Boundary-Layer Meteorology

, Volume 140, Issue 1, pp 87–103 | Cite as

A Lagrangian Model to Predict the Modification of Near-Surface Scalar Mixing Ratios and Air–Water Exchange Fluxes in Offshore Flow

  • Mark D. Rowe
  • Judith A. Perlinger
  • Christopher W. Fairall


A model was developed to predict the modification with fetch in offshore flow of mixing ratio, air–water exchange flux, and near-surface vertical gradients in mixing ratio of a scalar due to air–water exchange. The model was developed for planning and interpretation of air–water exchange flux measurements in the coastal zone. The Lagrangian model applies a mass balance over the internal boundary layer (IBL) using the integral depth scale approach, previously applied to development of the nocturnal boundary layer overland. Surface fluxes and vertical profiles in the surface layer were calculated using the NOAA COARE bulk algorithm and gas transfer model (e.g., Blomquist et al. 2006, Geophys Res Lett 33:1–4). IBL height was assumed proportional to the square root of fetch, and estimates of the IBL growth rate coefficient, α, were obtained by three methods: (1) calibration of the model to a large dataset of air temperature and humidity modification over Lake Ontario in 1973, (2) atmospheric soundings from the 2004 New England Air Quality Study and (3) solution of a simplified diffusion equation and an estimate of eddy diffusivity from Monin–Obukhov similarity theory (MOST). Reasonable agreement was obtained between the calibrated and MOST values of α for stable, neutral, and unstable conditions, and estimates of α agreed with previously published parametrizations that were valid for the stable IBL only. The parametrization of α provides estimates of IBL height, and the model estimates modification of scalar mixing ratio, fluxes, and near-surface gradients, under conditions of coastal offshore flow (0–50 km) over a wide range in stability.


Air–sea gas exchange Bulk Richardson number Internal boundary layer Offshore flow Stability 

List of Symbols


Land–lake air temperature modification


Land–lake dewpoint temperature modification


Fraction of h that defines the top of the surface layer


Flux per unit area at the surface


Acceleration due to gravity


Integral depth scale


Upper portion of the integral depth scale above the surface layer


Lower, surface-layer portion of the integral depth scale


Height of the internal boundary layer


Turbulent eddy diffusivity


Atmospheric gas transfer velocity


Obukhov length


Exponent that determines the shape of the IBL mixing ratio profile


Atmospheric pressure


Gas constant


Bulk Richardson number


Bulk Richardson number defined using upstream, overland meteorological Variables at 10-m reference height


Gas mixing ratio as a function of height


Upstream, overland mixed layer gas mixing ratio


Gas mixing ratio at the surface


Absolute temperature


Mean wind speed in the x direction


Wind speed at 10-m height


Wind speed averaged vertically over the IBL


Friction velocity


Horizontal dimension aligned with the mean wind


Fetch: distance travelled by the air mass over water from the coast


Vertical dimension, positive upward


Profile matching height; border between the surface layer and the IBL


Aerodynamic roughness length


Reference height at which wind speed or scalar has a known value


IBL growth rate coefficient


Lapse rate: deviation of temperature or mixing ratio vertical profile from well-mixed condition


Dry adiabatic lapse rate, γd = −0.0098 K m−1


Environmental lapse rate


Potential temperature


Virtual potential temperature


Upstream, overland mixed layer θv


θv of air at equilibrium with the water surface


von Kármán constant, assumed to have a value of 0.4

\({\Phi_{\rm H}(z/L)}\)

MOST gradient profile function for potential temperature


MOST integral profile function for wind speed


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Angevine W, Hare J, Fairall C, Wolfe D, Hill R, Brewer W, White A (2006a) Structure and formation of the highly stable marine boundary layer over the Gulf of Maine. J Geophys Res 111: D23S22. doi:10.1029/2006JD007465 CrossRefGoogle Scholar
  2. Angevine WM, Tjernstrom M, Zagar M (2006b) Modeling of the coastal boundary layer and pollutant transport in New England. J Appl Meteorol 45: 137–154CrossRefGoogle Scholar
  3. Blomquist BW, Fairall CW, Huebert BJ, Kieber DJ, Westby GR (2006) DMS sea–air transfer velocity: direct measurement by eddy covariance and parameterization based on the NOAA/COARE gas transfer model. Geophys Res Lett 33: 1–4CrossRefGoogle Scholar
  4. Craig R (1946) Measurements of temperature and humidity in the lowest 1000 feet of the atmosphere over Massachusetts Bay. Pap Phys Oceanogr Meteorol 10: 1–47Google Scholar
  5. Croley TE II (1989) Verifiable evaporation modeling on the Laurentian Great Lakes. Water Resour Res 25(5): 781–792CrossRefGoogle Scholar
  6. Croley TE, Hunter TS (1996) Great lakes monthly hydrologic data. Great Lakes Environmental Research Laboratory. Accessed 9 October 2009
  7. Draxler R, Stunder B, Rolph G, Stein A, Taylor A (2009) HYSPLIT (Hybrid single-particle Lagrangian integrated trajectory) model, v. 4.9. National Oceanic and Atmospheric Administration Air Resources Laboratory. Accessed 9 October 2009
  8. Environment Canada (2009) National climate data and information archive. Accessed 10 October 2009
  9. Fairall CW, Hare JE, Edson JB, McGillis W (2000) Parameterization and micrometeorological measurement of air–sea gas transfer. Boundary-Layer Meteorol 96: 63–105CrossRefGoogle Scholar
  10. Fairall CW, Bradley EF, Hare JE, Grachev AA, Edson JB (2003) Bulk parameterization of air–sea fluxes: updates and verification for the COARE algorithm. J Clim 16: 571–591CrossRefGoogle Scholar
  11. Fairall CW, Bariteau L, Grachev AA, Hill RJ, Wolfe DE, Brewer WA, Tucker SC, Hare JE, Angevine WM (2006) Turbulent bulk transfer coefficients and ozone deposition velocity in the International Consortium for Atmospheric Research into Transport and Transformation. J Geophys Res 111: 1–19CrossRefGoogle Scholar
  12. Garratt JR (1987) The stably stratified internal boundary layer for steady and diurnally varying offshore flow. Boundary-Layer Meteorol 38: 369–394CrossRefGoogle Scholar
  13. Garratt JR (1990) The internal boundary layer—a review. Boundary-Layer Meteorol 50: 171–203CrossRefGoogle Scholar
  14. Hsu SA (1989) A verification of an analytical formula for estimating the height of the stable internal boundary layer. Boundary-Layer Meteorol 48: 197–201CrossRefGoogle Scholar
  15. Mahrt L (1999) Stratified atmospheric boundary layers. Boundary-Layer Meteorol 90: 375–396CrossRefGoogle Scholar
  16. McGillis WR, Edson JB, Zappa CJ, Ware JD, McKenna SP, Terray EA, Hare JE, Fairall CW, Drennan W, Donelan M, DeGrandpre MD, Wanninkhof R, Feely RA (2004) Air–sea CO2 exchange in the Equatorial Pacific. J Geophys Res 109: C08S02. doi:10.1029/2003JC002256 CrossRefGoogle Scholar
  17. Melas D (1989) The temperature structure in a stably stratified internal boundary layer over a cold sea. Boundary-Layer Meteorol 48: 361–375CrossRefGoogle Scholar
  18. Mulhearn P (1981) On the formation of a stably stratified internal boundary-layer by advection of warm air over a cooler sea. Boundary-Layer Meteorol 21: 247–254CrossRefGoogle Scholar
  19. Perlinger JA, Tobias DE, Morrow PS, Doskey PV (2005) Evaluation of novel techniques for measurement of air–water exchange of persistent bioaccumulative toxicants in Lake Superior. Environ Sci Technol 39: 8411–8419CrossRefGoogle Scholar
  20. Perlinger JA, Rowe MD, Tobias DE (2008) Atmospheric transport and air–water exchange of hexachlorobenzene in Lake Superior. Organohalogen Compd 70: 598–601Google Scholar
  21. Phillips DW, Irbe JG (1978) Land-to-lake comparison of wind, temperature, and humidity on Lake Ontario during the International Field Year for the Great Lakes (IFYGL). Atmospheric Environment Service, Environment Canada, Downsview, Ontario, 51 ppGoogle Scholar
  22. Seinfeld JH, Pandis SN (1998) Atmospheric chemistry and physics. Wiley, New York, p 1326Google Scholar
  23. Smedman A-S, Bergström H, Grisogono B (1997) Evolution of stable internal boundary layers over a cold sea. J Geophys Res 102(C1): 1091–1099CrossRefGoogle Scholar
  24. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer, Dordrecht, p 670Google Scholar
  25. Taylor G (1915) Eddy motion in the atmosphere. Phil Trans Roy Soc London Ser A 215: 1–26. Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Mark D. Rowe
    • 1
    • 2
  • Judith A. Perlinger
    • 1
  • Christopher W. Fairall
    • 3
  1. 1.Department of Civil and Environmental EngineeringMichigan Technological UniversityHoughtonUSA
  2. 2.Large Lakes and Rivers Forecasting Research BranchU.S. Environmental Protection AgencyGrosse IleUSA
  3. 3.Earth System Research LaboratoryNational Oceanic and Atmospheric AdministrationBoulderUSA

Personalised recommendations