ATM OCN 100 Summer 2002 1 ATM OCN 100 - Spring 2002 LECTURE 20 (con’t.) THE THEORY OF WINDS: PART...

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ATM OCN 100 - Spring 2002 ATM OCN 100 - Spring 2002 LECTURE 20 LECTURE 20 (con’t.)(con’t.)

THE THEORY OF WINDS: THE THEORY OF WINDS: PART III - RESULTANT ATMOSPHERIC PART III - RESULTANT ATMOSPHERIC MOTIONS MOTIONS (con’t.)(con’t.)

A.A. Introduction & AssumptionsIntroduction & AssumptionsBuys-Ballot LawBuys-Ballot Law

Buys Ballot RuleBuys Ballot Rule

Current Midwest Weather PlotCurrent Midwest Weather Plot

Current Midwest Weather AnalysisCurrent Midwest Weather Analysis

GoalGoal

Attempt to develop simple models to Attempt to develop simple models to explain atmospheric motions explain atmospheric motions appearing on surface weather mapsappearing on surface weather maps

ASSUMPTIONSASSUMPTIONS

For convenience, assume that:For convenience, assume that: Define motion in terms of Define motion in terms of

horizontal & vertical components. horizontal & vertical components. RationaleRationale::

– Winds are nearly horizontal;Winds are nearly horizontal;– Vertical motions typically much smaller.Vertical motions typically much smaller.

Make assumptions about the balance of forces:Make assumptions about the balance of forces:

Summary of Forces for selected modelsSummary of Forces for selected modelsSee Table 9.1 Moran & Morgan (1997)See Table 9.1 Moran & Morgan (1997)

Forces Hydrostatic Equilibrium

Geostrophic Wind

Gradient Wind

Surface Winds

Pressure Gradient

Vertical X Horizontal X X X

Centripetal X X

Coriolis X X X

Friction X

Gravity X

MODELSMODELS

B. HORIZONTAL EQUATION OF B. HORIZONTAL EQUATION OF ATMOSPHERIC MOTIONATMOSPHERIC MOTION

The 3-D vector Equation of Atmospheric The 3-D vector Equation of Atmospheric Motion can be written in terms of horizontal Motion can be written in terms of horizontal and vertical components: and vertical components:

Net force = Net force = Horizontal Pressure gradient force Horizontal Pressure gradient force + Vertical Pressure gradient force + Vertical Pressure gradient force + gravity + Coriolis force + friction + gravity + Coriolis force + friction..

HYDROSTATIC BALANCE CONCEPTHYDROSTATIC BALANCE CONCEPT

A Fundamental Assumption:A Fundamental Assumption:

– Earth’s atmosphere remains and is Earth’s atmosphere remains and is essentially in “hydrostatic balance”.essentially in “hydrostatic balance”.

The Model –The Model –

– This balance is between the vertically This balance is between the vertically oriented vector quantities:oriented vector quantities:

– gravity, gravity, &&

– acceleration due to acceleration due to vertical component of vertical component of pressure gradient forcepressure gradient force..

Concept of Hydrostatic BalanceConcept of Hydrostatic BalanceFig. 9.11 Moran & Morgan (1997)Fig. 9.11 Moran & Morgan (1997)

Components in Hydrostatic Balance ModelComponents in Hydrostatic Balance ModelFig. 9.11 Moran & Morgan (1997)Fig. 9.11 Moran & Morgan (1997)

Gravity Vector Direction:Gravity Vector Direction:“Down” toward Earth center“Down” toward Earth center Gravity Vector Magnitude:Gravity Vector Magnitude:

Decreases with altitude... Decreases with altitude... But But 9.8 m/s 9.8 m/s2 2 or 32 ft/sor 32 ft/s22

Components in Hydrostatic Balance ModelComponents in Hydrostatic Balance ModelFig. 9.11 Moran & Morgan (1997)Fig. 9.11 Moran & Morgan (1997)

Gravity Vector Direction:Gravity Vector Direction:“Down” toward Earth center“Down” toward Earth center Gravity Vector Magnitude:Gravity Vector Magnitude:

Decreases with altitude... Decreases with altitude... But But 9.8 m/s 9.8 m/s2 2 or 32 ft/sor 32 ft/s22

Vert. Press. Grad. Force Vert. Press. Grad. Force Vector Direction:Vector Direction:“Up” from High “Up” from High to Low Pressureto Low Pressure

Vert. Press. Grad. Force Vert. Press. Grad. Force Vector Magnitude:Vector Magnitude:

Depends upon Depends upon Vert. Pressure Grad. &Vert. Pressure Grad. &

DensityDensity

Geostrophic Wind

Gradient Wind

Surface Winds

Pressure Gradient

Centripetal X X

Coriolis X X X

Friction X

Gravity X

MODELSMODELS

HYDROSTATIC BALANCE CONCEPT HYDROSTATIC BALANCE CONCEPT (con’t.)(con’t.)

As a resultAs a result– The atmosphere is maintained;The atmosphere is maintained;– Convection is somewhat limited.Convection is somewhat limited.

HORIZONTAL PRESSURE GRADIENT HORIZONTAL PRESSURE GRADIENT FORCEFORCE

Horiz. Press. Grad. ForceHoriz. Press. Grad. ForceVector Direction:Vector Direction:

High to Low & Perpendicular to the Isobars!

HORIZONTAL PRESSURE GRADIENT FORCEHORIZONTAL PRESSURE GRADIENT FORCE (con’t.)(con’t.)

See Fig. 9.1 Moran & Morgan (1997)See Fig. 9.1 Moran & Morgan (1997)

Magnitude of Pressure Gradient Magnitude of Pressure Gradient depends on isobar spacing!depends on isobar spacing!

As a Result of the HORIZONTAL As a Result of the HORIZONTAL PRESSURE GRADIENT FORCE PRESSURE GRADIENT FORCE (con’t.)(con’t.)

Horiz. Press. Grad. Force Horiz. Press. Grad. Force Vector Magnitude:Vector Magnitude:

Depends upon Depends upon Horiz. Pressure Gradient Horiz. Pressure Gradient

(i.e., isobar spacing)(i.e., isobar spacing)

C. FLOW RESPONDING TO C. FLOW RESPONDING TO PRESSURE GRADIENT FORCE - PRESSURE GRADIENT FORCE -

LOCAL WINDSLOCAL WINDS

Assumptions:Assumptions:– Only Pressure gradient force operates due to Only Pressure gradient force operates due to

local pressure differences;local pressure differences;– Horizontal flow.Horizontal flow. Net force = pressure gradient forceNet force = pressure gradient force

Examples:Examples:– Sea-Land Breeze CirculationSea-Land Breeze Circulation– Mountain-Valley Breeze CirculationMountain-Valley Breeze Circulation– City-Country CirculationCity-Country Circulation

VERTICAL PRESSURE GRADIENTS - VERTICAL PRESSURE GRADIENTS - Dependency on density (temperature)Dependency on density (temperature)

Sea-Land Breeze Circulation RegimeSea-Land Breeze Circulation RegimeFigure 12.2 Moran & Morgan (1997)Figure 12.2 Moran & Morgan (1997)

Sea (Lake) BreezeSea (Lake) Breeze(Graphics from UIUC WW2010)(Graphics from UIUC WW2010)

REASONS FOR LAND-SEA REASONS FOR LAND-SEA TEMPERATURE DIFFERENCESTEMPERATURE DIFFERENCES

Water has higher heat capacityWater has higher heat capacity– Smaller temperature response for heat addedSmaller temperature response for heat added

Water is a fluidWater is a fluid– Mixing warm water downwardMixing warm water downward

Water is transparentWater is transparent– Sunlight penetrates to depthSunlight penetrates to depth

Water surface experiences evaporationWater surface experiences evaporation– Evaporative coolingEvaporative cooling

Sea (Lake) BreezeSea (Lake) Breeze (con’t.)(con’t.)

(Lake)

See Fig. 12.2 A Moran & Morgan (1997)See Fig. 12.2 A Moran & Morgan (1997)

Lake Breeze Circulation over Lake MichiganLake Breeze Circulation over Lake MichiganFigure 12.3 Moran & Morgan (1997)Figure 12.3 Moran & Morgan (1997)

Edge of lake breeze Edge of lake breeze on southern Lake Michiganon southern Lake Michigan Modis 21 May 2002Modis 21 May 2002

Land BreezeLand Breeze

Land BreezeLand Breeze (con’t.)(con’t.)

See Fig. 12.2 See Fig. 12.2 BB Moran & Morgan (1997) Moran & Morgan (1997)

Mountain BreezeMountain Breeze

Valley BreezeValley Breeze

D. STRAIGHT-LINE, BALANCED, D. STRAIGHT-LINE, BALANCED, FRICTIONLESS MOTIONFRICTIONLESS MOTION

- “GEOSTROPHIC FLOW” - “GEOSTROPHIC FLOW”

A powerful conceptual modelA powerful conceptual model involving horizontal motion on involving horizontal motion on rotating planet; rotating planet;

Background & Word Derivation:Background & Word Derivation:– Named by Sir Napier Shaw in 1916:Named by Sir Napier Shaw in 1916:

““Geo” = earth + “strephein” = to turn.Geo” = earth + “strephein” = to turn.

Geostrophic Wind

Gradient Wind

Surface Winds

Pressure Gradient

Centripetal X X

Coriolis X X X

Friction X

Gravity X

MODELSMODELS

““GEOSTROPHIC FLOW” GEOSTROPHIC FLOW” (con’t.)(con’t.)

AssumptionsAssumptions

Straight isobars

Parallel isobars

No friction

Horizontal flow

Geostrophic AdjustmentGeostrophic Adjustment See Fig. 9.12 Moran & Morgan (1997)See Fig. 9.12 Moran & Morgan (1997)

Geostrophic AdjustmentGeostrophic Adjustmenthttp://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/geos.rxmlhttp://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/geos.rxml

Geostrophic WindGeostrophic Wind See Fig. 9.12 Moran & Morgan (1997)See Fig. 9.12 Moran & Morgan (1997)

Represents a balance betweenRepresents a balance between

Horiz. Pressure Gradient ForceHoriz. Pressure Gradient Force

Horiz. Coriolis ForceHoriz. Coriolis Force

Geostrophic Wind VectorGeostrophic Wind Vector See Fig. 9.12 Moran & Morgan (1997)See Fig. 9.12 Moran & Morgan (1997)

Vector Direction:Vector Direction:•Parallels isobarsParallels isobars•LowLow to left in NH to left in NH

Vector Magnitude Vector Magnitude depends ondepends on::1. 1. Pressure GradientPressure Gradient2. 2. LatitudeLatitude

““GEOSTROPHIC FLOW” GEOSTROPHIC FLOW” (con’t.)(con’t.)

Implications of Geostrophic BalanceImplications of Geostrophic Balance– Geostrophic wind (VGeostrophic wind (Vgg) is:) is:

a hypothetical winda hypothetical wind a balance between a balance between

– horizontal pressure gradient horizontal pressure gradient (isobar spacing) (isobar spacing)

– latitude (latitude (oror Coriolis effect) Coriolis effect) DilemmaDilemma

Current Midwest Weather AnalysisCurrent Midwest Weather Analysis

E. BALANCED FLOW E. BALANCED FLOW in FRICTION LAYER in FRICTION LAYER

The Nature of FrictionThe Nature of Friction The Friction LayerThe Friction Layer The Effect of Friction upon the The Effect of Friction upon the

Geostrophic WindGeostrophic Wind AssumptionsAssumptions

– Same as for geostrophic wind case, Same as for geostrophic wind case, exceptexcept F FFriction Friction is is not not zero. zero.

Flow in Friction LayerFlow in Friction LayerSee Fig. 9.15 Moran & Morgan (1997)See Fig. 9.15 Moran & Morgan (1997)

FrictionFrictionSubgeostrophicSubgeostrophic

No FrictionNo FrictionGeostrophicGeostrophic

Wind Vector in Friction LayerWind Vector in Friction LayerSee Fig. 9.15 Moran & Morgan (1997)See Fig. 9.15 Moran & Morgan (1997)

Vector Direction:Vector Direction:•Angles across isobarsAngles across isobars

•TowardToward Low Low in in either hemisphereeither hemisphere

Vector MagnitudeVector Magnitude1. 1. Depends on FrictionDepends on Friction2. 2. Less than Less than

Geostrophic WindGeostrophic Wind

Buys Ballot RuleBuys Ballot Rule

Observation:Observation:““Right with Height”Right with Height”

Variation of Friction Effects with HeightVariation of Friction Effects with HeightSee Fig. 9.16 Moran & Morgan (1997)See Fig. 9.16 Moran & Morgan (1997)

NOTE: “Right with height”NOTE: “Right with height”

Varying effects of Surface RoughnessVarying effects of Surface Roughness

Variations in Surface Roughness leads Variations in Surface Roughness leads to divergence/convergence patternsto divergence/convergence patterns

F. CURVED, HORIZONTAL BALANCED F. CURVED, HORIZONTAL BALANCED MOTIONMOTION - -

“GRADIENT FLOW” “GRADIENT FLOW”

AssumptionsAssumptions– Without FrictionWithout Friction

Two CasesTwo Cases

Geostrophic Wind

Gradient Wind

Surface Winds

Pressure Gradient

Centripetal X X

Coriolis X X X

Friction X

Gravity X

MODELSMODELS

““GRADIENT” FLOW: ANTICYCLONIC CaseGRADIENT” FLOW: ANTICYCLONIC CaseSee Fig. 9.13 Moran and Morgan (1997):See Fig. 9.13 Moran and Morgan (1997):

““GRADIENT” FLOW: CYCLONIC CaseGRADIENT” FLOW: CYCLONIC Case See Fig. 9.14 Moran and Morgan (1997):See Fig. 9.14 Moran and Morgan (1997):

G. GRADIENT FLOW WITH FRICTIONG. GRADIENT FLOW WITH FRICTION

Resultant flow with FrictionResultant flow with Friction F FCentripetalCentripetal = = FFPG,HPG,H + F + FCor Cor + F+ FFriction Friction

(A vector summation)(A vector summation)..

Geostrophic Wind

Gradient Wind

Surface Winds

Pressure Gradient

Centripetal X X

Coriolis X X X

Friction X

Gravity X

G. GRADIENT FLOW WITH FRICTIONG. GRADIENT FLOW WITH FRICTION

Resultant flow with FrictionResultant flow with Friction F FCentripetalCentripetal = = FFPG,HPG,H + F + FCor Cor + F+ FFriction Friction

(A vector summation)(A vector summation).. Applicability to the AtmosphereApplicability to the Atmosphere SituationSituation Resultant DiagramsResultant Diagrams

Anticyclonic Flow in Friction LayerAnticyclonic Flow in Friction LayerFig. 9.17 Moran & Morgan (1997)Fig. 9.17 Moran & Morgan (1997)

Cyclonic Flow in Friction LayerCyclonic Flow in Friction LayerFig. 9.18 Moran & Morgan (1997)Fig. 9.18 Moran & Morgan (1997)

Near-Surface WindsNear-Surface Winds in each Hemispherein each Hemisphere See Figs. 9.17 & 9.18 Moran & Morgan (1997)See Figs. 9.17 & 9.18 Moran & Morgan (1997)

Geostrophic Wind

Gradient Wind

Surface Winds

Pressure Gradient

Centripetal X X

Coriolis X X X

Friction X

Gravity X

MODELSMODELS

H. RELATIONSHIPS BETWEEN H. RELATIONSHIPS BETWEEN HORIZONTAL HORIZONTAL && VERTICAL MOTIONS VERTICAL MOTIONS

DilemmaDilemma Convergence / DivergenceConvergence / Divergence Principle of Mass ContinuityPrinciple of Mass Continuity

Features in a Surface Low Features in a Surface Low (Convergence & Ascent)(Convergence & Ascent)

Features in a Surface High Features in a Surface High (Sinking & Divergence)(Sinking & Divergence)

H. RELATIONSHIPS BETWEEN H. RELATIONSHIPS BETWEEN HORIZONTAL HORIZONTAL && VERTICAL MOTIONS VERTICAL MOTIONS (con’t.)(con’t.)

Dines’ CompensationDines’ Compensation Resultant Vertical MotionsResultant Vertical Motions

Implications of Dines' CompensationImplications of Dines' Compensation

I. VORTICES & VORTICITYI. VORTICES & VORTICITY

DefinitionsDefinitions Characteristic Vortex FeaturesCharacteristic Vortex Features

VorticityVorticity

Types of VorticityTypes of Vorticity

Cyclonic VorticityCyclonic Vorticity

Anticyclonic VorticityAnticyclonic Vorticity

VorticityVorticity

Conservation of VorticityConservation of Vorticity

ATM OCN 100 Summer 2002 1 ATM OCN 100 - Spring 2002 LECTURE 20 (con’t.) THE THEORY OF WINDS: PART...

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