**3.5 Tephigrams**

To represent the vertical structure of the atmosphere and interpret its state, a number of diagrams is commonly used. The most common are *emagrams*, *Stüve diagrams*, *skew T- log p diagrams*, and *tephigrams*.

Referring to fig. 4, *A(p)* represent the shaded area between the environment and the air parcel temperature profiles. An air parcel initially in A is bound inside a "potential energy well" whose depth is proportional to the dotted area, and that is termed *Convective Inhibition (CIN)*. If forcedly raised to the level of free convection, it can ascent freely, with an available potential energy given by the shaded area, termed *CAPE (Convective Available Potential* 

In absence of entrainment and frictional effects, all this potential energy will be converted into kinetic energy, which will be maximum at the level of neutral buoyancy. CIN and CAPE are measured in J/Kg and are indices of the atmospheric instability. The CAPE is the maximum energy which can be released during the ascent of a parcel from its free buoyant level to the top of the cloud. It measures the intensity of deep convection, the greater the CAPE, the more vigorous the convection. Thunderstorms require large CAPE of more than

CIN measures the amount of energy required to overcome the negatively buoyant energy the environment exerts on the air parcel, the smaller, the more unstable the atmosphere, and the easier to develop convection. So, in general, convection develops when CIN is small and CAPE is large. We want to stress that some CIN is needed to build-up enough CAPE to eventually fuel the convection, and some mechanical forcing is needed to overcome CIN.

CAPE is weaker for maritime than for continental tropical convection, but the onset of

We have neglected entrainment of environment air, and detrainment from the air parcel , which generally tend to slow down convection. However, the parcels reaching the highest altitude are generally coming from the region below the cloud without being too much

Convectively generated clouds are not the only type of clouds. Low level stratiform clouds and high altitude cirrus are a large part of cloud cover and play an important role in the Earth radiative budget. However convection is responsible of the strongest precipitations, especially in the Tropics, and hence of most of atmospheric heating by latent heat transfer. So far we have discussed the stability behaviour for a single air parcel. There may be the case that although the air parcel is stable within its layer, the layer as a whole may be destabilized if lifted. Such case happen when a strong vertical stratification of water vapour is present, so that the lower levels of the layer are much moister than the upper ones. If the layer is lifted, its lower levels will reach saturation before the uppermost ones, and start cooling at the slower pseudoadiabat rate, while the upper layers will still cool at the faster adiabatic rate. Hence, the top part of the layer cools much more rapidly of the bottom part and the lapse rate of the layer becomes unstable. This *potential* (or *convective*) *instability* is frequently encountered in the lower leves in the Tropics, where there is a strong water

It can be shown that condition for a layer to be potentially unstable is that its equivalent

To represent the vertical structure of the atmosphere and interpret its state, a number of diagrams is commonly used. The most common are *emagrams*, *Stüve diagrams*, *skew T- log p*

This can be provided by cold front approaching, flow over obstacles, sea breeze.

convection is easier in the maritime case due to smaller CIN.

*Energy)*.

1000 Jkg-1.

diluted.

vapour vertical gradient.

*diagrams*, and *tephigrams*.

**3.5 Tephigrams** 

potential temperature *θe* decreases within the layer.

An *emagram* is basically a *T-z* plot where the vertical axis is *log p* instead of height *z*. But since *log p* is linearly related to height in a dry, isothermal atmosphere, the vertical coordinate is basically the geometric height.

In the *Stüve diagram* the vertical coordinate is *p(Rd /cp )* and the horizontal coordinate is *T*: with this axes choice, the dry adiabats are straight lines.

A *skew T- log p diagram*, like the emagram, has *log p* as vertical coordinate, but the isotherms are slanted. *Tephigrams* look very similar to skew T diagrams if rotated by 45°, have *T* as horizontal and *log θ* as vertical coordinates so that isotherms are vertical and the isentropes horizontal (hence tephi, a contraction of *T* and *Φ*, where *Φ = cp log θ* stands for the entropy). Often, tephigrams are rotated by 45° so that the vertical axis corresponds to the vertical in the atmosphere.

A tephigram is shown in figure 5: straight lines are isotherms (slope up and to the right) and isentropes (up and to the left), isobars (lines of constant p) are quasi-horizontal lines, the dashed lines sloping up and to the right are constant mixing ratio in g/kg, while

the curved solid bold lines sloping up and to the left are saturated adiabats.

Fig. 5. A tephigram. Starting from the surface, the red line depicts the evolution of the Dew Point temperature, the black line depicts the evolution of the air parcel temperature, upon uplifting. The two lines intersects at the LCL. The orange line depicts the saturated adiabat crossing the LCL point, that defines the wet bulb temperature at the ground pressure surface.

Two lines are commonly plotted on a tephigram – the temperature and dew point, so the state of an air parcel at a given pressure is defined by its temperature *T* and *Td*, that is its water vapour content. We note that the knowledge of these parameters allows to retrieve all the other humidity parameters: from the dew point and pressure we get the humidity mixing ratio w; from the temperature and pressure we get the saturated mixing ratio ws, and relative humidity may be derived from 100\*w/ws, when w and ws are measured at the same pressure.

When the air parcel is lifted, its temperature *T* follows the dry adiabatic lapse rate and its dew point *Td* its constant vapour mixing ratio line - since the mixing ratio is conserved in

Atmospheric Thermodynamics 65

second inversion layer is present in the temperature sounding between 800 hPa and 750 hPa, such that the air parcel becomes colder than the environment, hence negatively buoyant between 800 hPa and 700 hPa. If forcedly uplifted beyond this stable layer, it again

As the tephigram is a graph of temperature against entropy, an area computed from these variables has dimensions of energy. The area between the air parcel path is then linked to the CIN and the CAPE. Referring to the early morning sounding, the area between the black and the grey line between the surface and 600 hPa is the CIN, the area between 600 hPa and

Clouds play a pivotal role in the Earth system, since they are the main actors of the atmospheric branch of the water cycle, promote vertical redistribution of energy by latent

Clouds may form when the air becomes supersaturated, as it can happen upon lifting as explained above, but also by other processes, as isobaric radiative cooling like in the formation of *radiative fogs*, or by mixing of warm moist air with cold dry air, like in the

*Cumulus* or *cumulonimbus* are classical examples of convective clouds, often precipitating, formed by reaching the saturation condition with the mechanism outlined hereabove. Other types of clouds are *alto-cumulus* which contain liquid droplets between 2000 and 6000m in mid-latitudes and cluster into compact herds. They are often, during summer,

*Cirrus* are high altitude clouds composed of ice, rarely opaque. They form above 6000m in mid-latitudes and often promise a warm front approaching. Such clouds are common in the Tropics, formed as remains of anvils or by in situ condensation of rising air, up to the tropopause. *Nimbo-stratus* are very opaque low clouds of undefined base, associated with persistent precipitations and snow. *Strato-cumulus* are composed by water droplets, opaque or very opaque, with a cloud base below 2000m, often associated with weak

*Stratus* are low clouds with small opacity, undefined base under 2000m that can even reach the ground, forming fog. Images of different types of clouds can be found on the Internet

In the following subchapters, a brief outline will be given on how clouds form in a saturated environment. The level of understanding of water cloud formation is quite advanced, while

We could think that the more straightforward way to form a cloud droplet would be by condensation in a saturated environment, when some water molecules collide by chance to form a cluster that will further grow to a droplet by picking up more and more molecules from the vapour phase. This process is termed *homogeneous nucleation*. The survival and further growth of the droplet in its environment will depend on whether the Gibbs free energy of the droplet and its surrounding will decrease upon further growth. We note that,

heat capture and release and strongly influence the atmospheric radiative budget.

precursors of late afternoon and evening developments of deep convection.

(see, as instance, http://cimss.ssec.wisc.edu/satmet/gallery/gallery.html).

it is not so for ice clouds, and for glaciation processes in water clouds.

attains a positive buoyancy up to above 300 hPa.

generation of airplane contrails and *steam fogs* above lakes.

400 hPa is the CAPE.

precipitations.

**4.1 Nucleation of droplets** 

**4. The generation of clouds** 

unsaturated air - until the two meet a t the LCL where condensation may start to happen. Further lifting follows the Saturated Adiabatic Lapse Rate. In Figure 5 we see an air parcel initially at ground level, with a temperature of 30° and a Dew Point temperature of 0° (which as we can see by inspecting the diagram, corresponds to a mixing ratio of approx. 4 g/kg at ground level) is lifted adiabatically to 700 mB which is its LCL where the air parcel temperature following the dry adiabats meets the air parcel dew point temperature following the line of constant mixing ratio. Above 700 mB, the air parcel temperature follows the pseudoadiabat. Figure 5 clearly depicts the *Normand's rule*: The dry adiabatic through the temperature, the mixing ratio line through the dew point, and the saturated adiabatic through the wet bulb temperature, meet at the LCL. In fact, the saturated adiabat that crosses the LCL is the same that intersect the surface isobar exactly at the wet bulb temperature, that is the temperature a wetted thermometer placed at the surface would attain by evaporating - at constant pressure - its water inside its environment until it gets saturated.

Figure 6 reports two different temperature sounding: the black dotted line is the dew point profile and is common to the two soundings, while the black solid line is an early morning sounding, where we can see the effect of the nocturnal radiative cooling as a temperature inversion in the lowermost layer of the atmosphere, between 1000 and 960 hPa. The state of the atmosphere is such that an air parcel at the surface has to be forcedly lifted to 940 hP to attain saturation at the LCL, and forcedly lifted to 600 hPa before gaining enough latent heat of condensation to became warmer than the environment and positively buoyant at the LFB. The temperature of such air parcel is shown as a grey solid line in the graph.

Fig. 6. A tephigram showing with the black and blue lines two different temperature sounding, and with the grey and red lines two different temperature histories of an air parcel initially at ground level, upon lifting. The dotted line is the common *Td* profile of the two soundings.

The blue solid line is an afternoon sounding, when the surface has been radiatively heated by the sun. An air parcel lifted from the ground will follow the red solid line, and find itself immediately warmer than its environment and gaining positive buoyancy, further increased by the release of latent heat starting at the LCL at 850 hPa. Notice however that a

unsaturated air - until the two meet a t the LCL where condensation may start to happen. Further lifting follows the Saturated Adiabatic Lapse Rate. In Figure 5 we see an air parcel initially at ground level, with a temperature of 30° and a Dew Point temperature of 0° (which as we can see by inspecting the diagram, corresponds to a mixing ratio of approx. 4 g/kg at ground level) is lifted adiabatically to 700 mB which is its LCL where the air parcel temperature following the dry adiabats meets the air parcel dew point temperature following the line of constant mixing ratio. Above 700 mB, the air parcel temperature follows the pseudoadiabat. Figure 5 clearly depicts the *Normand's rule*: The dry adiabatic through the temperature, the mixing ratio line through the dew point, and the saturated adiabatic through the wet bulb temperature, meet at the LCL. In fact, the saturated adiabat that crosses the LCL is the same that intersect the surface isobar exactly at the wet bulb temperature, that is the temperature a wetted thermometer placed at the surface would attain by evaporating - at constant pressure - its water inside its environment until it gets

Figure 6 reports two different temperature sounding: the black dotted line is the dew point profile and is common to the two soundings, while the black solid line is an early morning sounding, where we can see the effect of the nocturnal radiative cooling as a temperature inversion in the lowermost layer of the atmosphere, between 1000 and 960 hPa. The state of the atmosphere is such that an air parcel at the surface has to be forcedly lifted to 940 hP to attain saturation at the LCL, and forcedly lifted to 600 hPa before gaining enough latent heat of condensation to became warmer than the environment and positively buoyant at the LFB.

The temperature of such air parcel is shown as a grey solid line in the graph.

Fig. 6. A tephigram showing with the black and blue lines two different temperature sounding, and with the grey and red lines two different temperature histories of an air parcel initially at ground level, upon lifting. The dotted line is the common *Td* profile of the

The blue solid line is an afternoon sounding, when the surface has been radiatively heated by the sun. An air parcel lifted from the ground will follow the red solid line, and find itself immediately warmer than its environment and gaining positive buoyancy, further increased by the release of latent heat starting at the LCL at 850 hPa. Notice however that a

saturated.

two soundings.

second inversion layer is present in the temperature sounding between 800 hPa and 750 hPa, such that the air parcel becomes colder than the environment, hence negatively buoyant between 800 hPa and 700 hPa. If forcedly uplifted beyond this stable layer, it again attains a positive buoyancy up to above 300 hPa.

As the tephigram is a graph of temperature against entropy, an area computed from these variables has dimensions of energy. The area between the air parcel path is then linked to the CIN and the CAPE. Referring to the early morning sounding, the area between the black and the grey line between the surface and 600 hPa is the CIN, the area between 600 hPa and 400 hPa is the CAPE.
