1. Introduction
The current computing performances of numerical weather prediction (NWP) and climate research models provide higher and higher spatial as well as temporal resolution. To improve accuracy, the models need to assimilate more and more measurements with greater precision (Dee et al. 2011). This is possible owing to progress in measurement techniques and instrumentation. Wind measurements come from weather stations, radiosonde balloons, pilot balloons, aircraft meteorological reports, wind profilers, and satellite imagery through atmospheric motion vectors (Borde et al. 2014, 2016). The troposphere is well monitored because of its easier access and its direct impact on human activities. The stratosphere, however, suffers from a clear lack of in situ wind measurements, even though it has been shown that tropospheric weather can be influenced by large-scale dynamical structures occurring in the middle atmosphere such as (i) the polar vortex (Baldwin and Dunkerton 2001; Thompson et al. 2002; Charlton et al. 2003; Charron et al. 2012), (ii) sudden stratospheric warmings (SSW) (Charlton et al. 2003; Charron et al. 2012; Sigmond et al. 2013; Kuttippurath and Nikulin 2012), and (iii) the quasi-biennial oscillation (QBO) (Thompson et al. 2002; Gerber et al. 2010). The study and numerical modeling of the stratosphere is therefore becoming an important issue for NWP centers, with numerical models considering an increasing number of horizontal grid points and vertical levels, and for most of them a model top at 0.01 hPa. They also benefit from the development of new assimilation schemes and an increase in computing facilities. Reanalyzed winds result from the model internal dynamics and from assimilated observations, which can be wind observations or mass-related quantities (e.g., temperature) in places where there is a balance between the mass and wind fields (as in the extratropics).
Most of the wind measurements in the upper troposphere and in the lower stratosphere are performed with radiosondes that are the only in situ measurements in the stratosphere, but radiosondes generally burst below 30 km (around 10 hPa). Other techniques can be used to probe the atmospheric wind at high altitude (stratosphere and mesosphere) by remote sensing. Infrasound technology (Le Pichon et al. 2005) gives relevant information on gravity waves (Blanc et al. 2014). Doppler lidar measurements provide measurements up to 60 km but only in some locations over the world (Hauchecorne and Chanin 1980; Chanin et al. 1989). Recently a microwave wind radiometer (WIRA) was developed at Bern University capable of measuring wind between 25 and 70 km (Rüfenacht et al. 2012). Le Pichon et al. (2015) have shown large discrepancies between WIRA observations and the European Centre for Medium-Range Weather Forecasts (ECMWF) operational model, ERA-Interim, and MERRA for both temperature and wind fields above 40-km altitude. Their study highlighted the increase in wind biases as a function of altitude. The last three techniques listed provide relevant wind information by remote sensing up to the mesosphere but with a smaller vertical resolution than in situ measurements. New infrastructures aiming to combine these different instrumentations are emerging [Atmospheric Dynamics Research Infrastructure in Europe (ARISE) project; http://arise-project.eu/].
Satellite measurements able to probe the temperature in the stratosphere are also expanding, such as AMSU (Kidder and von der Haar 1995) and the Infrared Atmospheric Sounding Interferometer (IASI) (Hilton et al. 2012).
Baron et al. (2013) summarized wind measurements from space available in the middle atmosphere from HRDI measurements in 1991 (Ortland et al. 1996) to the future European Space Agency (ESA) mission AEOLUS (Straume-Lindner et al. 2007). In their study they report the altitude range of the different measurements as well as their precision, which is between 3 and 10 m s−1 in the altitude range [10, 40] km. The vertical resolution of these wind measurements is 5–7 km. They show that using the passive microwave radiometer Superconducting Sub-Millimeter Limb Emission Sounder (SMILES) instrument operated on the International Space Station (ISS), good agreement between the horizontal wind components and the ECMWF analyses is reached in most of the stratosphere except for the zonal winds over the equator with a mean difference from 5 to 10 m s−1, whereas in the mesosphere differences greater than 20 m s−1 are observed in SMILES and ECMWF zonal winds, especially in the tropics.
The present study is based on observations collected during balloon flights performed by the Centre National d’Études Spatiales (CNES) to investigate in situ the stratosphere. The CNES operates several types of balloons: the zero-pressure balloon (ZPB; Durry and Hauchecorne 2005; Huret et al. 2006; Wetzel et al. 2013), the superpressure balloon (SPB; Vial et al. 2001; Hertzog et al. 2004, 2006; Knudsen et al. 2006; Christensen et al. 2007; Vincent and Hertzog 2014; Podglajen et al. 2014), and the infrared Montgolfier balloon (Knudsen et al. 2002, 2006; Christensen et al. 2007).
ZPBs carry heavy scientific payloads (from several hundred kilograms to 1 metric ton) to study the atmosphere (chemical composition and its dynamics), aeronomy, or astrophysics. The flight duration is from several hours to a few days or a few weeks. They have been intensively used to validate satellite measurements [Environmental Satellite (ENVISAT), Odin, Improved Limb Atmospheric Spectrometer (ILAS), etc.]. They can attain high-stratospheric altitudes up to 40 km.
SPBs are used in the upper troposphere–low stratosphere (UT–LS) for long-duration flights (1–3 months) on isopycnic surfaces. Several studies (Hertzog et al. 2004; Knudsen et al. 2006; Christensen et al. 2007; Boccara et al. 2008) have reported substantial differences between simulated balloon trajectories with analyzed winds and real trajectories using SPBs in the UT–LS, with differences of 1000 km between the forecast trajectory and the real one at mid- and high latitudes after a few days of flight. In equatorial regions this difference is higher and can attain 10 000 km after 10 days of trajectory forecast (Podglajen et al. 2014).
The balloon trajectory is driven by the wind, and balloons can be considered as good tracers if the vertical speed is not too high and if measurements of the balloon location are sufficiently accurate (Alexander et al. 1996).
In the present study we used ZPB (operated by CNES) trajectories in the 2000–11 period in order to retrieve the wind components (zonal u and meridional υ), the wind speed (FF), or wind direction (DD) and compare them with the ERA-Interim data. These in situ wind measurements allowed us to study the ability of ERA-Interim to represent the dynamics of the stratosphere up to 2 hPa above two balloon launch bases [Esrange, Sweden (67.9°N, 21.1°E) and Teresina, Brazil (5.1°S, 42.9°W)] in several dynamical conditions (winter and summer polar seasons, west and east phases of the quasi-biennial oscillation at the equator). It should be noted that the ERA-Interim process assimilates much less wind data in the stratosphere than in the troposphere (Dee et al. 2011).
In the present paper we first describe the balloon wind measurements and the retrieval method used as well as the methodology developed for comparing with ERA-Interim (Dee et al. 2011). We then assess the wind biases for each dynamical condition and we conclude by discussing the results in terms of specific processes/conditions that could explain the biases obtained as well as the methodology used.
2. Data and methodology
a. Zero-pressure balloon wind measurements
The typical duration of ZPB flights operated by CNES is from 6 h to a few days. Each flight profile is driven by scientific objectives depending on the payload, with four phases: 1) balloon ascent at typically 5 m s−1, 2) ceiling where the balloon is in equilibrium with the surrounding air thus the pressure level is stable (except for slow variations due to thermal effects induced by the diurnal cycle), 3) slow descent with a vertical speed that can be adjusted between 1 and 5 m s−1, and 4) rapid descent of the payload under parachutes down to the ground after balloon–payload separation (vertical speed can exceed 20 m s−1).
In our study the slow phase of ascent, the ceiling, and the slow descent (if present) were used to deduce the zonal wind component u and the meridional wind component υ from the balloon trajectory. The rapid descent cannot be used because of its high vertical speed. In this study we assume that the balloon is a perfect passive tracer for horizontal wind.
For each flight we retrieved u and υ from the global positioning system (GPS) position (longitude, latitude, altitude) of the balloon recorded every 10 s using a centered difference with two points separated by 10 time steps (100 s). This makes it possible to filter out the high frequencies generated by pendulum oscillations. The flight chain is between 100 and 200 m long and thus (considering a simple gravity pendulum in the small-angle approximation) the oscillation period is between 20 and 30 s. For ZPBs the time duration of the ceiling can attain 1 day. During this phase at float a large number of measurements are recorded at a roughly constant pressure. To avoid oversampling during the ceiling we downsampled the measurements with a time step of 15 min [the same sampling was used by Hertzog et al. (2004) with SPB trajectories].
From horizontal GPS coordinates, the accuracy of the balloon payload location is better than 10 m in the horizontal. Uncertainty due to GPS accuracy on the horizontal component is therefore 0.2 m s−1. The pressure uncertainty is about 0.5 hPa (capacitive transducer probe). Such an uncertainty is too high for our study in the stratosphere because it corresponds to an error higher than several hundred meters at 10 hPa. The GPS altitude with an accuracy of 20 m was therefore used. Because the GPS antenna is not located at the center of balloon drag, to obtain the altitude of the wind measurement points we added an offset to the GPS altitude. It corresponds to the distance between the GPS module and the mean position of the helium bubble center, including the flight chain length. Because during the ascent of the balloon the helium bubble volume varies because of a pressure decrease, its center is located at the geometric balloon center only during the ceiling. Knowing the volume of helium for each flight at ground we calculate the position of the helium bubble center at 200 hPa assuming that the volume occupied by the gas is spherical. Then we add to the balloon radius the half distance between the geometric balloon center (at the ceiling the balloon is completely inflated) and the helium bubble center at 200 hPa. For balloons of 400 000 and 12 000 m3, these offsets are respectively 110 and 78 m. The vertical uncertainty due to the displacement of the helium bubble center is equal to these half distances (±37 and ±22 m, respectively). Adding the GPS accuracy to the maximum value of the vertical uncertainty (for a 400 000-m3 balloon), this gives an error on the altitude of the measurement points of ±57 m for all flights. It includes the accuracy of the GPS altitude and the variation in the location of the helium bubble center during the ascent.
Wind measurements were retrieved from flights above Esrange and Teresina, delivering a unique source of wind measurements in the stratosphere. They are shown in Fig. 1 for both zonal and meridional wind components (77 084 points).
Measurements of (a) zonal and (b) meridional wind velocity components between 10 and 40 km, corresponding to 200 and 2 hPa, respectively. Dark blue: above Esrange (67.9°N, 21.1°E) in December–March; light blue: above Esrange (67.9°N, 21.1°E) in June–August; black: above Teresina (5.1°S, 42.9°W) in 2005 (easterly QBO); gray: above Teresina (5.1°S, 42.9°W) in 2008 (westerly QBO).
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
We distinguish winter and summer circulation for polar flights and the QBO phase for equatorial flights. The winter polar circulation (49 flights from Esrange in December–February) is characterized by westerly circulation with strong zonal winds up to 60 m s−1 corresponding to the edge of the polar vortex—that is, polar night jet (Krishnamurti 1959; Kuroda and Kodera 2001; Hitchcock et al. 2013). During polar summer (22 flights in June–August) the easterly circulation is less intense.
For flights above Teresina (May–July) we observe westerly winds (QBO west) for the seven flights in 2008 in the range [20, 34] km and easterly winds (QBO east) for the 12 flights in 2005 in the range [22, 34] km. The maximum value of the vertical gradients of both wind components is 15 m s−1 km−1 at high level for equatorial flights.
The meridional wind velocities for polar summer and QBO east and west phases do not exceed 10 m s−1 in absolute values. For polar winter the meridional component is more variable and can attain 50 m s−1 in absolute values for some flights, likely caused by strong planetary waves.
An added value of this dataset is that wind measurements are available above 30 km in the stratosphere, while studies using meteorological radiosondes are limited to measurements below 30 km (e.g., Houchi et al. 2010; Moffat-Griffin et al. 2011).
b. ERA-Interim data
The ECMWF model is one of the best NWP models, producing analysis and reanalysis data at a global scale (Martineau and Son 2010; Jakobson et al. 2012). The current operational model or Integrated Forecast System (IFS) has been used systematically for trajectory forecasting during CNES balloon campaigns. Over the last 20 years the IFS model has been regularly updated to include new parameterizations, data assimilation, and a larger number of horizontal grid points and vertical levels. To compare with our measurements obtained from 2000 to 2011 we need results coming from the same “stable” model to perform model–balloon comparisons. We therefore chose to perform a systematic comparison with ERA-Interim (Dee et al. 2011) as the underlying dynamics of the model did not change over the reanalysis period.
The main assimilation sources in the stratosphere are radiance observations. By using the Toulouse Offline Model of Chemistry and Transport (TOMCAT) model (Chipperfield 2006) in ERA-Interim, an improvement was obtained compared to ERA-40 (Uppala et al. 2005), which encountered difficulties in representing the Brewer–Dobson circulation (Dee and Uppala 2008). Dee et al. (2011) present a table summarizing the number of wind measurements and their quality, used for ERA-40 and ERA-Interim (their table III). Their numbers are the same in 1995, but in 2006 more wind measurements were assimilated by the model. However above 100 hPa (i.e., in the stratosphere) only a few wind measurements are available compared to the troposphere.
We used the ERA-Interim wind, pressure, temperature, and geopotential height outputs on the 60 model levels with a horizontal resolution of 0.75° × 0.75° in latitude and longitude and a time step of 6 h (for details, see IFS documentation http://www.ecmwf.int/sites/default/files/IFS_CY40R1_Part3.pdf).
Spatiotemporal interpolations were performed for each wind measurement by considering three latitude points, three longitude points, two vertical levels, and three time steps. Horizontal and time interpolations were quadratic whereas the vertical interpolation was linear. For the vertical interpolation, the geopotential height and the GPS altitude were used because of the poor precision of the operational pressure measurements on board ZPBs. The error associated with the uncertainty in GPS vertical positions when we perform the vertical interpolation of reanalyzed winds depends on the wind vertical gradient, which reaches 15 m s−1 km−1 combined with the uncertainty on the altitude of the measurement points (±57 m, detailed in section 2a). We estimated that the interpolation error was ±0.85 m s−1. The estimated uncertainty on individual horizontal wind measurements including the accuracies of the GPS on the horizontal axis, vertical axis, uncertainty on the position of the helium bubble center, and interpolation is therefore ±1.05 m s−1. We consider an additional source of error for equatorial flights because of the strong vertical wind gradient. In that case the GPS could be not aligned with the helium bubble center. If we consider an angle of ±22.5° between the flight chain and the vertical axis this induces a shift of roughly ±23 m on the horizontal axis and ±10 m on the vertical axis. This could induce an additional uncertainty of ±0.7 m s−1. For equatorial flights we then consider an estimated uncertainty on individual wind measurements of ±1.75 m s−1 reported in each figure.
c. Methodology
The wind biases (i.e., the mean of the difference between model and measurements) were calculated in pressure bins with two different pressure interval widths with a constant offset of the interval center in log pressure between 100 and 2 hPa (5 hPa at 100 hPa). The two pressure interval widths are shown in Fig. 2: large pressure intervals (LPI) in red and small pressure intervals (SPI) in green. Vertical levels of ERA-Interim are shown in blue in Fig. 2.
Rolling pressure intervals considered to calculate biases: LPI (red) and SPI (green). Model levels of ERA-Interim data are in blue.
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
More details can be found in Huret et al. (2015). The intervals correspond to a vertical thickness from 3.3 km at 100 hPa to 3.7 km at 5 hPa for SPI and from 8.8 km at 100 hPa to 10.3 km at 5 hPa for LPI. Biases calculated using LPI could then be compared to those from Le Pichon et al. (2015) with the WIRA instrument, which provides wind measurements in a layer with an 8-km thickness (between 30 and 38 km) or those from Baron et al. (2013) with the SMILES instrument on the ISS with a vertical resolution of 5–7 km from 35 to 70 km.
The number of measurement points within each interval is almost constant as a function of the mean pressure up to intervals centered at 5 hPa. This allowed us to compare our results with those obtained in the different intervals—that is, to analyze the results as a function of altitude. The order of magnitude of the number of points in each LPI is 10 000, 6000, and 5000, respectively, for polar winter, polar summer, and QBO east and west. For SPI, the number of points is lower, with 4000, 2500, and 2000 points, respectively. At high altitude when the mean pressure is less than 5 hPa, the number of points strongly decreases. The number of points for equatorial flights is smaller than for polar flights owing to the limited number of campaigns in equatorial regions (2005 and 2008).
For each interval we calculated the bias, the standard deviation, the skewness, and the kurtosis for both wind components. We also calculated the standard error on the bias (standard deviation divided by the square root of the number of points) to ensure that our results were statistically significant. It is important to note also that because numerous independent flights were used, the wind measurements obtained are independent.
3. Results
In this section we analyze the biases obtained in the four geophysical conditions (polar winter, polar summer, QBO east, and QBO west).
a. Wind biases above the Esrange launch base
1) Winter condition
The biases in the zonal component u (Fig. 3) are small between −0.2 and + 0.2 m s−1 in the pressure range [100, 10] hPa for both LPI and SPI. In the [10, 5]-hPa pressure range, the u biases increase slightly to reach −1.2 m s−1 at the mean pressure of 5.95 hPa for LPI and −1.5 m s−1 for SPI at the mean pressure of 6.60 hPa.
Wind biases and standard deviation as a function of pressure obtained during winter season (December–March) above Esrange for LPI (red) and SPI (green); see section 2c for details. (a) Zonal component; (b) meridional component. Blue horizontal lines correspond to ERA-Interim model levels. Vertical black solid lines correspond to estimated uncertainty on wind component combining instrumental errors and interpolation of ECMWF data.
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
The values of the standard deviations increase with the altitude and are roughly 2 times higher at 5-hPa mean pressure than at 100 hPa (4.6 vs 2.3 m s−1 for both LPI and SPI). For each altitude they are greater than the estimated wind uncertainty. In each interval the standard errors are less than 0.1 m s−1 for both LPI and SPI. The bias values of the meridional component υ are small. They remain in the range [−0.1, 0.7] m s−1 for LPIs and in the range [−0.4, 1.1] m s−1 for SPIs. The standard deviations are constant (~2.3 m s−1) in the UT–LS up to 50 hPa and then increase up to 5 hPa with a value of almost 6 m s−1. They are larger than the estimated wind uncertainty. The standard errors are less than 0.1 m s−1 for LPI and 0.2 m s−1 for SPI.
At all levels for both wind components the standard deviations are greater than the individual measurement uncertainty for LPI and SPI. They increase with altitude, highlighting that the modeled winds reproduce less and less the variability of the observed winds. Baron et al. (2013) compared SMILES measurements and ECMWF analyses. During the 2009/10 winter they report meridional and zonal bias values lower than ±2 m s−1 in the stratosphere (above 10 hPa), which does not disagree with our study but they obtain very high standard deviations (13 m s−1) compared to us. The processes responsible for wind flow perturbations during winter in polar regions are those associated with sudden stratospheric warming (SSW) events at large scale and gravity wave activity at small scales. The major SSW event occurring in winter 2009/10 (Kuttippurath and Nikulin 2012) is associated with a polar jet oscillation (PJO) and vortex split (Ern et al. 2016). The latter study analyzing gravity activity reported that such a combination of major SSW and PJO leads to the enhancement of gravity wave activity. The propagation conditions are improved and the activity of gravity wave sources is stronger. Mountain waves are more excited and jet-generated gravity wave sources more active. This could explain the high standard deviation reported by Baron et al. (2013) for the 2009/10 winter.
In our study the increase in the standard deviations as a function of altitude can also be explained by gravity wave activity given that Scandinavian mountains are a hot spot for mountain waves, as has been highlighted by numerous authors working on polar stratospheric clouds (e.g., Rivière et al. 2000; Brogniez et al. 2003; Dörnbrack et al. 2002). However, our results are based on numerous winter observations (before SSW or after, winter with or without SSW)—that is, with or without strong wave activity—which probably reduces the value of standard deviations.
ERA-Interim slightly underestimates the zonal wind component above 10 hPa. The u biases at high altitude ([10, 5]-hPa pressure range) are relatively small compared to the u mean value (~40 m s−1) and do not exceed 8%. The υ biases are slightly larger and can reach 11% at 23 hPa. The increase in the standard deviations with altitude highlights the difficulties of ERA-Interim in representing the wind variability observed due to gravity waves at small scale and their interaction with SSW events at large scale.
A specific comparison was conducted between our results around 70 hPa and the previous study by Hertzog et al. (2004, hereafter H2004). H2004 compared the two wind components deduced from six SPB trajectories obtained in 2002 in polar vortex conditions to the ECMWF operational outputs (0.5° × 0.5°). Their results combined two sets of measurements obtained in the [85.1, 82.8]- and [64.7, 58.6]-hPa pressure ranges.
The pressure ranges of H2004 are included in the SPI at the mean pressure of 69.83 hPa. Figure 4 presents the histograms of differences between ERA-Interim and our wind measurements, and Table 1 summarizes the characteristics of our results and those of H2004. The histograms of differences we obtained present a Gaussian shape with small biases of 0.1 and 0.2 m s−1 for u and υ, respectively. The standard deviations obtained are similar to those of H2004. Skewness and kurtosis are larger in our study (except for the zonal wind skewness). We have half as many points as H2004 and our standard error is 0.04 m s−1 for both u and υ biases, which is smaller than the biases we obtained. Even if the biases we get are lower than the estimated uncertainty, the standard error remains lower than the biases. Moreover the standard deviations are of the same order as those of H2004. This comparison with H2004, at this specific pressure range in the low stratosphere, supports our decision to use ZPB trajectories to investigate biases between model results and measurements and the associated standard deviation.
Histograms of differences between ERA-Interim and measurements above Esrange from 2000 to 2010, for the SPI [90.78, 53.72] hPa at the mean pressure of 69.83 hPa. (a) Zonal component; (b) meridional component.
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
Statistics of ERA-Interim/operational ECMWF data minus wind measurements for both zonal and meridional components (m s−1), considering measurements retrieved from ZPB trajectories from 2000 to 2011 above Esrange and SPB trajectories obtained in the polar vortex in 2002 (H2004), respectively.
2) Summer conditions
The zonal and meridional wind biases obtained in polar summer are presented in Fig. 5. For the zonal component between 100 and 10 hPa, and for the meridional component up to 5 hPa, the biases are very small, close to 0 m s−1, slightly positive or negative and in all cases lower that the estimated uncertainty. Above 10 hPa the zonal biases increase, reaching −1.1 m s−1 at 5 hPa. The standard deviations obtained are smaller than in polar winter conditions, in good agreement with climatologies of gravity waves that show the same characteristics at high altitude (Ern et al. 2011). They remain roughly constant (~2 m s−1) up to 35 hPa and then increase up to 3.5 m s−1 at high altitude for both wind components. The standard errors on u and υ biases are less than 0.1 m s−1 for LPI and less than 0.2 m s−1 for SPI. During the summer season ERA-Interim represents both horizontal components of the wind above Esrange up to 5 hPa well. The relative u biases (considering a mean zonal wind velocity of −5 and −10 m s−1) are less than 10% for the u component, and because the meridional wind is weak (Fig. 1), the relative meridional biases can attain 30%.
As in Fig. 3, but for summer season (June–August) above Esrange.
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
b. Wind biases above Teresina, Brazil
The dynamical conditions of the equatorial stratosphere are modulated by the QBO (Baldwin et al. 2001). In 2008 (May–June) flights took place during the westerly QBO phase whereas in 2005 (June–July) flights occurred during the easterly phase.
1) Easterly QBO phase
Biases calculated for the easterly QBO phase for both wind components are shown for LPI and SPI in Fig. 6 as well as standard deviations.
As in Fig. 3, but above Teresina in June and July 2005 (during the easterly QBO phase).
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
The u biases obtained with LPI and SPI are mainly negative in the low levels from 100 to 25 hPa, with values between −0.5 and −3.0 m s−1 (sometimes greater than the estimated uncertainty). Above 25 hPa, the u biases obtained with SPI present large variations from negative to positive values. For SPI, local extrema are observed at two specific mean pressures: −3.1 m s−1 at 20.39 hPa and 9.9 m s−1 at 9.94 hPa. For these two levels LPI give a slightly positive value of 0.1 m s−1 at 20.39 hPa and 5.1 m s−1 at 9.94 hPa, which is approximatively a twofold-lower value than the SPI bias. The biases are greater than the uncertainty over almost the entire vertical profile. Unlike SPI and LPI biases calculated from polar flights, those from equatorial flights present very different vertical profiles. The standard deviations for both LPI and SPI increase as a function of altitude, reaching more than 6 m s−1 above 7 hPa. The standard errors are less than 0.1 m s−1 for LPI and 0.3 m s−1 for SPI. They are greater than those obtained in the polar region due to the smaller number of measurement points in each pressure interval but they remain lower than the biases obtained. It is important to point out that the relative biases for u can exceed 50% in some extreme cases.
The meridional biases are mainly slightly negative. They are between −2.3 and −0.4 m s−1 and between −3.4 and 0.3 m s−1 for LPI and SPI, respectively. The standard deviations present several different regions. The minimum values obtained between 30 and 20 hPa for SPI and LPI are 3 m s−1 greater than the estimated uncertainty. The standard errors are below 0.1 m s−1 for LPI and 0.2 m s−1 for SPI. As for the zonal component, the relative biases for υ are large and can reach 60% (considering a meridional wind velocity of ~5 m s−1).
To better understand the vertical variations in u biases we present the two histograms of differences between ERA-Interim and our measurements at 20.39 and 9.94 hPa in Fig. 7.
Histograms of differences between ERA-Interim and zonal wind measurements (m s−1) obtained for the easterly QBO phase (those of Fig. 6) at the mean pressure levels (a) 9.94 and (b) 20.39 hPa for LPI (red) and SPI (green).
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
For a mean pressure of 9.94 hPa (Fig. 7a) where SPI present a larger positive bias value than the LPI bias value, the histograms of differences show a wide scatter, with differences between model and measurements ranging from −10 to +21 m s−1. The histogram of biases for LPI presents a frequency distribution that is different from SPI with more negative bias values. This explains the shift of the biases to smaller values for LPI compared to SPI.
When the SPI bias is minimum and the LPI bias close to zero (at 20.39 hPa; Fig. 7b) the SPI histograms present a more Gaussian shape. In that case the extent of the distribution is very different for LPI and SPI. LPI includes more positive bias values. This explains the different bias obtained for LPI and SPI: the LPI shift results in positive biases. When analyzing both these histograms and the vertical distribution of u measurements (Fig. 1), and taking into account the fact that the vertical extents of LPIs are roughly 9.5 km, it can be seen that LPIs take into account measurement points associated with the well-established easterly circulation as well as measurement points associated with the strong wind gradients in the vertical direction. SPI biases give information on a smaller-altitude range (roughly 3.5 km) and the largest differences between ERA-Interim and wind measurements (in absolute value) are observed where the abrupt vertical transition in the zonal wind direction occurs. Hence, LPIs appear to be too large, leading to a smoothing of the derived vertical bias profiles, while SPIs are more accurate to characterize the biases when wind shear exists.
Baron et al. (2013) showed a u bias of 5–10 m s−1 at 10 hPa compared with the ECMWF analysis field over the equator. In line with our results, their υ biases are small, close to zero. Their results were obtained with a vertical resolution of 5–7 km (i.e., in between the resolution of SPIs and LPIs) and our zonal biases (LPI: 7 m s−1 and SPI: 10 m s−1) and meridional biases are in agreement with their findings. The biases in the present study are 2- or 3-times-lower values than those of Baron et al. (2013), which refine the characterization of the biases existing between measurements using winds deduced from balloon trajectories and model outputs. Similar to ECMWF analyses, ERA-Interim seems to have difficulties capturing the altitude of the vertical transition in the zonal wind direction or the intensity of this change.
2) Westerly QBO phase
Biases calculated for the westerly QBO phase for both wind components are shown for LPI and SPI in Fig. 8 as well as the standard deviations.
As in Fig. 3, but above Teresina in July and August 2008 (during the westerly QBO phase).
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
Negative u biases are obtained with LPI above 20 hPa, reaching −6 m s−1 at 5.11 hPa. Below this pressure, the biases are almost equal to zero or slightly positive. The u biases obtained with SPI vary widely, as for easterly QBO conditions [see section 3b(1)], with local extrema at specific mean pressures—namely, 2 m s−1 at 46.43 hPa and −10.6 m s−1 at 6.94 hPa. In the pressure range of [12.85, 28.04] hPa the biases are slightly negative, close to the estimated uncertainty, but with a smaller standard deviation of 3 m s−1 than below and above with roughly 6 m s−1. The standard errors calculated are smaller than 0.1 m s−1 for LPI and 0.2 m s−1 for SPI. The relative u biases can exceed 40% for the extreme values. The layer [12.85, 28.04] hPa is characterized by easterly circulation whereas above and below the circulation reverses and the standard deviations increase.
The biases for the meridional wind υ are mainly positive in the [100, 35]- and [15, 5]-hPa pressure ranges and negative in the [35, 15]-hPa pressure range for both LPI and SPI. The values of υ biases reach 1.8 m s−1 at 81.45 hPa for LPI, −3.5 m s−1 at 23.78 hPa for SPI, and 1.9 m s−1 at 7.31 hPa for SPI. The standard deviations are mainly between 4 and 7 m s−1. The standard errors calculated are below 0.8 m s−1 for LPI and 0.2 m s−1 for SPI. The relative υ biases can exceed 100% because the meridional circulation is weak (considering a meridional wind velocity of ~4–5 m s−1; see Fig. 1).
The same behavior as for easterly QBO conditions is observed with considerable differences between u biases for LPI and SPI, but not at the same altitude. Analysis of both vertical profiles of u biases and u measurements (Fig. 1) shows that the two maxima (in absolute value) of u biases with SPI are obtained close to altitudes where the vertical u gradient is a maximum; the minimum u biases with SPI are obtained in layers where vertical u gradients are a minimum. Once again the greater difference between ERA-Interim winds and wind measurements (uEra-I − uobs) comes from the layers where a zonal wind vertical transition in the east-to-west wind direction occurs. As before, the difference between LPI and SPI u biases obtained at these layers can also be explained by the histograms of distribution (not shown). LPI take into account more vertical levels, which induces a wider distribution of uEra-I − uobs, thus reducing the biases when maximum bias values (in absolute value) for SPI are observed and increasing the biases when minimum bias values for SPI are observed. This means that if LPI intervals are used, smoothing occurs and the differences between reanalysis and observations are not well captured. The standard errors calculated for SPI are lower than the biases obtained, meaning that a sufficient number of data points were considered to extract the information on the u biases with SPI.
At low levels we can compare our results to those of Podglajen et al. (2014), who estimated biases with ERA-Interim by analyzing two SPB flights in the [55, 65]-hPa pressure range. Their bias values were −2.7 and −0.1 m s−1 and standard deviations of 5.1 and 3.8 m s−1 for the zonal and meridional components, respectively. The standard deviations were similar to our results on both wind components. The biases for the zonal component were below the estimated uncertainty in our study and close to 0 m s−1 in this range of altitude.
As a partial conclusion on equatorial investigations, whatever the QBO phase considered ERA-Interim does not fully capture the vertical structure of the zonal wind, and the difference between measurements and model can attain more than 7 m s−1 at high altitude, with a large standard deviation. Results are very sensitive to the vertical resolution, with an underestimated bias value when the zonal circulation reverses considering a vertical resolution close to 10 km. As a result, SMILES measurements from ISS or ground-based WIRA measurements provide information about the order of magnitude of the bias but do not capture the strong bias values.
4. Discussion
For both zonal and meridional wind components, biases between ERA-Interim winds and wind measurements deduced from ZPB trajectories depend on the location, the season, and the mean pressure. Whatever the conditions considered, the standard deviations increase with altitude. It is important to note that for each location/season no correlation was found between the vertical bias variations and the ERA-Interim levels, showing that interpolation errors can be neglected. For the different biases calculated, the standard errors are always lower than the biases obtained (even in the equatorial region with a smaller number of balloon flights, hence fewer measurements) and almost all standard deviations are greater than the estimated uncertainty. This means that even in cases of small biases, ERA-Interim seems to have difficulty representing the wind field variability in the stratosphere at high altitude.
We have seen that the biases obtained when considering LPI and SPI are similar for measurements obtained in the polar region but that differences appear for measurements obtained in the equatorial region. The explanation for this is that in the event of a rapid change in wind direction, small pressure intervals are better suited for calculating biases. In addition, when large vertical wind gradients exist, ERA-Interim encounter difficulty capturing these changes. The meridional component wind biases are always small but in relative value can attain 30%.
In the previous part we analyzed the zonal and meridional components independently, but they are not uncorrelated and it is also interesting to determine the differences between ERA-Interim and balloon measurements for FF and DD [the notations FF and DD are the norms used for radiosondes (WMO 1995)]. Figure 9 shows the FF and DD biases for the four geophysical conditions investigated with SPI.
Wind biases and standard deviation as a function of pressure obtained with SPI for (a) FF and (b) DD above Esrange. Dark blue: December–March; light blue: June–August. (c) FF and (d) DD above Teresina. Black: easterly QBO in 2005; gray: westerly QBO in 2008. Vertical black solid lines correspond to estimated uncertainty on wind component combining instrumental errors and interpolation of ECMWF data.
Citation: Journal of the Atmospheric Sciences 74, 6; 10.1175/JAS-D-16-0137.1
a. Polar flights
In the polar region (winter and summer season; Fig. 9a), the absolute differences between ERA-Interim and measurements in the [100, 20]-hPa pressure range never exceed 1 m s−1. In the [100, 50]-hPa pressure range Dee et al. (2011) showed the global average of the root-mean-square (RMS) errors of winds from several sets of ECMWF reanalyses. This RMS can be compared with the standard deviation that we calculated on the wind speed. In the troposphere, ERA-Interim compared to wind from radiosoundings present an RMS peak of ~5.7 m s−1 at 250 hPa. It then decreases, reaching 4 m s−1 at 100 hPa and ~3.2 m s−1 at 50 hPa. The standard deviations we obtained for the wind speed for polar flights are on the same order of RMS magnitude, with values of 3 m s−1 during winter and 1.5 m s−1 during summer. This confirms that ERA-Interim are robust in the low stratosphere, in good agreement with other previous studies assessing the quality of the ECMWF model in the lower stratosphere (H2004; Hertzog et al. 2006; Knudsen et al. 2006; Christensen et al. 2007; Boccara et al. 2008; Houchi et al. 2010).
ERA-Interim encounter some difficulties representing wind speed at higher altitudes (above 20 hPa). The FF biases increase almost linearly, reaching −2.3 m s−1 at 5 hPa in winter conditions and a lower value in summer conditions. ERA-Interim underestimates slightly the wind speed above 20 hPa. This altitude corresponds to the altitude rarely attained by radiosondes and consequently above 20 hPa no wind measurements can be assimilated in the model.
The DD biases can be considered as zero for polar winter conditions but with a standard deviation between 12° and 23°. In polar summer, wind direction bias can reach 20° (in absolute value) with a very strong standard deviation greater than 60°. During summer in the polar region the wind speed is small (see Fig. 1) with a meridional component very close to zero. Thus, even a slight bias on u or υ leads to a significant bias on DD.
Schroeder et al. (2009) using SABER temperature measurements evaluated the ability of the ECMWF model to resolve gravity waves at 30 km. They highlighted weaknesses of the model for representing gravity wave amplitude at high latitudes. Since most of the ZPBs attain 40 km of altitude, their trajectories reflect these small-scale perturbations in the wind circulation. The increase in the standard deviations we obtained is probably due to this weakness.
b. Equatorial flights
For equatorial flights (Figs. 9c and 9d), the ERA-Interim data are less accurate for both FF and DD than for polar flights. As seen in the previous parts, the values of u biases obtained for both QBO phase conditions rise with altitude and present maxima at different well-identified pressure levels.
For the easterly and westerly QBO phases (Fig. 9c) the wind speed is mostly underestimated by the model below 50 hPa. Above this pressure level the FF biases are successively positive and negative without exceeding ±4 m s−1 up to 15 hPa. Then for the easterly QBO phase a FF bias maximum value of −10.1 m s−1 is encountered at 10 hPa. The FF standard deviation increases with altitude with a maximum value of 5 m s−1 at 10 hPa. The strong biases previously highlighted regarding zonal wind drive the strong biases for FF. The standard deviations are between 2 and 5 m s−1 in the pressure range [15, 50] hPa, whereas in the low stratosphere they can attain 6 m s−1 and at high level more than 12 m s−1.
For the westerly QBO phase DD biases oscillate between positive and negative values with +22° at 10 hPa and −30° at 7 hPa. For the easterly QBO phase the DD biases are small (<8°) up to 10 hPa but reach −19° in the pressure range [9, 6.5] hPa. Low levels (below 32 hPa) and high levels (above 10 hPa) are characterized by high DD standard deviations that can attain 50°. For both QBO phases a layer with small DD standard deviation (lower than 10° for the easterly QBO phase) can be seen, which corresponds to the well-established zonal circulation.
These results highlight that discrepancies between ERA-Interim and observed winds appear at levels where the zonal circulation reverses (reversal of wind direction). Because the vertical gradients are strong (Fig. 1) a slight vertical shift in ERA-Interim can induce the strong biases highlighted here. Even if the models capture the main characteristics of the QBO (Baldwin and Gray 2005; Huang et al. 2012; Lehmann and Névir 2012), vertical dynamical structure changes in the equatorial stratosphere remain difficult to represent. Schroeder et al. (2009) show the poor representation in the ECMWF model of the waves generated by convection in tropical regions. As for polar winter flights, the strong biases and standard deviations we obtained very likely denote this feature.
Above the two launch bases (polar and equatorial) and for each geophysical condition considered, the biases obtained and the standard deviations increase sharply above 20 hPa (~30 km). This pressure level corresponds to the level where radiosondes burst. The lack of measurements in the high stratosphere is probably responsible for the low quality of the wind from ERA-Interim at high altitude. Le Pichon et al. (2015) highlight an increase in biases as a function of altitude above 40 km in the middle atmosphere using WIRA measurements. Baron et al. (2013) showed negative bias values in the middle equatorial stratosphere on the zonal component and strong positive values in the mesosphere. Combining these findings with our study, it appears that after a decrease in the wind biases above the tropopause (Dee et al. 2011), in the stratosphere (this study) up to the mesosphere (Le Pichon et al. 2015; Baron et al. 2013), the wind biases increase as well as the standard deviations.
The lack of wind measurements in the middle and high stratosphere means that models have to extrapolate fields in these regions or have to use the brightness temperatures measured by satellite to deduce the geostrophic wind (Rüfenacht et al. 2012; Baron et al. 2013). However, this approximation breaks down owing to strong wave activity especially in the tropics where the Coriolis parameter vanishes (Žagar et al. 2004; Polavarapu et al. 2005, Schroeder et al. 2009) but also in the polar region as shown by Ern et al. (2016).
5. Conclusions
We have retrieved wind profiles in the stratosphere using trajectories from zero-pressure balloons launched in polar and equatorial regions (above Esrange, Sweden, and Teresina, Brazil, respectively) between 2000 and 2011. The dataset obtained provides unique in situ measurements in the midstratosphere up to 2 hPa. This dataset has been used to assess ERA-Interim through a methodology designed for studying wind biases and standard deviations as a function of pressure. In addition we consider two types of pressure intervals (with thicknesses of roughly 3.5 and 10 km) to discuss the most suitable vertical resolution to evaluate the model results.
ERA-Interim presents relatively small biases for zonal and meridional wind components in the lower stratosphere during winter above the polar launch base. These results are consistent with those of H2004 obtained with ECMWF analysis at a specific pressure range for the 2002 polar vortex condition. This result attests the good quality of ERA-Interim in the lower stratosphere and the slight underestimation of the zonal wind and the wind speed at high levels above 20 hPa by ERA-Interim. The standard deviations obtained increase with altitude above 20 hPa up to 4 m s−1 for the zonal and meridional components. They are greater for the wind speed during winter (6 m s−1) than during summer (4 m s−1). Wind direction in the polar summer condition appears to be considerably more variable in the observed winds than in the model with a standard deviation reaching 80° at 5 hPa. Because of the small wind intensity during summer, a small bias on wind components induces a strong standard deviation on wind direction.
The equatorial results revealed a much larger wind bias. The largest differences can exceed 50% where/when the QBO phase changes. In addition in the event of complex vertical variations in the zonal circulation such as QBO, the zonal wind biases are very sensitive to the vertical resolution considered. They are underestimated with a vertical resolution close to 10 km compared to results with a resolution close to 3.5 km. For both wind components the standard deviations are maxima at high altitude (up to 10 m s−1).
Our study highlights that ERA-Interim underestimates the stratospheric wind speed whatever the geophysical conditions (albeit to a lesser degree in the polar region than in the equatorial region). As a result the variability of both wind components and wind speed observed are not well represented by ERA-Interim, especially at high levels above 20 hPa or in the QBO regime (complex vertical dynamical structure). Given that winds are modulated by gravity waves (with amplitude increasing with altitude), the model appears to encounter difficulties in representing small-scale wave activities.
This study was initiated by the DEDALE working group at the Centre National d’Etudes Spatiales (CNES), including links with the CSTB committee (http://www.lmd.polytechnique.fr/cstb/), INSU/CNRS, CNES, and the ARISE project, funded by the H2020 European Commission. We particularly thank Thien Lam-Trong for his initial support. This study was funded by the French Research Ministry, the Ecole Doctorale (EMSTU) of the Université d’Orléans (Ph.D. grant). The Region Centre, the Labex VOLTAIRE (ANR-10-LABX-100-01), and SPARC/WMO (http://www.sparc-climate.org/) contributed to the diffusion of the results at various conferences. We thank the CNES balloon direction for providing the raw balloon trajectory files and Institut Pierre Simon Laplace (IPSL) for access to the ERA-Interim data. We thank all members of the CNES balloon launching team for their commitment during campaigns in the last two decades. We would also like to thank the two anonymous reviewers for their comments, which resulted in a greatly improved paper.
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