1. AMBIENT AIR CONCENTRATION MODELING Types of Pollutant Sources Point Sources e.g., stacks or vents Area Sources e.g., landfills, ponds, storage piles Volume Sources e.g., conveyors, structures with multiple vents Factors Affecting Dispersion of pollutants in the Atmosphere Source Characteristics Emission rate of pollutant Stack height Exit velocity of the gas Exit temperature of the gas Stack diameter Meteorological Conditions Wind velocity Wind direction Ambient temperature Atmospheric stability

2. GAUSSIAN MODELS Advantages Produce results that match closely with experimental data Incorporate turbulence in an ad-hoc manner Simple in their mathematics Quicker than numerical models Do not require super computers Disadvantages Not suitable if the pollutant is reactive in nature Fails to incorporate turbulence in comprehensive sense Unable to predict concentrations beyond radius of approximately 20 Km For greater distances, wind variations, mixing depths and temporal variations become predominant

3. SOURCES OF ERROR IN GAUSSIAN MODEL

4. NUMERICAL SOLUTIONS Involves solving a system of partial differential equations Equations mathematically represent the fate of pollutants downwind concentration The number of unknown parameters must be equal to number of equations System of equation is written in numerical form with appropriate numerical scheme and solved using computer codes Classes of Numerical Models Three Dimensional Equations (k-Theory) Model Higher Order Closure Models (k-  Type)

5. Difference between Numerical Models and Gaussian Model The degree of completeness in the mathematical description of the atmospheric dispersion processes Type of releases i.e., stack, jet or area source are easy to handle manually The models are designed to handle, degree of completeness in the description of non-transport processes like chemical reactions Terrain feature complexities for which the model is designed

6. Sources of Error In Numerical Models Based on K-Theory

7. General Eddy Diffusivity Profile Used in Numerical Models Based on K-theory

8. CONVECTIVE DIFFUSIVE EQUATION

9. GRADIENT TRANSFER THEORY The turbulent mass flux is computed using gradient transfer theory as follows: where, K’s = Eddy Diffusivity Constants (m 2 /sec) C = Pollutant concentration (kg/m 3 ) q = Turbulent mass flux (kg/m 2 /sec) Q = Pollutant source strength (kg/m 3 /sec) Q r = Rate of loss or gain of pollutant due to reaction (kg/m 3 /sec) Q a = Pollutant ground absorption rate (kg/m 3 /sec) t = Time (sec) V = Wind field (m/sec)

10. GAUSSIAN MODEL Assumption: Constant wind speed No wind shear Flat topography Gaussian Plume Model where, C (x,y,z) - Concentration in air at (x,y,z) (gm/m 3 ) Q - Emission rate from the stack (m/sec) U s - Wind speed at source height (m/sec)  y - Horizontal dispersion coefficient (m)  z - Vertical dispersion coefficient (m) y - Cross - wind distance (m) z - Vertical distance (m) h - Effective stack height (m)

11. METHODS TO INCORPORATE PLUME RISE The effective Source Height Method The variable Plume Model Method

12. EFFECTIVE SOURCE HEIGHT METHOD Independent of downwind distance, x Effective source height, h = hs +  h - ht where, hs = Physical chimney height ht = Maximum terrain height between the source and receptor VARIABLE PLUME METHOD Takes into account the tilt of the plume

13. SIMPLIFIED FORMS OF A GAUSSIAN PLUME MODEL (GPM) GPM for Ground Level Concentration (z = 0) GPM for Centerline Ground Level Concentrations (y = 0)

14. GPM for a Ground Source (non fumigation) with negligible plume rise GPM for small downwind distances i.e near the source where, q o = Initial volume flux (m 2 /sec)

15. MODIFICATIONS IN GAUSSIAN PLUME MODEL Simplified Equations for Maximum Ground Level Concentration Location of maximum concentration Ground Level Concentration during Limited Mixing Condition where, L = Mixing Height (m)

16. GPM Model for Puff Plume (Ground Level Release) Gaussian Distribution Used in Gaussian Model where,  is any real number  is any real number > 0

17. GPM Model for Line Sources where, Q = Source strength per unit distance (g/s.m) =

18. Concentration Estimate for Various Sampling Times C 2 = C 1 (t 1 /t 2 ) q where, q lies between 0.17 and 0.5

19. PLUME DISPERSION PARAMETERS Different Methods to Calculate Sigmas Experimental data Modified Experimental Curves Lagrangian Auto Correlation Function Moment-Concentration Method Taylor's Statistical Theory Factors Considered while Calculating Sigmas Nature of Release Sampling Time Release Height Terrain Features Velocity Field

20. PASQUILL CURVES Curves are based on smoke plume elevation H sp (visible portion) and angular spread q using the relations  z = H sp /2.14  y = q x /4.28 The numerical coefficient 2.14 is just the 10% ordinate of the normal error curve

21. BNL DISPERSION PARAMETERS The  y data are based on actual measurements while  z is derived using where, F g - Adjustment term for the Gaussian equation C - Measured Concentration U has invariably been assumed constant (however it should increase with height)

22. TVA DISPERSION COEFFICIENTS Sigma's are calculated as:  p = Area / [C peak *(2*  ) 0.5 ] where, Area = Base times the average height of Concentration Profile along the axis C peak = Maximum concentrations in that profile In a number of cases,  z is calculated using C max = Q / [2*U*  y *  z *  ] and thus, the distribution is considered Gaussian i.e., C = C max exp[-0.5*(x g /  ) 2 ]

23. SUTTON CURVES Sutton used vertical diffusion coefficients (C y and C z ) to obtain Sigma's where,  =  Kinematic viscosity of the air v', w' = Eddy velocities across wind and in the vertical 2  i 2 = C i 2 * x 2n i = y or z