Compute saturation vapor push using the Clausius-Clapeyron equation;Convert in between humidity variables. Differentiate between relative humidity, details humidity, pure humidity, wet-bulb temperature, mixing ratio, and dew point;Describe the problems for saturation to occur;Apply the moist adiabatic lapse rate;Use the principles of phase adjust and latent heating to define why the moist adiabatic lapse price is less than the dried adiabatic slide away rate.

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Water can exist as a solid, liquid, or gas at common conditions uncovered on Earth. Together we learned, the process of liquid water coming to be water vapor is dubbed evaporation and also this process absorbs or requires energy. The opposite process is dubbed condensation, where water vapor becomes liquid water, releasing energy. Condensation is specifically important in atmospheric science due to the fact that this is the process that allows clouds come form.

Phase changes of water from gas (water vapor) to fluid (water) to solid (ice) with the names because that the processes additionally labeled. (CC by 2.0).

Clouds are composed that millions and billions the tiny liquid water droplets. How do they form? Why are they there?

Water droplets condensed top top a glass surface (CC by 2.0).

Before we have the right to understand clouds in the atmosphere, we should explore principles like how humidity is defined and also what saturation means.

In general, humidity is the amount of water vapor in the air. You’ve most likely heard of family member humidity and dew allude temperature, however what carry out these quantities median physically?


Imagine a closed jar to fill halfway with water. In ~ the initial time, an ext water molecules evaporate from the water surface ar than the number the return. However, after some time, the variety of molecules evaporating native the surface ar will be same to the number of molecules condensing ago into the water surface. As soon as condensation and also evaporation are equal, this is referred to as saturation.

Saturation occurs once air has the maximum amount of water vapor feasible for its provided temperature. The is why condensation equals evaporation. If evaporation occurs, the air cannot contain much more water vapor, therefore some need to condense. Now let’s acquire quantitative.

Vapor press at saturation

Every gas in the atmosphere exerts pressure, because that example, vapor pressure makes increase a portion of the full atmospheric pressure. In the complying with equation, every one of the gases in earth atmosphere add to the complete atmospheric pressure Patmosphere.


Specifically because that water vapor, the an ext water vapor that is included to the atmosphere, the higher the vapor pressure PH2O. The units for vapor push are the exact same as pressure and can it is in in Pascals, hectoPascals, or kiloPascals. Due to the fact that we space staying continuous with Roland Stull’s Practical Meteorology textbook, us will usage kiloPascals (kPa) transparent this chapter.

The lot of water vapor that the environment can contain counts on temperature. Lower temperature air cannot contain as much water vapor as higher temperature air. If us think the this quantitatively in terms of pressure,saturation vapor pressure refers to the push exerted by the movement of water vapor molecules exerted over a surface ar of fluid water. As soon as the partial press exerted through water vapor is equal to the saturation vapor pressure, the air is saturated.

The Clausius-Clapeyron equation provides the approximate relationship between saturation vapor press (es) and temperature in the atmosphere

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where the water-vapor gas constant ℜv is 461 J·K–1·kg–1, T0is 273.15 K, e0is 0.6113 kPa, and also Lv is the latent warmth of vaporization, 2.5×106 J·kg–1. Thisresults in Lv/ℜv being same to 5423 K. In this equation, systems for temperature must be in Kelvin. Note that in the equation above, exp indicates the exponential role ex, but it is written on one line for visual purposes.

A graph that the saturation vapor press as a function of temperature showing the exponential relationship between the two from the Clausius-Clapeyron equation (Modified fromCC BY-SA 4.0).

The image shows the relationship between temperature and saturation vapor pressure based on the Clausius-Clapeyron equation. Reduced temperatures are saturated with respect to water vapor at lower vapor pressures, while higher temperatures need greater vapor pressures to it is in saturated. Temperature is the primary variable determining water vapor saturation.

In the graph the saturation vapor push vs. Temperature an alert the saturation vapor pressure value at the boil temperature, 100°C. The saturation vapor press value es(100°C)=101.325 kPa, is the exact same value as the atmospheric surface ar pressure. Water boils in ~ the earth’s surface when the saturation vapor pressure is equal to the atmospheric pressure, which is why water boils at 100°C. Will certainly water cook at the same temperature in ~ the height of mountain Everest?
Humidity Variables

Vapor pressure is one way of defining humidity, however there are many others. Below is a non-comprehensive perform of humidity variables and their typical units.

e = vapor pressure (kPa)r = mixing proportion (g·kg–1)q= particular humidity (g·kg–1)ρv = pure humidity (g·m-3)RH = relative humidity (%)zLCL = lifting condensation level (km)Td = dew suggest (temperature) (°C)Tw = wet-bulb temperature (°C)

Vapor Pressure

We’ve currently discussed saturation vapor pressure, es, however you can likewise compute vapor pressure, e. However, because Tdis regularly unknown, the easiest means is typically through relative humidity.

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Again, e0is 0.6113 kPa,Lv is 2.5×106 J·kg–1, ℜv is 461 J·K–1·kg–1, T0is 273.15 K, and also Td is dew point temperature, which will be defined later.

Mixing Ratio

Mixing ratio, r, is the ratio of the mass of water vapor come the massive of dried air. The is frequently expressed as grams of water vapor per kilogram of waiting (g·kg–1).



Pressure (P) have to be in the exact same units as vapor pressure (e).The constantε is 0.622, is the ratio between the gas continuous for dried air and the gas continuous for water vapor.


Saturation mix ratio, rs, is computed the same way as the mix ratio but with saturation vapor pressure, es, instead of e.


When calculating mixing ratio, the press units on the peak of the fraction will cancel through the press units top top the bottom the the fraction. When it shows up unit-less, that technically not based on its an interpretation of mass of water vapor as contrasted to mass of dried air. View the agree Tip below for much more information.

Pro Tip: plenty of units of moisture are provided in g·kg-1 or kg·kg-1so technically the units might cancel and it could be unitless! nothing let this silly you. That is vital to remember the the mass in the numerator and denominator are different. In the instance of mixing ratio, the worth is provided in massive of water vapor proportional come the mass of dry air.

Specific Humidity

Specific humidity, q, is the ratio of the mass of water vapor to the complete mass of waiting (dry air and also water vapor combined). The is expressed together grams the water vapor every kilogram of wait (g·kg–1).



Again, saturation specific humidity, qs, is computed v es instead of e.


Absolute Humidity

Absolute humidity,ρv, is the ratio of the fixed of water vapor come the volume of air. The is expressed together grams of water vapor in a cubic meter of waiting (g·m-3). It is properly water vapor density.



Again, saturation pure humidity,ρvs, uses es instead of e.


Relative Humidity

Relative humidity, RH, is the ratio of the lot of water vapor current in the air to the maximum quantity of water vapor required for saturation in ~ a details pressure and temperature. That is frequently multiplied by 100 and expressed as a percent. Relative humidity shows exactly how close the waiting is to being saturated, not exactly how much water vapor the wait contains. Because that this reason, RH is no a an excellent indicator that the quantitative quantity of water vapor in the air. The is just a relative measure the is highly dependent on the air temperature. Relative humidity better than 100% is called supersaturation.




Imagine 2 parcels of air v the same volume, pressure, and also relative humidity. Package 1 has actually an wait temperature that 20°
C when Parcel 2 has actually an waiting temperature that 30°C. I beg your pardon parcel contains more water vapor?

Dew suggest Temperature

The dew allude temperature, Td, is the temperature come which the air need to be cooled to reach saturation, without an altering the moisture or waiting pressure. It procedures the actual moisture content of a thoreau of air. Saturation occurs as soon as the dew point temperature amounts to the air temperature.

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When the dew suggest temperature is reduced than the freezing point of water, the is also called the frost point.

Wet-Bulb Temperature

Wet-bulb temperature, Tw, is the shortest temperature that have the right to be accomplished if water evaporates within the air. When the family member humidity is 100%, the wet-bulb temperature is same to the air temperature because there is no evaporation.

The wet-bulb temperature is an overwhelming to calculate however easy come measure. To measure the wet-bulb temperature, every you require is a thermometer with a wet cloth wrapped about the bulb. Typically this thermometer is attached to an apparatus called a sling psychrometer to make it easy to spin approximately in the waiting to develop lots of air flow over the wet fabric on the thermometer. The evaporation from the wet towel cools the temperature measured, for this reason the wet-bulb temperature is always lower 보다 the wait temperature (or dry-bulb temperature) when relative humidity is less than 100%.

You can additionally estimate the wet pear temperature making use of lines top top a graph. Normand’s Rule is offered to calculation the wet-bulb temperature native the wait temperature and also the dew allude temperature. The wet-bulb temperature is constantly between the dew suggest and the dry-bulb temperature (Td TwT). This deserve to be implemented on thermodynamic diagrams, such together the Skew-T log P, which is disputed in much more detail in the next chapter.

Take keep in mind of this summary for later. To discover the wet-bulb temperature top top a Skew-T log in Pdiagram, monitor the dry adiabatic lapse rate line upward from the waiting temperature. Next, usage the dew suggest temperature and follow an isohume (line of continuous relative humidity) upward. The point where these 2 lines satisfy is called the lifting condensation level (LCL). From the conference point, follow the moist (saturated) adiabatic slide away rate earlier down to achieve the wet-bulb temperature value. This is most likely confusing in ~ this allude because we have actually not disputed the LCL or the moist adiabatic slide away rate, but don’t worry, we’ll repeat this reasonable again in the next chapter come make sure this is clear.

Why do We care So Much about Moisture?

You may be wondering at this suggest why we care so much around moisture and also why we require so plenty of definitions that (almost) the exact same thing. The reason is the moisture is very important atmospheric property. Water deserve to exist in 3 phases (vapor, liquid, ice) in ~ the environment at common pressures and temperatures. It has actually an especially big impact top top the person experience—think about a humid day, foggy conditions, rain, snow, or also hail! Less obvious is its influence on atmospheric stability, which cd driver the abovementioned conditions.

For now, let’s think about the process of water vapor condensing to type liquid water. Over there is one final an interpretation of humidity that will be helpful.

Lifting Condensation Level

The lifting condensation level, zLCL, is the altitude wherein clouds form. In ~ the LCL, temperature equates to the dew point temperature, resulting in saturation and also therefore condensation. The elevation (z) the the LCL is


where a is 0.125 km°C-1. Us can likewise define the temperature at the LCL as follows.


Moist Adiabatic slide away Rate

In the critical chapter, we disputed how temperature changes as a dry parcel of waiting is lifted in the atmosphere. You will certainly recall that as an waiting parcel is lifted, the temperature autumn by 9.8 K every kmdue come the work-related the wait parcel have to do to the setting as the expands. Let’s include moisture come the discussion and see exactly how this changes things.

If the air parcel reaches saturation (100% family member humidity) and water vapor condenses to fluid water within the parcel, latent heat will be released. In the case of a rising air parcel that is cooling native adiabatic expansion, this included heat indigenous condensation counterbalances several of the cooling. Hence, the waiting parcel will certainly no much longer cool in ~ the dry adiabatic slide out rate yet at the smaller sized moist adiabatic lapse rate (Γm). Unlike the dried adiabatic lapse, the moist adiabatic lapse price is not consistent and varies based upon the temperature and also moisture the the waiting parcel.

We will certainly approximate the moist adiabatic lapse rate with the following value.


The difference between the dry adiabatic lapse rate (Γm) and also the moist adiabatic lapse price (Γm)is significant and has profound affect on atmospheric stability, the object of the complying with chapter.

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Chapter 4: concerns to Consider

Explain the conditions needed for saturation to occur.What is the saturation vapor press of air at 26°C?Explain the difference between specific humidity and relative humidity.If the temperature is 10°C and also the pressure is 700 hPa, calculate the saturation particular humidity and also the saturation mixing ratio.Explain why the moist adiabatic lapse rate is less than the dry adiabatic lapse rate.

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