Lecture 2-2024 for environment engineering
- 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 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 30o 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