# Analytically Modelling Mean Wind and Stress Profiles in Canopies

- 460 Downloads
- 3 Citations

## Abstract

An analytical model for mean wind profiles in sparse canopies (W. Wang, Boundary-Layer Meteorol 142:383–399, 2012) has been further developed, with (1) an explicit solution being derived, and (2) a linear term being added to the \(K\)-closure scheme to improve the shear-stress parametrization when the contribution of non-local transport is significant. Results from large-eddy simulations and from laboratory experiments are used to evaluate the model and adjust model parameters, showing that the model can well simulate canopy wind and stress profiles not only for sparse-canopy scenarios, but also for dense-canopy scenarios. The analytical solution converges exactly to the standard surface-layer logarithmic wind profile in the case of zero canopy density, and tends to an exponential wind profile for a dense canopy.

## Keywords

Analytical wind model Canopy mean wind profile Canopy stress profile Large-eddy simulation Non-local transport## Notes

### Acknowledgments

The author is grateful to two anonymous reviewers for their constructive comments and suggestions. This work is partly supported by the National Natural Science Foundation of China under Grant No. 41075039 and 41375058.

## References

- Albini FA (1981) A phenomenological model for wind speed and shear stress profiles in vegetation cover layers. J Appl Meteorol 20(11):1325–1335CrossRefGoogle Scholar
- Ayotte KW, Finnigan JJ, Raupach MR (1999) A second-order closure for neutrally stratified vegetative canopy flows. Boundary-Layer Meteorol 90(2):189–216Google Scholar
- Bailey BN, Stoll R (2013) Turbulence in sparse, organized vegetative canopies: a large-eddy simulation study. Boundary-Layer Meteorol 147(3):369–400CrossRefGoogle Scholar
- Belcher SE (2005) Mixing and transport in urban areas. Philos Trans Math Phys Eng Sci 363(1837):2947–2968CrossRefGoogle Scholar
- Belcher SE, Jerram N, Hunt JCR (2003) Adjustment of a turbulent boundary layer to a canopy of roughness elements. J Fluid Mech 488:369–398CrossRefGoogle Scholar
- Belcher SE, Finnigan JJ, Harman IN (2008) Flows through forest canopies in complex terrain. Eco Appl 18(6):1436–1453CrossRefGoogle Scholar
- Brunet Y, Finnigan JJ, Raupach MR (1994) A wind tunnel study of air flow in waving wheat: single point velocity statistics. Boundary-Layer Meteorol 70:95–132CrossRefGoogle Scholar
- Bryan GH, Fritsch JM (2002) A benchmark simulation for moist nonhydrostatic numerical models. Mon Weather Rev 130(12):2917–2928CrossRefGoogle Scholar
- Cescatti A, Marcolla B (2004) Drag coefficient and turbulence intensity in conifer canopies. Agric For Meteorol 121(3–4):197–206CrossRefGoogle Scholar
- Cheng H, Castro IP (2002) Near wall flow over urban-like roughness. Boundary-Layer Meteorol 104(2):229–259CrossRefGoogle Scholar
- Cionco RM (1965) A mathematical model for air flow in a vegetative canopy. J Appl Meteorol 4(4):517–522CrossRefGoogle Scholar
- Coceal O, Belcher SE (2004) A canopy model of mean winds through urban areas. Q J R Meteorol Soc 130(599):1349–1372CrossRefGoogle Scholar
- Cowan IR (1968) Mass, heat and momentum exchange between stands of plants and their atmospheric environment. Q J R Meteorol Soc 94:523–544CrossRefGoogle Scholar
- Deardorff JW (1966) The counter-gradient heat flux in the lower atmosphere and in the laboratory. J Atmos Sci 23:503–506CrossRefGoogle Scholar
- Deardorff JW (1980) Stratocumulus-capped mixed layers derived from a 3-dimensional model. Boundary-Layer Meteorol 18(4):495–527CrossRefGoogle Scholar
- Denmead OT, Bradley EF (1985) Flux–gradient relationships in a forest canopy. In: Hutchison BA, Hicks BB (eds) The forest-atmosphere interaction. D. Reidel, Dordrecht, pp 421–442CrossRefGoogle Scholar
- Di Sabatino S, Solazzo E, Paradisi P, Britter R (2008) A simple model for spatially-averaged wind profiles within and above an urban canopy. Boundary-Layer Meteorol 127(1):131–151CrossRefGoogle Scholar
- Dwyer MJ, Patton EG, Shaw RH (1997) Turbulent kinetic energy budgets from a large-eddy simulation of airflow above and within a forest canopy. Boundary-Layer Meteorol 84(1):23–43CrossRefGoogle Scholar
- Finnigan JJ (1985) Turbulent transport in flexible plant canopies. In: Hutchison BA, Hicks BB (eds) The forest–atmosphere interaction. D. Reidel, Dordrecht, pp 443–480CrossRefGoogle Scholar
- Finnigan JJ (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32(1):519–571CrossRefGoogle Scholar
- Finnigan JJ, Belcher SE (2004) Flow over a hill covered with a plant canopy. Q J R Meteorol Soc 130(596):1–29CrossRefGoogle Scholar
- Finnigan JJ, Shaw RH (2000) A wind tunnel study of airflow in waving wheat: an EOF analysis of the structure of the large-eddy motion. Boundary-Layer Meteorol 96:211–255CrossRefGoogle Scholar
- Finnigan JJ, Shaw RH, Patton EG (2009) Turbulence structure above a vegetation canopy. J Fluid Mech 637:387–424CrossRefGoogle Scholar
- Frech M, Mahrt L (1995) A two-scale mixing formulation for the atmospheric boundary layer. Boundary-Layer Meteorol 73(1):91–104CrossRefGoogle Scholar
- Harman I, Finnigan J (2007) A simple unified theory for flow in the canopy and roughness sublayer. Boundary-Layer Meteorol 123(2):339–363CrossRefGoogle Scholar
- Holtslag AAM, Moeng C-H (1991) Eddy diffusivity and countergradient transport in the convective atmospheric boundary layer. J Atmos Sci 48:1690–1698CrossRefGoogle Scholar
- Inoue E (1963) On the turbulent structure of air flow within crop canopies. J Meteorol Soc Jpn 41:317–326Google Scholar
- Kang S-L, Davis KJ (2008) The effects of mesoscale surface heterogeneity on the fair-weather convective atmospheric boundary layer. J Atmos Sci 65(10):3197–3213CrossRefGoogle Scholar
- Kono T, Tamura T, Ashie Y (2010) Numerical investigations of mean winds within canopies of regularly arrayed cubical buildings under neutral stability conditions. Boundary-Layer Meteorol 134(1):131–155CrossRefGoogle Scholar
- Landsberg JJ, James GB (1971) Wind profiles in plant canopies: studies on an analytical model. J Appl Ecol 8(3):729–741CrossRefGoogle Scholar
- Macdonald RW (2000) Modelling the mean velocity profile in the urban canopy layer. Boundary-Layer Meteorol 97(1):25–45CrossRefGoogle Scholar
- Massman WJ (1997) An analytical one-dimensional model of momentum transfer by vegetation of arbitrary structure. Boundary-Layer Meteorol 83(3):407–421CrossRefGoogle Scholar
- Nepf HM (2012) Flow and transport in regions with aquatic vegetation. Annu Rev Fluid Mech 44(1):123–142CrossRefGoogle Scholar
- Novak MD, Warland JS, Orchansky AL, Ketler R, Green S (2000) Wind tunnel and field measurements of turbulent flow in forests. Part I: uniformly thinned stands. Boundary-Layer Meteorol 95(3):457–495CrossRefGoogle Scholar
- Patton EG, Katul GG (2009) Turbulent pressure and velocity perturbations induced by gentle hills covered with sparse and dense canopies. Boundary-Layer Meteorol 133(2):189–217CrossRefGoogle Scholar
- Pietri L, Petroff A, Amielh M, Anselmet F (2009) Turbulence characteristics within sparse and dense canopies. Environ Fluid Mech 9(3):297–320CrossRefGoogle Scholar
- Pinard JDJ-P, Wilson JD (2001) First- and second-order closure models for wind in a plant canopy. J Appl Meteorol 40(10):1762–1768CrossRefGoogle Scholar
- Poggi D, Katul GG, Albertson JD (2004a) Momentum transfer and turbulent kinetic energy budgets within a dense model canopy. Boundary-Layer Meteorol 111(3):589–614CrossRefGoogle Scholar
- Poggi D, Porporato A, Ridolfi L, Albertson JD, Katul GG (2004b) The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol 111(3):565–587CrossRefGoogle Scholar
- Polyanin AD, Zaitsev VF (2003) Handbook of exact solutions for ordinary differential equations. CRC Press, Boca Raton, 720ppGoogle Scholar
- Raupach MR, Thom AS (1981) Turbulence in and above plant canopies. Annu Rev Fluid Mech 13:97–129CrossRefGoogle Scholar
- Raupach MR, Finnigan JJ, Brunei Y (1996) Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol 78(3):351–382CrossRefGoogle Scholar
- Ross AN (2008) Large-eddy simulations of flow over forested ridges. Boundary-Layer Meteorol 128(1):59–76CrossRefGoogle Scholar
- Shaw RH, Patton EG (2003) Canopy element influences on resolved- and subgrid-scale energy within a large-eddy simulation. Agric For Meteorol 115(1–2):5–17CrossRefGoogle Scholar
- Shaw RH, Schumann U (1992) Large-eddy simulation of turbulent-flow above and within a forest. Boundary-Layer Meteorol 61(1–2):47–64CrossRefGoogle Scholar
- Shaw RH, Finnigan JJ, Patton EG, Fitzmaurice L (2006) Eddy structure near the plant canopy interface. Preprints, 27th conference on agricultural and forest meteorology and the 17th symposium boundary layers and turbulence, San Diego, USA, May 2006, Paper J2.1Google Scholar
- Stevens B (2000) Quasi-steady analysis of a pbl model with an eddy-diffusivity profile and nonlocal fluxes. Mon Weather Rev 128:824–836CrossRefGoogle Scholar
- Su HB, Schmid HP, Vogel CS, Curtis PS (2008) Effects of canopy morphology and thermal stability on mean flow and turbulence statistics observed inside a mixed hardwood forest. Agric For Meteorol 148(6–7): 862–882CrossRefGoogle Scholar
- Thom AS (1971) Momentum absorption by vegetation. Q J R Meteorol Soc 97:414–428CrossRefGoogle Scholar
- Wang W (2009) The influence of thermally-induced mesoscale circulations on turbulence statistics over an idealized urban area under a zero background wind. Boundary-Layer Meteorology 131(3):403–423CrossRefGoogle Scholar
- Wang W (2010) The influence of topography on single-tower-based carbon flux measurements under unstable conditions: A modeling perspective. Theor Appl Climatol 99(1):125–138CrossRefGoogle Scholar
- Wang W (2012) An analytical model for mean wind profiles in sparse canopies. Boundary-Layer Meteorol 142(3):383–399CrossRefGoogle Scholar
- Wang W, Davis KJ (2008) A numerical study of the influence of a clearcut on eddy-covariance fluxes of CO\(_{2}\) measured above a forest. Agric For Meteorol 148(10):1488–1500Google Scholar
- Wang W, Rotach M (2010) Flux footprints over an undulating surface. Boundary-Layer Meteorol 136(2): 325–340CrossRefGoogle Scholar
- Wang W, Yi C (2013) A new nonlinear analytical model for canopy flow over a forested hill. Theor Appl Climatol 109:549–563Google Scholar
- Wilson NR, Shaw RH (1977) A higher order closure model for canopy flow. J Appl Meteorol 16:1198–1205CrossRefGoogle Scholar
- Yi C (2008) Momentum transfer within canopies. J Appl Meteorol Climatol 47:262–275CrossRefGoogle Scholar
- Zeng P, Takahashi H (2000) A first-order closure model for the wind flow within and above vegetation canopies. Agric For Meteorol 103:301–313CrossRefGoogle Scholar