# Examination of the Performance of a Three-Phase Atmospheric Turbulence Model for Line-Source Dispersion Modeling Using Multiple Air Quality Datasets

^{*}

## Abstract

**:**

^{2}, MG, VG, MSLE, and MAPE. The results indicate that the ADMS and SLINE 1.1 models perform better than CALINE4 and SLSM. SLINE 1.1 tends to overpredict for stable atmospheric conditions and underpredict for unstable atmospheric conditions. A trial test was performed to implement the TPT model in the basic line-source model (SLSM). The results indicate that the majority (FB, NMSE, R

^{2}, and MSLE) of the indicators have improved and are in the satisfactory range of a good model performance level.

## 1. Introduction

^{2}values of 0.6928 and 0.9415, with a slope of linear regression of 0.7341 and 1.094 respectively. The overall results in this study indicated that both models showed a good agreement with the measured data [8]. From the above literature review, very few studies for mobile source modeling have been reported using multiple data sets. It is important to determine whether the models are performing well using several field studies. In early 2021, Madiraju and Kumar developed a line-source dispersion model (SLINE 1.0) incorporating the effect of wind shear near the ground level, and presented the evaluation results from the Idaho field study [9].

## 2. Material Methods

#### 2.1. Line Source Models

- SLINE: This is a recently developed line-source dispersion model that incorporates the effect of wind shear (magnitude) on the dispersion of gaseous pollutants. The assumptions used in the SLINE 1.0 model are: (i) the wind direction is always perpendicular to the highway; (ii) the dispersion is of a non-fumigation type; (iii) the velocity profile with height above ground level is assumed to be the same for all downwind distances; (iv) a power-law profile is assumed for the velocity, i.e., the magnitude of the wind velocity near the ground level changes rapidly and follows a power law; (v) the eddy diffusivity profile is a conjugate of the velocity profile; and (vi) the emission rate is constant. The SLINE 1.1 model follows a TPT model which is a function of downwind distance. The expression for calculating the ground-level concentration for stable and unstable atmospheric conditions is given as Equations (1) and (2) [9]:$${C}_{\left(x,z\right)}=\frac{q}{{u}_{1}Sin\theta \gamma \left(s\right)}{[\frac{2}{{\left[\frac{a{u}_{*}x}{{U}_{e}+{b}_{s}{u}_{*}{\left(\frac{x}{L}\right)}^{\frac{2}{3}}}+{m}_{t}\right]}^{2}{\left(m-n+2\right)}^{2}}]}^{s}\mathit{exp}\left[-\frac{2{z}^{m-n+2}}{{\left[\frac{a{u}_{*}x}{{U}_{e}+{b}_{s}{u}_{*}{\left(\frac{x}{L}\right)}^{\frac{2}{3}}}+{m}_{t}\right]}^{2}{\left(m-n+2\right)}^{2}}\right]$$$${C}_{\left(x,z\right)}=\frac{q}{{u}_{1}Sin\theta \gamma \left(s\right)}{[\frac{2}{{\left[\frac{a{u}_{*}x\left(1+{b}_{u}\frac{{u}_{*}}{{U}_{e}}\frac{x}{L}\right)}{{U}_{e}}+{m}_{t}\right]}^{2}{\left(m-n+2\right)}^{2}}]}^{s}\mathit{exp}\left[-\frac{2{z}^{m-n+2}}{{\left[\frac{a{u}_{*}x\left(1+{b}_{u}\frac{{u}_{*}}{{U}_{e}}\frac{x}{L}\right)}{{U}_{e}}+{m}_{t}\right]}^{2}{\left(m-n+2\right)}^{2}}\right]$$q (g/m/s) is the emission rate of pollutants,x (m) is the downwind distance,z (m) is the vertical height of the receptor above the ground,u (m/s) is the wind velocity at the vertical height z,${U}_{e}$ (m/s) is the effective wind velocity,m is the exponent of the power-law velocity profile,n is the exponent for the eddy diffusivity profile,s is the stability parameter based on m and n. (s = (m + 1)/(m − n + 2)),θ (degrees) is the angle between the line source and the wind direction,${u}_{*}$(m/s) is the surface friction velocity,L is the Monin–Obukhov length,a, ${b}_{s}$ and ${b}_{u}$ are the empirical coefficients,${m}_{t}$ vertical spread due to mobile turbulence, andH is the height of the source.The model will be called SLINE 1.1 because the turbulence model is revised as given in Section 2.2 for this paper.
- CALINE4: This is a line-source Gaussian plume dispersion model used for regulatory purposes for predicting the concentrations of pollutants near roadways. The roadway geometry, worst-case meteorological parameters, anticipated traffic volumes, and receptor positions are the initial input parameters for the model for regulatory work. The approach followed by CALINE4 assumes (i) a homogeneous wind flow field (both vertically and horizontally), (ii) steady-state conditions, and (iii) negligible along-wind diffusion. The horizontal and vertical dispersion are adequately described as unimodal. The CALINE4 model contains improved algorithms for vertical and horizontal dispersion. However, the focus of this study is on the generic equation (see Equation (3)) of CALINE4 [16].$${C}_{\left(x,y\right)}=\frac{q}{\pi u{\sigma}_{z}}\underset{{y}_{1}-y}{\overset{{y}_{2}-y}{{\displaystyle \int}}}exp(\frac{-{y}^{2}}{2{\sigma}_{y}^{2}})dy$$${y}_{1}$ and ${y}_{2}$ are the finite line-source endpoints in y-coordinates (${y}_{2}$> ${y}_{1}$).
- ADMS: The Cambridge Environmental Research Consultants (CERC) developed the ADMS model. Roads are modeled as line sources with no plume rise and with modifications to account for traffic-produced turbulence, and street canyons, which is an optional feature. The vertical plume spread parameter (${\sigma}_{{z}_{roads}}$) is increased to consider the extra vertical turbulence produced by traffic on busy roads [17]. Similarly, an extra component is included (not for street canyons) in the lateral plume spread parameter to model the effect of lateral turbulence. The predicted concentration (C) from a finite crosswind line source of length ${L}_{s}$ is given by Equation (4) [17].$${C}_{\left(x,y,z\right)}=\frac{q}{2\sqrt{2}\pi {\sigma}_{z}\left(x\right)U}\mathit{exp}\left(-\frac{{\left(z-{z}_{p}\right)}^{2}}{2{\sigma}_{z}^{2}}\right)\ast [\mathit{erf}\left(\frac{y+\frac{{L}_{s}}{2}}{\sqrt{2}{\sigma}_{y}}\right)-\mathit{erf}\left(\frac{y-\frac{{L}_{s}}{2}}{\sqrt{2}{\sigma}_{y}}\right)]+\mathrm{reflection}\mathrm{terms}$$${z}_{p}$ is the height of the plume above the ground (m), and U is the wind speed at the plume height (m/s),
- SLSM: SLSM is a simple line-source model used to calculate the concentration of the pollutant from a mobile source using basic meteorological data and source information. The concentration is uniform in the y-direction at any given downwind distance. The wind direction is considered normal to the line of emission. If the wind direction is not normal to the line of emission, then θ (the angle between the wind direction and line source) is considered, and Sinθ appears in the equation. The Sinθ is not used in the equation if the angle is less than 45 degrees. The equation is taken from the textbook by Wark et al. [14].$${C}_{\left(x,0\right)}=\frac{2q}{{\left(2\pi \right)}^{\frac{1}{2}}{\sigma}_{z}uSin\theta}\mathit{exp}[-\frac{1}{2}{\left(\frac{H}{{\sigma}_{z}}\right)}^{2}]$$

#### 2.2. Turbulence Parametrization

_{u}, and b

_{s}) in the dispersion coefficient expressions were adjusted based on the trial-and-error method to achieve the maximum accuracy at respective atmospheric stability using the curves reported by Benson and Chock for mobile sources.

#### 2.3. Field Data and Atmospheric Stability

_{i}) [27], temperature gradient (dT/${\sigma}_{z}$), and standard deviation of vertical wind direction (${\sigma}_{\varnothing})$ [28]. The ranges of atmospheric stability indicators are given in Table 2. The atmospheric stability of the field data is categorized based on Table 2 depending upon the available information from the field study. The model predictions are simulated using the generic expressions discussed in Section 2.1 for stable and unstable atmospheric conditions and compared with the observed concentration values of the gaseous pollutants in the field. The results are discussed in Section 3.

#### 2.4. Statistical Evaluation Methods

- (a)
- Fractional Bias (FB): The fractional bias is a ratio between the difference of the average values and the summation of the average values of the observed and predicted concentration of pollutants, multiplied by two. It is a dimensionless number. In the ideal case, the value of FB is equal to zero. However, if its value is between −2.0 and +2.0, then the model can be referred to as better performing. If the FB value is less than −0.67, then the model is underpredicting, and if the value is less than −2.0, then the model is extremely underpredicting. If the value is higher than +0.6, then the model is overpredicting, and if the value is higher than +2.0, then the model is extremely overpredicting. The value of FB is influenced by infrequently occurring high concentration values [30,31].$$\mathrm{FB}=2\left(\frac{\overline{{C}_{o}}-\overline{{C}_{p}}}{\overline{{C}_{o}}+\overline{{C}_{p}}}\right)$$
- (b)
- Normalized Root Mean Square Error (NMSE): The scatter in the data collected is then normalized by the product of the average values of observed and predicted concentrations of pollutants. In the ideal case, the value of NMSE is zero. A smaller NMSE value denotes that the model is better performing. NMSE values cannot be used for accessing the model predicted concentrations that are over- or underpredicted [30,32].$$\mathrm{NMSE}=\frac{\overline{{({C}_{p}-{C}_{o})}^{2}}}{\overline{{C}_{o}}\xb7\overline{{C}_{p}}}$$
- (c)
- Coefficient of Determination (R
^{2}): The coefficient of determination is the square of the correlation between the predicted and observed values. R^{2}values range from 0 to 1. For example, an R^{2}of 0.50 means there is 50 percent of the variance needed to predict the actual observed value [30,33].$${\mathrm{R}}^{2}=1-\frac{{{\displaystyle \sum}}_{i-1}^{n}{\left({C}_{p}-{C}_{o}\right)}^{2}}{{{\displaystyle \sum}}_{i-1}^{n}{\left({C}_{p}-\overline{{C}_{o}}\right)}^{2}}$$ - (d)
- Geometric Mean Bias (MG): The MG value is reliable when the magnitude of the observed and predicted concentrations of the pollutants varies significantly. Extremely low values of concentrations also have strong influences on the MG value. In the ideal case, the MG value is equal to 1. If the MG value is equal to +0.5, then the model is underpredicting, and if the value is equal to +2.0, then the model is overpredicting [30,34].$$\mathrm{MG}=\mathit{exp}(\overline{\mathrm{ln}{C}_{o}}-\overline{\mathrm{ln}{C}_{p}})$$
- (e)
- Geometric Variance (VG): In ideal cases, VG values are equal to 1. Similar to MG, the VG value also shows similar properties of performance measures except in the identification of over- and underprediction [30,35].$$\mathrm{VG}=\mathit{exp}\overline{{(\mathrm{ln}{C}_{o}-\mathrm{ln}{C}_{o})}^{2}}$$
- (f)
- Mean Squared Log Error (MSLE): Its values lie between 0 and ∞. A smaller value of MSLE indicates that the model is performing better [36].$$\mathrm{MSLE}=\frac{1}{n}{\displaystyle \sum}_{i=0}^{n-1}{\left(lo{g}_{e}\left(1+{C}_{o}{}_{i}\right)-lo{g}_{e}\left(1+{C}_{p}{}_{i}\right)\right)}^{2}$$
- (g)
- Mean Absolute Percentage Error (MAPE): MAPE is a measure of the accuracy of the model as a percentage. MAPE can be calculated as the average absolute percent error for each predicted concentration minus the observed concentration divided by the observed concentration [37].$$\mathrm{MAPE}=\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}\left|\frac{{C}_{o}{}_{i}-{C}_{p}{}_{i}}{{C}_{o}{}_{i}}\right|\ast 100$$

## 3. Results and Discussion

#### 3.1. Cp/Co Plots

#### 3.2. Statistical Evaluation Results

^{2}) assesses how strong the linear relationship is between predicted and observed concentration values. This measure is represented as a value between 0.0 and 1.0, where a value of 1.0 indicates a perfect fit, and is thus a highly reliable model for future predictions, while a value of 0.0 would indicate that the model fails to accurately model the data at all [43]. As per this analysis, the SLINE 1.1 model tends to possess a chance of 75% to 88% to accurately predict the concentration values, whereas the ADMS has a 76% to 88% chance of accurately predicting the simulations. However, CALINE4 and SLSM seem to have a chance range of 65% to 74% and 58% to 74%, respectively. Even though R

^{2}is a complex idea centered on the statistical analysis of models for data, it can be used to explain variability. The variable chance of ranges mentioned in this paragraph is based on the three considered data sets.

#### 3.3. Role of Quantile-Quantile (Q-Q) Plots

#### 3.4. Performance of the Basic Line-Source Model (SLSM) Using Three-Phase Turbulence Parameterization

^{2}values are visible. The MG and VG values have also improved. The MAPE values for Data 2 for both stable and unstable conditions increased when compared to other data sets. Note that the P–G dispersion coefficients used in the SLSM model were developed based on the work of Pasquill over 70 years ago and it is suggested that these dispersion coefficients should be replaced with the proposed turbulence parametrization.

#### 3.5. Summary

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- US EPA. Air Quality Dispersion Modeling. Available online: https://www.epa.gov/scram/air-quality-dispersion-modeling (accessed on 18 October 2021).
- Holmes, N.S.; Morawska, L. A Review of Dispersion Modelling and Its Application to the Dispersion of Particles: An Overview of Different Dispersion Models Available. Atmos. Environ.
**2006**, 40, 5902–5928. [Google Scholar] [CrossRef][Green Version] - Hanna, S.R.; Egan, B.A.; Purdum, J.; Wagler, J. Evaluation of the ADMS, AERMOD, and ISC3 Dispersion Models with the OPTEX, Duke Forest, Kincaid, Indianapolis and Lovett Field Datasets. Int. J. Environ. Pollut.
**2001**, 16, 301–314. [Google Scholar] [CrossRef] - Levitin, J.; Härkönen, J.; Kukkonen, J.; Nikmo, J. Evaluation of the CALINE4 and CAR-FMI Models against Measurements near a Major Road. Atmos. Environ.
**2005**, 39, 4439–4452. [Google Scholar] [CrossRef] - Broderick, B.; O’Donoghue, R. Spatial Variation of Roadside C2–C6 Hydrocarbon Concentrations during Low Wind Speeds: Validation of CALINE4 and COPERT III Modelling. Transp. Res. Part D Transp. Environ.
**2007**, 12, 537–547. [Google Scholar] [CrossRef] - Righi, S.; Lucialli, P.; Pollini, E. Statistical and Diagnostic Evaluation of the ADMS-Urban Model Compared with an Urban Air Quality Monitoring Network. Atmos. Environ.
**2009**, 43, 3850–3857. [Google Scholar] [CrossRef] - Heist, D.; Isakov, V.; Perry, S.; Snyder, M.; Venkatram, A.; Hood, C.; Stocker, J.; Carruthers, D.; Arunachalam, S.; Owen, R.C. Estimating Near-Road Pollutant Dispersion: A Model Inter-Comparison. Transp. Res. Part D Transp. Environ.
**2013**, 25, 93–105. [Google Scholar] [CrossRef] - Agharkar, A. Model Validation and Comparative Performance Evaluation of MOVES/CALINE4 and Generalized Additive Models for Near-Road Black Carbon Prediction. Ph.D. Thesis, University of Cincinnati, Cincinnati, OH, USA, 2017. [Google Scholar]
- Madiraju, S.V.H.; Kumar, A. Development and Evaluation of SLINE 1.0, a Line Source Dispersion Model for Gaseous Pollutants by Incorporating Wind Shear Near the Ground under Stable and Unstable Atmospheric Conditions. Atmosphere
**2021**, 12, 618. [Google Scholar] [CrossRef] - Yu, Y.-T. Parameterization of Vertical Dispersion Coefficient (σ
_{z}) near Roadway: Vehicle Wake, Density and Types. Ph.D. Thesis, Illinois Institute of Technology, Chicago, IL, USA, 2020. [Google Scholar] - Macdonald, R. Theory and Objectives of Air Dispersion Modelling. Modelling Air Emissions for Compliance. MME 474A Wind Engineering. 2003, pp. 1–27. Available online: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.409.9932&rep=rep1&type=pdf (accessed on 18 October 2021).
- Carruthers, D.; Di Sabatino, S.; Hunt, J. Urban Air Quality: Meteorological Processes. Air Pollut. Sources Stat. Health Eff.
**2021**, 163–191. [Google Scholar] [CrossRef] - Benson, P.E. Modifications to the Gaussian Vertical Dispersion Parameter, Σz, near Roadways. Atmos. Environ.
**1982**, 16, 1399–1405. [Google Scholar] [CrossRef] - Wark, K.; Warner, C.F.; Davis, W.T. Air Pollution: Its Origin and Control; Addison-Wesley: Boston, MA, USA, 1998; ISBN 0-673-99416-3. [Google Scholar]
- CERC. Environmental Software. Available online: https://www.cerc.co.uk/environmental-software.html (accessed on 18 October 2021).
- Johnson, R.A.; Anderson, M.; Lilly, E.; Hok, C. Implementation of CALINE4; University of Alaska-Fairbanks: Fairbanks, AK, USA, 1988. [Google Scholar]
- Road Sources; Cambridge Environmental Research Group: Cambridge, UK, 2020; pp. 1–3.
- Chock, D.P. General Motors Sulfate Dispersion Experiment. Bound. -Layer Meteorol.
**1980**, 18, 431–451. [Google Scholar] [CrossRef] - Snyder, M.G.; Venkatram, A.; Heist, D.K.; Perry, S.G.; Petersen, W.B.; Isakov, V. RLINE: A Line Source Dispersion Model for near-Surface Releases. Atmos. Environ.
**2013**, 77, 748–756. [Google Scholar] [CrossRef] - Thykier-Nielsen, S.; Deme, S.; Mikkelsen, T. Description of the Atmospheric Dispersion Module RIMPUFF; Riso National Laboratory: Roskilde, Denmark, 1999; pp. 1–58. [Google Scholar]
- Kumar, A. Effects of Cross-Wind Shear on Horizontal Dispersion. J. Environ. Eng.
**1986**, 112, 1–11. [Google Scholar] [CrossRef] - Chock, D.P. A Simple Line-Source Model for Dispersion near Roadways. Atmos. Environ.
**1978**, 12, 823–829. [Google Scholar] [CrossRef] - Benson, P.E. Caline 4-A Dispersion Model for Predictiong Air Pollutant Concentrations Near Roadways; Federal Highway Administration Report FHWA/CA/TL-84/15 (NTIS PB 85 211498/AS); California State Department of Transportation: Sacramento, CA, USA, 1984. [Google Scholar]
- Finn, D.; Clawson, K.L.; Carter, R.G.; Rich, J.D.; Eckman, R.M.; Perry, S.G.; Isakov, V.; Heist, D.K. Tracer Studies to Characterize the Effects of Roadside Noise Barriers on Near-Road Pollutant Dispersion under Varying Atmospheric Stability Conditions. Atmos. Environ.
**2010**, 44, 204–214. [Google Scholar] [CrossRef] - Venkatram, A.; Isakov, V.; Thoma, E.; Baldauf, R. Analysis of Air Quality Data near Roadways Using a Dispersion Model. Atmos. Environ.
**2007**, 41, 9481–9497. [Google Scholar] [CrossRef] - Baldauf, R.; Thoma, E.; Hays, M.; Shores, R.; Kinsey, J.; Gullett, B.; Kimbrough, S.; Isakov, V.; Long, T.; Snow, R.; et al. Traffic and Meteorological Impacts on Near-Road Air Quality: Summary of Methods and Trends from the Raleigh Near-Road Study. J. Air Waste Manag. Assoc.
**2008**, 58, 865–878. [Google Scholar] [CrossRef] [PubMed] - Leelőssy, Á.; Molnár, F.; Izsák, F.; Havasi, Á.; Lagzi, I.; Mészáros, R. Dispersion Modeling of Air Pollutants in the Atmosphere: A Review. Open Geosci.
**2014**, 6, 257–278. [Google Scholar] [CrossRef] - Scire, J.S.; Robe, F.R.; Fernau, M.E.; Yamartino, R.J. A User’s Guide for the CALMET Meteorological Model; Earth Tech LLC: Land O’Lakes, FL, USA, 2000. [Google Scholar]
- CMAS. Community Modeling and Analysis System. Available online: https://www.cmascenter.org/download/data.cfm (accessed on 18 October 2021).
- Model Evaluation. Available online: http://www.eng.utoledo.edu/aprg/courses/dm/hmodel.html (accessed on 10 April 2021).
- Boylan, J.W.; Russell, A.G. PM and Light Extinction Model Performance Metrics, Goals, and Criteria for Three-Dimensional Air Quality Models. Atmos. Environ.
**2006**, 40, 4946–4959. [Google Scholar] [CrossRef] - Moursi, A.S.; El-Fishawy, N.; Djahel, S.; Shouman, M.A. An IoT Enabled System for Enhanced Air Quality Monitoring and Prediction on the Edge. Complex Intell. Syst.
**2021**, 7, 2923–2947. [Google Scholar] [CrossRef] - Chicco, D.; Warrens, M.J.; Jurman, G. The Coefficient of Determination R-Squared Is More Informative than SMAPE, MAE, MAPE, MSE and RMSE in Regression Analysis Evaluation. PeerJ Comput. Sci.
**2021**, 7, e623. [Google Scholar] [CrossRef] - Amoatey, P.; Omidvarborna, H.; Affum, H.A.; Baawain, M. Performance of AERMOD and CALPUFF Models on SO2 and NO2 Emissions for Future Health Risk Assessment in Tema Metropolis. Hum. Ecol. Risk Assess. Int. J.
**2019**, 25, 772–786. [Google Scholar] [CrossRef] - Zwain, H.M.; Nile, B.K.; Faris, A.M.; Vakili, M.; Dahlan, I. Modelling of Hydrogen Sulfide Fate and Emissions in Extended Aeration Sewage Treatment Plant Using TOXCHEM Simulations. Sci. Rep.
**2020**, 10, 1–11. [Google Scholar] - Botchkarev, A. Performance Metrics (Error Measures) in Machine Learning Regression, Forecasting and Prognostics: Properties and Typology. arXiv
**2018**, arXiv:1809.03006. [Google Scholar] - Tofallis, C. Measuring Relative Accuracy: A Better Alternative to Mean Absolute Percentage Error; Hertfordshire Business School Working Paper; University of Hertfordshire Business School, University of Hertfordshire, Hatfield: Hertfordshire, UK, 2013. [Google Scholar] [CrossRef]
- Vijay, P.; Shiva Nagendra, S.M.; Gulia, S.; Khare, M.; Bell, M.; Namdeo, A. Performance Evaluation of UK ADMS-Urban Model and AERMOD Model to Predict the PM10 Concentration for Different Scenarios at Urban Roads in Chennai, India and Newcastle City, UK. In Urban Air Quality Monitoring, Modelling and Human Exposure Assessment; Springer Transactions in Civil and Environmental Engineering; Springer: Cham, Switzerland, 2021; pp. 169–181. ISBN 9789811555114. [Google Scholar]
- Dėdelė, A.; Miškinytė, A. Estimation of Inter-Seasonal Differences in NO 2 Concentrations Using a Dispersion ADMS-Urban Model and Measurements. Air Qual. Atmos. Health
**2015**, 8, 123–133. [Google Scholar] [CrossRef] - Jamshidi Kalajahi, M.; Khazini, L.; Rashidi, Y.; Zeinali Heris, S. Development of Reduction Scenarios Based on Urban Emission Estimation and Dispersion of Exhaust Pollutants from Light Duty Public Transport: Case of Tabriz, Iran. Emiss. Control Sci. Technol.
**2020**, 6, 86–104. [Google Scholar] [CrossRef] - Shishegaran, A.; Saeedi, M.; Kumar, A.; Ghiasinejad, H. Prediction of Air Quality in Tehran by Developing the Nonlinear Ensemble Model. J. Clean. Prod.
**2020**, 259, 120825. [Google Scholar] [CrossRef] - Bruce, P.; Bruce, A. Practical Statistics for Data Scientists; O’Reilly Media, Inc.: Newton, MA, USA, 2017; ISBN 978-1-4919-5296-2. [Google Scholar]
- Moriasi, D.N.; Arnold, J.G.; van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Patryla, L.; Galeriua, D. Statistical Performances Measures—Models Comparison; CEA: Paris, France, 2011. [Google Scholar]
- Patel, V.C.; Kumar, A. Evaluation of Three Air Dispersion Models: ISCST2, ISCLT2, and SCREEN2 for Mercury Emissions in an Urban Area. Environ. Monit. Assess.
**1998**, 53, 259–277. [Google Scholar] [CrossRef] - Hedges, L.V.; Olkin, I. Statistical Methods for Meta-Analysis; Academic Press: Cambridge, MA, USA, 2014; ISBN 0-08-057065-8. [Google Scholar]
- Jauvion, G.; Cassard, T.; Quennehen, B.; Lissmyr, D. DeepPlume: Very High Resolution Real-Time Air Quality Mapping. arXiv
**2020**, arXiv:2002.10394. [Google Scholar] - Li, X.; Peng, L.; Yao, X.; Cui, S.; Hu, Y.; You, C.; Chi, T. Long Short-Term Memory Neural Network for Air Pollutant Concentration Predictions: Method Development and Evaluation. Environ. Pollut.
**2017**, 231, 997–1004. [Google Scholar] [CrossRef] - Chang, J.C.; Hanna, S.R. Technical Descriptions and User’s Guide for the BOOT Statistical Model Evaluation Software Package, Version 2.0; George Mason University and Harvard School of Public Health: Fairfax, VA, USA, 2005. [Google Scholar]
- Kadiyala, A.; Kumar, A. Guidelines for Operational Evaluation of Air Quality Models; LAP LAMBERT Academic Publishing: Chisinau, Republic of Moldova, 2012; ISBN 978-3-8465-3277-5. [Google Scholar]
- Goss-Sampson, M. Statistical Analysis in JASP: A Guide for Students; University of Greenwich: Amsterdam, The Netherlands, 2019. [Google Scholar] [CrossRef]
- Kadiyala, A.; Kaur, D.; Kumar, A. Development of Hybrid Genetic-Algorithm-Based Neural Networks Using Regression Trees for Modeling Air Quality inside a Public Transportation Bus. J. Air Waste Manag. Assoc.
**2013**, 63, 205–218. [Google Scholar] [CrossRef] [PubMed][Green Version]

**Figure 1.**Cp/Co for SF

_{6}using CALRANS99 data (Data 1) for stable atmospheric conditions concerning the downwind distances.

**Figure 2.**Cp/Co for SF

_{6}using CALRANS99 (Data 1) for unstable atmospheric conditions concerning the downwind distances.

**Figure 3.**Cp/Co for SF

_{6}using the Raleigh 2006 NO experiment (Data 2) for stable atmospheric conditions concerning the downwind distances.

**Figure 4.**Cp/Co for SF

_{6}using the Raleigh 2006 NO experiment (Data 2) for unstable atmospheric conditions concerning the downwind distances.

**Figure 5.**Cp/Co for SF

_{6}using the Idaho Falls Tracer Experiment (Data 3) for stable atmospheric conditions concerning the downwind distances.

**Figure 6.**Cp/Co for SF

_{6}using the Idaho Falls Tracer Experiment (Data 3) for unstable atmospheric conditions concerning the downwind distances.

**Table 1.**Revised empirical coefficients for Equations (1) and (2) under different stability conditions.

Atmospheric Stability | Empirical Coefficients | Value |
---|---|---|

Unstable conditions | a | 0.40 |

b_{u} | 2.00 | |

Weakly unstable conditions | a | 0.75 |

b_{u} | 3.50 | |

Weakly stable conditions | a | 0.58 |

b_{s} | 2.00 | |

Stable conditions | a | 0.55 |

b_{s} | 3.00 |

Atmospheric Stability | Pasquill Class [14] | Monin Obukhov Length (m) [27] | Richardson Number (R _{i}) [27] | Temperature Gradient (Degree Centigrade/100m) [14] | Standard Deviation of Vertical Wind Direction $\left({\mathit{\sigma}}_{\varnothing}\right)$ (Degree) [14] |
---|---|---|---|---|---|

Extremely unstable conditions | A | −2 to −3 | −0.86 | ≤−1.9 | ≤12 |

Moderately unstable conditions | B | −4 to −5 | ≥−0.86 to <−0.37 | −1.9 to ≤−1.7 | ≥10 to <12 |

Slightly unstable conditions | C | −12 to −15 | ≥−0.37 to <−0.10 | −1.7 to ≤−1.5 | ≥7.8 to <10 |

Neutral conditions | D | Infinite | ≥−0.10 to <0.053 | −1.5 to ≤−0.5 | ≥5 to <7.8 |

Slightly stable conditions | E | 35 to 75 | 0.053 ≤ to <0.134 | −0.5 to ≤−1.5 | ≥2.4 to <5 |

Moderately stable conditions | F | 8 to 35 | 0.134≤ | 1.5 to ≤4.0 | <2.4 |

Extremely Stable | G | - | - | >4.0 | - |

Statistical Indicator | FB | NMSE | R^{2} | MG | VG | MSLE | MAPE | |
---|---|---|---|---|---|---|---|---|

Ideal Values | 0 | 0 | 1 | 1 | 1 | 0 | 0 | |

CALRANS99 (Data 1) Stable Conditions | SLINE 1.1 | 0.11 | 0.05 | 0.88 | 0.89 | 1.20 | 0.00258 | 0.12 |

CALINE4 | −0.26 | 0.37 | 0.75 | 1.44 | 1.35 | 0.00946 | 0.19 | |

ADMS | −0.14 | 0.10 | 0.86 | 1.24 | 1.22 | 0.00328 | 0.12 | |

SLSM | −0.26 | 0.35 | 0.73 | 1.41 | 1.48 | 0.01561 | 0.23 | |

CALRANS99 (Data 1) Unstable Conditions | SLINE 1.1 | −0.16 | 0.14 | 0.87 | 1.28 | 1.13 | 0.00530 | 0.15 |

CALINE4 | −0.31 | 0.54 | 0.71 | 1.48 | 1.41 | 0.02019 | 0.28 | |

ADMS | −0.19 | 0.21 | 0.86 | 1.33 | 1.24 | 0.00860 | 0.19 | |

SLSM | −0.28 | 0.47 | 0.72 | 1.44 | 1.49 | 0.01602 | 0.25 | |

Raleigh 2006 experiment (Data 2) Stable Conditions | SLINE 1.1 | 0.15 | 0.05 | 0.75 | 0.88 | 1.22 | 0.00408 | 0.14 |

CALINE4 | −0.29 | 0.12 | 0.65 | 1.45 | 1.49 | 0.00172 | 0.26 | |

ADMS | −0.10 | 0.02 | 0.76 | 1.20 | 1.27 | 0.00206 | 0.09 | |

SLSM | −0.33 | 0.17 | 0.58 | 1.49 | 1.51 | 0.02117 | 0.28 | |

Raleigh 2006 experiment (Data 2) Unstable Conditions | SLINE 1.1 | −0.11 | 0.02 | 0.87 | 1.11 | 1.11 | 0.00219 | 0.10 |

CALINE4 | −0.23 | 0.09 | 0.68 | 1.46 | 1.46 | 0.01020 | 0.21 | |

ADMS | −0.14 | 0.03 | 0.86 | 1.25 | 1.22 | 0.00360 | 0.13 | |

SLSM | −0.25 | 0.11 | 0.66 | 1.49 | 1.47 | 0.01235 | 0.23 | |

Idaho Falls 2008 (Data 3) Stable Conditions | SLINE 1.1 | 0.14 | 0.04 | 0.80 | 0.86 | 1.22 | 0.00546 | 0.16 |

CALINE4 | −0.32 | 0.18 | 0.73 | 1.48 | 1.51 | 0.02130 | 0.27 | |

ADMS | −0.22 | 0.07 | 0.87 | 1.24 | 1.25 | 0.00546 | 0.20 | |

SLSM | −0.26 | 0.11 | 0.69 | 1.48 | 1.47 | 0.02130 | 0.22 | |

Idaho Falls 2008 (Data 3) Unstable Conditions | SLINE 1.1 | −0.12 | 0.03 | 0.85 | 1.13 | 1.24 | 0.00382 | 0.12 |

CALINE4 | −0.26 | 0.10 | 0.74 | 1.42 | 1.48 | 0.01491 | 0.24 | |

ADMS | −0.17 | 0.04 | 0.83 | 1.29 | 1.33 | 0.00570 | 0.16 | |

SLSM | −0.26 | 0.11 | 0.74 | 1.41 | 1.49 | 0.01433 | 0.24 |

^{2}—Coefficient of determination, MG—Geometric Mean Bias, VG—Geometric Mean-Variance, MSLE—Mean Square Logarithmic Error, MAPE—Mean Absolute Percentage Error).

Statistical Indicator | FB | NMSE | R^{2} | MG | VG | MSLE | MAPE |
---|---|---|---|---|---|---|---|

Data 1 (Stable) | −0.17 | 0.26 | 0.79 | 1.35 | 1.38 | 0.01032 | 0.21 |

Data 1 (unstable) | −0.19 | 0.34 | 0.78 | 1.32 | 1.37 | 0.01125 | 0.22 |

Data 2 (Stable) | −0.22 | 0.13 | 0.69 | 1.36 | 1.39 | 0.01984 | 0.30 |

Data 2 (unstable) | −0.14 | 0.09 | 0.72 | 1.33 | 1.35 | 0.00987 | 0.37 |

Data 3 (Stable) | −0.17 | 0.10 | 0.75 | 1.34 | 1.35 | 0.01863 | 0.25 |

Data 3 (unstable) | −0.17 | 0.09 | 0.80 | 1.32 | 1.38 | 0.01104 | 0.20 |

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## Share and Cite

**MDPI and ACS Style**

Madiraju, S.V.H.; Kumar, A. Examination of the Performance of a Three-Phase Atmospheric Turbulence Model for Line-Source Dispersion Modeling Using Multiple Air Quality Datasets. *J* **2022**, *5*, 198-213.
https://doi.org/10.3390/j5020015

**AMA Style**

Madiraju SVH, Kumar A. Examination of the Performance of a Three-Phase Atmospheric Turbulence Model for Line-Source Dispersion Modeling Using Multiple Air Quality Datasets. *J*. 2022; 5(2):198-213.
https://doi.org/10.3390/j5020015

**Chicago/Turabian Style**

Madiraju, Saisantosh Vamshi Harsha, and Ashok Kumar. 2022. "Examination of the Performance of a Three-Phase Atmospheric Turbulence Model for Line-Source Dispersion Modeling Using Multiple Air Quality Datasets" *J* 5, no. 2: 198-213.
https://doi.org/10.3390/j5020015