METEO 300
Fundamentals of Atmospheric Science

3.5 The Skew-T Diagram: A Wonderful Tool!

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The skew-T is widely used in meteorology to examine the vertical structure of the atmosphere as well as to determine which processes are likely to happen.

Need a refresher?

Check out this video (1:23):

Click for a transcript for Skew-T Basics Video

You know a little about the skew-T from your previous study, but for those who did not take a previous course or who need a refresher, there are many useful websites that can help you understand the skew-T and how to use it. Two useful resources are the following:

Weatherprediction.com Review of Skew-T Parameters

Introduction to Mastering the Skew-T Diagram Video

In this video (1:24) I will show you how the skew-T relates to a cumulus cloud:

Click here for a transcript of the Skew-T and Cloud Video

First, familiarize yourself with all of the lines. Look at a radiosonde ascent, such as the one from the National Center for Atmospheric Research Research Applications Laboratory (type of plot: GIF of skew-T). The atmospheric sounding line to the right (higher temperature) is the atmospheric temperature. The line to the left (lower temperature) is the dewpoint temperature and at the same time is the water vapor mixing ratio, since w = ws(Td). If you are unsure about all the other lines, refer back to your notes or look it up online.

Skew T-Diagram. See caption and text above and below image.
Skew-T diagram for Pittsburgh PA on April 28, 2015 at 0000 UTC.
Credit: NOAA

Please also note the following:

  • The dry adiabat is the same line as an isentrope (curved red dash lines tilting to the upper left).
  • The water vapor mixing ratio is the saturation water vapor mixing ratio at the dewpoint temperature, Td, for each pressure level (gold dot-dash lines tilting to the upper right).
  • In clear air, for air parcels moving vertically:
    • air parcels move along the dry adiabat and the potential temperature remains constant, even if they contain moisture;
    • the water vapor mixing ratio is constant (but notice that Td changes!);
    • Td of an air parcel moving vertically (and adiabatically) is decreasing, but not as fast as T if that air parcel is decreasing.
  • Eventually, an air parcel moving vertically (along the dry adiabat) will have a temperature and dewpoint temperature that are the same, thus saturated.
  • At this altitude level, called the Lifting Condensation Level (LCL), the relative humidity = 100%, T = Td, and w = ws, and e = es. At this pressure and temperature, a cloud forms. Actually, the formation of a cloud requires a relative humidity that exceeds 100% by a few tenths of a percent, but generally use 100% for the skew-T calculations. We will see why this extra relative humidity is necessary in the next lesson.

See the video below (1:19) for further explanation:

Finding LCL
Click here for transcript of the Finding LCL Video.

Let's see how to find the lifting condensation level, the LCL. The LCL's the level where a cloud will form if the air mass near a surface is pushed upward. We have two quantities that are conserved when lifted. The potential temperature, or theta, and the water vapor mixing ratio, w. As the air parcel is pushed up, then w goes up the constant w line and theta goes up the dry adiabat, which is the constant theta line. Note that both the temperature and the dew point temperature are changing and getting closer to each other as the air parcel ascends. When the two lines meet, the relative humidity is 100%, a cloud forms, and this is the lifting condensation level. Once the LCL has been reached and the cloud is formed, any further ascent will be in the cloud. The air parcel temperature will follow the moist adiabat, which is less than the dry adiabat. Because as water condenses it gives up its energy to warm the air a little bit. If the air were pushed down, its temperature would follow the moist adiabat, as long as it was above the LCL. But below the LCL, it will follow the dry adiabat. And the water vapor mixing ratio will follow the constant w line.

Moist Adiabat

When the air parcel is in a cloud, ascent causes a temperature decrease while the air remains saturated (i.e., w=w­s, RH=100%). Since ws decreases, the amount of water in the vapor phase decreases while the amount in the liquid or solid phase increases, but the total amount of water is constant (unless it rains!). As water vapor condenses, energy is released into the air and warms it a little bit. Thus, the lapse rate of the moist adiabat (curved dot-long-dash green lines tilting toward the upper left) is less than the lapse rate of the dry adiabat (9.8 K/km).

As long as it doesn’t rain or snow, an air parcel will move up and down a moist adiabat as long as it is in a cloud and will move up and down a dry adiabat when w < ws below the LCL.

  • Once a cloud forms, any further rise of the air parcel will follow the moist adiabat (condensation of water vapor heats the air so that the temperature decrease with height is less than the dry adiabat). As long as the ascent is in the cloud, the relative humidity will remain near 100% and w = ws(T). Since T decreases on ascent, ws decreases, and more water goes into the liquid or ice phase.
  • If the air parcel descends, it will descend along the moist adiabat until it reaches the LCL in temperature and more of the water evaporates or sublimates into the vapor phase. Just below the LCL, all of the water will be vapor and the air parcel temperature will descend down the dry adiabat and the water vapor mixing ratio will be constant.

The following is a summary for air parcel ascent and descent:

  • Find initial p, T (or ws), and Td (or w).
  • Move the parcel up the dry adiabat that intercepts T.
  • Move w up the constant w line. Note that Td is continually changing, so use w.
  • Where the two lines intercept is the Lifting Condensation Level (LCL).
  • A cloud will form.
  • If the air parcel continues to rise inside the cloud,
    • w will always equal ws.
    • the air parcel will follow the moist adiabat.
  • If the parcel then descends,
    • it will follow the moist adiabat down to the LCL.
    • it will follow the dry adiabat below that.
    • w will follow the w line below that.

The following video (1:43) discusses The process of adiabatic cooling and heating.

Adiabatic Heating and Cooling
Click here for transcript of the Adiabatic heating and cooling video.

We've all seen clouds build up on one side of the mountain and then on the other side just dissipate into blue sky. Maybe you want to know why that happens. Like most natural events, this one has an impressive scientific term attached to it. It's called adiabatic cooling and heating, and occurs because of changes in air pressure. Here's some time lapse video that shows what happens. Basically, as a parcel of air encounters a mountain, it is forced upward. As air pressure decreases with altitude, the air parcel expands. Expansion causes air to cool. When the air cools to its so-called dew point, the water vapor in the air condenses and becomes visible as a cloud. If there's enough moisture and the adiabatic cooling is strong enough, it rains or snows. Essentially the opposite occurs on the other side of the mountain. The cool air sinks and compresses. Compression results in increased temperature. When temperature rises above the dew point, the cloud dissipates into invisible water vapor. In Wyoming, especially in winter, most of the moisture-laden air masses come from the Pacific, approaching our mountains from the west. So as adiabatic cooling occurs, more rain and snow is dumped on west-facing slopes. As warmer, drier air descends on the eastern slopes, it accounts for another famous phenomenon of the plains, the so-called Chinook winds. So we've looked at clouds from both sides now. Knowing why they form and disappear does not diminish their beauty. But if it weren't for our mountains and the dynamic processes that occur, one, we would be a much drier place, and frankly, much less interesting. I'm Tom Hill from the University of Wyoming Cooperative Extension Service exploring the nature of Wyoming.

Other Potential Temperatures

There are other potential temperatures that are useful because they are conserved in certain situations and therefore can help you understand what the atmosphere is doing and what an air parcel is likely to do.

Virtual Potential Temperature

Virtual potential temperature is the potential temperature of virtual temperature, where density differences caused by water vapor are taken into account in the virtual temperature by figuring out the temperature of dry air that would have the same density:

θ v = ( p o p ) ( γ1) γ T v = ( p o p ) ( γ1) γ T( 1+0.61q ) This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

[3.14]

This quantity is useful when comparing the potential temperatures (and thus densities) of air parcels at different pressures.

Wet Bulb Potential Temperature

The wet-bulb temperature is the temperature a volume of air would have if it were cooled adiabatically while maintaining saturation by liquid water; all the latent heat is supplied by the air parcel so that the air parcel temperature when it descends to 1000 hPa is less than its temperature would be had it descended down the dry adiabat.

The wet bulb temperature at any given pressure level is found by finding the LCL and then bringing the parcel up or down to the desired pressure level on the moist adiabat.

The wet bulb potential temperature, Θw, is the wet bulb temperature at p=1000 hPa. 

How can we use the wet bulb potential temperature? The wet bulb potential temperature is conserved, meaning it does not change, when an air mass undergoes an adiabatic process, such as adiabatic uplift or descent. If we consider large air masses that acquire similar temperature and humidity, then this entire air mass can take on the same wet bulb potential temperature. Colder, drier air masses will have a lower Θw. The Θw of this air mass can change if a diabatic process occurs, such as a cold air mass moving over warm land and warming, or the air mass cooling by radiating to space during the night, but these processes can sometimes take days. So an 850-mb map of Θw is one indicator of air masses and the fronts between air masses. 

See the video below (:32) for further explanation:

Finding Wetbulb Θ
Click here for transcript of the Finding Wetbulb Θ Video.

Let's see how to find the wet-bulb potential temperature on the Skew-T. The first step is to find the LCL. Once we find the LCL, then we have a saturated air parcel. And it's temperature is the wet-bulb temperature. To find the wet-bulb potential temperature, we simply follow the moist adiabat down to a pressure of 1,000 millibar. We see that the wet-bulb potential temperature is about 19 C, while the potential temperature is about 34 C.

Equivalent Potential Temperature

The equivalent potential temperature is potential temperature that an air parcel would have if it were lifted to the LCL, then lifted along the moist adiabat all the way to the stratosphere so that all the water vapor condensed into liquid, and then lost all the condensed water, and returned down to 1000 hPa along a dry adiabat. Equivalent potential temperature accounts for the effects of condensation or evaporation on the change in the air parcel temperature.

Every 1 g/kg (g water vapor to kg of dry air) causes Θe to increase about 2.5K. So, a moist air parcel with w = 10 g kg-1, which is not uncommon, will have Θe that is 25K greater than Θ.

Approximately,

θ e θ+ l v w c p This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

[3.15]

Where Θ is the potential temperature, lv is the latent heat of vaporization, w is the water vapor mixing ratio, and cp is the specific heat capacity, constant pressure.

How can we use the equivalent potential temperature? The equivalent potential temperature, Θe is conserved when an air parcel or air mass undergoes an adiabatic process, just like the wet bulb potential temperature, Θw, is. Note also the total amount of water in vapor, liquid, and ice form is also conserved during adiabatic processes. So, if we look at Θe and total water, we can learn a lot about the history of an air parcel. These conserved quantities are very useful to understand the history of air parcels around clouds. For example, if Θe changes but the total water mixing ratio is constant, then the air parcel was either heated or cooled by a non-adiabatic process. On the other hand, if both Θe and wt change proportionally, then two air parcels with different initial values for Θe and wt have mixed. On a larger, more synoptic scale, gradients in Θe can be used to indicate the presence of fronts. 

Another use of Θe is as an indicator of unstable air. Air parcels that have higher Θe tend to be unstable. Thus regions of high Θe air are regions where thunderstorms might form if the surface heating is great enough to erase a temperature inversion. 

See the video (1:01) below for further explanation:

Finding Θe
Click here for transcript of the Finding Θe video.

Let's see how to find the equivalent potential temperature, called theta-e, on this Skew-T. The equivalent potential temperature is the potential temperature that an air parcel would have if all this water vapor were converted to liquid water, thus warming the air. And then the liquid water was removed. To find theta-e, we find the LCL. Go up to the moist adiabat until it's parallel with the dry adiabat. And then go down the dry adiabat that matches the moist adiabat until we reach the pressure of 1,000 millibar. In this case, theta-e is about 330 Kelvin, or 57 degrees C. Note that the lines aren't marked with such high temperatures. But we can determine which temperature this line represents by looking at the 360 Kelvin dry adiabat. And then counting one, two, three lines over, where the lines are in intervals of 10 K.

Quiz 3-4: Using the skew-T.

  1. Find Practice Quiz 3-4 in Canvas. You may complete this practice quiz as many times as you want. It is not graded, but it allows you to check your level of preparedness before taking the graded quiz.
  2. When you feel you are ready, take Quiz 3-4. You will be allowed to take this quiz only once. Good luck!