1. Introduction
Gravity waves (GWs) play a crucial role in the middle atmosphere. They propagate vertically away from their tropospheric sources (i.e., topography, convection, fronts, and unbalanced jets) and force the mean flow in the middle atmosphere when they dissipate because of critical levels or density effects. In particular, the deposition of GW momentum flux closes the jet in the mesosphere (Andrews et al. 1987). GWs also force the stratospheric circulation, like the quasi-biennial oscillation in the tropics (Baldwin et al. 2001). Their intrinsic frequency range being bounded by the planetary vorticity f and the buoyancy frequency N, they usually occur on relatively small scales from a few to hundreds of kilometers (Fritts and Alexander 2003). Therefore, since they have scales smaller than the typical resolvable scales by the climate models (500–1000 km) their effects need to be represented by parameterizations.
Parameterizations generally distinguish two main types of GWs at midlatitudes: the orographic gravity waves (OGWs), which are excited by the topography, and nonorographic gravity waves (NOGWs) emitted by frontal systems and unbalanced jets (Plougonven and Zhang 2014) or by convection. OGWs and NOGWs show different physical properties (quasi stationary versus nonstationary). Unlike the OGWs for which the sources are known, NOGWs lack observational constraints and physical understanding and their sources are consequently represented arbitrarily and tuned in the NOGW parameterizations. The discrepancies in these parameterizations lead to uncertainties in the simulation of the middle atmosphere, and one of the main motivation for studying GWs is thus to provide constraints for their parameterizations (Alexander et al. 2010).
Improving the current parameterizations necessitates obtaining GW characteristics from observations and simulations (Alexander et al. 2010). Superpressure balloon (SPB) flights constitute unique datasets well adapted to study GWs because they provide in situ observations in the framework moving with the mean flow. Thus, it is possible to observe directly all characteristics of the GW field, in particular their intrinsic frequencies. During the Concordiasi campaign (Rabier et al. 2010), 18 SPBs were launched during the austral spring 2010/11 from the McMurdo station in Antarctica. Each balloon flew in the lower stratosphere at 19–20-km altitude for durations of 3 months typically, performing measurements of position, altitude, pressure, and temperature with a frequency of 30 s−1. The time resolution was increased relative to previous campaigns (15 min−1) (Hertzog et al. 2007) and allows observation of the entire GW spectrum. Hence, this campaign provides an unprecedented dataset for the study of GWs in the austral lower stratosphere and complements the climatology derived by Hertzog et al. (2008).
Because of the recent increase in spatial resolution (0.125° horizontally and 91 vertical levels) in the European Centre for Medium Range Forecasts (ECMWF) operational model, as well as improvements of parameterizations (Orr et al. 2010), dynamical core, and data assimilation systems, studies are beginning to examine the realism of the GW in ECMWF analyses by comparison to observations (Eckermann et al. 2006; Alexander and Teitelbaum 2007; Wu and Eckermann 2008; Ern et al. 2008; Schroeder et al. 2009). Plougonven and Teitelbaum (2003) compared the characteristics of inertio-gravity waves (IGWs) derived from radio soundings from the FASTEX campaign and the ECMWF analyses. Their results suggested that the ECMWF analyses can be used for qualitative indications on the location and time of generation of large-scale IGWs. Alexander and Teitelbaum (2007) analyzed a case study of large-amplitude mountain wave event that occurred over the Antarctic Peninsula on 10 September 2003 using measurements from the Atmospheric Infrared Sounder (AIRS) on the Aqua satellite and the ECMWF forecasts and analyses. They found similar properties between AIRS and the ECMWF in general with correct agreement on horizontal and vertical wavelengths, propagation direction, wave amplitude, and approximate timing of the event. Moreover, they checked and did not find significant differences between the fields in the ECMWF forecasts and analyses. Wu and Eckermann (2008) compared the GW variances obtained from the Microwave Limb Sounder (MLS) on the Aura satellite to the waves in the ECMWF model. They observed similar enhanced GW variances over regions with large background wind speeds and over regions with topographic and convective forcing. Ern et al. (2008) and Schroeder et al. (2009) have compared temperature variances attributed to GW in the infrared limb sounder instrument, Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER), and the ECMWF analyses. The minimum resolvable horizontal and vertical wavelengths for SABER are ~400 and ~4.5 km, respectively (Geller et al. 2013), therefore resolving a smaller portion of GW than the ECMWF. They found a good agreement for OGWs (emitted by the southern tip of the Andes and Scandinavia) and for NOGWs near the edge of the winter polar vortex. However, they noted significant low biases on the amplitude of the waves by a factor of 2–3. Shutts and Vosper (2011) compared estimates from High Resolution Dynamics Limb Sounder (HIRDLS) measurements with those derived from the ECMWF and concluded that the ECMWF is capable of capturing the overall strength and distribution of GW activity. More recently, Preusse et al. (2014) have analyzed the sources of GWs using backward ray tracing in the ECMWF to discriminate between orographic and convective effects, assuming the validity of the simulated fields a priori. Those studies suggest a potential for various observations to investigate the realism of the ECMWF GW field and validate the model. Such GW validation in the ECMWF operational analyses is arguably needed as the community using the mesoscale information in these meteorological products is increasing. GW field in operational analyses may furthermore provide in the near future a reference used to tune GW drag (GWD) parameterizations in lower-resolution climate models so as to reduce biases associated with GW effects in these models. Among those biases, Butchart et al. (2011) considers particularly challenging those associated with the springtime breakup of the polar vortex in both hemispheres and the generally poor performance of climate models in the Southern Hemisphere. McLandress et al. (2012) addressed the issue of the delayed springtime vortex breakdown and attribute the climate model deficiencies to missing GWD at 60°S. While not fully discarding nonorographic GWD (NOGWD) effects in their study, they suggest that one likely cause for this missing drag may be associated with OGW generated by islands located near 60°S in the Southern Ocean, which are not treated as land in the model because of their subgrid size (Alexander et al. 2009). Alexander et al. (2009) and Alexander and Grimsdell (2013) specifically investigated the island contribution and concluded that this contribution could actually represent a significant portion of the missing drag in these regions, yet likely not the whole of it. On the other hand, Hendricks et al. (2014) used ECMWF products and AIRS observations to provide evidence that identify NOGWs as a major source of GWs in winter over the Southern Ocean. Another potential effect that may contribute to this missing drag is the meridional propagation of lower-latitude gravity waves into the stratospheric jet core located at 60°S (Sato et al. 2009), which is ignored in GWD parameterizations where waves are assumed to only propagate vertically.
Hence, our goals in the present study are 1) to compare the GW in the ECMWF analyses to in situ observations from SPBs during the Concordiasi campaign (Rabier et al. 2010) to estimate the realism of the wave field in the ECMWF operational fields and 2) use those datasets to provide a climatology of the momentum fluxes over the austral regions including Antarctica and the oceans, quantify the seasonal variations, distinguish the OGWs from the NOGWs, and quantify their intermittency. In doing so, we take benefit of the very high resolution of the ECMWF model and will thus only focus on the resolved waves in the ECMWF analyses. In particular, our goal is not to assess the total GW forcing in the ECMWF model, which includes parameterized waves. 3) Finally, we use the Concordiasi observations to provide elements to revisit McLandress et al.’s (2012) conclusions on the source of the missing GWD to interpret the systematic biases in the Southern Hemisphere stratosphere in models.
The paper is organized as follows: In section 2, we describe the Concordiasi and the ECMWF datasets and the methodology to calculate the momentum fluxes. In Section 3, we describe the global comparison between the ECMWF and Concordiasi and identify the hot spots of GW, then we investigate the seasonal and regional variability. We present a comparison on two case studies of OGWs and NOGWs and provide a validation of the model for those events. Sections 5 and 6 provide a discussion of our results and our conclusions.
2. Data and methodology
a. Stratospheric superpressure balloons from the Concordiasi campaign
During the Concordiasi field campaign (Rabier et al. 2010), 18 long-duration stratospheric SPBs were launched from August to September 2010 from the McMurdo station (78°S, 166°E) in Antarctica by the Centre National d’Etudes Spatiales (CNES, the French space agency). Those balloons drift on isopycnic surfaces and the collected dataset is aimed at studying the circulation and chemical species in the lower stratosphere. In particular, measurements of pressure and temperature were retrieved by the Thermodynamic Sensor (TSEN) meteorological package aboard the balloons, while the wind was calculated using the successive positions of the balloon throughout the flight measured by GPS. Each balloon flew for a typical period of 3 months in the lower stratosphere at typical altitudes of 19–20 km (50–70 hPa). The density of measurements is high enough to sample numerous GW events and derive climatologies for the southern austral regions. The SPBs retrieve all the characteristics of the GWs in the referential moving with the mean flow, at high frequency (the sampling period is 30 s) and for a wide temporal and spatial coverage, therefore they constitute a unique and well adapted dataset to study the GWs.
b. ECMWF operational analyses
We use the ECMWF analyses available four times a day (0000, 0006, 1200, and 1800 UTC) that result from the four-dimensional variational data assimilation (4D-Var) operational system (Rabier et al. 2000; Mahfouf and Rabier 2000; Klinker et al. 2000) and provide the initial atmospheric conditions for the 10-day lead time deterministic operational forecasts. The model has a T1279 spectral truncation that corresponds to a horizontal resolution of 0.125° × 0.125° of longitude and latitude—that is, an approximate grid spacing of 16 km and 91 vertical model levels corresponding to about a 500-m vertical grid spacing (137 as of 2013), with an increased resolution near the surface. In addition, the GWs in the ECMWF are divided in a parameterized part and explicit part. The finite resolution of the ECMWF model contains the minimum resolvable GW scales in the simulation: typically 6Δx ~ 80 km horizontally and a few kilometers vertically. Thus, it is expected that the fluxes in the ECMWF underestimate those from the observations since the model only describes, at best, waves with horizontal wavelengths larger than 80 km, whereas the balloons observe the full spectrum of GW.
c. Calculation of momentum fluxes and Gini coefficients
The methodology described in Boccara et al. (2008) and updated to the increased sampling in time and in the resolution of measurements (Vincent and Hertzog 2014) was applied to the balloon observations of pressure, zonal, and meridional velocities to estimate the vertical total momentum fluxes. A wavelet analysis is applied to select the disturbances solely induced by GWs, and the momentum fluxes are obtained by calculation of the cospectra. In contrast with previous studies using the Vorcore dataset (Plougonven et al. 2013), the increased sampling (one observation every 30 s) allows us to apply our analysis to the entire GW spectrum.
In the ECMWF analyses, the velocity perturbations are obtained by removing the atmospheric base state defined by the 15 first zonal modes from the total velocity fields using spectral truncation. The density and the local correlation between horizontal and vertical components (i.e., u′w′) are then calculated to yield the vertical total momentum fluxes. Note that, since the calculation of the fluxes in the ECMWF analyses involve velocity perturbations, those fluxes correspond to the resolved GWs in the model.
To quantify the intermittency of the momentum fluxes, calculations of the Gini coefficient (Gini 1955) is done. For the Concordiasi observations, the wavelet analysis directly provides a wave packet average, and hence this is done directly on the momentum-flux time series. That is not the case for the ECMWF fluxes, thus we average the fluxes on a 2.5° grid (i.e., 3 times the minimum resolvable wavelength) in order to obtain wavepacket-averaged fluxes (i.e., 
3. Overall comparison between the ECMWF analyses and the Concordiasi observations
Our goal in this section is to compare the GW field in the ECWMF and in the Concordiasi balloon observations. We chose to compare quantities relevant for modeling and parameterizations—that is, momentum fluxes and intermittency (Alexander et al. 2010; Hertzog et al. 2012). First, we aim to verify whether the GW momentum fluxes and spatial repartition agree overall. Second, we examine the intermittency of the momentum fluxes and their seasonal evolution from September 2010 to January 2011.
a. Comparison of momentum fluxes
The GW momentum fluxes derived from the balloon observations and in the ECMWF analyses at 70 hPa, averaged over the period September 2010–January 2011, are shown in Fig. 1. To provide a field that can be compared to the observations, the location of the balloons at each time step needs to be taken into account so as to sample the same wave events in the ECMWF analyses. The figure has been split into four panels representing the ECMWF momentum fluxes with native resolution (0.125°; Fig. 1a), the ECMWF fluxes averaged to a horizontal resolution of 2.5° (Fig. 1b), the ECMWF fluxes (multiplied by 5) taking into account the balloon sampling (Fig. 1c), and the fluxes from the Concordiasi balloons (Fig. 1d). We have chosen to rescale the momentum fluxes in the ECMWF by a factor of 5 in order to compare fields that have approximately the same mean as in the observations. We use a logarithmic color scale to handle the large variety of momentum-flux amplitudes that arise in the datasets. For example, the mean value of the flux in Concordiasi and the ECMWF respectively are 9 and 1.8 mPa, with local values as high as 150 mPa. Note that we have also multiplied the momentum fluxes in Fig. 1c by 5 so that the ECMWF has the same mean value visually as the observations. The remarkable features for the GW momentum fluxes are the following:
The hot spots of gravity waves are clearly revealed in the ECMWF analyses with full resolution (Fig. 1a): topography (Andes, Antarctic Peninsula, Transantarctic Mountains, small islands in the Southern Ocean, New Zealand, and Tasmania) with typical values of approximately 100 mPa (peninsula), coasts and islands with values approximately 10 mPa and over oceans (denoting fronts and jets) with typical values slightly below 10 mPa.
We observe a severe discrepancy on the magnitude of the momentum fluxes in the ECMWF: the model underestimates them on average by a factor of 5. We will show later that this underestimation in the ECMWF is likely related to the spectral truncation in the model and numerical (implicit or explicit) diffusion.
We remark a correct agreement overall on the spatial structure of the GW momentum fluxes, but for the contrast between the Antarctic plateau and the rest (mountains and ocean), which is stronger in the ECMWF than in Concordiasi. To illustrate that contrast, the ratio of the mean fluxes for regions located north of 75°S to that for regions south of 75°S calculated in the ECMWF and the observations yields factors of 6 and 2, respectively. Thus, the difference is a factor of 3. The only major discrepancies are Transantarctic Mountains that do not show up in the ECMWF after applying the Concordiasi sampling. The factor of 5 is valid over the oceanic regions but leads to an overestimation of the fluxes in the ECMWF over the mountains (Andes and Antarctic Peninsula). This allows an investigation of the sampling of the balloon campaign. In contrast with the ECMWF fluxes at full resolution, the structures over the oceans (high activity from the Lazarev Sea to the Somov Sea located in the latitude band of 60°–45°S, and weaker activity in the Amunsen Sea and Weddell Sea) are difficult to identify with the balloon sampling in ECMWF and in the balloon measurements. This reveals that we do not have enough measurements for those regions.
Time-averaged momentum fluxes (a)–(c) from the ECMWF analyses and (d) from the Concordiasi observations at 19 km. The ECMWF fluxes are shown (a) with full resolution, (b) averaged on the same grid as the Concordiasi data, and (c) sampled at the same times as the Concordiasi balloons. The ECMWF fluxes represented in (c) have been multiplied by 5.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Time-averaged momentum fluxes (a)–(c) from the ECMWF analyses and (d) from the Concordiasi observations at 19 km. The ECMWF fluxes are shown (a) with full resolution, (b) averaged on the same grid as the Concordiasi data, and (c) sampled at the same times as the Concordiasi balloons. The ECMWF fluxes represented in (c) have been multiplied by 5.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Time-averaged momentum fluxes (a)–(c) from the ECMWF analyses and (d) from the Concordiasi observations at 19 km. The ECMWF fluxes are shown (a) with full resolution, (b) averaged on the same grid as the Concordiasi data, and (c) sampled at the same times as the Concordiasi balloons. The ECMWF fluxes represented in (c) have been multiplied by 5.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
b. Intermittency
We have seen in the previous section that mean GW momentum fluxes vary significantly spatially. Their amplitudes also fluctuate rapidly in time about their mean values, revealing their intermittent behavior. Quantifying this intermittency is necessary to give a realistic picture of the GWs in model parameterizations. A good tool to examine the intermittency is to use momentum-flux probability density functions (PDFs) as in previous studies (Plougonven et al. 2013; Hertzog et al. 2012; Jewtoukoff et al. 2013). In this section, ECMWF PDFs are calculated on the native ECMWF high-resolution grid.
Figure 2b shows the PDF of absolute momentum fluxes calculated in the ECMWF (thick lines) and derived from the Concordiasi observations (thin lines) for the peninsula and the oceanic regions depicted in Fig. 2a. The peninsula is representative of the regions with the OGW events, whereas the ocean regions devoid of (and far from) any topography are associated mainly with NOGWs. The PDFs from ECMWF and Concordiasi exhibit long tails that account for highly intermittent GWs (Hertzog et al. 2012) and are consistent with the momentum fluxes time evolution (not shown) that oscillates between weak fluxes (<10 mPa) and rare intense events where the fluxes exceed 500 mPa locally (in Concordiasi). The PDFs in the ECMWF and Concordiasi are very similar in shape, irrespective of their different means. The PDFs, over mountains and oceans, are almost indistinguishable for fluxes smaller than 10 mPa in the ECMWF and 20 mPa in Concordiasi. For larger fluxes (>40 mPa), the contrast between OGWs and NOGWs increases with a decrease in the frequency of large nonorographic events. For the larger values of momentum fluxes, occurrence frequency over mountains remains approximately one order of magnitude bigger than that over oceans. Moreover, calculations of the 90th percentiles show that 72% and 43% of the total flux are due to the 10% largest GW events over topography and smooth terrain respectively in the ECMWF. In Concordiasi, they account for 64% and 29% of the flux over mountains and oceans. In accordance, calculation of the Gini coefficient yields values of 0.6 and 0.5 for OGWs and NOGWs momentum fluxes respectively. Hence, this results in more occurrences of larger fluxes over mountains than over smooth terrain, which is consistent with the findings of Hertzog et al. (2012).
(a) Map denoting the mountain (black) and ocean (red) regions and (b) regional PDFs of the momentum fluxes in ECMWF (at 19 km) and in Concordiasi.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
(a) Map denoting the mountain (black) and ocean (red) regions and (b) regional PDFs of the momentum fluxes in ECMWF (at 19 km) and in Concordiasi.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
(a) Map denoting the mountain (black) and ocean (red) regions and (b) regional PDFs of the momentum fluxes in ECMWF (at 19 km) and in Concordiasi.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
c. Time and spatial variability of the GW fluxes and their intermittency
We mentioned earlier the importance of quantifying time and spatial variations of the GW momentum fluxes to take this variability into account in the parameterizations. In the previous section we have examined the geographical distribution of the wave fluxes averaged over the Concordiasi time period, and we now focus on the time evolution of these fluxes.
Figure 3 (left panel) displays the monthly averaged GW momentum fluxes calculated in the ECMWF at full resolution from September to December 2010. As for the mean fluxes, applying the balloon sampling in ECMWF analyses and multiplying the ECMWF fluxes by a factor of 5 enables us to obtain a good agreement with the balloonborne monthly averaged momentum fluxes. Still, once again, it is found that ECMWF tends to underestimate the wave fluxes over the Antarctic Plateau and Amundsen Sea. The maps notably highlight a continuous decrease in GW activity in the polar lower stratosphere throughout this 4-month period. In ECMWF and Concordiasi, the decrease of 85%–90% in momentum flux over the peninsula (see Table 1) from November to December is particularly striking, compared to the 20%–30% decrease of NOGW fluxes for the same period. We have also represented the monthly averaged isotachs at 70 hPa on the different panels of Fig. 3 to identify the lower-stratospheric jets. They provide first evidence that the decrease seen in both NOGW and OGW may be related to the weakening of the lower-stratospheric winds when entering the Southern Hemisphere summer in December.
Monthly averaged momentum fluxes at 19 km from (left) ECMWF, (center) ECMWF with the balloon sampling (multiplied by 5), and (right) Concordiasi, for September, October, November, and December. The black contours in (left) represent isotachs at 19 km with increments of 15 m s−1.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Monthly averaged momentum fluxes at 19 km from (left) ECMWF, (center) ECMWF with the balloon sampling (multiplied by 5), and (right) Concordiasi, for September, October, November, and December. The black contours in (left) represent isotachs at 19 km with increments of 15 m s−1.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Monthly averaged momentum fluxes at 19 km from (left) ECMWF, (center) ECMWF with the balloon sampling (multiplied by 5), and (right) Concordiasi, for September, October, November, and December. The black contours in (left) represent isotachs at 19 km with increments of 15 m s−1.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Monthly means 
This is furthermore confirmed in Fig. 4, which displays the monthly mean wave fluxes in ECMWF from October to December and from 10- to 40-km altitude. The momentum fluxes do not show significant variability from October to December in the upper troposphere, so that the variability of the source intensity does not seem to be the main factor explaining the decrease of wave fluxes in the lower stratosphere (20-km altitude). On the other hand, the weakening of the zonal-mean zonal wind over the ocean represented in Fig. 5 from the upper troposphere and throughout the stratosphere is obvious during this time period. But we also note the most dramatic decrease of the wave fluxes occur at 30 km and above from November on. This altitude and time period also correspond to the progressive reversal of the stratospheric jet and the associated strong shear. This evidence therefore suggests that the filtering of relatively low phase speed GWs by the background wind is essentially driving the wave fluxes in the polar stratosphere.
Monthly averaged ECMWF momentum fluxes at 10-, 20-, 30-, and 40-km altitude for October, November, and December.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Monthly averaged ECMWF momentum fluxes at 10-, 20-, 30-, and 40-km altitude for October, November, and December.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Monthly averaged ECMWF momentum fluxes at 10-, 20-, 30-, and 40-km altitude for October, November, and December.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Vertical profiles of the zonal-mean zonal wind over the ocean for October (black), November (red), and December (blue).
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Vertical profiles of the zonal-mean zonal wind over the ocean for October (black), November (red), and December (blue).
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Vertical profiles of the zonal-mean zonal wind over the ocean for October (black), November (red), and December (blue).
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
We have finally represented the PDFs of the GW fluxes averaged over each month during the entire Concordiasi period in Fig. 6, distinguishing the contributions from OGWs and NOGWs using the regions as in Fig. 2a. The balloon sampling is obviously very limited in September as the balloons are progressively released from the launching base and, in December, at the end of the flights. However despite this issue, the balloonborne and ECMWF PDFs reproduce the same robust seasonal variability than that depicted in Fig. 3, with a monthly decrease of the mean momentum fluxes in time, illustrated by the disappearance of the PDF tails in December. This decrease of the tails also reveals a drop in intermittency with a minimum for the OGW momentum fluxes in December. This is consistent with the weakening of the wind at 19–20 km of altitude during this period that filters out GWs with lower phase speeds, which carry the largest portion of momentum flux. Yet, the ECMWF PDFs show again a significantly smaller contrast between OGWs and NOGWs than that in the balloon observations. We also note that the PDF above oceans show less variability than those above mountains, which is also evidenced by the calculation of the 90th percentile. In October, the amount of GW activity explained by the 10% largest events reduces from 79% to 52% for OGWs in December in the ECMWF, while it is only reduced from 45% to 41% for NOGWs. In the Concordiasi observations, the OGW value reduces from 64% to 26%, and the NOGW value reduces from 31% to 27%. Values of the Gini coefficient (see Table 1) are consistent with this observed decrease in intermittency from October throughout December. Nonetheless, Gini coefficients from the ECMWF are usually larger than those derived from the observations by 25% for the NOGWs on (spatial) average, suggesting a possible effect of the balloon sampling.
Monthly PDFs of the ECMWF and Concordiasi momentum fluxes by regions for (a) September, (b) October, (c) November, and (d) December.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Monthly PDFs of the ECMWF and Concordiasi momentum fluxes by regions for (a) September, (b) October, (c) November, and (d) December.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Monthly PDFs of the ECMWF and Concordiasi momentum fluxes by regions for (a) September, (b) October, (c) November, and (d) December.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
4. Case studies
Case studies of large OGW and NOGW localized events are presented in this section to assess the realism of the individual wave episodes in the ECMWF and compare to the balloon observations. The synoptic meteorological conditions are presented using the ECMWF analyses, and the mean spatial distribution of momentum fluxes and their magnitude are compared to Concordiasi for each case.
a. OGW event: 8–11 October 2010
The synoptic meteorological situation for 1200 UTC 9 October 2010 is illustrated in Fig. 7. At midlevels, the situation consists in a large cyclone west of the peninsula and rather weak winds over the peninsula. The upper-air analysis depicts a jet exit region at the tropopause in the lee of the southern Andes and the peninsula. Given the spatial distribution of the fluxes, we assume that the observed waves are generated by the flow over the peninsula mountain range.
(a) Map showing the balloon trajectories between 8 and 11 Oct 2010, (b) map of vertical vorticity at the surface (shaded contours) and height of the 500-hPa geopotential surface (black contours; one contour every 100 m), and (c) map of vertical vorticity (shaded contours) and isotachs (black contours; one contour every 15 m s−1, starting at 15 m s−1) on the 200-hPa isobaric surface (i.e., near the tropopause); (b),(c) are valid 1200 UTC 9 Oct.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
(a) Map showing the balloon trajectories between 8 and 11 Oct 2010, (b) map of vertical vorticity at the surface (shaded contours) and height of the 500-hPa geopotential surface (black contours; one contour every 100 m), and (c) map of vertical vorticity (shaded contours) and isotachs (black contours; one contour every 15 m s−1, starting at 15 m s−1) on the 200-hPa isobaric surface (i.e., near the tropopause); (b),(c) are valid 1200 UTC 9 Oct.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
(a) Map showing the balloon trajectories between 8 and 11 Oct 2010, (b) map of vertical vorticity at the surface (shaded contours) and height of the 500-hPa geopotential surface (black contours; one contour every 100 m), and (c) map of vertical vorticity (shaded contours) and isotachs (black contours; one contour every 15 m s−1, starting at 15 m s−1) on the 200-hPa isobaric surface (i.e., near the tropopause); (b),(c) are valid 1200 UTC 9 Oct.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
The maps of mean momentum fluxes are displayed in Fig. 8 and represent the ECMWF fluxes (Fig. 8a) at full resolution, fluxes with the balloon sampling (multiplied by 5; Fig. 8b), and the fluxes derived from Concordiasi (Fig. 8c). The GW fluxes calculated in the ECMWF with native resolution denote large OGW events generated by the Andes and the peninsula with local values as high as 100 mPa and smaller values over the ocean in their lee in the region 50°–20°W. We note a connection between the activity upstream (~20 mPa) and over the peninsula (~80 mPa). The geographical distribution of the large values of GW momentum fluxes (>30 mPa) agree very well in the ECMWF and Concordiasi. Over the oceans, general regions with fluxes between 10 and 50 mPa within the 55°–65°S band coincide, but identifying structures clearly is still difficult owing to the balloon sampling, as previously. On the other hand, the contrast between the peninsula and continental Antarctica (south of 75°S) is higher for the ECMWF than for Concordiasi. The mean value of the momentum flux for the region shown in Fig. 8 is 19.8 mPa in Concordiasi.
Time-averaged momentum fluxes for the period 8–11 Oct 2010 (a),(b) from ECMWF analyses and (c) from Concordiasi observations at 19 km. The ECMWF fluxes are shown (a) with full resolution and (b) sampled at the same times as the Concordiasi balloons. The ECMWF fluxes represented in (b) have been multiplied by 5.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Time-averaged momentum fluxes for the period 8–11 Oct 2010 (a),(b) from ECMWF analyses and (c) from Concordiasi observations at 19 km. The ECMWF fluxes are shown (a) with full resolution and (b) sampled at the same times as the Concordiasi balloons. The ECMWF fluxes represented in (b) have been multiplied by 5.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Time-averaged momentum fluxes for the period 8–11 Oct 2010 (a),(b) from ECMWF analyses and (c) from Concordiasi observations at 19 km. The ECMWF fluxes are shown (a) with full resolution and (b) sampled at the same times as the Concordiasi balloons. The ECMWF fluxes represented in (b) have been multiplied by 5.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
b. NOGW event: 21–24 October 2010
On 1200 UTC 22 October 2010 the meteorological situation consisted of a surface front oriented meridionally at 0°–10°E, a longwave trough at midlevels (Fig. 9b), and a relatively strong jet at the tropopause that intercepts the peninsula (Fig. 9c). The balloons were flying above the peninsula and rather close to the shore in the Southern Ocean, observing this intense OGW episode and the high momentum fluxes in the lee of the mountains and also farther above the ocean (Fig. 9a).
As in Fig. 7, but for the period 21–24 Oct 2010. (b),(c) Valid 1200 UTC 22 Oct.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
As in Fig. 7, but for the period 21–24 Oct 2010. (b),(c) Valid 1200 UTC 22 Oct.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
As in Fig. 7, but for the period 21–24 Oct 2010. (b),(c) Valid 1200 UTC 22 Oct.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
The momentum fluxes in the ECMWF with full resolution depicted in Fig. 10a show a region with high values (~100 mPa) in the vicinity of the peninsula and a larger region with smaller values within a range of 10–50 mPa over the Southern Ocean collocated with the tropopause jet between 0° and 30°W, disconnected from the activity above the peninsula (in contrast with the first case) and thus likely associated with NOGWs. We focus on that particular wave packet here. The spatial distributions show a fair agreement on the location of the high values of the flux, although not as good as for the previous case. The observed fluxes are smaller (10–30 mPa) than those for OGWs (~100 mPa) but cover a wider area (region 60°–70°S, 0°–40°E versus region 60°–70°S, 50°–70°W). The activity is collocated with the edge of the jet at the tropopause located at 60°S. The factor of 5 used here for the ECMWF slightly overestimates the values over the ocean. Once again, we note the large contrast between ocean and plateau in the ECMWF data. The mean value of the momentum flux (8.7 mPa) is smaller than for the first case by a factor of 2, owing to NOGW momentum fluxes that are weaker locally than OGWs in general.
As in Fig. 8, but for the period 21–24 Oct 2010.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
As in Fig. 8, but for the period 21–24 Oct 2010.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
As in Fig. 8, but for the period 21–24 Oct 2010.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
5. Discussion
Momentum fluxes derived from the ECMWF analyses and the Concordiasi observations compare fairly well for geographic and time distributions, but yield a difference by a factor of 5 for their mean amplitude. In this section, we discuss this difference and compare our values to those found in previous studies. Finally, the issue of the missing drag is revisited in the last part of the section.
a. Gravity waves in ECMWF analyses
We now examine an issue related to the use of the ECMWF analyses for gravity wave study—that is, the fact that resolved GWs may be modified during the assimilation process, or that spurious waves may be generated during the assimilation cycle. For this, we have compared the fluxes at 20 km for October in the analyses and in the 24-h forecasts. Maps of momentum fluxes from ECMWF analyses and forecasts are nearly indistinguishable (not shown). Similar values of domain-averaged, monthly mean momentum fluxes were found (respectively 2.5 and 2.3 mPa for the analyses and forecasts, suggesting that the impact of assimilation on the GW field is not a major concern).
Another issue is related to the simplified topography used in the ECMWF model. To keep time integration stable, model topography is spectrally fitted to ensure consistency between orography and model resolution. For instance, in the ECMWF model, the maximum heights of South Georgia and Heard Islands are approximately 2000 m lower than in reality. Hence, it is expected that the model underestimates orographic gravity waves, especially from small-scale obstacles like the islands. This is why we did not emphasize the relative weight of the OGWs generated by the islands represented in Fig. 11b and relied on the balloon observations for their estimation.
Zonal mean of the momentum fluxes for October 2010 at 70 hPa (a) from the Concordiasi observations and (b) from the ECMWF analyses. The thick black bar represents an estimation of the uncertainty resulting from the uneven balloon sampling. We have also overlaid the parameterized momentum flux from LMDZ [using the setup as in Lott and Guez (2013)] in gray on the observations. Islands denote the region with small isolated islands located in the 55°–60°S latitude band [region 3 in Plougonven et al. (2013)’s Fig. 5]. Note the different scales for the momentum fluxes. The difference between the blue curve and the sum of the red and black curves corresponds to waves generated above mainland orography (Andes and Antarctic Peninsula).
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Zonal mean of the momentum fluxes for October 2010 at 70 hPa (a) from the Concordiasi observations and (b) from the ECMWF analyses. The thick black bar represents an estimation of the uncertainty resulting from the uneven balloon sampling. We have also overlaid the parameterized momentum flux from LMDZ [using the setup as in Lott and Guez (2013)] in gray on the observations. Islands denote the region with small isolated islands located in the 55°–60°S latitude band [region 3 in Plougonven et al. (2013)’s Fig. 5]. Note the different scales for the momentum fluxes. The difference between the blue curve and the sum of the red and black curves corresponds to waves generated above mainland orography (Andes and Antarctic Peninsula).
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Zonal mean of the momentum fluxes for October 2010 at 70 hPa (a) from the Concordiasi observations and (b) from the ECMWF analyses. The thick black bar represents an estimation of the uncertainty resulting from the uneven balloon sampling. We have also overlaid the parameterized momentum flux from LMDZ [using the setup as in Lott and Guez (2013)] in gray on the observations. Islands denote the region with small isolated islands located in the 55°–60°S latitude band [region 3 in Plougonven et al. (2013)’s Fig. 5]. Note the different scales for the momentum fluxes. The difference between the blue curve and the sum of the red and black curves corresponds to waves generated above mainland orography (Andes and Antarctic Peninsula).
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
b. Comparison between Concordiasi and Vorcore
Thus, spectral truncation explains a factor of 2, while differences in sampling and interannual variability likely account for the rest. Hence the differences between our present estimate and the previous one from Vorcore are consistent with limitations due to the resolution and the uncertainty tied to sampling and interannual variability.
c. On the missing drag near 60°S
We now revisit an issue discussed by McLandress et al. (2012): an important bias of the chemistry–climate models (CCMs) is the delay in the springtime breakdown of the stratospheric polar vortex (Eyring et al. 2010; Butchart et al. 2010). Using analyses increments, McLandress et al. (2012) state that this bias arises primarily because missing GWD at 60°S cannot act to decelerate the stratospheric jet. It is unclear whether resolved or parameterized GW are concerned (Eyring et al. 2010), but the fact that there is insufficient GWD in the Southern Hemisphere stratosphere in winter and spring represents a general consensus. The main source for this missing GWD does not.
McLandress et al. (2012) suggested that this gap in GWD was likely due to orographic GWD (OGWD) from small localized islands located at those latitudes, but they do not fully rule out NOGWD. Indeed, both effects are not well represented in GWD parameterizations; therefore, they both remain potential candidates to explain this missing drag. In an analysis of the contribution of South Georgia Island to GWs in AIRS observations, Alexander et al. (2009) suggested that OGWs may be an important missing source of drag. Alexander and Grimsdell (2013) reexamined the issue and concluded that OGWs from islands as well as horizontally propagating OGWs could partially fill the gap in drag at 60°S. Sato et al. (2012) used high-resolution simulations from a global circulation model (GCM) to characterize the GWs in the Southern Hemisphere and observed an asymmetry of the GW activity about the South Pole, with the maximum of the wave energy leeward of the southern Andes and Antarctic Peninsula. They attribute this activity to leeward advection of OGWs by the mean wind and, thus, suggest that OGWD can be present over regions devoid of topography far away from their sources. On the other hand, Hendricks et al. (2014) correlated the GW momentum fluxes in ERA-Interim to the baroclinic growth rates and high-latitude winter storm tracks, suggesting a NOGWD effect.
The Concordiasi observations are well adapted to provide elements for this discussion. The zonally averaged momentum fluxes for October calculated from Concordiasi are represented in Fig. 11a. We observe a general progressive poleward decrease of the total GW fluxes south of 72°S, consistent with satellite calculations of momentum fluxes from SABER (Geller et al. 2013). The peak at 70°–75°S here is likely associated to the Antarctic Peninsula. More relevant to the question of the missing drag are the contributions from OGWs by the islands in the 55°–60°S latitude band (black line) and the NOGWs over the ocean (red line). NOGWs peak significantly higher (16–17 mPa) than OGWs (less than 1.5 mPa). Hence, at least in our balloon dataset, the primary momentum contribution above the oceans is associated with NOGWs and clearly dominates the secondary contribution from small islands in this region. The uncertainty on the balloon-derived fluxes over the small islands related to the limited amount of measurements over these regions is detailed in the appendix, and we show that an upper bound for the flux over the islands is approximately 2.5 mPa. Our results are therefore consistent with the results of Hendricks et al. (2014). We nevertheless acknowledge that our observational data are limited temporally and only cover one single spring, and thus cannot account for any interannual variability. McLandress et al. (2012) for instance advocate using climatologies over five years. However, it would be surprising that interannual variability induces very large variations of the fluxes [say larger than a few tens of a percent; see Alexander and Grimsdell (2013)’s Fig. 4].
The zonally averaged momentum fluxes from the ECMWF are also plotted (Fig. 11b). They tend to agree with the balloon fluxes both on the shape of the fluxes north of 75°S and on the relative contributions of OGW and NOGW over the Southern Ocean. We nevertheless note that the fluxes due to small islands in ECMWF analyses may be underestimated because the island’s orography is imperfectly resolved in the model: for instance, in the ECMWF model, the maximum heights of South Georgia and Heard Islands are approximately 2000 m lower than in reality. This may contribute to an underestimation of the wave generation by the Islands in the model, although the wave fluxes are not directly proportional to the mountain height.
Another potential reason for the reported missing drag mentioned in McLandress et al. (2012) is the meridional propagation of mountain waves into the jet core (Sato et al. 2009). Hovmöller diagrams of momentum fluxes at different heights (Fig. 12) are used to provide insights into these processes. The longitude sector associated with the Antarctic Peninsula and the Andes (50°–75°W) obviously stands out in this figure and corresponds to a standing hot spot of wave activity. Yet, most of the activity above the oceans appears to be linked to propagating features that occur either upstream or downstream of this sector and are reminiscent of tropospheric disturbances. The respective contributions of the peninsula and the oceanic region to the momentum fluxes are, respectively, 2.9 and 4.3 mPa at 20-km altitude and 0.6 and 0.4 mPa at 40-km altitude. Hence, while most of the flux in the lower stratosphere at 60°S seems to be associated with nonorographic wave, the contribution of orographic and nonorographic waves is more balanced in the upper stratosphere. Still, the momentum-flux maps in October and November at 40 km (Fig. 4) highlight that the advection of orographic gravity waves are limited to the 50°–75°W longitude sector.
Hovmöller diagram of the momentum fluxes averaged within the band 65°–55°S for October and November (days), at (a) 40-, (b) 30-, and (c) 20-km altitude. The white line at 60°W longitude denotes the approximate location of the Antarctic Peninsula.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Hovmöller diagram of the momentum fluxes averaged within the band 65°–55°S for October and November (days), at (a) 40-, (b) 30-, and (c) 20-km altitude. The white line at 60°W longitude denotes the approximate location of the Antarctic Peninsula.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Hovmöller diagram of the momentum fluxes averaged within the band 65°–55°S for October and November (days), at (a) 40-, (b) 30-, and (c) 20-km altitude. The white line at 60°W longitude denotes the approximate location of the Antarctic Peninsula.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
Last, we show the parameterized fluxes in the LMDZ GCM in (Fig. 11a) (gray line) [details about parameterizations used are available in Lott and Guez (2013)]. In this model, the parameterized fluxes are typically 10 mPa weaker than the balloon fluxes equatorward of 75°S. This comparison therefore supports the McLandress et al. (2012) conclusion about the missing GW drag in climate models. Both the balloon dataset and ECMWF analyses suggest that a part of this drag is associated with NOGWs. Note that this 10-mPa difference fortuitously corresponds to the momentum flux artificially added by McLandress et al. (2012) in their OGWD parameterization (at the source level) to reduce the model biases in spring.
6. Summary
We have examined and compared the GW momentum fluxes at 19–20 km of altitude in the Southern Hemisphere derived from in situ measurements performed during the Concordiasi SPB flights (Rabier et al. 2010) and in the ECMWF operational analyses at 0.125° horizontal resolution for the period September 2010–January 2011. The Concordiasi balloons constitute an unprecedented and unique dataset well adapted for studying the entire spectrum of GWs for long duration and over wide regions. The main goals of this study were 1) to assess, through comparison with the Concordiasi observations, the realism of the ECMWF GW field and 2) to provide mean climatologies of the GW momentum fluxes in the Southern Hemisphere polar lower stratosphere, examine their intermittency, and study the seasonal and regional variability.
First, we analyzed a mean spatial distribution of momentum fluxes. We found a good agreement between both datasets on the geographical locations of GW hot spots (southern tip of the Andes, Antarctic Peninsula, islands, and over the ocean), but we noted that ECMWF analyses generally underestimate the balloon GW momentum fluxes by a factor of 5, likely resulting from the scale truncation in the ECMWF model. These results are confirmed on case studies of both orographic and nonorographic gravity waves. We also reported that the wave fluxes above the Antarctic Plateau in ECMWF analyses are even further underestimated, which may be either due to missing weak local sources (Sato and Yoshiki 2008) or to inadequate simulation of the horizontal propagation of short vertical wavelength, inertio-gravity waves. In any case, this region has only very weak GW momentum fluxes, so this difference is a priori not a major concern.
The PDFs of the GW momentum fluxes exhibit similar shapes with long tails for the highest values, with evidence of a more intermittent behavior over mountainous regions than oceans. For the ECMWF, we show that the 10% largest wave events account for 86% of the total momentum flux in regions with topography and 55% in regions with flat terrain. In the Concordiasi observations, the 10% largest wave events explain 64% of the total flux over topography and 29% over oceans. In other words, the modeled fluxes describe a more intermittent GW field than the observations. A part of this difference may result from an insufficient sampling of the most intense events during the balloon flights.
Seasonal maps of the fluxes at 70 hPa show a decrease of the GW activity between late spring and early summer, which we related to the weakening of the stratospheric jet that filters the GWs with low ground-relative phase speeds. This seasonal evolution, which is even more important at higher altitudes, also corresponds to a decrease of the wave intermittency and the disappearance of the long PDF tails.
We finally highlighted that, both in the balloon dataset and in the ECMWF analyses, nonorographic gravity waves provide a major contribution to the total momentum flux at 60°S in the stratosphere from September through November. These waves, which are likely generated by weather systems embedded in the Southern Hemisphere storm tracks, may thus account for a significant part of the drag that is currently missing in climate models in the stratosphere during the austral spring.
The results from the present study show that ECMWF is capable of representing accurately the geographical and seasonal variations of the resolved GW momentum fluxes. This implies that the ECMWF analyses can be used to study the spatial, seasonal, and interannual variability of the GW field. Modeled amplitudes of the momentum fluxes should yet be treated with caution, knowing that real fluxes are estimated to be about 5 times larger than the fluxes in the analyses at the resolution used here. One should also be aware that the modeled fluxes somewhat emphasize the contrast between regions or times with GWs and those without. Nonetheless, the present study brings support and justification to studies using the analyses to obtain information on the gravity wave field, as has already been done (Plougonven and Teitelbaum 2003; Wu and Eckermann 2008; Yamashita et al. 2010; Shutts and Vosper 2011). This opens the way for global studies on the variability of the gravity wave field.
Acknowledgments
The authors gratefully acknowledge helpful discussions with Guillaume Lapeyre and Hector Teitelbaum. Concordiasi is an international project, currently supported by the following agencies: Meteo-France, CNES, CNRS/INSU, NSF, NCAR, University of Wyoming, Purdue University, University of Colorado, the Alfred Wegener Institute, the Met Office, and ECMWF. Concordiasi also benefits from logistic or financial support of the operational polar agencies (Institut Polaire Francais Paul Emile Victor) IPEV, Programma Nazionale di Ricerche in Antartide (PNRA), United States Antarctic Program (USAP), and (British Antarctic Survey) BAS, and from Baseline Surface Radiation Network (BSRN) measurements at Concordia. Concordiasi is part of The Observing System Research and Predictability Experiment International Polar Year (THORPEX-IPY) cluster within the International Polar Year effort.
APPENDIX
Uncertainty on the GW Momentum Fluxes Related to the Balloon Sampling over the Islands
In this section, the uncertainty on the mean GW momentum flux over the Southern Ocean islands related to the limited number NI of balloon passes over these islands is estimated. We first assume that the peninsula, where NP balloon measurements are collected, is well sampled so that the momentum-flux distribution derived from the balloon measurements over the peninsula accurately represents the “real” momentum-flux PDF there. In the Concordiasi dataset, we have NP = 1565 and NI = 71. We then randomly undersample this momentum-flux PDF over the peninsula with NI “observations,” and, based on these NI points, we compute an average flux. We repeat this operation 10 000 times, and we show in Fig. A1 the PDF of the mean flux obtained with the 10 000 individual estimations. We obviously check that the mean estimator is unbiased: the mean of the PDF shown in Fig. A1 equals the mean flux computed with all the balloon observations over the peninsula (35.6 mPa). We are then able to calculate the 95% confidence interval (blue area) on this mean value. Note that, owing to the shape of the initial momentum-flux PDF, the confidence interval is not symmetric about the mean value, so that we may overestimate the true mean momentum flux more than we may underestimate it. We finally rescale this confidence interval by the ratio of the observed mean flux over the islands to that over the peninsula. This yields a confidence interval of [−1.4, 0.6] mPa about the mean flux over the islands, which is represented by the error bar in Fig. 11a. We therefore determine that the upper bound for the mean flux over the islands is approximately 2.5 mPa—that is, about 17% of the total flux observed by the balloons at that latitude.
PDF of the mean value of the momentum fluxes over the peninsula estimated using NI samples (black line) and mean of the distribution (in red). The area in blue represents the 95% confidence interval.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
PDF of the mean value of the momentum fluxes over the peninsula estimated using NI samples (black line) and mean of the distribution (in red). The area in blue represents the 95% confidence interval.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
PDF of the mean value of the momentum fluxes over the peninsula estimated using NI samples (black line) and mean of the distribution (in red). The area in blue represents the 95% confidence interval.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0324.1
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