Abstract
A one-dimensional analytical model that predicts foliage CO2 uptake rates, turbulent fluxes, and mean concentration throughout the roughness sub-layer (RSL), a layer that extends from the ground surface up to 5h, where h is canopy height, is proposed. The model combines the mean continuity equation for CO2 with first-order closure principles for turbulent fluxes and simplified physiological and radiative transfer schemes for foliage uptake. This combination results in a second-order ordinary differential equation in which soil respiration (R) and CO2 concentration well above the RSL are imposed as lower and upper boundary conditions, respectively. An inverse version of the model was tested against datasets from two contrasting ecosystems: a tropical forest (h = 40m) and a managed irrigated rice canopy (h = 0.7m), with good agreement noted between modelled and measured mean CO2 concentration profiles within the entire RSL. Sensitivity analysis on the model parameters revealed a plausible scaling regime between them and a dimensionless parameter defined by the ratio between external (R) and internal (stomatal conductance) characteristics controlling the CO2 exchange process. The model can be used to infer the thickness of the RSL for CO2 exchange, the inequality in zero-plane displacement between CO2 and momentum, and its consequences on modelled CO2 fluxes. A simplified version of the solution is well suited for being incorporated into large-scale climate models. Furthermore, the model framework here can be used to a priori estimate relative contributions from the soil surface and the atmosphere to canopy-air CO2 concentration, thereby making it synergetic to stable isotopes studies.
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References
Baldocchi D, Finnigan JJ, Wilson K et al (2000) On measuring net ecosystem carbon exchange over tall vegetation on complex terrain. Boundary-Layer Meteorol 96(1–2): 257–291
Cava D, Katul GG, Scrimieri A et al (2006) Buoyancy and the sensible heat flux budget within dense canopies. Boundary-Layer Meteorol 118(1): 217–240
Collatz GJ, Ball JT, Grivet C et al (1991) Physiological and environmental-regulation of stomatal conductance, photosynthesis and transpiration—a model that includes a laminar boundary-layer. Agric For Meteorol 54(2–4): 107–136
da Rocha HR, Goulden ML, Miller SD et al (2004) Seasonality of water and heat fluxes over a tropical forest in eastern Amazonia. Ecol Appl 14(4): S22–S32
Domingues TF, Berry JA, Martinelli LA et al (2005) Parameterization of canopy structure and leaf-level gas exchange for an eastern Amazonian tropical rain forest (tapajos national forest, para, brazil). Earth Interact 9(17): 1–23
Farquhar GD, Caemmerer SV, Berry JA (1980) A biochemical-model of photosynthetic CO2 assimilation in leaves of c-3 species. Planta 149(1): 78–90
Finnigan JJ (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32: 519–571
Finnigan JJ, Clement R, Malhi Y et al (2003) A re-evaluation of long-term flux measurement techniques - Part I: Averaging and coordinate rotation. Boundary-Layer Meteorol 107(1): 1–48
Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, UK, p 316
Goulden ML, Miller SD, da Rocha HR et al (2004) Diel and seasonal patterns of tropical forest CO2 exchange. Ecol Appl 14(4): S42–S54
Harman IN, Finnigan JJ (2007) A simple unified theory for flow in the canopy and roughness sub-layer. Boundary-Layer Meteorol 123(2): 339–363
Harman IN, Finnigan JJ (2008) Scalar concentration profiles in the canopy and roughness sub-layer. Boundary-Layer Meteorol 129(3): 323–351
Högström U (1996) Review of some basic characteristics of the atmospheric surface layer. Boundary-Layer Meteorol 78(3–4): 215–246
Jackson PS (1981) On the displacement height in the logarithmic velocity profile. J Fluid Mech 111: 15–25
Juang JY, Katul GG, Siqueira MB et al (2008) Investigating a hierarchy of Eulerian closure models for scalar transfer inside forested canopies. Boundary-Layer Meteorol 128(1): 1–32
Katul GG, Albertson JD (1999) Modeling CO2 sources, sinks, and fluxes within a forest canopy. J Geophys Res-Atmos 104(D6): 6081–6091
Katul GG, Geron CD, Hsieh CI et al (1998) Active turbulence and scalar transport near the forest-atmosphere interface. J Appl Meteorol 37(12): 1533–1546
Katul GG, Ellsworth DS, Lai CT (2000) Modelling assimilation and intercellular CO2 from measured conductance: a synthesis of approaches. Plant Cell Environ 23(12): 1313–1328
Katul GG, Leuning R, Kim J et al (2001) Estimating CO2 source/sink distributions within a rice canopy using higher-order closure model. Boundary-Layer Meteorol 98(1): 103–125
Katul GG, Cava D, Poggi D et al (2004) Stationarity, homogeneity, and ergodicity in canopy turbulence. In: Lee X (eds) Handbook of micrometeorology. Kluwer Academic Press, Dordrecht, pp 161–180
Katul GG, Palmroth S, Oren R (2009) Leaf stomatal responses to vapour pressure deficit under current and CO2-enriched atmosphere explained by the economics of gas exchange. Plant Cell Environ 32: 968–979
Konrad W, Roth-Nebelsick A, Grein M (2008) Modelling of stomatal density response to atmsospheric CO2. J Theor Biol 253: 638–658
Lai CT, Katul G, Oren R et al (2000) Modeling CO2 and water vapor turbulent flux distributions within a forest canopy. J Geophys Res-Atmos 105(D21): 26333–26351
Lefsky MA, Cohen WB, Parker GG et al (2002) Lidar remote sensing for ecosystem studies. Bioscience 52(1): 19–30
Leuning R, Denmead OT, Miyata A et al (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(3): 233–249
Miller SD, Goulden ML, Menton MC et al (2004) Biometric and micrometeorological measurements of tropical forest carbon balance. Ecol Appl 14(4): S114–S126
Miyata A, Leuning R, Denmead OT et al (2000) Micrometeorological measurement of methane and CO2 fluxes over an intermittently drained paddy field. Agric For Meteorol 102: 287–303
Novick K, Oren R, Stoy P et al (2009) The relationship between reference canopy conductance and simplified hydraulic architecture. Adv Water Resour 32: 808–819
Raupach MR, Shaw RH (1982) Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol 22(1): 79–90
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
Reid CD, Maherali H, Johnson HB et al (2003) On the relationship between stomatal characters and atmospheric CO2. Geophys Res Lett 30(19): 1983
Schulze ED, Kelliher FM, Korner C et al (1994) Relationships among maximum stomatal conductance, ecosystem surface conductance, carbon assimilation rate, and plant nitrogen nutrition—a global ecology scaling exercise. Annu Rev Ecol System 25: 629–660
Siqueira M, Katul G (2002) Estimating heat sources and fluxes in thermally stratified canopy flows using higher-order closure models. Boundary-Layer Meteorol 103(1): 125–142
Siqueira M, Lai CT, Katul G (2000) Estimating scalar sources, sinks, and fluxes in a forest canopy using lagrangian, eulerian, and hybrid inverse models. J Geophys Res-Atmos 105(D24): 29475–29488
Stoy PC, Katul GG, Siqueira M et al (2006) Separating the effects of climate and vegetation on evapotranspiration along a successional chronosequence in the southeastern US. Glob Chang Biol 12(11): 2115–2135
Stoy PC, Palmroth S, Oishi AC et al (2007) Are ecosystem carbon inputs and outputs coupled at short time scales? A case study from adjacent pine and hardwood forests using impulse-response analysis. Plant Cell Environ 30(6): 700–710
Wilson JD (1988) A 2nd-order closure-model for flow through vegetation. Boundary-Layer Meteorol 42(4): 371–392
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Siqueira, M.B., Katul, G.G. An Analytical Model for the Distribution of CO2 Sources and Sinks, Fluxes, and Mean Concentration Within the Roughness Sub-Layer. Boundary-Layer Meteorol 135, 31–50 (2010). https://doi.org/10.1007/s10546-009-9453-8
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DOI: https://doi.org/10.1007/s10546-009-9453-8