Announcements Homeworks 1-5: Have been graded and are available up front; please retrieve yours Answer Keys are posted on the Web at: http://www.aos.wisc.edu/~hopkins/aos100/homework; 2nd Hour Exam: Has been graded and will be returned in “just a little bit” The exam stats will be posted at: http://www.aos.wisc.edu/~hopkins/aos100/exams. Please stay tuned for more info!!! Happy Thanksgiving!!

MADISON’S CURRENT WEATHER at 900 AM CST WED NOV 21 2001 Updated twice an hour at :05 and :25 Sky/Weather: SUNNY (CLEAR!!) Temperature: 40 F (4 C) Dew Point: 27 F (-2 C) Relative Humidity: 59% Wind: VRB6 MPH Barometer: 29.79S

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Surface Weather Map from Today with Isobars & Fronts

Current Temperatures (oF) & Isotherms

24 hour Temperature Change (Fahrenheit Degrees) [Current – Sun AM] (oF) & Isotherms

Current Dewpoints (oF)

Tomorrow’s 7AM Forecast Happy Thanksgiving!

ATM OCN 100 - Summer 2002 LECTURE 18 THE THEORY OF WINDS: PART II - FUNDAMENTAL FORCES A. INTRODUCTION How do winds originate? What factors influence the winds?

B. EXPLANATIONS of ATMOSPHERIC MOTION Practical Problems Historical Concepts Forces of Motion & Newton's Laws

NEWTON’S EQUATIONS of MOTION 1st Law (Conservation of Inertia) Object at rest will remain at rest or object moving at constant velocity will continue until acted upon by a net force. 2nd Law Force = mass x acceleration. 3rd Law For every action, an equal & opposite reaction exists.

B. EXPLANATIONS of ATMOSPHERIC MOTION (con’t.) Implications of Newtonian Laws Vectors, Forces and Units Velocity -- a vector (speed & direction) Speed or magnitude of velocity-- a scalar [mph or meters per second, etc.] Acceleration or rate of change of a velocity vector -- a vector [ft/sec/sec or meter/sec2] Force -- a vector -- What causes a mass to accelerate. [pounds, or Newtons]

C. DESCRIBING ATMOSPHERIC MOTION Reasons for Atmospheric Motions: Buoyancy Effects or Dynamic Effects

C. DESCRIBING ATMOSPHERIC MOTION An Equation of Motion Complications involved with Atmospheric Motion: Spherical planet; Rotating planet & non-inertial frame of reference.

An example of an equation of motion NASA http://www.allstar.fiu.edu/aero/fltmidfly.htm

DESCRIBING ATMOSPHERIC MOTION (con’t.) Three-Dimensional Equation of Motion for the Atmosphere A vector equation; Entails specification of all forces per unit mass (i.e., equivalent to acceleration); All forces do not act alone; Vector sum of individual forces equals net force.

Numerical Weather Prediction

Numerical Weather Prediction

Numerical Weather Prediction

FORCES ASSOCIATED WITH ATMOSPHERIC MOTION Following forces influence motion of air parcels: Pressure Gradient Force Gravitational Force or Gravity Coriolis Effect or "Force" Frictional Force or Friction Centripetal Force or more specifically --

PRESSURE GRADIENT FORCE Generated by differences in pressure within a fluid element; Responsible for initiation of all air motion;

Explaining Differences in Air Pressure Low Pressure High Pressure

L Current Winds L H H

PRESSURE GRADIENT FORCE (con’t.) A 3-dimensional vector that has: Magnitude of pressure gradient force vector depends: directly upon difference in pressure over a given distance (i.e., slope or grade equals “pressure gradient”). Direction of pressure gradient force vector is: from High pressure to Low pressure, along steepest direction of pressure gradient.

PRESSURE GRADIENT FORCE (con’t.)

PRESSURE GRADIENT FORCE (con’t.)

GRAVITATIONAL FORCE or GRAVITY Produced by mutual physical attraction between massive bodies; Gravity refers to acceleration; Acts continuously, regardless of motion; A vector quantity that has: Direction – toward center of earth. Magnitude ~ 9.8 m/s2 (32 ft/s2)

CORIOLIS EFFECT or FORCE Produced by earth’s rotation; A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference;

CORIOLIS EFFECT or FORCE Produced by earth’s rotation; A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference; Run coriolis.mpg from http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml

CORIOLIS EFFECT or FORCE (con’t.) Speed is dependent upon latitude:

An example of the Coriolis Effect Fig. 9.5 Moran & Morgan (1997) Time 1 Time 2

CORIOLIS EFFECT or FORCE (con’t.)

Coriolis Effects upon the Wind Fig. 9.6 Moran & Morgan (1997)

CORIOLIS EFFECT or FORCE (con’t.) Produced by earth’s rotation; A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference; Acts only after motion is initiated; Can only modify direction of motion; A 3-dimensional vector, but consider only horizontal component described by:

CORIOLIS EFFECT or FORCE (con’t.) Magnitude of horizontal Coriolis force vector depends upon: Rotation rate of earth (Direct relationship); Speed of object; (Direct relationship) Latitude (specifically, sine of latitude).

CORIOLIS EFFECT or FORCE (con’t.) Direction of horizontal component of Coriolis force vector: Causes a deflection of moving object to right of direction of motion in Northern Hemisphere; but Deflects moving object to left of intended motion in Southern Hemisphere.

FRICTIONAL FORCE or FRICTION Produced by “viscosity” (interactions of moving fluid elements with one another or with a boundary surface) due to: random molecular motions; large random turbulent motions of fluid associated with either: thermal turbulence mechanical turbulence

An example of Turbulent Viscosity Fig. 9.5 Moran & Morgan (1997)

FRICTIONAL FORCE (con’t.) Acts only after motion is initiated; Acts to retard motion; Magnitude of friction force vector depends upon: Speed of motion of fluid; Type of surface, e.g., “surface roughness”; Temperature structure of fluid. Direction of friction force vector is opposite motion vector.

Relative Surface Roughness Source: Stull, 1995

Centripetal Force Fig. 9.3 Moran & Morgan (1997)

CENTRIPETAL FORCE Produces curved motion; Opposite the “centrifugal force”; Acts only after motion is initiated; In reality, a net force Used to describe imbalance of other forces in curved motion;

CENTRIPETAL FORCE VECTOR (con’t.) Centripetal force vector is described by: Magnitude of centripetal force vector depends upon: Speed of instantaneous motion (a direct relationship); Radius of curvature (an inverse relationship). Direction of centripetal force vector is inward toward center of curvature.

SUMMARIZING A 3-D Equation of Motion for Atmosphere (in word form): Net force = Pressure gradient force + gravitation force + Coriolis force + friction. Notes: The above is a vector equation! Since a unit mass is used, force is equivalent to an acceleration.