What Goes Up ...

Hot Air Balloon over
Watershed Farm  at the crest of
the Oak Ridges Moraine 2002

What Goes Up ... must come down. One of my topics to teach in the Training Branch of the then Atmospheric Environment Service in the mid-eighties, was the Tephigram (invented by Napier Shaw in 1915). The apparent mash of lines baffled many of the students but the Tephigram Thermodynamic Chart was really a thing of beauty. Those lines could reveal the nuances of the current state of the atmosphere that were unavailable elsewhere. The Tephigram was all about conserving energy (entropy) - not only the energy in the atmosphere but the work required by meteorologists to really understand the weather.  

I have frequently used the metaphor of "hot air balloons" to place the image of air parcels in the reader's imagination. The atmosphere's reality is even simpler and starts with the Ideal Gas Law. There will be no complex mathematics or science but at the end of this blog, you will be able to read the cloud shapes to deduce the vertical profile of the atmospheric ocean - and vice versa.  It really is that simple. 

The Ideal Gas Law states that for a parcel of air, the multiple of Pressure times Volume is directly proportional to its Temperature (PV=nRT). If we do not change the energy content of that parcel, one can follow the air in its vertical travels within the atmosphere. If the hot air balloon (of constant volume) remains warmer than its environment, it will continue to rise away from its starting point - an unstable situation. A balloon that becomes cooler than its environment must sink back to where it again matches the temperature of the vertical profile- a stable environment. This is the basis of thermodynamic graphs like the Canadian Tephigram or the American Skew-T. These graphs both have a vertical axis of height that mimics the height in the real atmosphere. 

Knowledge of the vertical profile of the atmosphere is absolutely essential if one wants to understand and forecast the weather. Here is where my favourite type of balloon was essential. For every parcel of air, meteorologists need to know the pressure, dry-bulb temperature, dew-point temperature and wind. The drift of the balloon in time and space allows the calculation of the atmospheric winds. 

Sable Island Radiosonde "Shack" May 1985 off the
southeast shore of Nova Scotia. Releasing a weather balloon
 is far more challenging than you might suspect. 

These atmospheric measurements are typically measured twice a day using radiosonde instruments tethered to a weather balloon. Similar measurements can now be more economically made using satellite data. In addition, commercial aircraft can continuously sample these quantities and relay the information to be fed into the computer simulations of the atmosphere. Times may have changed, the the vertical information about the atmosphere is still the crux of the forecast. 

Introducing the Lines of the Tephigram 

The pressure at any level of the atmosphere is just the weight of the air above that level. As one travels upward within the air column, there must be less air above and thus the pressure must be lower. Keeping the energy content of the constant volume air parcel unchanged, the temperature of the air parcel must decrease as the pressure decreases (P varies directly with T). These are adiabatic motions in which neither heat nor moisture are added to the parcel. A parcel of air that is not saturated, cools at the dry adiabatic lapse rate of 9.8 degrees Celsius per kilometre rise in altitude. The "Dry Adiabats" are straight brown lines in the Tephigram. 

But air parcels contain moisture! If the moisture in that air parcel remains as water vapour, that air parcel still cools at the dry adiabatic lapse rate of 9.8 degrees Celius per kilometre. That rate of cooling continues until the temperature of the air parcel reaches the dewpoint. At that temperature, the air parcel is saturated and can no longer contain all of the water vapour - some of which must condense out as water droplets. That precipitation falls out of the parcel and is gone... 

The dashed, brown Mixing Ratio Lines in the above graphic, start at the Parcel Dew Point Temperature. The dew point which is a measure of the amount of water vapour that a saturated air parcel can hold at that pressure has a lapse rate of about 1.8 degrees Celius per kilometre (the dashed, brown, straight lines). The amount of moisture within that air parcel is read in grams of water per kilogram of dry air. That quantity is the brown number read by following the Mixing Ratio Lines down to the bottom of the Tephigram. 

The condensation process releases the heat of vaporization (latent heat) into the air parcel which offsets some of the cooling of the dry adiabatic lapse rate.  From this point upward, the parcel of air is saturated and the excess water vapour is shed as precipitation while the latent heat energy is contained within the air parcel. 

The moist adiabatic lapse rate is only about half of the dry adiabatic lapse rate - 4 to 6 degrees Celius per kilometre. The amount of heat of vaporization released into the parcel is dependent on the amount of water vapour condensed out. There is less water vapour in the upper atmosphere so these curved moist adiabatic lapse rate lines straighten out at higher elevations to become nearly parallel to the dry adiabatic lapse rates. The "Moist Adiabats" are shaded, curved brown areas on the Tephigram. 

Note that the amount of moisture remaining in the saturated parcel rising along the moist adiabat can be read by following the Mixing Ratio Lines down to the bottom of the Tephigram. 

When saturated parcels of air start to descend, they immediately are no longer saturated and warm at the dry adiabatic lapse rate. This is what happens when virga falls from elevated clouds but evaporates before reaching the ground and becoming classified as bonafide precipitation. 

The vertical, adiabatic path of any parcel in the atmosphere can be followed or predicted using these simple concepts and the graphs that describe them. The main reason that tephigrams are used by the Meteorological Service of Canada is the property that areas contained by the curves have equal energies for equal areas. This is immensely valuable when diagnosing convective storms.

Applying the Tehpigram Concepts to a Convectively Unstable Atmosphere

The following graphic summarizes the main points of interest for a convectively unstable Environmental Temperature Profile (ETP) which is the heavy black line in the following graphic. The above concepts will be revisited and perhaps better explained using this example. 

A simplified version of the Tephigram with the Important Levels Labelled
The Wet Bulb Potential Temperature is a conservative property characteristic
of  an air mass

An air parcel rising from Level A at Pressure p0 immediately becomes cooler than the Environmental Temperature Profile, ETP. That parcel will stop rising unless the Convective Inhibition (CIN) energy is provided by some lifting mechanism like wind turbulence. 

At point D, the parcel cooling along the dry adiabat matches the dew point that was lifted along the mixing ration lines. At Level B, the air parcel becomes saturated and can hold no more moisture. The  Lifted Condensation Level (LCL) is the base of the cloud. 

From Point D to C, the air parcel is still cooler than the environment and reliant on the lifting mechanism to keep it going upward. Wind turbulence is the most likely agent to get this work done. 

At Point C the parcel becomes warmer than the environment and rises like a hot air balloon. This is the Level of Free Convection (LFC). From C to E, the parcel accelerates upward gaining kinetic energy (the red hatched area identified as CAPE, Convective Available Potential Energy) on its journey. The level of maximum buoyancy is where the temperature excess above that of the environment is maximized. 

At Point E, the parcel becomes colder than the environment but gets to spend the kinetic energy that it picked up above C and the level of free convection. The rising parcel spends all of its convective energy (CAPE)  to reach Point F - and the convective cloud is Finished. 

Vertical Stability Determined by the Orientation of the  Environmental Temperature Profile (ETP)

The concept of vertical stability on the Environmental Temperature Profile (ETP) is essential to understand the clouds. Those ideas are explained again using the relative orientations of the ETP as compared to the moist and dry adiabats. 

Now to apply this information to cloud watching:

The cloudy bases at the Lifted Condensation Level (LCL) will reveal how the air parcel arrived at that level:

• surface heating and convective air parcel ascent
• turbulent wind mixing 

The cloud tops will reveal:

• how much energy the air parcels gained on their ascent
• the strength of the inversion

The cloud depth is either:

• for convective clouds the extent of the unstable layer from LCL through the LFC to E and finally F where all of the CAPE has been used up. 
• the amplitude of the gravity waves in the stable environment

If the air parcels are lifted by heating from the ground, the "hot air balloons" rise in an organized fashion to reach the lifted condemnation level. The cloud bases must be level and uniform.

If the cloud tops are like cauliflower blooms, the air parcels are rising vigorously in an unstable atmosphere with lots of convective, buoyant energy (CAPE). 

If the cloud tops are flat and smooth, the air parcels have reached their equilibrium level and expended all of their accumulated convective energy (at F for finished in the above graphic). 

Towering Cumulus viewed over New York State looking south across the St. Lawrence River from Brockville. An example of an unstable  Environmental Temperature Profile (ETP). Daytime heating of the surface does all of the work to lift the air parcels to the LCL and LFC. 

Suppose the air parcels are lifted by turbulent mixing, especially over rugged terrain. In that case, the cloud bases must be turbulent. As well as the lifted condensation level is distorted by the terrain and the nonuniform mixing of the air parcels.

Turbulent stratocumulus viewed over eastern Ontario looking northwest across some fine farmland. An example of turbulent winds lifting the air parcels to the LCL.

A stable environment is where the air parcel rises into a warmer environment which encourages the cooler parcels to return to their original level - starting point. A parcel that is descending in a stable environment remains warmer than the atmosphere and returns buoyant back to where it starts. The air parcel behaves like a rubber ducky in the bathtub. If one adds a horizontal wind to blow the rubber duck, the trace of the path of the duck is a gravity wave oriented perpendicular to that wind. 

If the environment is stable, look for stratiform, layered clouds and gravity waves. The wind at cloud level must be perpendicular to those gravity waves like waves on a lake. 

Regular bands of smooth-edged clouds reveal the gravity waves of air rising into and through the wave crests and then sinking into the troughs of the gravity waves. Classic gravity wave patterns are revealed when the flow straddles the lifted condensation level. One may be able to watch the cloud form on the upwind edges approaching the wave crest and dissipating tendrils subsiding into the troughs: The entire pattern tends to shift with the wind in the atmospheric frame of reference. 

The same circulations occur with or without moisture tracers. When the LCL is above the circulation there will be no cloud created. If the LCL is below the layer of gravity waves, all that might be witnessed is the regular cloud thickening in the crest regions or thinning in the wave troughs. 

In an unstable environment, a rising air parcel remains warmer than its environment and continues to climb away from its starting level. If the environment is unstable, look for cumuliform, convective clouds and cloud streets or streaks.  The wind at cloud level must be parallel to those Langmuir-type circulations. 

Langmuir Conceptual Model of Streaks in an Unstable Environment

Since the wind parallels the cloud bands, the lines will not shift significantly in any lateral direction. Individual cloud elements will move along that line in the direction of the wind.

Langmuir streaks are most commonly witnessed as snowsqualls which result when cold air flows over a warm body of water. Langmuir streaks also parallel the jet stream if the atmosphere has an unstable layer below the tropopause. 

The next step in making the Tephigram a vital tool to employ in understanding the weather is to add the hodograph the vertical plot of observed winds to the side of the chart. The hodograph includes the earth-frame winds as measured from the surface to as high as the weather balloon goes before it pops. Shifting winds in the vertical determine many meteorological quantities like thermal advection, helicity and storm structure.  

The Tephigram provides a great deal of information about the atmosphere. This Blog just scratches the surface but provides enough to understand and appreciate the cloud shapes.  

Phil the Forecaster at Training Branch 1986

The secrets of the real atmosphere are now at your fingerprints although I much prefer the atmospheric frame of reference winds - but that is another story. 

The characteristics of the bottom, sides and top of every cloud can be deduced by keeping this simplified Tephigram in mind. The Tephigram was my friend and a vital requirement to understand the actual atmospheric ocean - along with remote sensing (satellite and radar) of course... I never put myself in harm's way of the weather when I could study even the most severe conditions from a safe distance.

Warmest regards and keep your paddle in the water,

Phil the Forecaster Chadwick

PS: If you made it this far, give yourself a gold star! You are on the way to understanding the wonder of the weather.