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