Abstract
We present results of a technique for examining the scale-dependence of the gradient Richardson number, Ri, in the nighttime residual layer. The technique makes use of a series of high-resolution, in situ, vertical profiles of wind speed and potential temperature obtained during CASES-99 in south-eastern Kansas, U.S.A. in October 1999. These profiles extended from the surface, through the nighttime stable boundary layer, and well into the residual layer. Analyses of the vertical gradients of both wind speed, potential temperature and turbulence profiles over a wide range of vertical scale sizes are used to estimate profiles of the local Ri and turbulence structure as a function of scale size. The utility of the technique lies both with the extensive height range of the residual layer as well as with the fact that the sub-metre resolution of the raw profiles enables a metre-by-metre ‘sliding’ average of the scale-dependent Richardson number values over hundreds of metres vertically. The results presented here show that small-scale turbulence is a ubiquitous and omnipresent feature of the residual layer, and that the region is dynamic and highly variable, exhibiting persistent turbulent structure on vertical scales of a few tens of metres or less. Furthermore, these scales are comparable to the scales over which the Ri is less than or equal to the critical value of Ri c of 0.25, although turbulence is also shown to exist in regions with significantly larger Ri values, an observation at least consistent with the concept of hysteresis in turbulence generation and maintenance. Insofar as the important scale sizes are comparable to or smaller than the resolution of current models, it follows that, in order to resolve the observed details of small Ri values and the concomitant turbulence generation, future models need to be capable of significantly higher resolutions.
Similar content being viewed by others
References
Angevine WM, Bakwin PS, Davis KJ (1998) Wind profiler and RAQSS measurements compared with measurements from a 450 m tower. J Atmos Oceanic Technol 12: 818–825
Balsley BB, Jensen ML, Frehlich R (1998) The use of state-of-the-art kites for profiling the lower atmosphere. Boundary-Layer Meteorol 87: 1–25
Balsley BB, Frehlich RG, Jensen ML, Meillier Y, Muschinski A (2003) Extreme gradients in the nocturnal boundary layer: structure, evolution, and potential causes. J Atmos Sci 60: 2496–2508
Balsley BB, Frehlich RG, Jensen ML, Meillier Y (2006) High-resolution in situ profiling through the stable boundary layer: examination of the SBL top in terms of minimum shear, maximum stratification, and turbulence decrease. J Atmos Sci 63: 1291–1307
Banta R, Newsom R, Lundquist J, Pichugina Y, Coulter R, Mahrt L (2002) Nocturnal low-level jet characteristics over Kansas during CASES-99. Boundary-Layer Meteorol 105: 221–252
Banta R, Pechugina Y, Newsom R (2003) Relationship between low-level jet properties and turbulence kinetic energy in the nocturnal stable boundary layer. J Atmos Sci (Notes and Correspondence) 60: 2549–2555
Basu S, Porté-agel F, Foufoula-Georgiou E, Vinuesa J-V, Pahlow M (2006) Revisiting the local scaling hypothesis in stably stratified atmospheric boundary-layer turbulence: an integration of field and laboratory measurements with large-eddy simulations. Boundary-Layer Meteorol 119: 473–500
Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Clarendon Press, Oxford, p 652
Chimonas G (2002) On internal gravity waves associated with the stable boundary layer. Boundary-Layer Meteorol 102: 139–155
Cohn SA, Angevine WM (2000) Boundary layer height and entrainment zone thickness measured by lidars and wind profiling radars. J Appl Meteorol 39: 1233–1248
Corsmeier U, Kalthoff N, Kolle O, Kotsian M, Fiedler F (1997) Ozone concentration jump in the stable nocturnal boundary layer during a LLF-event. Atmos Environ 31: 1977–1989
Coulter R, Doran J (2002) Spatial and temporal occurrences of intermittent turbulence during CASES-99. Boundary-Layer Meteorol 105: 329–349
Coulter R, Kallistratova M (2004) Two decades of progress in SODAR techniques: a review of 11 ISARS proceedings. Meteor Atmos Phys 85: 3–19
Eaton F, Mclaughlin A, Hines JR (1995) A new frequency-modulated continuous wave radar for studying planetary boundary layer morphology. Radio Sci 30: 75–88
Fochesatto GJ, Drobinski P, Flamant C, Guedalia D, Sarrat C, Flamant PH, Pelon J (2001) Evidence of dynamical coupling between the residual layer and the developing convective boundary layer. Boundary-Layer Meteorol 99: 451–464
Frehlich RG, Meillier Y, Jensen ML, Balsley BB (2003) Turbulence measurements with the CIRES TLS (Tethered Lifting System) during CASES-99. J Atmos Sci 60: 2487–2495
Frehlich RG, Meillier Y, Jensen ML, Balsley BB (2004) A statistical description of small-scale turbulence in the low-level nocturnal jet. J Atmos Sci 61: 1079–1085
Fritts DC, Nappo C, Riggin CM, Balsley BB, Eichinger WE, Newsom RK (2003) Analysis of ducted motions in the stable nocturnal boundary layer during CASES-99. J Atmos Sci 60: 2450–2472
Garratt JR (1994) The atmospheric boundary layer. Cambridge University Press, U.K., 316 pp
Glickman T (ed) (2000) Glossary of meteorology, 2nd edn. Amer Meteor Soc 855 pp
Gossard EE, Gaynor JE, Zamora RJ, Neff WD (1985) Finestructure of elevated stable layers observed by sounder and in situ tower sensors. J Atmos Sci 42: 2156–2169
Hines C (1988) Generation of turbulence by atmospheric waves. J Atmos Sci 45: 1269–1278
Holden J, Derbyshire S, Belcher S (2000) Tethered balloon observations of the nocturnal stable boundary layer in a valley. Boundary-Layer Meteorol 97: 1–24
Jacobitz F, Surkar S (1998) The effect of nonvertical shear on turbulence in a stably stratified medium. Phys Fluids 10: 1158–1168
Jacobson MZ (1999) Fundamentals of atmospheric modeling. Cambridge University Press, U.K., 656 pp
Kolev I, Savov P, Kaprielov B, Parvanov O, Simeonov V (2000) Lidar observation of the nocturnal boundary layer formation over Sofia, Bulgaria. Atmos Environ 34: 3223–3235
Mahrt L (1999) Stratified atmospheric boundary layers. Boundary-Layer Meteorol 90: 375–396
Mahrt L, Sun J, Blumen W, Delaney T, Oncley S (1998) Nocturnal boundary layer regimes. Boundary-Layer Meteorol 88: 255–278
Mahrt L, Vickers D (2002) Contrasting vertical structures of nocturnal boundary layers. Boundary-Layer Meteorol 103: 351–363
Majda A, Shefter M (1998a) The instability of stratified flows at large Richardson number. Proc Natl Acad Sci USA 93: 7850–7853
Majda A (1998b) Elementary stratified flows with instability at large Richardson number. J Fluid Mech 376: 319–350
Mauritsen T, Svensson G (2007) Observations of stably stratified shear-driven atmospheric turbulence at low and high richardson numbers. J Atmos Sci 64: 645–655
Meillier Y (2004) Periodic modulation of fine-scale turbulence by gravity waves above the nocturnal boundary layer: experimental validation using in situ measurements. PhD Thesis, University of Colorado, Boulder, Colorado, 145 pp
Mengesha YG, Taylor PA, Lenschow DH (2001) Boundary layer turbulence over the Nebraska sand hills. Boundary-Layer Meteorol 100: 3–46
Miles JW (1961) On the stability of heterogeneous shear flow. J Fluid Mech 10: 496–508
Muschinski A, Frehlich R, Jensen ML, Hugo R, Hoff A, Eaton F, Balsley BB (2001) Fine-scale measurements of turbulence in the lower troposphere: an intercomparison between a kite- and balloon-borne, and a helicopter-borne measurement system. Boundary-Layer Meteorol 98: 219–250
Muschinski A, Frehlich R, Balsley BB (2004) Small-scale and large-scale intermittency in the boundary layer and residual layer. J Fluid Mech 515: 319–351
Nappo CJ (2002) An introduction to gravity atmospheric waves. International Geophysics Series, 85, Academic Press, San Diego, USA, 279 pp
Nilsson ED, Rannik U, Kulmala M, Buzorius G, O’Dowd CD (2001) Effects of continental boundary layer evolution, convection, turbulence and entrainment, on aerosol formation. Tellus Series B-Chem Phys Meteorol 53(4): 441–461
Poulos GS, Blumen W, Fritts DC, Lundquist JK, Sun J, Burns SP, Nappo C, Banta R, Newsom R, Cuxart J, Terradellas E, Balsley BB, Jensen ML (2002) CASES-99: a comprehensive investigation of the stable nocturnal boundary layer. Bull Am Meteorol Soc 83: 555–581
Reitebuch O, Strassburger A, Emeis S, Kuttler W (2000) Nocturnal secondary ozone concentration maxima analysed by sodar observations and surface measurements. Atmos Environ 34: 4215–4329
Rohr JJ, Itsweire E, Helland K, Van Atta CW (1988) Growth and decay of turbulence in a stably stratified shear flow. J Fluid Mech 195: 77–111
Rotach MW, Vogt R, Bernhofer C, Batchverova E, Christen A, Clappier A, Feddersen B, Gryning S-E, Martucci G, Mayer H, Mitev V, Oke TR, Parlow E, Richner H, Roth M, Roulet Y-A, Ruffieux D, Salmond JA, Schatzmann M, Voogt JA (2005) BUBBLE – an urban boundary layer meteorology project. Theor Appl Climatol 81: 231–261
Salmond JA, McKendry IG (2002) Secondary ozone maxima in a very stable nocturnal boundary layer: observations from the lower Fraser valley BC. Atmos Environ 36: 5771–5782
Siebert H, Wendisch M, Conrath T, Teichmann U, Heintzenberg J (2002) A new tethered balloon-borne payload for fine-scale observations in the cloudy boundary layer. Boundary-Layer Meteorol 106: 461–482
Strauch RG, Campbell WC, Chadwick RB, Moran KP (1976) Microwave FM-CW Doppler radar for boundary layer probing. Geophys Res Lett 3: 193–196
Stull R (1993) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht, 666 pp
Vickers D, Mahrt L (2003) The co-spectral gap and turbulent flux calculations. J Atmos Oceanic Technol 20: 660–672
Yi C, Davis KJ, Berger BW, Bakwin PS (2001) Long-term observations of the dynamics of the continental planetary boundary layer. J Atmos Sci 58: 1288–1299
Zang J, Rao ST (1999) The role of vertical mixing in the temporal evolution of ground-level ozone concentrations. J Appl Meteorol 38: 1674–1691
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Balsley, B.B., Svensson, G. & Tjernström, M. On the Scale-dependence of the Gradient Richardson Number in the Residual Layer. Boundary-Layer Meteorol 127, 57–72 (2008). https://doi.org/10.1007/s10546-007-9251-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10546-007-9251-0