Chapter 5

Soundings

• There are four basic types of sounding observations.– (1) Radiosondes

• An instrument package lifted by a balloon with sensors for pressure, temperature, humidity.

– (2) Pibals (Pilot balloons)Carry no instruments. Are usually

tracked with theodolite. The balloon is assumed to rise at a constant rate once the correct amount of gas is placed in the balloon.

By knowing the time of flight and the elevation and azimuth angle to the balloon, the position of the balloon, thus the wind speed and direction at various heights can be obtained.

– (3) RawinsondesCombines radiosonde

(instrument package) and method of tracking:

Tracked by either a radio direction finder antenna, a radar, or by GPS

– (4) Dropsondes- dropped from an

aircraft or from a constant pressure balloon

A new advanced category:Remote Sounding Technologies

• Satellite Soundings– T, WV, Feature Tracked Winds– IR, Microwave, GPS Met and Occultation– Responsible for advances in NWP, survival in the

face of less traditional U/A obs

• Other technologies– Wind Profilers (+RAS)– SODAR– Surface-Based Microwave

(2) Upper-air Maps• Remember the format for

plotting data on an upper-air map.

• Error on pg. 5

Radiosonde/rawinsonde - a circle.Aircraft observation - a square.Satellite derived wind - a star.

–The height tendency is plotted to the lower-right of the station circle.–This is not the position of the pressure tendency on surface maps.

•That goes to the right of the station circle.

(3) Sounding Diagrams• Sounding diagrams are used to

represent the character of the air by profiles of temperature, moisture, wind as measured vertically through the atmosphere above a location.

• Common ones used are:– Stuve diagram (textbooks)– Emagram (Europe)– Tephigram (UK and Canada)– Skew-T log-P diagram (real women and

men)

• Pressure may be plotted on a linear vertical scale, or on a logrithmic vertical scale.

• Temperature is plotted on the horizontal axis - opposite to the convention of plotting data which puts the independent parameter on the horizontal axis.

A Log-pressure diagram A linear pressure diagram

A Stuve diagram A Skew-T log-P diagram

• There are several sets of lines on these diagrams and a point plotted on the diagram has a different meaning depending on which set of lines you are considering.

• Other lines on the Skew-T diagram– Potential Temperature (also called dry

adiabats).• Potential temperature is the temperature a

parcel of air would have if it descended to a particular pressure level (no exchange of heat with the environment).

• The standard reference pressure is 1000 mb.• Can by calculated by Poisson’s Equation.

TPoP

Rdc p

Po = reference pressureRd=gas constant for dry air 287J/kgcp=specific heat of dry air at constant pressure, 1004J/kg

• (Water Vapor) Mixing Ratio: Ratio of mass of water vapor to mass of dry air (g/kg, usually).

• Saturation Mixing Ratio lines: the value of the mixing ratio of saturated air at the given temperature and pressure with respect to a flat water surface.

• Determined using the Clausius-Clapeyron Equation:

rs ro e

L

Rv

1

To

1

T

ro = 0.611kPaTo=273.15oKRv=461J/kg oKLv=2.5 x 106 J/oKLd=2.83 x 106 J/oK

This uses “r” to represent mixing ratio. More often “w” is used.

• Equivalent Potential Temperature: The temperature a parcel of air at a given temperature and pressure would have if it were saturated, and if all that water were condensed and removed and the parcel brought down to some reference level, usually 1000 mb.

• Converting water vapor to liquid water releases latent heat which is then absorbed by the gas molecules of the air, so the air temperature increases. So, an air temperature’s equivalent potential temperature is always warmer than its potential temperature.

• On board, the four lines and their relationship.

(5) Vertical Derivatives and the Hydrostatic Equation

• Consider the vertical derivative of temperature with respect to pressure. This is simply the instantaneous change of temperature with pressure at some level; or

• One could also determine

P

T

P

T

Tz

• Procedure:– Pick the level (pressure) at which you wish to

compute the derivative. – Draw a line tangent to the temperature profile at

that level. – Going from higher pressure to lower pressure, pick

a point about 50mb lower along the tangent line and determine the pressure and temperature.

– Pick a point about 50mb above along the tangent line and determine the pressure and temperature.

– Determine (P1-P2) and (T1-T2) from these values, making certain that P1 and T1 are the values lower in the atmosphere.

• We usually would like to have these derivatives (of some element); such as temperature, with respect to height. So, it is useful to be able to convert from pressure derivatives to height derivatives.

• We can get that using the Hydrostatic Equation.

• The Hydrostatic Equation results from considering the vertical forces acting on an air parcel which is not moving. – These are gravity (directed down) and – the vertical pressure gradient force

(directed up) which results from pressure being higher near the Earth’s surface and less as height increases.

• If the air is not moving vertically, the magnitude of these forces are the same.

• If we consider unit mass (mass=1), then we can cancel it on both sides and we are essentially dealing with accelerations.

m

Pz

mg

• or• The Hydrostatic equation. • However, this has density in it which is

difficult to measure and most thermodynamic diagrams don’t have scales for density.

• We can get rid of density using the Ideal Gas Law equation.

1

Pz

g

Pz

g

•Considering the Ideal Gas Law equation:–V = volume–n = number of molecules (moles) of the gas.

–R* = universal gas constant = 8.3169 J/moleoK •If we divide both sides by V, volume and, if we multiply both sides by:

Where md is the molecular mass of dry air/mole, we get:

But, (n × md) is simply the mass, so we can replace with density, ρ.

PV nR*T

mdmd

P n mdR

*T

mdV

n mdV

• And, is simply the gas constant for dry air, Rd which equals 287 J/kgoK. (note error, pg. 17).

• This results in:• Then, we can combine the hydrostatic and ideal gas law

equation.

• Writing the Ideal Gas Law equation for an expression for density gives:

• and substituting into the Hydrostatic Equation gives:

R*

md

P RdT

Pz

g

P

RdT

Pz

Pg

RdT

• Consider this equation for dry air, we can write it as:

• Which is:• We can see that pressure decreases in a natural

logarithmic manner from the equation showing the derivative of pressure with height.

• And, that change of pressure with height is dependent on temperature.

• If a layer of the atmosphere is isothermal, changes in height of pressure surfaces are directly proportional to the logarithm of pressure.

1

P

dP

dz

g

RdT

TR

g

dz

Pd

d

ln

• The heights, as related to pressure, on a sounding diagram are from the standard atmosphere, and would not be correct for the actual atmosphere. However, we can make a height scale on the sounding diagram which fits the actual atmosphere.

(6) Lapse Rate

• Lapse rate is the rate at which temperature decreases with height.

• The Environmental Lapse Rate is the real atmosphere as observed or modeled (forecast sounding). It varies on a real sounding, of course (the slope of the T trace)

• 9.8 (~10) C/km is the dry adiabatic lapse rate. Commit to memory for life.

• The moist adiabatic lapse rate varies with height, but it is around 6 C/km in lower trop.

Tz

(7) Vertical Momentum Equation and the Buoyancy Equation• Suppose the atmosphere is not “in balance” as

expressed by the Hydrostatic equation. Then, there is vertical motion.

• The Vertical Momentum Equation expresses this situation.

• This is the acceleration produced because of a difference between the gravitational force/unit mass and the pressure gradient force/unit mass.

• “D” is called the total derivative - the rate of change of the value of a quantity associated with a particular air parcel (Following the motion).

Dw

Dt g

1

Pz

• This expresses what is happening to an air parcel that is moving vertically.

• The term is normally negative, since pressure decreases upward and positive “z-direction” is upward.

• (Note: error, first line, paragraph 4, pg. 21. Drop the word force.

1

Pz

• The air around the parcel - assuming it is not moving vertically - is expressed by the hydrostatic equation which, if we move all terms to the right of the equal sign, can be written as:

• Where o is the density of the environmental air.

• The density of the parcel can be written as a perturbation of the environmental air density; or: o + ’

0 g 1

o

Pz

• The vertical momentum equation then becomes:• Subtracting the environmental hydrostatic equation

from this one (change sign and add) gives:• Combining terms and rearranging gives:

• From the second term above, we can see that: • So we can substitute - g for

• And get:

Dw

Dt g

1

o '

Pz

0 g 1

o

Pz

Dw

Dt

1

o

Pz

1

o '

Pz

Dw

Dt

1

o

Pz

'

o '

g 1

o

Pz

1

o

Pz

Dw

Dt g

'

o '

• So, if ’ is negative, (density is less than the environment - which occurs when the temperature of the parcel is warmer than the environment) then the right side of the equation is positive and the parcel accelerates upward.

Dw

Dt g

'

o '

• However, as an air parcel rises of sinks through other air, air molecules drag against the parcel creating a drag force. This is usually small enough that for most purposes it can be ignored.

• The vertical momentum equation can also be written using potential temperature.

• The right side does not have a negative sign, because a warm parcel would have a higher potential temperature, just as it would have a lower density. (The density term is not in the equation.)

Dw

Dtg

'

o

(8) The Thermodynamic Equation

• This equation expresses how the potential temperature of an air parcel changes over time due to various processes (primarily adding or removing heat energy by phase changes or with the environment).

• If there is no phase change occurring, and assuming no exchange of heat with the environment, the right side is zero and there is no change of potential temperature.

• On a thermodynamic diagram, you are following parallel to the dry adiabats.

DDt

T

Q

c p

• If we take a parcel of air and lift it, (assuming it is not saturated), we follow parallel to the dry adibats (potential temperature lines).

(9) Latent Heat Release

• What happens if the air becomes saturated and continues to rise?

• If Latent Heat is being added, what is happening to θ?

• Remember: It becomes saturated at the Lifting Condensation Level.

Wallace and Hobbs(the text you bought)

• Read sections 3.4, 3.5, 3.6. Especially concentrate on Conditional Instability, which is not covered in the online text.

• A parcel is conditionally unstable when it is stable when lifted dry adiabatically, but unstable (warmer than the environmental temperature) when lifted while saturated (moist adiabatically)

Stability and Observed/Environmental Lapse Rate (Γ)

(1) Is Absolutely Unstable Air.

(2) Is Absolutely Stable Air.

(3) Is Conditionally Unstable Air.

Real World Examplesof Static Stability

• Cross your fingers

Homework (Due next Wed.)

1. Find a current/recent sounding in the warm sector of a mid-latitude system, and print it as a Skew-T. Identify which layers are stable, conditionally unstable, isothermal (or nearly so), and inversions. Note: If there are no conditionally unstable layers, get another sounding.

2. Are there any unstable layers? Why or why not?

3. What does an isothermal layer look like on a Skew-T? What is the stability?