Abstract
A knowledge of the distribution of the contribution of upwind sources to measurements of vertical scalar flux densities is important for the correct interpretation of eddy covariance data. Several approaches have been developed to estimate this so-called footprint function. Here a new approach based on the ensemble-averaged Navier—Stokes equations is presented. Comparisons of numerical results using this approach with results from other studies under a range of environmental conditions show that the model predictions are robust. Moreover, the approach outlined here has the advantage of a potential wide applicability, due to an ability to take into account the heterogeneous nature of underlying surfaces. For example, the model showed that any variations in surface drag, such as must occur in real life heterogeneous canopies, can exert a marked influence of the shape and extent of flux footprints. Indeed, it seems likely that under such circumstances, estimates of surface fluxes will be weighted towards areas of highest foliage density (and therefore quite likely higher photosynthetic rates) close to the measurement sensor.
Three-dimensional footprints during the day and night were also determined for a mixed coniferous forest in european Russia. A marked asymmetry of the footprint in the crosswind direction was observed, this being especially pronounced for non-uniform plant distributions involving vegetation types with different morphological and physiological properties. The model also found that, other things being equal, the footprint peak for forest soil respiration is typically over twice the distance from the above canopy measurement sensor compared to that for canopy photosynthesis. This result has important consequences for the interpretation of annual ecosystem carbon balances by the eddy covariance method.
Similar content being viewed by others
References
Arneth, A., Kurbatova, J., Kolle, O., Shibistova, O., Lloyd, J., Vygodskaya, N. N., and Schulze, E.-D.: 2002, ‘Comparative Ecosystem-Atmosphere Exchange of Energy and Mass in a European Russian and a Central Siberian Bog II. Interseasonal and Interannual Variability of CO2 Fluxes’, Tellus 54B, 514–530.
Baldocchi, D.: 1997, ‘Flux Footprint within and over Forest Canopies’, Boundary-Layer Meteorol. 85, 273–292.
Baldocchi, D., Valentini, R., Oechel, W., and Dahlman, R.: 1996, ‘Strategies for Measuring and Modelling Carbon Dioxide and Water Vapour Fluxes over Terrestrial Ecosystems’, Global Change Biol. 2, 159–168.
Baldocchi, D. D., Falge, E., Gu, L., Olson, R. J., Hollinger, D Y., Running, S. W., Anthoni, P., Bernhofer, C., Davis, K., Evans, R. D., Fuentes, J., Goldstein, A., Katul, G., Law, B., Lee, X., Malhi, Y., Meyers, T., Munger, W., Oechel, W., Paw U, K. T., Pilegaard, K., Schmid, H. P., Valentini, R., Verma, S., Vesala, T., Wilson, K., and Wofsy, S.: 2001, ‘FLUXNET: A New Tool to Study the Temporal and Spatial Variability of Ecosystem-Scale Carbon Dioxide,Water Vapour and Energy Flux Densities’, Bull. Amer. Meteorol. Soc. 82, 2415–2434.
Denmead, O. T. and Bradley, E. F.: 1985, ‘Flux-Gradient Relationships in a Forest Canopy' in B. A. Hutchison and B. B. Hicks (eds.), The Forest-Atmosphere Interaction, Reidel, Dordrecht, pp. 421–442.
Falge, E., Baldocchi, D., Tenhunen, J., Aubinet, M., Bakwin, P., Berbigier, P., Bernhofer, C., Burba, G., Clement, R., Davis, K. J., Elbers, J. A., Goldstein, A. H., Grelle, A., Granier, A., Guomundsson, J., Hollinger, D., Kowalski, A. S., Katul, G., Law, B. E., Malhi, Y., Meyers, T., Monson, R. K., Munger, J. W., Oechel, W., Paw, U. K.-T., Pilegaard, K., Rannik, U., Rebmann, C., Suyker, A., Valentini, R., Wilson, K., and Wofsy, S.: 2002, ‘Seasonality of Ecosystem Respiration and Gross Primary Production as Derived from FLUXNET Measurements’, Agric. For. Meteorol. 113, 53–74.
Finnigan, J. J., Clement, R., Malhi, Y., Leuning, R., and Cleugh, H. A.: 2003, ‘A Re-Evaluation of Long-Term Flux Measurement Techniques Part I: Averaging and Coordinate Rotation’, Boundary-Layer Meteorol. 107, 1–48.
Flesch, T. K.: 1996: ‘The Footprint for Flux Measurements, from Backward Lagrangian Stochastic Models’, Boundary-Layer Meteorol. 78, 399–404.
Garratt, J. R.: 1992, The Atmospheric Boundary Layer, Cambridge University Press, Cambridge, 316 pp.
Goulden, M. L., Munger, J. W., Fan, S.-M., Daube, B. C., and Wofsy, S. C.: 1996, ‘Measurements of Carbon Sequestration by Long-Term Eddy Covariance: Methods and a Critical Evaluation of Accuracy’, Global Change Biol. 2, 169–182.
Grace, J., Lloyd, J., McIntyre, J., Miranda, A. C., Meir, P., Miranda, H. S., Nobre, C. R., Moncrieff, J., Wright, I. R., and Gash, J. H. C.: 1995, ‘Carbon Dioxide Uptake by an Undisturbed Tropical Rainforest in Southwest Amazonia, 1992-1993’, Science 270, 778–780.
Gross, G.: 1987, ‘Some Effects of Deforestation on Nocturnal Drainage Flow and Local Climate: A Numerical Study’, Boundary-Layer Meteorol. 38, 315–337.
Gross, G.: 1993, Numerical Simulation of Canopy Flows, Springer Verlag, Berlin, 168 pp.
Hadfield, M. G.: 1994, ‘Passive Scalar Diffusion from Surface Sources in the Convective Boundary Layer’, Boundary-Layer Meteorol. 69, 417–448.
Horst, T. W. and Weil, J. C.: 1992, ‘Footprint Estimation for Scalar Flux Measurements in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 59, 279–296.
Horst, T. W. and Weil, J. C.: 1994, ‘How Far is Far Enough?: The Fetch Requirements for Micrometeorological Measurement of Surface Fluxes’, J. Atmos. Oceanic Tech. 11, 1018–1025.
Janssens, I. A., Lankreijer, H., Matteucci, G., K owlaski, A. S., Buchmann, N., Epron, D., Pilegaard, K., Kutsch, W., Longdoz, B., Grünwald, T., Montagnani, L., Dore, S., Rebmann, C., Moors, E. J., Grelle, A., Rannik, Ñ., Morgenstern, K., Oltchev, S., Clement, R., Guomundsson, J., Minerbi, S., Berbigier, P., Ibrom, A., Moncrieff, J., Aubinet, M., Bernhofer, C., Jensen, N. O., Vesala, T., Granier, A., Schulze, E.-D., Lindroth, A., Dolman, A. J., Jarvis, P. G., Ceulemans, R., and Valentini, R.: 2001, ‘Productivity Overshadows Temperature in Determining Soil and Ecosystem Respiration across European Forests’, Global Change Biol. 7, 269–278.
Karpov, V. (ed.): 1983: Regulating Factors of a Spruce Forest Ecosystem, Nauka, Leningrad, 320 pp. (in Russian).
Kasibhatla, P., Heimann, M., Rayner, P., Mahowald, N., Prinn, R. G., and Hartley, D. E. (eds.): 1999, Inverse Methods in Global Biogeochemical Cycles, Vol. 114, Geophysical Monograph Series, 324 pp.
Kljun, N., Kormann, R., Rotach, M. W., and Meixer, F. X.: 2003, ‘Comparison of the Langrangian Footprint Model LPDM-B with an Analytical Footprint Model’, Boundary-Layer Meteorol. 106, 349–355.
Knohl, A., Kolle, O. E. E., Minayeva, T. I., Milyukova, I. M., Vygodskaya, N. N., Foken, T., and Schulze, E.-D.: 2002, ‘Carbon Exchange of a Russian Boreal Forest after Windthrow’, Global Change Biol. 8, 231–246.
Kolmogorov, A.: 1942, ‘Turbulence Flow Equations of an Uncompressible Fluid’, Trans. USSR Acad. Sci., Book ‘Physics’ 6, 56–58 (in Russian).
Kormann, R. and Meixner, F. X.: 2001, ‘An Analytical Footprint Model for Non-Neutral Stratification’, Boundary-Layer Meteorol. 99, 207–224.
Kurz, H.: 1977, Turbulente Diffusion in einer atmosphärischen Grenzschicht mit Rossby-Zahl-Ähnlichkeit, Ph.D. Dissertation, Meteorology Institute, TH Darmstadt, 164 pp.
Law, B. E., Ryan, M. G., and Anthoni, P. M.: 1999, ‘Seasonal and Annual Respiration of a Ponderosa Pine Ecosystem’, Global Change Biol. 5, 169–182.
Leclerc, M. Y. and Thurtell, G. W.: 1990, ‘Footprint Prediction of Scalar Fluxes Using a Markovian Analysis’, Boundary-Layer Meteorol. 52, 247–258.
Leclerc, M. Y., Shen, S. H., and Lamb, B.: 1997, ‘Observations and Large-Eddy Simulation Modelling of Footprints in the Lower Convective Boundary Layer’, J. Geophys. Res. 102, 9323–9334.
Li, Y. J., Miller, D. R., and Lin, J. D.: 1985, ‘A First-Order Closure Scheme to Describe Counter-Gradient Momentum Transport in Plant Canopies’, Boundary-Layer Meteorol. 33, 77–83.
Lloyd, J.: 1999, ‘Current Perspectives on the Terrestrial Carbon Cycle’, Tellus 51B, 336–342.
Lloyd, J., Grace, J., Miranda, A. C., Meir, P., Wong, S. C., Miranda, H. S., Wright, I. R., Gash, J. H. C., and McIntyre, J.: 1995, ‘A Simple Calibrated Model of Amazon Rainforest Productivity Based on Leaf Biochemical Properties’, Plant Cell Environ. 18, 1129–1145.
Mahrt, L.: 1999, ‘Stratified Atmospheric Boundary Layers’, Boundary-Layer Meteorol. 90, 375–396.
Markkanen, T., Rannik, Ñ., Markolla, B., Cescatti, A., and Vesala, T.: 2003, ‘Footprints and Fetches for Fluxes over Forest Canopies with Varying Structure and Density’, Boundary-Layer Meteorol. 106, 437–459.
Milyukova, I. M., Kolle, O., Varlagin, A., Vygodskaya, N., Schulze, E.-D., and Lloyd, J.: 2002, ‘Carbon Balance of a Southern Taiga Spruce Stand in European Russia’, Tellus 54B, 429–442.
Moncrieff, J. B., Massheder, J. M., de Bruin, H., Elbers, J., Friborg, T., Heusinkveld, B., Kabat, P., Scott, S., Soegaard, H., and Verhoef, A.: 1997, ‘A System to Measure Surface Fluxes of Energy, Momentum and Carbon Dioxide’, J. Hydrol. 188-189, 589–611.
Monin, A. and Yaglom, A.: 1965, Statistical Fluid Mechanics. Part 1, Nauka, Moscow, 640 pp. (in Russian).
Orr, J. C., Maier-Reimer, E., Mikolajewicz, U., Monfray, P., Sarmiento, J. L., Toggweiler, R. J., Taylor, N. J., Palmer, J., Gruber, N., Sabine, C. L., Le Quéré, C., Key, R. M., and Boutin, J.: 2001, ‘Estimates of Anthropogenic Carbon Uptake from Four 3-D Global Ocean Models’, Global Biogeochem. Cycles 15, 43–60.
Pacala, S. W., Hurtt, G. C., Houghton, R. A., Birdsey, R. A., Heath, L., Sundquist, E. T., Stallard, R. F., Baker, D., Peylin, P., Ciais, P., Moorcroft, P., Caspersen, J., Shevliakova, E., Moore, B., Kohlmaier, G., Holland, E., Gloor, M., Harmon, ME., Fan, S.-M., Sarmiento, J. L., Goodale, C., Schimel, D., and Field, C. B.: 2001, ‘Convergence of US Carbon Flux Estimates from Inventories of Ecosystems and Inversions of Atmospheric Data’, Science 292, 2316–2320.
Prentice, C., Farquhar, G. D., Fasham, M., Goulden, M., Heimann, M., Jaramillo, V., Kheshgi, H., Le Quéré, C., Scholes, R., and Wallace, D.: 2001, ‘The Carbon Cycle and Atmospheric CO2’, in J. Houghton and D. Yihui, D. (eds.), Climate Change, The Scientific Basis: The Contribution of WGI of the IPCC to the IPCC Third Assessment Report (TAR), Cambridge University Press, Cambridge, pp. 183–237.
Rannik, Ñ., Aubinet, M., Kurbanmuradov, O., Sabelfeld, K., Markkanen, T., and Vesala, T.: 2000, ‘Footprint Analysis for Measurements over a Heterogeneous Forest’, Boundary-Layer Meteorol. 97, 137–166.
Rannik, Ñ., Markkanen, T., Raittila, J., Hari, P., and Vesala, T.: 2003, ‘Turbulence Statistics inside and over Forest: Influence on Footprint’, Boundary-Layer Meteorol. 109, 163–189.
Raupach, M. R.: 1988: ‘Canopy Transport Processes’, in W. L. Steffen and O. T. Denmead (eds.), Flow and Transport in the Natural Environment: Advances and Application, Springer Verlag, Berlin, pp. 95–127.
Schmid, H. P.: 1994, ‘Source Areas for Scalars and Scalar Fluxes’, Boundary-Layer Meteorol. 67, 293–318.
Schmid, H. P.: 2002, ‘Footprint Modelling for Vegetation Atmosphere Exchange Studies: A Review and Perspective’, Agric. For. Meteorol. 113, 159–183.
Schuepp, P. H., Leclerc, M. Y., Macpherson, J. I., and Desjardins, R. L.: 1990; 'Footprint Prediction of Scalar Fluxes from Analytical Solutions of the Diffusion Equation’, Boundary-Layer Meteorol. 50, 353–373.
Shibistova, O., Lloyd, J., Zrazhewskaya, G., Arneth, A., Kolle, O., Astrakhantceva, N., Shijneva, I., Knohl, A., and Schmerler, J.: 2002a, ‘Ecosystem Respiration Budget for a Pinus sylvestris Stand in Central Siberia’, Tellus 54B, 552–567.
Shibistova, O., Lloyd, J., Evgrafova, S., Savushkina, N., Zrazhewskaya, G., Arneth, A., Knohl, A., Kolle, O., and Schulze, E.-D.: 2002b, ‘Seasonal and Spatial Variability in Soil CO2 Efflux Rates for a Central Siberian Pinus sylvestris Forest’, Tellus 54B, 568–589.
Sogachev, A., Menzhulin, G., Heimann, M., and Lloyd, J.: 2002, ‘A Simple Three Dimensional Canopy-Planetary Boundary Layer Simulation Model for Scalar Concentrations and Fluxes’, Tellus 54B, 784–819.
Su, H.-B. and Leclerc, M. Y.: 1998, ‘Large-Eddy Simulation of Trace Gas Footprints from Infinite Crosswind Line Sources inside a Forest Canopy’, in preprint, 23rd Conference on Agricultural and Forest Meteorology of the American Meteorological Society, Boston, MA, pp. 388–391.
Valentini, R., Dore, S., Marchi, G., Mollicone, D., Panfyorov, M., Rebmann, C., Kolle, O., and Schulze, E. D.: 2000, ‘Carbon and Water Exchanges of Two Contrasting Central Siberian Landscape Types: Regenerating Forest and Bog’, Funct. Ecol. 14, 87–96.
Valentini, R., Matteucci, G., Dolman, A., Schulze, E., Rebmann, C., Moors, E., Granier, A., Gross, P., Jensen, N., Pilegaard, K., Lindroth, A., Grelle, A., Bernhofer, C., Grünwald, T., Aubinet, M., Ceulemans, R., Kowalski, A., Vesala, T., Rannik, Ñ., Berbigier, B., Lousteau, D., Guðmundsson, J., Thorgeirsson, H., Ibrom, A., Morgenstern, K., Clement, R., Moncrieff, J., Montagnani, L., Minerbi, S., and Jarvis, P.: 2000, ‘Respiration as the Main Determinant of Carbon Balance in European Forests’, Nature 404, 861–865.
van Ulden, A. P.: 1992, ‘A Surface-Layer Similarity Model for the Dispersion of a Skewed Passive Puff near the Ground’, Atmos. Environ. 26A, 681–692.
Varlagin, A.: 2000, Transpiration in Coniferous Forests at the Levels of Leaf, Tree and Stand, Ph.D. Dissertation, IPEE RAS, Moscow, 132 pp. (in Russian).
Wofsy, S. C., Goulden, M., Munger, J., Fan, S., Bakwin, P., Daube, B., Bassow, S., and Bazzaz, F.: 1993, ‘Net Exchange of CO2 in a Midlatitude Forest’, Science 260, 1314–1317.
Zeng, P. and Takahashi, H.: 2000, ‘A First-Order Closure Model for the Wind Flow within and above Vegetation Canopies’, Agric. For. Meteorol. 103, 301–313.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sogachev, A., Lloyd, J. Using a One-and-a-Half Order Closure Model of the Atmospheric Boundary Layer for Surface Flux Footprint Estimation. Boundary-Layer Meteorology 112, 467–502 (2004). https://doi.org/10.1023/B:BOUN.0000030664.52282.ee
Issue Date:
DOI: https://doi.org/10.1023/B:BOUN.0000030664.52282.ee