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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 Advantages: • 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 Adiabat 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 BT Thermodynamics Pressure Isotherms (T) Adiabats (θ) 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) Adiabats (θ) 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 BT 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) Adiabats (θ) Pseudo-adiabats (θe) 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 The saturation adiabats are lines of constant equivalent potential temperature and they represent pseudoadiabatic processes 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 Dry-adiabatic 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