Introduction: Precipitation, any process whereby atmospheric water is transferred to the earth's surface, is a complex phenomenon. Central to understanding this process is the concept of Relative Humidity which is itself rather complex. We will achieve an understanding of both relative humidity and the precipitation process by first introducing some fundamental concepts and then by using analogies or heuristics to model the concept of relative humidity and the precipitation process.
Basic Concepts: Before moving on to relative humidity, we need to understand two other measures of humidity.
1. Actual Mixing Ratio (AMR): As the name implies, AMR is a measure of how much water vapor (water in the gas phase) is actually present in a mass of air. The units are grams of water vapor to kilograms of dry air in a given parcel or blob of air.Here is a helpful way of summarizing the concepts of AMR and SMR by way of a heuristic.2. Saturation Mixing Ratio (SMR): This is a measure of the maximum amount of water vapor air can "hold" given its temperature and pressure. How does SMR react to temperature and pressure?
a) We all know that warm air "holds" more water vapor than cold air. This is why you use a hot blow drier rather than a refrigerator to dry your hair...at least I hope so!RULE: There is a Positive Relationship Between Temperature and SMR.
b) Here is a useful heuristic. Imagine that air acts like a sponge when it comes to water vapor. Like your hand squeezing a sponge, the higher the air pressure the less water vapor air can hold. Or like releasing your grip on a sponge, the lower the air pressure the more water vapor air may hold.
RULE: There is a Negative Relationship Between Pressure and SMR.
I'll bet you have already figured out what Relative Humidity is. Let's see.
Relative Humidity Defined: Relative humidity is the ratio of the actual amount of water vapor in the air to the maximum amount that the air could hold given the temperature and pressure. More simply put, relative humidity (RH) is how full the coffee mug is. Is it half full, RH = 50% or three-quarters full, RH = 75%? The simple formula for relative humidity is shown below.
Relative Humidity Calculation: There are three bits of information needed to calculate RH, the AMR, the Temperature, and the Pressure. For most all problems, AMR, temperature, and pressure are given to you. So how do you get SMR? You will need a Saturation Mixing Ratio chart like the one shown below (you have one in your packet of handouts).
How to Read the SMR Chart: Note that each column on the chart has a heading. The headings are for standard pressures with 1,050mb on the extreme left and 500mb on the extreme right side of the chart. Each row is assigned a temperature with -25°C at the top and 34°C at the bottom. Let's do a SMR lookup example. What would the SMR be if the current pressure is 1,050mb and the current temperature is 14°C? Find where the 14°C row and the 1,050mb column intersect (green arrows). The number 9.654 is found at this intersection meaning that the maximum amount of water vapor that air may hold at the stated temperature and pressure is 9.654 grams. Read up the chart from this intersection. Note that as temperatures drop SMRs drop. Read down the chart from our original intersection. Note that SMRs increase as temperatures increase. Now return to our original intersection one more time and now read to the right along the same row. What you are doing is lowering the pressure while maintaining 14°C. Note that SMRs increase as pressure drops (the reverse is also true).Dew Point: Dew Point is the temperature at which a particular parcel or blob of air will reach 100% relative humidity. Let's determine the Dew Point (DP) for our previous example. Locate the 1,000mb, 14°C intersection. Since air must cool for DP to be reached, just read up the 1,000mb column from the 14°C starting point until you find an SMR that matches our given AMR of 6.771 (blue arrows). Note that at 8°C the SMR matches our given AMR. This means that if the air were to cool to 8°C the RH would reach 100%; dew point would have been reached.Sample RH Calculation: What will the RH be if the AMR is 6.771, the pressure is 1,000mb, and the current temperature is 19°C?
-the SMR at 1,000mb and 19°C is 14.03 (red arrows on the chart).
The Precipitation Process: The following diagram is a heuristic, an instructive model that is analogous to reality. In this example, we have a coffee cup that represents SMR. So, if cooling occurs, the cup gets smaller (the SMR drops). If warming occurs, the cup gets larger (the SMR increases). The coffee in the cup is the AMR. The relationship between the amount of coffee in the cup and the size of the cup is analogous to percent relative humidity (see below).
Example Interpretation:A The mug holds 10oz so the SMR is 10. There is 6oz of coffee actually in the mug so the AMR is 6. The RH is (6/10) x 100 = 60%.Terms to Know: If you come across any of the following terms, all the others are implied.B With cooling, the SMR or the mug size drops to 8. There is still 6oz in the mug so the RH has now risen RELATIVELY to (6/8) x 100 = 75%.
C As the air cools further, the SMR or mug size continues to drop which drives up RH. Here we are at cup-full. Now AMR and SMR are equal so we are at 100% RH. We have reached Dew Point although we do not know the actual temperature.
D Even though we had already achieved cup-full at C, with continued cooling SMR must drop. RH must, however, not go over 100% even though SMR is still dropping. If RH went above 100%, this would mean that somehow coffee would be suspended above the brim of the mug (shown in red). This does not happen. Instead, 100% RH is maintained by having the AMR drop at the same rate as the SMR. This would require the coffee to spill out of the cup. This is analogous to precipitation. Rain, or any other form of precipitation, occurs when 100% RH is reached and air continues to cool.
E Now the air begins to warm. This will cause the mug to get larger as SMR is positively related to temperature. Notice the AMR. It is now 4 since that is all that remained in the air following step D. Clearly as air warms, the RH goes down (the mug is now relatively less full). The RH is now (4/8) x 100 = 50%.
100% RH Dew Point Rain AMR = SMR Condensation Snow Saturation Cloud Formation Precipitation Cup-full Fog Frost
