5.3: Skew-T Log-P Diagram

There are many different types of thermodynamic diagrams, but the main one we will discuss are Skew-T Log-P diagrams, so-named because the isotherms (lines of equal temperature, \(T\)) on the diagram are slanted (skewed) and the isobars (lines of equal pressure, \(P\)) on the diagram are in log space. Here we will focus on how to read and utilize Skew-T Log-P diagrams (often shortened to Skew-T diagram) to determine parcel buoyancy and atmospheric stability.

An example Skew-T Log-P diagram from Lihue on August 31st, 2018. The sounding was retrieved from the Upper Air Soundings portion of the University of Wyoming Weather Web: http://weather.uwyo.edu/upperair/sounding.html (Copyright 2018 by University of Wyoming Department of Atmospheric Science, used with permission.)

The radiosonde balloon sounding plotted here was launched from Lihue on Kauai (see the top left, labelled as station “91165 PHLI Lihue”). You can see the vertical environmental temperature profile (\(T\)) plotted as the black jagged line on the right. The dew point temperature (\(T_d\)) with height is plotted with the black jagged line on the left. Although this figure may be overwhelming to read at first, we’ll walk through it together. The horizontal axis is temperature in \({ }^{\circ} C\), with temperatures increasing to the right. The vertical axis is air pressure in \(hPa\), decreasing with height, so higher heights are toward the top of the chart. When the \(T\) and \(T_d\) lines are close together, the environment has a high relative humidity and the air is closer to saturation. In this particular sounding, there is a lot of moisture near the surface, but dries out in the mid-levels.

Radiosonde balloons are launched twice a day (\(\text { ooZ }\) and \(12Z\)) from many locations around the world. The latitude and longitude for the station is given in the top of the list on the right where station latitude (SLAT) is given as 21.99 degrees North and SLON is -159.34 degrees West. The station elevation SELV is 30 m. The sounding time and date is given in the bottom left, and the bottom right says “University of Wyoming” because in this particular example, the University of Wyoming is the organization that gathered and archived the dataset. You can find soundings for other locations and dates at this website: http://weather.uwyo.edu/upperair/sounding.html.

Let’s go through the lines one by one.

Isobars (horizontal, lines of constant pressure) and isotherms (slanted, lines of constant temperature) (CC BY-NC-SA 4.0).

The horizontal lines on a Skew-T are isobars, or lines of equal air pressure. You will typically see them given in \(hPa\), but the lines in the above figure are in \(kPa\). The isobars have larger spaces as you get toward the top of the diagram because they are logarithmic with height. The evenly-spaced solid lines that slant up and to the right are isotherms, or lines of equal temperature (\(T\)). This allows colder temperatures to be plotted on the diagram.

Isohumes (slanted dashed lines), lines of constant mixing ratio (CC BY-NC-SA 4.0).

The dashed lines that run up and to the right are isohumes, or lines of constant mixing ratio. These are typically given in units of g·kg^–1. If you use a Skew-T where these lines are not dashed or color-coded, remember that these are spaced more closely together than isotherms and are more steep. They also do not line up with the temperature labels on the x-axis.

Dry adiabatic lapse rate reference lines, also known as lines of constant potential temperature (CC BY-NC-SA 4.0).

The evenly-spaced curved solid lines that run from bottom right to top left are dry adiabats, and depict the dry adiabatic lapse rate (9.8 K·km^-1). The dry adiabatic lapse rate is considered a constant, but you can see here that over large changes in temperature and pressure, it varies a little. Don’t worry about these variations—we still consider it a constant. Dry adiabatic lapse rate reference lines are also called lines of constant potential temperature (\(\theta\)). The dry adiabats always curve upward from right to left in a concave way.

Moist adiabatic lapse rate reference lines. (CC BY-NC-SA 4.0).

The uneven, dashed, lines that curve up and to the left are the moist adiabats. The moist adiabatic lapse rate varies with both temperature and moisture content, but is close to the dry adiabatic lapse rate at high altitudes due to cold temperatures and small moisture content. These lines are parallel to the dry adiabats higher up on the Skew-T Log-P diagram. These are also lines of constant equivalent potential temperature (\(\theta_e\)).

A complete Skew-T Log-P diagram, used to visualize changes in the atmosphere with altitude. (CC BY-NC-SA 4.0).

Here is a complete Skew-T Log-P diagram. All of the lines look confusing and complicated when combined, but each represents a constant change in one variable.

Let’s look at another real balloon sounding. This time launched from Hilo during Hurricane Lane.

Balloon sounding launched from Hilo as Hurricane Lane impacted the Big Island. The sounding was retrieved from the Upper Air Soundings portion of the University of Wyoming Weather Web: http://weather.uwyo.edu/upperair/sounding.html. (Copyright 2018 by University of Wyoming Department of Atmospheric Science, used with permission.)

On this Skew-T diagram, all of the same lines are there. Horizontal blue lines are isobars, slanted blue lines are isotherms, slanted purple lines are isohumes, the green lines are the dry adiabats, and the blue curved lines are the moist adiabats. The \(T\) (right) and \(T_d\) (left) black lines are close together and sometimes overlap in the lowest 500 hPa of the atmosphere because the lower levels are incredibly moist, and a deep cloud layer extended up to nearly 6 km altitude.

Finding the Lifting Condensation Level (LCL)

When plotting a sounding on a Skew-T diagram, you may have a selection of data similar to the example given below. You will likely have pressure, temperature (\(T\)), and a dew point temperature (\(T_d\)) with altitude.

Sample atmospheric data to be plotted on the skew-T diagrams (CC BY-NC-SA 4.0).

In order to plot the sounding, it is easiest to start by finding the pressure level and then move to the right to plot the temperature and dew point temperature. Pay careful attention to the fact that the isotherms are skewed. Rotate the axis in your mind when you plot your temperature and dew point. Once you have plotted all of your temperatures and dew points, you will have a vertical temperature and humidity profile of the atmosphere.

Sample example plotted (CC BY-NC-SA 4.0).

Now that we plotted the sounding, it is useful to know how a rising air parcel will behave when placed in this environment. Is the atmosphere stable, unstable, or conditionally unstable? We can determine this by estimating the rate at which a rising parcel will cool and drawing a parcel path upward. A rising air parcel will cool at the dry adiabatic lapse rate until it is saturated, after which it will cool at the moist adiabatic lapse rate. How do we know when a parcel will be saturated? First we need to find the Lifting Condensation Level (LCL).

The Lifting Condensation Level (LCL) is the level at which the water vapor in an air parcel that is lifted dry adiabatically will be saturated.

The red dot is air temperature and the blue circle is dew point temperature. This diagram is an example of of an unsaturated air parcel. Stull Figure 5.7 (CC BY-NC-SA 4.0).

To find the LCL, start at the surface (or the pressure level closest to the surface, typically 1000 hPa) and plot the temperature and dewpoint temperature. In the case of the example above, the surface pressure level must be at a raised elevation with \(P_{\text {surf }}=90 kPa\) or 900 hPa, \(T = 30 { }^{\circ} C\), and \(T_d = -10 { }^{\circ} C\). Imagine that the air parcel has the same temperature and dewpoint temperature as the environment at first. Initially, it will cool at the dry adiabatic lapse rate as it rises. First, follow the surface temperature upward along a dry adiabat. In all likelihood, the temperature will not be directly along a marked dry adiabat line as it is in the example so follow a line upward parallel to a dry adiabat. Similarly, start at your surface dew point and follow the isohume (constant mixing ratio line) upward because the moisture content of the air parcel does not change with dry lifting. Draw these lines upward until they intersect. This intersection will give you the level of the lifting condensation level (LCL).

Follow the dry adiabat and isohume lines until they intersect (CC BY-NC-SA 4.0).

The place where the two lines intersect is the lifting condensation level (CC BY-NC-SA 4.0).

In this example, the surface temperature and dewpoint temperature line up nicely with an isohume and a dry adiabat line, but this typically won’t be the case with a real sounding. The procedure, however, will be the same. The LCL marks the approximate cloud base height for convective clouds (cumulus type), where rising air first becomes saturated.

After the air parcel has been lifted dry adiabatically to the LCL, it becomes saturated. As we know, a saturated air parcel cools at the smaller moist adiabatic lapse rate. From the LCL, follow a line parallel to a moist adiabat upward to get the approximate lapse rate of your parcel as it rises. In the example soundings from Hilo and Lihue shown earlier, this same line is plotted in a light grey color from the surface all the way up in the atmosphere. It shows the temperature a surface based parcel would have when lifted through the troposphere.

As you follow an air parcel temperature upward moist adiabatically, the point at which it intersects the environmental temperature profile (where your parcel becomes warmer than its environment) is called the Level of Free Convection, or the LFC.

As you continue following the air parcel path upward moist adiabatically from the LFC, the point where it intersects the sounding again (the point where your parcel becomes cooler than its environment) is called the Equilibrium Level (EL).

Normand’s Rule for Wet-bulb Temperature

You can estimate the surface wet bulb temperature by taking the LCL example one step further. Normand’s Rule is used to calculate the wet-bulb temperature from the air temperature and the dew point temperature. The wet bulb temperature is always between the dew point and the dry bulb temperature (\(T_d \leq T_w \leq T\)). To find the wet bulb temperature on a Skew-T Log-P diagram, follow the surface \(T\) upwards along a dry adiabat, and the surface \(T_d\) upwards along a isohume. Where they meet is the LCL, as just explained. Next, follow a moist adiabat back down to the surface. Where the moist adiabat intersects the surface is the wet-bulb temperature value.