## When does it rain?

Insights/Curriculum Highlights:

• One of the components of air is water in its gaseous or vapor state.

• Water vapor makes up only a few percent of air.

• There is a limit to how much water vapor air can hold.

• If that limit is exceeded, then condensation or rainfall occurs.

• That limit is a law of nature, which applies to all bodies of air,all over the world.

• The amount of water vapor thatair can hold depends on its temperature. Warm air can hold more watervapor than cold air.

• Within a given parcel of air,the limit can be exceeded and rainfall or condensation triggered, bycooling the parcel of air. In nature, this could happen as the parcel ofair rises.

• Alternatively, within a given parcel of air, the limit can be exceeded and rainfall or condensationtriggered, by increasing the amount of water vapor in the parcel of air.In nature, this could happen as the parcel of air travels across an oceanor large lake.

Thinking Skills / PedagogicalHighlights:

• Making connection between laboratory scale observations and atmosphere-scale data sets.

• Drawing on laboratoryobservations to explain an aspect of a natural system.

• Making connection between dataand every day observations (e.g. blow drying of hair).

• Thinking about phenomena (e.g.water vapor) that are invisible.

• Linking visible-scale processes(e.g. condensation) to microscopic or molecular scale processes (e.g.vibration of molecules).

• Building chain of reasoning fromcause to effect.

• Building chain of reasoning from observation to interpretation.

• Using time series graphs, comparing how different parameters vary through time.

• Thinking about a process withtwo variables (changes in either vapor content or temperature of air cantrigger rainfall/condensation).

1. Introductory Hands-onInvestigation: Cold Soda Can:

Take a soda can outof the freezer. Have students observe what happens to the outside of thecan: tiny droplets of water form.

Discussion. Points to note:

- What are the droplets made outof? (water)

- Where did they come from? (out of the air;they were vapor previously, then turned to liquid)

- What made the water turn from vapor to liquid? (the air near the can wascooled by contact with the cold can. When the air cools, some of the vaporcondenses)

2. Directed, data-basedinvestigation: Saturated Vapor Pressure

Each student-pair works with data from one site. Black Rock Forest OpenLowland works especially well for this investigation. Data intervalsshould be chosen to avoid sub-zero temperatures (when precipitation dataare less reliable). Data should behourly or 15 min (not daily averages).

For this data set, thestudent-pair prepares a scatter plot of temperature versus water vapor.

- figure 1: graph of airtemperature versus water vapor pressure from Open Lowland site, hourlydata.

Students examine anddescribe the resulting graph. Points to note:

- There is a wide range oftemperatures in the data.

- There is a range of vapor pressures in the data.

- There are some data points with high temperature and high water vapor.

- There are some data points with high temperature and low water vapor.

- There are some data points with low temperature and low water vapor.

- But there are no data points with lowtemperature and high water vapor. This combination of conditions neverhappens.

- There is a very abrupt line between the partof the graph with data (higher temperature/lower water vapor) and the partof the graph with no data (lower temperature/higher water vapor).

- The presence of this abrupt line is auniversal property of the atmosphere, no matter where you look around theworld, the same relationship is found.

Students try to explain the existence of this boundary in terms of theirhands-on experience with the soda can: if temperature gets too low (oramount of vapor in the air gets too high) condensation occurs.

Teacher introduces vocabularyfor this concept: saturated vapor pressure curve.

To verify students'understanding of this concept, have the students plot a few points by hand,superimposed upon the temp/vapor pressure graph created above. For eachpointthat the students plot by hand, have them try to visualize the weatherconditions indicated by that data point:

- what kind of day was it?

- would you have needed a raincoat?

- would you have needed a sweater?

For each point thatthey plot by hand, students should state whether or not condensation wouldoccur.

- figure 2: student worksheet:condensation or no condensation?

- figure 4: temperature versus vapor pressuregraph, with hand-graphed data points superimposed

3. Hands-on Investigation:Dewpoint

Students are given a beaker, ice cubes, a thermometer, water. They putthe ice cubes in the water in the beaker, and stir gently with thethermometer. Eventually droplets are observed on the outer surface of thebeaker. The temperature in the beaker at the time the droplets first form is noted.

Discussion of what happened.Points to note:

- What are the droplets made out of(water)? Where did the droplets come from? through the glass or out ofthe air? and how do you know? out of the air, water condensed outof air.

- Water, in its gaseous or vapor state, ispart of air.

- What made the water vapor change fromgaseous to liquid state? If a given body of air is cooled, water willcondense out of it.

- Did all groups observe the droplets forming when the beaker was at thesame temperature?

Teacher develops theidea of dewpoint:: the temperature to which a body of air would need to be cooled in order forcondensation to occur. What is the dewpoint for the air in our classroomtoday?

Different parcels of air have different dewpoints. The dewpoint variesfrom day to day and from place to place. Now return totemperature/saturated vapor pressure graph made in step #2. Point to anydata point. This point represents a parcel of air. What would be the temperature to which that parcel of air would have tobe lowered to cause condensation to occur? What would be the dew point ofthat parcel of air?

To verify students grasp of thisconcept, have them plot some points on the graph by hand. For each pointwhich they plot, have them determine the dew point for the parcel of airrepresented by that data point.

- figure 5: student worksheet fordewpoint and relative humidity

- figure 7: temp/vapor pressure graph with explanation of dewpointsuperimposed

(Optional) Teacherfurther develops the idea of what it means to condense and what itmeans to evaporate. Relation between heat and molecular vibration. Relation among heat,vibrational energy of molecules, how tightly bound molecules are to eachother, changes of state

4. Directed, data-basedinvestigation: Relative Humidity

NumericalData/calculator exercise:

- Initially, students work with asmall table of data from a small number of days containing hourly airtemp, vapor pressure, relative humidity.

- By hand, students plot each data point onthe graph created above according to its temperature, vapor pressure value.Note that the "vapor pressure" value is the actual amount of vapor that was in the air when the data point was recorded.

- For each data point, students determine themaximum amount of water vapor that could potentially be heldwithin that air mass, by reading off saturated vapor pressure from thegraph created above.

- (figure 5: worksheet for dewpoint andrelative humidity)

- (figure 8: temp/vapor pressure graph withexplanation of relative humidity superimposed)

- For each data point, students calculate aratio between the actual amount of water vapor and the potential amount ofwater vapor, and express this ratio as a percentage. This percentage isentered into the data table, and also written on the graph next to the applicable data point.

- Teacher introduces vocabulary for thisratio: "relative humidity."

Data Harvesterexercise:

- Students begin with the vaporpressure versus temperature scatter plot created in part 2.

- Students are asked to point out where on this plot are the points thatcorrespond to parcels of air with 100% relative humidity? Where are thepoints that correspond to parcels of air with 50% relative humidity? 75%relative humidity?

- Students use the Data Harvester third parameter (color) to display relative humidity.The color bands of relative humidity roughly parallel the saturated vaporpressure curve, diverging towards the warmer temperature. What does thismean?

- (figure 9: temperature versus vaporpressure curve with relative humidity in color.)

5. Discussion: Relating allthis to everyday experience.

Keeping in mind what we havelearned about relative humidity and saturated vapor pressure, explain thefollowing:

- why do people blow dry their hairafter swimming or showering?

- why do sales of skin moisturizer and chapstick go up in the wintertime?

- why do clothes usually dry faster in a clothes drier than on a clothesline?

- why do people put pans of water on their radiators in the wintertime?

6. Directed, data-basedinvestigation: When does it rain?

Students begin withthe vapor pressure versus temperature scatterplot created in part 2.

Set the Data Harvester's thirdparameter (color) to equal the amount of precipitation. Examine the graph.Set the color bar scale so that data points representing times of some rainare clearly differentiated from data points representing times of no rain.

- (figure 10: saturated vapor pressurecurve with rainy points colored)

Students examine scatterplot. Points to note and discuss:

- In most cases, the (temp, vaporpressure) data points recorded while it was raining fall on the saturatedvapor pressure curve (i.e. the line separating the field with data from thefield with no data).

- A few data points recorded while it wasraining fall in the undersaturated field (i.e. amid all the other datapoint not on the saturated vapor pressure curve.)

-Develop the idea that rainfall occurs when temperature falls, or vaporpressure rises, to intersect the saturated vapor pressure curve.

7. Discussion: Relationship tonatural processes:

We have learned thatprecipitation or condensation may occur when a parcel of air coolssuffiently that it reaches the saturated vapor curve OR when the watervapor of a parcel of air increases so that it reaches the saturated vapor curve.

In nature, what could cause thetemperature of a parcel of air to cool, such that it reaches the saturatedvapor curve?

- nightfall > dew at night

- autumn > September fogs

- rising through troposphere > clouds andrainfall

In nature, what couldcause the vapor content of a parcel of air to increase, such that itreaches the saturated vapor curve?

- traversing across a large lake orocean

Exploratory Extension #1: DataAnomalies

Try to figure outwhat is going on with those few data points representing hours when itrained but that don't fall on the saturated vapor pressure curve. Points toconsider:

- Rainfall occurs when the atmospherereaches saturated vapor pressure someplace high above the earth's surface.Our measurements were made at the earth's surface, not up in theclouds.

- Temperature and vapor pressure data are only available as hourlyaverages. Conditions may have changed within the hour; if so the hourlyaverage data might not be representative of the conditions at the momentthe rain began.

- Try plotting precipitation and relative humidity as a time series, on thesame graph. Look at a week of data at a time.

- Generalize from the points above. When trying to figure out why datadiffer from predictions, it's often useful to think about the variations intime and space within the data set.

- Generalize even further: When trying to figure out why data differ frompredictions, three things could be going on: (1) the data could be wrong,(2) the model from which the predictions were made could be wrong, or (3)the model could be misapplied, for example

Exploratory Extension #2:Change the dewpoint

Start with theexperimental setup for the hands-on investigation of dewpoint, above.Students are then givenaccess to additional materials, which could include: another liquid (e.g.grape juice), salt, a fan, a room humidifier. They are told to try toalter the temperature at which moisture first appear on the outside of thebeaker, i.e. the dewpoint.

Discussion about what happened.Points to note:

- It doesn't make any differencewhat fluid (fresh water, salt water, grape juice) is inside the beaker;droplets will still form on the outside of the beaker at the sametemperature.

- Does it make a difference if the beaker is cooled down slowly (few ice cubes) or fast (a lot of ice cubes)? If so,why?

- Does it make a difference if you fan the beaker set up while you arecooling it down? If so, why?

- If you use the humidifier to increase the humidity around theexperimental setup, the dewpoint gets higher. Why?

- (figure 11: for two parcels of air with the same initial temperature,the dewpoint can be altered by changing the ambient humidity)

Students articulate a"word model" (aka an "explanation") of what controls when the water beginsto condense out of the air.

Exploratory Extension #3:weather and climate

Weather is what happens in a given place from day to day. Climate can be thought of aspatterns (or characteristics) in the weather. Weather is to mood asClimate is to personality.

Temperature and moisture areimportant components of climate. One way to think about and visualizeclimate is to use the vapor pressure/temperature scatterplot we madeearlier. The weather at one spot on the earth during one hour is represented by one point on thisscatterplot. Climate can be represented by a region or "field" on thescatterplot, covering a range of both temperature and humidity. A smallfield represents a climate with little variability in temperature or humidity over the course of the year.

On the scatterplot created inDirected Investigation part 5 (the one with the colored relative humiditypoints), sketch the field which you think would represent the climateof:

- a tropical island, where theseabreeze blows constantly day and night, and the temperature is alwaysbalmy.

- the Sahara Desert

- a continental climate, such as Minnesota

- a Mediterranean climate, such as Greece or Italy

On the World Wide Web, find temperature and relative humidity data fromplaces representing each of these climates (e.g. Hawaii, Cairo, etc.) Dothe data fall within the field which you have sketched for that climatezone?

In literature, find vivid descriptions of weather in one place in different seasons. Estimate where on the scatterplot the weather ineach of these descriptions would fall; then sketch the climate "field" thatwould describe the climate of the region.

Created by Kim Kastens (1997), Lamont-Doherty Earth Observatory (kastens@ldeo.columbia.edu).
May be freely used for educational purposes provided appropriate credit is given.

Revised Sept 15, 1997, Kim Kastens, with commentsfrom Earth Curriculum Workshop, changed order, added soda can; movedexperiment with humidifier to Extension; removed Extension with artificial rain in Bio2; removed display of precip and relativehumidity as time series (it now appears as a suggestion only, in the dataanomalies extension).