ATM OCN 100 Summer ATM OCN Spring 2002 LECTURE 20 (con’t.) THE THEORY OF WINDS: PART III - RESULTANT ATMOSPHERIC MOTIONS (con’t.) A. Introduction & Assumptions Buys-Ballot Law Hydrostatic Balance Relationship B. Horizontal Equation of Motion Local Winds Geostrophic Winds Winds in Friction Layer

ATM OCN 100 Summer A AB B BC C D F< 39 Mean = 70

ATM OCN 100 Summer Announcements u Homework 6: –Has been posted at – –Will be due 1 week from today (3 Dec. 2001) u Homeworks 1-5: –Have been graded and are available up front; please retrieve yours –Answer Keys are posted on the Web at: – u 2 nd Hour Exam: –Has been graded and returned (up front) –The exam stats are posted at: –

MADISON’S CURRENT WEATHER At 900 AM CST WED NOV Updated twice an hour at :05 and :25 Sky/Weather: CLOUDY Temperature: 35 F (1 C) Dew Point: 33 F (0 C) Relative Humidity: 92% Wind: NE8 MPH Barometer: 30.27R

ATM OCN 100 Summer Last 24 hrs in Madison Example of Cold Front Passage & Cold Air Advection

ATM OCN 100 Summer Surface Weather Map from Today with Isobars & Fronts

ATM OCN 100 Summer CURRENT IR

ATM OCN 100 Summer CURRENT VISIBLE

ATM OCN 100 Summer Surface Weather Map from Today with Isobars & Fronts

ATM OCN 100 Summer Current Temperatures ( o F) & Isotherms

ATM OCN 100 Summer hour Temperature Change (Fahrenheit Degrees) [Current – Sun AM] ( o F) & Isotherms

ATM OCN 100 Summer Current Dewpoints ( o F)

ATM OCN 100 Summer Tomorrow’s 7AM Forecast

MADISON’S CURRENT WEATHER Madison Weather at 1000 AM CDT 30 JUL 2002 Updated twice an hour at :05 and :25 Sky/Weather: SUNNY Temperature: 80 F (26 C) Dew Point: 69 F (20 C) Relative Humidity: 69% Wind: SW8 MPH Barometer: 30.00F ( mb)

ATM OCN 100 Summer Last 24 hrs in Madison FOG

ATM OCN 100 Summer

17 CURRENT VISIBLE

ATM OCN 100 Summer CURRENT IR

ATM OCN 100 Summer Current Surface Weather Map with Isobars (“iso” = equal & “bar” = weight), Fronts and Radar Tight Isobar Packing

ATM OCN 100 Summer Current Surface Winds with Streamlines & Isotachs (“iso” = equal & “tach” = speed) L L H L L L H L H H H LL H L Strong winds with Tight Isobar Packing H L L H H

ATM OCN 100 Summer Current Temperatures ( ° F) & Isotherms (“iso” = equal +”therm” = temperature)

ATM OCN 100 Summer Current Temperatures ( o F) – 24 Hrs Ago Cold Advection + Drier Air

ATM OCN 100 Summer Current Dewpoints ( o F)

ATM OCN 100 Summer Tomorrow AM Forecast Map

ATM OCN 100 Summer Announcements u 2 nd Hour Exam has been returned. u See exam statistics on u Homework #4 also has been returned. Answer Key is posted at u If you have ??, please see me.

ATM OCN 100 Summer ATM OCN Spring 2002 LECTURE 20 (con’t.) THE THEORY OF WINDS: PART III - RESULTANT ATMOSPHERIC MOTIONS (con’t.) A. Introduction & Assumptions Buys-Ballot Law Hydrostatic Balance Relationship B. Horizontal Equation of Motion

ATM OCN 100 Summer ATM OCN Spring 2002 LECTURE 20 (con’t.) THE THEORY OF WINDS: PART III - RESULTANT ATMOSPHERIC MOTIONS (con’t.) A. Introduction & Assumptions Buys-Ballot Law

ATM OCN 100 Summer ATM OCN Spring 2002 LECTURE 20 THE THEORY OF WINDS: PART III - RESULTANT ATMOSPHERIC MOTIONS A. INTRODUCTION –Why do winds circulate around low pressure in a counterclockwise motion? –Buys-Ballot Rule; –Fundamental assumptions.

ATM OCN 100 Summer Buys Ballot Rule

ATM OCN 100 Summer Current Midwest Weather Plot

ATM OCN 100 Summer Current Midwest Weather Plot

ATM OCN 100 Summer Isobars - - lines of equal barometric pressure - use sea level corrected pressure

ATM OCN 100 Summer Current Midwest Weather Analysis

ATM OCN 100 Summer Current Midwest Weather Analysis L H

ATM OCN 100 Summer BUYS-BALLOT RULE u Empirical relationship stated by Dutch meteorologist Buys-Ballot in 1850’s; u With your back to wind, Low pressure is to your left in Northern Hemisphere; u However, in Southern Hemisphere, Low is to your right ; u Mathematically proved by American meteorologist Wm. Ferrel in 1850’s.

ATM OCN 100 Summer Current Midwest Weather Analysis

ATM OCN 100 Summer Current Winds LLLH H

ATM OCN 100 Summer Goal u Attempt to develop simple models to explain atmospheric motions appearing on surface weather maps

ATM OCN 100 Summer ASSUMPTIONS For convenience, assume that: u Define motion in terms of horizontal & vertical components. u Rationale : –Winds are nearly horizontal; –Vertical motions typically much smaller. u Make assumptions about the balance of forces:

ATM OCN 100 Summer Summary of Forces for selected models See Table 9.1 Moran & Morgan (1997) MODELS

ATM OCN 100 Summer ASSUMPTIONS For convenience, assume that: u Winds are nearly horizontal; u Atmosphere is in nearly “hydrostatic balance” i.e., air parcels do not accelerate upward or downward; u Define motion in terms of horizontal & vertical components.

ATM OCN 100 Summer B. HORIZONTAL EQUATION OF ATMOSPHERIC MOTION u The 3-D vector Equation of Atmospheric Motion can be written in terms of horizontal and vertical components: Net force = Horizontal Pressure gradient force + Vertical Pressure gradient force + gravity + Coriolis force + friction.

ATM OCN 100 Summer HYDROSTATIC BALANCE CONCEPT u A Fundamental Assumption: –Earth’s atmosphere remains and is essentially in “hydrostatic balance”. u The Model – –This balance is between the vertically oriented vector quantities: –gravity, & –acceleration due to vertical component of pressure gradient force.

ATM OCN 100 Summer Concept of Hydrostatic Balance Fig Moran & Morgan (1997)

ATM OCN 100 Summer Components in Hydrostatic Balance Model Fig Moran & Morgan (1997) Gravity Vector Direction: “Down” toward Earth center Gravity Vector Magnitude: Decreases with altitude... But  9.8 m/s 2 or 32 ft/s 2

ATM OCN 100 Summer Components in Hydrostatic Balance Model Fig Moran & Morgan (1997) Gravity Vector Direction: “Down” toward Earth center Gravity Vector Magnitude: Decreases with altitude... But  9.8 m/s 2 or 32 ft/s 2 Vert. Press. Grad. Force Vector Direction: “Up” from High to Low Pressure Vert. Press. Grad. Force Vector Magnitude: Depends upon Vert. Pressure Grad. & Density

ATM OCN 100 Summer Summary of Forces for selected models See Table 9.1 Moran & Morgan (1997) MODELS

ATM OCN 100 Summer HYDROSTATIC BALANCE CONCEPT See Fig Moran & Morgan (1997)

ATM OCN 100 Summer THE VERTICAL PRESSURE GRADIENT FORCE u Magnitude of Vertical Pressure Gradient force vector is: – a function of both air density & vertical component of pressure gradient. u Direction of Vertical Pressure Gradient force is: – always pointed upward, from high pressure (near surface) to low pressure (aloft).

ATM OCN 100 Summer HYDROSTATIC BALANCE CONCEPT (con’t.) u Assume that acceleration of gravity is essentially constant with altitude; u Air pressure ALWAYS decreases with increased altitude in atmosphere; u But, rate of pressure decrease with altitude depends upon density of air column: –Decrease is more rapid in cold, dense air column than in warm, less dense column.

ATM OCN 100 Summer VERTICAL PRESSURE GRADIENTS - Dependency on density (temperature)

ATM OCN 100 Summer VERTICAL PRESSURE GRADIENTS Fig. 2 pg. 251 Moran & Morgan (1997)

ATM OCN 100 Summer HYDROSTATIC BALANCE CONCEPT (con’t.)  In summary, acceleration vectors of gravity and vertical pressure gradient are equal in magnitude, but opposite in direction: F Net, V = 0 = F PG,V + g or F PG,V = - g (A vector summation). u A balance exists between these vertically oriented vector quantities, meaning no net vertical force nor acceleration!

ATM OCN 100 Summer HYDROSTATIC BALANCE CONCEPT (con’t.) u A balance exists between: –vertical pressure gradient force –gravity – meaning no net vertical force nor acceleration!

ATM OCN 100 Summer HYDROSTATIC BALANCE CONCEPT (con’t.) u As a result –The atmosphere is maintained; –Convection is somewhat limited.

ATM OCN 100 Summer THE HORIZONTAL PRESSURE GRADIENT FORCE u Parcels are accelerated in horizontal direction from High to Low pressure. u Direction of force & resulting accelerating motion is perpendicular to isobars on a surface weather map. u Magnitude of acceleration is inversely proportional to isobar spacing. – (i.e., greater horizontal pressure gradient force with tightly packed isobars).

ATM OCN 100 Summer HORIZONTAL PRESSURE GRADIENT FORCE Horiz. Press. Grad. Force Vector Direction: Vector Direction: High to Low & Perpendicular to the Isobars!

ATM OCN 100 Summer HORIZONTAL PRESSURE GRADIENT FORCE (con’t.) See Fig. 9.1 Moran & Morgan (1997) Magnitude of Pressure Gradient depends on isobar spacing!

ATM OCN 100 Summer As a Result of the HORIZONTAL PRESSURE GRADIENT FORCE (con’t.) Horiz. Press. Grad. Force Vector Magnitude: Depends upon Horiz. Pressure Gradient (i.e., isobar spacing)

ATM OCN 100 Summer AS A RESULT - u The 3-D vector Equation of Atmospheric Motion can be rewritten:  Horizontal Component: Net horizontal force = Horizontal Pressure gradient force + + Coriolis force + friction; F Net, H = F PG,H + F Cor + F Friction (A vector summation).

ATM OCN 100 Summer AS A RESULT (con’t.)  Vertical Component: Vertical Pressure gradient force + gravity Since: Net vertical force = 0 = Vertical Pressure gradient force + gravity F PG,V + g = 0. (A vector summation). (a statement of Hydrostatic Balance Assumption ).

ATM OCN 100 Summer Modeling of Atmospheric Motion - u The 3-D vector Equation of Atmospheric Motion can be rewritten: u Vertical Component Net vertical force = 0 = Vertical Pressure gradient force + gravity u Horizontal Component: Net horizontal force = Horizontal Pressure gradient force + + Coriolis force + friction; (A vector summation).

ATM OCN 100 Summer Recall VERTICAL PRESSURE GRADIENTS - Dependency on density (temperature)

ATM OCN 100 Summer C. FLOW RESPONDING TO PRESSURE GRADIENT FORCE - LOCAL WINDS u Assumptions: –Only Pressure gradient force operates due to local pressure differences; –Horizontal flow. –  Net force = pressure gradient force u Examples: –Sea-Land Breeze Circulation –Mountain-Valley Breeze Circulation –City-Country Circulation

ATM OCN 100 Summer VERTICAL PRESSURE GRADIENTS - Dependency on density (temperature)

ATM OCN 100 Summer Sea-Land Breeze Circulation Regime Figure 12.2 Moran & Morgan (1997)

ATM OCN 100 Summer Sea (Lake) Breeze (Graphics from UIUC WW2010)

ATM OCN 100 Summer REASONS FOR LAND-SEA TEMPERATURE DIFFERENCES u Water has higher heat capacity – Smaller temperature response for heat added u Water is a fluid – Mixing warm water downward u Water is transparent – Sunlight penetrates to depth u Water surface experiences evaporation – Evaporative cooling

ATM OCN 100 Summer Sea (Lake) Breeze (con’t.)

ATM OCN 100 Summer Sea (Lake) Breeze (con’t.)

ATM OCN 100 Summer Sea (Lake) Breeze (con’t.)

ATM OCN 100 Summer Sea (Lake) Breeze (con’t.)

ATM OCN 100 Summer Sea (Lake) Breeze (con’t.)

ATM OCN 100 Summer Sea (Lake) Breeze (con’t.) (Lake)

ATM OCN 100 Summer Sea (Lake) Breeze (con’t.) See Fig A Moran & Morgan (1997)

ATM OCN 100 Summer Lake Breeze Circulation over Lake Michigan Figure 12.3 Moran & Morgan (1997)

ATM OCN 100 Summer Edge of lake breeze on southern Lake Michigan Modis 21 May 2002

ATM OCN 100 Summer Land Breeze

ATM OCN 100 Summer Land Breeze (con’t.)

ATM OCN 100 Summer Land Breeze (con’t.)

ATM OCN 100 Summer Land Breeze (con’t.) See Fig B Moran & Morgan (1997)

ATM OCN 100 Summer Mountain Breeze See Fig Moran & Morgan (1997)

ATM OCN 100 Summer Valley Breeze See Fig Moran & Morgan (1997)

ATM OCN 100 Summer D. STRAIGHT-LINE, BALANCED, FRICTIONLESS MOTION - “GEOSTROPHIC FLOW” u A powerful conceptual model involving horizontal motion on rotating planet; u Background & Word Derivation: –Named by Sir Napier Shaw in 1916: “Geo” = earth + “strephein” = to turn.

ATM OCN 100 Summer Summary of Forces for selected models See Table 9.1 Moran & Morgan (1997) MODELS

ATM OCN 100 Summer “GEOSTROPHIC FLOW” (con’t.) u Assumptions –horizontal flow (F PG,V + g = 0); –balanced flow (F Net, H = 0); –no friction (F Friction = 0); –straight line flow (with straight isobars) (F Centripetal = 0); –parallel and equally spaced isobars (F PG,H = constant). u Initiation of Geostrophic Flow

ATM OCN 100 Summer “GEOSTROPHIC FLOW” (con’t.) Assumptions Straight isobars Parallel isobars No friction Horizontal flow

ATM OCN 100 Summer Geostrophic Adjustment See Fig Moran & Morgan (1997)

ATM OCN 100 Summer Geostrophic Adjustment

ATM OCN 100 Summer Geostrophic Wind See Fig Moran & Morgan (1997) Represents a balance between Horiz. Pressure Gradient Force Horiz. Coriolis Force

ATM OCN 100 Summer “GEOSTROPHIC FLOW” (con’t.) u Resultant Geostrophic Flow –Balance between horizontal components of pressure gradient & Coriolis forces, or 0 = F PG,H + F Cor (A vector summation). u Geostrophic Wind vector (V g ) can be described as:

ATM OCN 100 Summer Geostrophic Wind Vector See Fig Moran & Morgan (1997) Vector Direction: Parallels isobarsParallels isobars Low to left in NHLow to left in NH Vector Magnitude depends on : 1. Pressure Gradient 2. Latitude

ATM OCN 100 Summer “GEOSTROPHIC FLOW” (con’t.) u Direction of V g vector is: –parallel to isobars, with L ow pressure to left (in Northern Hemisphere); u Magnitude of V g vector is related: –Directly to pressure gradient; –Inversely to Coriolis force (i.e., latitude).

ATM OCN 100 Summer “GEOSTROPHIC FLOW” (con’t.) u Implications of Geostrophic Balance –Geostrophic wind (V g ) is: F a hypothetical wind F a balance between –horizontal pressure gradient (isobar spacing) –latitude (or Coriolis effect) u Dilemma

ATM OCN 100 Summer Current Midwest Weather Analysis L H

ATM OCN 100 Summer E. BALANCED FLOW in FRICTION LAYER u The Nature of Friction u The Friction Layer u The Effect of Friction upon the Geostrophic Wind u Assumptions –Same as for geostrophic wind case, except F Friction is not zero.

ATM OCN 100 Summer Flow in Friction Layer See Fig Moran & Morgan (1997) FrictionSubgeostrophic No Friction Geostrophic

ATM OCN 100 Summer Wind Vector in Friction Layer See Fig Moran & Morgan (1997) Vector Direction: Angles across isobarsAngles across isobars Toward Low in either hemisphereToward Low in either hemisphere Vector Magnitude 1. Depends on Friction 2. Less than Geostrophic Wind

ATM OCN 100 Summer FLOW IN FRICTION LAYER (con’t.) u Resultant Motion 0 = F PG,H + F Cor + F Friction (A vector summation). –Magnitude of flow is less than geostrophic wind. –Direction of flow is turned at angle across isobars toward L ow pressure in either hemisphere.

ATM OCN 100 Summer Buys Ballot Rule

ATM OCN 100 Summer Observation: “ Right with Height”

ATM OCN 100 Summer Variation of Friction Effects with Height See Fig Moran & Morgan (1997) NOTE: “Right with height”

ATM OCN 100 Summer FLOW IN FRICTION LAYER (con’t.) u Variations of Near-Surface Winds with Height –Wind speeds reach zero at surface & increase to geostrophic at top of friction layer; –Wind direction at lower levels turned more toward L ow, then become parallel to isobars; –The result, a wind spiral is formed.

ATM OCN 100 Summer Varying effects of Surface Roughness

ATM OCN 100 Summer Variations in Surface Roughness leads to divergence/convergence patterns See Fig Moran & Morgan (1997)

ATM OCN 100 Summer F. CURVED, HORIZONTAL BALANCED MOTION - “GRADIENT FLOW” u Assumptions –horizontal flow ( F PG,V + g = 0); –no friction (F Friction = 0); –curved flow (with curved isobars) (F Centripetal = F Net, H ); –concentric and equally spaced isobars (F PG,H = constant).

ATM OCN 100 Summer F. CURVED, HORIZONTAL BALANCED MOTION - “GRADIENT FLOW” u Assumptions –Without Friction u Two Cases

ATM OCN 100 Summer Curved Flow

ATM OCN 100 Summer Summary of Forces for selected models See Table 9.1 Moran & Morgan (1997) MODELS

ATM OCN 100 Summer “GRADIENT” FLOW: ANTICYCLONIC Case See Fig Moran and Morgan (1997):

ATM OCN 100 Summer “GRADIENT” FLOW: ANTICYCLONIC Case See Fig Moran and Morgan (1997):

ATM OCN 100 Summer “GRADIENT” FLOW: CYCLONIC Case See Fig Moran and Morgan (1997):

ATM OCN 100 Summer “GRADIENT” FLOW: CYCLONIC Case See Fig Moran and Morgan (1997):

ATM OCN 100 Summer “GRADIENT FLOW” (con’t.)  Resultant flow without Friction F Centripetal = F PG,H + F Cor (A vector summation). u Two cases: –Cyclonic Flow (around a low pressure cell) –Anticyclonic Flow (around a high pressure cell)

ATM OCN 100 Summer “GRADIENT FLOW” (con’t.) See Moran and Morgan (1997): u Figure 9.14 Cyclonic Flow u Figure 9.13 Anticyclonic Flow

ATM OCN 100 Summer G. GRADIENT FLOW WITH FRICTION  Resultant flow with Friction F Centripetal = F PG,H + F Cor + F Friction (A vector summation).

ATM OCN 100 Summer Summary of Forces for selected models See Table 9.1 Moran & Morgan (1997)

ATM OCN 100 Summer G. GRADIENT FLOW WITH FRICTION  Resultant flow with Friction F Centripetal = F PG,H + F Cor + F Friction (A vector summation). u Applicability to the Atmosphere u Situation u Resultant Diagrams

ATM OCN 100 Summer Anticyclonic Flow in Friction Layer Fig Moran & Morgan (1997)

ATM OCN 100 Summer Cyclonic Flow in Friction Layer Fig Moran & Morgan (1997)

ATM OCN 100 Summer Near-Surface Winds in each Hemisphere See Figs & 9.18 Moran & Morgan (1997)

ATM OCN 100 Summer Summary of Forces for selected models See Table 9.1 Moran & Morgan (1997) MODELS

ATM OCN 100 Summer H. RELATIONSHIPS BETWEEN HORIZONTAL & VERTICAL MOTIONS u Dilemma u Convergence / Divergence u Principle of Mass Continuity

ATM OCN 100 Summer Features in a Surface Low (Convergence & Ascent)

ATM OCN 100 Summer Features in a Surface High (Sinking & Divergence)

ATM OCN 100 Summer H. RELATIONSHIPS BETWEEN HORIZONTAL & VERTICAL MOTIONS (con’t.) u Dines’ Compensation u Resultant Vertical Motions u Implications of Dines' Compensation

ATM OCN 100 Summer H. RELATIONSHIPS BETWEEN HORIZONTAL & VERTICAL MOTIONS u Dilemma u Convergence / Divergence u Principle of Mass Continuity u Dines' Compensation u Resultant Vertical Motions u Implications of Dines' Compensation

ATM OCN 100 Summer I. VORTICES & VORTICITY u Definitions u Characteristic Vortex Features

ATM OCN 100 Summer Vorticity u Types of Vorticity Cyclonic Vorticity Anticyclonic Vorticity

ATM OCN 100 Summer Vorticity u Conservation of Vorticity

ATM OCN 100 Summer LOCAL WINDS (con’t.)