Boundary-layer effects on mountain waves: a new look at some historical studies

Abstract

Early studies of mountain waves reported various results that have rarely been investigated since. These include: large-amplitude mountain waves above an unstable boundary layer much higher than the mountains; a repeated downwind drift and upwind jump of mountain waves; and larger vertical wind magnitude near sunrise and/or sunset. These are investigated using over 3,000 radiosondes and meso-strato-troposphere (MST) radar. Superadiabatic temperature gradients are found beneath mountain waves, explainable by convection which appears to raise the mountain-wave launching height. Movement of mountain-wave patterns is studied by a new method using height–time vertical wind data. A swaying motion of mountain waves, with period of a few minutes, appears to be equally upwind and downwind, rather than asymmetric at the heights measurable. Also, vertical wind shows no change in mean, variance or extreme values near sunrise and sunset, despite the expected diurnal changes of boundary-layer structure. An explanation for differences between MST radar and other measurements and models of mountain waves is suggested in terms of more than one variety of mountain wave. Type 1 has stable air near the ground; type 2 is above a convective/turbulent boundary layer of significant height as compared to the mountains.

Appendix: Pioneering studies of mountain-wave rotors and convection waves (Steinig, Küttner, Höhndorf, Georgii)

Another example of the reviving of a historical research area is the T-REX campaign (Grubišić et al. 2008), modern work on rotors beginning with Doyle and Durran (2002). Grubišić and Lewis (2004) review work from the 1950s. Also, Grubišić and Orlić (2007) draw attention to an early paper on rotors (Mohorovičič 1889) which had fallen into obscurity. However, a group of pioneering twentieth century papers on this subject is still unknown to the modern scientific literature. The opportunity is, therefore, taken to cite and briefly review these works, in a forgotten group of journals and branch of the literature.

Most are published in the journal Deutsche Luftwacht Ausgabe Luftwelt, also known as Luftwelt, its sister journal Deutsche Luftwacht Ausgabe Luftwissen, and Luftfahrt und Schule. They appear not to be cited in the contemporary Bibliography of Meteorological Literature and possibly the Bibliographie Météorologique Internationale. The reason may be that the journals were aimed at a German national not international readership, and contained significant amounts of politics alongside scientific papers. Worthington (2013) gives a wider historical review.

According to conventional history of mountain waves, “Queney in his paper Influence du relief sur les éléments météorologiques, published in 1936, can claim to have predicted mountain waves before their occurrence in the atmosphere had been properly appreciated—a rare event in meteorological progress” (Queney et al. 1960). Blumen (1990) writes that Queney “did in fact provide the theoretical explanation of the so-called mountain lee wave in 1936 before this phenomenon was properly depicted by observational means”.

However, the first glider flights in mountain waves, by W Hirth and H Deutschmann, were written up in 1933 (Hirth 1933; Slater 1933). Then, Steinig (1935, 1936a, b, 1937), Küttner (1937a, b, c) describe glider flights in mountain wave and rotors, finding large $w$ to extend through the troposphere, and setting height records. The first observational description in a meteorological rather than aviation journal appears to be Küttner (1938).

Reviewing convection waves, Bradbury (1990) gives an earliest reference from 1960. However, convection waves were also known since the 1930s. Höhndorf (1937a, b) writes about lenticular clouds caused by rapidly rising cumulus and cumulonimbus which have taken over the role of orographic obstacle. Georgii (1940) suggests that waves above thunderstorms and storm fronts could be soarable as high as the stratosphere. Stranz (1943) describes a series of wave clouds, formed from warm air rising above an industrial heat source, reaching an inversion layer and oscillating about its equilibrium level. Georgii (1949) writes about standing waves, stationary relative to cold fronts which take the place of a mountain. Sirretta (1950) writes of convection as ‘meteorological relief’, causing larger waves than mountain relief.

Table 1 Percentage probability of various combinations of superadiabatic and inversion temperature gradients in individual radiosondes

Fig. 1

Land height map centred on the MST radar, also showing locations of the anemometer and radiosonde launch site at Aberporth

Fig. 2

Occurrence of superadiabatic lapse rate from radiosondes at four times of day, as a function of simultaneous vertical wind magnitude measured by MST radar at 1.7–5 km height. Vertical grey lines represent individual radiosondes, with overlapping black dots showing regions of each ascent with temperature gradient $<$–9.8 $^{\circ }$C km$^{-1},$ fitted over a 200-m height interval centred on each dot. Larger grey dots show a histogram of land height in a 150 km $\times$ 150 km area centred on the MST radar

Fig. 3

Diurnal and seasonal variation of MWLH in metres, derived as in Fig. 10 of Worthington (1999b) using radiosondes at 5, 11, 17, 23 UT, their times marked by dotted lines. The unshaded region is day, and shaded region is night

Fig. 4

Percentage probability of (1) superadiabatic, (2) weakly stable, (3) intermediate and (4) inversion temperature gradients as function of height, measured by radiosondes. Also shown is land height as in Fig. 2 (grey dots)

Fig. 5

As Fig. 2 for inversions, temperature gradient $>$0 $^{\circ }$C km$^{-1}$

Fig. 6

A Oscillation of $w$ with height for one vertical wavelength of a mountain wave. The grey line shows unsmoothed data; a, b, c, d mark regions of phase 0–$\frac{\pi }{2},$ $\frac{\pi }{2}$–$\pi ,$ $\pi$–$\frac{3\pi }{2},$ $\frac{3\pi }{2}$–$2\pi .$ B Vertical cross-section through the wave in A, showing phase lines (dashed lines) tilted upwind with increasing height. Airflow is from left to right. a, b, c, d mark regions of phase corresponding to plot A. Positive $w$ is shown as upward. The radar is at the centre of the horizontal distance axis. C Time variation of $w$ for a wave pattern repeatedly drifting downwind and reforming upwind (Förchtgott 1957), for the phases in plot A

Fig. 7

a Height–time plot of $w$ smoothed with a 2-km running mean, showing a mountain wave. b Upwind or downwind drift of the wave using the data in a; white is downwind and black is upwind drift, showing rapid upwind and downwind movements often with vertical continuity over a few km height

Fig. 8

As Fig. 7 for mountain waves in easterly wind, the waves not propagating above $\sim 10$ km height, with calm vertical wind above

Fig. 9

Probability distribution of a, b surface wind speed and c, d $w$ at 1.7–2.5 km height as a function of time from sunrise and sunset. Plotted values are number of data points per 1 min $\times$ 0.25 m s$^{-1}$ bin in a, b and 5 min $\times$ 0.02 m s$^{-1}$ bin in c, d