Biogeosciences www.biogeosciences.net 1726-4170 1726-4189 7 4 2010 10.5194/bg-7-1271-2010 http://www.biogeosciences.net/7/1271/2010/ http://www.biogeosciences.net/7/1271/2010/bg-7-1271-2010.html http://www.biogeosciences.net/7/1271/2010/bg-7-1271-2010.pdf 1271 1278 2010-04-19 Surface layer similarity in the nocturnal boundary layer: the application of Hilbert-Huang transform J. Hong jhong@nims.re.kr J. Kim H. Ishikawa Y. Ma National Institute for Mathematical Sciences, Daejeon, Korea Global Environment Lab, Department of Atmospheric Sciences, Yonsei University, Seoul, Korea Global Center for Sustainable Urban Regeneration, Institute of Industrial Science, The University of Tokyo, Tokyo, Japan Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China Turbulence statistics such as flux-variance relationship are critical information in measuring and modeling ecosystem exchanges of carbon, water, energy, and momentum at the biosphere-atmosphere interface. Using a recently proposed mathematical technique, the Hilbert-Huang transform (HHT), this study highlights its possibility to quantify impacts of non-turbulent flows on turbulence statistics in the stable surface layer. The HHT is suitable for the analysis of non-stationary and intermittent data and thus very useful for better understanding the interplay of the surface layer similarity with complex nocturnal environment. Our analysis showed that the HHT can successfully sift non-turbulent components and be used as a tool to estimate the relationships between turbulence statistics and atmospheric stability in complex environments such as nocturnal stable boundary layer. Basu, S., Porte-Agel, F., Foufoula-Georgiou, E., Vinuesa, J F., and Pahlow, M.: Revisiting the local scaling hypothesis in stably stratified atmospheric boundary-layer turbulence: An integration of field and laboratory measurements with large-eddy simulations, Bound.-Lay. Meteorol., 119, 473–500, 2006. Bendat, J S. and Piersol, A G.: Random Data: Analysis and Measurement Procedures, Wiley-Interscience, New York, 3~Edn., 2000. Brunet, Y. and Collineau, S.: Wavelet analysis of diurnal and nocturnal turbulence above a maize crop, in: Wavelets in Geophysics, edited by Foufoula-Georgiou, E. and Kumar, P., pp. 129–150, Academic Press, 1994. Cheng, Y. and Brutsaert, W.: Flux-profile relationships for wind speed and temperature in the stable atmospheric boundary layer, Boundary-Layer Meteorol., 114, 519–538, 2005. Cheng, Y., Parlange, M., and Brutsaert, W.: Pathology of Monin-Obukhov similarity in the stable boundary layer, J. Geophy. Res., 110, D06101, \doi10.1029/2004JD004923, 2005. Choi, T., Hong, J., Kim, J., Lee, H C., Asanuma, J., Ishikawa, H., Tsukamoto, O., Zhiqiu, G., Ma, Y., Ueno, K., Wang, J., Koike, T., and Yasunari, T.: Turbulent Exchange of Heat, Water Vapor and Momentum over a Tibetan Prairie by Eddy Covariance and Flux-Variance Measurements, J. Geophy. Res., 109, D21106, \doi10.1029/2004JD004767, 2004. Claerbout, J F.: Fundamentals of Geophysical Data Processing, McGraw-Hill Press, Oxford, 1976. Collineau, S. and Brunet, Y.: Detection of turbulent coherent motions in a forest canopy. Part I: Wavelet analysis, Bound.-Lay. Meteorol., 65, 357–379, 1993. Cuxart, J., Morales, G., Terradellas, E., and Yagüe, C.: Study of coherent structures and estimation of the pressure transport terms for the nocturnal stable boundary layer, Bound.-Lay. Meteorol., 105, 305–328, 2002. de~Bruin, H. A R.: Analytic solutions of the equations governing the temperature fluctuation method, Bound.-Lay. Meteorol., 68, 67–81, 1994. Dias, N L. and Brutsaert, W.: Radiative effects on temperature in the stable surface layer, Bound.-Lay. Meteorol., 89, 141–159, 1998. Dias, N L., Brutsaert, W., and Wesely, M L.: Z-less stratification under stable conditions, Bound.-Lay. Meteorol., 75, 175–187, 1995. Dias, N L., Hong, J., Leclerc, M., Black, T A., Nesic, Z., and Krishnan, P.: A simple method for scalar flux estimates over forests, Boundary-Layer Meteorol., 132, 401–414, 2009. Duffy, D G.: The application of Hilbert-Huang transforms to meteorological datasets, in: Hilbert-Huang Transform and Its Applications, edited by Huang, N E. and Shen, S P., pp. 129–147, World Scientific, Singapore, 2005. Einaudi, F. and Finnigan, J J.: The interaction between an internal gravity wave and the planetary boundary layer. Part I: The linear analysis, Quart. J. Roy. Meteorol. Soc., 107, 793–806, 1981. Finnigan, J J.: A note on wave-turbulence interaction and the possibility of scaling the very stable boundary layer, Bound.-Lay. Meteorol., 90, 529–539, 1999. Foken, T. and Wichura, B.: Tools for quality assessment of surface-based flux measurements, Agricultural and Forest Meteorology, 78, 83–105, 1996. Gabor, D.: Theory of communications, J. IEE, 93, 429–457, 1946. Grachev, A A., Fairall, C W., Persson, P. O G., Andreas, E L., and Guest, P S.: Stable boundary-layer scaling regimes: The Sheba data, Bound.-Lay. Meteorol., 116, 201–235, 2005. Högstrom, U.: Analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions, J. Atmos. Sci., 47, 1949–1972, 1990. Hong, J., Choi, T., Ishikawa, H., and Kim, J.: Turbulence structures in the near-neutral surface layer on the Tibetan plateau, Geophy. Res. Lett., 31, L15016, \doi10.1029/2004GL 019935, 2004. Hong, J.: Note on turbulence statistics in z-less stratification, Asia-Pacific, J. Atmos. Sci., 46, 113–117, 2010. Howell, H. and Mahrt, L.: An Adaptive Decomposition: Application to Turbuelnce, in: Wavelets in Geophysics, edited by Foufoula-Georgiou, E. and Kumar, P., pp. 107–128, Academic Press, 1994. Huang, N E., Shen, Z., Long, S R., Wu, M C., Shih, H H., Zheng, Q., Yen, N., Tung, C C., and Liu, H H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysys, Proc. R. Soc. Lond. A, 454, 903–995, 1998. Huang, N E., Shen, Z., and Long, S R.: A new view of nonlinear water waves: The Hilbert spectrum, Ann. Rev. Fluid Mech., 31, 417–457, 1999. Kaimal, J C. and Finnigan, J J.: Atmospheric Boundary Layer Flows, Oxford University Press, New York, 1994. Lundquist, J K.: Intermittent and elliptical inertial oscillations in the atmospheric boundary layer, J. Atmos. Sci., 60, 2661–2673, 2003. Mahrt, L.: Bulk formulation of surface fluxes extended to weak-wind stable conditions, Quart. J. Roy. Meteorol. Soc., 134, 1–10, 2008. Malhi, Y S.: The significance of the dual solutions for heat fluxes measured by the temperature fluctuation method in stable conditions, Boundary-Layer Meteorol., 74, 389–396, 1995. McNaughton, K G. and Brunet, Y.: Townsend's hypothesis, coherent structures and Monin-Obukhov similarity, Bound.-Lay. Meteorol., 102, 161–175, 2002. McNaughton, K G., Clement, R J., and Moncrieff, J B.: Scaling properties of velocity and temperature spectra above the surface friction layer in a convective atmospheric boundary layer, Non. Proc. Geophy., 14, 257–271, 2007. Monin, A S. and Yaglom, A M.: Statistical Fluid Mechanics: Mechanics of Turbulence, vol 1, MIT Press, Cambridge, 1971. Nappo, C J. and Johansson, P.: Summary of the Lövånger international workshop on turbulence and diffusion in the stable planetary boundary layer, Bound.-Lay. Meteorol., 90, 345–374, 1999. Nieuwstadt, F. T M.: Some aspects of the turbulent stable boundary layer, Bound.-Lay. Meteorol., 30, 31–55, 1984. Pahlow, M., Parlange, M B., and Porte-Agel, F.: On Monin-Obukhov similarity in the stable atmospheric boundary layer, Boundary-Layer Meteorol., 99, 225–248, 2001. Schmid, H P.: Experimental design for flux measurements: matching scales of observations and fluxes, Agric. For. Meteorol., 87, 179–200, 1997. Shen, S. S P., Shu, T., Huang, N E., Wu, Z., North, G R., Karl, T R., and Easterling, D R.: The application of Hilbert-Huang transforms to meteorological datasets, in: Hilbert-Huang Transform and Its Applications, edited by Huang, N E. and Shen, S P., pp. 187–210, World Scientific, 2005. Smedman, A S., Högstrom, U., and Hunt, J. C R.: Effects of shear sheltering in a stable atmospheric boundary layer with strong shear, Quart. J. Roy. Meteorol. Soc., 130, 31–50, 2004. Sorensen, D C., Lehoucq, R B., Yang, C., and Maschhoff, K.: ARPACK, rice University, 2001. Stull, R B.: An Introduction to Boundary Layer Meteorology, Kluwer Academic Publisher, Dordrecht, 1988. Sun, J L., Burns, S P., Lenschow, D H., Banta, R., Newsom, R., Coulter, R., Frasier, S., Ince, T., Nappo, C., Cuxart, J., Blumen, W., Lee, X., and Hu, X Z.: Intermittent turbulence associated with a density current passage in the stable boundary layer, Bound.-Lay. Meteorol., 105, 199–219, 2002. Terradellas, E., Soler, M R., Ferreres, E., and Bravo, M.: Analysis of oscillations in the stable atmospheric boundary layer using wavelet methods, Bound.-Lay. Meteorol., 114, 489–518, 2005. Vickers, D V. and Mahrt, L.: The cospectral gap and turbulent flux calculations, J. Atmos. Ocean. Tech., 20, 660–672, 2003. Wyngaard, J C. and Coté, O R.: The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer, J. Atmos. Sci., 28, 190–201, 1971. Wyngaard, J C. and Coté, O R.: Cospectral Similarity in the Atmospheric Surface Layer, Quart. J. Roy. Meteorol. Soc, 98, 590–603, 1972. Yagüe, C., Viana, S., Maqueda, G., and Redondo, J M.: Influence of stability on the flux-profile relationships for wind speed, $\phi_m$, and temperature, $\phi_h$, for the stable atmospheric boundary layer, Nonlin. Proc. Geophy., 13, 185–203, 2006.