2. Conservation laws and basic equations
|
|
- Lorin Potter
- 5 years ago
- Views:
Transcription
1 2. Conservation laws and basic equations Equatorial region is mapped well by cylindrical (Mercator) projection: eastward, northward, upward (local Cartesian) coordinates:,, velocity vector:,,,, material (Lagrange) time derivative:, (t: time) (1),, Three conservation laws (four equations) (i) Equation of motion (Newton s 2 nd law; Angular momentum conservation law): 1 3 (ii) Equation of continuity (Mass conservation law): 1, 4 (iii) Equation (1 st law) of thermodynamics (Entropy conservation law): ln, Six variables:, (pressure), (temperature), (density), (specific humidity), (condensation ratio) (2) / potential temperature 5 Parameters: 0,0,, 2Ωsin (Coriolis; Ω: rotation angular. velocity; : latitude) ; 0, 0, : gravity acceleration and : gas constant and constant-pressure specific heat for dry air ; : Latent heat for water condensation External sources:,, ),, : momentum (friction), heat (net radiation), water vapor (evaporation)
2 Concept of continuum Actual matter = Σ molecule - Density = Σ molecular mass / unit volume = molecular mass number / unit volume - Pressure = Σ molecular momentum / unit time / unit area = molecular force / unit area - Temperature = Σ molecular kinetic energy / molecular number / Boltzmann constant (atmosphere) (ocean, ) (earth) Phase of matter: Gas, Liquid, Solid Continuum: Fluid, Plastic, Elastic, Rigid
3 Forces (interactions) working in the nature Intermolecular (electromagnetic) force saturation homogeneous nucleation - Kelvin s curvature effect supercooled tiny droplet - Raoult s solute effect vapor pressure / boiled point depression - Henry-Dalton s partial pressure law for a mixed gas Unsaturated surface of a droplet molecular diffusion evaporation Condensation at a solid surface (heterogeneous nucleation) large droplet Planetary gravitational force Density (hydrostatic) stratification Ocean - Photochemical / volcanic water vapor production - Gravitational separation / photodissociation Hydrogen escape / oxidation Ocean loss Precipitation (coalescence / sublimation) process - Gravity, radiation Equatorial tropopausal cold trap - Orography / sea-land heat contrast forced convection - Conditional instability moist convection (c) (d) Strong/weak nuclear & intermolecular electromagnetic forces (Israelachvili, 1985, 1992) Cloud/precipitation processes (Wallace & Hobbs, 1972, 2006) Planetary gravitation (Israelachvili, 1985, 1992)
4 Various fluid flows in the Earth System [(i) Momentum and (ii) continuity eqs. are common for any cases] Global atmosphere (Meteorology) Ocean (Oceanography) River (Hydrology) Compressible [+thermodynamics (iii)(iv)] Almost closed Zonal dominant Moisture effect [(v)] Almost free Incompressible [+thermal expansion] Almost closed Horizontal dominant Salinity effect Coastal effect Incompressible [+Level/stream change] Opened Almost one-dimensional Complex boundary
5 General principles governing planetary fluid Planetary (or geophysical) fluid: Gas/liquid under - sphericity: a=6370 km (for the earth) latitude φ, longitude λ, altitude z eastward displacement: dx = a cosφ dλ northward displacement: dy = a dφ - rotaion: Ω = 2π/86164s (for the earth) Coriolis parameter: f = 2Ω sinφ Rossby parameter: β= df/dy =2Ω cosφ - gravitation: g = 9.8 m/s 2 (for the earth) Variables: (6 for dry atmosphere) - wind (or stream) velocity components: (u, v, w) - thermodynamical state variables: (T, p, ρ) [ - humidity (or salinity): q ]
6 Centrifugal and Coriolis Forces Centrifugal force Ω must be balanced with pressure gradient etc. (: mass, : rotation radius, Ω: angular velocity, Ω : moving speed) CFF CFF Gravity If the body moves eastward by (relative to the earth) at latitude, Horizontal component of total centrifugal force cos Ω Ω sin 2 2Ω sin tan Coriolis parameter f sin
7 Exercise 2 (1) Explain the three terms in the last equation in the previous slide. (2) How different the Coriolis force in the northern and southern hemispheres? How about at the equator? (3) Do you think the motorcycle rider and the bathtub vortex must feel the Coriolis force of the earth s rotation? How about the Coriolis for the solar system, or of galaxy? Answers: (1) Ω cos sin 2Ω sin Coriolis force only considerable not separated from small gravity (neglectable) (2) Sin changes sign and direction of Coriolis force becomes opposite in northern/southern hemispheres. It becomes 0 and Coriolis force vanishes at the equator. (3) No, because the earth s rotation is in the time scale of 1 day. Similarly, we can neglect the earth s revolution around the sun with 365 days >> 1 day, as well as the solar revolution in our galaxy with 20 million years.
8 (a) A planet observed from space (b) A planet observed on itself velocity Sun planet (Earth) solar gravitation acceleration solar gravitation centrifugal force (c) A body (an air parcel) at rest on Earth observed from space normal force (pressure gradient) (d) An air parcel at rest observed on Earth pressure gradient (e) An air parcel moving with geostrophic westerly pressure gradient acceleration gravitation gravitation gravity centrifugal force due to Earth s rotation gravity Coriolis force
9 Traditional approximation Taking only the vertical component of rotation: cos Ω sin cos 1 2 Ω sin 2 2Ω sin tan the first term (maximum at 45º latitude, about 1/300 of g ellipticity of Earth) is involved in the gravity and excluded here Ω Ω a cos φ a φ Centrifugal Obtaining only the horizontal component of Coriolis and centrifugal forces: 2Ω cos sin φ Ω sin φ φ centrifugal x sin φ The other term on Ωcos is neglected even in the tropics (Phillips, 1966; Gill, 1982, 7.4).
10 Leonhard Euler (1707~1783) function : y = f (x) π, e, i (1748) Trigonometric expansion ( Fourier series) Newton s 2 nd law ( equation of motion ) (1736) F = m a Continuity equation for incompressible inviscid fluid (1757) u x w z 0. z w > 0 z z u > 0 u < 0 = + w < 0 x x x
11 2. Basic equations (cont.) Additional two laws (three equations; one variable: saturation water vapor pressure) (iv) Equation of ideal gas (Boyle-Charles law):, (v) Equation of water vapor saturation (Clapeyron-Clausius) :, 1 7 Parameters: and : molecular mass of dry air and water vapor Basic Eqs. (3)-(7) Horizontal mean Chapter 3 Vertical profiles (8)-(9) Zonal mean Chapter 4 Meridional distributions (23)-(27) All phenomena are governed by limited number of physical laws. Nonlinearity and complex sources produce complex phenomena. Chapter 5 Waves. (45)-(49) Chapter 6 Convections (69)-(74)
12 Julius Robert von Mayer ( ) James Prescott Joule ( ) /dc/pc/mayer.jpg (Roscoe, 1906; wiki/james_prescott_jou le) German scientist cruised in 1840 to East Jawa as a Dutch ship doctor, and noticed a concept called energy at present as exchangeable quantity between motion and heat. After returning to Germany in 1841, he submitted a paper to a journal of physics, but rejected. In 1842 his paper was accepted by a journal of chemistry, but was not so highly evaluated. In 1845 his second paper was rejected even by the chemical journal. After that he never submitted any papers to journals but published them by himself. In 1850 he became a farmer until his death. In 1854 von Helmholz recognized that Mayer was the first person discovering the energy. English brewer studied physics without any post at university or institute. He discovered the Joule s law and the mechanical equivalent of heat in early 1840s.
1/18/2011. Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis ESS227 Prof. Jin-Yi Yu
Lecture 2: Basic Conservation Laws Conservation Law of Momentum Newton s 2 nd Law of Momentum = absolute velocity viewed in an inertial system = rate of change of Ua following the motion in an inertial
More informationConservation of Mass Conservation of Energy Scaling Analysis. ESS227 Prof. Jin-Yi Yu
Lecture 2: Basic Conservation Laws Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis Conservation Law of Momentum Newton s 2 nd Law of Momentum = absolute velocity viewed
More informationControl Volume. Dynamics and Kinematics. Basic Conservation Laws. Lecture 1: Introduction and Review 1/24/2017
Lecture 1: Introduction and Review Dynamics and Kinematics Kinematics: The term kinematics means motion. Kinematics is the study of motion without regard for the cause. Dynamics: On the other hand, dynamics
More informationLecture 1: Introduction and Review
Lecture 1: Introduction and Review Review of fundamental mathematical tools Fundamental and apparent forces Dynamics and Kinematics Kinematics: The term kinematics means motion. Kinematics is the study
More informationDynamics and Kinematics
Geophysics Fluid Dynamics () Syllabus Course Time Lectures: Tu, Th 09:30-10:50 Discussion: 3315 Croul Hall Text Book J. R. Holton, "An introduction to Dynamic Meteorology", Academic Press (Ch. 1, 2, 3,
More information1. The vertical structure of the atmosphere. Temperature profile.
Lecture 4. The structure of the atmosphere. Air in motion. Objectives: 1. The vertical structure of the atmosphere. Temperature profile. 2. Temperature in the lower atmosphere: dry adiabatic lapse rate.
More informationGeophysics Fluid Dynamics (ESS228)
Geophysics Fluid Dynamics (ESS228) Course Time Lectures: Tu, Th 09:30-10:50 Discussion: 3315 Croul Hall Text Book J. R. Holton, "An introduction to Dynamic Meteorology", Academic Press (Ch. 1, 2, 3, 4,
More information1/3/2011. This course discusses the physical laws that govern atmosphere/ocean motions.
Lecture 1: Introduction and Review Dynamics and Kinematics Kinematics: The term kinematics means motion. Kinematics is the study of motion without regard for the cause. Dynamics: On the other hand, dynamics
More informationLecture 1. Equations of motion - Newton s second law in three dimensions. Pressure gradient + force force
Lecture 3 Lecture 1 Basic dynamics Equations of motion - Newton s second law in three dimensions Acceleration = Pressure Coriolis + gravity + friction gradient + force force This set of equations is the
More informationd v 2 v = d v d t i n where "in" and "rot" denote the inertial (absolute) and rotating frames. Equation of motion F =
Governing equations of fluid dynamics under the influence of Earth rotation (Navier-Stokes Equations in rotating frame) Recap: From kinematic consideration, d v i n d t i n = d v rot d t r o t 2 v rot
More informationNWP Equations (Adapted from UCAR/COMET Online Modules)
NWP Equations (Adapted from UCAR/COMET Online Modules) Certain physical laws of motion and conservation of energy (for example, Newton's Second Law of Motion and the First Law of Thermodynamics) govern
More informationATS 421/521. Climate Modeling. Spring 2015
ATS 421/521 Climate Modeling Spring 2015 Lecture 9 Hadley Circulation (Held and Hou, 1980) General Circulation Models (tetbook chapter 3.2.3; course notes chapter 5.3) The Primitive Equations (tetbook
More informationGravity Waves. Lecture 5: Waves in Atmosphere. Waves in the Atmosphere and Oceans. Internal Gravity (Buoyancy) Waves 2/9/2017
Lecture 5: Waves in Atmosphere Perturbation Method Properties of Wave Shallow Water Model Gravity Waves Rossby Waves Waves in the Atmosphere and Oceans Restoring Force Conservation of potential temperature
More information2. Meridional atmospheric structure; heat and water transport. Recall that the most primitive equilibrium climate model can be written
2. Meridional atmospheric structure; heat and water transport The equator-to-pole temperature difference DT was stronger during the last glacial maximum, with polar temperatures down by at least twice
More informationNeeds work : define boundary conditions and fluxes before, change slides Useful definitions and conservation equations
Needs work : define boundary conditions and fluxes before, change slides 1-2-3 Useful definitions and conservation equations Turbulent Kinetic energy The fluxes are crucial to define our boundary conditions,
More information1/27/2010. With this method, all filed variables are separated into. from the basic state: Assumptions 1: : the basic state variables must
Lecture 5: Waves in Atmosphere Perturbation Method With this method, all filed variables are separated into two parts: (a) a basic state part and (b) a deviation from the basic state: Perturbation Method
More informationGoals of this Chapter
Waves in the Atmosphere and Oceans Restoring Force Conservation of potential temperature in the presence of positive static stability internal gravity waves Conservation of potential vorticity in the presence
More informationwhere p oo is a reference level constant pressure (often 10 5 Pa). Since θ is conserved for adiabatic motions, a prognostic temperature equation is:
1 Appendix C Useful Equations Purposes: Provide foundation equations and sketch some derivations. These equations are used as starting places for discussions in various parts of the book. C.1. Thermodynamic
More informationMeteorology 6150 Cloud System Modeling
Meteorology 6150 Cloud System Modeling Steve Krueger Spring 2009 1 Fundamental Equations 1.1 The Basic Equations 1.1.1 Equation of motion The movement of air in the atmosphere is governed by Newton s Second
More informationChapter 5. Shallow Water Equations. 5.1 Derivation of shallow water equations
Chapter 5 Shallow Water Equations So far we have concentrated on the dynamics of small-scale disturbances in the atmosphere and ocean with relatively simple background flows. In these analyses we have
More informationTemperature (T) degrees Celsius ( o C) arbitrary scale from 0 o C at melting point of ice to 100 o C at boiling point of water Also (Kelvin, K) = o C
1 2 3 4 Temperature (T) degrees Celsius ( o C) arbitrary scale from 0 o C at melting point of ice to 100 o C at boiling point of water Also (Kelvin, K) = o C plus 273.15 0 K is absolute zero, the minimum
More informationAtmosphere, Ocean and Climate Dynamics Answers to Chapter 8
Atmosphere, Ocean and Climate Dynamics Answers to Chapter 8 1. Consider a zonally symmetric circulation (i.e., one with no longitudinal variations) in the atmosphere. In the inviscid upper troposphere,
More informationDynamics of the Zonal-Mean, Time-Mean Tropical Circulation
Dynamics of the Zonal-Mean, Time-Mean Tropical Circulation First consider a hypothetical planet like Earth, but with no continents and no seasons and for which the only friction acting on the atmosphere
More informationIntroduction to Physical Oceanography Homework 3 - Solutions. 1. Volume transport in the Gulf Stream and Antarctic Circumpolar current (ACC):
Laure Zanna 10/17/05 Introduction to Physical Oceanography Homework 3 - Solutions 1. Volume transport in the Gulf Stream and Antarctic Circumpolar current (ACC): (a) Looking on the web you can find a lot
More informationDynamic Meteorology - Introduction
Dynamic Meteorology - Introduction Atmospheric dynamics the study of atmospheric motions that are associated with weather and climate We will consider the atmosphere to be a continuous fluid medium, or
More informationLecture 5: Atmospheric General Circulation and Climate
Lecture 5: Atmospheric General Circulation and Climate Geostrophic balance Zonal-mean circulation Transients and eddies Meridional energy transport Moist static energy Angular momentum balance Atmosphere
More informationTopic 1 The Atmosphere and Atmospheric Variables
Name Notes: Topic 1 The Atmosphere Regents Earth Science Topic 1 The Atmosphere and Atmospheric Variables What is the atmosphere? Meteorology is the study of A. Structure of the Atmosphere: What two gases
More informationCHAPTER 4. THE HADLEY CIRCULATION 59 smaller than that in midlatitudes. This is illustrated in Fig. 4.2 which shows the departures from zonal symmetry
Chapter 4 THE HADLEY CIRCULATION The early work on the mean meridional circulation of the tropics was motivated by observations of the trade winds. Halley (1686) and Hadley (1735) concluded that the trade
More informationSIO 210 Introduction to Physical Oceanography Mid-term examination November 3, 2014; 1 hour 20 minutes
NAME: SIO 210 Introduction to Physical Oceanography Mid-term examination November 3, 2014; 1 hour 20 minutes Closed book; one sheet of your own notes is allowed. A calculator is allowed. (100 total points.)
More informationPHYS 432 Physics of Fluids: Instabilities
PHYS 432 Physics of Fluids: Instabilities 1. Internal gravity waves Background state being perturbed: A stratified fluid in hydrostatic balance. It can be constant density like the ocean or compressible
More informationLecture 2. Lecture 1. Forces on a rotating planet. We will describe the atmosphere and ocean in terms of their:
Lecture 2 Lecture 1 Forces on a rotating planet We will describe the atmosphere and ocean in terms of their: velocity u = (u,v,w) pressure P density ρ temperature T salinity S up For convenience, we will
More informationp = ρrt p = ρr d = T( q v ) dp dz = ρg
Chapter 1: Properties of the Atmosphere What are the major chemical components of the atmosphere? Atmospheric Layers and their major characteristics: Troposphere, Stratosphere Mesosphere, Thermosphere
More informationAtmospheric Dynamics: lecture 2
Atmospheric Dynamics: lecture 2 Topics Some aspects of advection and the Coriolis-effect (1.7) Composition of the atmosphere (figure 1.6) Equation of state (1.8&1.9) Water vapour in the atmosphere (1.10)
More informationLecture 3: Light and Temperature
Lecture 3: Light and Temperature terrestrial radiative cooling Solar radiative warming (Light) Global Temperature atmosphere ocean land Light Temperature Different forms of energy Energy conservation energy,
More informationEATS Notes 1. Some course material will be online at
EATS 3040-2015 Notes 1 14 Aug 2015 Some course material will be online at http://www.yorku.ca/pat/esse3040/ HH = Holton and Hakim. An Introduction to Dynamic Meteorology, 5th Edition. Most of the images
More informationThermodynamics Review [?] Entropy & thermodynamic potentials Hydrostatic equilibrium & buoyancy Stability [dry & moist adiabatic]
Thermodynamics Review [?] Entropy & thermodynamic potentials Hydrostatic equilibrium & buoyancy Stability [dry & moist adiabatic] Entropy 1. (Thermodynamics) a thermodynamic quantity that changes in a
More informationPlanetary Atmospheres. Structure Composition Clouds Photochemistry Meteorology Atmospheric Escape
Planetary Atmospheres Structure Composition Clouds Photochemistry Meteorology Atmospheric Escape Photochemistry We can characterize chemical reactions in the atmosphere in the following way: 1. Photolysis:
More informationLecture 12: Angular Momentum and the Hadley Circulation
Lecture 12: Angular Momentum and the Hadley Circulation September 30, 2003 We learnt last time that there is a planetary radiative drive net warming in the tropics, cooling over the pole which induces
More informationAPPENDIX B. The primitive equations
APPENDIX B The primitive equations The physical and mathematical basis of all methods of dynamical atmospheric prediction lies in the principles of conservation of momentum, mass, and energy. Applied to
More informationRadiative equilibrium Some thermodynamics review Radiative-convective equilibrium. Goal: Develop a 1D description of the [tropical] atmosphere
Radiative equilibrium Some thermodynamics review Radiative-convective equilibrium Goal: Develop a 1D description of the [tropical] atmosphere Vertical temperature profile Total atmospheric mass: ~5.15x10
More informationQ.1 The most abundant gas in the atmosphere among inert gases is (A) Helium (B) Argon (C) Neon (D) Krypton
Q. 1 Q. 9 carry one mark each & Q. 10 Q. 22 carry two marks each. Q.1 The most abundant gas in the atmosphere among inert gases is (A) Helium (B) Argon (C) Neon (D) Krypton Q.2 The pair of variables that
More informationThe atmosphere: A general introduction Niels Woetmann Nielsen Danish Meteorological Institute
The atmosphere: A general introduction Niels Woetmann Nielsen Danish Meteorological Institute Facts about the atmosphere The atmosphere is kept in place on Earth by gravity The Earth-Atmosphere system
More informationWinds and Currents in the Oceans
Winds and Currents in the Oceans Atmospheric Processes Density of air is controlled by temperature, pressure, and moisture content. 1. Warm air is less dense than cold air and moist air is less dense than
More informationThe atmosphere in motion: forces and wind. AT350 Ahrens Chapter 9
The atmosphere in motion: forces and wind AT350 Ahrens Chapter 9 Recall that Pressure is force per unit area Air pressure is determined by the weight of air above A change in pressure over some distance
More informationEART164: PLANETARY ATMOSPHERES
EART164: PLANETARY ATMOSPHERES Francis Nimmo Last Week Radiative Transfer Black body radiation, Planck function, Wien s law Absorption, emission, opacity, optical depth Intensity, flux Radiative diffusion,
More information( u,v). For simplicity, the density is considered to be a constant, denoted by ρ 0
! Revised Friday, April 19, 2013! 1 Inertial Stability and Instability David Randall Introduction Inertial stability and instability are relevant to the atmosphere and ocean, and also in other contexts
More informationESCI 485 Air/Sea Interaction Lesson 1 Stresses and Fluxes Dr. DeCaria
ESCI 485 Air/Sea Interaction Lesson 1 Stresses and Fluxes Dr DeCaria References: An Introduction to Dynamic Meteorology, Holton MOMENTUM EQUATIONS The momentum equations governing the ocean or atmosphere
More information4. Atmospheric transport. Daniel J. Jacob, Atmospheric Chemistry, Harvard University, Spring 2017
4. Atmospheric transport Daniel J. Jacob, Atmospheric Chemistry, Harvard University, Spring 2017 Forces in the atmosphere: Gravity g Pressure-gradient ap = ( 1/ ρ ) dp / dx for x-direction (also y, z directions)
More informationwarmest (coldest) temperatures at summer heat dispersed upward by vertical motion Prof. Jin-Yi Yu ESS200A heated by solar radiation at the base
Pole Eq Lecture 3: ATMOSPHERE (Outline) JS JP Hadley Cell Ferrel Cell Polar Cell (driven by eddies) L H L H Basic Structures and Dynamics General Circulation in the Troposphere General Circulation in the
More informationTorben Königk Rossby Centre/ SMHI
Fundamentals of Climate Modelling Torben Königk Rossby Centre/ SMHI Outline Introduction Why do we need models? Basic processes Radiation Atmospheric/Oceanic circulation Model basics Resolution Parameterizations
More informationMeteorology. I. The Atmosphere - the thin envelope of gas that surrounds the earth.
Meteorology I. The Atmosphere - the thin envelope of gas that surrounds the earth. A. Atmospheric Structure - the atmosphere is divided into five distinct layers that are based on their unique characteristics.
More information( ) = 1005 J kg 1 K 1 ;
Problem Set 3 1. A parcel of water is added to the ocean surface that is denser (heavier) than any of the waters in the ocean. Suppose the parcel sinks to the ocean bottom; estimate the change in temperature
More informationAtmospheric Fronts. The material in this section is based largely on. Lectures on Dynamical Meteorology by Roger Smith.
Atmospheric Fronts The material in this section is based largely on Lectures on Dynamical Meteorology by Roger Smith. Atmospheric Fronts 2 Atmospheric Fronts A front is the sloping interfacial region of
More information5) The amount of heat needed to raise the temperature of 1 gram of a substance by 1 C is called: Page Ref: 69
Homework #2 Due 9/19/14 1) If the maximum temperature for a particular day is 26 C and the minimum temperature is 14 C, what would the daily mean temperature be? (Page Ref: 66) 2) How is the annual mean
More informationWATER IN THE ATMOSPHERE
WATER IN THE ATMOSPHERE During a rainstorm, the air feels moist On a clear, cloudless day, the air may feel dry As the sun heats the land and oceans, the amount of water in the atmosphere changes Water
More informationChapter 7. Water and Atmospheric Moisture. Water on Earth Unique Properties of Water Humidity Atmospheric Stability Clouds and Fog
Chapter 7 Water and Atmospheric Moisture Robert W. Christopherson Charlie Thomsen Water kept both the terrestrial and marine ecosystems closely linked with the atmosphere. (1) Air carries water vapor and
More informationDynamics Rotating Tank
Institute for Atmospheric and Climate Science - IACETH Atmospheric Physics Lab Work Dynamics Rotating Tank Large scale flows on different latitudes of the rotating Earth Abstract The large scale atmospheric
More informationTransient/Eddy Flux. Transient and Eddy. Flux Components. Lecture 7: Disturbance (Outline) Why transients/eddies matter to zonal and time means?
Lecture 7: Disturbance (Outline) Transients and Eddies Climate Roles Mid-Latitude Cyclones Tropical Hurricanes Mid-Ocean Eddies (From Weather & Climate) Flux Components (1) (2) (3) Three components contribute
More informationChapter 1. Governing Equations of GFD. 1.1 Mass continuity
Chapter 1 Governing Equations of GFD The fluid dynamical governing equations consist of an equation for mass continuity, one for the momentum budget, and one or more additional equations to account for
More informationAtmospheric circulation
Atmospheric circulation Trade winds http://science.nasa.gov/science-news/science-at-nasa/2002/10apr_hawaii/ Atmosphere (noun) the envelope of gases (air) surrounding the earth or another planet Dry air:
More informationINTRODUCTION TO METEOROLOGY PART TWO SC 208 DECEMBER 2, 2014 JOHN BUSH
INTRODUCTION TO METEOROLOGY PART TWO SC 208 DECEMBER 2, 2014 JOHN BUSH Meteorology ATMOSPHERIC SCIENCES Short term weather systems in time spans of hours, days, weeks or months Emphasis is on forecasting
More informationGeneral Circulation. Nili Harnik DEES, Lamont-Doherty Earth Observatory
General Circulation Nili Harnik DEES, Lamont-Doherty Earth Observatory nili@ldeo.columbia.edu Latitudinal Radiation Imbalance The annual mean, averaged around latitude circles, of the balance between the
More informationRadiative-Convective Models. The Hydrological Cycle Hadley Circulation. Manabe and Strickler (1964) Course Notes chapter 5.1
Climate Modeling Lecture 8 Radiative-Convective Models Manabe and Strickler (1964) Course Notes chapter 5.1 The Hydrological Cycle Hadley Circulation Prepare for Mid-Term (Friday 9 am) Review Course Notes
More informationAT 620 Notes. These notes were prepared by Prof. Steven A. Rutledge. (and adapted slightly for the Fall 2009 course, and again slightly for this year)
AT 620 Notes These notes were prepared by Prof. Steven A. Rutledge (and adapted slightly for the Fall 2009 course, and again slightly for this year) You may access Prof. Cotton s notes, password cloud9
More informationToday s Lecture: Atmosphere finish primitive equations, mostly thermodynamics
Today s Lecture: Atmosphere finish primitive equations, mostly thermodynamics Reference Peixoto and Oort, Sec. 3.1, 3.2, 3.4, 3.5 (but skip the discussion of oceans until next week); Ch. 10 Thermodynamic
More informationP sat = A exp [B( 1/ /T)] B= 5308K. A=6.11 mbar=vapor press. 0C.
Lecture 5. Water and water vapor in the atmosphere 14 Feb 2008 Review of buoyancy, with an unusual demonstration of Archimedes principle. Water is a polar molecule that forms hydrogen bonds. Consequently
More informationThe Equations of Motion in a Rotating Coordinate System. Chapter 3
The Equations of Motion in a Rotating Coordinate System Chapter 3 Since the earth is rotating about its axis and since it is convenient to adopt a frame of reference fixed in the earth, we need to study
More informationThe Atmosphere - Chapter Characteristics of the Atmosphere
Section Objectives Describe the composition of Earth s atmosphere. Explain how two types of barometers work. Identify the layers of the atmosphere. Identify two effects of air pollution. The Atmosphere
More informationChapter 2. Quasi-Geostrophic Theory: Formulation (review) ε =U f o L <<1, β = 2Ω cosθ o R. 2.1 Introduction
Chapter 2. Quasi-Geostrophic Theory: Formulation (review) 2.1 Introduction For most of the course we will be concerned with instabilities that an be analyzed by the quasi-geostrophic equations. These are
More informationQuasi-equilibrium Theory of Small Perturbations to Radiative- Convective Equilibrium States
Quasi-equilibrium Theory of Small Perturbations to Radiative- Convective Equilibrium States See CalTech 2005 paper on course web site Free troposphere assumed to have moist adiabatic lapse rate (s* does
More informationCHAPTER 2 - ATMOSPHERIC CIRCULATION & AIR/SEA INTERACTION
Chapter 2 - pg. 1 CHAPTER 2 - ATMOSPHERIC CIRCULATION & AIR/SEA INTERACTION The atmosphere is driven by the variations of solar heating with latitude. The heat is transferred to the air by direct absorption
More information+ ω = 0, (1) (b) In geometric height coordinates in the rotating frame of the Earth, momentum balance for an inviscid fluid is given by
Problem Sheet 1: Due Thurs 3rd Feb 1. Primitive equations in different coordinate systems (a) Using Lagrangian considerations and starting from an infinitesimal mass element in cartesian coordinates (x,y,z)
More information1. CLIMATOLOGY: 2. ATMOSPHERIC CHEMISTRY:
What is meteorology? A. METEOROLOGY: an atmospheric science that studies the day to day changes in the atmosphere 1. ATMOSPHERE: the blanket of gas that surrounds the surface of Earth; the air 2. WEATHER:
More informationThe dynamics of high and low pressure systems
The dynamics of high and low pressure systems Newton s second law for a parcel of air in an inertial coordinate system (a coordinate system in which the coordinate axes do not change direction and are
More informationChapter 2 Case Studies and Study Guide: Energy Sources of Earth Processes and Disasters
Chapter 2 Case Studies and Study Guide: Energy Sources of Earth Processes and Disasters Key Concepts The four principal types of energy relevant to natural disasters are kinetic, potential, rotational
More informationModels of ocean circulation are all based on the equations of motion.
Equations of motion Models of ocean circulation are all based on the equations of motion. Only in simple cases the equations of motion can be solved analytically, usually they must be solved numerically.
More informationTemperature. Vertical Thermal Structure. Earth s Climate System. Lecture 1: Introduction to the Climate System
Lecture 1: Introduction to the Climate System T mass (& radiation) T & mass relation in vertical mass (& energy, weather..) Energy T vertical stability vertical motion thunderstorm What are included in
More informationLecture 07 February 10, 2010 Water in the Atmosphere: Part 1
Lecture 07 February 10, 2010 Water in the Atmosphere: Part 1 About Water on the Earth: The Hydrological Cycle Review 3-states of water, phase change and Latent Heat Indices of Water Vapor Content in the
More informationGEO1010 tirsdag
GEO1010 tirsdag 31.08.2010 Jørn Kristiansen; jornk@met.no I dag: Først litt repetisjon Stråling (kap. 4) Atmosfærens sirkulasjon (kap. 6) Latitudinal Geographic Zones Figure 1.12 jkl TØRR ATMOSFÆRE Temperature
More informationIV. Atmospheric Science Section
EAPS 100 Planet Earth Lecture Topics Brief Outlines IV. Atmospheric Science Section 1. Introduction, Composition and Structure of the Atmosphere Learning objectives: Understand the basic characteristics
More informationPart-8c Circulation (Cont)
Part-8c Circulation (Cont) Global Circulation Means of Transfering Heat Easterlies /Westerlies Polar Front Planetary Waves Gravity Waves Mars Circulation Giant Planet Atmospheres Zones and Belts Global
More informationChapter 4 Lesson 1: Describing Earth s Atmosphere
Chapter 4 Lesson 1: Describing Earth s Atmosphere Vocabulary Importance of Earth s Atmosphere The atmosphere is a thin layer of gases surrounding Earth. o Contains the oxygen and water needed for life.
More informationReferences: Parcel Theory. Vertical Force Balance. ESCI Cloud Physics and Precipitation Processes Lesson 3 - Stability and Buoyancy Dr.
References: ESCI 340 - Cloud Physics and Precipitation Processes Lesson 3 - Stability and Buoyancy Dr. DeCaria Glossary of Meteorology, 2nd ed., American Meteorological Society A Short Course in Cloud
More informationChapter 1 Fluid Characteristics
Chapter 1 Fluid Characteristics 1.1 Introduction 1.1.1 Phases Solid increasing increasing spacing and intermolecular liquid latitude of cohesive Fluid gas (vapor) molecular force plasma motion 1.1.2 Fluidity
More informationThe Behaviour of the Atmosphere
3 The Behaviour of the Atmosphere Learning Goals After studying this chapter, students should be able to: apply the ideal gas law and the concept of hydrostatic balance to the atmosphere (pp. 49 54); apply
More informationFundamentals of Weather and Climate
Fundamentals of Weather and Climate ROBIN McILVEEN Environmental Science Division Institute of Environmental and Biological Sciences Lancaster University CHAPMAN & HALL London Glasgow Weinheim New York
More informationIntroduction to Climate ~ Part I ~
2015/11/16 TCC Seminar JMA Introduction to Climate ~ Part I ~ Shuhei MAEDA (MRI/JMA) Climate Research Department Meteorological Research Institute (MRI/JMA) 1 Outline of the lecture 1. Climate System (
More informationUnit 2 Meteorology Test **Please do not write on this test** 5. El Nino & La Nina 6. Photosynthesis 7. Coriolis Effect 8.
Matching (2 points each) 1. weather 2. climate 3. Greenhouse Effect 4. Convection Unit 2 Meteorology Test **Please do not write on this test** 5. El Nino & La Nina 6. Photosynthesis 7. Coriolis Effect
More informationThe Earth s Hydrosphere. The volatile component of rocky planets (hydrospheres and atmospheres) Earth water reservoirs Rollins (2007)
The Earth s Hydrosphere Oceans The volatile component of rocky planets (hydrospheres and atmospheres) Planets and Astrobiology (2016-2017) G. Vladilo The Earth is the only planet of the Solar System with
More informationMeasurement of Rotation. Circulation. Example. Lecture 4: Circulation and Vorticity 1/31/2017
Lecture 4: Circulation and Vorticity Measurement of Rotation Circulation Bjerknes Circulation Theorem Vorticity Potential Vorticity Conservation of Potential Vorticity Circulation and vorticity are the
More informationChapter 9 External Energy Fuels Weather and Climate
Natural Disasters Tenth Edition Chapter 9 External Energy Fuels Weather and Climate Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 9-1 Weather Versus Climate
More informationExamples of Pressure Gradient. Pressure Gradient Force. Chapter 7: Forces and Force Balances. Forces that Affect Atmospheric Motion 2/2/2015
Chapter 7: Forces and Force Balances Forces that Affect Atmospheric Motion Fundamental force - Apparent force - Pressure gradient force Gravitational force Frictional force Centrifugal force Forces that
More informationLecture 10 March 15, 2010, Monday. Atmospheric Pressure & Wind: Part 1
Lecture 10 March 15, 2010, Monday Atmospheric Pressure & Wind: Part 1 Speed, Velocity, Acceleration, Force, Pressure Atmospheric Pressure & Its Measurement Ideal Gas Law (Equation of State) Pressure Gradient
More informationProject 3 Convection and Atmospheric Thermodynamics
12.818 Project 3 Convection and Atmospheric Thermodynamics Lodovica Illari 1 Background The Earth is bathed in radiation from the Sun whose intensity peaks in the visible. In order to maintain energy balance
More informationThe Atmosphere. Characteristics of the Atmosphere. Section 23.1 Objectives. Chapter 23. Chapter 23 Modern Earth Science. Section 1
The Atmosphere Chapter 23 Modern Earth Science Characteristics of the Atmosphere Chapter 23 Section 1 Section 23.1 Objectives Describe the composition of Earth s atmosphere. Explain how two types of barometers
More informationEAS270, The Atmosphere Mid-term Exam 27 Oct, 2006
EAS270, The Atmosphere Mid-term Exam 27 Oct, 2006 Professor: J.D. Wilson Time available: 50 mins Value: 20% Instructions: For all 32 multi-choice questions, choose what you consider to be the best (or
More informationModel equations for planetary and synoptic scale atmospheric motions associated with different background stratification
Model equations for planetary and synoptic scale atmospheric motions associated with different background stratification Stamen Dolaptchiev & Rupert Klein Potsdam Institute for Climate Impact Research
More informationIntroduction to Atmospheric Circulation
Introduction to Atmospheric Circulation Start rotating table Cloud Fraction Dice Results from http://eos.atmos.washington.edu/erbe/ from http://eos.atmos.washington.edu/erbe/ from http://eos.atmos.washington.edu/erbe/
More informationThe Hydrostatic Approximation. - Euler Equations in Spherical Coordinates. - The Approximation and the Equations
OUTLINE: The Hydrostatic Approximation - Euler Equations in Spherical Coordinates - The Approximation and the Equations - Critique of Hydrostatic Approximation Inertial Instability - The Phenomenon - The
More informationThe Transfer of Heat
The Transfer of Heat Outcomes: S2-4-03 Explain effects of heat transfer within the atmosphere and hydrosphere on the development and movement of wind and ocean currents. Coriolis Effect In our ecology
More information