As is shown in Table   3, the percentages of the bins which will meet the accuracy requirements of ESA are 77.19% and 74.71% for orbit 15:00 and 12:00 respectively, close equivalent to the percentage of Aeolus without the impact of SBR (76.46%). In addition, the percentages of the bins are up to 89.04% and 77.34% for orbit 15:00 and 12:00, of which the accuracy of observations equals to or exceeds the accuracy level of Aeolus. Considering the accuracy requirements of ESA and accuracy level of Aeolus, while 465 taking the existing technical level into account, the laser energy of the two new spaceborne DWLs is set to 80 mJ. In this way, at least half of the bins can reach the accuracy level of Aeolus, and the percentages of bins that meet the ESA's accuracy requirements will be higher than 85% for the two new spaceborne DWLs as Table 5 illustrates. Table 53. Percentages of bins which will meet the specific accuracy requirements with certain laser pulse energiesy for spaceborne DWLs.  Provided that the three spaceborne DWLs operate operating on the sun-synchronous orbits shown in Fig. 1. , and The the instrument parameters of Aeolus keep unchanged. As to the two new Aeolus-type spaceborne DWLs, the other instrument parameters are set as same as those of Aeolus except for the laser pulse energiesy of 80 70 mJ. The wind observation uncertainty 475 distributions of the three spaceborne DWLs is are derived as is shown in Fig. 68. Note that Figs. 8 (a, b) are identical to those of Figs. 5 (a, b), for that both of them are obtained with laser energies of 60 mJ. Table 3, when the laser pulse energies of three spaceborne DWLs are 60, 70, and 70 mJ respectively, the percentages of bins which meet the accuracy requirements of ESA are close (71.35%, 77.19%, and 74.71%). And Fig. 8 illustrates that the bins that reach ESA's accuracy requirements are of high consistency in latitude and height distributions. 480

As illustrated in
Comparisons among Fig. 8 (c-f) and Fig. 4 illustrate that the wind observation accuracy promotes much in the hemisphere that less affect by SBR. However, limited improvement happens in the other hemisphere. The fact indicates that increasing the laser energy to 70 mJ cannot compensate the negative influence of large SBR. Comparisons among Fig. 8 (c-f)  The contour lines in Fig. 6 (c, d) and (e, f) illustrate that most of bins of the two new spaceborne DWLs could meet the accuracy requirements of ESA with laser pulse energy of 80 mJ. As Table 5 shows that about 89.33% of the bins of the spaceborne DWL operating on the orbit with LTAN of 15:00 could reach the accuracy requirements, and the percentage is 86.40% for the orbit of 12:00. The comparisons between Fig. 6 (c, d) (e, f) and (a, b) indicate that the wind observation accuracy 500 of the three spaceborne DWLs operating on the three sun-synchronous orbits is of consistence using the instrument parameter proposal provided in this paper. The accuracy of wind observations of the two new spaceborne DWLs with laser pulse energy of 80 mJ is slightly higher than that of Aeolus in the troposphere, and lower than that of Aeolus in the stratosphere. The averaged uncertainties of the three spaceborne DWLs operating on the three orbits in troposphere and stratosphere are shown in Table 6. And Table 6 illustrates that the differences of the averaged uncertainties range from 0.06 to 0.33 m/s among the 505 three spaceborne DWLs, which also demonstrates the consistence in wind observation accuracy. Comparisons among Fig. 6(cf) and Fig. 3(c-f) illustrate that, as for the two new spaceborne DWLs, when the laser energy increases from 60 mJ to 80 mJ, the observation accuracy could be improved significantly.

Summary and conclusions 510
The successful launch of Aeolus is significant for people to observe the global wind field. Aeolus operates on the sunsynchronous dawn-dusk orbit to minimize the impact of SBR on the accuracy of wind observations. If the future spaceborne DWLs operate on other sun-synchronous orbits for their specific observation purposes, the received SBR may become larger which would lead to higher observation uncertainties. In this paper, the influence of the LTAN crossing of sun-synchronous on the wind observation accuracy of Aeolus-type spaceborne DWLs was studied.In general, for sun-synchronous orbits, the 515 spaceborne DWL running on the dawn-dusk orbit (LTAN of 18:00) will receive minimum SBR, and the spaceborne DWL running on the noon-midnight orbit (LTAN of 12:00) will receive maximum SBR. In this paper, the influence of the LTAN crossing of sun-synchronous on the wind observation accuracy offor Aeolus-type spaceborne DWLs was studied. And the spaceborne DWL running on three sun-synchronous orbits with LTANs of 18:00, 15:00, and 12:00 respectively were proposed.
And The method of increasing laser pulse energy of spaceborne DWLs was used to lower the observation uncertainties. 520 Furthermore, the method to quantitatively design laser pulse energy to meet the specific accuracy requirements was also studied.
Assuming two new Aeolus-type spaceborne DWLs operate on the sun-synchronous orbits with LTAN of 15:00 and 12:00.
The global distributions of SBR illustrate that the increments of averaged SBR range from 39 to 56 mW⋅m −2 ⋅sr −1 ⋅nm −1 on the two new orbits near summer and winter solstices compared to that of Aeolus under clear cloud-free skies, which will lead to the averaged uncertainty increments of 0.3 to 0.40.19 m/s in the tropospherefor 15:00 orbit and 0.9 to 1.427 m/s for 12:00 525 orbitin the stratosphere, respectively. Considering that the impact of SBR on the wind observations is minimal on dawn-dusk orbit, and reach maximum on noon-midnight orbit, the phenomenon indicates the selection of the LTAN of sun-synchronous To quantitatively design the required laser pulse energiesy of the new spaceborne DWLs to meet specific accuracy 540 requirements, i.e. to meet the accuracy requirements of ESA, or to reach the similar accuracy level of Aeolus, the relationship between SNR and the uncertainty of response function of Rayleigh channel is established based on some assumption and simplifications, which is proven of wide feasibility by simulation experiments as is shown in Appendix. Finally, the method to derive the required laser energiesy according to accuracy requirements is proposed.
According to the method, the required energy is determined by temperature, pressure, wind uncertainty, SBR, and noise 545 of instrument, thus the required laser pulse energies are different in different bins. Therefore, the laser pulse energies of the spaceborne DWLs should be determined through the statistics. Considerations are given to both of reaching the accuracy level of Aeolus and improving the forecast results of the NWP, taking existing technical level of spaceborne DWLs into account, the laser pulse energies of two new spaceborne DWLs are set to 70 mJ, while other parameters are the same as those of Aeolus.
Based on the parameter proposal, 89.04% and 77.34% of the bins can reach the accuracy level of Aeolus on the two new orbits. 550 And the percentages of bins that meet the ESA's accuracy requirements are 77.19% and 74.71% for the two new spaceborne DWLs, of which values are higher than that of Aeolus (71.35%), and are closely equivalent to the percentage of 76.46% when Aeolus are free of the impact of SBR. The averaged uncertainties of the two new spaceborne DWLs with laser pulse energies of 70 mJ in free troposphere and stratosphere are 2.62 and 2.69 m/s respectively, which perform better than that of Aeolus (2.77 m/s). Furthermore, when the laser pulse energies of two new spaceborne DWLs increase from 60 mJ to 70 mJ, the global 555 averaged wind observation uncertainties will decrease about 0.34 m/s under the impact of maximum SBR. In summary, it is necessary to increase the laser pulse energies of two new Aeolus-type spaceborne DWLs operating on the sun-synchronous orbits with LTANs of 15:00 and 12:00. The wind measurement accuracy has been greatly improved when laser pulse energies increase from 60 mJ to 70 mJ.

560
If the accuracy requirements of the two new spaceborne DWLs are to reach the accuracy level of Aeolus, the global distributions of the derived laser pulse energy demonstrate that it is necessary to increase the laser pulse energy. If the purpose of the new spaceborne DWLs is to improve the results of NWP, the wind observation accuracy should be meet the accuracy requirements of ESA. It is demonstrated that the wind observation uncertainty of most bins can meet the requirements even when the laser pulse energy of the two new spaceborne DWLs is set as the same as that of Aeolus. Considerations are given 565 to both of reaching the accuracy level of Aeolus and improving the forecast results of the NWP, taking existing technical level of spaceborne DWLs into account, the laser pulse energy of two new spaceborne DWLs is set to 80 mJ, while other parameters are the same as those of Aeolus. Based on the parameter proposal, at least half of the bins can reach the accuracy level of Aeolus, and the percentages of bins that meet the ESA's accuracy requirements will be higher than 85% for the two new spaceborne DWLs. The differences of the averaged observation uncertainties are between 0.06 and 0.33 m/s among the three The essence of lowering the wind observation uncertainties of spaceborne DWLs by increasing the laser pulse energiesy is to increase the SNR of received signal. Other methods can be used to improve the SNR of received signal, such as enlarging the telescope aperture or reducing vertical resolution. Once the quantitative relationship between these instrument parameters and the SNR is established, we can also quantitatively adjust these parameters according to our accuracy requirements as the 575 method shown in this paper.
The reanalysis data is obtained from the 20th Century Reanalysis Project (Compo et al., 2011). In the validation 600 experiment, the monthly averaged 24 level profiles of temperature, pressure, u-and v-component wind with 1°×1° spatial resolution are obtained from the reanalysis data. In this study, the reanalysis data for June 2015 and December 2015 are used as the atmospheric condition in summer and winter respectively. As is shown in Fig. A1, the verification process of Eq. (A7A3) can be described as follows: (1) The off-nadir points of spaceborne DWLs are obtained using orbit simulation software based on the orbit information 605 of spaceborne DWLs.
(2) The profiles of temperature, pressure, wind speed, aerosol optical parameters, and surface albedo are interpolated into the off-nadir points.
(3) The SBR of the off-nadir points are derived using RTM libRadtran with the inputs provided in step (2).
(4) The profile values of , and , , , are figured out using spaceborne DWL simulation system mentioned 610 in Subsect. 2.2 with the inputs of SBR and atmospheric conditions of off-nadir points.
(5) The values of and are obtained using Eqs.
(3), (4), and (6). In addition, according to ADM-Aeolus ATBD Level1B products (Reitebuch et al., 2018), the noise of detection chain for each measurement is 4.7 e -/pixel. And 30 measurements are include in one observation, therefore, = 2 2 = 2 × (4.7 × 30) 2 = 39762 in Eq. (10) which cannot be negligible.In this study, the value of is assumed to be zero, which means the dark current of the detectors on 615 Rayleigh channel is negligible. The scatters of and 1/ are plotted to verify the accuracy of Eq. (A7A3), as is shown in Fig. A2. The spatial resolution of the reanalysis data is 1°×1°, so the earth is divided into 1°×1° grid during the verification process, and one 620 off-nadir point in each grid is selected as the verification point. Considering the SBR in summer and winter, and excluding some grid points with invalid data, a total of 28460 profiles are used in this verification. Each profile contains 24 bins, the verification uses 683040 scattered points.
In the verification, the HLOS wind components derived from u-and v-wind component ranges from -73.02 to 33.14 m/s. Figure Fig. A2 illustrate that the scatter plot between reciprocal SNR and uncertainty of response function of Rayleigh channel 625 is very close to the line = with little residuals, which demonstrates that the assumption and simplifications used in deriving the relationship between the laser pulse energy and the uncertainty of wind observation are reasonable, and Eq. (A7A3) is of wide feasibility in the real atmosphere. is also needed, which is the function of temperature and pressure, and can be obtained through a pre-calculated lookup table. The verification results of Eq. (11) are shown in Fig. A3.
635 Figure A3. The scatter plot of the values of which are derived from Eq. (11) and simulation system which is the sum of and respectively.
As is shown in Fig. A3, the fitting line of the scatter plot of value derived from Eq. (11) and simulation system is very close to the line = . Furthermore, the residuals between the scattered points and the fitted line are very small, which indicate the wide feasibility of Eq. (11). In addition, it is noteworthy that the scattered points of Fig. A3 are mostly located 640 below the line = , which indicates that the value of calculated by Eq. (11) is smaller than the actual value. According to Subsect. 3.43, the laser pulse energy is derived based on the equation ≈ 2 1 ⁄ ⁄ . And 1 is obtained from simulation system, which is regarded to be close to real value. The smaller 2 may lead to smaller , which is about 0.96 97 times to the real value.

645
Code and Data availability. The codes in this article are mainly compiled using matlab and are available upon request from the first author by email, zhang01020@hotmail.com. The databases used in this paper include: OMI database, which provided the latitude-averaged temperature, pressure, and ozone, can be accessed via anonymous ftp from toms.gsfc.nasa.gov/ pub/LLM_climatology; LIVAS database, providing the golabl aerosol optical properties with 1°×1° grid, offered by Dr. V.
Amiridis from Institude for space applications and remote sensing, National observatory of Athens, and can be assessed from 650 http://lidar.space.no a.gr:8080/livas/; the global LER database is available upon request from the authors, Dr. R. B. A.
Koelemeijer from Air Research Laboratory, National Institute of Public Health and the Environment, robert.koelemeijer@rivm.nl; and the reanalysis data of 20th Century Reanalysis provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at https://www.esrl.noaa.gov/psd/.