Abstract
Exploration of the flow inside the roughness sublayer often suffers from sub-sampling of its complex three-dimensional and non-homogeneous flow fields. Based on detailed particle image velocimetry within a randomly-ordered canopy model, we analyze the potential differences between single-location flow statistics and their spatially-averaged values. Overall, higher variability exists inside the canopy than above it, and is two to four times higher than found inside similar, however ordered, canopy arrangements. The local mean absolute percentage error (MAPE), vertically averaged within three different regions (below, above, and at canopy height), provides a measure for quantifying and characterizing the spatial distribution of errors for various flow properties (mean velocity and stresses). We calculated the value of MAPE at predefined farthest-locations based only on geometric considerations (i.e., farther away from surrounding roughness elements), as commonly done in the field. Interestingly, most of the vertical profiles at the farthest locations lie within the interquartile range of the measured spatial variability for all studied flow and turbulent properties. Additionally, our results show that, for at least 23% of the total canopy plan area, the double-averaged streamwise velocity component and its variance inside the canopy can be reproduced from a single measured profile for which the value of MAPE does not exceed 25%. These regions also constitute most of the farthest locations. The property that exhibits the highest MAPE value inside the canopy is the Reynolds stress (up to \(130\%\)); however, these errors are dramatically reduced in the upper half of the canopy. Furthermore, at the canopy interface and above it, the errors rarely exceed \(20\%\). The variability is also manifested in the computed integral length scales. The single-point velocity autocorrelation always underestimates the length scales obtained from the two-point statistics. These findings have implications for canopy flow and transport modelling inside the roughness sublayer and can help explain and evaluate the source of discrepancies between measurements and transport models.
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References
Asner GP, Scurlock JM, Hicke AJ (2003) Global synthesis of leaf area index observations: implications for ecological and remote sensing studies. Glob Ecol Biogeog 12(3):191–205
Bai K, Katz J, Meneveau C (2015) Turbulent flow structure inside a canopy with complex multi-scale elements. Boundary-Layer Meteorol 155(3):435–457
Baldocchi D, Falge E, Gu L, Olson R, Hollinger D, Running S, Anthoni P, Bernhofer C, Davis K, Evans R et al (2001) Fluxnet: a new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapor, and energy flux densities. Bull Am Meteorol Soc 82(11):2415–2434
Baldocchi DD, Xu L, Kiang N (2004) How plant functional-type, weather, seasonal drought, and soil physical properties alter water and energy fluxes of an oak-grass savanna and an annual grassland. Agric For Meteorol 123(1–2):13–39
Barker MG, Pinard MA (2001) Forest canopy research: sampling problems, and some solutions in tropical forest canopies: ecology and management. Springer, Dordrecht, pp 23–38
Barlow JF (2014) Progress in observing and modelling the urban boundary layer. Urban Clim 10:216–240
Belcher S, Jerram N, Hunt J (2003) Adjustment of a turbulent boundary layer to a canopy of roughness elements. J Fluid Mech 488:369–398
Böhm M, Finnigan JJ, Raupach MR, Hughes D (2013) Turbulence structure within and above a canopy of bluff elements. Boundary-Layer Meteorol 146(3):393–419
Bohrer G, Katul GG, Walko RL, Avissar R (2009) Exploring the effects of microscale structural heterogeneity of forest canopies using large-eddy simulations. Boundary-Layer Meteorol 132(3):351–382
Bou-Zeid E, Anderson W, Katul GG, Mahrt L (2020) The persistent challenge of surface heterogeneity in boundary-layer meteorology: a review. Boundary-Layer Meteorol 177(2):227–245
Brunet Y, Finnigan J, Raupach M (1994) A wind tunnel study of air flow in waving wheat: single-point velocity statistics. Boundary-Layer Meteorol 70:95–132
Castro IP (2017) Are urban-canopy velocity profiles exponential? Boundary-Layer Meteorol 164(3):337–351
Chagot L, Moulin FY, Eiff O (2020) Towards converged statistics in three-dimensional canopy-dominated flows. Exp Fluids 61(2):1–18
Chen JM, Rich PM, Gower ST, Norman JM, Plummer S (1997) Leaf area index of boreal forests: theory, techniques, and measurements. J Geophys Res Atmos 102(D24):29429–29443
Cheng H, Castro IP (2002) Near wall flow over urban-like roughness. Boundary-Layer Meteorol 104(2):229–259
Coceal O, Thomas T, Castro I, Belcher S (2006) Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol 121(3):491–519
Dias NL, Chamecki M, Kan A, Okawa CM (2004) A study of spectra, structure and correlation functions and their implications for the stationarity of surface-layer turbulence. Boundary-Layer Meteorol 110(2):165–189
Dupont S, Patton EG (2012) Momentum and scalar transport within a vegetation canopy following atmospheric stability and seasonal canopy changes: the chats experiment. Atmos Chem Phys 12(13):5913–5935
Finnigan J (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32(1):519–571
Florens E, Eiff O, Moulin F (2013) Defining the roughness sublayer and its turbulence statistics. Exp Fluids 54(4):1500
Grimmond CSB (2006) Progress in measuring and observing the urban atmosphere. Theor Appl Climatol 84(1):3–22
Gurka R, Liberzon A, Hefetz D, Rubinstein D, Shavit U (1999) Computation of pressure distribution using PIV velocity data. 3rd International workshop on particle image velocimetry, 16–18 September, 1999. Santa Barbara, CA, pp 671–676
Harman IN, Böhm M, Finnigan JJ, Hughes D (2016) Spatial variability of the flow and turbulence within a model canopy. Boundary-Layer Meteorol 160(3):375–396
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
Hong J, Toloui M, Chamorro LP, Guala M, Howard K, Riley S, Tucker J, Sotiropoulos F (2014) Natural snowfall reveals large-scale flow structures in the wake of a 2.5-MW wind turbine. Nat Commun 5:4216
Irvine J, Law B, Kurpius M, Anthoni P, Moore D, Schwarz P (2004) Age-related changes in ecosystem structure and function and effects on water and carbon exchange in ponderosa pine. Tree Physiol 24(7):753–763
Katul GG, Parlange MB (1995) Analysis of land surface heat fluxes using the orthonormal wavelet approach. Water Resour Res 31(11):2743–2749
Kremien M, Shavit U, Mass T, Genin A (2013) Benefit of pulsation in soft corals. Proc Nat Aca Sci 110(22):8978–8983
Lenschow D, Mann J, Kristensen L (1994) How long is long enough when measuring fluxes and other turbulence statistics? J Atmos Ocean Technol 11(3):661–673
Manes C, Pokrajac D, McEwan I (2007) Double-averaged open-channel flows with small relative submergence. J Hydraul Eng 133(8):896–904
Moltchanov S (2013) Dispersive stresses in canopy flows. PhD Thesis, Technion IIT, Haifa, Israel
Moltchanov S, Shavit U (2013) A phenomenological closure model of the normal dispersive stresses. Water Resour Res 49(12):8222–8233
Moltchanov S, Bohbot-Raviv Y, Shavit U (2011) Dispersive stresses at the canopy upstream edge. Boundary-Layer Meteorol 139(2):333–351
Moltchanov S, Bohbot-Raviv Y, Duman T, Shavit U (2015) Canopy edge flow: a momentum balance analysis. Water Resour Res 51(4):2081–2095
Nepf H, Vivoni E (2000) Flow structure in depth-limited, vegetated flow. J Geophys Res Ocean 105(17):547–557
Oke TR (1988) Street design and urban canopy layer climate. Energy Buil 11(1–3):103–113
Patton EG, Horst TW, Sullivan PP, Lenschow DH, Oncley SP, Brown WO, Burns SP, Guenther AB, Held A, Karl T et al (2011) The canopy horizontal array turbulence study. Bull Am Meteorol Soc 92(5):593–611
Poggi D, Porporato A, Ridolfi L, Albertson J, Katul G (2004) The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol 111(3):565–587
Pokrajac D, Campbell LJ, Nikora V, Manes C, McEwan I (2007) Quadrant analysis of persistent spatial velocity perturbations over square-bar roughness. Exp Fluids 42(3):413–423
Raupach M (1989) A practical lagrangian method for relating scalar concentrations to source distributions in vegetation canopies. Q J R Meteorol Soc 115(487):609–632
Raupach MR, Shaw R (1982) Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol 22(1):79–90
Sathe A, Mann J (2013) A review of turbulence measurements using ground-based wind lidars. Atmos Meas Tech 6:3147–3167
Scherer D, Ament F, Emeis S, Fehrenbach U, Leitl B, Scherber K, Schneider C, Vogt U (2019) Three-dimensional observation of atmospheric processes in cities. Meteorol Z 28(2):121
Shaw R, Brunet Y, Finnigan J, Raupach M (1995) A wind tunnel study of air flow in waving wheat: two-point velocity statistics. Boundary-Layer Meteorol 76(4):349–376
Shnapp R, Shapira E, Peri D, Bohbot-Raviv Y, Fattal E, Liberzon A (2019) Extended 3D-PTV for direct measurements of lagrangian statistics of canopy turbulence in a wind tunnel. Sci Rep 9(1):7405
Sullivan PP, Horst TW, Lenschow DH, Moeng CH, Weil JC (2003) Structure of subfilter-scale fluxes in the atmospheric surface layer with application to large-eddy simulation modelling. J Fluid Mech 482:101–139
Sveen J (2004) An introduction to MatPIV v 1.6.1 mechanics and applied mathematics. Department of Mathematics. University of Oslo, Norway
Van Hout R, Zhu W, Luznik L, Katz J, Kleissl J, Parlange M (2007) PIV measurements in the atmospheric boundary layer within and above a mature corn canopy. part i: statistics and energy flux. J Atmos Sci 64(8):2805–2824
Yu M, Liu Y, Dai Y, Yang A (2013) Impact of urbanization on boundary layer structure in beijing. Climatic Change 120(1):123–136
Zhu W, van Hout R, Katz J (2007a) On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy. Boundary-Layer Meteorol 124(2):205–233
Zhu W, Van Hout R, Katz J (2007b) PIV measurements in the atmospheric boundary layer within and above a mature corn canopy. part ii: Quadrant-hole analysis. J Atmos Sci 64(8):2825–2838
Acknowledgements
We would like to acknowledge the financial support of the Israel Science Foundation (Grants 620/07 and 1487/10), the state of Lower-Saxony and the Volkswagen Foundation, Hannover, Germany and the Centre for Life in Flow (CLiF) at the Inter-university Institute for Marine Sciences (IUI), Eilat, Israel. We thank the reviewers for their thoughtful comments.
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Duman, T., Bohbot-Raviv, Y., Moltchanov, S. et al. Error Estimates of Double-Averaged Flow Statistics due to Sub-Sampling in an Irregular Canopy Model. Boundary-Layer Meteorol 179, 403–422 (2021). https://doi.org/10.1007/s10546-020-00601-1
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DOI: https://doi.org/10.1007/s10546-020-00601-1