Which Of The Following Changes Raises Relative Humidity?

Chapter v: Atmospheric Stability

Alison Nugent and David DeCou

Learning Objectives

Past the end of this affiliate, you should be able to:

Interpret stability based on the dry and moist adiabatic lapse rates
Sympathize how stability relates to vertical movement in the atmosphere
Describe and differentiate between the many lines on a Skew-T log-P diagram
Find the LCL, regions of CAPE and CIN, and the tropopause from a Skew-T log-P diagram

A cumulonimbus cloud rises and expands as a production of instability within the atmosphere (Public Domain).

When you lot think of the give-and-take "stable," you typically call back of an object that is unlikely to change or something that is counterbalanced. The opposite is truthful with something that is "unstable". An unstable object is likely to fall or change position with time. The same is true with clouds. When you meet a fluffy cumulus cloud, you might discover them irresolute shape from one minute to the next. Such clouds are in a constant state of change, and thus represent the atmosphere in an unstable state.

A perfect cumulus cloud just west of Magic Island (photo by Sarah Williamson).

Instability in the temper is a concept that is intimately connected with thunderstorms, cumulus development, and vertical move. In order to visualize the concept of stability, you lot might imagine a boulder sitting at the bottom of a coulee surrounded by steep hills, as depicted in the figure below by the blue circle. If yous were potent enough to push the boulder from its initial position partway upwards one of the hills, it would roll back to the lesser once you permit go. Despite exerting a force on the boulder and causing an initial displacement, it would return to its initial position, and the net displacement would be zero. To visualize the concept of instability, imagine the aforementioned boulder at the top of a loma (carmine circle below). If you were able to push the boulder just a little bit in any management, it would begin to scroll downward and advance away from its initial position. Still, if the same boulder were to be placed on flat footing (green circle below) and y'all were to button information technology, it would change position, just remain in its new position. This is an example of neutral stability.

Each of these concepts tin can be applied to motions of air parcels in the atmosphere. The topic of stability in atmospheric science is important considering the formation of clouds is closely related to stability or instability in the atmosphere. In this chapter nosotros will connect these concepts to the buoyancy of air parcels, and learn to use thermodynamic diagrams to visualize motion.

Examples of stability and instability in relation to air and parcel temperatures (created by Britt Seifert).

Adiabatic Processes

When discussing stability in atmospheric sciences, we typically think about air parcels, or imaginary blobs of air that tin expand and contract freely, just do non mix with the air around them or break apart. The key slice of information is that movement of air parcels in the atmosphere can be estimated every bit an adiabatic procedure. Adiabatic processes exercise non substitution heat and they are reversible.

Imagine you have a parcel of air at the Earth's surface. The air bundle has the same temperature and force per unit area every bit the surrounding air, which we will telephone call the environment. If you were to lift the air bundle, information technology would observe itself in a place where the surrounding environmental air pressure is lower, because we know that pressure decreases with height. Because the environmental air pressure outside the parcel is lower than the pressure level inside the packet, the air molecules inside the packet will effectively push outward on the walls of the package and expand adiabatically. The air molecules inside the parcel must apply some of their own energy in order to aggrandize the air parcel's walls, so the temperature inside the package decreases as the internal free energy decreases. To summarize, rising air parcels expand and cool adiabatically without exchanging rut with the environment.

At present imagine that you move the same air parcel dorsum to Globe's surface. The air parcel is moving into an environment with higher air pressure. The higher environmental pressure level will push inward on the package walls, causing them to shrink, and raise the within temperature.

The process is adiabatic, so again, no heat is exchanged with the environment. Nonetheless, temperature changes in the air parcel tin still occur, merely it is not due to mixing, information technology is due to changes in the internal free energy of the air parcel.

Dry Adiabatic Lapse Rate

As long every bit an air parcel is unsaturated (relative humidity < 100%), the rate at which its temperature will change will be abiding. A decrease in temperature with height is called alapse rate and while the temperature decreases with altitude, it is divers as positive because information technology is a lapse rate. Call up from affiliate 3 that the dry adiabatic lapse rate, Γ_d , is equal to 9.8 Thousand·km^-i = 9.8 °C·km^-1 . This drop in temperature is due to adiabatic expansion and a subtract in internal energy.

Let's get back to the topic of atmospheric stability. Stability in the temper refers to a condition of equilibrium. Every bit discussed with the example of the boulder on a hill or valley, some initial movement resulted in either more than (unstable), less (stable), or no alter (neutral). Given some initial change in the top of an air parcel, if the air is in stable equilibrium, the packet will tend to return back to its original position after it is forced to rising or sink. In an unstable equilibrium, an air parcel will accelerate away from its initial position after existence pushed. The move could exist upward or down, but generally unstable atmospheres favors vertical motions. Finally, in a neutral equilibrium, some initial change in the elevation of an air parcel will not result in any additional movement.

Determining Stability

How practice yous know if an air parcel will be stable afterward some initial displacement? Stability is adamant by comparing the temperature of a rising or sinking air packet to the environmental air temperature. Imagine the post-obit: at some initial time, an air parcel has the same temperature and pressure equally its environment. If y'all lift the air parcel some altitude, its temperature drops by ix.eight Grand·km^-ane, which is the dry adiabatic lapse rate. If the air parcel is colder than the environment in its new position, it volition accept higher density and tend to sink dorsum to its original position. In this example, the air is stable considering vertical move is resisted. If the ascension air is warmer and less dense than the surrounding air, it volition continue to rise until it reaches some new equilibrium where its temperature matches the environmental temperature. In this case, considering an initial modify is amplified, the air parcel is unstable. In social club to figure out if the air packet is unstable or non nosotros must know the temperature of both the rising air and the environs at unlike altitudes.

Ane way this is done in practice is with a weather airship. We can get a vertical profile of the environmental lapse rate by releasing a radiosonde attached to a weather balloon. A radiosonde sends back information on temperature, humidity, wind, and position, which are plotted on a thermodynamic diagram. This vertical plot of temperature and other variables is known as a sounding.

Dry Stability

If an air parcel is dry, meaning unsaturated, stability is relatively straightforward. An atmosphere where the environmental lapse charge per unit is the same equally the dry out adiabatic lapse rate, meaning that the temperature in the environment also drops by 9.8 K·km^-1, will be considered neutrally stable. After some initial vertical displacement, the temperature of the air package will always exist the same equally the surround so no further change in position is expected.

If the environmental lapse rate is less than the dry out adiabatic lapse charge per unit, some initial vertical displacement of the air parcel volition result in the air parcel either existence colder than the environment (if lifted), or warmer than the environment (if pushed downward). This is because if lifted, the temperature of the air parcel would drib more the temperature of the environment. This is a stable state of affairs for a dry air parcel and a typical scenario in the temper. The global boilerplate tropospheric lapse rate is half-dozen.5 Thousand·km^-1 , which is stable for dry out lifting.

Finally, if the environmental lapse rate is greater than the dry adiabatic lapse rate, some initial vertical displacement of the air packet will result in the air packet either beingness warmer than the environment (if lifted), or colder than the environment (if pushed downward). This is because if lifted, the temperature of the air parcel would drop less than the temperature of the environment. This is an unstable state of affairs for a dry air parcel.

In full general for a dry out air bundle, the post-obit is truthful.

$\begin{align*} \Gamma_d = \Gamma_{env} \:\:\:\:\: NEUTRAL \end{align*}$

$\begin{align*} \Gamma_d < \Gamma_{env} \:\:\:\:\: STABLE \end{align*}$

$\begin{align*} \Gamma_d > \Gamma_{env} \:\:\:\:\: UNSTABLE \end{align*}$

Moist Adiabatic Lapse Rate

When moisture is added, everything gets more complicated. In Affiliate 4 we learned that whether or not an air package is saturated depends primarily on its temperature and, of course, its wet content. The graph of the Clausius-Clapeyron relationship shows us that given the same amount of moisture, air is more likely to be saturated at a lower temperature.

We know that as an air bundle is lifted, its temperature drops co-ordinate to the dry adiabatic lapse rate. So what happens when the air parcel is cold enough that the air becomes saturated with respect to h2o vapor? The brusk answer is that if it continues to absurd, water vapor volition condense to liquid water to form a cloud.

When water vapor condenses, information technology goes from a higher energy state to a lower energy state. Energy is never created nor destroyed, especially in phase changes, and then what happens to all that excess energy? The energy gets released in the form of latent heat. The latent estrus of condensation is approximately equal to 2.5 * 10⁶ J·kg^-1, which means that for every kg of h2o vapor that condenses to form liquid h2o, ii.5 *x⁶ Joules of energy are released.

This has big consequences for the lapse rate of an air package and distinguishes the dry adiabatic lapse rate from the moist adiabatic lapse charge per unit. As latent heat is added from the process of condensation, it offsets some of the adiabatic cooling from expansion. Because of this, the air bundle volition no longer cool at the dry adiabatic lapse charge per unit, but will cool as a slower rate, known equally the moist adiabatic lapse rate. To summarize, a parcel will cool at the dry adiabatic rate until it is saturated, after which it won't cool as quickly due to condensation. The moist adiabatic lapse charge per unit varies a lilliputian past temperature, only in this class we will consider it a abiding for simplicity:Γ_thousand = 4.5 K·km^-i = 4.5 °C·km^-1

Moist Stability

The furnishings of wet change the lapse rate of the air parcel and, therefore, affects stability. However, the concepts are still the same and we still compare the air package temperature to the ecology temperature. We have just ane added complication to worry almost—we need to know whether the air packet is dry or moist. Some definitions are included beneath, which take into account both dry and moist adiabatic lapse rates.

A thermodynamic diagram showing the stability of the atmosphere based on the dry (Γ_d =9.8 G km^-i) and moist (Γ_thousand= 4.5 K km^-1) adiabatic lapse rates (Created past Britt Seifert).

The atmosphere is said to be absolutely stable if the environmental lapse rate is less than the moist adiabatic lapse rate. This means that a rising air package will e'er cool at a faster rate than the environment, even afterwards information technology reaches saturation. If an air parcel is cooler at all levels, and so it will not exist able to rise, even later information technology becomes saturated (when latent heating will annul some cooling).

The atmosphere is said to exist absolutely unstable if the environmental lapse rate is greater than the dry adiabatic lapse rate. This means that a ascent air package will always cool at a slower rate than the environment, even when it is unsaturated. This means that information technology volition exist warmer (and less dense) than the environment, and allowed to rise.

The atmosphere is said to be conditionally unstable if the ecology lapse rate is between the moist and dry adiabatic lapse rates. This means that the buoyancy (the ability of an air parcel to rise) of an air packet depends on whether or not it is saturated. In a conditionally unstable atmosphere, an air package volition resist vertical move when it is unsaturated, because it will cool faster than the surroundings at the dry adiabatic lapse charge per unit. If it is forced to rise and is able to become saturated, however, it volition cool at the moist adiabatic lapse rate. In this example, it will cool slower than the environment, become warmer than the environment, and volition rise.

Hawaiian Focus Box

Effectually Hawaii, the atmosphere is almost ever conditionally unstable, meaning that the ecology lapse rate lies somewhere between the dry and moist adiabatic lapse rates. For this reason, Hawaii near ever has convective clouds. Convective clouds are clouds where the edges are bumpy and cumuliform, like cauliflower. The clouds are convective because the atmosphere is stable to dry lifting and unstable to moist lifting. Once the air is saturated, instability sets in and vertical motion takes off. This is especially mutual as air is lifted over our mountainous islands. The forced lifting from the terrain creates clouds and rain correct over the mountains! In scientific terms, the initial lifting of the stable low level dry air by the terrain causes the air to adiabatically expand and achieve saturation, at which bespeak the environment is unstable to moist lifting and convection is the result.

There are many different types of thermodynamic diagrams, but the principal one we will discuss are Skew-T Log-P diagrams, so-named considering 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 infinite. Hither we will focus on how to read and use Skew-T Log-P diagrams (often shortened to Skew-T diagram) to determine parcel buoyancy and atmospheric stability.

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

The radiosonde balloon sounding plotted here was launched from Lihue on Kauai (see the summit left, labelled equally station "91165 PHLI Lihue"). You can see the vertical environmental temperature profile (T) plotted equally the black jagged line on the correct. The dew point temperature (T_d) with height is plotted with the black jagged line on the left. Although this figure may exist overwhelming to read at first, nosotros'll walk through it together. The horizontal centrality is temperature in °C, with temperatures increasing to the right. The vertical axis is air pressure in hPa, decreasing with acme, then higher heights are toward the top of the chart. When the T and T_d lines are shut together, the environment has a high relative humidity and the air is closer to saturation. In this particular sounding, at that place is a lot of moisture virtually the surface, simply dries out in the mid-levels.

Radiosonde balloons are launched twice a day (00Z and 12Z) from many locations around the earth. The breadth and longitude for the station is given in the superlative of the list on the right where station latitude (SLAT) is given equally 21.99 degrees North and SLON is -159.34 degrees Due west. The station elevation SELV is thirty grand. The sounding time and appointment is given in the bottom left, and the bottom right says "University of Wyoming" considering in this particular example, the Academy of Wyoming is the organization that gathered and archived the dataset. You tin can notice soundings for other locations and dates at this website: http://conditions.uwyo.edu/upperair/sounding.html.

Let's go through the lines one by one.

Isobars (horizontal, lines of abiding pressure level) 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 force per unit area. You lot will typically meet them given in hPa, simply the lines in the above figure are in kPa. The isobars accept larger spaces equally y'all get toward the tiptop of the diagram because they are logarithmic with superlative. 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 k·kg^–one. If you employ 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 likewise do not line upward with the temperature labels on the x-axis.

Dry out adiabatic lapse rate reference lines, too known equally lines of abiding potential temperature (CC BY-NC-SA 4.0).

The evenly-spaced curved solid lines that run from lesser right to top left are dry adiabats, and describe the dry adiabatic lapse charge per unit (9.8 K·km^-i). The dry adiabatic lapse rate is considered a constant, but you lot can see here that over large changes in temperature and pressure, it varies a little. Don't worry about these variations—we notwithstanding consider it a constant. Dry out adiabatic lapse rate reference lines are besides called lines of abiding potential temperature (θ). The dry out adiabats always curve up from right to left in a concave way.

Moist adiabatic lapse rate reference lines. (CC Past-NC-SA four.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 wet content, but is close to the dry out adiabatic lapse charge per unit at high altitudes due to common cold temperatures and modest moisture content. These lines are parallel to the dry adiabats higher up on the Skew-T Log-P diagram. These are also lines of abiding equivalent potential temperature (θ_east).

A complete Skew-T Log-P diagram, used to visualize changes in the atmosphere with distance. (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, just each represents a constant change in one variable.

Allow's await at some other real airship sounding. This fourth dimension 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 past University ofWyoming Department of Atmospheric Science, used with permission.)

On this Skew-T diagram, all of the same lines are there. Horizontal blueish lines are isobars, slanted bluish lines are isotherms, slanted purple lines are isohumes, the light-green lines are the dry adiabats, and the blue curved lines are the moist adiabats. The T (correct) and T_d (left) blackness lines are shut together and sometimes overlap in the lowest 500 hPa of the atmosphere considering the lower levels are incredibly moist, and a deep deject 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 accept a selection of data similar to the case given below. You will likely take force per unit area, temperature (T), and a dew bespeak temperature (T_d) with distance.

Sample atmospheric information to exist plotted on the skew-T diagrams (CC Past-NC-SA 4.0).

In lodge to plot the sounding, it is easiest to start by finding the force per unit area and and so 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 signal. Once you have plotted all of your temperatures and dew points, yous will take a vertical temperature and humidity contour of the temper.

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 charge per unit at which a rising parcel will absurd and drawing a bundle path upward. A rising air parcel volition cool at the dry adiabatic lapse charge per unit until information technology is saturated, afterwards which information technology will cool at the moist adiabatic lapse rate. How do we know when a parcel will be saturated? Start nosotros need to observe the Lifting Condensation Level (LCL).

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

The red dot is air temperature and the blue circle is dew betoken temperature. This diagram is an example of of an unsaturated air parcel. Stull Figure 5.7 (CC BY-NC-SA iv.0).

To find the LCL, start at the surface (or the pressure level level closest to the surface, typically thousand hPa) and plot the temperature and dewpoint temperature. In the case of the case above, the surface force per unit area must be at a raised summit with P_surf= xc kPa or 900 hPa, T = 30 °C, and T_d= -10 °C. Imagine that the air parcel has the same temperature and dewpoint temperature as the environment at outset. Initially, information technology volition cool at the dry adiabatic lapse rate as it rises. Outset, follow the surface temperature upwards forth a dry adiabat. In all likelihood, the temperature will not be direct forth a marked dry adiabat line as it is in the instance so follow a line upward parallel to a dry adiabat. Similarly, start at your surface dew point and follow the isohume (abiding mixing ratio line) upward because the wet content of the air package does not alter with dry lifting. Draw these lines upwards 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 four.0).

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

In this instance, the surface temperature and dewpoint temperature line up nicely with an isohume and a dry adiabat line, only this typically won't be the case with a existent sounding. The procedure, nonetheless, volition exist the same. The LCL marks the approximate deject base of operations height for convective clouds (cumulus type), where rising air outset becomes saturated.

Later the air parcel has been lifted dry out adiabatically to the LCL, it becomes saturated. Every bit we know, a saturated air parcel cools at the smallermoist adiabatic lapse rate. From the LCL, follow a line parallel to a moist adiabat upward to become the approximate lapse rate of your bundle every bit it rises. In the example soundings from Hilo and Lihue shown before, this aforementioned line is plotted in a calorie-free grey color from the surface all the fashion up in the atmosphere. Information technology shows the temperature a surface based parcel would have when lifted through the troposphere.

As y'all follow an air packet temperature upward moist adiabatically, the betoken at which information technology intersects the ecology 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 packet path upward moist adiabatically from the LFC, the indicate where it intersects the sounding over again (the point where your parcel becomes cooler than its environs) is called the Equilibrium Level (EL).

Normand'due south Rule for Moisture-seedling Temperature

You tin can estimate the surface moisture bulb temperature by taking the LCL example 1 footstep further. Normand'southward Rule is used to calculate the moisture-bulb temperature from the air temperature and the dew point temperature. The moisture bulb temperature is ever between the dew point and the dry out bulb temperature (T_d ≤ T_west ≤ T). To find the wet seedling temperature on a Skew-T Log-Pdiagram, 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. Adjacent, follow a moist adiabat dorsum downwardly to the surface. Where the moist adiabat intersects the surface is the wet-bulb temperature value.

Cape & CIN

The "positive area" between the parcel path and the environmental temperature profile, traced out between the LFC and the EL (where the bundle is warmer than the environment) gives a measure of the Convective Available Potential Energy, or Cape, given in units of J·kg^–1. This is an estimate of the buoyant energy of a parcel and can provide a means of estimating the strength of any convection that may occur. CAPE can too provide an gauge of the maximum updraft intensity in a thunderstorm.

$\begin{align*} w_{max} \sim 0.60\cdot(2\cdot CAPE)^{\frac{1}{2}} \end{align*}$

due west_max is the estimated maximum vertical motility as a issue of Greatcoat.

Convective Inhibition, or CIN is substantially negative CAPE, also in J·kg^–1. It is the negative area between the bundle path and the ecology temperature curve where the packet is cooler than the surround. The larger the value of CIN, the greater the negative buoyant energy that acts against CAPE. CIN sometimes acts every bit a "cap" on convection. If yous have large CAPE but as well large CIN, your Cape may non be fully realized as buoyant energy and y'all may not have any convection. However, if your parcel is able to break through the cap, that is, if information technology is able to rise and become warmer than the environment, convection may exist strong.

The figure below shows the locations of the LFC and EL, and shades in both positive and negative areas betwixt the parcel path and the environmental temperature contour.

The locations of the LFC and EL in the vertical sounding are shown, plant as the positive and negative areas betwixt the package path and the environmental temperature profile (Public Domain).

In the Lihue and Hilo soundings shown previously, values of Greatcoat and CIN are given in J·kg^–1 in the cavalcade on the right mitt side. Annotation that CIN is written every bit "CINS" and denoted as a negative value.

Locating the Tropopause

Recall that the standard temperature decreases with summit within the troposphere, only becomes isothermal with height within the the tropopause, and increases with height in the stratosphere. With this knowledge, the location of the tropopause, given by its pressure level, tin exist determined by examining a plotted sounding. In the upper office of your sounding, await for where the temperature profile becomes isothermal (parallel to your skewed isotherms) or for an inversion (where the temperature increases with top, which will be tilted to the right more your isotherms). The base of the isothermal layer in your sounding is the tropopause.

A plotted sounding with two isothermal layers and a temperature inversion denoted (CC BY-NC-SA 4.0).

There are many things we tin can learn almost the temper from Skew-T Log-P diagrams. Here we've provided just the nuts to get you started.

Chapter v: Questions to Consider

Drag and drop terms to their correct position in the atmospheric stability diagram below:
What does the Lifting Condensation Level (LCL) represent? How can it be found on a Skew-T diagram?
What is CAPE? How can it exist found on a Skew-T diagram?

Selected Do Question Answers:

Source: http://pressbooks-dev.oer.hawaii.edu/atmo/chapter/chapter-5-atmospheric-stability/

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