An approximate analytical model for footprint estimation of scalar fluxes in thermally stratified atmospheric flows
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743 citations
Cites background or methods from "An approximate analytical model for..."
...More modern ‘footprint’ models are routinely employed (Horst and Weil, 1992; Hsieh et al., 1997, 2000; Leclerc et al., 1997; Schmid, 2002) to define the two-dimensional spatial extent of the source areas for heat and vapor that contribute to the particular H or E measurement....
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...Horst and Weil (1992), Hsieh et al. (1997, 2000), Leclerc et al. (1997), and Schmid (2002) applied Lagrangian stochastic and large eddy simulation (LES) strategies along with Gaussian or non-Gaussian diffusion assumptions to estimate three-dimensional distribution of point source or line source…...
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...The ‘footprint’ of a flux or scalar measurement represents the upwind surface area that is statistically responsible for the conditioning of the measurement (Hsieh et al., 2000; Foken and Leclerc, 2004)....
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674 citations
Cites background or methods or result from "An approximate analytical model for..."
...Footprint estimates of the present parameterisation were compared with corresponding estimates of Hsieh et al. (2000), who also used results of a Lagrangian stochastic dispersion model to derive a footprint parameterisation. Their model differs from LPDM-B in that it is one-dimensional and based on Gaussian turbulence. Unlike in LPDM-B, the skewness of the vertical velocity, the covariance u′w′, as well as the longitudinal turbulence, are not considered in their model. Hsieh et al. (2000) derived a scaling procedure for the streamwise extent of the footprint and, using their model results, obtained a parameterisation for footprint estimates....
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...Hsieh et al. (2000) derived a scaling procedure for the streamwise extent of the footprint and, using their model results, obtained a parameterisation for footprint estimates....
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...Footprint estimates of the present parameterisation were compared with corresponding estimates of Hsieh et al. (2000), who also used results of a Lagrangian stochastic dispersion model to derive a footprint parameterisation....
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...We also thank an anonymous reviewer for drawing our attention to similarities in the approach of Hsieh et al. (2000)....
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...Existing footprint modelling studies offer the potential for simple parameterisations as, for example, proposed by Horst and Weil (1992, 1994), Weil and Horst (1992), Schmid (1994) or Hsieh et al. (2000)....
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524 citations
497 citations
Cites background or methods from "An approximate analytical model for..."
...LS footprint models for flow above short vegetation A footprint model that follows an analogous approach to (18) and (23) was first presented by Leclerc and Thurtell (1990) ....
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...Hsieh et al. (2000)presented a hybrid approach, combining elements fromCalder’s (1952)analytical solution with results from an LS model....
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...LS footprint models for flow above short vegetation A footprint model that follows an analogous approach to (18) and (23) was first presented by Leclerc and Thurtell (1990) . Their two-dimensional model considered Lagrangian dispersion in vertical direction by Gaussian turbulence, and advection with the mean flow in streamwise direction. The flow and turbulence profiles were described by standard M–O similarity relations. They presented model results of the crosswind integrated footprint over a range of conditions and demonstrate a strong dependence on measurements height, roughness and stability (in decreasing order of magnitude). The results for neutral stability were compared to the simple analytical model by Schuepp et al. (1990) , who found good qualitative agreement between the two approaches, and quantitative agreement if theSchuepp et al....
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...LS footprint models for flow above short vegetation A footprint model that follows an analogous approach to (18) and (23) was first presented by Leclerc and Thurtell (1990) . Their two-dimensional model considered Lagrangian dispersion in vertical direction by Gaussian turbulence, and advection with the mean flow in streamwise direction. The flow and turbulence profiles were described by standard M–O similarity relations. They presented model results of the crosswind integrated footprint over a range of conditions and demonstrate a strong dependence on measurements height, roughness and stability (in decreasing order of magnitude). The results for neutral stability were compared to the simple analytical model by Schuepp et al. (1990) , who found good qualitative agreement between the two approaches, and quantitative agreement if theSchuepp et al. (1990) model uses the local wind velocity at measurement height, rather than the layer average velocity (see (7)). Leclerc and Thurtell (1990)also presented various curves of the cumulative footprint as a function of fetch, in analogy to Gash (1986) ....
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...LS footprint models for flow above short vegetation A footprint model that follows an analogous approach to (18) and (23) was first presented by Leclerc and Thurtell (1990) . Their two-dimensional model considered Lagrangian dispersion in vertical direction by Gaussian turbulence, and advection with the mean flow in streamwise direction. The flow and turbulence profiles were described by standard M–O similarity relations. They presented model results of the crosswind integrated footprint over a range of conditions and demonstrate a strong dependence on measurements height, roughness and stability (in decreasing order of magnitude). The results for neutral stability were compared to the simple analytical model by Schuepp et al. (1990) , who found good qualitative agreement between the two approaches, and quantitative agreement if theSchuepp et al. (1990) model uses the local wind velocity at measurement height, rather than the layer average velocity (see (7))....
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463 citations
References
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"An approximate analytical model for..." refers methods in this paper
...With L as the key variable, we propose the following two dimensionless groups (Pi groups [20,24]) and write...
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...where U(z) is the mean wind velocity under neutral condition and is estimated from Monin±Obukov similarity theory (MOST [15,24]), and z denotes height....
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1,223 citations
"An approximate analytical model for..." refers background or methods in this paper
...For this purpose, similarity theory (dimensional analysis) in conjunction with the Lagrangian stochastic dispersion model [25] simulation outputs are used to construct the relationships among parameters (i....
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...Using Thomson's [25] Lagrangian model mentioned above, we calculated the 90% ̄ux fetch requirements (i....
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...In this section, a brief review of the Eulerian analytical models proposed by Gash [6] and Horst and Weil [8] and the Lagrangian particle trajectory model of Thomson [25] is provided....
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...(a) Comparison between ̄ux estimated by the models of Horst and Weil [8] (closed circles), Thomson [25] Lagrangian stochastic (open squares), and the proposed (open circles) as a function of fetch under unstable condition, where zm 4 m, z0 0:04 m, L ÿ50 m (top pane1); (b) same as (a) but for footprint (bottom panel)....
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...With L as the key variable, we propose the following two dimensionless groups (Pi groups [20,24]) and write x L f zu L : 14 Using Thomson's [25] Lagrangian model mentioned above, we calculated the 90% ¯ux fetch requirements (i.e., the x values for reaching F =S0 0:9) for a wide range of zm, z0, and L values....
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1,153 citations
"An approximate analytical model for..." refers background or methods in this paper
...where U(z) is the mean wind velocity under neutral condition and is estimated from Monin±Obukov similarity theory (MOST [15,24]), and z denotes height....
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...By MOST [15], the horizontal mean wind pro®le, U(z), is calculated as U z u k ln z=z0 ÿ wm z=L ; B:1 where Wm is taken as (A.5) for z=L P 0 and (A.8) for z=L < 0, and the vertical velocity standard deviation pro®le, rw , is expressed as rw 1:25u 1ÿ 3z=L 1...
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...With zp calculated by the Lagrangian similarity equation [26] dzp dx k 2 ln pzp=z0 ÿ wm pzp=L ÿ /h pzp=L A:1 and Businger±Dyer [2,15] formulas for the stability correction function for velocity (wm) and heat (/h) pro®les, Horst and Weil [8] derived x z0 W zp ÿW z0 : A:2 In (A1), L is the Obukhov length de®ned as L ÿu 3 T kghwhi ; A...
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...In (3), Uu is de®ned as Uu zm R zm z0 U z dzR zm z0 dz u k ln zm=z0 ÿ 1 z0=zm ; 4 where U(z) is the mean wind velocity under neutral condition and is estimated from Monin±Obukov similarity theory (MOST [15,24]), and z denotes height....
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...and Businger±Dyer [2,15] formulas for the stability correction function for velocity (wm) and heat (/h) pro®les, Horst and Weil [8] derived...
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825 citations
"An approximate analytical model for..." refers methods in this paper
...From previous model results [8,12,18,22], the fetch (x) is a function of F, zm, z0, and the atmospheric stability parameter (zm/L), where L is the Obukhov length (see Appendix A for de®nition)....
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