This page contains the answers to the questions embedded throughout the Tutorial on Humidity. This page contains only those sections of the tutorial that include questions:
For example, a parcel of air at sea level, at a temperature of 25 degrees C, would be completely saturated if there were 20 grams of water vapor in every kilogram of dry air.
The measure we are using is mixing ratio: grams of water vapor per kilogram of dry air.
If this air actually contains 20 grams of water vapor per kilogram of dry air, we would say that the relative humidity is 100%.
The relative humidity would be 50%. 10 grams water vapor/kg dry air compared to 20 grams water vapor/kg dry air is 10/20=50%.
Relative humidity would be 18/20=90%.
Adiabatic Processes and Lapse Rates
For the atmosphere, the drop in temperature of rising, unsaturated air is about 10 degrees C/1000 meters (5.5 deg F per 1000 feet) altitude. If a parcel of air is at 24 degrees C at sea level, and it rises to 1000 meters, its temperature will go down to 14 degrees C. If it goes up to 2000 meters, its temperature will go down to 4 degrees C.
The temperature would be minus 6 degrees C.
This rate of temperature change of unsaturated air with changing altitude is called the dry adiabatic lapse rate: the rate of change of the temperature of rising or subsiding air when no condensation is taking place (we’ll talk about the condensation part shortly).
If the air subsides, it also changes temperature. It warms up, and it is warming up at the dry adiabatic lapse rate. So, if the air at 4000 meters altitude has a temperature of -10 degrees C, and it subsides to 3000 meters, its temperature will warm up to 0 degrees C. If it continues to subside, then at 2000 meters, its temperature will be 10 degrees C.
Its temperature would be 20 degrees C.
Make sure you notice that we are talking about moving air (rising or subsiding), not still air. The change in temperature of still air (that is, air that is not rising or subsiding) follows the environmental lapse rate, which varies considerably, but averages about 6.5 deg C/1000 meters (3.6 deg/1000 feet). In still air, if you went up in a hot air balloon, carrying a thermometer and taking the air temperature every 1000 meters, on average the temperature would drop 6.5 degrees C every 1000 meters. The rate of temperature change as you rise in still air is not as great as the rate of change of rising air; that is, the air parcel does not cool off as fast.
For instance, the air temperature at sea level is 28 degrees C. Climb into your balloon, release the tethers, and go up 1000 meters in the still air.
The temperature will be 21.5 degrees C.
The temperature will be 18 degrees C, cooler than the still air; the dry adiabatic lapse rate is greater than the environmental lapse rate.
Let’s abandon the still air for the moment, and return to the air which is rising, and getting colder. Remember what happens to relative humidity when air temperature decreases? Ok then.
If the temperature of the parcel of air decreases, the relative humidity increases. This is a KEY point. If you did not answer this correctly, you really should go back and review the explanation of relative humidity.
You can maybe see what’s coming next. If the air is rising and cooling at a rate of 10 deg C/1000 meters, (5.5 deg/1000 feet), eventually, it’s going to cool off enough for the relative humidity to reach 100%, and condensation can take place. The dew point is the temperature at which the air becomes saturated and condensation takes place (note: dew point is a temperature, given in degrees C or F). The lifting condensation level is the altitude at which condensation begins (note: lifting condensation level is an altitude, given in meters or feet). You can look up at the windward sides of mountains and see where the lifting condensation level is, because that is where you will see the bases of clouds that have formed.
Here’s where it gets a bit complicated. Remember what happens when water changes state?
So, if condensation is taking place, latent heat is being released to the surrounding air. So you have two opposing trends going on at the same time within this parcel of air. It’s rising and cooling, but it’s also condensing and being warmed. Which one will win out? That is, will the air get colder, or will it get warmer?
Well, what happens is that the air will still cool off, but not as fast. If water vapor in the air is condensing, the adiabatic rate is lower. The air is only cooling off at a rate of about 5 degrees C/1000 meters (2.7 deg per 1000 feet). This is called the saturated adiabatic lapse rate (or the wet adiabatic lapse rate, or the moist adiabatic lapse rate, depending on the textbook you are using). The saturated lapse rate varies with the original temperature of the air parcel, but 5 degrees C/1000 meters is a commonly used value.
So, let’s assume a rising parcel of air reaches the lifting condensation level at 2000 meters, at a dew point temperature of 12 degrees C. At this point, clouds will form. As the air continues to rise, it will continue to decrease in temperature, but more slowly than it cooled off before condensation began.
The temperature at 3000 meters will be approximately 7 degrees C. The saturated adiabatic lapse rate is given as 5 deg C/1000 meters, so if you go up 1000 meters, the air will cool off 5 degrees. 12-5=7.
Air which is subsiding will be increasing in temperature. If we assume that there is no moisture left in the air (which may not always be the case), the applicable rate is the dry adiabatic lapse rate.
Ok, here’s the mountain.
It is exactly 3000 meters in elevation, rising from sea level, since it is located right on the coast. It is in the middle latitudes, and the prevailing westerly winds blow from the ocean on to the shore. The air temperature at sea level is 26 degrees C. The moving air strikes the mountain, and is forced to rise along the windward slopes until it gets to the top. Then it can subside down the leeward slopes.
The first question is, what happens to the temperature of the air as it rises up the side of the mountain?
The temperature decreases.
The next question is, how much will the temperature change? To answer this, you first have to decide which lapse rate to use. We know that the air is rising, and we will also state that condensation is not taking place in the rising air (that is, the temperature of the air has not reached dew point). Therefore..
The dry adiabatic lapse rate. If you did not get this right, quit wasting your time on this, and go read the section on Adiabatic Processes.
The next thing we need to do is give some lapse rates you can work with. Here they are:
Also, we will state that the dew point temperature for this parcel of air is 6 degrees C.
So, since we have already determined that we will be cooling the air parcel off using the dry adiabatic lapse rate, let’s see what happens to this air.
The air starts at sea level with a temperature of 26 degrees C.
The temperature will be 16 degrees C. The air rose up 1000 meters, so it cooled off by 10 degrees C. If you said that the air temperature would be 36 degrees C, you made a common mistake. Don’t feel bad, but be careful in the future.
The temperature will be 6 degrees C.
Remember that 6 degrees C is dew point.
100% relative humidity at dew point
For this particular situation, 2000 meters is the altitude at which condensation takes place. This is called the lifting condensation level. Please note the difference between dew point and lifting condensation level. Dew point is a temperature and is given in degrees C or F, while the lifting condensation level is an altitude (the altitude at which dew point is reached) and is given in meters or feet.
So, as the air continues to rise, it cools to a lower temperature (because it is rising), but it doesn’t cool off as rapidly (because latent heat is being released). Therefore, the lapse rate changes.
Saturated adiabatic lapse rate (also known as the wet adiabatic lapse rate, or moist adiabatic lapse rate)
Notice that condensation is taking place, so clouds (composed of tiny droplets of liquid water) will form, though it may or may not rain.
The air temperature will be 1 degree C.
Once the air reaches the top of the mountain, it can begin subsiding down the leeward slopes. It subsides because it is cooler than the surrounding air.
As the air subsides, its temperature will rise.
No, condensation will not take place. If the temperature is rising, the relative humidity will drop, and condensation will stop.
Let’s assume that no more moisture remains in the subsiding parcel of air.
The dry adiabatic lapse rate will be used if the air is subsiding and no evaporation is taking place.
The temperature will be 11 degrees C. 1 degree at 3000 meters plus a 10-degrees increase in temperature (following the dry adiabatic lapse rate) equals 11 degrees C.
The temperature will be 21 degrees C.
The temperature will be 31 degrees C.