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Statistical evaluation of model results using Eq. (13) and Eq. (38), eddy diffusivity Eq. (47), similarity wind profile Eq. (50) and lateral dispersion parameter Eq. (44) (Kinkaid experiment) stability class using the curves from Turner (1970). The second method M-2 is the split sigma approach. In this method 0; is determined by the temperature gradient as in the standard method, but 0, is based on a stability class determined by the standard deviation of azimuth angle over the test period. The third procedure M-3 is similar to the standard method, except that the values of dispersion parameters are developed at the INEL. The final approach M-4 is based on the segmented plume method (Zannetti, 1990), that is a simple way to account for plume meander is to divide each test into small intervals and make separate calculations for each interval. Fig. 9 shows the scatter diagrams between the measured and predicted concen- tration data for INEL experiment using GILTT method. Analyzing the results encountered depicted in the Table 6, we can say that, under statistical point of view, the results attained present a good comparison with the experimental data.

Figure 9 Statistical evaluation of model results using Eq. (13) and Eq. (38), eddy diffusivity Eq. (47), similarity wind profile Eq. (50) and lateral dispersion parameter Eq. (44) (Kinkaid experiment) stability class using the curves from Turner (1970). The second method M-2 is the split sigma approach. In this method 0; is determined by the temperature gradient as in the standard method, but 0, is based on a stability class determined by the standard deviation of azimuth angle over the test period. The third procedure M-3 is similar to the standard method, except that the values of dispersion parameters are developed at the INEL. The final approach M-4 is based on the segmented plume method (Zannetti, 1990), that is a simple way to account for plume meander is to divide each test into small intervals and make separate calculations for each interval. Fig. 9 shows the scatter diagrams between the measured and predicted concen- tration data for INEL experiment using GILTT method. Analyzing the results encountered depicted in the Table 6, we can say that, under statistical point of view, the results attained present a good comparison with the experimental data.

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Concerning the fourth experiment, the solution for low wind conditions (Eq. (30)) was evaluated against data obtained from the INEL experiment (Sagendorf and Dickson, 1974) (stable case). The data used to evaluate the performance of the model are constituted by a series of diffusion tests Fig. 1. Convergence of the GILTT method for three different source distances: a) x=1900 m; b) x=3900 m and c) x=5300 m.
Concerning the fourth experiment, the solution for low wind conditions (Eq. (30)) was evaluated against data obtained from the INEL experiment (Sagendorf and Dickson, 1974) (stable case). The data used to evaluate the performance of the model are constituted by a series of diffusion tests Fig. 1. Convergence of the GILTT method for three different source distances: a) x=1900 m; b) x=3900 m and c) x=5300 m.
Fig. 2. Isolines of the concentration (cuh/Q; Z=z/h; X=xw./uh) predicted for different source height: a) H,/h=0.1; b) Hs/h=0.25; c) H./h=0.5 and d) H,/h=0.75. of the experiment was provided by Doran and Horst (1985). Data were obtained from six dual-tracer releases located at 100, 200, 800, 1600 and 3200 m from the source during moderately stable to near-neutral conditions. However, the deposition velocity was evaluated only for the last 3 distances. The release time was 30 min except in run five, when it was 22 min. The terrain roughness was 3 cm. Two tracers, one depositing and one non-depositing, were released simulta- neously from a height of 2 m. Zinc sulfide (ZnS) was chosen for the depositing tracer, while sulfur hexafluoride (SF,) was the non-depositing tracer. The lateral separation between the SF, and ZnS release points was less than 1 m. The near-surface release height and the atmospheric stability conditions were chosen to produce differences between the depositing and non-depositing tracer concentrations that could be easily measured. The data collected during the field tests were Regarding the fifth experiment, the GILTT method was evaluated against data obtained at Hanford in stable condi- tions (Doran et al., 1984). This experiment was conducted in May-June, 1983 on a semi-arid region of south eastern Washington on generally flat terrain. The detailed description
Fig. 2. Isolines of the concentration (cuh/Q; Z=z/h; X=xw./uh) predicted for different source height: a) H,/h=0.1; b) Hs/h=0.25; c) H./h=0.5 and d) H,/h=0.75. of the experiment was provided by Doran and Horst (1985). Data were obtained from six dual-tracer releases located at 100, 200, 800, 1600 and 3200 m from the source during moderately stable to near-neutral conditions. However, the deposition velocity was evaluated only for the last 3 distances. The release time was 30 min except in run five, when it was 22 min. The terrain roughness was 3 cm. Two tracers, one depositing and one non-depositing, were released simulta- neously from a height of 2 m. Zinc sulfide (ZnS) was chosen for the depositing tracer, while sulfur hexafluoride (SF,) was the non-depositing tracer. The lateral separation between the SF, and ZnS release points was less than 1 m. The near-surface release height and the atmospheric stability conditions were chosen to produce differences between the depositing and non-depositing tracer concentrations that could be easily measured. The data collected during the field tests were Regarding the fifth experiment, the GILTT method was evaluated against data obtained at Hanford in stable condi- tions (Doran et al., 1984). This experiment was conducted in May-June, 1983 on a semi-arid region of south eastern Washington on generally flat terrain. The detailed description
Fig. 3. Vertical profile of concentration (C*=cuh/Q) for three downstream non-dimensional distances (X=0.25, 0.5 and 0.75) and non-dimensional source height: a) H,/h=0.05; b) H,/h=0.1 and c) H,/h=0.25. Mangia et al., 2002). The eddy diffusivity Eq. (47) was used. The statistical indices in the table point out that a good agreement is obtained between experimental data and the GILTT method. Analysing the statistical indices (Hanna, 1989) we notice that these models simulate satisfactorily the observed concentrations, regarding the NMSE, FB and FS values relatively near to zero and COR relatively near to 1.
Fig. 3. Vertical profile of concentration (C*=cuh/Q) for three downstream non-dimensional distances (X=0.25, 0.5 and 0.75) and non-dimensional source height: a) H,/h=0.05; b) H,/h=0.1 and c) H,/h=0.25. Mangia et al., 2002). The eddy diffusivity Eq. (47) was used. The statistical indices in the table point out that a good agreement is obtained between experimental data and the GILTT method. Analysing the statistical indices (Hanna, 1989) we notice that these models simulate satisfactorily the observed concentrations, regarding the NMSE, FB and FS values relatively near to zero and COR relatively near to 1.
Statistical evaluation of model results using Eq. (13), eddy diffusivity Eq. (47) and similarity wind profile Eq. (50) (Copenhagen experiment) Table 1 Fig. 5a shows the observed and predicted scatter diagram of crosswind ground-level concentrations for Copenhagen using the solution of the Eq. (13) with vertical eddy diffusivity given by Eq. (47). Fig. 5b shows the observed and predicted scatter diagram of crosswind ground-level concentrations for Copenhagen using the solution of the Eq. (21). In this respect, it is important to note that the model reproduced fairly well the observed concentration for this experiment.
Statistical evaluation of model results using Eq. (13), eddy diffusivity Eq. (47) and similarity wind profile Eq. (50) (Copenhagen experiment) Table 1 Fig. 5a shows the observed and predicted scatter diagram of crosswind ground-level concentrations for Copenhagen using the solution of the Eq. (13) with vertical eddy diffusivity given by Eq. (47). Fig. 5b shows the observed and predicted scatter diagram of crosswind ground-level concentrations for Copenhagen using the solution of the Eq. (21). In this respect, it is important to note that the model reproduced fairly well the observed concentration for this experiment.
Statistical evaluation of model results using Eq. (13), eddy diffusivity Eq. (47) and similarity wind profile Eq. (50) (Prairie Grass experiment)
Statistical evaluation of model results using Eq. (13), eddy diffusivity Eq. (47) and similarity wind profile Eq. (50) (Prairie Grass experiment)
Statistical evaluation of model results using Eq. (21), eddy diffusivity Eq. (47) and similarity wind profile Eq. (50) (Copenhagen experiment)
Statistical evaluation of model results using Eq. (21), eddy diffusivity Eq. (47) and similarity wind profile Eq. (50) (Copenhagen experiment)
Statistical evaluation of model results using Eq. (13) and Eq. (38), eddy diffusivity Eq. (47), power wind profile Eq. (51) and lateral dispersion parameter Eq. (44) (Copenhagen experiment) (centerline concentrations) diffusivity Eq. (47) was used. The statistical indices of the table point out that a good agreement is obtained between experi- mental data and the GILTT method. Analysing the statistical indices (Hanna, 1989) we notice that these models simulate satisfactorily the observed concentrations, regarding the NMSE, FB and FS values relatively near to zero and COR relatively near to 1.
Statistical evaluation of model results using Eq. (13) and Eq. (38), eddy diffusivity Eq. (47), power wind profile Eq. (51) and lateral dispersion parameter Eq. (44) (Copenhagen experiment) (centerline concentrations) diffusivity Eq. (47) was used. The statistical indices of the table point out that a good agreement is obtained between experi- mental data and the GILTT method. Analysing the statistical indices (Hanna, 1989) we notice that these models simulate satisfactorily the observed concentrations, regarding the NMSE, FB and FS values relatively near to zero and COR relatively near to 1.
Statistical evaluation of model results using Eq. (30), eddy diffusivity Eq. (49), power wind profile Eq. (51) and lateral dispersion parameter Eq. (46) (INEL experiment)
Statistical evaluation of model results using Eq. (30), eddy diffusivity Eq. (49), power wind profile Eq. (51) and lateral dispersion parameter Eq. (46) (INEL experiment)
Fig. 5. Observed (Co) and predicted (Cp) scatter plot of crosswind ground- level concentration using similarity wind profile and: a) Copenhagen Experiment with Eq. (13); b) Copenhagen experiment with Eq. (21) (normalized with emission rate (c/Q)). Data between dotted lines correspond to ratio Co/Cp <[0.5,2].
Fig. 5. Observed (Co) and predicted (Cp) scatter plot of crosswind ground- level concentration using similarity wind profile and: a) Copenhagen Experiment with Eq. (13); b) Copenhagen experiment with Eq. (21) (normalized with emission rate (c/Q)). Data between dotted lines correspond to ratio Co/Cp <[0.5,2].
Fig. 6. Scatter diagram for the solution (13) together with Eq. (38): Observed (Co) and predicted (Cp) centerline ground-level concentration (c/Q) (Copen- hagen experiment). Data between dotted lines correspond to ratio Co/ Cp €<[0.5,2].
Fig. 6. Scatter diagram for the solution (13) together with Eq. (38): Observed (Co) and predicted (Cp) centerline ground-level concentration (c/Q) (Copen- hagen experiment). Data between dotted lines correspond to ratio Co/ Cp €<[0.5,2].
Fig. 7. Observed (Co) and predicted (Cp) scatter plot of crosswind ground- level concentration using Eq. (13) and similarity wind profile (Prairie Grass experiment). Data between dotted lines correspond to ratio Co/Cp €[0.5,2]. We have evaluated the performances of the solution of Eq. (41) using the Prairie-Grass data set, power wind profile Eq. (51), eddy diffusivity Eq. (47) and putting in Eq. (41) the
Fig. 7. Observed (Co) and predicted (Cp) scatter plot of crosswind ground- level concentration using Eq. (13) and similarity wind profile (Prairie Grass experiment). Data between dotted lines correspond to ratio Co/Cp €[0.5,2]. We have evaluated the performances of the solution of Eq. (41) using the Prairie-Grass data set, power wind profile Eq. (51), eddy diffusivity Eq. (47) and putting in Eq. (41) the
Statistical evaluation of model results using Eq. (18), eddy diffusivity Eq. (48), power wind profile Eq. (51) (Hanford experiment) Table 7
Statistical evaluation of model results using Eq. (18), eddy diffusivity Eq. (48), power wind profile Eq. (51) (Hanford experiment) Table 7
Fig. 8. Observed (Co) and predicted (Cp) scatter plot of centerline ground- level concentration (c/Q) using Eq. (13) and similarity wind profile (Kinkaid experiment). Data between dotted lines correspond to ratio Co/Cp €[0.5,2].
Fig. 8. Observed (Co) and predicted (Cp) scatter plot of centerline ground- level concentration (c/Q) using Eq. (13) and similarity wind profile (Kinkaid experiment). Data between dotted lines correspond to ratio Co/Cp €[0.5,2].
Fig. 9. Observed (Co) and predicted (Cp) scatter diagram of near ground-level centerline concentrations. Data between dotted lines correspond to ratio Co/Cp €[0.5,2]. skewness S;, equal to 1, as suggested by van Dop and Verver (2001). Fig. 11 shows an example of the concentrations in function to the distance from the source with and without the counter-gradient term for a run of Prairie Grass characterized by a wind velocity at 10 m height of 5.1 m/s, a friction velocity of 0.37 m/s and a Monin-Obukhov length of -10 m. The experimental data are showed in the figure also. It is possible to see that the influence of counter-gradient term is confined near the source only. Analyzing the Fig. 11, we promptly realize an improvement of the numerical results, comparing with the K model, for the counter-gradient model for the low source problem and for points near the source considering S,=1.0.
Fig. 9. Observed (Co) and predicted (Cp) scatter diagram of near ground-level centerline concentrations. Data between dotted lines correspond to ratio Co/Cp €[0.5,2]. skewness S;, equal to 1, as suggested by van Dop and Verver (2001). Fig. 11 shows an example of the concentrations in function to the distance from the source with and without the counter-gradient term for a run of Prairie Grass characterized by a wind velocity at 10 m height of 5.1 m/s, a friction velocity of 0.37 m/s and a Monin-Obukhov length of -10 m. The experimental data are showed in the figure also. It is possible to see that the influence of counter-gradient term is confined near the source only. Analyzing the Fig. 11, we promptly realize an improvement of the numerical results, comparing with the K model, for the counter-gradient model for the low source problem and for points near the source considering S,=1.0.
Fig. 10. Observed (Co) and predicted (Cp) scatter plot of crosswind ground- level concentration using similarity wind profile and: a) Hanford experiment with Eq. (13) and (c/Q); b) Hanford experiment with Eq. (18) (c/Q). Data between dotted lines correspond to ratio Co/Cp €[0.5,2]. We also present the application of this methodology for a problem with the wind speeds evaluated by Large Eddy Simulation (LES) with a grid of 64x64. We simulate a
Fig. 10. Observed (Co) and predicted (Cp) scatter plot of crosswind ground- level concentration using similarity wind profile and: a) Hanford experiment with Eq. (13) and (c/Q); b) Hanford experiment with Eq. (18) (c/Q). Data between dotted lines correspond to ratio Co/Cp €[0.5,2]. We also present the application of this methodology for a problem with the wind speeds evaluated by Large Eddy Simulation (LES) with a grid of 64x64. We simulate a
Fig. 11. Crosswind integrated ground-level concentration as a function of the source distance with $,=0.0 and S,=1.0 for a run of Prairie Grass data set. We begin our final analysis recalling that the solution of the advection-diffusion equation can be written in two equivalent forms: integral and series expansion solutions. In this work, focusing our attention to the task of pollution
Fig. 11. Crosswind integrated ground-level concentration as a function of the source distance with $,=0.0 and S,=1.0 for a run of Prairie Grass data set. We begin our final analysis recalling that the solution of the advection-diffusion equation can be written in two equivalent forms: integral and series expansion solutions. In this work, focusing our attention to the task of pollution
Fig. 12. Isolines of the concentration (cuh/Q; Z=z/h; X=xw./uh) predicted for source height H,=0.25h with wind speeds from LES model.
Fig. 12. Isolines of the concentration (cuh/Q; Z=z/h; X=xw./uh) predicted for source height H,=0.25h with wind speeds from LES model.
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Atmospheric ScienceAtmospheric sciencesLaplace TransformAtmospheric Boundary LayerAtmospheric DispersionLaplace transformationPlanetary boundary layer
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