Down to Earth Meteorology

#2056 "Singleton Sunset Shades"

These thoughts are designed to lead you full circle back into the planar earth world of meteorology. From my first blog entry in this meteorological series until now, I have empathized thinking in three or even four dimensions to better understand the atmosphere and the weather. Now we are going to simplify that back to the flat earth and a simple piece of paper. And that is OK!

In “Cloud Shapes and Lines in the Atmosphere” I illustrated that cloud patterns are much simpler if you examine them from the atmospheric frame of reference. Our earthly frame of observation is not where the weather lives. But puffs, swirls and lines are all part of the same conceptual model and we are going to dramatically simplify that concept. Moisture in the air makes these otherwise invisible air flows obvious. These patterns relate directly to the weather. The use of your hand and the presence of any cloud, will tell the rest of the story. 

The atmospheric frame of reference (green box in the graphic) moves with the average speed in the atmosphere (purple circle with vector). Every wind observed in the earth frame (purple box) can be expressed as this average plus a small difference from the mean (green box). 

Vector addition to get from the
Atmospheric Frame to the Earth Frame 
and back again

This simple but important example is when the west wind in the earth frame simply decreases a bit. In the atmospheric frame of reference (green box), this is represented by two small opposing puffs. The average wind in the atmospheric frame is zero. In the accompanying graphic, the dashed light purple arrows in the earth frame (purple box) on the left are added to the average wind (purple circle with vector) to achieve the purple arrows of the decreasing wind in the earth frame. The paired puffs of air in the atmospheric frame each produce a “smoke ring”. 

Each puff of smoke reveals a single smoke ring but 
there is an invisible, smoke ring paired with each of those. 

A deformation zone skin separates these opposing, three dimensional smoke rings. Typically the air on one side of the deformation zone is more moist while the other is drier. The moisture tracers can only reveal the smoke ring circulation on the moist side.  

The opposing puffs in the Atmospheric Frame
creates the Deformation Zone Conceptual Model

Imagine the complexity of the mathematics required to describe the paired smoke rings in 3D. The human mind can easily visualize the circulations and understand the weather implications but the math is much more challenging. The weather and the atmosphere are very three or four dimensional and it is actually easier and better to consider the bigger picture in the atmospheric frame of reference. My friends at COMET in Boulder, Colorado could make some terrific animations to make these concepts all come alive. Until that happens, a flat piece of paper will suffice. 

The Deformation Zone Conceptual Model
of opposing puffs along the axis of contraction

To recap in 3D: These paired smoke rings are generated by a simple decrease in the wind as measured from the earth’s surface. The pair of rings is separated by a three dimensional deformation zone skin. The relative intensity of the swirls define the shape of the deformation zone skin and vice versa.

The atmosphere is thin - thinner that the skin of an apple in a comparative sense.  More importantly, cloud layers are generally two dimensional and move parallel to the earth’s surface on the constant energy surfaces (see Isentropic Surfaces - Science and Art Merges). The quasi horizontal layered cloud intersects the 3D Deformation Zone Conceptual Model in essence making a horizontal cross-sectional. 

Meteorologists have typically just considered the quasi-horizontal cross-sections of the 3D Deformation Zone Conceptual Model. This is a rare case when it is absolutely acceptable to simplify the 3D conceptual model into the two dimensional plane because that is what the clouds do. 

The three dimensional smoke rings is thus reduced to companion X’s and N’s that straddle the axis of contraction puffs that blow inward within the cross-section. By convention the red “X” is considered to be positive or cyclonic. The blue “N” is considered to be negative or anti-cyclonic rotation. The fingers of your hand will curl in the direction of the circulation when you thumb points upward at an X and downward at an N. Use your right hand if you are in the northern hemisphere and keep your left hand for doing meteorology south of the equator. 

The Companion Vortices are associated
 with the same 3D Smoke Ring
The Paired Vortices across the green
Deformation Zone (Axis of Dilatation)
are with different Smoke Rings but still influence each other

The 3D deformation zone skin becomes the axis of dilatation line (the double headed green arrow) when the quasi horizontal cloud intersects the conceptual model. 

For simplification, we will focus on the 2D Deformation Zone Conceptual Model in the above graphic for the next few meteorological blogs. It is a powerful tool that I built my career of weather prediction around. I cannot imagine how many times I sketched that pattern and its many variations... 

So we have finally come down to earth and the simplified deformation zone conceptual model. I venture to say that this concept is the most important tool to use in understanding patterns in any fluid. This lines and the associated swirls are universal and have a lot to say… Give me any one of the five components of the Deformation Zone Conceptual Model and the others simply fall into place. 

The swirls and lines in "Singleton Sunset Shades" are easily explained. Art is science. Enjoy!

Keep you paddle in the water (making swirls) and warmest regards,

Phil the Forecaster Chadwick

The Solution to Cloud Swirls Can Be Found in Your Hands

#2361 "Singleton Sunset Swirl"

In the atmospheric frame of reference, every cloud shape can be considered in terms of a swirl. If you align the fingers of your hand in the direction of the cloud curvature, your thumb must point either up or down. Why and what does it mean? 

A movie played in my mind when I was attempting to explain this stuff years ago, arms flailing and pencil and paper flying. My friends at COMET turned some of those into animations and graphics. I will try again with a different approach. 

Imagine yourself at the equator with you back to the rising sun. Life is good with the warmth on your back. You can’t feel it but you are in a non-inertial frame of reference. The Earth is spinning as it orbits the “stationary” sun. Fictitious forces that result from the rotation of the Earth include the Coriolis and centrifugal forces. These forces make weather even more interesting as they shape the lines in the sky. 

Imagine I am at the equator at sunrise looking west...

Now stretch your arms outward and curl your fingers out as well. Your right arm must point north while your left arm is directed toward the south. The fingers of both hands are curled cyclonically. Both thumbs of your cyclonically curved hands must point upward. 

The previous entries in the Weather Blogs all mentioned the “right hand rule” because the selected weather examples were in the northern hemisphere.  When I participated in the Solar Car Race in the Australian Outback in 1996, I employed the “left hand rule” instead. Both rules describe cyclonic rotation. 

The effects of the Coriolis force at the equator are not noticeable - in fact, they are zero. An observer stationary with respect to the sun, could watch you standing at the equator. They would see that your back does not turn at all as the Earth does it daily spin. 

If you could stretch your arms gradually until your hands reach the poles, the Coriolis force gets really interesting. The same solar stationary observer, would see your right hand complete one entire, cyclonic rotation each and every day. Gumby standing at the equator with his right hand stretched to the North Pole would not feel any difference but Gumby is within the non-inertial frame of reference. An observer looking down on the North Pole would see Gumby’s hand rotate cyclonically counter clockwise. At the same time, Gumby’s left hand would also complete one full cyclonic rotation every day. An observer above the South Pole looking downward would see Gumby’s left hand rotate clockwise. 

My Friend Gumby

The impact of the fictitious Coriolis force increases dramatically from the equator to the poles. This explains why the swirls and deformation zones are more obvious and dynamic over the higher latitudes. 

Everything that I explained in the earlier Weather Blogs can now be employed in the Southern Hemisphere remembering to employ the “left-hand cyclonic rule" south of the equator. Cyclonic rotation has the same meteorological implications in both hemispheres but you have to use the appropriate hand. 

Another visualization is to shoot arrows from the Poles. An archer at the North Pole aiming toward the south (the only available direction) would see the arrow deflected to the right as the Earth rotates counter-clockwise underneath. The fingers of the archer’s right hand will curl counter-clockwise as well when the thumb points up. Similarly an Antarctic archer at the South Pole shooting northward (an impossible to miss shot) would see the Coriolis force deflect that arrow to the left. From the South Pole perspective the Earth is rotating clockwise in the direction of the fingers of your left hand with the thumb pointing upward. 

There are many ways to look at the fictitious Coriolis created by the spinning Earth. The take away messages are:

• The Coriolis force increases from zero at the equator to a maximum at the poles.
• The deflection is always perpendicular to the motion and to the right in the Northern Hemisphere but to the left in the Southern Hemisphere.
• The rotation of the Earth defines the cyclonic sense of rotation. Cyclonic is counter-clockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
• Differential advection of cyclonic rotation with height results in upward vertical motion as indicated by the direction of your thumb (Trust me on this one).

Rotation creates the swirls in the atmosphere. Simple conceptual models based on these swirls can explain everything you need to know about the atmosphere and the weather. The following graphic explains the weather painted in #2361 "Singleton Sunset Swirl". You can do it as well with just a few lessons and lots of sky gazing practice. 

Keep you paddle in the water and warmest regards,

Phil the Forecaster Chadwick