Global Balanced Wind Derived from SABER Temperature and Pressure Observations and its Validations

Zonal winds in the stratosphere and mesosphere play important roles in the atmospheric dynamics and aeronomy. However, the direct measurement of winds in this height range is difficult. We present a dataset of the monthly mean zonal wind in the height range of 18-100 km and at latitudes of 50°S-50°N from 2002 to 2019, which is derived by the gradient balance wind theory and the temperature and pressure observed by the SABER instrument. The tide alias above 80 km at the 20 equator is replaced by the monthly mean zonal wind measured by a meteor radar at 0.2°S. The dataset (named as BU) is validated by comparing with the zonal wind from MERRA2 (MerU), UARP (UraU), HWM14 empirical model (HwmU), meteor radar (MetU) and lidar (LidU) at seven stations from 53.5°N to 29.7°S. At 18-70 km, BU and MerU have (1) nearly identical zero wind lines, (2) year-to-year variations of the eastward/westward wind jets at middle and high latitudes, (3) the quasi-biennial oscillation (QBO) and semi-annual oscillation (SAO), especially the anormal QBO in early 2016. The 25 comparisons among BU, UraU and HwmU show good agreement in general below 80 km. Above 80 km, the agreements among BU, UraU, HwmU, MetU and LidU are good in general, except some discrepancies at limited heights and months. The BU data are archived as netCDF files and can be available at https://dx.doi.org/10.12176/01.99.00574 (Liu et al., 2021).

Because the direct global measurement of zonal wind in the upper stratosphere and mesosphere is difficult, the balance wind (BU) has been derived by Smith et al. (2017). The gradient wind balance theory (Randel, 1987) and the geopotential height observed by the Aura Microwave Limb Sounder (MLS) (Schwartz et al., 2008) from 2004 to 2016 and the pressure and temperature measured by the Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) instrument (Russell et al., 1999) on the TIMED satellite from 2002 to 2015 were used. They showed the semi-annual oscillations (SAO) 70 of zonal wind and their relations with quasi-biennial oscillations (QBO) in the tropical upper stratosphere and mesosphere. Smith et al. (2017) noted that the BU is reasonable below ~84 km but not above ~84 km. This is because the aliasing of diurnal tide to mean wind is notable above 84 km (Mclandress et al., 2006;Xu et al., 2009).
The focus of this work is to provide a global dataset of the monthly mean zonal wind (short for BU dataset) at 18-100 km, which is based on the gradient wind balance theory and calculated from the temperature and pressure measured by the SABER 75 instrument. The BU dataset extends from 2002 to 2019 and from 50°S to 50°N. To overcome the unrealistic BU above 84 km over the equator (Smith et al., 2017), we replace the BU above 80 km by the zonal wind measured by the meteor radar at Kototabang (0.20°S, 100.32°E). Therefore, the BU dataset can be used to study the seasonal, inter-annual, QBO of zonal winds in the stratosphere and mesosphere. The validation of the BU dataset will be performed by comparing with those from MERRA2, UARP, and meteor radar and lidar observations from 53.5°N to 29.7°S. 80 zonal wind (HwmU). We note that the monthly zonal wind does not depend on longitude since the stationary planetary waves and migrating tides reproduced by HWM14 can be removed on a time scale of one month (Drob et al., 2015).
The zonal winds measured by meteor radars and lidar are used to improve the BU over the equator and to validate BU at 100 middle and high latitudes. The radars' locations and their data periods are listed in Table 1. For the meteor radars, they measure the zonal and meridional winds at 80-100 km with a vertical interval of 2 km and a temporal interval of 1 hour. The zonal winds measured by these meteor radars are averaged over each calendar month to get the monthly zonal winds (MetU). The MetU spans from 53.5°N to 29.7°S and is useful to compare the BU at 80-100 km and in both the northern (NH) and southern hemispheres (SH). Especially, the MetU at KT (0.2°S) can be used to replace the tidal aliased BU over the equator since the 105 aliasing for tides on BU (Mclandress et al., 2006;Xu et al., 2009;Smith et al., 2017). Affected by the weather conditions, the zonal winds measured by the CSU lidar (LidU) from 2002 to 2008 are rearranged in a composite year according to calendar month in 80-100 km with a vertical interval of 0.5 km. The LidU is used to compare with the BU in the climatology sense.
The detailed description of the meteor radars and lidar, as well as their measurement uncertainties, can be found in the references listed in Table 1. 110 The BU is derived from the temperature and pressure profiles (level 2A, version 2.07) measured by the SABER instrument (Russell et al., 1999) from 2002 to 2019. These profiles cover ~15-110 km and latitudes of 53°S-83°N or 83°S-53°N. The temperature accuracy is 1-3 K from 30 to 80 km and 5-10 K from 90 to 100 km (Remsburg et al., 2008). The detailed procedure of deriving BU is described in the next subsection.

Method of Deriving Balanced Wind 115
The method of deriving BU is ascribed to the following two steps. The first step is to derive the zonal mean temperature and pressure. All the original profiles are interpolated linearly to 18-108 km with vertical interval of 1 km. Then these profiles are sorted into latitude bands, which have width of 5° with centers offset by 2.5° and extend from 50°S to 50°N. At each latitude band ( ) and height ( ), the temperature can be expressed as , ( is longitude). Then the zonal mean temperature in Here both the ascending and descending data are used for the fitting. The fitting function is expressed as, , , , cos .
( 2 ) https: //doi.org/10.5194/essd-2021-192 Open Access Here, 2 24 hour ⁄ , 1, 2, 3, 4 is the frequency (unit of 1/day) of migrating tides. and are the amplitude and phase of the migrating tides with frequency of . , is the zonal mean temperature in a LT day. In the same way, the zonal mean pressure ̅ , can be obtained. 130 The second step is to calculate the BU from and ̅ . At 10°N-50°N and 10°S-50°S, the zonal mean of the momentum equation in the zonal direction is used to calculate the gradient balance wind (Randel, 1987;Fleming et al., 1990;Xu et al., 2009), Here, 2Ω sin is the Coriolis factor, Ω 2 24 60 60 ⁄ is the earth rotation frequency (unit of radꞏs-1), is the radius of the earth. and ̅ ̅ ⁄ are the BU and zonal mean density, respectively. is the gas constant for dry air. 135 Equation (3) can be applied to equatorward of 8°N/S (Smith et al., 2017) and to poleward of 70°N/S (Fleming et al., 1990).
We restrict Equation (3) at 10°N-50°N and 10°S-50°S due to the un-continuous sampling of the SABER measurements poleward of 53°N/S. At the equator, Eq. (3) can be simplified as (Fleming et al., 1990;Swinbank & Ortland, 2003), ( 4 ) 140 Here the BU below 80 km is obtained from Eq. (4). Due to the alias of diurnal tide to the BU above 84 km at the equator (Mclandress et al., 2006;Xu et al., 2009;Smith et al., 2017), the BU in 80-100 km calculated by Eq. (4) will be replaced by the MetU at KT (0.2°S). Consequently, the reconstructed BU should be reliable throughout the height ranges from 18 to 100 km. The replaced BU will be described in the next subsection.
At 2.5°N-7.5°N and 2.5°S-7.5°S, the BU is estimated by a cubic spline interpolation of the BU at 10°N-50°N, 10°S-50°S and 145 the reconstructed BU at the equator (Smith et al., 2017).

Modification of Balance Wind at the Equator by MetU at KT
The MetU measured at KT (0.20°S) provides a unique advantage to modify the BU at the equator. Such that one can get reliable BU up to 100 km. Fig. 1 shows the daily mean (black) and monthly mean (red) zonal wind at 86 km measured by the meteor radar at KT station. We can see that the wind data are continuous from November 2002  (2) Constructing the predictor variables of MLR. The first predictor variable is constant of 1. Its regression coefficient represents the mean wind of each segment. The second predictor variable is the wind 160 data in segment b. Fig. 1 shows that the temporal variations of winds in segments a, c, and d are similar to that in the segment b but have slightly different oscillations' amplitudes. After inspecting each segment, we see that the prominent oscillations have periods of 12 and 6 months, which are used as the 3 rd and 4 th predictor variables. To reproduce more realist regression, we also include oscillations of periods of 36, 24, 4, and 3 months as the 5 th -8 th predictor variables. (3) Using the predictor variables mentioned in step (2), we perform MLR on the segments a, c and d, respectively. Then the missing observations are 165 filled with MLR predictions (shown as blue line with dots in Fig. 1). Fig. 1 shows that the MLR fittings coincide well with the observed monthly mean zonal winds when observations were available. It is reasonable to expect that the MLR predictions in the time intervals of missing observations (e.g., 2013 and 2014, before November 2002 and after September 2017) and can be used to construct BU.
After applying the MLR on the zonal wind measured by the KT meteor radar at 80-100 km, we obtain a continuous dataset of 170 MetU. This continuous dataset is composed by the observed data when they were available and predicted values when the observed data were missing. Then this continuous dataset is used to replace the BU calculated by Equation (4) at 80-100 km.
Combined with the BU calculated by Equation (4) at 18-80 km and the MetU measured by the KT meteor radar at 80-100 km, we can get a reconstructed BU at 18-100 km. Fig. 2 shows the BU at 18-100 km calculated by Equation (4) at the equator (2a) and the reconstructed BU (2b and 2c). We note that the reconstructed BU is smoothed by 3-point running mean in height and 175 time, respectively. Fig. 2 shows that the BU above 80 km (a) is in the eastward direction during most of months, which is opposite to the replaced BU (b and c). This is because the BU above 80 km shown in Fig. 2(a) is aliased by the diurnal tide over the equator (Mclandress et al., 2006;Xu et al., 2009;Smith et al., 2017).

Validations of the Balance Wind
To validate the BU derived from the SABER observations and modified by meteor radar wind observations near the equator, 180 we will compare the BU with (1) monthly mean zonal winds from MERRA2 data (MerU), (2) the UARP wind (UarU) and the zonal wind calculated from HWM14, (3) the zonal winds observed by meteor radars (MetU) at latitudes of 29.7°S-53.5°N and a Na lidar (LidU) at 40.6°N. solid rectangle) formed within the eastward phase of QBO at 18-23 km. Meanwhile the eastward wind shift to a higher height (above 23 km) (Newman, et al., 2016;Osprey, et al., 2016). Subsequently, the westward wind (highlighted by a red dashed rectangle) occurred in the eastward phase of QBO in ~30-35 km during late 2016; (5) at ~40-50 km, the fast westward jet (denoted as white rectangles) seems an extension of the westward phase of QBO to a higher height just after the QBO changing its phase from eastward to westward. This feature can also be seen in Fig. 6 of Smith et al. (2017), which showed the BU 195 derived from the SABER observations. At 30°N/S (Fig. 3), the excellent agreements between BU and MerU can be summarized as the following three points: (1) at 30°S (Fig. 3a and 3b), the eastward jets are asymmetry around June with peaks at a lower (higher) height during early (later) summer of most years; (2) at 30°N (Fig. 3c and 3d), the eastward jets of both BU and MerU have two relative weaker peaks below ~60 km. Then with the increasing height, the two peaks merge into one strong peak above ~70 km during winter of 200 most years; (3) both BU and MerU have nearly identical patterns of zero wind lines and westward wind jets.

Comparisons with MerU
At 50°N/S (Fig. 4), the eastward jets of both BU and MerU are stronger at 50°S than those at 50°N below ~70 km. Moreover, the westward jets of both BU and MerU reach their peaks at higher heights than those of the eastward jets. At 50°S, the BU and MerU agree well with each other and can be described as the following four aspects: (1)  and heights (~50 km) of the eastward wind jets, (4) the nearly identical of times (around January) and heights (~70 km) of the westward wind jets. At 50°N, the well agreements between BU and MerU exhibits the four aspects mentioned above. Moreover, the double-peak structure can be seen both in both BU and MerU during winter of some years (e.g., 2003, 2004, 2006, 2008, 2009, 2012, 2013, 2015, 2019). These double-peak structures caused by the sudden stratospheric warmings (SSWs), which reduce eastward wind during minor SSW or even reverse the eastward wind to westward during major SSW (Butler et al., 210 2015;.

Comparisons with the UraU and HwmU in a Composite Year
To compare the UraU with the BU, the UarU is interpolated to geometric height with vertical interval of 1 km and latitude interval of 2.5°. Moreover, the BU is rearranged in a composite year, which is calculated by averaging the BU in the same jet shifts from high to low latitudes with the increasing height. During summer in the NH and winter in the SH, the westward jet shifts from low to high latitudes with the increasing height. During spring (March, April) and autumn (September, October), the westward winds, which occur at low and middle latitudes and below ~45 km or above ~70 km, are separated by eastward 225 winds at ~45-70 km. These comparisons show the good agreement between BU and UraU below ~80 km.
Above 80 km and at middle to high latitudes, Both BU and UraU exhibit similar eastward jets during winter in the SH and during summer in the NH. During summer in the SH and winter in the NH, both BU and UraU exhibit decreasing eastward wind with the increasing height and even reverse to westward near 100 km. This is different from the MetU at MH (53.5°N) and BJ (40.3°N) (red lines in Fig. 7), in which the westward winds occur only around March and April. The comparisons 230 among the BU, MetU and UraU will be shown in the next subsection.
Around the equator and above 80 km, both BU and UraU exhibit westward winds but have different height and latitudinal coverages. At ~90 km, the UraU is eastward throughout the composite year except during February-April. However, the BU is eastward only during June and December and westward during other months. By analyzing the zonal winds measured by the medium frequency (MF) radars at Christmas Island (2°N, 157°W), Tirunelveli (8.7°N, 77.8°E) and Pameungpeuk (7.4°S, 235 107.4E°) and meteor radar at Koto Tabang (0.2°S, 100.3°E) and Jakarta (6°S, 107°E), Rao et al. (2012) showed that the composite zonal winds is westward except around June, July and December. This supports the BU derived here. Comparing between the BU calculated from Equation (4) (Fig. 2a) and the reconstructed BU ( Fig. 2b and 2c) above 80 km, we find that the BU calculated from Equation (4) is eastward in general. While the reconstructed BU is largely westward and coincides with the results of Rao et al. (2012). Thus, the reliability of the BU around the equator above 80 km is improved greatly after 240 we combine the BU derived from the SABER observations and MetU measured by meteor radar at KT (0.2°S).
In a same manner as Fig. 5, we show in Fig. 6 the HwmU and BU in a composite year. Below ~85 km the eastward jets of BU and HwmU agree good during winter in the NH and summer in the SH. Meanwhile, the westward jets of HwmU and BU agree good during summer in the NH and winter in the SH. During spring and autumn and at low and middle latitudes, the westward winds below ~45 km or above ~70 km surround the eastward winds at ~45-70 km. These comparisons show the well agreement 245 between BU and HwmU below ~80 km.
Around the equator and at ~90 km, the eastward HwmU occurs during May-July and November-December, which lasts a shorter time interval than that of the UraU. At ~20-40°N, above the peaks of the eastward jets (at ~70 km), there are weak eastward jets in UraU (HwmU) during September-November (September-December) at 80-90 km with peak at ~85 km.