1. Introduction
Internal atmospheric gravity waves, hereafter referred to as gravity waves, result from a forced vertical displacement of air in a stable layer, with gravity acting as the restoring force. They occur on a wide range of associated scales and are well studied both observationally (Scorer 1952; Queney 1952; Holmboe and Klieforth 1957; Kuettner et al. 1987; Koch and O'Handley 1997) and theoretically (Turner 1973; Holton 1992). Gravity waves can be forced by penetrative convection from thermals below (Clark et al. 1986; Balaji and Clark 1988; Sang 1991), by significant speed shear in the inversion (Kuettner et al. 1987; Rogers et al. 1995), by local features of the terrain (Scorer 1949; Durran 1986), or by large-scale atmospheric processes (Koch and O'Handley 1997). For shear-driven processes, gravity waves tend to align perpendicular to the mean ambient wind shear in the layer where the oscillation is forced (Kuettner et al. 1987; Rogers et al. 1995). In order for shear-driven processes to generate waves, the Richardson number must be less than 0.25 (Miles 1961). Examples of external forcing mechanisms that lead to shear-induced wave generation include flows around thermal plumes and cumulus clouds, or wave–wave interaction. For terrain-driven gravity waves, there must be a significant component of wind normal to the terrain (Durran 1986). Previous observations indicate that the minimum magnitude of this wind component should be between 7 and 15 m s–1 (Queney et al. 1960).
It has long been known that gravity waves can and do exist in inversions and other stable layers on top of convective boundary layers Kuettner et al. (1987), for example, reported observations of what they termed “widespread” gravity wave activity over a convectively active boundary layer. They found that these internal gravity waves had characteristic wavelengths ranging from 5 to 15 km and had vertical velocity amplitudes of ±1 to ±3 m s–1. They also found that in all cases the magnitude of the background vertical wind shear exceeded 3 × 10–3 s–1. However, while many studies show that gravity waves can propagate either along inversions or up into the troposphere, their influence within the underlying boundary layer has received less attention. Theoretical studies (e.g., Wilson 1996) have indicated that internal gravity waves at the top of convective boundary layers can modulate the wind speed within the convective boundary layer. Balaji and Clark (1988) simulated gravity waves that interacted with boundary layer rolls to alter the spacing of the rolls, and hence the pattern of surface stress generated by the rolls. However, predictions and observations of gravity waves directly influencing surface-layer stress through a convective boundary layer are lacking. The single exception, to our knowledge, is the Sierra Wave Project (Queney 1952; Holmboe and Klieforth 1957), which showed via observations that rotor circulations—essentially breaking gravity waves—generated downstream of the Rocky Mountains can influence the wind within the surface layer underlying those circulations.
The advance of spaceborne remote sensing techniques for observing surface wind stress signatures associated with both the footprints of gravity waves and boundary layer convection has provided unprecedented opportunities for observing these phenomena with unprecedented resolution. For example, synthetic aperture radar (SAR) has been effectively used as a remote sensing tool for observing spatial variations in the effects of wind-induced surface stress over the oceans and other large bodies of water such as the Great Lakes. This is because centimeter-scale surface waves, whose amplitudes are rapidly modulated in space and time by the surface wind, are efficient scatterers at SAR wavelengths. This fact, in conjunction with the high resolution of SAR (on the order of 100 m), allows detailed observations of near-surface, instantaneous wind stress patterns not available from other remote sensing methods. Atmospheric boundary layer phenomena observed with SAR and relevant here include convection (Sikora et al. 1995; Mourad and Walter 1996; Müller et al. 1999; Mourad et al. 2000; Vandemark et al. 2001) and gravity waves (Thomson et al. 1992; Vachon et al. 1994; Alpers and Stilke 1996; Zheng et al. 1998; Worthington 2001). (For a review of these and other atmospheric processes visible in SAR images, see Mourad 1999.) Also, SAR backscatter images can be converted to high-resolution (O(1–5 km)2), two-dimensional wind maps by following the procedure of Thompson and Beal (2000) and Monaldo et al. (2001). Thus, SAR images of the surface of bodies of water can provide insight into the instantaneous spatial structure of the surface wind field in the marine atmospheric boundary layer overlying that water.
In this paper, we present analyses of synthetic aperture radar and Advanced Very High Resolution Radiometer (AVHRR) data that show the superposition of gravity waves and convection during cold air outbreaks over Lake Superior on two separate days. Unique to this study is evidence that the wind stress on the lake surface is strongly influenced by the presence of gravity waves centered on the inversion. This influence by the gravity waves occurs despite the presence of an intervening highly convective boundary layer and despite the fact that the source of gravity waves is weak relative to the Rockies, namely, flow over a 340-m-high series of ridges upstream of Lake Superior. Also unique to this study is its detailed view of spatial variability in the interaction between gravity waves and two types of boundary layer convection, all within a spatially evolving atmospheric boundary layer. In particular, the first of these days, 29 December 1998, shows the collocation of gravity waves and cellular convection. The second day, 9 January 2000, shows the collocation of gravity waves and roll convection.
2. Data and methods
The supporting meteorological data used in this study consist of routinely available surface observations of the Great Lakes region (Fig. 1), including both the United States and Canada, by the Coastal Marine Automated Network (C-MAN). In addition, routinely available upper-air soundings from 0000 UTC on 30 December 1998 and 1200 UTC on 21 January 2000, including wind and temperature data, were also used in this study. These soundings were taken at International Falls, MN, (INL), and Alpena, MI (APX). The INL sounding, located at 48.57°N, 93.78°W, approximately 250 km upwind of Lake Superior, is the closest upstream sounding. The APX sounding, located at 44.55°N, 84.43°W, approximately 280 km downwind of the eastern half of Lake Superior, is the nearest downstream sounding. The INL sounding provides information on the stability structure and wind profile upstream of Lake Superior. The APX sounding provides an estimate of how the boundary layer was modified by Lake Superior. (This is an estimate because the effect of synoptic-scale subsidence on the height of the inversion between the lakeshore and Alpena is not measured.) However, because of the distance of both upper-air stations from the lakeshore (>250 km) and the complexity of the intervening environments, these data cannot be used as a basis for quantitative calculations of boundary layer properties or of the properties of the convection and gravity waves we describe in this paper. Therefore, these soundings are used primarily to provide a plausibility argument that (1) the environment around Lake Superior was conducive to the formation of vertically trapped gravity waves and (2) a convective boundary layer developed over Lake Superior. The soundings also provide an estimate of the layer's depth over the lake.
Three AVHRR images were used in this study: a National Oceanic and Atmospheric Administration (NOAA)-12 image obtained from the National Environmental Data and Information Service's Satellite Active Archive (SAA) for 2339 UTC on 29 December 1998, a NOAA-14 image for 0947 UTC on 21 January 2000, and a NOAA-15 image from 1318 UTC on 21 January 2000. Because of the time of day, visible imagery was not available for any of the AVHRR image times; therefore channel 4 (centered on 10.82 μm) was used for all image analysis discussed here. In each case, the data were calibrated for the nonlinear response of the AVHRR channels using Environment for Visualizing Images (ENVI) processing software available from Research Systems Incorporated in Boulder, CO. The final brightness temperature image was projected onto a polar stereographic map with a spatial resolution of 1.1 km. The brightness temperatures were not corrected for atmospheric interference; therefore, they will have a cold bias (Rees and James 1992; Emery et al. 1994), which does not affect the geometric information we extract from these images.
The SAR images used in this study are two RADARSAT ScanSAR Wide images processed at the Canadian Space Agency (CSA) facility at Gatineau, QC, and obtained from the SAA. The first image was taken at 2349 UTC on 29 December 1998, and the second image was taken at 1211 UTC on 21 January 2000. Both images have an original pixel spacing of 100 m. To take advantage of this resolution, the original image was used for all analyses of wavelength and orientation angle because these analyses do not depend on accurate calibration of the brightness values. However, for the analyses of the amplitude of the wind speeds associated with gravity waves, the imagery was converted from radar backscatter to an estimate of wind speed as follows.
Both images were converted to normalized radar cross sections using a calibration procedure specified by the Gatineau facility. These cross-section values were then converted to wind speed following the method described in Thompson and Beal (2000) and Monaldo et al. (2001), using the wind directions given by the C-MAN stations over Lake Superior. The mean wind speed calculated via this procedure for 29 December 1998 was higher than the C-MAN observations over the lake. The wind speeds in this image were therefore scaled to match those measured by the C-MAN stations. We note here that calibration of ScanSAR images such as the ones used in this study is generally very difficult and, in particular, that the calibration coefficients provided by Gatineau for ScanSAR Wide images may not be accurate (Katsaros et al. 2000; Vachon et al. 2000). The same wind speed conversion procedure was applied to the 21 January 2000 image. In this case, the resulting wind speed values were in agreement with the C-MAN values, so no scaling was necessary. It is not clear to us why there is a significant difference in agreement with the C-MAN wind speeds between the two images. However, for the analysis discussed in this paper, where we are concerned only with wind speed variations, not the mean value of wind speed, we believe this problem does not affect our conclusions.
3. Image analysis
In this section, we analyze the images collected on both dates, exploiting the specific advantages offered by each set of data. The 29 December 1998 data are exploited for their nearly coincident AVHRR and SAR imagery (approximately 10 min apart) showing gravity waves and cellular convection; the 21 January 2000 data are exploited for their depiction of the superposition between gravity waves and roll (vs cellular) convection over the lake. In both cases, upper-air soundings from upstream (INL) and downstream (APX) are used to estimate the vertical structure of the atmosphere within 30 min of the time of the SAR images. The upstream sounding is used to document that the vertical wind characteristics and the thermodynamic profile on both days are capable of supporting vertically trapped gravity waves. The downstream sounding (APX) is used to estimate an upper bound on the depth of the convective boundary layer that develops over Lake Superior. These upper-air soundings, coupled with high-resolution blowups (subimages) of sections of the SAR images, show the transition of the atmosphere over Lake Superior from stable to convective, while the SAR and AVHRR images together show the convective structures within the evolving boundary layer and their modulation by gravity waves. Finally, the two cases, together with a terrain map of Lake Superior, are used to provide evidence that the gravity waves present on both days are likely terrain forced.
a. 29 December 1998
Figure 2 shows the AVHRR IR brightness temperature image of western Lake Superior for 2339 UTC on 29 December 1998. Figure 3 shows the SAR image taken the same day at 2349 UTC. The cloud and radar backscatter patterns over Lake Superior consist of two distinct phenomena. The first, and most striking, is a series of linear bands aligned approximately parallel to the northern coast of Lake Superior. These bands are regularly spaced and the cloud patterns are consistent with the well-known cloud signature associated with internal gravity waves (see, e.g., Durran 1986). These linear patterns begin immediately offshore on the SAR image and approximately 15 km offshore in the AVHRR image. The spacing between the linear cloud features on the AVHRR image is 6.1 ± 1.1 km (mean ± one pixel spacing, where one pixel = 1.1 km). The spacing between the linear wind speed bands in the SAR wind image is 6.1 ± 0.5 km (mean ± one standard deviation; one pixel spacing = 0.2 km). Similar bands are evident in the SAR image (Fig. 3). However, the amplitude and clarity of the radar backscatter signature of the gravity waves in the SAR image decrease significantly with downstream fetch. The amplitude and clarity of their cloud manifestations in the AVHRR image remain readily apparent with increasing fetch, however they become somewhat obscured by the appearance of convective clouds offshore. Linear cloud patterns of this sort are well known to be associated with the existence of gravity waves. These qualitative statements are made quantitative later.
As mentioned earlier, the second signature evident on both Figs. 2 and 3 are those of boundary layer convection over the southern half of the lake. [See Mourad and Brown (1990) for a review of the relevant literature before 1990 and Atkinson and Zhang (1996) for a recent update as well as Weckwerth et al. (1997, 1999).] The convective cloud patterns have a preferred orientation of 310° relative to true north near the northern cloud edge veering to 325° near the southern shore. However, they also have a decidedly three-dimensional overall structure, a “string of pearls” appearance. Thus, we will refer to the boundary layer circulations that induce them as cellular. The first detectable cloud patterns clearly associated with this convection begin approximately 23 km off the northern shore of the lake. Other cloud features begin approximately 15 km offshore, features associated with gravity waves.
The SAR image shows features similar to those in Fig. 2. First, there is a mottled appearance to the SAR backscatter, characteristic of three-dimensional boundary layer convection (Thompson et al. 1983; Sikora et al. 1995; Mourad 1999). This is similar in visual manifestation to laboratory-based Bernard convection, or strings of pearls in convective cloud structure. Interestingly, while the cloud patterns indicate convective roll circulations over the lake aligned with the wind, the SAR subimages (labeled ‘a’ and ‘b’ in order of increasing fetch) indicate a transition from streaks near the northern shore to cellular convection with an aspect elongated in the along-wind direction over the rest of the lake. This is consistent with the idea that lake-derived heating of the atmospheric surface layer increases with fetch, and that the resulting coherent structures in the atmospheric surface layer are changing from dynamically organized, highly elongated structures (with linear, nearly one-dimensional footprints in SAR) to convectively driven, more three-dimensional structures (with ellipsoidal, two-dimensional footprints in SAR) as they evolve with fetch, with an overall organization imposed by the boundary layer–scale roll vortices.
To quantify the spatial structure of the wind speed variance generated by the gravity waves and convection, radar backscatter data from the SAR image along a 10-km-wide section of coast centered on line segment A′B′ (Fig. 3) was translated into wind speed following the procedure described in Thompson and Beal (2000) and Monaldo et al. (2001). Figure 4a shows the wind speed perturbations plotted as a function of cross-shore distance. The gravity wave perturbations initially have an amplitude of approximately 2.5 to 3.0 m s–1. The amplitude of these gravity waves then decreases as a function of fetch to less than 0.5 m s–1 over the southern half of the lake, where the gravity waves are nearly indistinguishable from the background flow.
Figure 4b shows the results of an analysis, similar to those presented in Fig. 4a for the SAR image, performed on the AVHRR brightness temperature image for the same section of coast. At the northern shore, there is a sharp jump in brightness temperature as the satellite senses emission from the warm water. Then a nearly linear trend exists as fetch increases, reflecting the general increase in colder cloud coverage and a cloud-top cooling associated with the deepening convective boundary layer. Superimposed on this linear trend, however, is a set of oscillations that are associated with the gravity wave cloud patterns. While the cloud patterns do indicate that the gravity wave signatures become somewhat disorganized near the southern shore, the cloud oscillations remain evident as fetch increases, and reduce in amplitude only by a factor of 2 near the southern end of the lake from their north-lake values. This suggests that the cloud signatures of the gravity waves are not weakening substantially with fetch even as their surface signatures do. This is consistent with the idea of gravity waves being ducted along the base of the inversion of a deepening boundary layer. Such a situation would lead to decreasing surface wind speed amplitude versus fetch associated with the gravity wave due to its exponential decay in amplitude away from the inversion towards the lake surface, expected in a neutral or slightly unstable boundary layer under the inversion (i.e., Holton 1992). This idea is discussed more in section 3c.
b. 21 January 2000
In the second case when gravity waves and convection occurred simultaneously over western Lake Superior, the SAR and AVHRR images were offset significantly in time. Figure 5a shows an AVHRR NOAA-14 channel 4 image taken at 0914 UTC on 21 January 2000, and Fig. 5b shows a NOAA-15 channel 4 image taken at 1318 UTC on 21 January 2000. Figure 6 shows the corresponding RADARSAT-1 SAR image, which was taken at 1211 UTC on 21 January 2000. All three images show patterns similar to those described in section 3a in that they indicate the existence of gravity waves occurring simultaneously with boundary layer convection over western Lake Superior. What is different is that the AVHRR images indicate that southern Lake Superior is cloudier on this day than on 29 December. In addition, the SAR wind signatures and the AVHRR brightness temperature signatures of convection are much more two-dimensional than those on 29 December. This is particularly evident in the SAR subimages (labeled a–c in Fig. 6). Figure 6a shows the northern shore of Lake Superior and the first few gravity wavelengths downstream. There is weak evidence of convective structure in the first bright band offshore. The second and third bright bands, however, show linear features (rolls) oriented approximately perpendicular to the gravity wave bands. These interactions are labeled on Fig. 6a. Figures 6a and 6b shows regions of the lake where both gravity waves and rolls exist simultaneously. Fig. 6c shows a region of the lake where the gravity wave signatures are no longer detectable but the roll signatures remain significant.
The wavelengths of the gravity waves varied on this day, depending on the sample location. For the two AVHRR cloud images, which bracketed the SAR image in time, the average wavelength ranged from 5.2 ± 1.1 km along cut AB (Fig. 5a) to 5.0 ± 1.1 km along cut CD (Fig. 5a) and from 5.3 ± 1.1 km along cut A′B′ (Fig. 5b) to 4.8 ± 1.1 km along cut C′D′ (Fig. 5b). The SAR-derived wavelengths ranged from 6.0 km ± 0.5 km along cut A″B″ (Fig. 6) to 5.2 ± 0.8 km along cut C″D″ (Fig. 6). The wavelengths of gravity wave features derived from the SAR and the AVHRR images are of comparable magnitude but differ quantitatively, likely due to the temporal evolution of the boundary layer.
Similar to the case on 29 December, the wind speed signatures due to gravity waves on 21 January exhibit a decrease in amplitude as fetch increases. Figure 7 is the same as Fig. 4a but for a carefully selected region of Fig. 6 centered on cut A″B″ where the wind speed fluctuations associated with gravity waves were the most independent of fetch. Figure 7 indicates that the amplitude of the gravity waves decreases. Specifically, the initial amplitude of the gravity waves, as measured from the wind speed fluctuations, is approximately 3 m s–1; this decreases to less than 0.5 m s–1 over the southern half of the lake, where wind speed fluctuations due to gravity waves become unidentifiable.
c. Gravity wave and boundary layer characteristics
In this section we first show that the vertical structure of the atmosphere at the times of both of the SAR images was capable of supporting vertically trapped waves. We also show that the trigger mechanism for these gravity waves is likely the terrain near the northern shore of Lake Superior. Finally, we use the sounding from APX to illustrate that a convective boundary layer did develop over Lake Superior on both days, and we use the depth of the convective boundary layer at APX as an upper bound on the depth of the lake-modified convective boundary layer.
To demonstrate that vertically trapped internal gravity waves were possible on both days, data from the INL upper-air station were used to document the vertical structure of the atmosphere at the times of both images. To document the lake-modification process, data from the APX upper-air station were used. On both days, the trajectory of the wind upstream of APX crossed over Lake Superior. While it is true that APX is not directly downwind from INL, it is reasonable to assume that the air passing APX has been modified in a similar fashion to that downstream of INL. However, as discussed earlier, we can only assume that the boundary layer depth at APX represents an estimate of the lake-modified boundary layer downstream of Lake Superior, not that it is an accurate measure of the boundary layer depth just downstream of western Lake Superior. This is because of the likely effects of synoptic-scale subsidence on the inversion height measured at APX, which would tend to produce a negative trend in Zi between the southern shore of Lake Superior and the site of the APX sounding. Figure 9a shows the profiles of virtual potential temperature calculated from the original soundings for 0000 UTC on 30 December 1998 at INL and APX. Figure 9b shows the same data for 1200 UTC on 21 January 2000. On both days, strong inversions exist at INL from the surface to well above the height of the terrain surrounding Lake Superior. Such a thermodynamic structure is necessary for the existence of gravity waves and suggests that buoyancy-driven oscillations could occur, but it is not sufficient to determine if vertically trapped gravity waves are possible. Figure 10 shows vertical estimates of the Scorer parameter on both days, as calculated by Eq. (1) from the INL upper-air observations. Because the variable vertical spacing between observations of pairs of wind and temperature measurements, it was necessary to interpolate both the wind and temperature soundings onto an evenly spaced vertical grid in order to estimate both the lapse rate and the second-derivative term in (1). This was accomplished by fitting a fifth-order polynomial to each of the temperature and wind profiles and then evaluating that polynomial at 50-m increments to calculate the derivative. Using a fifth-order polynomial was a subjective decision; however, fourth-, sixth-, seventh-, and eighth-degree polynomial fits were also examined to determine if the order of the polynomial fit significantly affected the Scorer parameter profile. In each case there were some changes in the details of the profiles. However, the rapid decrease in the Scorer parameter with height shown in Fig. 10 was present with all of the fits, indicating that the atmosphere was capable of supporting trapped gravity waves, particularly in the lowest 1 km.
Given that similar gravity wave characteristics (location and orientation angle relative to true north and wavelength of the gravity wave structures) occur on both days, it is likely that terrain is the triggering mechanism. The inset in Fig. 1 shows the terrain around western and central Lake Superior. The features hypothesized to be responsible for the gravity wave structures visible on both days are labeled. The terrain features, with a maximum height of 340 m, are oriented parallel to the coastline near Grand Marais, MN, and are aligned parallel with the long axis of Isle Royale, MI. In both cases, the terrain is aligned at an angle of 240° relative to true north, although there is some curvature along the crest of the western terrain. Given that the mean wind in the lowest kilometer of the atmosphere at INL was from 313° on 29 December 1998 and from 328° on 21 January 2000 (i.e., that there was a significant wind component perpendicular to the mean ridge alignment), it seems reasonable to hypothesize that the gravity wave signatures visible on both images are forced by the terrain labeled on Fig. 11. Further support for this hypothesis is provided by the fact that the gravity wave signatures are located directly downstream from these two fluctuations in the local terrain on two separate days. On 29 December the gravity wave crests several wavelengths downstream are still oriented at an angle of 237°; however, on 21 January the crests have rotated 15° counterclockwise to 222°. This behavior can be seen in Fig. 6 as an apparent along-crest bending of the surface wind speed fluctuations associated with the gravity wave patterns on the SAR imagery.
d. Discussion
The imagery analysis presented in the previous sections allow us to hypothesize the structure of the boundary layer during situations such as these where terrain-forced gravity waves interact with a deepening convective boundary layer. The bright bands on the SAR images correspond to locations where the along-wind perturbation associated with the gravity wave oscillation is maximized (most positive relative to the mean wind), providing the largest additive effect. The dark bands occur where the perturbation wind speed is minimized (most negative relative to the mean wind), providing largest cancellation. The cuts presented in Fig. 4 indicate that the AVHRR cloud features are located above the dark SAR bands, where the boundary layer is deepest for any given gravity wave.
An additional characteristic of the gravity waves is seen from the data analysis in this section: a decrease in surface-layer wind speed variance caused by the gravity waves as a function of fetch. On both days, the surface wind speed fluctuations associated with the gravity wave signatures decreased in amplitude from 2 to 3 m s–1 near the northern shore to less than 0.5 m s–1 downstream. However, Fig. 4b (the AVHRR brightness temperature cross section) indicated that the cloud patterns associated with the gravity waves only decreased by a factor of 2 in amplitude with increasing fetch. This suggests that in the inversion, the gravity wave signature maintained its amplitude, but at the surface, the amplitude decayed. This can be explained by the development of a lake-induced convective boundary layer on both days. It is well known that gravity wave signatures attenuate in neutral and unstable layers (see e.g., Holton 1992). Eventually, the convective boundary layer is sufficiently deep and the attenuation of the gravity wave signature sufficiently large that the surface wind speed signature is undetectable. Thus, at the inversion, the amplitude stays the same but may be modulated by the convection from below (see e.g., Kuettner et al. 1987). As a result, the cloud signatures associated with the gravity waves do not weaken as a function of fetch.
4. Summary and conclusions
In this paper, we present the results of an analysis of nearly coincident SAR and AVHRR images of Lake Superior containing the signatures of boundary layer convection and of atmospheric gravity waves forced by local terrain on the northern shore of the lake. Over the western half of the lake downstream of Grand Marais, MN, the wavelength of the gravity waves was approximately 6.0 km on 29 December 1998 and ranged from approximately 5.3 to 6.0 km on 21 January 2000. On both days, the crests were oriented parallel with the upstream terrain and approximately perpendicular to the mean wind vector observed in the surface-based inversion at INL. Finally, wind speed variance estimates from the SAR image indicated that the wind speed associated with these gravity waves decreased with increasing fetch. Based on these observations, we constructed a conceptual model of gravity waves over and in a convective boundary layer. Of great significance is the observation of variations in surface-layer stress created by the gravity waves through the intervening deep and highly convective boundary layer. The only comparable observation with which we are familiar was that of rotor waves generated by the Rockies, a much more energetic source for gravity waves than present here.
In summary, we believe that the high-resolution imaging capability of SAR can provide a powerful complement to more conventional meteorological techniques. As indicated in this paper, such high-resolution capability can be especially useful in coastal waters or the Great Lakes where accurate environmental monitoring is extremely important but where conventional meteorological monitoring is sometimes limited. Furthermore, because of their high-resolution, SAR wind maps can be a useful diagnostic tool for assessing the stability of the marine boundary layer. In fact, high-resolution estimates of the two-dimensional surface wind field are probably impossible to obtain by any other means except SAR. It is clear that SAR wind maps contain significant information important to meteorologists and climatologists as well as oceanographers. With continued research, such maps could soon become routine tools for coastal forecasting.
Acknowledgments
The authors thank Yanling Yu for her help with the AVHRR image processing; Robert Schaaf for his help in obtaining the surface and upper-air data, specifically the soundings; the Satellite Active Archive for access to the RADARSAT imagery shown here; and Ray Sterner at the Applied Physics Laboratory, Johns Hopkins University, for the high-resolution terrain map presented here. Additionally, the authors are eternally grateful to Prof. George Young for extremely insightful discussions concerning the interpretation of the results presented in this paper. Finally, the authors are profoundly grateful to Dr. Tammy Weckwerth and two additional, anonymous reviewers for their valuable suggestions for improving the manuscript.
REFERENCES
Alpers, W., and G. Stilke, 1996: Observations of a nonlinear wave disturbance in the marine atmosphere by the synthetic aperture radar aboard the ERS-1 satellite. J. Geophys. Res., 101 , 6513–6525.
Atkinson, B. W., and J. W. Zhang, 1996: Mesoscale shallow convection in the atmosphere. Rev. Geophys., 34 , 403–431.
Balaji, V., and T. L. Clark, 1988: Scale selection in locally forced convective fields and the initiation of deep cumulus. J. Atmos. Sci., 45 , 3188–3211.
Clark, T. L., T. Hauf, and J. P. Kuettner, 1986: Convectively forced internal gravity waves: Results from two-dimensional numerical experiments. Quart. J. Roy. Meteor. Soc., 112 , 899–926.
Durran, D. R., 1986: Mountain waves. Mesoscale Meteorology and Forecasting, P. S. Ray, Ed., Amer. Meteor. Soc., 793 pp.
Emery, W. J., Y. Yu, G. A. Wick, P. Schluessel, and R. W. Reynolds, 1994: Correcting infrared satellite estimates of sea surface temperature for atmospheric water vapor attenuation. J. Geophys. Res., 99 , 5219–5236.
Holmboe, J., and H. Klieforth, 1957: The mountain wave. University of California, Los Angeles, Final Rep. Contract AF19(604)-728 (DDC No. AD 133606), 290 pp.
Holton, J. R., 1992: An Introduction to Dynamic Meteorology. Academic Press, 511 pp.
Katsaros, K. B., P. W. Vachon, P. G. Black, P. P. Dodge, and E. W. Uhlhorn, 2000: Wind fields from SAR: Could they improve our understanding of storm dynamics? Johns Hopkins APL Tech. Dig., 21 , 86–93.
Kelly, R. D., 1984: Horizontal roll and boundary-layer interrelationships observed over Lake Michigan. J. Atmos. Sci., 41 , 1816–1826.
Koch, S. E., and C. O'Handley, 1997: Operational forecasting and detection of mesoscale gravity waves. Wea. Forecasting, 12 , 253–281.
Kuettner, J. P., P. A. Hildebrand, and T. L. Clark, 1987: Convection waves: Observations of gravity wave systems over convectively active boundary layers. Quart. J. Roy. Meteor. Soc., 113 , 445–468.
Miles, J. W., 1961: On the stability of heterogeneous shear flows. J. Fluid Mech., 10 , 496–508.
Monaldo, F. M., D. R. Thompson, R. C. Beal, W. G. Pichel, and P. Clementé-Colón, 2001: Comparison of SAR-derived wind speed with model predictions and ocean buoy measurements. IEEE Trans. Geosci. Remote Sens., 39 , 2587–2600.
Mourad, P. D., 1999: Footprints of atmospheric turbulence in synthetic aperture radar images of the ocean surface—A review. Air–Sea Exchange: Physics, Chemistry, Dynamics, and Statistics, G. L. Geernaert, Ed., Kluwer Academic, 269–290.
Mourad, P. D., and R. A. Brown, 1990: Multiscale large eddy states in weakly stratified planetary boundary layers. J. Atmos. Sci., 47 , 414–438.
Mourad, P. D., and B. A. Walter, 1996: Viewing a cold air outbreak using satellite-based synthetic aperture radar and Advanced Very High Resolution Radiometer Imagery. J. Geophys. Res., 101 , 16391–16400.
Mourad, P. D., D. R. Thompson, and D. C. Vandemark, 2000: Extracting fine-scale wind fields from synthetic aperture radar images of the ocean surface. Johns Hopkins APL Tech. Dig., 21 , 108–115.
Müller, G., B. Brümmer, and W. Alpers, 1999: Roll convection within an Arctic cold air outbreak: Interpretation of in situ aircraft measurements and spaceborne SAR imagery by a three-dimensional atmospheric model. Mon. Wea. Rev., 127 , 363–380.
Queney, P., 1952: Sierra Wave Project. Air Force Scientific Rep. 1, University of California, Los Angeles, 150 pp.
Queney, P., G. Corby, N. Gerbier, H. Koschmeider, and J. Zirep, 1960: The airflow over mountains. WMO Tech. Note 34, 135 pp.
Rees, W. G., and S. P. James, 1992: Angular variation of the infrared emissivity of ice and water surfaces. Int. J. Remote Sens., 13 , 2873–2886.
Rogers, D. P., D. W. Johnson, and C. A. Friehe, 1995: The stable internal boundary layer over a coastal sea. Part II: Gravity waves and momentum balance. J. Atmos. Sci., 52 , 684–696.
Sang, J. G., 1991: On formation of convective roll vortices by internal gravity waves: A theoretical study. Meteor. Atmos. Phys., 46 , 15–28.
Scorer, R. S., 1949: Theory of waves in the lee of mountains. Quart. J. Roy. Meteor. Soc., 75 , 41–56.
Scorer, R. S., . 1952: Airflow over mountains. Sci. Prog., 40 , 466–473.
Sikora, T. D., G. S. Young, R. C. Beal, and J. B. Edson, 1995: On the use of spaceborne synthetic aperture radar imagery of the sea surface in detecting the presence and structure of the convective marine atmospheric boundary layer. Mon. Wea. Rev., 123 , 3623–3632.
Thompson, D. R., and R. C. Beal, 2000: Mapping high resolution wind fields using synthetic aperture radar. Johns Hopkins APL Tech. Dig., 21 , 58–67.
Thomson, R. E., P. W. Vachon, and G. A. Borstad, 1992: Airborne synthetic aperture radar imagery of atmospheric gravity waves. J. Geophys. Res., 97 , 14249–14257.
Thompson, T. W., W. T. Liu, and D. E. Weissman, 1983: Synthetic aperture radar observation of ocean roughness from rolls in an unstable marine boundary layer. Geophys. Res. Lett., 10 , 172–1175.
Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, 367 pp.
Vachon, P. W., O. M. Johannessen, and J. A. Johannessen, 1994: An ERS-1 synthetic aperture radar image of atmospheric lee waves. J. Geophys. Res., 99 , 22483–22490.
Vachon, P. W., and Coauthors. 2000: Canadian progress toward marine and coastal applications of synthetic aperture radar. Johns Hopkins APL Tech. Dig., 21 , 33–41.
Vandemark, D., P. D. Mourad, T. L. Crawford, C. A. Vogel, J. Sin, S. A. Bailey, and B. Chapron, 2001: Measured changes in ocean surface roughness due to atmospheric boundary layer rolls. J. Geophys. Res., 106 (C3) 4639–4654.
Weckwerth, T. M., J. W. Wilson, R. Wakimoto, and N. A. Crook, 1997: Horizontal convective rolls: Determining the environmental conditions supporting their existence and characteristics. Mon. Wea. Rev., 125 , 505–526.
Weckwerth, T. M., T. W. Horst, and J. W. Wilson, 1999: An observational study of the evolution of horizontal convective rolls. Mon. Wea. Rev., 127 , 2160–2179.
Wilson, D. K., 1996: Empirical orthogonal function analysis of the weakly convective atmospheric boundary layer. Part I: Eddy structures. J. Atmos. Sci., 53 , 801–823.
Worthington, R. M., 2001: Alignment of mountain lee waves viewed using NOAA AVHRR imagery, MST radar, and SAR. Int. J. Remote Sens., 22 , 1361–1374.
Zheng, Q., X. Yan, V. Klemas, C. Ho, N. Kuo, and Z. Wang, 1998: Coastal lee waves on ERS-1 SAR images. J. Geophys. Res., 103 , 7979–7993.
Digital map of Lake Superior and surrounding regions showing the near-shore terrain hypothesized to be responsible for the gravity waves. In addition, the locations of the sounding sites INL and APX are labeled and the location of the three C-MAN stations from which synoptic-scale wind directions were obtained are labeled. (Figure courtesy of Ray Sterner at the Johns Hopkins University Applied Physics Laboratory)
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
AVHRR NOAA-12 channel-4 (centered on 10.82 μm) image taken 2339 UTC 29 Dec 1998, presented as brightness temperature. A length scale is indicated in the SW corner. The cut labeled AB is centered on the 10-km-wide section of coast from which the cross section shown in Fig. 4b is taken. Where the line AB is white, it is over Lake Superior. Where it is black, the line is over land. The vector associated with W marks the wind direction over the lowest 1 km, while that associated with N points to north
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
RADARSAT-1 SAR image taken 2349 UTC 29 Dec 1998. Radar backscatter from a 10-km-wide swath centered on the line segment labeled A′B′ was used to construct Fig. 4a. The two boxes labeled (a) and (b), respectively, on the overview image indicate the locations of the two images shown below. Various aspects of each subimage are labeled. The circle on image (a) shows one alongshore location containing wind streaks suggestive of a preexisting internal boundary layer. Image (b) shows the weakening gravity wave signatures with cellular convective structures that are elongated in the along-wind direction superimposed. The hypothesized cellular convection/gravity wave interaction is indicated by the labeled circle. Each image measures 25 km to a side. The vector associated with W marks the wind direction while that associated with N points to north
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
(a) Along-coast avg wind speed perturbations, converted from radar backscatter, centered on cut A′B′ in Fig. 3. The values were averaged over an along-coast distance of 10 km to minimize small-scale fluctuations. (b) Along-coast average brightness temperature values centered on cut AB in Fig. 1. The values were averaged over an along-coast distance of 10 km to minimize noise
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
(a) AVHRR NOAA-14 channel-4 (centered on 10.82 μm) IR image taken 0947 UTC 21 Jan 2000, given in terms of brightness temperature. A length scale is indicated in the SW corner. The line segments labeled AB and CD indicate the cuts along which the two separate wavelength analyses were centered. Where the lines AB and CD are white, they are over Lake Superior. Where they are black, the lines are over land. The vector associated with W marks the wind direction over the lowest 1 km, while that associated with N points to north. (b) AVHRR NOAA-15 channel-4 (centered on 10.82 μm) IR image taken 1318 UTC 21 Jan 2000, given in terms of brightness temperature. A length scale is indicated in the SW corner. The line segments labeled A′B′ and C′D′ indicate the cuts along which the two separate wavelength analyses were centered. Where the lines A′B′ and C′D′ are white, they are over Lake Superior. Where they are black, the lines are over land
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
(top) RADARSAT-1 SAR image taken 1213 UTC 21 Jan 2000. The line segment labeled A″B″ is centered on the 10-km-wide section of coast from which the cross section shown in Fig. 7 was taken. Line segments A″B″ and C″D″ indicate the cuts along which the two separate wavelength analyses were centered. Relevant features are labeled on each image. Arrows point to the crests of gravity waves associated with wind speed. In addition, the growth of the convective boundary layer is shown by the initial formation of convective rolls (a). In (b), hypothesized roll convection/gravity wave interactions are circled. Finally, (c) indicates where only roll convection is evident
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
Along-coast average wind speed, converted from radar backscatter, centered on cut A″B″ in Fig. 6. The values were averaged over an along-coast distance of 10 km to minimize small-scale fluctuations. Both the northern and southern coastlines are labeled
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
Average roll spacing plotted as a function of fetch for 21 Jan 2000. These observations were obtained by measuring the distance from cloud to cloud (AVHRR), clear to clear (AVHRR), bright to bright (SAR) and dark to dark (SAR) at various values of offshore fetch. In addition, error bars representing ±1 standard deviation are included to indicate variability
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
Profiles of virtual potential temperature calculated from original soundings at INL and APX for (a) 0000 UTC 30 Dec 1998 and (b) 1200 UTC 21 Jan 2000. These data were obtained from the temperature and moisture parameters reported at both stations
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
Scorer parameter estimated for (a) 0000 UTC on 30 Dec 1998 and (b) 1200 UTC 21 Jan 2000. The parameters were calculated using Eq. (1) and the appropriate INL sounding
Citation: Monthly Weather Review 130, 11; 10.1175/1520-0493(2002)130<2764:DIOGWO>2.0.CO;2
