Lecture 2-2024 for environment engineering

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1. Atmospheric Sciences-EnSE 6254
•INSTRUCTOR: JUMA SELEMANI
•NELSON MANDELA AFRICAN INSTITUTION OF
SCIENCE AND TECHNOLOGY
•2024/2025

2. Coverage
•Climate definition and theories
•Motions in the atmosphere
-Conservation of mass (Equation of continuity)
-Conservation of momentum
-Conservation of Energy (Thermodynamic Equation)

3. Climate definition and theories
•The Earth Radiation Budget
-Balance between the incoming
energy from the sun and the
outgoing thermal (longwave) and
reflected (shortwave) energy
from the earth.
-Climate change occurs because
of imbalance between incoming
and outgoing radiation

4. Factors affecting global radiation balance
1.Earth’s rotation: Earth’s rotation causes
daily variations in net radiation.
2.Earth-Sun geometry: It causes annual
variations in net radiation
3.Latitude: Equator receives more incoming
shortwave radiation
4.Altitude: With increase in altitude, there is
less atmospheric
reflection/scattering/absorption which leads
to more incoming shortwave radiation
(Rs↓) received at the surface
5.Surface color: Darker surface absorbed
more solar radiation.
6.Greenhouse gases:prevent earth’s
radiation
Read: when the
earth is closer to the
sun and vice verse

5. Greenhouse Effect
•a phenomenon occurs when gases
in the atmosphere trap heat emitted
by the planet
•Greenhouse gases are
naturally/man-made gases in
atmosphere that trap heat, while
allowing sunlight to pass through
•What will happen if there is
balance between incoming and
outgoing radiation?
•Are greenhouse gases good or bad?
•The greenhouse effect is an
essential process that keeps our
planet habitable

6. Motions in the atmosphere
•Circulation occurs because atmosphere tries to maintain balance
i.e. Circulation form because the atmosphere adjusting to remove
imposed imbalances
•Driving forces in the atmosphere are:
-Pressure gradient, Coriolis and friction forces
• How the wind blows
-Wind blows from high pressure to low pressure
-Movement of wind establishes the local climate and their average
form global climate
•What would happen if the Earth was heated evenly?

7. Air movement
•Air movement in the atmosphere, is
governed by several factors
including sun's energy, the Earth's
rotation, and gravity
•Winds are critical for climate
because they transport heat/energy
•Affect the formation of clouds by
carrying condensables and
noncondensables
-Why air moves from the equator to the
poles?
-Why warmer at the equator?
-Why colder at the poles?
-Why more deserts located nearby 30
o

north and south of equator

8. Ocean Circulation
•Ocean Circulation: is the
large scale movement of
waters in the ocean basins
•What factors drive ocean
circulation:
(a)Winds,
(b)Density differences in water
masses
(c)Earthquakes
•Reading Questions:
1.Explain how air and water
circulation occurs?
2.How air and water circulation
influence climate?

9. Theories governing motions in the atmosphere
•There are sets of equations describing atmospheric motions e.g.
equation of state, conservation of momentum, mass and energy
•Atmosphere is a fluid medium (the gaseous envelope surrounding
the earth)
•A fluid does not have a defined shape
•When pressure acts on fluid, it changes its shape continuously
•Air can either be state variables or dynamical variables
•State variable describes physical properties of air e.g. temperature,
pressure,
•Equation of state is used to describe physical properties of air
•Also known as the ideal gas law given as P=ρRT
•Where R is the gas constant 8.3144621 J/mol·K for dry air and T is
temperature

10. Thermodynamic Equation
•Changes of temperature of a parcel of air are governed by
the First Law of Thermodynamics
•A system possesses macroscopic kinetic and potential energy as well
as internal energy (u) due to the kinetic and potential energy of its
molecules or atoms
•This relationship can be expressed in differential form as:
•dq = du+dw
•dq = differential increment of heat added to the system
•dw=differential increment of work done by the system
•du = differential increase in internal energy of the system
•The work done by the gas (dW) is equal to the pressure (p) exerted by
the gas multiplied by the change in volume (dV) of the gas
•From dW =Fdx (force x distance) and P=F/A and V=area x distance
•dW = pAdx = pdV

11. Thermodynamic Equation
•The first law of thermodynamics is then expressed as:
•dW = pAdx = pdV
•dq = du + pdα--------(1)
•Specific heat: The ratio of the heat added to a system to the change
in temperature of the system (= dq/dT )
•Specific heat at constant volume (cv)
•Cv= (dq/dT)
•At constant volume a gas does no work and the first law of
thermodynamics reduces to dq = du
•From cvdT= dq
•CvdT= du
•Substituting in equation (1)
•dq=CvdT +pdα----- (2)

12. Thermodynamic Equation
•Specific heat at constant pressure (cp)
•Cp=dq/dT
•dq = cvdT + pdα can also be written as dq = cvdT + d(pα) –αdp
•From equation of state pα = RT
•d(pα) = d(RT) = RdT
•dq = cvdT + RdT –αdp
•dq=(cv + R)dT - αdp but cp=cv+R
•Therefore equation 2 can become dq=cpdT-αdp This can be used to
express the first law of thermodynamics
•Thermodynamic and other energy equations are tools in the
forecasting of storm development.

13. Conservation of mass
•This theory describes how mass, energy or any other quantity is
conserved as parcel of fluid or air moves from one point to another.
•Continuity equation is one of the various fundamental principles of
Physics used for the analysis of the uniform flow of fluids
Where
t = Time
ρ = Fluid density
u = flow velocity vector field.

∇⋅
is divergence,
The equation is also called
continuity equation

14. Conservation of momentum
•The law states that the amount of momentum remains constant in a
closed system
•In a closed system the total momentum of bodies acting each other
remains constant unless an external force is applied
•From second newtons law rate of change of momentum
Coriolis force
Centrifugal force

15. Primitive equations
are set of nonlinear partial differential equations that are used to
approximate global atmospheric flow and are used in most atmospheric
models
is describing zonal movement
is describing meridional movement
is hydrostatic equation
is continuity equation
is thermodynamic equation
Φ is the geopotential, f is Coriolis force estimated by 2Ωsinθ where Ω
is angular velocity of the earth, θ is degree of latitude

16. Scalar and vector fields
•A scalar quantity has size/magnitude but no direction e.g.
Speed, Distance, Time, Mass Temperature and humidity
•A vector quantity has both magnitude and direction e.g.
Acceleration, Force, electromagnetic field and Weight
•Give examples of scalar and vector in atmospheric circulation

17. Next week
•Circulation theorems,
•Geostrophy and quasigeostrophy
•Boundary layer dynamics
•Waves in the atmosphere