(extracted from a series of posts on the Facebook page of meteo.guru)
We all know that warm air is lighter than cold air. So will start this series with a fun question.
First of all, do you know how much air is 1kg of air?
Most people are surprised by the real weight of air. A good way to remember it is - 1l of water weights 1kg, 1m³ of water weights 1 ton, 1m³ of air weights 1kg (or 1,2kg to be exact) - at 25°C and at sea level pressure. If you are reading this in a an average room, chances are that there will be around 30kg to 40kg of air in this room.
So, on to our fun question: If warm air is lighter than cold air, and we take 1m³ of air at 25°C at sea level and we warm it up to 30°C, how much will it weight?
As some of you have noticed, the mass of a body is the sum of the masses of its atoms. Apart from the special case of atomic destruction and direct transformation into energy (E=mc²) during a nuclear explosion or inside a star or a nuclear reactor - in all other cases one of the most fundamental laws in nature applies - the law of conservation of the mass. As long as there is no nuclear reaction, no matter what we do with a body, its mass will remain constant. For example, when burning gasoline in a combustion engine, the sum of the mass of the exhaust gas and the solid particles is exactly the same as the mass of the burnt fuel.
(Small reminder: as long as you're on Earth, mass and weight are the same. When you're on the Moon, the mass is the same as on Earth, but the weight is much less.)
So how does hot air rise if its weight stays constant? We all know that wood floats in water. If you put a 1kg plank in the water it will float. Same goes for the 2kg plank. What if we put in 1 ton of wood? It will still float.
To push this to absurdity, I will mention that if we inject 10g of water vapor into a 1kg parcel of air, then this new parcel, whose weight will obviously be 1kg and 10g in all cases, then this mass will be lighter than the ambient air and it will start to rise.
So is it the weight that determines the buoyancy? Buoyancy, caused by the Archimedes' principle, depends on the density, ie, the ratio between weight and volume.
As somebody noticed that air density at 30°C and at sea level pressure is approximately 1.16kg/m3 and given that our air mass is strictly the same weight as before, there can be only one explanation - its volume is not the same as before. Its volume went up from 1m³ to 1.2/1.16=1.03m³. The parcel has expanded. The first effect of temperature in a gas is pressure. When you the temperature rises, so does the pressure. When we heat an air parcel, under the effect of its higher pressure, it will "push away" the ambient air and it will take up more space with a lower density.
Before discussing the properties of humidity in the air, we should start by defining it. Generally, the term moist air is reserved for air mixed with water vapour, both substances being gaseous. Water vapor is a gas that is completely transparent.
Air that carries microdroplets of liquid water light enough to remain in suspension and that appears as a white mist, such as clouds, in a hammam or the visible part in the above photo is not considered humid air. In meteorology, we speak of air that contains hydrometeors.
Air can contain more or less water vapor - of all the gases that make up the Earth's atmosphere, it is the only one whose quantity varies very considerably. Its properties mean that it is also the only gas that can easily pass from the gaseous state to the liquid state and to the solid state at the temperatures and pressure generally observed on Earth. Oxygen and nitrogen need extreme temperatures and pressures to become liquid.
The amount of water vapor that an air parcel can dissolve is limited and depends on its temperature and pressure. This quantity can be measured in at least five different ways:
- Relative humidity, which is the measurement best known to most, since it best represents the effect of humidity on the human body - ranging from 0%, air completely deprived of water vapor to 100%, air saturated with vapor - this is when the white mist appears as part of it begins to condense
- Absolute humidity, which is very rarely seen outside of a strictly scientific context, which measures the amount of water vapor per volume of air, in grams per cubic meter
- The mixing ratio, which we prefer in meteorology and which is plotted on the emagrams, which measures the water vapor in grams of water vapor per kilogram of dry air
- The specific humidity, which is almost the same except that it takes the mass of the water vapor in grams of water vapor per kilogram of the total mass of the air - 1g/1kg of mixing ratio is equal to 1g/1.001kg of specific humidity - as we add the 1g - in practice it is the same for real world values
- The dew point, preferred in aviation, which is the temperature at which an air mass will be at 100% saturation - when we lower the temperature of an air mass, its absorption capacity of vapor decreases which causes its relative humidity to increase
All these parameters are of course related since they all express the same physical variable. These relationships also depend on temperature and pressure. Between the five ways of measuring humidity and temperature and pressure, three variables are sufficient to calculate the other four. What is the reason for privileging specific humidity over emagrams? Of all the measurements, this one has one quality that makes it very practical in our context - it does not vary when an air mass undergoes a thermodynamic change. Let's take a typical Alpine air mass in the valley, at an altitude of 300m, in summer and at the start of the day - 15°C and 75% relative humidity. The dew point is then 10°C. This means that if the temperature of this air mass drops to 10°C, then the relative humidity will be 100%, since its maximum water vapor capacity will be reduced.
If we apply the formula, which is complex enough t we obtain a specific humidity of 8g per kg of air. As we have already seen, no matter what we subject this parcel of air to, it will always remain 1kg and it will always contain 8g of water vapour. This is the only way to measure vapor that will always be constant. For example, the dew point also resists temperature changes but it is affected by pressure changes. Now this air parcel is heated by the sun and it goes to 25°C. It still contains 8g/kg of water vapour. Its dew point is always 10°C. Its new relative humidity is 40% - since at 25°C the air can absorb much more humidity - now we have extra space.
The air parcel begins to rise, it arrives at an altitude of 1500m at the level of 850hPa / FL50. As the pressure here is much lower, the air parcel has undergone adiabatic expansion. Its temperature has dropped from 25°C to 13°C (1200m of elevation is equivalent to about 12° - or 11.71°C if we want to be 100% precise). Now its relative humidity is 74%. It still contains 8g/kg of water vapour, but we have lost total capacity - now at 8g/kg we are 74% full. Its dew point is now at 8.5°C. At 1500m altitude and 850 hPA pressure the rules of condensation are no longer the same. This is very important and many people ignore it. The dew point of an air parcel varies with pressure. If we have an air parcel whose dew point is 10°C, it is not enough to raise it to the level of 10°C in temperature to obtain condensation - since at this level its dew point will no longer be at 10°C.
The only absolute measurement is therefore the specific humidity - and not the absolute humidity, unfortunately we are dealing with a rather consequent imprecision of language uncommon in the scientific world. Our air parcel continues to rise. It arrives at 2000m / 800hPa / FL65. Under the effect of adiabatic expansion, its temperature is now 8°C. Its relative humidity is now above 100% - which means that our air parcel has become a cloud. It will continue its ascent for some time following a much more complex transformation that we will see later.
Before continuing on to the second part on the humidity in air, we will have to see a little more about water itself, a remarkable substance with unique properties.
It is one of the only substances that we encounter, in our everyday life, in three of its phases: solid, liquid and gaseous.
When we talk about phase transitions, most people have a much too simplistic vision of these phenomena: they believe that if we cool a body, it becomes a solid, if we heat it up, it becomes a liquid and in the end, if it is heated sufficiently, it evaporates and becomes a gas. This is normal, as most people lack experience in an environment where the ambient pressure is highly variable. In reality, the state of matter depends on both temperature and pressure. You can liquefy a gas by compressing it and if you expose a liquid to a vacuum, it will immediately evaporate regardless of its temperature. A diagram that shows the relationship between the phase of a substance and the pressure and ambient temperature is called a phase diagram:
The first thing we notice on this diagram is that water vapor can exist even if the temperature is negative. Many people believe that the water vapor present in the very high layers of the atmosphere is actually composed of ice crystals. Cirrus clouds are actually made up of ice crystals - instead of the droplets of the lower-layer clouds - but these cannot form if there is no vapor in the first place.
Second thing - direct transitions between ice and vapor are also possible - they are called sublimation and deposition.
And finally, there are also other phases of matter - that come after gas in terms of pressure and temperature - in particular the supercritical fluid and the plasma, but they are of little interest for meteorology.
The liquid and gaseous states always exist in parallel. If there is liquid water, there is also have evaporation - it is possible even if the temperature is at 0°C (or even below 0°C but it requires an unusual environment). The same goes for condensation, there can be condensation even if the temperature is at 400°C. Temperature and pressure determine which one of the two is the more active. The true definition of relative humidity is in fact the ratio between the rate of evaporation and the rate of condensation. At 100% relative humidity the two are in equilibrium. If the humidity exceeds 100%, condensation takes over. If it is lower, evaporation takes over. Under atmospheric conditions, the humidity level can never exceed 101% to 102% since the condensation becomes much too rapid - as there are only a few grams of water vapor per kilogram of air, but in laboratory conditions, one can obtain air with a humidity level well above 100% - so called supersaturated air - if all the rigid particles which serve as condensation nuclei are removed.
(note: it is exactly this equilibrium that explains the "capacity" of air to hold water vapor - which has nothing to do with the air, but which is entirely a consequence of the properties of the water itself - any other gas would behave identically)
Another remarkable quality of water is that these transitions between vapor and liquid are very energetic. Evaporation consumes heat. Condensation produces heat in strictly identical quantities. To always remember which is which, think about perspiration, our body's natural mechanism that allows us to release our heat in the atmosphere. The evaporation of one liter of water requires 2500kJ at room temperature. Its condensation releases back this heat. To realize how huge this value is - we can transform it into kW/h - we obtain 0.7 kW/h. The condensation of one liter of water produces as much heat as an average 2kW kitchen oven at maximum power over 20 minutes. This also applies to the transition between solid and liquid - everyone who lives near a mountain lake is aware of the weather effect of the lake freezing - but the proportions are not the same - the energy of this transition is 333kJ per litre. Sublimation and deposition produce, of course, the sum of the two.
Now, we can finally discuss the (in-)famous adiabatic and pseudo-adiabatic coefficients.
Many pilots, when they first start learning, have a hard time understanding this part. It's like trying to learn electronics before knowing what is electricity.
We have seen what happens when the air is dry and it is relatively simple. Its pressure rises under the effect of temperature and it pushes away the surrounding air until the pressure equalizes. Thus, its volume increases and it becomes less dense.
When it rises, it finds itself surrounded by air whose pressure is lower and it expands more to equalize this pressure. When it expands, tss temperature drops. If we decide to write and develop the differential equations that express the relationships between temperature, pressure and altitude, we realize that most of the variables can be eliminated so that in the end only (1) remains. g9.81m/s is the Earth's acceleration, C1005J/kgK is the heat capacity of air and as a reminder, one joule is one newton per meter, so one newton per joule is one meter. You can see the full derivation here:
https://www.tec-science.com/.../barometric-formula-for.../
The result is a constant, very practical, since very close to 1°C / 100m. When an air mass rises, it cools by one degree every 100m due to adiabatic expansion.
(just for information, this formula does not take into account the heat capacity of water vapor, which means that in reality it is not a constant, but the variation is less than 1% in the lower layers of the atmosphere) Unfortunately, when the air contains vapor, we cannot eliminate the variables. Ask around, how many people can give you the value of the wet coefficient, or even the formula. Me personally, after 4 years of experience on a weather site dedicated to soaring flight, I am not able to write it without copying it from a book.
Once the air mass has risen to its saturation level, some of the water is now in a liquid state. This has two consequences - the liquid part is no longer affected by the same equations that describe the behavior of gases, and on top of that there has been a very considerable release of heat caused by this condensation. It is because of this additional heat that we can no longer really speak of an adiabatic process - and we call this coefficient the pseudo-adiabatic lapse rate of humid air. It is always because of this additional heat that this mass of air, which is actually a thermal, will live a second life after having exhausted its heat reserve obtained near the ground - and will be propelled further upwards in the form of a cloud - this is the vertical development. The moist coefficient depends on both temperature and pressure. At very low temperature and near the ground, it is close to the dry coefficient - 0.95°C/100m at -40°C and 1013 hPa. At 40°C temperature, it is only 0.3°C/100m. This is why winter cumulonimbus clouds are much rarer and less intense - between 0.95 and 0.98, the additional heat reserve is next to none. On the other hand, between 0.3 and 0.98, it is qualitative change. Unless there is a huge blocking inversion, at this temperature, the atmosphere is almost always unstable and all it takes is a little moisture on the ground to render the condensation at altitude explosive.