GEO214 Midterm Class 3.1-3.2

What are the parent questions for class 3.1?

1. How well does the DALR actually explain the real atmosphere’s lapse rate?

2. Where does a rising parcel form a cloud, and why?

3. What three ingredients must come together for a cloud to form?

4. Why does a saturated parcel cool more slowly than a dry one?

The simple “why’s” for parent questions 3.1

1. How well does the DALR actually explain the real atmosphere’s lapse rate?

DALR predicts rising air cool at a rate of 9.8 K/km → as air rises, the pressure decreases → lower pressure lets the parcel expand → uses internal energy → decreases the temperature → hence the DALR, but real atmosphere does not cool that fast → because the actual troposphere is closer to 6 K/km not 9.8 K/km → because the DALR assumes the parcel is completely dry and ignores condensation + latent heat → but as a real parcel rises, it reaches its “dew point” → which is when the temperature drops while the water vapor stays the same so the relative humidity reaches 100% eventually → this is where condensation occurs, known as the LCL → condensation releases latent heat → vapor turning into a liquid releases energy into the parcel → so the parcel can cool more slowly than the DALR predicts → thus above the LCL, the air parcel follows the MALR instead → so the DALR really only works well for unsaturated rising air below the LCL where the parcel has not reached saturation

2. Where does a rising parcel form a cloud, and why?

Cloud forms when rising air becomes saturated → meaning RH = 100% and parcel temperature = dew point or T = Td → at which the air cannot hold anymore water vapor and thus condenses → this is because as parcel rises and temp decreases → pressure decreases → low pressure means expansion → expansion means internal energy use → so parcel cools dry adiabatically → dewpoint remains the same → but as temp falls, and the dew point stays the same, the temperature dropping eventually reaches a temperature where the dew point is reached relative to the constant water vapor content → condensation begins and this level is the LCL or cloud base → nearby parcels are in the same situation → so they group together to form a cloud

3. What three ingredients must come together for a cloud to form?

There needs to be something to condense → water vapor → cloud droplets form from changing gas to liquid → but the temperature must cool to reach saturation → T = Td and RH = 100% → so excess water vapor can condense → and there must be a condensation nuclei → because water vapor cannot simply condense into droplets itself → it needs to ind to something to condense onto

4. Why does a saturated parcel cool more slowly than a dry one?

Rising air parcel cools → because of pressure decrease → and expansion → thus loss of energy → so decreasing temperature → called adiabatic cooling → and for dry air if the parcel is unsaturated no condensation occurs → because all the water remains vapor → and there’s no extra heat to offset the cooling → so DALR is followed → but once the parcel reaches saturation at RH100% and T=Td condensation begins → because air cant keep all the water as vapor anymore → some changes into liquid now → this occurs above LCL → and since condensation releases latent heat → from energy released by liquid formation → parcel thus gains heat as it rises → released latent heat offsets the expansion cooling → so cooling is still occurring but not as fast → and this is the MALR → so no 10 K/km as per DALR but more 6 K/km or even 3 K/km → because condensation amount depends on water vapor present → so MALR isn’t fixed because warm humid air releases more latent heat and thus cools more slowly → but cold dry air releases heat too, just less → so behaves more similarly to the DALR

The in-depth “why’s” for “How well does the DALR actually explain the real atmosphere’s lapse rate?”

What is the DALR?

Dry Adiabatic Lapse Rate

• This is the temperature change of a parcel of unsaturated air that rises without exchanging heat with its surroundings

The first step begins with the reason why rising air cools at all.

• As a parcel rises, the air above it presses down on it

• But the higher you go, the less air there is above it, which is referred to as pressure

• Lower pressure means the parcel has more room to expand

• That expansion though requires work

• And that work must come from something

• That something is the parcel’s own energy

• As it takes from its own internal energy to work, the lower the temperature of the parcel becomes

• Rising air thus cools, and sinking air warms, no environmental heat exchange required

The second step is understanding the DALR where:

• Td = -g/cp where g = gravity and cp = specific heat of air

• Td = 9.8 K/km

• So every 1km a dry parcel rises, it cools by around 10°C

• But is that accurate to the real atmosphere?

• No, it cools at around 6.5 K/km actually

• The DALR overpredicts cooling with respect to the observed atmosphere

• So what failed?

The third step, the failure in the word “dry”… The DALR assumes that there is:

• No condensation

• No clouds

• No latent heat being released

This is not accurate to the observed atmosphere we know. Air contains water vapor, and we know that when it rises, it cools, and reaches saturation.

So when RH = 100%, and T = Td, the LCL is reached, known as the base of the cloud. Above the LCL, condensation occurs and water vapor is turned into liquid droplets in which latent heat is released from the energy. And THAT is where the answer lies.

The air parcel, above the LCL, is still cooling from expansion but now also being heated as it condenses… This competition doesn’t balance each other out, but simply cools the parcel slower than if there was no condensation and thus heat generation.

So, enter the Moist Adiabatic Lapse Rate, or MALR. Above the LCL, the air parcel follows this path, no longer the DALR. It is often:

• 6 K/km or 3 K/km

• But in cold, dry air it comes closer to the DALR’s 10 K/km because less moisture means less heat being released

Note that the MALR is not constant, unlike the DALR which is fixed at 9.8 K/km. This is because latent heat depends on multiple things.

1. Temperature

2. How much moisture there is

3. Pressure

All three can change how air and moisture interact, impacting it’s ascent.

Thus, the DALR can not explain anything above the LCL and therefore definitely not the stratosphere as the DALR states that temperature decreases with height. However, we know that in the stratosphere the higher the altitude the warmer it is as a result of the ozone layer.

But, it does explain the tropospheric environment below the LCL where there unsaturated air rises.

The in-depth “why’s” for “Where does a rising parcel form a cloud, and why?”

Step 1:

When an air parcel rises, it’s usually because the surface is warmed by the incoming solar radiation. That warm air becomes less dense than the surrounding cool air, becoming buoyant, and rising. As it rises, the pressure decreases, and the parcel expands, using internal energy, thus cooling from the loss. This is adiabatic cooling, as no outside source beyond the internal energy of the air parcel led to the temperature change. Below the cloud base, the air parcel cools following the DALR at 10°C per km.

Step 2:

Before condensation begins, the parcel is unsaturated. But as the parcel temperature decreases, the actual water vapor content stays the same. It’s the capacity that changes, and in this case, shrinks. The dew point temperature remains constant during dry ascent as well, since the dew point depends on the amount of vapor present, which doesn’t change.

Step 3:

Since that capacity decreases with temperature, the relative humidity therefore increases. The water vapor content, however, remained constant. So as the relative humidity increases as per the shrinking capacity to hold water vapor and the constant amount of water vapor but growth compared to the shrinking capacity, the RH eventually reaches RH = 100%, saturating the air parcel and reaching the temperature that equals the dew point.

Step 4:

Condensation then begins, as the air cannot hold all that water as a vapor. Liquid forms, and the excess water forms the visible clouds. The LCL is the cloud base, where everything above it is saturated cloudy air and below it is moist and humid air that isn’t saturated enough to form a cloud.

Note: The control for the LCL height is dependent on,

• Surface temperature (T)

• Dew point temperature (Td)

• And the gap between them

If the surface temperature, or T, is warmer than the dew point temperature Td, then the parcel must cool a lot before saturation. So the LCL, and cloud base, are higher. The same case vice versa.

The in-depth “why’s” for “What three ingredients must come together for a cloud to form?”

A cloud needs three things.

1. Water Vapor

2. Cooling to saturation

3. Condensation nuclei (CCN)

Ingredient 1: A cloud is made of water, therefore it needs water vapor.

• Clouds specifically form from the transition of water vapor to liquid water

Thus, if there is no moisture in the air, there is nothing to condense into a liquid. This is why you do not see clouds in deserts.

Ingredient 2: Moist air does not mean a cloud, saturation does.

• When RH = 100% and T = Td, an air parcel becomes fully saturated with water vapor.

This is because the parcel rises → pressure decreases → parcel expands → parcel cools → but dew point and water vapor content remain constant. But eventually, the temperature falls enough to read the dew point, hence T = Td. The altitude in which this is met is called the LCL, and is the base of the cloud.

No cooling to saturation = No cloud

Ingredient 3: Water vapor cannot condense by itself.

• Water molecules cannot simply connect to one another, they need a binder to stick onto.

This surface is found on tiny particles called the CCN. Some examples include dust, smoke, ash, pollen, etc. Water can stick onto these particles, and grow as droplets the more water sticks. It is necessary for a visible cloud to form.

This is why in round 2 with saturated air but no smoke, there was weak cloud formation. But in round 3, with saturated air and smoke there was visible clouds. The smoke provided the stickable surface.

The in-depth “why’s” for “Why does a saturated parcel cool more slowly than a dry one?”

First, what is true for both dry and saturated air?

• A rising air parcel cools because pressure decreases with height

• Lower pressure = expansion

• Expansion = work

• Work comes from internal energy, and that loss drops the parcel’s temperature

This cooling process is consistent between both dry and saturated air.

An unsaturated parcel means there is no condensation occurring, no cloud droplets, no phase changes and no latent heat being released. The parcel has one thing impacting it’s temperature: the cooling from expansion.

• This is the dry adiabtic lapse rate

As for a saturated parcel, it continues to cool as it rises. But, it reaches a point where RH = 100% and the parcel’s temperature is now equal to the dew point. Thus, condensation begins. This is at the LCL. Above that, air parcels become saturated. The parcel is not just expanding and cooling like the unsaturated dry parcel, but it’s condensing into liquid.

This is the key, because condensation releases energy in it’s process which releases latent heat. This heat warms the parcel, but not enough to stop it’s cooling. This heat does not come from anything other than the parcel itself, thus remaining adiabatic.

• This is the moist adiabatic lapse rate

The key difference between both is that of the two, one has a new input albeit from itself. This input, latent heat, makes it so that a saturated parcel cools more slowly.

What are the parent questions for class 3.2?

1. Why do some clouds stop as flat cumulus puffs while others grow into 13-km-tall cumulonimbus?

2. Why can two storms with the same cloud-top height still differ in intensity?

3. Why do operational meteorologists use a skew-T log-p diagram instead of the simple linear T-vs-z plot we used in class?

The simple “why’s” for parent questions 3.2

1. Why do some clouds stop as flat cumulus puffs while others grow into 13-km-tall cumulonimbus?

Clouds start the same with air parcel rising → eventually reaching saturation → leading to condensation → thus the LCL, or cloud base, is created → but the LCL only says where the cloud starts, not how tall → height depends on parcel staying warmer than environment above LCL → because it keeps accelerating upward above the LFC → as buoyancy keeps accumulating, cloud grows into tall cumulonimbus → but then the parcel matches the temp of the environment → loses buoyancy → no longer goes upward and hits a ceiling called the EL → if EL is low, shallow cloud, if high, tall cloud → when it reaches EL, it can’t rise so it goes sideways and builds the anvil

2. Why can two storms with the same cloud-top height still differ in intensity?

Cloud top height only says when the parcel stopped rising, not strength → cloud top is usually the EL → and two storms can have the same EL → but what matters is the strength of the upward acceleration of parcel below EL and above LFC → and acceleration is determined by temperature in that warmer air rises faster → albeit warmth isn’t the only factor → vertical distance is too → think fetch, more distance means more time to grow in power → positive buoyancy over a deep layer creates stronger updrafts → this is CAPE where the energy of a rising parcel is converted into motion → so one storm may be a little warmer than the environment as it goes to the EL while another is a lot warmer with that same depth → both have the same height → but one is a lot stronger because more available energy from the parcel being warmer than environment leads to stronger updrafts

3. Why do operational meteorologists use a skew-T log-p diagram instead of the simple linear T-vs-z plot we used in class?

The atmosphere works through pressure changes, not simply height → air rises, pressure decreases, etc etc causes cooling → parcel motion controlled by pressure, not so much height → meteorologists track the atmosphere in hPa, not km, m or ft → and pressure controls buoyancy and adiabatic cooling → and since pressure decreases with height exponentially the air gets thinner upward so a linear axis would distort atmosphere → so log pressure is used so that plotting and interpreting vertically is easier → plus the rising parcel must be followed easily with respect to the environment such as → is it warmer → is it buoyant → is it colder → will it sink → so they need to see dry and moist adiabatic rise, dew point, cloud base, and storm top all together → so T-vs-z becomes limited with all those variables → since if temperature were straight lines the references lines pile on top of one another and cannot be read → so the temperature lines are tilted → and skewing them makes all the variables easier to separate and read visually → and because the format makes the plot easy to put all the necessary variables, it is easy to identify the LCL, LFC, EL, CAPE, CIN in the diagram → this is better for forecasting unlike the T-vs-z

The in-depth “why’s” for “Why do some clouds stop as flat cumulus puffs while others grow into 13-km-tall cumulonimbus?”

Some context,

• The LCL tells you where the cloud first appears, but not how tall it will be

Once a parcel becomes saturated and visible as a cloud, the next thing is whether or not the parcel is still warmer than the environment above it.

• If it is, it stays buoyant and continues to accelerate upward

• If not, and it becomes colder, it becomes negatively buoyant and stops rising

Thus, the cloud height is controlled by the temperature difference between the air parcel and it’s environment, not condensation.

Note that a cloud becomes tall only if it’s parcel path remains on the warm side of the environment temperature profile for a long vertical distance.

• This matters because at that same pressure, warmer air is less dense and less dense means positive buoyancy. Thus, the growth of a cloud is reliant on the buoyancy.

But some clouds remain shallow, which forms when parcel rises to the LCL, becomes visible, but then stops fairly soon. This can be for two reasons:

1. The parcel itself didn’t get much warmer than it’s surrounding environment, so even though it condensed and formed a cloud the positive buoyancy it had may not have been enough to keep rising far.

2. The parcel temperature became equal to the environmental temperature, stopping the upward acceleration. This level is called the Equilibrium Level, or EL.

However, some clouds grow into huge cumulonimbus clouds. This cloud forms when the parcel remains warmer than the surrounding environment through a very large vertical layer. Thus,

• The parcel maintains positive buoyancy

• Continues to accelerate upward

• The updraft stays strong

• So cloud growth continues, sometimes for many kilometers

This happens when the parcel rises past the Level of Free Convection, or LFC. This is the level where the parcel switches from negative buoyancy to positive buoyancy. Above the LFC, the parcel is warmer than the environment so it does not need to be pushed upward mechanically. It simply can rise on it’s own.

If the layer between the LFC to the EL is long, the parcel has a wide distance over which it can continue to gain upward motion. This is where the tall convective tower comes from.

As for the cloud top, it flattens out into an anvil because it reaches the EL. The parcel is no longer warmer than the environment, and it loses it’s positive buoyancy so it can no longer move upward. Rather, it spreads sideways hence the anvil.

Another thing yet to be mentioned which plays an important role is CIN, or Convective Inhibition. From the surface to an altitude, the parcel is cooler than it’s environment, therefore it is negatively buoyant. This layer is the CIN barrier, which is an energy barrier resisting the ascent of an air parcel. So even if the ingredients for a deep storm are there, if there is not something to force the air parcel through the barrier then a storm will not form.

Examples of that “something” include:

• Strong surface heating

• Frontal lifting

• Convergence

If the parcel cannot get through the CIN to the LFC, there is not much significance. So, for a cumulonimbus to form, you need to be able to punch through the CIN to the LFC and have a deep positive buoyant layer.

The in-depth “why’s” for “Why can two storms with the same cloud-top height still differ in intensity?”

Cloud top height is not associated with storm intensity. It simply tells you how high the parcel got before it was no longer positively buoyant. Not how intense that parcel buoyancy was. Hence why two clouds can have the same EL, but different severity. To compare strength, the acceleration of a parcel along a height is what matters, not where it stops.

Then, the question becomes how much upward acceleration did the parcel experience between the LFC and EL?

• How much is the air being pushed upward?

• If the parcel is warmer than the environment at the same pressure, it’s less dense and so more buoyant, accelerating it upward

• So strength of a storm depends on how much warmer the parcel is than it’s environment and how deep through the vertical layer the positive buoyancy lasts

This is known as…

CAPE, or Convective Available Potential Energy.

• Shallow cumulus clouds have a small CAPE value

• Deep cumulonimbus clouds have a large CAPE value

A higher CAPE values is related to stronger acceleration, updrafts, and severity, hence “convective potential”.

CAPE is specifically the amount of positive buoyant energy that can be turned into upward motion. Or, accumulated total positive buoyancy from the LFC to the EL.

The in-depth “why’s” for “Why do operational meteorologists use a skew-T log-p diagram instead of the simple linear T-vs-z plot we used in class?”

Meteorologists need a diagram that plots multiple variables, like:

• Pressure

• Parcel lift

• Dry and moist adiabats

• Dew point

• LFC

• LCL

• EL

• CAPE

• CIN

All together on the same plot.

Thus, the Skew-T log-p diagram was born.

The issue with a simple T-vs-z plot is that we are not examining height, but pressure because that is how the atmosphere is measured. Pressure is reflective of the amount of air above an air parcel, which controls expansion, buoyancy, adiabatic cooling, and more. It is fundamentally more ingrained into atmospheric explanations than height.

The y-axis must also be logarithmic because pressure doesn’t decrease linearly, it decreases exponentially. The vertical spacing is different between different pressure levels, so a linear graph would distort the atmosphere. When turned into log, the spacing is more clear and easier to read/interpret.

Pressure increases downward because surface has the highest pressure, that’s it. But the tremperature lines are skewed, which is confusing. They are diagonal, not vertical because if the temperature were straight the reference lines would become unreadable. Skewing the temperature axis lets us read the dry and moist adiabat lines, mixing ratio line, and dew point lines cleanly without confusion so we can trace the path of the parcel without losing it.

We also need the dry and moist adiabat lines so we can trace the path of a lifted parcel from the surface, through the dry adiabat, to the LCL, past it to the moist adiabat, and identify where the LFC, EL, CAPE, and CIN are. With a Skew-T, we can plot where CAPE is based on if the parcel is warmer than the environment on the Skew-T plot because it is the shaded region ebtween the temperature lines.