Atmospheric Chemistry and Physics Discussions www.atmos-chem-phys-discuss.net 1680-7367 1680-7375 8 4 2008 10.5194/acpd-8-13667-2008 http://www.atmos-chem-phys-discuss.net/8/13667/2008/ http://www.atmos-chem-phys-discuss.net/8/13667/2008/acpd-8-13667-2008.html http://www.atmos-chem-phys-discuss.net/8/13667/2008/acpd-8-13667-2008.pdf 13667 13688 2008-07-17 The von Kármán constant retrieved from CASE-97 dataset using a variational method Y. Zhang J. Ma Jianmin.ma@ec.gc.ca Z. Cao Zhuhai Air Traffic Management Station CAAC, Zhuhai International Airport, Sanzao, Zhuhai 519040, Guangdong, P. R. China Air Quality Research Division, Science and Technology Branch, Environment Canada, 4905 Dufferin Street, Toronto, Ontario M3H 5T4, Canada Meteorological Service of Canada, 4905 Dufferin Street, Toronto, Ontario M3H 5T4, Canada A variational method is developed to retrieve the von Kármán constant κ from the CASES-97 dataset, collected near Wichita, Kansas, the United States from 6 April to 24 May 1997. In the variational method, a cost function is defined to measure the difference between observed and computed gradients of wind speed, air temperature and specific humidity. An optimal estimated von Kármán constant is obtained by minimizing the cost function through adjusting values of the von Kármán constant. Under neutral stratification, the variational analysis confirms the conventional value of κ(=0.40). For non-neutral stratification, however, κ varies with stability. The computational results show that the κ decreases monotonously from stable to unstable stratification. The variational calculated mean value of the von Kármán constant is 0.390 when the atmospheric stratification is taken into consideration. Relations between κ and surface momentum and heat flux are also examined. Andreas, E., Claffey, K. J., Jordan, R. E., Fairall, C. W., Guest, P. S., Persson, P. O., and Grachev, A. A.: Evaluations of the von Kármán constant in the atmospheric surface layer, J. Fluid Mech., 559, 117–149, doi:10.1017/S0022112006000164, 2006. Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: Flux profile relationships in the atmospheric surface layer, J. Atmos. Sci., 28, 181–189, 1971. Cai, X. M. and Steyn, D. G.: The von Kármán constant determined by large eddy simulation, Bound.-Lay. Meteorol., 78, 143–164, 1996. Cao, Z. and Ma, J.: An application of the variational method to computation of sensible heat flux over a deciduous forest, J. Appl. Meteorol., 44, 144–152, 2005 Cao, Z., Ma, J., and Wayne R. R.: Improving computation of sensible heat flux over a water surface using the variational method, J. Hydrometeorol., 7, 678–686, 2006. Fleagle, R. G. and Businger, J. A.: An Introduction to Atmospheric Physics, 2dn Ed., Academic Press, New York, 1980. Frenzen, P. and Vogel, C. A.: On the magnitude and apparent range of variation of the von Karman constant in the atmospheric surface layer, Bound.-Lay. Meteorol., 72, 371–392, 1995. Garratt, J. R.: The Atmospheric Boundary Layer, Cambridge University Press, New York, 1992. Högström, U.: Review of some basic characteristics of the atmospheric surface layer, Bound.-Lay. Meteorol., 78, 215–246, 1996. Kondo, J. and Sato, T.: The Determination of the von Karman constant, J. Meteorol. Soc. Jpn., 60, 461–470, 1982. Ma, J. and Daggupaty, S. M.: Using all observed information in a variational approach in measuring z$_\rm 0m$ and z$_\rm 0t$, J. Appl. Meteorol., 39, 1391–1401, 1999. Parlange, M. B. and Katul, G. G.: Watershed scale stress from Tethersonde wind profile measurements under near neutral and unstable atmospheric stability, Water Resour. Res., 31, 961–968, 1995. Sheppard, P. A.: The aerodynamic drag of the Earth's surface and the value of Karman's constant in the lower atmosphere, Proc. R. Soc. Lon. Ser.-A, 188, 208–222, 1947. Wieringa, J.: A revaluation of the Kansas mast influence on measurements of stress and cup anemometer overspeeding, Bound.-Lay. Meteorol., 18, 411–430, 1980. Yaglom, A. M.: Comments on wind and temperature flux-profile relationships, Bound.-Lay. Meteorol., 11, 89–102, 1977. Zhang, S. F., Oncley, S. P., and Businger, J. A.: Evaluation of the von Karman constant from a new surface layer experiment, Proc. Eighth Symp. On Turbulence and Diffusion, San Diego, CA, 25–29 April, Amer. Meteorol. Soc., 148–150, 1988.