Abstract
This Chapter examines theoretical and operational aspects of coordinate systems. A distinction is made between the vector basis, a local property of a coordinate system, and the overall coordinate frame consisting of the vector basis and coordinate lines, a global property of the flow that is determined by the flow field in three dimensions. Point measurements can only define the vector basis. Because in field campaigns many components that enter into the mass balance in complex flows are severely under-sampled, a properly chosen coordinate frame for point measurements should optimize our estimates of the surface-air exchange and should maximize information for diagnostics purposes.
The strengths and weaknesses of three operational coordinate systems for point measurements (instrument, natural wind, and planar fit) are examined in detail. That error in scalar fluxes due to coordinate tilt is usually small for small tilt angles does not negate the need for coordinate rotation because the tilt error can introduce a systematic bias to the time integrated flux. On the other hand, it is also important that over-rotation be avoided in post-field data analysis. Tilt errors caused by contamination from the streamwise and cross-wind fluxes should be treated differently.
Appendix B outlines a method for rotation into the planar fit coordinate. The scheme relies on the straightforward vector operation and avoids the need for rotation angles.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Batchelor, G. K.: 1967, An Introduction to Fluid Mechanics, Cambridge University Press, New York.
Baldocchi, D., Finnigan, J., Wilson, K., Paw U, K. T.: 2000, “On measuring net ecosystem carbon exchange over tall vegetation in complex terrain”, Bound.-Layer Meteorol. 96, 257–291.
Bradshaw, P.: 1973, “Effects of streamline curvature on turbulent flow”, AGARDo-graph No. 169, National Technical Information Service, USDept. of Commerce, pp. 125.
Ferziger, J. H., Peric, M.: 1997, Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin.
Finnigan, J. J.: 2004, “A re-evaluation of long-term flux measurement techniques. Part II: coordinate systems”, Bound.-Layer Meteorol. in review.
Finnigan, J. J., Clements, R., Malhi, Y., Leuning, R., Cleugh, H.: 2003, “A re-evaluation of long-term flux measurement techniques. Part I: averaging and coordinate rotation”, Bound.-Layer Meteorol. 107, 1–48.
Finnigan, J. J.: 1990, “Streamline coordinates, moving frames, chaos and integrability in fluid flow”, Topological Fluid Mechanics, Proc. IUTAM Symp. Topological Fluid Mechanics, Eds Moffat, H. K., Tsinober A., Cambridge University Press, Cambridge, 64–74.
Finnigan, J. J.: 1983, “A streamline coordinate system for distorted two-dimensional shear flows”, J. Fluid Mech. 130, 241–258.
Finnigan, J. J., Bradley, E. F.: 1983, “The turbulent kinetic energy budget behind a porous barrier: an analysis in streamline coordinates”, J. Wind Eng. Ind. Aerodyn. 15, 157–168.
Geissbuhler, P., Siegwolf, R., Eugster, W.: 2000, “Eddy covariance measurements on mountain slopes: the advantage of surface-normal sensor orientation over a vertical set-up”, Bound.-Layer Meteorol. 96, 371–392.
Goulden, M.L., Munger, J.W., Fan, S.-M., Daube, B.C., Wofsy, S.C.: 1996, “Measurements of carbon sequestration by long-term eddy covariance methods and a critical evaluation of accuracy”, Global Change Biology 2, 169–183.
Howarth, L.: 1951, “The boundary-layer in three dimensional flow. Part I: derivation of the equations for flow along a general curved surface”, Phil. Mag. 42, 239–243.
Irvine, M. R., Gardiner, B. A., Hill, M. K.: 1997, “The evolution of turbulence across a forest edge”, Bound.-Layer Meteorol. 94, 467–497.
Kaimal, J.C., Finnigan, J.J.: 1994, Atmospheric Boundary Layer Flows: Their Structure and Measurement, Oxford University Press, New York.
Kaimal, J. C., Gaynor, J. E., Zimmerman, H. A., Zimmerman, G. A.: 1990, “Minimizing flow distortion errors in a sonic anemometer”, Bound.-Layer Meteorol. 53, 103–115.
Kaimal, J. C., Haugen, D. A.: 1969, “Some errors in the measurement of Reynolds stress”, J. Appl. Meteorol. 8, 460–462.
Lee, X.: 2004, “Forest-atmosphere exchanges in non-ideal conditions: the role of horizontal eddy flux and its divergence” Forest at the Land-Atmosphere Interface (Mencuccini, M. et al. Eds), CAB International, pp 145–157.
Lee, X., Hu, X.: 2002, “Forest-air fluxes of carbon and energy over non-flat terrain”, Bound.-Layer Meteorol. 103, 277–301.
Lee, X.: 1998, “On micrometeorological observations of surface-air exchange over tall vegetation”, Agric. Forest Meteorol. 91, 39–49.
Li, Z., Lin, J. D., Miller, D. R.: 1990, “Air flow over and through a forest edge: a steady state numerical simulation”, Bound.-Layer Meteorol. 51, 179–197.
Liu, H. P, Peters, G., Foken, T.: 2001, “New equations for sonic temperature variance and buoyancy heat flux with an omnidirectional sonic anemometer”, Bound.-Layer Meteorol. 100, 459–468.
Massman, W. J., Lee, X.: 2002, “Eddy covariance flux corrections and uncertainties in long-term studies of carbon and energy exchanges”, Agric. Forest Meteorol. 113, 121–144.
McMillen, R. T.: 1988, “An eddy correlation technique with extended applicability to non-simple terrain”, Bound.-Layer Meteorol. 43, 231–245.
Paw U, K. T., Baldocchi, D., Meyers, T. P., Wilson, K. B.: 2000, “Correction of eddy-covariance measurements incorporating both advective effects and density fluxes”, Bound.-Layer Meteorol. 97, 487–511.
Paw U, K. T., Falk, M., Suchanic, T. H., Ustin, S. L., Chen, J., Park, Y.-S., Winner, W. E., Thomas, S. C., Hsiao, T. C., Shaw, R. H., King, T. S., Pyles, R. D., Schroeder, M., Matista, A. A.: 2004, “Carbon dioxide exchange between an old growth forest and the atmosphere”, Ecosystems, in press.
Pielke, R. A.: 1984, Mesoscale Meteorological Modeling, Academic Press, New York.
Raupach, M. R.: 2001 “Inferring Biogeochemical sources and sinks from atmospheric concentrations: general considerations and applications in vegetation canopies”, In Shulze, E-D., Heimann, M., Harrison, S., Holland, E., Lloyd, J., Prentice, I. C., Schimel, D. (Eds) Global Biogeochemical Cycles in the Climate System, Academic Press, 41–59.
Sakai, R. K., Fitzjarrald, D. R., Moore, K. E.: 2001, “Importance of low-frequency contributions to eddy fluxes observed over rough surfaces”, J. Appl. Meteorol. 40, 2178–2192.
Tanner, C. B., Thurtell, G. W.: 1969, “Anemoclinometer measurements of Reynolds stress and heat transport in the atmospheric surface layer”, Research and Development Tech. Report ECOM 66-G22-F to the US Army Electronics Command, Dept. Soil Science, Univ. of Wisconsin, Madison, WI.
Wilczak, J. M., Oncley, S. P., Sage, S. A.: 2001, “Sonic anemometer tilt correction algorithms”, Bound.-Layer Meteorol. 99, 127–150.
Zeman, O., Jensen, N. O.: 1987, “Modification of turbulence characteristics in flow over hills’”, Quart. J. Roy Meteorol. Soc. 113, 55–80.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Kluwer Academic Publishers
About this chapter
Cite this chapter
Lee, X., Finnigan, J., Paw U, K.T. (2004). Coordinate Systems and Flux Bias Error. In: Lee, X., Massman, W., Law, B. (eds) Handbook of Micrometeorology. Atmospheric and Oceanographic Sciences Library, vol 29. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2265-4_3
Download citation
DOI: https://doi.org/10.1007/1-4020-2265-4_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-2264-7
Online ISBN: 978-1-4020-2265-4
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)