1. Tephigrams and Hodographs

2. TEPHIGRAM APPLICATIONS
Determining Frontal Heights
Temperature Forecasting
Wind Forecasting
Stratiform Cloud Layers
Fog & Stratus Forecasting
Precipitation Typing
Identifying Significant Icing Layers & FZLVL
Anomalous Propagation
Convective & SVR WX forecasting
Many other possibilities
XTH Tephi Program provides calculations related to Icing, Thermal Advection, Cloud Layers, convective indicies, etc..
(demonstrated in lab 1)
…. To make optimal use of tephigram and hodograph information, background knowledge is required.

3. The Tephigram

4. Tephigrams and Hodographs
143 radiosonde ascents in NA every 12 hrs
radiosondes measure T, Td, p, wind dir, wind speed, height
information is displayed on tephigrams and hodographs
information also plotted on constant pressure charts

5. Tephigram tephi (temperature - phi) gram (diagram)
temperature - entropy diagram
thermodynamic chart
area is proportional to energy (work)

7. TO PRINT FOR STUDENTS….
1. What Isopleth does the Orange line represent? Mixing Ratio Line
2. What is the exact value of this line (with proper units)?
4 gm water vapour per kg dry air or 4gm/kg
3.  What Isopleth does the Yellow line represent? Isotherm
4. What is the exact value of this line (with proper units)? 10ºC
5. What Isopleth does the Blue line represent?
Dry Adiabat or Line of constant Entropy or Isentrop
6. What is the exact value of this line (with proper units)? 290K
2 ways to find ….
(1) read directly off side bar
(2) run down to 1000 hPa and read off temp & add to 273K.
7. What Isopleth does the Pink line represent? Isobar
8. What is the exact value of this line (with proper units)?850 hPa
9. What Isopleth does the Purple line represent? Saturated (or Wet) Adiabat
10. What is the exact value of this line (with proper units)? 14ºC

8. Isopleths on the Tephi
isobars (hPa) (also labelled gpm/gpf for the ICAO standard atmosphere)
isotherms (oC)
dry adiabats (oK at 1000 hPa)
saturated adiabats or pseudo-adiabats (oC at 1000 hPa)
saturation mixing ratio (g water vapour per kg dry air) (wrt water T > -40 oC)

9. A Tephigram has 3 lines plotted on it.
(1) the Dry Bulb Temp (T) curve (solid line), which describes the ELR
(2) the Wet Bulb Temp (Tw) curve (dashed middle line)
(3) the Dew Point Temp Curve (Td) (left-most dashed line)
At a specific place (KBIS) and at a specific time (12Z Mar 8, 2005).
Simply point out the three curves plotted on the tephigram
(Radiosonde measures the T and Td and calculates the Tw)
Dry Bulb Temperature Curve (T)
Wet Bulb Temperature Curve (Tw)
Dew point Temperature Curve (Td)
- And when we assess the ELR – we look at the Dry Bulb Curve of the environment.

10. Frost-Point Nomogram

12. Nomograms

13. Most Important Temperature and Humidity Parameters
T = dry bulb temperature (oC)
Td = dewpoint temperature (oC)
Tf = frost point temperature (oC)
Tw = wet-bulb temperature (or adiabatic wet-bulb temperature or pseudo-wet-bulb temperature) (oC)
θ (theta) = potential temperature (oK)
θw (theta w) = wet-bulb potential temperature (oC)

14. Td dew point temperature
temperature to which a parcel of air must be cooled at constant pressure and constant water vapour in order for saturation to occur
for vertical motion, Td warms or cools along the same r (mixing ratio) line if no vapour added or subtracted

15. Tw adiabatic wet-bulb temperature or simply the wet-bulb temperature
slightly less than Tiw the actual wet-bulb temperature
can be treated as the actual wet-bulb with little error
temperature an air parcel would have after:
a) adiabatic cooling (ascent) to saturation and;
b) adiabatic compression (descent) to the original pressure in a saturated-adiabatic process.

16. Theta w potential temperature
potential wrt a selected reference level (1000 mb)
1. Potential temperature: if the temperature parameter is unsaturated, the parcel is taken dry adiabatically to 1000 mb at which point the potential temperature parameter is read. In this manner is determined from the values of T.
2. Saturated Potential temperature : if the temperature parameter is saturated, the parcel is taken along the saturated adiabat to 1000 mb at which point the saturated potential temperature, w is read.

17. More Important Parameters
r = mixing ratio (g/ kg dry air)
rs = saturation mixing ratio (g/ kg dry air)
Tv = virtual temperature (temp of dry air with same density) (oC)
RH = relative humidity (%) = e/es ~ r/ rs x 100%

19. Hodograph winds are plotted on polar coordinate graph
direction (degrees from N) and speed (kt)
wind at any level is presented by a point (labelled with height in 1000s of feet)
the wind at this level corresponds to the vector from the origin to the point
the wind shear is the vector between successive points

21. Conservative Properties
a conservative property of an airmass is one which does not change during a given meteorological process
Td, r, theta, thetaw are conservative
this makes analysis of aimass changes possible for certain processes
meteorologists can add value to model output through careful analysis of tephis

22. Processes Adiabatic: parcel does not exchange heat with environment
heat is added to or removed from parcel by external source
Isobaric:
one at constant pressure
Pseudo-adiabatic
during parcel expansion, saturation and condensation, with latent heat remaining but water precipitated out

23. Adiabatic Process
A process during which temperature may change, but no heat is gained from or lost to an external source.
Example:
1. Adiabatic expansion cooling of rising air parcels
2. Compression heating of sinking air parcels
ADIABATIC PROCESSES:
> Air is constantly moving in the atmosphere (moving up and down).
> When air moves rises or sinks, it moves into an environment with a different pressure than from where it came.
> The air will either expand, if it has risen to lesser pressures or compress, if it sank to greater pressures.
> At the same time as compressing or expanding in volume, the air’s temperature undergoes a change.
ENTROPY & ADIABATIC PROCESSES:
> No heat is being added or removed means the process is adiabatic and entropy remains constant.
> Whatever the change is in the internal energy, it will be proportionally matched by temperature.
An adiabatic process is also an ISENTROPIC PROCESS.

24. ASCENT/DESCENT LAPSE RATES
DALR =3°C is a physical constant; and
is used for unsaturated air only.
DRY
Temperature changes according to the DALR

25. POTENTIAL TEMPERATURE ()
The temperature a parcel would have if it were lifted up (or lowered down) dry adiabatically to 1000 hPa.
Can read the value of the corresponding dry adiabat
OR...
280°K
Bring parcel down dry adiabat and read T at 1000 hPa and add 273
a Dry Adiabat is a line of “Constant Potential Temperature”. (The entropy value does not change for an adiabatic process; nether will the potential temperature value.)
The given parcel, regardless of its pressure level, always has the same potential temperature value. (ex. 280°K above)
q Can be determined by: (in Kelvin)
a) lifting or lowering the parcel parallel to the dry adiabats to 1000 hPa, reading the corresponding temperature at 1000 hPa, and adding 273°C to convert into “Kelvin”.
b) an easier way is to read the value of the corresponding dry adiabat. A dry adiabat is a line of equal potential temperature.
7°C + 273= 280°K

26. Temperature changes according to the SALR
For Saturated Air.. SALR < DALR since latent heat release slows adiabatic cooling.
SALR varies depending on temperature & pressure; and assumes condensation or evaporation is taking place.
MOIST
If a parcel is saturated (RH = 100%)
As air rises … Cloud forms (condensation) - latent heat is RELEASED … and offsets the cooling (cools slower than the DALR) …
As air sinks … Clouds dissipate (evaporation) - latent heat is REQUIRED … and offsets the compression warming (warms slower than DALR)
Temperature changes according to the SALR
SALR
DALR

27. Wet Bulb Potential Temperature (w)
The temperature a saturated parcel would have if it were lifted/lowered moist adiabatically to 1000 hPa. This will be used for air mass I.D. -2
Can read the value of the corresponding wet adiabat
OR...
Өw can be determined by:
a) lifting or lowering the saturated parcel parallel to the moist adiabats to 1000 hPa, reading the corresponding temperature.
b) an easier way is to read the value of the corresponding moist adiabat running through qw (top left of tephigram).
Bring parcel down wet adiabat and read T at 1000 hPa
-2°C

28. Why Wet Adiabats Curve Example: For of a parcel of rising air…
At high mixing ratios:
More wv condenses
More latent heat is released
Smaller SALR & greater difference from DALR.
At low mixing ratios:
Less WV condenses
Less latent heat is released
Greater SALR (closer to the DALR)
Air holds a certain amt of moisture at a given temp & press
With decreasing T and decreasing P – the amount of moisture decreases
Thus the amount latent heat released varies too. Since it is the release of latent heat which offsets the cooling caused by expansion, if it varies so will the SALR
HENCE,
- In dryer air, the SALR is close to the DALR (i.e. since there isn’t much latent heat released… the SALR cools faster than at higher moisture when more latent heat is released)
The wet adiabats start out nearly vertical with a small SALR at high mixing ratios and bend to nearly the same slope as the dry adiabats at low mixing ratios.
Wet adiabats curve because the SALR constantly changes for different mixing ratios.

29. Normand’s Point: point where a dry parcel first reaches saturation when lifted.
> Located at the intersection 2 isopleths extending from: T (dry adiabat), Tw (wet adiabat) or Td(mixing ratio).
Normand’s Point (LCL) Td Tw T

30. Relative Humidity
Actual mixing ratio (r) is the value of the mixing ratio running through the Td.
Saturation mixing ratio (rw) is the value of the mixing ratio running through T.
RH(%) = r / rw X 100
950 hPa
RH = 4/8 x 100 = 50% 8 T 4 Td

31. STABILITY = the Atmosphere’s Tendency to Resist or Favor Vertical Motion.
5 Stability Types:
- Absolute Stability
Absolute Instability
Conditional Instability
Dry Neutral
Wet Neutral

32. STATIC STABILITY CLASSIFICATIONS
To classify a layer for its static stability, we look at the dry
bulb ELR as well as whether air is saturated or dry.
5 Classes of Static Stability:
1. ABSOLUTE STABILITY (Dry Bulb ELR = Inversion, Isothermal,Shallow)
2. WET NEUTRAL STABILITY (Dry Bulb ELR = Saturated Adiabatic)
3. CONDITIONAL INSTABILITY (Dry Bulb ELR = Average)
4. DRY NEUTRAL STABILITY (Dry Bulb ELR= Dry Adiabatic)
5. ABSOLUTE INSTABILITY (Dry Bulb ELR= Steep)
The different dry bulb ELRs represent environments which can either support or hinder vertical motion. There are 5 stability scenarios to be considered. See next slide for a pictorial overview.

33. For Convection Need an extra trigger for the following: (i.e. terrain)
Absolute Instability
Conditional Instability
Need an extra trigger for the following: (i.e. terrain)
Dry Neutral
Wet Neutral

34. Conditional Instability Dry NeutralDA SA
ISO.
Wet Neutral
Conditional Instability
Dry Neutral
Absolute Instability
Absolute Stability
This is a pictorial overview of the stability type areas on a tephigram. Hand out a copy to each student for reference.
It is animated, starting with absolute stability, then wet neutral, etc.
Point out for each classification, that “if the Dry Bulb ELR falls within this area for any atmospheric layer, then this will be the stability class for that layer”.
This will be detailed fully in the coming slides.

35. ABSOLUTE STABILITY Dry Air: Stable Saturated Air: Stable
Dry Bulb ELR must be an inversion, isothermal, or shallow. (Surface cooling, fronts, subsidence)
Layer resists vertical motion of any air parcels within the layer, whether saturated or dry.
Any ascent/descent must be forced (-ve area on ).
ExampleELR
Dry Air: Stable
In the case above, the dry bulb ELR is isothermal,
Both moist and dry parcels want to return to their original position = ABSOLUTE STABILITY.
A) In the case of an UPWARD PUSH, the parcel soon becomes colder (denser) than the environment and wants to sink back down to its initial level, where the temperature is the same as the environment.
B) In the case of an DOWNWARD PUSH, the parcel soon becomes warmer (lighter) than the environment and wants to rise to return to its initial level, where the temperature is the same as the environment.
Saturated Air: Stable

36. Saturated air: Neutral
WET NEUTRAL STABILITY
Dry bulb ELR = is along a wet adiabat (found sometimes within clouds).
Layer neither favours nor resists vertical motion of saturated parcels. (neutral)
Layer resists vertical motion of dry parcels (stable)
The dry bulb ELR lies along the saturated adiabat.
With this scenario, when a saturated parcel rises or sinks, it will remain at its new position along the same wet adiabat (SALR), and its temperature never varies from the the environment. It is neither stable nor unstable since it does not resist or favor vertical motion.
We call that neutral stability.
If the parcel should happen to be dry, it will rise or fall along a DALR. Its temperature will become colder than the environment while ascending, and will become warmer than the environment while descending. Therefore the layer resists the vertical motion of dry parcels.
Favorable atmospheric conditions: ELR found in clouds sometimes, especially if convective.
ELR=SALR
Saturated air: Neutral
Dry Air Stable

37. CONDITIONAL INSTABILITY Saturated air: Unstable
Dry bulb ELR must be between wet and dry adiabats… average. Common in various situations.
Layer favours vertical motion of saturated air.
Layer resists vertical motion of dry air.
ELR
Saturated air: Unstable
Dry Air Stable
Will occur when the ELR is average. Stability depends on whether the air is saturated or dry.
Average lapse rate common in many situations.
Slide animated. First the bullets above, then moist air discussion, then dry air discussion.
Layer favours vertical motion of saturated air, and thus is unstable for moist air.
Layer resists vertical motion of dry air, and thus is stable for dry air.

38. Saturated Air: Unstable
DRY NEUTRAL STABILITY
Dry bulb ELR along a dry adiabat. Occurs with surface heating or mechanical mixing.
Layer favours vertical motion of saturated air.
Layer is neutral to vertical motion of dry air.
ELR=DALR
Saturated Air: Unstable
The ELR lies along the dry adiabat.
With this scenario, when a dry parcel rises or sinks, its temperature never varies from the the environment. It is neither stable nor unstable since it does not resist or favor vertical motion. Its behavior is “neutral”.
If the parcel should happen to be saturated, its temperature will become warmer than the environment while ascending, and will become colder than the environment while descending. Therefore moist parcels favour vertical motion.
Favorable atmospheric conditions: daytime heating, advective heating, mechanical mixing.
Dry Air:
Neutral

39. Saturated Air: Unstable
ABSOLUTE INSTABILITY
Dry bulb ELR must be steep. Daytime heating.
Layer favours vertical motion for both saturated & dry air.
Vertical motion occurs with slight “kick”. (+ve area on 
Saturated Air: Unstable
ELR
In case above ELR is STEEP. If the temperature of the parcel is compared to the environment as the parcel gets displaced, it will be noted that moist and dry parcels will continue in the direction of the initial push.
A) In the case of an upward push, the parcel (wet or dry) soon becomes warmer (lighter) than the environment and continues to rise.
B) In the case of an downward push, the parcel soon becomes colder (denser) than the environment and continues to sink.
Both DRY and MOIST parcels favor vertical motion.
Dry Air: Unstable

40. POTENTIAL INSTABILITY
Potential instability occurs when a whole mass or layer of air is lifted and eventually becomes unstable.
This can happen at fronts, large mountain chains, or with upper level divergence (Most often combined with low level convergence).
The lifted layer has more moisture at the bottom than at the top. The bottom saturates first thus cooling at the slower rate (SALR), while the top cools at the greater rate (DALR). Continued lift destabilizes the dry bulb ELR within the lifted layer.
Potential instability is more common than latent instability, since it can occur with any large scale lift (synoptic) lift at fronts and mountain chains, unlike latent instability which occurs on the mesoscale at isolated hills and peaks (more on a later slide).
Potential instability produces convective cells embedded within a stratiform deck of cloud.
The entire ELR of the layer changes, becoming more unstable.
potential instability—(Also called convective instability or thermal instability.) The state of an unsaturated layer or column of air in the atmosphere with a wet-bulb potential temperature (or equivalent potential temperature) that decreases with elevation. If such a column is lifted bodily until completely saturated, it will become unstable (i.e., its temperature lapse rate will exceed the saturation-adiabatic lapse rate) regardless of its initial stratification.
There is a file saved “The Intricacies of Instabilities”, which is worth reading. A little complicated, but among many other things, it refers to how potential instability cannot create isolated stand along convection.

41. LATENT INSTABILITY Latent means “hidden”
If parcels of air within a layer at a lower height can be force lifted and become buoyant at some point aloft, the layer below has Latent Instability.
The layer itself is not lifted, but only parcels within it, like lift at an isolated hill or mountain peak. The parcel temperature is compared to the undisturbed air nearby.
For latent instability to be realized, parcels of air have to be force lifted, while the atmosphere nearby must be left undisturbed.
This situation cannot occur with fronts or large scale orographic lift, since deep layers are disturbed moving upward.
This situation could occur with isolated hills or mountains, or at least isolated mountain peaks among lesser hills or mountains.
The picture on the next slide helps to visualize this.

42. Wet Bulb Potential Temperature
thetaw is conserved for lifting, condensation and subsidence
e.g. ascent over mountains followed by descent

44. Under what conditions is T conserved?

45. Under what conditions is T conserved?
no vertical displacement, adiabatic, isobaric
horizontal advection with no upslope downslope or diabatic effects
surface convergence/ divergence
moisture can be added without changing temperature?

46. Under what conditions is RH conserved?

47. Under what conditions is RH conserved?
r/rs is constant
difficult to achieve

48. Under what conditions is Td conserved?

49. Under what conditions is Td conserved?
diabatic / isobaric processes
surface heating by sun
radiation cooling at night (no condensation)
cloud top cooling

50. Under what conditions is r conserved?

51. Under what conditions is r conserved?
adiabatic processes with no condensation
surface convergence/ divergence/ ascent/ descent
upslope flow/ downslope flow
diabatic processes
surface heating by sun
radiation cooling (no condensation)

52. Under what conditions is theta conserved?

53. Under what conditions is theta conserved?
adiabatic dry ascent/ descent

54. Under what conditions is thetaw conserved?
adiabatic ascent (dry or saturated)
adiabatic descent

55. Under what conditions is e conserved?

56. Rain falling into a layer below cloud
r goes up
T goes down (evaporation)
thetaw conserved
Tw defined by evaporation

57. Calculating layer mean value of a parameter from tephi
average value of a parameter in a layer is often more important than the value at a specific level
T, Td, r, theta, thetaw

58. Layer mean values
Isopleth Identification: identify the isopleths of the parameter for which the layer mean value is required.
Curve Identification: identify the curve that defines the values of the parameter through the layer in question.
Areal Equalization: choose an isopleth that cuts the curve so that the areas between the curve and the identified isopleth are the same on either side of the line.

60. Why do we want mean layer values of parameters?
mean temperature is critical to precipitation type when near 0 oC
take mean potential temperature to approximate turbulent mixing near the surface - on a sunny day the temperature near the surface will follow along a dry adiabat if the PBL is well mixed

61. Why do we want mean layer values of parameters?
a well mixed PBL has a dewpoint trace which follows a line of constant mixing ratio - averaging a Td trace around a mixing ratio line approximates the effect of daytime mixing
layer mean thetaw is useful for identifying air masses - also useful for temperature under continuous rain - temperature in thunderstorm cold outflow

62. Philosophy of mean layer values
it is possible to come up with averages which have no apparent application
mean Td
mean Tw
mean RH
think about processes

63. Radiosonde measurement of Temperature and Humidity
thermistor and hygristor response and accuracy

64. Static Stability
a radiosonde sounding represents an instantaneous state of a column of air above a station (a point)
this state can be called the ‘‘basic’’ state
the tendency of the basic state to resist or to damp out vertical accelerations is a quality of the stratification known as the static stability

66. Static Stability
the statically stable environment resists change from the basic state
the neutral environment does not resist change from the basic state
the unstable environment accelerates changes from the basic state

67. Beyond Static Stability
a stratification may be stable for minor (or local) perturbations but not for large perturbations
latent instability

69. Static Stability
in general the static stability is always changing as result of air motion and physical processes
how do we assess it?
parcel method

70. Parcel Ascent parcel represented by T, Td at a level
introduce upward finite perturbation (lift)
parcel ascends along dry adiadat if unsaturated
parcel ascends along moist adiabat if saturated

71. Determination of Static Stability
if the lifted parcel is cooler than the environment it is negatively buoyant and resists perturbation - stable
if the lifted parcel is warmer than the environment it is positively buoyant and will continue to rise (accelerate) beyond the finite perturbation - unstable
if the parcel remains at the temperature of the environment there is no net force and it will remain at the end point of the perturbation (or continue with no accleration) - neutral

74. Absolutely unstable this category is not frequently observed
those that are observed are not deep or persistent
mostly occurs with rapid heating of earth’s surface (super adiabatic lapse rate)
spontaneously produces small scale turbulent mixing (autoconvection) which tends to establish a neutral lapse rate

76. Surface based convection
convection more interesting when there is enough moisture to achieve saturation
cumulus clouds, showers and thundershowers become a possibility

81. Convective cloud bases and tops
cloud base at the LFC
average cloud tops at E (equilibrium level)
max cloud tops at EBL (energy balance level)

82. Being mechanical

83. Non Surface Based Convection
mid-level instability can result from differential thermal advection, i.e. warm advection in low levels or cold advection aloft or a combination of these
the amount of moisture present is critical

85. Cloud Bases and Tops Non Surface Based Convection
the lifted cloud base will be at the LCL
the base of the convective cloud is at the LFC
that is, the cloud character changes at the LFC
cloud is considered to be ACC or CB (not TCU)
note no mixing or entrainment considered

86. Other Instability Diagnosis
a seemingly stable sounding can become unstable with the forcing of vertical motion of a parcel or a layer
Latent Instability (LI)
deals with parcel ascent
Potential Instability (PI)
deals with significant layers of air

87. Latent Instability given a large vertical displacement of a parcel
if the parcel acquires a positive excess temperature
the level where the parcel originates has latent instability
there is usually a layer involved, not a single level

89. Prime Conditions for LI
layers of LI can occur at any height
favoured by steep lapse rates aloft - high moisture low levels

90. Summer LI greatest instability occurs during summer
cloud top cooling
cold pools in mid levels
surface heating
for severe convection
the layer should be based near the surface
it should have significant depth

91. Winter LI
surface based convection usually limited to cold air over warm water
mid level instability quite common (CB)
steep lapse rates above cloud layers
trend in destabilization (differential advection in temperature or moisture or both)
cold air advecting over warmer - PVA area
a factor in development of winter cyclones

92. Potential Instability
a layer is said to have potential instability if:
given sufficient lift
layer acquires unstable lapse rate
not thinking about parcel lift (air bubbles to ~1 square km)
lift of layers in large scale sense
synoptic scale vertical motion with a system
forced ascent over a large area due to upslope

94. Lifting a Layer Two basic cases
the layer remains unsaturated
part of the layer becomes saturated durig lift
when lifting a layer, lift the top and the bottom the same delta p, e.g. 100 mb

96. Two Cases layer remains unsaturated
very deep vertical motions are required to significantly alter the stability
not likely to be important
part of the layer becomes saturated during ascent
lapse rate always becomes steeper
lifting a layer which is more moist at the bottom will destabilize it

97. Diagnosis of PI
if the bottom of a layer is more moist than the top, i.e higher thetaw it will become more unstable if lifted sufficiently
converse is also true
this is equivalent to:
a layer is potentially unstable if the Tw lapse rate is greater than the wet adiabatic lapse rate

100. Inversions the other extreme relative to instability definition:
a stable layer of the atmosphere in which the temperature increases with height
operationally this definition has been broadened to include lapse rates less than the moist adiabatic lapse rate

101. 5 Environmental Lapse Rates - ELRS
WET ADIABAT
Isotherm
DRY ADIABAT
Shallow
Steep
Average
Inversion al
Inversions: @ SFC – Nocturnal or Arctic
Aloft – Subsidence or frontal
Isothermal: weak front & found just above the tropopause
Shallow: weak fronts, weak raditional cooling, weak advective cooling
Wet Adiabatic: in cloud layers
Average: Most common
Dry Adiabatic: Daytiem heating at the surface
Steep: Hot calm days (very unstable), radiational or advective heating
BASE OF LAYER
From the base of the layer, compare the 3 adiabats to the ELR of the layer.

103. Types of Inversions frontal radiation subsidence turbulence tropopause
continental arctic air
local inversions

111. Local Surface Effects Inversions
marine inversion
sea breeze inversion