MET 61 1 MET 61 Introduction to Meteorology MET 61 Introduction to Meteorology - Lecture 10 Atmospheric Dynamics Dr. Eugene Cordero Ahrens: Chapter 9 W&H: Chapter 7, pg Class Outline:  Principle forces in the atmosphere  Pressure gradient  Coriolis  Geostrophic wind

MET 61 2 MET 61 Introduction to Meteorology Atmospheric forces  Fundamental Forces in the atmosphere – – – –

MET 61 3 MET 61 Introduction to Meteorology Atmospheric forces  Fundamental Forces in the atmosphere –Pressure Gradient Force –Gravity –Rotation of the Earth –Friction

MET 61 4 MET 61 Introduction to Meteorology Pressure  Ultimately responsible for our weather

MET 61 6 MET 61 Introduction to Meteorology Horizontal Pressure Changes  Determines the direction and speed of winds: –Predominate force in atmospheric flows  Can help explain general circulation of atmosphere.

MET 61 7 MET 61 Introduction to Meteorology

MET 61 9 MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Pressure Gradient Force  Pressure gradient: –Dependent on spacing between isobars – –

MET MET 61 Introduction to Meteorology Pressure Gradient Force  Pressure gradient: –Dependent on spacing between isobars –Dense or tight clustering of isobars - strong or large pressure gradient –Weak clustering of isobars - weak pressure gradient Pressure gradient directed from high to low pressure

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Reading a weather map  Orient yourself (location, date and time)  Identify what you are looking at  Determine the interval of the field

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

1.At what local time is this map valid? 2.What fields are we looking at? 3.Indicate the direction of the pressure gradient force at points A-C. A A C C B B

MET MET 61 Introduction to Meteorology 1.At what local time is this map valid? 2.What fields are we looking at? 3.Indicate the direction of the pressure gradient force at points A-C. A A C C B B

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Atmospheric Thickness

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Hypsometric Equation  Combination of ideal gas law with hydrostatic balance.  Relates atmospheric thickness with average temperature.  Thickness of atmosphere relates to difference between two atmospheric layers; z t (m) = thickness between two pressure levels

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology knots

MET MET 61 Introduction to Meteorology The rotation of the Earth  Rockets, migrating birds, and large scale weather systems are all deflected due to the rotation of the Earth.  The Earth’s rotation causes both – –  The Coriolis Force is the name of this rotational force that deflects motion.

MET MET 61 Introduction to Meteorology The rotation of the Earth  Rockets, migrating birds, and large scale weather systems are all deflected due to the rotation of the Earth.  The Earth’s rotation causes both –Translational movement –Rotational movement  The Coriolis Force is the name of this rotational force that deflects motion.

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Coriolis Force Affects direction, not speed of object Maximum at the poles Zero at the equator (only translational movement)  - omega - Earth’s rotational rate  =360 degrees/24 hours or v - wind speed  - latitude

MET MET 61 Introduction to Meteorology Coriolis Force Affects direction, not speed of object Maximum at the poles Zero at the equator (only translational movement) F c =2  v sin   - omega - Earth’s rotational rate  =360 degrees/24 hours or v - wind speed  - latitude 2  radians/86400 seconds=7.27x10 -5 s -1 Calculate Coriolis force for wind moving at 10m/s 2(7.27x10 -5 s -1 )(10m/s)(sin37)=8.8e-4 m/s 2

MET MET 61 Introduction to Meteorology Coriolis Force  Take home message: –N. Hem - deflects air to the right –S. Hem - deflects air to the left –Relatively small acceleration, thus requires long periods of time to influence motion.

MET MET 61 Introduction to Meteorology Geostrophic balance  Geostrophic balance is balance between: and  Result: flow of air is parallel to isobars 

MET MET 61 Introduction to Meteorology Geostrophic balance  Geostrophic balance is balance between: Pressure gradient force and Coriolis force  Result: flow of air is parallel to isobars  friction is assumed to be zero

MET MET 61 Introduction to Meteorology Geostrophic Wind example 1000 mb 1004 mb 1008 mb Northern Hemisphere

MET MET 61 Introduction to Meteorology Geostrophic Wind example L H 1000 mb 1004 mb 1008 mb Pressure Gradient Force Geostrophic Wind Coriolis Force Northern Hemisphere

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

A A C C B B 1.Indicate with arrows the pressure gradient and Coriolis force at A, B and C. 2.Indicate the direction of the wind at each point. 3.Which point do you think the wind will be stronger?

MET MET 61 Introduction to Meteorology Geostrophic Wind Assume friction is zero Flow is parallel to isobars Balance between pressure gradient and Coriolis force  - density, f - Coriolis parameter (2  sin  v - wind speed d – distance between isobars p - pressure

MET MET 61 Introduction to Meteorology Geostrophic Wind Assume friction is zero Flow is parallel to isobars Balance between pressure gradient and Coriolis force  - density, f - Coriolis parameter (=2  sin  V g - geostrophic wind speed  d – distance between isobars  p – pressure difference

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Estimate the geostrophic wind speed for this situation

MET MET 61 Introduction to Meteorology Assume  (500mb) = 0.71 kg/m 3 d=200km=2x10 5 m  p=4mb=400N/m 2 F=2  sin  =9.34x10 -5 V g ~ 30 m/s

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Geostrophic Wind with Friction 1000 mb 1004 mb 1008 mb Northern Hemisphere

MET MET 61 Introduction to Meteorology Geostrophic Wind with Friction L H 1000 mb 1004 mb 1008 mb Pressure Gradient Force Geostrophic Wind Coriolis Force Northern Hemisphere Friction Friction decreases speed of wind, thus Coriolis force is weaker.

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology A B

MET MET 61 Introduction to Meteorology A B

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Jet Stream  Result of North-South temperature gradient  Stronger the pressure gradient, stronger the zonal wind.  Kinks in jet stream due to wave instability: Result is exchange of heat from tropics to poles

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Terminology  Cyclone:  Anticyclone:  At the surface, pressure cells are often closed. However, at higher altitudes, pressure cells are often elongated, forming ridges and troughs. –Low pressure systems - –High pressure systems -

MET MET 61 Introduction to Meteorology Terminology  Cyclone:  Anticyclone:  At the surface, pressure cells are often closed. However, at higher altitudes, pressure cells are often elongated, forming ridges and troughs. –Low pressure systems - –High pressure systems - refers to closed low pressure system refers to a closed high pressure system Troughs Ridges

MET MET 61 Introduction to Meteorology Upper atmosphere pressure gradients  Meteorologist often examine the upper level pressure gradients to determine the prevailing weather conditions.  However, it is not convenient to simply calculate the pressure gradient because of it’s dependence on density.  Rather, meteorologist calculate the height of a particular pressure surface. The slope of these heights determines the pressure gradient force.

MET MET 61 Introduction to Meteorology

MET MET 61 Introduction to Meteorology Soccer example x 12m F c =2  v sin , where, 2  = 1.45x10 -4 s -1 Say, v=12m/s, thus t=1s F c =2  v sin  =(1.45x10 -4 s -1 )(12m/s)(sin 37)=1.05 x m/s 2 Note, that F c is really the acceleration, a. So, from x=v 0 t + ½at 2, then if v0 = 0 we have x= ½at 2 = (0.5)(1.05 x m/s 2 )(1s) 2 =5.2 x m = 0.52 mm

MET MET 61 Introduction to Meteorology Quiz 3: Part A 1.Write down the component form of the Geostrophic wind. 2.Explain the difference between the total derivative and the local derivative, and show how these are different mathematically.

MET MET 61 Introduction to Meteorology Quiz 3: Part B 1.Write down the component form of the momentum equations. Be sure to show all your work (how you got each term). 2.For each term in your above equations, provide a physical description (explanation) for what it means.

MET MET 61 Introduction to Meteorology 3.Indicate the temperature advection at points A and B. Justify your answer. B A

MET MET 61 Introduction to Meteorology Quiz 2: Part A  Explain in words why the jet stream is westerly in both the northern and southern hemispheres.  Describe the three basic conservations laws?

MET MET 61 Introduction to Meteorology Activity 9: Due April 11 th 1.Use links found on the department web page to explore wind speed and direction from maps of model output such as shown in class. From these maps, calculate geostrophic wind using either pressure or height information (if you use height, then use equations given on pg of Stull). Compare your answer with model wind information (isotachs). Show calculations and maps from at least two locations. 2. Compute by how much a soccer ball will be deflected during a 12m penalty kick due to the coriolis force.