GG 140: The Atmosphere, the Ocean, and Environmental Change
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The Atmosphere, the Ocean, and Environmental Change
GG 140 - Lecture 11 - Clouds and Precipitation (Cloud Chamber Experiment)
Chapter 1: Interactions between Visible Light and the Atmosphere [00:00:00]
Professor Ron Smith: Well, when I lectured last on Wednesday of last week, we went through a long PowerPoint presentation about water in the atmosphere. And there’s a lot of information in that. And of course, that lecture’s been posted. But today we’re going to continue on from there. We’re not finished with water in the atmosphere. We’re going to move more towards the subject of precipitation–how precipitation forms.
And let me begin by just describing what you see when you look at a cloud. So I’ve got a little cartoon here. I’m going to make a cloud in just a minute. But what do you see when you look at a cloud? There’s a cloud. There’s you as the observer. You are–when you look away from the cloud, you’re seeing sunlight that has scattered off air molecules. And that light looks blue to you. When you look at the cloud itself, you see sunlight that is scattered off tiny condensed water droplets. And that cloud looks white to you. Under certain circumstances, if you look at the rain falling from the cloud and the light, the orientation of the illumination is just right, you’ll see a rainbow.
So what’s going on? Why do you see three such very different things when you look at a cloud? Well, it has to do with the different types of the way light scatters from particles. And so I wanted to just run through this before we got any further into clouds. If you imagine a photon of light with a certain wavelength lambda approaching a particle, it’s going to be scattered off by that particle in some direction. What matters is the ratio of the wavelength of the light to the diameter of the droplet, that ratio.
If the wavelength is much, much larger than the diameter of the droplet, that’s called Rayleigh scattering, named after the famous English physicist. And under that condition, the scattering, you say S, is proportional to one over the wavelength to the fourth power. In other words, the shorter the wavelength, the more is the scattering under that condition. The shorter the wavelength for the same particle, the more is the scattering.
Well, that’s why the sky is blue because the visible spectrum includes red on the long wave side, green in the middle, blue on the short wave side. So when light comes from the sun and encounters these small air molecules, the blue light is scattered more than the green and the red. And therefore, the light scattered to your eye–what you saw this morning as you walked up, the blue sky. That’s because that scattering is from very small molecules which places you into the Rayleigh scattering regime, where short wavelengths scatter more intensely than the longer wavelengths. So that’s why this sky is blue.
Now the cloud particles in the cloud are much larger than molecules. They’re typically 10 microns in size, which is of such a wavelength that it puts you into the so-called Mie scattering regime where wavelength is within one or two orders of magnitude of the diameter. It doesn’t have to be close to the same as the diameter but within a factor of 10 or 100 of the–I see you straining to see them. Let me pull this down, might help with it.
Mie scattering, if you’re in that regime, all wavelengths are scattered roughly equally. Red, green, blue light are scattered equally. That is whatever color you have illuminating the object, that’s the same color you will get reflecting from the object. So if you’re illuminating the object with white light, then the scattered light will be white as well, have the same mix of the different colors in the spectrum. So the cloud appears white to your eye because it’s scattering all those different solar wavelengths equally.
The other case—the third case is when the diameter of the object is much larger than the wavelength of light. That would apply, by the way, for a raindrop which has a diameter of about one millimeter. And remember the wavelength we’re talking about, for example, visible light, is only 0.5 microns. So that would easily satisfy that. And that’s the case where you can trace–it’s called geometric optics is the physical name for that scattering regime. That means you can actually trace a ray of light that comes into the raindrop, refracts as it enters, bounces off one side, refracts again, and comes back to your eye, splitting the color slightly because the refractive index—the bending of the light is a function of wavelength, therefore, giving you this special rainbow effect.
You couldn’t get that from cloud droplets because they’re too small. But the fact that they’re larger allows you to see that splitting of the light and the rainbow forming in that way. So that is basically what you see when you look at a cloud, and the sky, and the raindrops.
Chapter 2: Using Radar to Detect Precipitation [00:07:15]
A couple of other points though. There’s another way that meteorologists look at clouds, and that’s with radar–meteorological radar. I’ve sketched that here. You’ve got a dish antenna. You make a microwave signal. Usually that wavelength is about 10 centimeters, about like that. You send it towards the cloud. And it may or may not scatter back to your radar system. If it does, you can determine the distance from the time it takes the radar signal to get there and back. And you can learn something about the particles in that cloud. But remember, with a longer wavelength, the same cloud droplets, and even the raindrops, are going to be in the Rayleigh scattering regime. So with this longer wavelength, you’re almost always going to be in the Rayleigh scattering regime because your wavelength here is so much larger than the wavelength of visible light.
So with that strong inverse dependence on wavelength, and the diameter comes in too, it turns out that cloud droplets do not scatter radar effectively, but raindrops do. So when you’re looking at a radar image of a cloud, you are seeing only where it is raining. You do not see the cloud you see with the visible eye. With the visible eye, you see this white puffy thing full of cloud droplets. Radar doesn’t see that. Radar goes right through. But the radar will bounce off from the raindrops or the snowflakes within that cloud. So remember when using a meteorological radar, you are seeing precipitation rather than clouds per se. Of course, clouds produced precipitation, but they are different things. Any questions on that?
Chapter 3: Cloud Formation Experiment [00:09:13]
OK. Well, that is background. We can do a little experiment to make a cloud. I’ve got a vacuum pump hidden under here and a little grey chamber that I’m going to evacuate. I’m going to hook this up to the jar in this way. And then by twisting a valve, I’m going to allow some of the air from this jug to pass into this evacuated cylinder. When I do that, let’s say for the sake of argument that I take about that much of the air from here on up and suddenly remove it. Well, then the rest of the air in the jug is going to expand to fill the jug.
Now what happens when air expands suddenly? We’ve been over and over this, but now you’re going to see it in this new context. When air expands, it does work on its environment. And it adiabatically cools. Its temperature drops because of that work it’s done in expansion. When the temperature drops, the saturation vapor pressure drops as well. That is, the amount of water vapor that can be held in the vapor state suddenly decreases.
Well, if I’ve got—if this is the saturation vapor pressure, and this is the amount of water vapor that I actually have, the partial pressure of water vapor, and I suddenly drop the temperature, that’s going to drop this value down. I haven’t changed the amount of water in the air, but I’ve decreased the amount that can be held in the vapor state. And if I move it down to this level and slightly beyond, that excess must suddenly condense. It cannot remain in the vapor state. And therefore, I’m going to force a cloud to form in very much the same way that the atmosphere does, by adiabatic expansion. The only difference is instead of getting the adiabatic expansion by lifting a parcel up into the atmosphere, I’m doing it with this little apparatus of suddenly dropping the pressure. Are there questions on this?
Now I’m going to give it a few condensation nuclei because I prefer to form a large number of small droplets rather than a small number of large droplets. It’ll make the cloud more visible that way. So I’m just going to blow a little bit of smoke in there. You won’t be able to see this, but these will be very tiny—these will be very tiny aerosol particles just to give the water something to condense on to.
What you hear is a vacuum pump. I have a little gauge here to tell me whether or not it’s working, whether this chamber is being evacuated. I put it on this overhead projector to get nice illumination of the chamber. And you see it’s empty now. There’s nothing there. OK, I think we have a little bit of a vacuum in here. So I’m going to try suddenly opening–right now this valve is closed. So there’s low pressure here but normal–look–normal atmospheric pressure in the jar. But when I open that valve, some of the air is going to be sucked off. And we’ll see this doesn’t always work. But we’ll see if we can form a cloud this morning.
Three, two, one, there’s a cloud. Now this is a reversible process where I suddenly, to bring that parcel back down to the atmosphere or here just let the pressure build up, it would compress warm and remove the cloud. So on the count of three, I’m just going to rip the top out of there and let atmospheric pressure push that down again. Three, two, one. I’m going to repeat that again. Let me close this off. Let me take questions for a minute about what I’ve done here. Are there any questions about what I’m actually doing physically up here? Question?
Student: Can you explain it again?
Professor Ron Smith: So I’m evacuating this grey cylinder. It’s just a little reservoir of low pressure. When I open the valve, then some of this atmospheric pressure is going to bleed off into here allowing the rest of the air to expand suddenly. That’s just what happens when an air parcel rises up in the atmosphere and expands, cools adiabatically, drops the saturation vapor pressure, and the excess water vapor must then immediately condense. And it’s finding one of the small particles in there, condensation nuclei, to condense on.
Notice how small these particles are. You may have seen them swirling around. But they didn’t fall out. Let’s watch that the next time I do the experiment here. I think we’re set. I haven’t got a very good vacuum. Maybe this wasn’t closed properly. It’s OK. Three, two, one.
Now there are tiny particles in there, but you don’t see them falling. Sometimes you see them swirling around a little bit. There’s some air currents in there. But they’re so small that they don’t really fall out gravitationally. I’ll reverse the process now. Three, two, one. And it’s gone. OK. That is how a cloud forms. Are there questions on that? They’re must be some mysteries on what I’ve done here. Anything at all?
Student: Does the jar feel cold to the touch?
Professor Ron Smith: I’m sorry.
Student: Does the jar feel cold to the touch?
Professor Ron Smith: No. I don’t think the temperature drop is enough. And the mass of the jar itself is too large, I think, for that to be detectable, at least by my hand on the outside. If we had a proper sensor in there, we could probably measure it, if it was a fast response instrument, we could probably measure a several degree drop. I’m guessing–I haven’t done the calculation. I’m guessing it would be three or four degrees Celsius.
I’ve got a little bit of liquid water in here. So this air is pretty humid to start with. Probably–I’m guessing the air in there is probably 90% or 95% relative humidity, so I don’t have to cool it too much to bring it to saturation. But I doubt that I can feel that temperature difference there. But there is one, but I think it would have to have a good sensor inside to feel that. That’s a good question though. Temperature is a key here, and that part we can’t see. We could only see the response of the water vapor to that drop in temperature. Yes?
Student: Why do the particles start swirling after you have the cloud?
Professor Ron Smith: Well, when I suck the air out of there, remember if I suck it out, it’s not going to come out smoothly. It’s going to come out suddenly in one region more than another. And that’s going to produce some eddies in there just because I’ve suddenly drawn air out of one part of the chamber. So that’s just leftover from–it could also be a little bit because I’m heating it from the bottom. It could be a little bit of thermal convection. But I suspect it’s mostly just because I drew the air out very suddenly from one location in the bottle. Anything else on that? Yes?
Student: For the equation S≈1/λ4, is that for all the scattering or just for the Rayleigh scattering?
Professor Ron Smith: That’s just for Rayleigh scattering. Yes. In fact, for Mie scattering, you would write S is approximately independent of wavelength. And for geometric optics, it’s more complicated because the ray is actually bouncing around inside the raindrop and scattering in a different way. So that applies only to the Rayleigh scattering. That’s the property of–that is why the sky is blue when you scatter off very small particles. OK. Anything else on the experiment?
Chapter 4: Collision Coalescence Mechanism of Raindrop Formation [00:19:06]
Now the subject that we have to deal with today is how you take a cloud that is composed of these tiny cloud droplets, 10 microns in size, too small to fall gravitationally and occasionally get rain out of these clouds. As I mentioned last time, if you compare the diameter of a droplet to the diameter of a raindrop, there’s a factor of 100 difference. Their volumes are different by a factor of a million. That’s 100 cubed, because the volume of the sphere goes like the cube of the radius. So we’d have to bring together a million cloud droplets to form one raindrop.
How and under what circumstances are we going to do this? There are two theories. Your book is good in this. There are two outstanding theories for this. The first one is called collision-coalescence. If you have tiny cloud droplets, but they’re not all the same size, some are a little bit larger than others, they’re not falling very fast.
But the large one is going to be falling a little bit faster than the smaller ones. And therefore, up in the cloud, the larger ones are going to overtake the smaller ones. And when they collide, they may coalesce. They might not. They might bounce off each other. But with some degree of efficiency, they will coalesce and make a larger droplet.
Well, now it’s going to fall even faster. And so it’s going to sweep up smaller droplets at an increasing rate. And before you know it, you could sweep up a million droplets and form a raindrop. You may have seen something like this on a cold winter day with droplets condensing inside of your window at home. Sometimes a drop will start to move down the window. And then as it collects up other droplets, suddenly it will fall right to the bottom of the window. That’s kind of what I’m talking about with collision-coalescence. It’s not a very efficient process most of the time, because these cloud droplets are too similar to each other. There’s not enough of a range of large to small particles to get this going. But on occasion, especially over tropical oceans, this mechanism is thought to dominate.
Chapter 5: Ice Phase Mechanism of Raindrop Formation [00:21:36]
The other mechanism, a little more complicated, so follow this argument closely. It assumes that you have supercooled water droplets, tiny droplets at a temperature colder than zero degrees Celsius. It wants to freeze. It’s cold enough to freeze. But it needs something to trigger the freezing. That’s called a freezing nucleus. Some little particle of dust or some little speck of something or other that would trigger one of those to freeze.
So imagine you’ve got a cloud with supercooled liquid water. And something makes one of those droplets suddenly freeze. So I’ve drawn it now with a six-sided shape indicating it’s an ice crystal. It turns out, here’s the key, that ice at the same temperature as liquid water has a slightly lower saturation vapor pressure. Ice and water at the same temperature, the ice has a slightly lower saturation water vapor pressure. That means that the ice is a little more attractive to water vapor than the liquid is.
So I freeze one of these droplets. And immediately, it starts to draw water vapor towards it and grow. Meanwhile, the other droplets begin to shrink because the humidity is decreasing around, which starts to evaporate the cloud droplets that remain. So before long, this thing has grown to be quite large through a vapor deposition process, initially at least, a vapor deposition process.
This is a snowflake. And now it’s large. It will begin to fall out of the sky and may reach the ground as a snowflake if the temperature is warm enough. It may do other things. Once it starts to fall, it may start to hit. It may kind of go back to this mechanism. You might start to hit some of these supercooled liquid droplets. And they will freeze on impact. In which case, this will grow further by riming, by having supercooled droplets hit, and stick, and freeze when they hit.
Eventually, that could lead, for example, to a hail stone, where you first form a snowflake. And then as it falls out, you would collect by riming more of these supercooled water droplets. That would eventually produce a hail stone. Any questions on this ice phase mechanism?
This is believed to be the most common mechanism for producing rain and snow around the world. In fact, the rain we had over the weekend was almost certainly of this type. So most of the rain you’ve experienced unless spent over the tropical oceans has probably been formed in this way. Question? Yes?
Student: Why does the lower saturation vapor pressure mean it attracts more water?
Professor Ron Smith: So if you remember the definition of saturation vapor pressure, if I have a chamber with a condensed phase there and the vapor up here, saturation vapor pressure is a vapor pressure that will exist here when you’re in equilibrium with the condensed vapor. So if I suddenly change this from water to say ice, the ice is more attractive to the vapor and will suck a little bit of that extra water vapor out dropping this until the new equilibrium is reached. So I haven’t given you a, say, quantum mechanical explanation for why the vapor pressure over ice is lower. But I’ve explained what that means. I think that’s the best I can do at this stage.
This is a trickier mechanism. So I’d be happy to take questions on this if I haven’t made this clear. It’s called the ice phase mechanism for generating rain and snow. Sometimes it’s called the Bergeron mechanism after the Norwegian scientist that developed the idea.
Chapter 6: Mechanism of Precipitation Formation Based on Cloud Characteristics [00:26:17]
OK, now with that, then let’s talk about some different rain scenarios—rain or snow scenarios. If you have a shallow cloud, it’s warm at the surface. And you know somehow from a balloon sounding or an aircraft pattern that the top of that cloud is below the freezing level. That is the temperature is greater than zero degrees Celsius below, less above, but the cloud never reaches that height. And it’s raining. A simple process of elimination tells you that this must be the mechanism. It must be the collision-coalescence mechanism, because there’s no supercooled liquid water in this. All the liquid water in the cloud is at a temperature above zero degrees Celsius. So this mechanism is excluded. It must be a warm rain mechanism.
Let’s go on to the next phase. Let’s say this cloud is taller now. And the zero degrees Celsius line is there, meaning it’s colder above and warmer below. There’s a good section of this cloud then that will have supercooled liquid water in it. Probably what’s happening, if it’s raining out the bottom of this cloud, it’s probably because the ice phase mechanism is working, producing snowflakes up here. I’ve drawn my crude little snowflake. I made the cardinal sin of making it a five-pointed star when ice always has a six-fold symmetry. So I hope you can do better than that. You should put a Star of David there. That would at least have a six-fold symmetry.
So snow is being produced via this mechanism. Then it’s falling out. As soon as it falls and reaches the zero degrees Celsius line, it is going to melt and become a raindrop. And then it’ll fall as rain all the way to the ground. So again, the rain we had this weekend was almost certainly of that type formed as snow higher in the atmosphere. And as it fell, it melted and became a raindrop. And we felt it as rain. That’s the most common situation of all, by the way. This is extremely common, at least here in New Haven.
In the winter time, if you had temperatures less than zero degrees Celsius everywhere, if it was cold at the surface, and of course, even colder aloft in the troposphere, you could have the ice phase process forming snowflakes. And then they would simply fall all the way to the ground as a snowflake. That’s fine.
Occasionally, you may have encountered situations, or you will this winter if you keep your eyes open, where the temperature at the surface is almost exactly zero Celsius, within two or three degrees of zero Celsius. So that melting level is right about at the surface. What you’ll find then is that the snow that’s falling is wet and sticky. Because it’s actually begun its melting process in just the last few seconds as it’s fallen to Earth. But that’d be the special case somewhere just between these two where the zero line—zero degrees Celsius is just about at the surface of the Earth. Questions on these scenarios so far? OK.
Now here’s one that’s a little less common but can be quite important when it happens. It’s called an ice storm. And you have to imagine a temperature profile like I’ve drawn here. The vertical line for reference is the zero degrees Celsius line. So there’s a zero line aloft but another zero line close to the surface. In other words, cold, warm, and cold again near the surface.
So what’s going to happen? Well, up here it’s going to be just like this one. You’re going to have the ice phase mechanism producing snowflakes. They’re going to melt and become raindrops below that line. Now they are falling to Earth as a raindrop, a liquid drop. But then in the last few hundred meters before they hit the surface, they enter a cold layer of air. That air is going to cool down the droplet, probably even below the freezing mark. If that air temperature is say minus five Celsius, then it’s going to cool down that droplet to about that same temperature, minus five Celsius.
So now what do you have? The first time I mention this, but you now have a supercooled raindrop. Before I was talking about supercooled cloud droplets. Now I’m talking about a supercooled raindrop. It’s a millimeter in size. But it’s supercooled. That is going to freeze upon impact and coat everything with ice. The power lines are going to be drooping with the weight. The branches on the trees are going to be leaning and breaking over the weight of that ice freezing on impact as those supercooled raindrops hit the–
Student: So they’re raindrops?
Professor Ron Smith: Supercooled raindrops. Right. This is called freezing rain or an ice storm. And the damage is caused normally–well, of course, the roads are going to be dangerous too because the roads would be icy. But most of the damage is going to come, I think, from the weight of this on trees, and power lines, and so on, occasionally breaking them, making them come to the surface. But for that, you need this special behavior of the air temperature. Which around New England, you typically get once or twice each winter, you’ll get an ice storm that has this particular behavior to it. Any questions on that?
Chapter 7: Cloud Seeding [00:32:38]
Well, I can probably then say a few words about cloud seeding. Cloud seeding is an attempt to get clouds that are not raining to rain. You can imagine the frustration of a farmer who finds his crops withering for lack of rain. And yet all these clouds are passing by overhead with lots of condensed water. But it’s all in the cloud droplet form. Raindrops are not forming. He would give anything if he could just get this process–one of these two processes to work, the collision-coalescence or the ice phase process.
If the cloud has supercooled water, he might have a chance. And this is the way you do it. You inject into the cloud some freezing nuclei. You want to get a few of these droplets to freeze. And a good freezing nuclei would be a compound called silver iodide. AgI is the chemical formula for it. Because it has a crystal structure very much like that of ice. And so if a particle of silver iodide hits a supercooled cloud droplet, it is likely to cause it to freeze. And then this process could start.
So there is a big industry today in cloud seeding of cold clouds. I don’t know if I forgot to mention it, but a cloud which has no part of it at a temperature below freezing is often called a warm cloud. Well, that’s not going to work for silver iodide cloud seeding. You need to have supercooled water in that cloud for it to work. It would have to be something like this. In that case, you inject the silver iodide either from the ground, or from an aircraft, or from a rocket. And you hope that you’re putting in just enough and not too much.
What happens if you put in too much? If you put in too much, you’re going to freeze a large number of cloud droplets. And they’re all going to be competing for the same water. So they’re not going to grow. So on average, you have to freeze about one in a million. To make this most effective, you want to freeze about one in a million of the cloud droplets. Then you would get a million cloud droplets contributing to one snowflake. That would be ideal.
This is a bit of a dirty subject though because there is a lot of people doing this, a lot of cash being handed around and hopeful farmers paying for this. But the scientific, and I should say statistical evidence that this works is not so clear. And the National Science Foundation has stopped funding most research on cloud seeding because the people who were doing that work were not maintaining the highest standards of statistical verification of their work.
The problem is if you seed a cloud, and it rains, how do you know that it wasn’t going to rain anyway? That’s the big problem. So in order to do this properly, you would have to seed perhaps 1,000 clouds, half with a placebo. You do a blind test. Because if you allow the people that are doing the seeding to pick the clouds they’re going to seed, they may pick the clouds that look most likely to rain anyway. So you really need to maintain very high standards of statistical verification on this. And in the early days, this was not done. The field is beginning to come back now with a little higher level of statistical verification and beginning to become acceptable again scientifically.
But as I say, there’s still a big industry. For example, every year, seeding all along the Sierra Nevada range in California is done, and the claim is that has been increasing the snow pack every year. Even in the tropics, there is an industry claiming that they can seed warm clouds. This is even less likely to be the case.
First of all, silver iodide wouldn’t work. You’d have to have something else–in this case, you’d be trying to enhance this mechanism because it’s the only one that could work for a warm cloud. And the way you would do that would be perhaps to drop some kind of hydroscopic nuclei into it, like a salt particle, for example. Salt likes to pick up water. And if you could drop some salt crystals in there, you might be able to produce some droplets that are a little bit larger than the others. And that would enhance the collision-coalescence mechanism. But as I say, this is even less further along as a scientific development than is the seeding of cold clouds. Question? Yes?
Student: Are there any environmental concerns, putting silver iodide in–?
Professor Ron Smith: The question is, are there are environmental concerns? Well, yeah, that’s been discussed widely. Silver iodide, I think the saving thing here is that you don’t want to put very much in anyway. So you only put a small amount of silver iodide in. And there has been though–people have been able to find the remains of this in the environment. But as far as I know, silver iodide is not a particularly dangerous compound.
But do a check for yourself. Just Google silver iodide. AgI is the chemical formula. And see if it has any–as far as I know, except for recent literature, I haven’t followed, there been no environmental problems detected for that. But that’s a good question worth looking into. Other questions on rain? Yes?
Student: I guess the semi-legendary old belief that if you fired canons it would cause rain, does that have any basis in reality?
Professor Ron Smith: Not that I know of. I’ve heard that as well. Firing cannons was hoping to trigger this. I don’t think there’s any scientific evidence that that works. Anything else on this? OK.
Chapter 8: Precipitation Climatology [00:39:21]
So what are we looking for in terms of climatology? A given region of the Earth will have certain water vapor sources, nearby bodies of water. It will have certain characteristics that might make air rise. If you get the right conditions, you might get precipitation. But this will vary from place to place around the world. We’ll talk about the global climatology of rainfall in just a few days. But there are some regions of the Earth where it never rains. Why would that be? Why would there be a place on Earth where it never rains? Anybody have an idea?
Student: If it’s like right after a big mountain range, that like a cloud would have to lose all its water to pass over?
Professor Ron Smith: Yeah, that would be possible. But I think, even in that scenario, I would offer a slightly different explanation. And that is if you have a mountain range, and the wind is always from one side towards the other, you’d have rising motion on one side which would give you precipitation, but then always sinking motion on the other side. So even if you hadn’t rained out all the water, once you start the air descending, then you see you clear out the clouds. So I would like to take that option because I think it’s more universal.
Wherever you have on the globe, a place where the air is usually descending for whatever reason, you’re unlikely to form either clouds or precipitation. Wherever you have regions where the air is often ascending, then you are much more likely to have clouds or precipitation. There are people that say, well, we could make the deserts bloom by just adding more water vapor. And that will not work, because I don’t care how much water vapor you add to the atmosphere. If the air is always going to be descending, for example, in the Sahara Desert, what makes the Sahara Desert a desert is that the air there is usually descending. Adding water vapor, that’s not going to change it. The air is still going to be descending. You’re not going to make clouds.
So precipitation climatology usually has to do with where’s the air going up and where’s the air going down. It’s complicated in many ways. But in that sense, it’s very, very simple, rising air versus descending air.
Now a few numbers just to put this in your mind. We don’t know exactly what part of the Earth gets the absolute most rainfall. But we suspect that there are places on Earth that get as much as say 10 meters of rain per year. I did a project in the Caribbean last spring. And at the top of a mountainous island down there, we had a rain gauge installed for several years. And at that point, we got six meters of rainfall per year, which is a lot. Here in New haven, the average annual rainfall is about 1.5 meters, about that much rain per year on average.
In order to do rain-fed agriculture, not irrigated agriculture, but rain-fed agriculture, you need about 20 centimeters of rain per year, about that much rain per year. This will give you some idea what kind of numbers we are looking for when we try to understand rainfall around the globe, 20 centimeters about what you need to do. And it’s marginal. But that will allow you to do a little bit of rain-fed agriculture. Questions on this? OK.
Chapter 9: Evaporation [00:43:05]
We have just about enough time for me to mention the other side of this, and that is evaporation. If we now understand what makes it rain, then we have to understand how that water gets back into the atmosphere to balance the water budget of the atmosphere, so just a word about evaporation. For the most part, the rate of evaporation, well, it may depend on many things, like wind speed over the surface and the humidity of the air.
But the most important thing it depends on is the availability of heat. If you don’t have enough heat available, you’re not going to be able to evaporate water. Why is that? Because remember, the latent heat of condensation evaporation is a very large number, more than a million joules of heat required to evaporate every kilogram of water.
So if you tried to evaporate water without plenty of heat available, you’ll quickly cool that water down and the evaporation will cease. In order to sustain hour after hour evaporation, you’ve got to have a supply of heat. And that largely depends on the air temperature. So of all the possible controls that might be going on with evaporation, air temperature is the most important one.
I’ve put together a crude empirical formula. I wouldn’t use this if I had to do a very accurate calculation. But I use it all the time for quick back-of-the-envelope estimates of how much evaporation is likely to occur. And here’s the formula. Now PET means potential evapotranspiration. Evapotranspiration combines the words evaporation and transpiration, which means it includes both evaporation from water surfaces and transpiration from leaf surfaces.
Leaves are very effective evaporating agents. Trees bring water up from the ground in their roots. And then in the leaves, there are small pores that allow that water to escape into the atmosphere. So we combine that, evaporation and transpiration, and call it ET. But now this is the potential evapotranspiration. Because I want to remind you that if you don’t have water there to begin with, you can’t evaporate it.
So potential evapotranspiration is the evaporation rate you will have if there is water present. If there is water present. And here’s the formula, 5.7, a constant that I’ve developed, times the temperature expressed in degrees Celsius, if you want millimeters per month. If you want millimeters per day, just divide that by 30. And you get 0.17 millimeters per day per degrees Celsius multiplied by the temperature in Celsius.
Let’s do a quick example. Let’s say the average temperature today is going to be 20 degrees Celsius. So 20 degrees Celsius there, multiply that times 20. And what do you get? You get about four millimeters of evaporation. So my prediction today if the average temperature is 20 degrees, that you would get four millimeters of evaporation from the New Haven region. Part of it would come from puddles of water, part of it would come from leaves, part from grass. But on average with a temperature of 20 degrees Celsius, you get about two millimeters of evaporated water, water going from liquid into vapor during the day. Are there any questions on that? Yeah?
Student: Does that consider the relative humidity of–
Professor Ron Smith: No. So I’ve neglected a few effects that are rather important as well, such as relative humidity. If the air is drier, it’ll evaporate more quickly. If the wind is blowing strong, it’ll evaporate more quickly. So I have neglected that. And you should make a note about that, that this is not a very accurate method for doing it because it’s ignored such factors as the one that was just mentioned.
But I often use it–when I know what the precipitation is for some part of the world, and I want to know if that’s matched by evaporation, I’ll do a quick estimate of this, compare with what I know about that. And that’s usually the most important aridity index. To know how much it rains is not sufficient. To know whether a climate is going to be wet or dry, you need to compare the precipitation with the potential evapotranspiration. It’s only in that comparison that you get a reasonable number.
For example, in the high latitudes, up in Northern Canada, for example, it rains very little. But yet, it’s a very wet climate–mud, puddles of water everywhere. How can that be if it rains so little? Well, it’s cold, and therefore, the evaporation is even less. So a wet climate is one that has more precipitation than evapotranspiration. A dry climate is the reverse of that. You always must be comparing the two when you’re deciding whether a climate is wet or dry. We’re out of time. We’ll continue this on Wednesday.
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