### Thermodynamic Diagrams

```Introduction to Thermodynamic Diagrams
How thermodynamic diagrams are used to forecast thunderstorms?
Thermodynamics
M. D. Eastin
Introduction to Thermodynamic Diagrams
Outline:
 Basic Idea of Thermodynamic Diagrams
 Possible Diagrams
 Skew-T Log-P Diagram
 Rawinsondes
 Dropsondes
 Skew-T Applications
Thermodynamics
M. D. Eastin
Basic Idea of Thermodynamic Diagrams
• A visualization tool
• We can always use the mathematical formulas…
• Many of us learn better through visualization…
• Eliminates or simplifies the equations
• Can determine many quantities in a graphical format
Desired Qualities in a Thermodynamic Diagram:
1. For cyclic processes, the area should be proportional to the work done
or the heat exchanged
2. The lines should be straight (easy to use)
3. The angle between adiabats and isotherms should be as large as possible
(easy to distinguish variations in atmospheric stability → will air rise or sink)
(more on stability later…)
Thermodynamics
M. D. Eastin
Possible Thermodynamic Diagrams
P-V Diagrams?
Pros:
• Satisfies Requirement #1
• Good for illustrating basic concepts
Cons:
• Angle between isotherms and
adiabats is very small
• Isotherms and adiabats are not
straight lines
• We don’t observe volume
We need to use a different diagram
that satisfies all three requirements
and uses a coordinate system for
observable variables
Thermodynamics
p
Isobar
i
Isochor
Isotherm
f
V
M. D. Eastin
Basic Idea of Thermodynamic Diagrams
Area-Equivalent Transformations:
• P-V diagrams only satisfy Requirement #1: Enclosed area proportional to energy
dW  pdV
f
W   pdV
i
• Thus, we need to consider other variables for the coordinate systems
• Create a generic transformation from P, V → A, B
P
W
V
Thermodynamics
A
B
M. D. Eastin
Basic Idea of Thermodynamic Diagrams
Area-Equivalent Transformations:
WpV
P
A
V
WAB
B
f
f
WpV   pdV
WAB   AdB
i
i
WpV  WAB
Thermodynamics
M. D. Eastin
Possible Thermodynamic Diagrams
Tephigram:
Temperature
• Area proportional to energy
• 3 sets of nearly straight lines
• Isobars (p) are curved
• Pseudo-adiabats (θe) are curved
• 90º angle between adiabats
and isotherms
A  ln θ
BT
Thermodynamics
Pressure
Isotherms (T)
Saturation Mixing Ratio (w)
400
mb
600
mb
800
mb
1000
mb
Note: We will talk about the pseudo-adiabats (θe)
and saturation mixing ratio (w) lines later
in the course
M. D. Eastin
Possible Thermodynamic Diagrams
Emagram:
400
mb
Isobars (p)
Isotherms (T)
Saturation Mixing Ratio (w)
• Pseudo-adiabats (θe) are curved
• 45º angle between adiabats
and isotherms
Pressure
• Area proportional to energy
• 4 sets of nearly straight lines
600
mb
800
mb
1000
mb
A  ln p
BT
Thermodynamics
-40oC
-20oC
0oC
20oC
40oC
Temperature
Note: We will talk about the pseudo-adiabats (θe)
and saturation mixing ratio (w) lines later
in the course
M. D. Eastin
Possible Thermodynamic Diagrams
Skew-T Log-P Diagram:
• Area proportional to energy
• 3 sets of nearly straight lines
Isobars (p)
Isotherms (T)
Saturation Mixing Ratio (w)
See Example on Next Slide
• Adiabats (θ) are slightly curved
• Pseudo-adiabats (θe) are curved
• ~90º angle between adiabats
and isotherms
A  R ln p
B  T  ln p
Thermodynamics
Note: We will talk about the pseudo-adiabats (θe)
and saturation mixing ratio (w) lines later
in the course
M. D. Eastin
Possible Thermodynamic Diagrams
Skew-T Log-P Diagram:
Pressure (mb)
200
Isobars (p)
Isotherms (T)
Saturation Mixing Ratio (w)
300
400
500
600
700
800
900
1000
Temperature (oC)
Thermodynamics
M. D. Eastin
The Skew-T Log-P Diagram
Skew-T Log-P Diagram:
• Most commonly used diagram (we will use it too…)
• Come in a variety of shapes, sizes, and colors.
• All Skew-T Log-P diagrams provide the exact same information!
Thermodynamics
M. D. Eastin
The Skew-T Log-P Diagram
Note how the lines of
constant temperature
slope (or are skewed)
toward the upper left
Hence, “Skew-T”
These lines are always
solid and straight
but vary in color
Our Version:
Red solid lines
Thermodynamics
M. D. Eastin
The Skew-T Log-P Diagram
Note how the change
in pressure along the
Y-axis in non-uniform
Rather, it changes
logarithmically
Hence, “Log-P”
These lines are always
solid and straight
but may vary in color
Our Version:
Blue solid lines
Thermodynamics
M. D. Eastin
The Skew-T Log-P Diagram
The dry adiabats, or
lines of constant
potential temperature
slope at almost
right angles to the
isotherms
These lines are always
solid and slightly
curved, but may vary
in color
Our Version:
Light Blue Solid Lines
Thermodynamics
M. D. Eastin
The Skew-T Log-P Diagram
The lines of constant
saturation mixing
ratio are also skewed
toward the upper left
More on these in a
future lecture…
These lines are always
dashed and straight,
but may vary in color
Our Version:
Pink dashed Lines
Thermodynamics
M. D. Eastin
Skew-T Applications
are lines of constant
equivalent potential
temperature and they
More on these in a
future lecture…
These lines are always
dashed and curved,
but may vary in color
Our Version:
Dashed bluish-green
Thermodynamics
M. D. Eastin
Skew-T Log-P Diagram
Pressure (200 mb)
10ºC = 283K
Thermodynamics
M. D. Eastin
Skew-T Log-P Diagram
Plot Rawinsonde or Dropsonde Observations:
Temperature
Dewpoint
Temperature
Thermodynamics
M. D. Eastin
The Rawinsonde
Instrument Package attached to a Balloon:
• Launched twice daily (00 and 12 UTC)
• Regular launch locations
• Rise from the surface into the stratosphere before the balloon bursts
• Observe pressure (p), temperature (T), dewpoint temperature (Td),
altitude (z), and horizontal winds (speed, direction) at numerous
regular levels through the atmosphere.
Temperature and
Humidity Sensor
Thermodynamics
M. D. Eastin
The Global Rawinsonde Network
Standard 1200 UTC Rawinsonde Sites
Thermodynamics
M. D. Eastin
The Dropsonde
Instrument Package attached to a Parachute:
• Launched from aircraft or hot air balloons
over data sparse regions (e.g. the oceans)
• Used to improve “high-impact” forecasts
• Hurricane forecasts
• Winter storm forecasts
• Irregular launch times and locations
• Fall the from launching platform down to
the surface using a parachute that
controls the rate of descent
• Observe pressure (p), temperature (T),
dewpoint (Td), altitude (z), and horizontal
winds (speed, direction) at numerous
regular levels through the atmosphere.
Thermodynamics
M. D. Eastin
Skew-T Applications
Identify Temperature Inversions
Inversions are
layers where
temperature
increases
with height
Thermodynamics
M. D. Eastin
Skew-T Applications
Identify Dry Adiabatic Layers
layers have the
temperature
profile parallel
to a dry adiabat
Thermodynamics
M. D. Eastin
Skew-T Applications
Determine the Potential Temperature (θ) of any Air Parcel
Begin with
parcel at 400 mb
Bring air parcel down a
dry-adiabat to 1000 mb
Add 273 K to the T-value
T = 40ºC
θ = 313 K
Thermodynamics
M. D. Eastin
Introduction to Thermodynamic Diagrams
Summary:
• Basic Idea of Thermodynamic Diagrams
• Possible Diagrams
• Skew-T Log-P Diagram
• Rawinsondes
• Dropsondes
• Skew-T Applications
Thermodynamics
M. D. Eastin
References
Petty, G. W., 2008: A First Course in Atmospheric Thermodynamics, Sundog Publishing, 336 pp.
Tsonis, A. A., 2007: An Introduction to Atmospheric Thermodynamics, Cambridge Press, 197 pp.
Wallace, J. M., and P. V. Hobbs, 1977: Atmospheric Science: An Introductory Survey, Academic Press, New York, 467 pp.
Also (from course website):
NWSTC Skew-T Log-P Diagram and Sounding Analysis, National Weather Service, 2000
The Use of the Skew-T Log-P Diagram in Analysis and Forecasting, Air Weather Service, 1990
Thermodynamics
M. D. Eastin
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