Following meteorological factors should be understood before studying the diffusion theories: 1. Atmospheric Temperature Lapse Rate 2. Speed and Direction of Wind 3. Wind Velocity Profile 4. Richardson’s Number.

**Factor # 1. Atmospheric Temperature Lapse Rate:**

When the air has minimum velocity or more or less motionless, the accumulation of the pollution will be maximum. When the air is in turbulence, the pollution will be low. The turbulence is not measured by the observatories bit are calculated on the basis of vertical temperature profile. It has been noted that the stability of the atmosphere is its tendency to resist or enhance the vertical motion, in other words to suppress or augment existing turbulence.

As the atmosphere is cooler at higher altitudes, normally the temperature reduces at a rate of 1°C per 100 m height. This decrease in temperature is known as adiabatic lapse rate. But in most of the cases, there is decrease in temperature, but is less than adiabatic lapse rate. Such change is known as sub adiabatic rate and the atmosphere is known to be under stable. Under such conditions, the mixing of the pollutants and their dilution take’s place slowly.

When the rate of decrease of temperature with height is more than the adiabatic rate, it is known as super-adiabatic lapse rate and the atmosphere is under unstable condition. Such conditions are very good for mixing and dilution of the pollutants. The adiabatic lapse rate known as neutral condition is characterized by winds, cloudy days and night.

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Sometimes the temperature increases with height, which is known as inversion. Under this condition the diffusion of the pollutants cannot take place and it forms a blanket layer at the top.

The emission of pollutants occurs at or near the surface of the earth. But the depth of the layer into which they made turbulent or diffused varies both in space and time. The height above the surface of the atmosphere, where the adiabatic lapse rate intersects the observed vertical temperature profile is known as Maximum Mixing Depth (MMD).

When the mixing height is low, but still above plume height, ground level concentration will be relatively high, because in this state the pollutants are prevented from dispersing in the upward atmosphere.

**Factor # 2. ****Speed and Direction of Wind:**

Air in motion is known as wind. Its horizontal component is considered in terms of speed and direction. Wind is another atmospheric variable, which is taken into account while studying the dilution capacity of the atmosphere.

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**The wind speed determines:**

(1) The plume rise downwind of the stack, and

(2) The amount which a plume is diluted while leaving the stack.

These two factors effect the magnitude and distance to the maximum ground level concentration. It is also used in determining the travel time from a source to a given receptor. The direction of the wind determines the direction of transport of the plume. It is conventional to consider the wind direction as the direction from the wind blows, therefore an easterly wind will move pollutant to the west of the source.

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It has been noted that wind speed is usually found to increase with height above the ground, and wind direction turn clockwise with height. The intensity of these variations depends on the roughness, the surface and stability of the atmosphere.

Over rough terraces, mountainous or hilly or with numerous buildings and vegetation, the surface wind velocity may be in the order of half the speed of upper wind. The surface wind velocity is usually 0.9 times the upper wind in case of smooth terrace. During day time the variation of wind speed with height is least, because the turbulence is at maximum.

**Factor # 3.**** Wind Velocity Profile:**

In the unstable atmosphere, due to high momentum transfer, the variation in wind speed profile with height is less than stable condition. Therefore, the wind velocity profile indirectly measures the degree of turbulence.

By application of Taylor’s statistical correlation theory of turbulence, sultan shows that from aerodynamically smooth surfaces, the mean-wind speed can be calculated by the formula,

where u’ = mean wind speed at the fixed reference point Z_{1}

n = turbulence parameter

= 0.20 for high lapse rate

= 0.25 for isothermal or small lapse rate

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= 0.33 for moderate inversion

= 0.50 for marked inversion.

**Factor # 4. ****Richardson’s Number: **

It is expressed to denote the degree of turbulence based on lapse rate and the wind profile

where g = Acceleration due to gravity (9.8 m sec ^{2})

T = Temperature in °K at Z

R_{d} = Dry adiabatic lapse rate of atmosphere

R_{i} = Richardson’s number

na = Wind speed in m/sec.

Richardson’s number is based on reasoning that turbulence will subside if the work required to displace air from its equilibrium position in a stable atmosphere is greater than the work done by the eddy stresses.