Skip to main content

Advertisement

SpringerLink
Log in

Estimating a Lagrangian Length Scale Using Measurements of CO2 in a Plant Canopy

  • Article
  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

Analytical Lagrangian equations capable of predicting concentration profiles from known source distributions offer the opportunity to calculate source/sink distributions through inverted forms of these equations. Inverse analytical Lagrangian equations provide a practical means of estimating source profiles using concentration and turbulence measurements. Uncertainty concerning estimates of the essentially immeasurable Lagrangian length scale (\({\mathcal{L}}\)), a key input, impedes the operational practicality of this method. The present study evaluates \({\mathcal{L}}\) within a corn canopy by using field measurements to constrain an analytical Lagrangian equation. Measurements of net CO2 flux, soil-to-atmosphere CO2 flux, and in-canopy profiles of CO2 concentration provided the information required to solve for \({\mathcal{L}}\) in a global optimization algorithm for 30-min time intervals. For days when the canopy was a strong CO2 sink, the optimization frequently located \({\mathcal{L}}\) profiles that follow a convex shape. A constrained optimization then fit the profile shape to a smooth sigmoidal equation. Inputting the optimized \({\mathcal{L}}\) profiles in the forward and inverse Lagrangian equations leads to strong correlations between measured and calculated concentrations and fluxes. Coefficients of the sigmoidal equation were specific to each 30-min period and did not scale with any measured variable. Plausible looking \({\mathcal{L}}\) profiles were associated with negative bulk Richardson number values. Once the canopy senesced, a simple eddy diffusivity profile sufficed to relate concentrations and sources in the analytical Lagrangian equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Amiro BD, Barr AG, Black TA, Iwashita H, Kljun N, McCaughey JH, Morgenstern K, Murayama S, Nesic Z, Orchansky AL, Saigusa N (2006) Carbon, energy, and water fluxes at mature and disturbed forest sites, Saskatchewan, Canada. Agric For Meteorol 136: 237–251

    Article  Google Scholar 

  • Aster RC, Borchers B, Thurber CH (2005) Parameter estimation and inverse problems, international geophysics series. Elsevier Academic Press, Burlington MA, USA, 320 pp

  • Aubinet M, Vesala T, Papale D (eds.): 2012, Eddy covariance: a practical guide to measurement and data analysis. Springer, 438 pp

  • Baldocchi D (1992) A Lagrangian random-walk model for simulating water vapor, CO2 and sensible heat flux densities and scalar profiles over and within a soybean canopy. Boundary-Layer Meteorol 61: 113–144

    Article  Google Scholar 

  • Baldocchi D (2003) Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future. Glob Change Biol 9(4): 479–492

    Article  Google Scholar 

  • Coppin PA, Raupach MR, Legg BJ (1986) Experiments on scalar dispersion within a model plant canopy part II: an elevated plane source. Boundary-Layer Meteorol 35: 167–191

    Article  Google Scholar 

  • Corrsin S (1963) Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence. J Atmos Sci 20: 115–119

    Article  Google Scholar 

  • Corrsin S (1974) Limitations of gradient transport models in random walks and in turbulence. In: Frenkiel FN, Munn RE, Landsberg HE, van Mieghem J (eds) Turbulent diffusion in environmental pollution, vol 18. New York, USA, p. 25–60, Academic Press Inc, 462 pp

  • Denmead OT, Bradley EF (1987) On scalar transport in plant canopies. Irrigation Sci 8(2): 131–149

    Article  Google Scholar 

  • Denmead OT, Harper L, Sharpe R (2000) Identifying sources and sinks of scalars in a corn canopy with inverse Lagrangian dispersion analysis I. Heat. Agric For Meteorol 104: 67–73

    Article  Google Scholar 

  • Flesch TK, Wilson JD (1992) A two-dimensional trajectory-simulation model for non-Gaussian, inhomogeneous turbulence within plant canopies. Boundary-Layer Meteorol. 61: 349–374

    Article  Google Scholar 

  • Gifford FA (1955) A simultaneous Lagrangian–Eulerian turbulence experiment. Mon Weather Rev 85: 293–301

    Article  Google Scholar 

  • Hanna SR (1981) Lagrangian and Eulerian time-scale relations in the daytime boundary layer. J Appl Meteorol 20: 242–249

    Article  Google Scholar 

  • Hansen P (1994) Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numer Algorithms 6: 1–35

    Article  Google Scholar 

  • Harper L, Denmead OT, Sharpe R (2000) Identifying sources and sinks of scalars in a corn canopy with inverse Lagrangian dispersion analysis II. Ammonia. Agric For Meteorol 104: 75–83

    Article  Google Scholar 

  • Haverd V, Cuntz M, Leuning R, Keith H (2007) Air and biomass heat storage fluxes in a forest canopy: calculation within a soil vegetation atmosphere transfer model. Agric For Meteorol 147(3–4): 125–139

    Article  Google Scholar 

  • Haverd V, Leuning R, Griffith D, van Gorsel E, Cuntz M (2009) The turbulent Lagrangian time scale in forest canopies constrained by fluxes, concentrations and source distributions. Boundary-Layer Meteorol 130(2): 209–228

    Article  Google Scholar 

  • Hay JS, Pasquill F (1959) Diffusion from a continuous source in relation to the spectrum and scale of turbulence. Adv Geophys 6: 345–365

    Article  Google Scholar 

  • Hunt JCR, Weber AH (1979) A Lagrangian statistical analysis of diffusion from a ground-level source in a turbulent boundary layer. Q J R Meteorol Soc 105: 423–443

    Article  Google Scholar 

  • Ingber L (1996) Adaptive simulated annealing (ASA): lessons learned. Control Cybern 25: 33–54

    Google Scholar 

  • Katul G, Oren R, Ellsworth D, Hsieh CI, Phillips N (1997) A Lagrangian dispersion model for predicting CO2 sources, sinks, and fluxes in uniform lobolly pin (Pinus taeda L.) stand. J Geophys Res 102(D8): 9309–9321

    Article  Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598): 671–680

    Article  Google Scholar 

  • Leuning R, Denmead OT, Miyata A, Kim J (2000) Source/sink distributions of heat, water vapour, carbon dioxide and methane in a rice canopy estimated using Lagrangian dispersion analysis. Agric For Meteorol 104: 233–249

    Article  Google Scholar 

  • Massman WJ, Weil JC (1999) An analytical one-dimensional second-order closure model of turbulence statistics and the Lagrangian time scale within and above plant canopies of arbitrary structure. Boundary-Layer Meteorol 91(1): 81–107

    Article  Google Scholar 

  • Menke W (1989) Geophysical data analysis: discrete inverse theory. Academic Press Inc, San Diego, USA, 289 pp

  • Molder M, Klemedtsson L, Lindroth A (2004) Turbulence characteristics and dispersion in a forest—tests of Thomson’s random-flight model. Agric For Meteorol 127(3–4): 203–222

    Article  Google Scholar 

  • Nemitz E, Sutton MA, Gut A, Jose RS, Husted S, Schjoerring JK (2000) Sources and sinks of ammonia within an oilseed rape canopy. Agric For Meteorol 105(4): 385–404

    Article  Google Scholar 

  • Philip JR (1967) Relation between Eulerian and Lagrangian statistics. Phys Fluids 9(2): S69–S71

    Article  Google Scholar 

  • Poggi D, Porporato A, Ridolfi L, Albertson JD, Katul GG (2004) The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol 111: 565–587

    Article  Google Scholar 

  • Qiu G, Warland J (2006) Inferring profiles of energy fluxes within a soybean canopy using Lagrangian analysis. Agric For Meteorol 139: 119–137

    Article  Google Scholar 

  • Raupach MR (1987) A Lagrangian analysis of scalar transfer in vegetation canopies. Q J R Meteorol Soc 113: 107–120

    Article  Google Scholar 

  • Raupach MR (1989a) Applying Lagrangian fluid mechanics to infer scalar source distributions from concentration profiles in plant canopies. Agric For Meteorol 47(2–4): 85–108

    Article  Google Scholar 

  • Raupach MR (1989b) A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies. Q J R Meteorol Soc 115(487): 609–632

    Article  Google Scholar 

  • Raupach MR, Coppin PA, Legg BJ (1986) Experiments on scalar dispersion within a model-plant canopy Part I: the turbulence structure. Boundary-Layer Meteorol 35: 21–52

    Article  Google Scholar 

  • Raupach MR, Finnigan JJ, Brunet Y (1996) Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol 78(3–4): 351–382

    Article  Google Scholar 

  • Rochette P, Bertrand N (2008) Soil sampling and methods of analysis, Chapt. 65, pp. 851–862. Taylor and Francis Group., Boca Raton, FL, 2nd ed. edition, 1264 pp

  • Santos E, Wagner-Riddle C, Warland J (2011) Applying Lagrangian dispersion analysis to infer carbon dioxide and latent heat fluxes in a corn canopy. Agric For Meteorol 151: 620–632

    Article  Google Scholar 

  • Santos E, Wagner-Riddle C, Lee X, Warland JS, Brown SE, Kim K (2012) Use of the isotope flux ratio approach to investigate the C18O16O and 13CO2 exchange near the floor of a temperatedeciduous forest. Biogeosciences 9: 2385–2399

    Article  Google Scholar 

  • Siqueira M, Lai CT, Katul GG (2000) Estimating scalar sources, sinks, and fluxes in a forest canopy using Lagrangian, Eulerian, and hybrid inverse models. J Geophys Res 105(D24), 29, 475–29, 488

    Google Scholar 

  • Siqueira M, Leuning R, Kolle O, Kelliher FM, Katul GG (2003) Modelling sources and sinks of CO2, H2O and heat within a Siberian pine forest using three inverse methods. Q J R Meteorol Soc 129: 1373–1393

    Article  Google Scholar 

  • Styles JM, Raupach MR, Farquhar GD, Kolle O, Lawton KA, Brand WA, Werner RA, Jordan A, Schulzssssse ED, Shibistova O, Lloyd J (2002) Soil and canopy CO2, CO2−C13, H2O and sensible heat flux partitions in a forest canopy inferred from concentration measurements. Tellus B 54(5): 655–677

    Article  Google Scholar 

  • Tanner CB, Thurtell GW (1969) Aneclinometer measurements of Reynolds stress and heat transport in the atmosphere of the surface layer, final report. Technical Report TREMCOM 66-G22-F, University of Wisconsin, Madison, WI, USA

  • Tarantola A (2006) Popper, Bayes and the inverse problem. Nature 2: 492–494

    Google Scholar 

  • Taylor GI (1921) Diffusion by continuous moments. P L Math Soc 20: 196

    Article  Google Scholar 

  • Tiwary A, Fuentes JD, Barr JG, Wang D, Colls JJ (2007) Inferring the source strength of isoprene from ambient concentrations. Environ Modell Softw 22(9): 1281–1293

    Article  Google Scholar 

  • van Gorsel E, Harman IN, Finnigan JJ, Leuning R (2011) Decoupling of air flow above and in plant canopies and gravity waves affect micrometeorological estimates of net scalar exchange. Agric For Meteorol 151: 927–933

    Article  Google Scholar 

  • Wagner-Riddle C, Thurtell GW, Kidd GK, Beauchamp EG, Sweetman R (1997) Estimates of nitrous oxide emissions from agricultural fields over 28 months. Can J Soil Sci 77(2): 135–144

    Article  Google Scholar 

  • Warland JS, Thurtell G (2000) A Lagrangian solution to the relationship between a distributed source and concentration profile. Boundary-Layer Meteorol 96(3): 453–471

    Article  Google Scholar 

  • Wilson JD, Ward DP, Thurtell GW, Kidd GE (1982) Statistics of atmospheric turbulence within and above a corn canopy. Boundary-Layer Meteorol 24(4): 495–519

    Article  Google Scholar 

  • Wilton M (2010) The use of natural abundance \({\delta^{13}{C}}\) to identify and quantify sources of emitted carbon dioxide in a calcareous southern Ontario Luvisolic soil. Ph.D. thesis, University of Guelph, Guelph, Ontario, 151 pp

  • Wohlfahrt G (2004) Modelling fluxes and concentrations of CO2, H2O and sensible heat within and above a mountain meadow canopy: a comparison of three Lagrangian models and three parameterisation options for the Lagrangian time scale. Boundary-Layer Meteorol 113(1): 43–80

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Environmental Sciences, University of Guelph, Guelph, ON, N1G2W1, Canada

    Shannon E. Brown, Jon S. Warland & Claudia Wagner-Riddle

  2. Department of Agronomy, Kansas State University, Manhattan, Kansas, USA

    Eduardo A. Santos

  3. Climate Research Division, Environment Canada, Toronto, ON, Canada

    Ralf Staebler

  4. University of Waterloo, Waterloo, ON, Canada

    Meaghan Wilton

Authors
  1. Shannon E. Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jon S. Warland
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eduardo A. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Claudia Wagner-Riddle
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ralf Staebler
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Meaghan Wilton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shannon E. Brown.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brown, S.E., Warland, J.S., Santos, E.A. et al. Estimating a Lagrangian Length Scale Using Measurements of CO2 in a Plant Canopy. Boundary-Layer Meteorol 147, 83–102 (2013). https://doi.org/10.1007/s10546-012-9778-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-012-9778-6

Keywords

Search

Navigation