CEE 452/652. Week 3, Lecture 1 Mass emission rate, Atmospheric Stability. Dr. Dave DuBois Division of Atmospheric Sciences, Desert Research Institute

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1 CEE 452/652 Week 3, Lecture 1 Mass emission rate, Atmospheric Stability Dr. Dave DuBois Division of Atmospheric Sciences, Desert Research Institute

2 Today s topics Review homework Review quiz Mass emission rate Wind flow patterns Friction forces Hydrostatic equilibrium Stability Inversions and plumes

3 Homework #1 Short term solutions Water roads Slow people down, speed limit, enforce Long term solutions Pave road Dust suppressants

4 Quiz NOx and SO 2 NOx + VOC + light (hv) ozone C mass = C ppm 10-6 (MW x P)/RT

5 Mass Emission Rate Mass emissions rate = concentration in gas x volumetric flow rate of gas m & = Q C Q = volumetric flow rate of gas (m 3 s -1 ) C = concentration (g m -3 )

6 Mass Emission Rate Mass emissions rate = density x area x velocity dm = m& = ρ A v dt ρ = density of the fluid (g m -3 ) A = duct or stack cross sectional area (m) V = flow velocity (m s -1 )

7 Mass Emission Rate Mass emissions rate = concentration in gas x volumetric flow rate of gas M dot emitted pollutant = Cpollutant stackgas x Q stackgas Example: For NO in car exhaust at 1.0 ppm, with exhaust rate of 50 liters/second, what is mass emissions rate?

8 Idealized General Circulation Patterns Prevailing westerlies Trade winds Trade winds This assumes earth is 1. completely smooth 2. Uniform composition

9 Factors Affecting Winds Winds as a function of height Large scale (synoptic) weather patterns Topography (mountains, valleys) Surface heating (diurnal and seasonal) Surface heating changes in ground cover (water, rocks, deserts, forests, fields) Buildings, roofs

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11 Solar Spectrum This is the source of energy from the sun available to heat the earth

12 Ocean Albedo & Heating Angle of incidence 90 Sun Surface

13 Pressure Gradient Force High pressure Air Parcel Low pressure Unequal pressure produce a horizontal force = F P Net direction of air parcel

14 Pressure Gradient Force Force per unit volume, directed from high to low pressure F P = pressure change (mb) distance (km) 990 mb 1000 mb F P 980 mb

15 Coriolis Force Apparent force on moving objects on the rotating Earth It accelerates moving objects to their right in the Northern Hemisphere and to their left in the Southern Hemisphere There is no Coriolis force at the equator Force is at right angles to the motion, changing a moving object s direction but not its speed

16 Coriolis Force A function of Earth s rotation rate, latitude and speed of object A commercial jet flying from Seattle to Denver feels a sideways Coriolis force 0.1% of gravity If the jet starts flying toward Denver, it must tip its wings very slightly to compensate, else it would be deflected to Salt Lake City

17 Geostrophic Winds Air initially at rest will accelerate until it flows parallel to the isobars at a steady speed with the pressure gradient force balanced by the coriolis force In balance Starts here at rest

18 Geostrophic Winds Winds at balance between coriolis and pressure gradient force P = Pressure F P = Pressure Gradient Force F D = Coriolis Force u g = Geostrophic wind

19 Centrifugal Force Apparent force pulling outward from Earth s polar axis Sea level is pulled 20 km further from the center of the earth at the equator than at poles By redefining gravity to point perpendicular to sea level everywhere we can absorb centrifugal force into gravity

20 Gradient Winds

21 Frictional Forces in the Atmosphere

22 Hydrostatic Equilibrium height P + dp Column of air of cross sectional area = A Density of air = ρ dz z gravity P Sea level Remember that force = Pressure x Area Parcel of air will remain stationary if sum of all vertical forces on parcel = 0 PA (P+dP)A gρadz = 0 Gravitational force on the air mass

23 Hydrostatic Equilibrium PA (P+dP)A gρadz = 0 A s cancel, leaving P -P -dp-gρdz = 0 dp = - gρdz Pressure decreases with height Since air is compressible fluid, density varies with height so ρ = ρ(z)

24 Adiabatic Conditions Use 1 st Law of thermodynamics dh = C p dt VdP For an adiabatic process, no heat is added or taken away, so dh = 0 C p dt = VdP Use the relationship, Vρ = 1, when we use specific volume, V = m 3 kg -1

25 Adiabatic Conditions C p dt = dt C p dt dz = = dp ρ 1 ( ρgdz) ρ ρg g = = ρc p C p γ d Dry adiabatic lapse rate

26 Adiabatic Conditions So dry air cools adiabatically with height Dry adiabatic lapse rate is dt dz = g C p = γ d = 0.98 o C /100m

27 Adiabatic Cooling Cooling of ascending air. Dry air forced to rise 200 m over a ridge cools adiabatically by 2 C Dry adiabatic lapse rate = ΔT/Δz = 5.4 F/1000 feet = 9.8 C/km If phase change occurs, then heat is transferred and is not adiabatic

28 Unstable Conditions Actual lapse rate greater than dry adiabatic lapse rate γ > γ d A parcel of air moved upward cools at a slower rate than the surrounding air and is accelerated upward by buoyant forces. Moved downward, the parcel warms at a slower rate and is accelerated downward.

29 Neutral Stability γ = γ d During neutral conditions, upward and downward motion result in the parcel temperature changing at the same rate as the surroundings

30 Stable Conditions Actual lapse rate less than dry adiabatic lapse rate γ < γ d Here upward motion produces a parcel cooler than the surroundings, hence the parcel will settle back to its original elevation. Downward motion produces a warmer parcel, which will rise to its original elevation.

31 Temperature Inversions During stable conditions, lapse rate is less than the dry adiabatic lapse rate. Maximum stability occurs when the lapse rate becomes negative or when temperature increases with height Temperature Inversion defined during this condition Produces the most adverse mixing conditions, trapping pollutants near the ground

32 Frontal Inversions Frontal Inversions When warm air mass overruns a cold air mass below Associated with a front and moderate to high winds, so doesn t usually affect mixing conditions So not important from pollution control standpoint