Global evaluation of Doppler velocity errors of EarthCARE Cloud Profiling Radar using global storm-resolving simulation

. The Cloud Profiling Radar (CPR) on the Earth Clouds, Aerosol, and Radiation Explorer (EarthCARE) satellite is the first satellite-borne Doppler radar (EC-CPR). In our previous study, we examined the effects of horizontal (along-track) 10 integration and simple unfolding methods on the reduction of Doppler errors in the EC-CPR observations, and those effects were evaluated using two limited scenes in limited latitude and low pulse repetition frequency (PRF) settings. In this study, the amount of data used was significantly increased, and the area of the data used was extended globally. Not only low PRF but also high PRF settings were examined. We calculated the EC-CPR-observed Doppler velocity from pulse-pair covariances using the radar reflectivity factor and Doppler velocity obtained from a satellite data simulator and a global storm-resolving 15 simulation. The global data were divided into five latitudinal zones, and each standard deviation of Doppler errors for 5 dB Z e after 10 km integration were calculated. In the case of low PRF setting, the error without unfolding correction for the tropics reached a maximum of 2.2 m s -1 and then decreased toward the poles (0.43 m s -1 ). The error with unfolding correction for the tropics became much smaller at 0.63 m s -1 . In the case of high PRF setting, the error without unfolding correction for the tropics reached a maximum of 0.78 m s -1 and then decreased toward the poles (0.19 m s -1 ). The error with unfolding correction 20 for the tropics was 0.29 m s -1 , less than half the value without the correction. The results of the analyses of the simulated data indicated that the zonal mean frequency of precipitation echoes was highest in the tropics and decreased toward the poles. Considering a limitation of the unfolding correction for discrimination between large upward velocity and large precipitation falling velocity, the latitudinal variation of the standard deviation of Doppler error can be explained by the precipitation echo distribution.


Introduction
The Earth Clouds, Aerosol and Radiation Explorer (EarthCARE; hereafter EC) is a joint satellite mission by the Japan Aerospace Exploration Agency (JAXA) and European Space Agency (ESA) that will carry a Cloud Profiling Radar (CPR), an ATmospheric LIDar (ATLID), a Multi Spectral Imager (MSI), and a Broad Band Radiometer (BBR).From the derived 3D cloud and aerosol scene profiles, heating rates and radiation flux profiles are systematically determined with a resolution of 削除: mean of the hydrometer echo, including reflectivity-weighted particle fall speed and vertical air motion.Our forward model is based on the single scattering assumption.There are some studies on multiple scattering using Monte Carlo methods (e.g., Matrosov et al. 2008;Battaglia and Tanelli, 2011).Especially the effect of multiple scattering to the Doppler velocity is discussed in Battaglia and Tanelli (2011).In this study, we focus on Doppler errors caused by Doppler broadening and folding, so we do not consider multiple scattering for simplicity.This issue will be the subject of future research.The simulated data were then calculated along an EC orbit and interpolated into the EC-CPR sampling interval (100 m in vertical and 500 m in horizontal).
The radar reflectivity factor (Ze, jsim) and Doppler velocity (Vjsim) curtain data were obtained (hereinafter referred to as "NICAM/J-Sim data").In H22, only two scenes extracted from two orbits of data were used, but in this study, the amount of data used was significantly increased to 16 orbits of data, which is equivalent to one day of satellite tracks.
We note that there may be fast updrafts on the km or sub km scale.However, such events are rare globally and would be negligible in statistics such as latitudinal zonal means.This study focuses on global statistical results and therefore we use the NICAM.When higher horizontal resolution NICAM data becomes available, we would like to study similar evaluation with it.
In using the NICAM/J-Sim data, we first performed the following statistical analyses.We examined the zonal mean frequencies of hydrometeors obtained from the NICAM/J-Sim data and the CloudSat observations for 19 June 2008 (Fig. 1).We used the CloudSat Ze (the standard geometrical profile of cloud product, 2B-GEOPROF) (Stephens et al., 2008) for comparison with Ze, jsim.For the observed data, we defined the hydrometeor bin as where the cloud mask value is greater or equal than 20 from the CPR Level 2B-GEOPROF product, which means a weak, good, or strong echo detection (Marchand et al., 2008).These are estimated to gives an estimated false detection rate smaller than 5 %.This value is adopted in many other CloudSat-based hydrometeor studies (e.g., Sassen & Wang 2008).The frequency of cloud occurrence at a given altitude was defined as the number of cloud echo bins (Ze >-24 dBZe) divided by the total number of observations at that level.The bin size was 240 m in vertical and 2.0° latitude in horizontal.The overall frequencies of the NICAM/J-Sim simulated cloud field are comparable to the results of the CloudSat observations.We simulated the measured vertical Doppler velocity (Vm) as where Vrandom is the random error caused by the spread of Doppler velocities within the beam width.This is a Gaussian error distribution, and its SD of random error (SDrandom) is determined by perturbation approximation (Doviak and Zrnic, 1993) as and C is a correction factor.We set C = 1.3 following H22.The wavelength is l (l = 3.2 mm for EC-CPR), M is the number of pulse pairs within an integration length, r is the correlation function, and S/N is the SNR.In nominal operation, the EC-CPR will change the observation window, that is, low mode (-1 to 16 km altitude) at latitudes of 60 to 90° and high mode (-1 to 20 km) at latitudes of 0 to 60°.The PRF is determined on the basis of the satellite altitude and changes in the range of 6100 to 7500 Hz with the latitude and observation window, as illustrated in Fig. 2. The high mode has a lower PRF and worse Doppler accuracy, as discussed in H22, although cloud echoes up to an altitude of 20 km can be observed.On the other hand, the low mode has a higher PRF and better Doppler accuracy, but cloud echoes higher than 16 km cannot be observed.M is 357 to 420 for 500 m integration depending on the PRF.The SNR is determined by the received echo power calculated from the radar equation and estimated EC-CPR noise level.In the case of EC-CPR, the SNR is 0 dB, which is a signal equivalent to -21.2 dBZe echo intensity.If Ze, jsim is less than -24 dBZe, we assume the Doppler velocity of its echo to be random noise in this study.The correlation function r is defined as where sv is the total Doppler velocity spectrum width.
The width sv can be considered as a sum of contributions by each.That is, where ssm is the spread due to satellite motion, given by ssm ~ 0.3Vsatq3dB, Vsat is the satellite velocity, and q3dB is the beam width (Sloss and Atlas 1968).When Vsat is 7738 m/s and q3dB is 0.00166 rad (0.095°), ssm becomes 3.85 m/s.The spread st is due to turbulence and spsd to the distributions of hydrometeor falling velocities, respectively, which are assumed to be st = 1.0 m/s (Amayenc et al., 1993), and spsd = 0.5 m/s (Gossard et al., 1997).As for the latter term, it is reported to spread to 1.0 m/s for rain (Lhermitte 1963).In this study, we assumed the spsd, = 0.5 m/s so that sv becomes 4.01 m/s.
The EC-CPR measures the phase change of the echo between two successive pulses by pulse-pair processing to estimate the Doppler velocities.The real and imaginary parts of pulse-pair covariances Rt integrated onboard corresponding to a 500 m along-track are simulated in this study as V500m is calculated using the arctangent of the real and imaginary parts of the 500-m-integrated Rt simulated by Eqs. ( 5) and ( 6).The sign of Doppler velocity is defined as being those of radial Doppler velocity (i.e., downward motion is positive) following the EC-CPR data processing.To reduce random error, V1km and V10km are also calculated using 1 and 10 km horizontally integrated Rt respectively, that are calculated from the 500 m-integrated Rt.
Velocity folding or aliasing is inherent to Doppler radar.Vmax can be measured by the pulse-pair method and is defined by PRF (Vmax = l ⋅ PRF/4).In the PRF of the high mode (lower PRF), Vmax ranges from 4.9 to 5.2 m s -1 , whereas in the PRF of the low mode (higher PRF), it ranges from 5.7 to 6.0 m s -1 .
The simulated EC-CPR Doppler velocities are required for unfolding correction.To correct the velocity folding in spaceborne radar, it is difficult to use the conventional unfolding method generally used by ground-based Doppler weather radar (e.g., Bargen and Brown, 1980).From the ground-based vertically pointing cloud radar observations (Horie et al., 2000), upward motion above 3 m s -1 was rarely observed.On the basis of this, we thus assumed that the echoes with velocities higher than 3 m s -1 are upward folded precipitation echoes.We used the simple unfolding method as follows:

Results
We first evaluated the global mean SD of random Doppler errors in the PRF of the high mode (lower PRF) as well as PRF of the low mode (higher PRF).Then, we separated the NICAM/J-Sim data into five latitudinal zones (Arctic, Northern midlatitude, tropics, Southern midlatitude, and Antarctic).The SD of random errors for each latitudinal zone are investigated in both PRF modes.What has been described so far is consistent with what was shown in the analysis of the precipitation case in H22.Note that PRF varied from 6106 to 6464 Hz in the high mode illustrated in Fig. 2 but was a single value of 6279 Hz in the precipitation case in H22.The black lines in Fig. 3 are the result for H22, the dashed lines denote the SDdiff, and the lines indicate the SDdiff with unfolding correction (using the same method as in Eq. ( 7)).In both Figs.3a and 3b, the results in H22 are in good agreement with those of this study.
Figure 4 illustrates the global mean SD of random errors in the low-mode PRF.The dashed lines show SDdiff without unfolding correction and the solid lines indicate SDdiff with unfolding correction using Eq. ( 6).The PRF varies from 7156 to 7500 Hz, with a corresponding SDrandom of 0.8 to 1.5 for 0 to -19 dBZe (see Fig. 2 in H22).On the other hand, in the high mode, the PRF varies from 6106 to 6464 Hz, with a corresponding SDrandom of 1.5 to 3.4 for 0 to -19 dBZe.Similarly, Vmax takes values between 5.7 and 6.0 m s -1 , whereas in the high mode, it is between 4.9 and 5.2 m s -1 .Comparison of Figs. 3 and 4 clearly shows that the SD of random error is much smaller in the latter because of SDrandom described above.Furthermore, SDdiff without unfolding correction is smaller than that in the PRF of the high mode (lower PRF) because Vmax is larger in addition to the effect of SDrandom.
Since the frequencies of cloud and precipitation echoes differ in latitude and the PRF varies with latitude, as shown in Fig. 2, we investigated the change in SDdiff with latitude.We defined five latitudinal zones, namely, Arctic (>60°), Northern midlatitude (60° to 30°), tropics (30° to -30°), Southern midlatitude (-30° to -60°), and Antarctic (<-60°).In the following analysis, we focused on SDdiff of V10km.and 5d) are smaller than that for the tropics but slightly larger than or comparable to the global mean result.The SDdiff values for both polar regions (Figs.5a and 5e) are even smaller than those for both midlatitudes and smaller than the global mean result.SDdiff for the Antarctic in Fig. 5e shows the smallest value.The tendency of the magnitude relation of SDdiff for each latitudinal zone was the similar between without and with unfolding correction.From the PRF variation shown in Fig. 2, in the PRF of the high mode (lower PRF), the Doppler accuracy should be higher in the tropics and lower toward the poles.However, the results we have seen so far are opposite.On the other hand, the frequency of precipitation echoes is considered to be the highest in the tropics, and the folding Doppler This may be related to the frequency of precipitation echoes, as also explained in Figs.5a-5e.In the low-mode PRF, Vmax is larger and SDrandom is smaller owing to the higher PRF.
To summarize what has been discussed so far, the SDdiff values for the five latitudinal zones for 5 dBZe were extracted and shown in Fig. 6.The red crosses indicate SDdiff without unfolding correction of the high-mode PRF, and the red circles denote SDdiff with unfolding correction using Eq. ( 6).The red dashed line is SDdiff for 5 dBZe without unfolding correction, and the red solid line is that with unfolding correction shown in Fig. 3b.SDdiff without unfolding correction (red crosses) for the tropics is the largest at 2.2 m s -1 and decreases in both polar directions, with the smallest value at 0.43 m s -1 in the Antarctic.The SDdiff values for the Northern midlatitude and Arctic are slightly larger than those for the Southern midlatitude and Antarctic.In comparison with the global mean SDdiff without unfolding correction, the values for the tropics and  We examined the zonal mean frequencies of precipitation echoes obtained from the NICAM/J-Sim data for 19 June 2008.
First, to obtain precipitation echoes, we used the same method as in Fig. 1a but added a Doppler velocity condition (Vjsim > 3 m s -1 , downward motion).Then, using the same bin size as in Fig. 1a, we obtained Fig. 7.The extracted precipitation echoes show that the frequency decreases at higher altitudes compared with that shown in Fig. 1a.The frequency is high in the tropics and decreases toward the poles.The frequencies at altitudes of less than 5 km were averaged by latitudinal zone and found to be as follows: 27.8 % in the Arctic, 60.3 % in the Northern midlatitude, 68.5 % in the tropics, 36.7 % in the Southern midlatitude, and 2.6 % in the Antarctic.This is because it was summer in the Northern Hemisphere in the simulation.The latitudinal variation of SDdiff described so far can be explained on the basis of the precipitation echo distribution.

Conclusions
We examined the vertical Doppler velocity error due to Doppler broadening and velocity folding in the EarthCARE CPR (EC-CPR) observations throughout the globe.We used simulated observation data (NICAM/J-Sim Ze, jsim and Vjsim) for 16 satellite orbits with the same sampling interval as the EC-CPR, obtained using the NICAM and a satellite data simulator, the Joint-Simulator.The EC-CPR observed 500 m horizontally integrated pulse-pair covariances and Doppler velocity.The 1 and 10 km horizontally integrated Doppler velocities were calculated from them.We evaluated the Doppler error, i.e., the SD of random error (SDdiff), and investigated the effectiveness of error reduction by horizontal integration.We also evaluated the Doppler folding error by comparing the corrected Doppler velocities using our simple unfolding method.
We first evaluated the global mean SD of random error in the PRF of the high mode (lower PRF) as well as the PRF of the low mode (higher PRF) and compared the results with those of our previous study.In the PRF of the high mode (lower PRF), SDdiff without unfolding correction for 1 km integration decreases up to a certain value of Ze and increases after that value.
This decreasing feature is due to the decrease in the SD of random error as the SNR increases, and the increasing feature is the result of an increase in the frequency of the folded Doppler error of precipitation echoes.SDdiff without unfolding correction is much smaller for 10 km integration than for 1 km integration, because of the increased number of pulse pairs.When the unfolding correction is applied, SDdiff becomes considerably smaller regardless of the integration length and the PRF mode.
The results of PRF of the low mode (higher PRF) show very small SD of random error both without and with unfolding correction.
To investigate the latitudinal variation of SD of random error, we separated the data into five latitudinal zones, namely, Arctic (>60°), Northern midlatitude (60° -30°), tropics (30° to -30°), Southern midlatitude (-30° to -60°), and Antarctic (<-60°).In the present work, we focused on SDdiff for 10 km integration.In the PRF of the high mode (lower PRF), SDdiff for the tropics without unfolding correction is the largest and is larger than the global mean result.SDdiff without unfolding correction decreases toward the poles with the smallest value for the Antarctic, which is smaller than the global mean.The tendency of the magnitude relation of SDdiff for each latitudinal zone was similar between without and with unfolding correction.The frequency of precipitation echoes is expected to be highest in the tropics, and the folding Doppler error is also likely to be the largest.Therefore, SDdiff for the tropics without unfolding correction is considered to be the largest.SDdiff is much smaller in the PRF of the low mode (higher PRF) than in the PRF of the high mode (lower PRF), as shown by the global mean results described earlier.
In summary, SDdiff for the five latitudinal zones for 5 dBZe is described as follows.In the PRF of the high mode (lower PRF), SDdiff without unfolding correction for the tropics reached a maximum of 2.2 m s -1 and then decreased toward the poles.
SDdiff with unfolding correction for the tropics was much smaller at 0.63 m s -1 .In the PRF of the low mode (higher PRF), SDdiff without unfolding correction for the tropics reached a maximum of 0.78 m s -1 and then decreased toward the poles.SDdiff with unfolding correction for the tropics was 0.29 m s -1 , which is less than half the value without correction.As explained previously, the latitudinal variation of SDdiff can be attributed to the frequency of precipitation echoes.The zonal mean frequency of 削除: standard deviation 削除: Doppler 削除: (higher PRF) 削除: Doppler error 290 削除: Doppler error precipitation echoes obtained from the NICAM/J-Sim data was higher in the tropics and decreased toward the poles.Therefore, the latitudinal variation of SDdiff can be explained on the basis of the precipitation echo distribution.
We found that the SD of random error was higher in the tropics than in the other latitudes.In the tropics, the unfolding correction reduced the large SD of random error more efficiently.However, there is also a limitation of the unfolding correction for discrimination between large upward velocity and large precipitation falling velocity.Comparison of the results of the lowmode and PRF of the high mode (lower PRF) settings showed that the SD of random error for the PRF of the low mode (higher PRF) setting was significantly reduced, although cloud echoes for altitudes higher than 16 km cannot be observed.

Figure 2 .
Figure 2. Satellite altitude and PRF as functions of latitude and observation mode.

Figure 3 .
Figure 3. Standard deviation of random error of simulated Doppler velocities for PRF of the high mode (lower PRF) as a function of Ze for (a) 1 km integration and (b) 10 km integration.The solid lines denote the results with unfolding correction.The black lines indicate the precipitation case in Hagihara et al. (2022).

Figure 3
Figure3shows the global mean SD of random errors in the PRF of the high mode (lower PRF).The vertical axis indicates the SD of random error that is calculated from the difference between the simulated velocity (i.e., V1km, V10km) and Vjsim (hereafter, SDdiff).The horizontal axis indicates Ze of the NICAM/J-Sim data.The red dashed lines show SDdiff and the solid lines indicate SDdiff with unfolding correction using Eq.(7).Figure3ashows SDdiff of V1km and SDdiff of V1km with unfolding correction.SDdiff of V1km decreases for Ze below -10 dBZe.This is attributed to the reduction of random error owing to the increase in S/N and decrease in SDrandom in Eq. (2) as Ze increases.SDdiff of V1km increases for Ze above -10 dBZe.This is due to the increase in the occurrence of velocity folding.That is, an increase in Ze results in an increase in the intensity of precipitation echoes and an increase in mean fall velocity.When the unfolding method is applied, SDdiff of V1km is noticeably reduced because the folded negative velocities are corrected and the occurrence of the velocity folding is reduced.In Fig.3b, SDdiff of V10km decreases for Ze below -7 dBZe and increases for Ze above -7 dBZe.SDdiff of V10km is much smaller than that of V1km, reaching 0.8 m s -1 for -9 dBZe.This is because of the increase in M and the decrease in SDrandom in Eq. (2).If the unfolding method is applied, SDdiff of V10km becomes smaller since the effect of folding Doppler errors of precipitation echoes is reduced, as shown in Fig.3a.For instance, SDdiff of V10km is less than 0.5 m s -1 above -5 dBZe.

Figure 4 .
Figure 4. Standard deviation of random error of simulated Doppler velocities for PRF of the low mode (higher PRF) as a function of Ze for (a) 1 km integration and (b) 10 km integration.The solid lines denote the results with unfolding correction.
Figs. 5a-5e show the SD of random error for the five latitudinal zones in the PRF of the high mode (lower PRF).The dashed lines show SDdiff without unfolding correction and the solid lines indicate SDdiff with unfolding correction using Eq.(7).SDdiff of V10km without unfolding correction decreases up to a certain value of Ze and increases after that value.SDdiff with unfolding correction decreases as Ze increases.These tendencies observed in the five latitudinal zones are similar to those of the global mean SDdiff of V10km shown in Fig. 3b, although their magnitudes are not the same.We compared SDdiff without unfolding correction.SDdiff for the tropics, shown in Fig. 5c, has the largest value and is larger than the global mean result.The SDdiff values for both midlatitudes (Figs.5b

Figure 5 .
Figures.5f-5j demonstrate the SD of random error for the five latitudinal zones in the PRF of the low mode (higher PRF).The dashed lines show SDdiff without unfolding correction and the solid lines indicate SDdiff with unfolding correction using Eq.(7).Similarly to Figs.3 and 4, comparison of Figs.5a-5e and 5f--j shows that SDdiff is much smaller in the latter.There is a difference between with and without unfolding correction only for SDdiff for the tropics shown in Fig.5h, but not for the 210 others.

Figure 6 .
Figure 6.Standard deviation of random error of Doppler velocities with and without unfolding correction for 5 dBZe after 10 km integration as a function of latitude.Northern midlatitude are larger, but the other values are smaller.SDdiff with unfolding correction (red circles) for the tropics is 0.63 m s -1 , which is above the global mean result of 0.54 m s -1 in Fig. 3b.The SDdiff values with unfolding correction for the Southern midlatitude, Northern midlatitude, and Arctic are comparable to the global mean result, but the value for the Antarctic is smaller than the global mean result.Next, we examine the PRF of the low mode (higher PRF) results.The blue crosses indicate SDdiff without unfolding correction of the PRF of the low mode (higher PRF), and the blue circles denote SDdiff with unfolding correction using Eq.(7).The blue dashed line is SDdiff for 5 dBZe without unfolding correction, and blue solid line is the value with unfolding correction illustrated in Fig. 4b.SDdiff without unfolding correction (blue crosses) for the tropics is

Figure 7 .
Figure 7. Zonal mean frequency of precipitation echoes obtained by NICAM/J-Sim for 19 June 2008.