METR 200: Intro to Atmos & Ocean Physics & Thermodynamics The Skew-T Thermodynamic Diagram Dr. Dave Dempsey Dept. of Geosciences SFSU, Fall 2004

Thermodynamic diagrams are tools used by meteorologists to solve atmospheric temperature and humidity problems using graphical techniques instead of lengthy calculations. Meteorologists use thermodynamic diagrams to forecast cloud height and atmospheric stability. (Atmospheric stability is an indicator of the likelihood of severe weather.)

Meteorologists base their analyses on plots of vertical profiles of air temperature, dew-point temperature, and wind observed by a radiosonde (a balloon-borne instrument package with radio transmitter) at individual radiosonde launch stations.

One version of the thermodynamic diagram is the skew-T log-p diagram, or "skew-T" for short, so named because one of the primary axes of the graph (temperature) is skewed clockwise by 45°. (Another is the Stuve diagram, shown in our textbook. It is simpler one to read but less useful meteorologically.)

Construction of a Skew-T Diagram

A complete thermodynamic diagram, including the skew-T diagram, contains five sets of lines or curves:

1. isobars (lines of constant pressure)
2. isotherms (lines of constant temperature)
5. isohomes (lines of constant saturation mixing ratio)

On the next page is an example of part of a typical skew-T log-p diagram. (1) Isobars and (2) Isotherms

The pressure and temperature uniquely define the thermodynamic state of an air parcel at any time, and uniquely locate any given point on the diagram above. On the diagram, horizontal solid lines are isobars (lines of constant pressure, labeled in millibars along the left-hand edge), and solid lines sloped at a 45° angle (clockwise from the vertical) are isotherms (lines of constant temperature, labeled in °C along the bottom).

There is an infinite number of possible isobars and isotherms that could be drawn on the diagram, because every pressure lies on an isobar and every temperature lies on an isotherm. Showing them all would turn the diagram black with lines! Rather than show them all, only a select few, at regular intervals, are actually drawn. Locating an air parcel's temperature and pressure on the diagram usually entails interpolating between the lines actually drawn on the diagram.

The pressure of an air parcel serves as a surrogate for its altitude, but for most purposes the pressure is more important. That's because a parcel's pressure, and any subsequent changes in its pressure, are usually more important for determining changes in the state of the parcel (except for parcel's in contact with the earth's surface, where conduction plays an important role).

The slightly curved, solid lines sloping upward to the left on the diagram are called "dry adiabats". These lines describe the change in temperature that an unsaturated air parcel would undergo if the parcel moved up or down in the atmosphere and expanded or became compressed adiabatically as the pressure on it changed. If an air parcel rises from a known initial point to a final point, you can trace the amount of cooling by following the dry adiabat through the initial point. (Like isobars and isotherms, only selected dry adiabats are actually drawn on the diagram, so you'd usually have to interpolate between the nearest dry adiabats on both sides of the initial point.)

The slope of all dry adiabats is 9.8°C per kilometer, which represents the temperature change that an air parcel would undergo if it rose or sank adiabatically by 1 kilometer.

The set of curved, dashed lines are "saturation" or "moist" adiabats. These curves describe the temperature changes that a rising, saturated air parcel would undergo.

Saturation adiabats have slopes ranging from 2C°/km in warm air near the surface to a slope nearly the same as dry adiabats (9.8C°/km) in cold air aloft. (Notice how the saturation adiabats become more nearly parallel to dry adiabatics at lower pressures and temperatures). Saturation adiabats have smaller slopes than dry adiabats because rising, saturated air cools more slowly (that is, less per kilometer that it rises) thanks to the conversion of latent heat into sensible heat as water vapor condenses in the adiabatically cooling air. This conversion partly compensates for the adiabatic cooling.

As a saturated parcel rises, its lapse rate gradually increases because at cooler temperatures, each increment of adiabatic cooling causes less condensation to occur and hence less conversion of latent heat into sensible heat. (This is why plot of saturation mixing ratio versus temperature that you've worked with earlier in the semester is curved the way it is.)

(5) Isohumes

The dash-dotted curves that slope upward and to the right on the thermodynamic diagram are saturation mixing ratio lines, or isohumes. They describe the saturation mixing ratio of air and are labeled in grams per kilogram (g/kg) along the bottom of the diagram. For any particular pressure and temperature—that is, for any particular location on the diagram—the isohume passing through that location tells you the maximum amount (mass) of water vapor that could be present in each kilogram of dry air at that temperature and pressure.

Thermodynamic diagrams show only relations between temperature, pressure, and saturation mixing ratio but show nothing directly about mixing ratio, dew-point temperature, or relative humidity. However, if we know either a parcel's dew point temperature, its mixing ratio, or its relative humidity (in addition to its temperature and pressure), then we can determine the others indirectly from the diagram. Similarly, if a parcel's temperature, pressure, and/or moisture content changes, then we can determine changes in the other quantities.

To do this we take advantage of the definition of dew point temperature and the relation between relative humidity, mixing ratio and saturation mixing ratio. The reasoning needed to do this is described in our text as well as in class.