Xiaoli Guo Larsén,* Søren Larsen and Andrea N. Hahmann Risø National Laboratory for Sustainable Energy, Roskilde, Denmark

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1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 138: , January 2012 A Notes and Correspondence Origin of the waves in A case-study of mesoscale spectra of wind and temperature, observed and simulated : Lee waves from the Norwegian mountains Xiaoli Guo Larsén,* Søren Larsen and Andrea N. Hahmann Risø National Laboratory for Sustainable Energy, Roskilde, Denmark *Correspondence to: X. G. Larsén, Wind Energy Division, Risø National Laboratory, Technical University of Denmark, 4000 Roskilde, Denmark. xgal@risoe.dtu.dk This note uses SAR images, satellite cloud pictures and point measurements together with simulations using the Weather Research and Forecasting (WRF) model to identify the origin of the gravity waves over Denmark on 6 November 2006, studied recently. The wave characteristics, concerning their initiation and ending, propagation, spatial orientation and wavelength, are consistent among the different data sources. This evidence and the key wave parameters derived from the WRF simulation, including the Scorer parameter and wave tilt, all suggest that the waves are lee waves generated by uplift from the Norwegian mountains. Copyright c 2011 Royal Meteorological Society Key Words: trapped lee waves; SAR images; WRF simulation; Scorer parameter Received 28 February 2011; Revised 27 July 2011; Accepted 28 July 2011; Published online in Wiley Online Library 7 September 2011 Citation: Larsén XG, Larsen S, Hahmann AN Origin of the waves in A case-study of mesoscale spectra of wind and temperature, observed and simulated : Lee waves of the Norwegian mountains. Q. J. R. Meteorol. Soc. 138: DOI:.02/qj Introduction In Larsénet al. (2011) (hereinafter L2011), the spectra of the time series of wind and temperature were studied during a period where gravity waves were present over Denmark (6 November 2006). The basic wave characteristics were described based on a synthetic aperture radar (SAR) image and point measurements from an offshore site at Nysted in Denmark. However, the origin of those waves was not discussed in that article. Fundamental atmospheric studies have found that the behaviour of turbulence in the boundary layer could deviate from the classical theory in the presence of wave-induced turbulence (e.g. Mahrt, 1999; Nappo, 2002; Winstead et al., 2002). It was found in L2011 that gravity waves lead to the intrinsic wave frequency being Doppler-shifted in transforming the mesoscale wind spectra between time and space and this therefore limits the applicability of the Taylor hypothesis. Knowledge of the origin of the waves in a particular place will help to better understand the turbulence characteristics and the applicability of basic turbulence theories there. The purpose of this note is to supplement L2011 by providing evidence of the origin of those gravity waves through satellite cloud pictures, SAR images (section 3) as well as simulations using a mesoscale model (sections 2 and 3) together with wave theories. 2. WRF simulation The Weather Research and Forecasting (WRF) model with the Advanced Research WRF core was used, with the same physics and dynamics packages, as well as the same large-scale forcing data as in L2011. The simulated period was also the same, namely the four days from to 8 November To better focus on the origin of the gravity waves, the following changes were made in the model set-up: (i) the updated version of WRF was used; Copyright c 2011 Royal Meteorological Society

Lee Waves fom the Norwegian Mountains 27 Figure 1. Default domain set-up, showing three domains (I, II, III) of the WRF modelling, at resolutions of 18, 6 and 2 km, respectively.

2 Lee Waves fom the Norwegian Mountains 27 Figure 1. Default domain set-up, showing three domains (I, II, III) of the WRF modelling, at resolutions of 18, 6 and 2 km, respectively. Topography contours are shown for domain I. (ii) the domain was now shifted a little to the north in order to capture the waves that developed over the Norwegian mountains and extended towards Denmark (Figure 1); (iii) the vertical levels of the model were now set as 41, instead of 37; and (iv) the horizontal resolutions for the three domains were now 18 km (domain I), 6 km (domain II) and 2 km (domain III), instead of km. These changes were made to better visualize the spatial distribution of the waves. In domain III, there are now grid points. The damping layer depth was chosen to be 2 km, with damping coefficients 0.01 in all three domains. For mountain-generated waves, the representation of the mountains in the simulation domain is an important issue. Two more domain set-ups were tested in addition to that in Figure 1 and results are discussed in section The gravity waves on 6 November Our hypothesis Our hypothesis is that the waves studied in L2011, shown in the SAR image (their Figure 2), are lee waves generated by the atmospheric uplift from the Norwegian mountains. For such waves to be generated, in addition to the condition that N 2 > 0 (where g θ N = θ z is the Brunt Väisälä frequency and θ is the potential temperature), it is also required that there is a significant Figure 2. Wind field at m east of Denmark retrieved from satellite SAR observations by ENVISAT, at UTC on 6 November This figure is available in colour online at wileyonlinelibrary.com/journal/qj component of wind normal to the terrain with considerable strength (Durran, 1986, 2003; Holton, 1992). The gravity waves can propagate or be trapped vertically, depending on the Scorer parameter l, which is defined as l 2 = N2 U U U z 2, (1) with U being the background wind speed. If l decreases strongly with height, then the lee waves are trapped below a layer where the disturbance decays in the vertical Wave characteristics The SAR image which displays the waves in L2011 is valid at 203 UTC on 6 November On the same day at 0929 UTC, another SAR image shows that the gravity waves were already present (Figure 2). Even though the image quality at 0929 UTC is rather poor and the spatial coverage is limited, it can still be seen that the wave ridge orientation was similar to that at 203 UTC.

Satellite cloud picture, from the Terra satellite, channel 22, at 2026 UTC on 6 November 2006. is a close-up of (a). This figure is available in colour online at wileyonlinelibrary.

3 276 X. G. Larsén et al. (a) Figure 4. WRF-simulated wind vectors at m over domain II, at 0000 UTC on 6 November 2006 when the waves are newly generated. The magnitude of the first vector at the lower-left corner is m s 1. This figure is available in colour online at wileyonlinelibrary.com/journal/qj Figure 3. Satellite cloud picture, from the Terra satellite, channel 22, at 2026 UTC on 6 November is a close-up of (a). This figure is available in colour online at wileyonlinelibrary.com/journal/qj But SAR images can only provide information over water, preferably over open water. A satellite cloud picture from this day at 2026 UTC is given as Figure 3(a) over a larger region; Figure 3 is a close-up, focusing on the lee side of the Norwegian mountains. There are two distinctive wave patterns in Figure 3(a), namely those on the west and east sides of the Norwegian mountains. Those west of Norway are seemingly lee waves from the Scottish highlands, which could be identified from Figure 3(a); an Aqua satellite picture earlier on the same day around 123 UTC clearly shows this (not shown here but available at images/). These two groups of waves have distinct wavelengths and orientation. Accompanying the strong eastward wind, the waves over the Norwegian mountains clearly follow the higher peaks, and they extend on the lee side of the mountains continuously over the water to reach Denmark and the straits between Sweden and Denmark. The wavelength is comparable to those in the SAR image from 203 UTC. It is difficult to determine the height of the cloud top and even how it is distributed in space, but obviously the waves that are captured in the SAR image over the Danish waters are not all visible in this cloud picture. This could be considered as an indication that the waves in this area did not extend into the higher cloud layer or, in other words, that they were trapped below the cloud top. The results from the WRF simulation show that the waves over the domain started to develop early on 6 November, under conditions of stable stratification, as also indicated by measurements from the offshore site Nysted (Figure 4 in L2011). Figure 4 here shows the WRF simulated wind conditions at m at 0000 UTC on 6 November for domain II. Clearly there is a strong wind normal to the Norwegian mountain ridges at this time, with θ/ z > 0. The waves in the SAR image at 0929 UTC (Figure 2) are clearly present in the WRF-simulated wind at m for domain III in Figure. At the southern boundary, there seems to be no interaction of the waves with the terrain. Similarly, this is seen in the SAR image at 203 UTC (Figure 2 in L2011). This is very likely because the terrain of Denmark and Sweden at the boundary of domain III is very flat (Figure 1). Note that the waves are already rather well-resolved in domain II with a horizontal resolution of 6 km, although the pattern is rather vague (Figure (a)). Similarly, Figure 6 shows the wind field at m at 20 UTC, corresponding to the case studied in L2011. Note that, since the model domain does not contain the Scottish highlands, lee waves coming from the west of Norway are not simulated. Linear lee waves are stationary relative to the ground. Relative to the mean flow, the waves must propagate upwind at the mean wind speed, namely from east to west. In reality, the variation of the background mean wind and stability, in time as well as in space, will inevitably violate the linearity of the lee waves (Nance and Durran, 1997). As a result, the waves propagate in space and this is seen

4 Lee Waves fom the Norwegian Mountains (a) (a) Figure. Spatial distribution of the WRF-generated wind speed (m s 1 ) at m at 0900 UTC on 6 November 2006, showing wave patterns over (a) domain II, and domain III. Figure 6. As Figure, but at 200 UTC on 6 November in the spatial variation of the wave pattern. From the cloud picture, it is possible to see that the lee waves from the Scottish highlands change their distribution in space. Due to the nonlinear characteristic, the trapped Norwegian lee waves could be drifted upwind and interact with the lee waves from Scotland. In Figure 3, in the North Sea south of Norway the wave pattern corresponding to small wavelength and a west east ridge orientation could result from wave interactions. In this particular area, there is a discrepancy in the pattern simulated in Figure 6 and the cloud picture (Figure 3), because the simulation does not contain these waves from the west and therefore there is no interaction. In L2011, without discussing the origin of the waves, we estimated the phase velocity from point measurements and SAR images and determined the approximate wave direction with the help of linear wave theory. The results from L2011 were that, relative to the mean flow, the phase velocity is in the opposite direction with a similar magnitude to the mean flow speed averaged over the boundary layer. This estimate is consistent with the arguments here. In Figure 7(a), the variation of wind speed at 200 UTC at the lowest 17 vertical model levels are shown for a west east transect, approximately corresponding to 8.2 N. Over the grid points i = (Figure 7), which is about 0 km in length, there are about eight wave cycles, giving a wavelength of about 12 km, very close to what was observed in the SAR image in L2011 ( 11.6 km). The Scorer parameters from 0900 UTC at nine grid points in the upwind region, both from domain II and domain III, are presented in Figure 8(a) and as l2 varying with height. l is calculated from the wind speed and potential temperature profiles from the WRF simulation, which are obtained by fitting a seventh-order polynomial to the values from the lowest 20 vertical model levels, a method similar to that used in Winstead et al. (2002). Below 00 m, l2 decreases considerably with height, indicating that the atmosphere was capable of supporting trapped waves. At higher levels, the small values of l2 are quite sensitive to the fitting function used, and therefore larger uncertainties are expected. The trapped waves can propagate vertically in the lower layer, but they will not be tilted in the vertical because the wave energy is repeatedly reflected from the upper layer and the surface downstream of the mountains. This is supported by the results in Figure 7, which show that the amplitude of the wind speed variation decreased with height and became rather small at level 13 ( 1881 m) downwind of the mountain ridge. Throughout the lowest 13 levels, no tilt can be seen. According to the site measurements at Nysted (Figure 4 in L2011), the background stratification conditions changed to be unstable at the end of 7 November. This is reflected as well by the large-scale stratification conditions over most of the domain according to the simulation. As a result, the waves started to disappear in the simulation by this time. c 2011 Royal Meteorological Society Copyright 4. Discussion The purpose of this note is to find evidence supporting our hypothesis that the dominant waves over Denmark and adjacent waters on 6 November 2006 (as studied in L2011) were lee waves generated by the atmospheric uplifting by the Norwegian mountains. Our methodology is to make use of SAR images, cloud pictures, point measurements, wave theory together with simulations using a mesoscale model to interpret the origin of the these waves. Q. J. R. Meteorol. Soc. 138: (2012)

5 278 X. G. Larsén et al. (a) vertical layer 1 (a) Squared scorer parameter l 2, m 2 x Height m Height m Squared scorer parameter l 2, m 2 x 6 Figure 8. Squared Scorer parameter l 2 varying with height at 0900 UTC, from ten grid points from the upwind region in (a) domain II and domain III. The numbers on the curves correspond to grid points in domains II and III shown in the inset maps. Elevation, m 0 2. m s West east grid no West east grid no. Figure 7. The west east transect at 200 UTC, at 8.2 N, to be compared with Figure 6. (a) Normalized wind speed (u u)/u, at the model s lowest 17 vertical levels, with u as the mean of the winds for the transect. The 17 levels correspond to the heights above ground of about 14, 42, 70, 99, 127, 186, 304, 473, 687, 940, 1226, 141, 1881, 2243, 2626, 3022 and 3431 m. The first and last five grid points are in the nudging zone and therefore should be disregarded. shows the terrain elevation for the transect. This figure is available in colour online at wileyonlinelibrary.com/journal/qj The strong westerly wind caused waves not only over and downwind of the Norwegian mountains but also over and downwind of the Scottish highlands. The regular and consistent wave characteristics from morning to night on 6 November and the continuous extension of wave patterns in space from the mountain areas, as shown in SAR images and cloud pictures, strongly suggest that these were lee waves. Due to varying background wind and stability conditions, the waves cannot be explained by linear theory; they propagate and interact with each other. The cloud picture shows distinguishable wave characteristics west of and east of the Norwegian mountains. Note that the wavelength of the waves south of Norway is about one-third to one-half of that of the focused waves with wavelength of 12 km. In order to accurately reproduce the wave features, a model needs at least six grid points. The grid spacing of 2 km of our modelling is certainly a limitation for properly reproducing such waves of small wavelength. The cloud pictures also show that the impact of the waves from Scotland is no longer obvious over Denmark and eastwards. In order to focus on the waves downwind of the Norwegian mountains, the domain of the WRF simulation does not include the UK. Thus, this set-up will not reproduce the wave field exactly as seen in the real world on the west side of Denmark, but it certainly helps to clarify the origin of the waves downwind of the Norwegian mountains. Simulations using the mesoscale WRF model show high consistency in the wave characteristics with the dominant wave features as obtained from other data sources, including wavelength, orientation, propagation, and their initial and end times. The Scorer parameter in the upwind region and the wave tilt also support our hypothesis. Sensitivity tests were conducted with different sizes of domain III, including different portions of the Norwegian mountains. In addition to Figure 1, the domain was also set up in two other ways. In the first set-up, domain III included the main part of the mountain (with the northern boundary at about 61 N) and there was a considerable terrain gradient at the northern boundary, which normally is numerically problematic. Using this set-up, the results are very similar to those using the domains in Figure 1. That the terrain gradient did not produce numerical noise obscuring the wave pattern is also confirmed by the consistent results between domains II and III. In the second set-up, domain III only included the southern tip of the mountains. The major difference with this set-up from the default is that the simulated wave patterns were slightly smoother over the water west of Denmark. All in all, the wave patterns from the three domain set-ups were similar on the lee side of the mountains and over the water. It seems that the waves are quite realistically reproduced even when only the southern tip of Norway is included in domain III. This is likely because these waves are already quite well-resolved in domain II. This test suggests that, for this particular gravity wave case, neglecting the lee waves from the Scottish highlands is not problematic in the studied area over Denmark and eastward, as in L2011. To study the sensitivity to the model resolution, we performed additional simulations with nested domains with the horizontal resolutions km. The results from the 3 km domain (not shown) display structures in the mean wind speeds and vertical velocity consistent with the ones presented here (2 km), except that the resulting fields are smoother. The 1 km domain was positioned over the

6 Lee Waves fom the Norwegian Mountains 279 water body in domain III (Figure 1), with grid points. No finer-resolution structures within the horizontal and vertical wind fields were found in the 1 km simulation than in the 2 km or 3 km simulations.. Summary The results from the WRF model simulations provide information on the gravity waves observed over Denmark on 6 November 2006, consistent with a couple of SAR images, a satellite cloud picture and point measurements from an offshore site Nysted. The analysis in this note concerns the start and end of the wave life, the wave propagation, orientation and wavelength. The results from a WRF model simulation also provide temporal variations in the wind and temperature field, horizontally and vertically, that make it possible to examine some of the key wave parameters: the Scorer parameter and the wave tilt. The findings support our hypothesis that the regular wave patterns observed in the SAR images and point measurements from Nysted in L2011 are lee waves generated by the lifting due to the Norwegian mountains. Acknowledgements This work is supported by project Mesoscale Variability, We thank Larry Mahrt for initiating this study by questioning the origin of the waves and for the discussions about the waves. We appreciate the discussions with Jake Badger, Joakim Nielsen and Claire Vincent. We also thank Merete Badger for the SAR image, which is provided by the European Space Agency. The satellite cloud picture is provided by the NERC Satellite Receiving Station, Dundee University, Scotland at References Durran DR Mountain waves. In Mesoscale Meteorology and Forecasting. Ray PS. (ed.) Amer. Meteorol. Soc: Boston, MA, Durran DR Lee Waves and Mountain Waves. In Encyclopedia of Atmospheric Sciences. Holton JR, Pyle J, Curry JA. (eds) Elsevier Science: Amsterdam, Holton JR An Introduction to Dynamic Meteorology. Academic Press: San Diego, CA. Larsén XG, Larsen S, Badger M A case-study of mesoscale spectra of wind and temperature, observed and simulated. Q. J. R. Meteorol. Soc. 137: Mahrt L Stratified atmospheric boundary layers. Boundary-Layer Meteorol. 90: Nance LB, Durran DR A modeling study of nonstationary trapped mountain lee waves. Part I: Mean-flow variability. J. Atmos. Sci. 4: Nappo CJ An Introduction to Atmospheric Gravity Waves. Internat. Geophys. Series 8. Academic Press: San Diego, CA. Winstead NS, Sikora TD, Thompson DR, Mourad PD Direct influence of gravity waves on surface-layer stress during a cold air outbreaks, as shown by Synthetic Aperture Radar. Mon. Weather Rev. 130:

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