hey all we've been talking about how the air cools off so now I'm going to introduce now that we've gone through the basics I'm going to go through how the air actually cools off and we're going to look at different laps rate changes in the atmosphere and when we apply those different rates to different situations so this first one I'm going to talk about has to do with just how the atmosphere changes in the troposphere even if the air is relatively stable so let me emphasize that again what I'm going to show you here for the normal lapse rate or the environmental lapse rate which we abbreviate nlr or ELR that lapse rate is going to be for the troposphere for stable air now why does the troposphere cool down as you go up well for reasons we've talked about before right even if the air is not Rising okay even if the air is pretty stable the troposphere density changes right so part of what is occurring here is the heating that occurs is bottom up heating so energy comes in toward the surface and gets reradiated like we've talked about that's that bottom up heating effect for the troposphere remember because the atmosphere is denser closer to the surface that also means there's more greenhouse gases closer to the surface where the atmospheric density is higher so more heat gets trapped toward the surface and then the temperature cools off as you go higher into the troposphere remember too that air that is cold at the higher levels of the troposphere wants to sink so as that air sinks it warms up on the way back to the ground so for all these reasons the atmosphere in the bottom part in the troposphere that we talk about in weather and climate is warmer at the surface and cooler as you go up and it turns out that we can put a rate of change on that which is the normal lapse rate or the environmental lapse rate the nlr SLR as you go up in the troposphere on a stable Air Day the temperature will decrease by about three and a half degrees Fahrenheit per th000 ft and if you're going down in the troposphere right if you descend down a mountain for example the air is going to warm up by 3 and half degrees per th ft so we're going to learn how to apply why these calculations if the air is stable or it's unstable so remember this first example I'm showing you is for stable air the nlr so the example I like to use is the Grand Canyon because people like to visit the Grand Canyon and hike around the Grand Canyon and some of you may have been there or may want to go there at some point if you're able to but the Grand Canyon is a good example because people hike it and there's major elevations changes I also do it because we talk about mountains a lot so why not go in the reverse Direction and talk about Canyons for a little bit okay so the Grand Canyon in this case we're going to be hiking down into the Grand Canyon which means it's going to be colder where we start and it's going to be warmer as we go down into the Grand Canyon right it's the opposite of climbing a mountain and going up we're now going down into a can so let's just look at what the Grand Canyon looks like Okay so first of all if you look over on the left side of this picture this is the north rim of the canyon so this is the north rim and then the more popular tourist spot where a lot of the infrastructure is lodges camping stuff like that more of it is located over here on the south rim and then down here at the bottom of the canyon right it's the air that's sitting above the Colorado River right that flows through the inner Canyon so what's going to happen is as you hike down into the Grand Canyon okay and they have these different Trails this is the bright angel Trail here this is the South kbob Trail these are two of the more popular ones and then on the other side they have the north kbob okay what's going to happen as you go down into the canyon is the temperatures are going to warm up okay that's going to be important we're going to warm up as we descend into the canyon so let's just practice first with what we already know which elevation is depicted here by these temperature patterns which elevation is the lowest elevation which one is the highest and which one's in the middle so take a look at him for a second and think about it okay remember the highest elevation should be coldest and the warmest portion should be the lowest elevation because you could cool down as you go up and you warm up as you go down an elevation okay if you said the bottom one the highest elevation of the north rim which we should have taken note of on the previous Slide the north rim is the coldest portion because it is the highest elevation then we have the south rim which is a little bit warmer because it's a little bit lower in elevation and then the temperatures in the inner Canyon as we hike all the way down toward the river are going to be much higher because there's several ft lower in elevation than where we start off with at the north rim so when we think about these different things we're going to be talking about temperature and heat and those are important things to take note of again like we did earlier in class okay there is more heat content associated with the planet closer to the surface in the troposphere because there's more heat being trapped by greenhouse gases in turn that causes the temperature to go up but remember temperature is the average kinetic energy where heat is the total energy so earlier in class I talked about this with the Red Solo Cup example versus a swimming pool right the temperature of substances may be the same but where you have a lot more total molecules you have more total heat content and so what we're doing here is relating heat that gets trapped by the atmosphere that relates to our lapse rates and then we're able to fix figure out the temperature based on how these rates are changing so let's talk about that in terms of air that's unstable the Grand Canyon example I just told you about is the normal lapse rate or the environmental lapse rate so as you descend into the Grand Canyon on a stable Air day you use 3 and half degrees per th000 ft however when air is expanding it is losing energy faster to the surrounding area because it's expanding and losing Energy across a bigger boundary and so we have to use a different rate those rates that we use are related to something called adiabatic adiabatic are temperature changes that relate to unstable air anytime you see that the air is unstable you should be using adiabatic rates of change because expansion and compression causes the air to cool off or heat faster so what we're talking about air rising in the atmosphere in this case to form clouds and things like that is going to cause expansional cooling to result in a higher rate of change this is the same practical applied example of how a fire extinguisher works and that's why I have this on this slide if you touch a fire extinguisher on a wall it's roughly at room temperature right however when you release that pressure ized gas from the container it expands that expansion of the air allows it to lose its energy more quickly across that bigger boundary right it's compressed and pushed together really closely in that fire extinguisher but as it is released and goes to atmospheric pressure and it's no longer compressed it expands and cools down more quickly there's a video here here you can watch on the bottom from an old physics classroom that I think is kind of fun watch about how steam cools immediately as it's released from a pressurized container that has been heated we can also do this by blowing air out so I want you I know it sounds kind of silly but just for a second open your mouth real wide and blow the air out on your hand that air is hot right there's no expansion of that air coming out of your mouth it's just coming out of your mouth so it's the temperature that it would normally be now Burse your lips together okay close your lips Tighter and blow out now when you blow out the air feels Cooler why well the air is compressing going through your lips but then on the way out it expands and that results in cooling so that's why we blow on our food to cool it off by pursing our lips and allowing the air to expand you look kind of silly at Thanksgiving dinner or something like that if you're have your mouth wide open and you're blowing on your hot food with hot air right okay so taking these Concepts and something that seems as silly blowing on our hand to see how this works with expansional cooling applies to how the atmosphere cools down as air expands so the First Rate we're going to look at is something called the dry adiabatic lapse rate okay the dry rate is what we use when air is unstable and it's rising or sinking the air itself is rising or Sinking but the air is not saturated to 100% with humidity okay so the dry adiabatic laps rate or the dalr is used anytime you're told that the air is unstable it's rising or Sinking and it's not saturated with moisture the rate that we use is 5 a half degrees per th000 ft so if you're going up like on the left side of this diagram that's the pict icted if the air is rising you're going to use a 5 1/ 12° because the air is cooling on the right side we have compression depicted right and so as the air sinks and descends it warms up in the troposphere in that case you would use positive 55 degrees per th000 ft because the air is warming okay so now that we know about adiabatic and compressional versus expansional Heating and Cooling and we've talked a little bit about the normal lapse rate environmental lapse rate let's see how they differ in terms of how we calculate how the air cools off on stable days versus unstable days so what we're going to do is take the appropriate lapse rate so if we are in stable air we're going to use the normal lapse rate or environmental lapse rate if we're in unstable air we're going to use the dry rate if the air is unsaturated okay like it will be for this example here so in our example we're going to say that it's 100 degrees at the surface and on our stationary Air day we want to know what the temperature of the atmosphere would be at 5,000 ft if the atmosphere is not in motion if the atmosphere is very still that day it's still going to cool off because there's more gases again closer to the surface trapping heat and less going up so the troposphere is still going to cool off but on a stationary or stable Air day that means we need to be careful about the rate we use in this case it's like the Grand Canyon I talked about even if the air is stable in the Grand Canyon it's still going to change because you're changing elevation and the atmosphere cools off at 3 and2 de per th000 ft if you're going up and it warms up at 3 and2 de per th000 feet going down in this case we're saying the air is not Rising because it's stable but we want to know what happens if we go from 0 feet here to 5,000 ft up here how does the air temperature change even if it's stable so there's our 5,000 ft there's our rate of change and we just take 5,000 * - 3 and5 degrees per th000 ft we're using a minus because we're going up and the air is cooling so 5 * minus 3 1/2 = 172 That's How much cooling we have okay but we're not done with figuring out the air temperature that's just how much the air temperature cooled so if we start at 100° and that's what I told you up here we're starting at a temperature of 100° we then subtract 175 degrees of change and so our air temperature on a stable Air day at 5,000 ft would be 82.5 degrees F let's see how this differs with adiabatic and expansional Cooling and having to use the D for dry adiabatic laps rate we're going to assume the same same conditions in terms of elevations remember the atmospheric conditions are different because we're saying that air is rising and expanding okay as it cools off and pressure goes down but in this case we have to use the dalr of minus 55 per th000 ft because in this case the air is expanding so if you change elevations 5,000 ft Time 5 1/ 12° per th000 ft you wind up up with - 27.5 remember we're cooling so we're going down in temperature so our final calculation down here we start off at 100° at the surface we subtract 272 and so we wind up with a final air temperature of 72.5 this is important to understand that expansional cooling results in 10 more degrees of cooling or change compared to stable air this is why we have to make sure we use the right rates when we're calculating these things for our different problems we need to make sure we pay attention if the air is stable if the air is unstable if we're rising and cooling or if we're descending and warming we need to make sure we're using the right rates in positive or negative so these changes in terms of dry adiabatic lapse rate changes or adiabatic in general can cause big temperature changes so let's look at this example here we're going to say the tropopause or the boundary between the troposphere and Stratosphere on a given day is 3.75 miles above the surface the temperature up there is going to be pretty cold so let's put it at -4° okay as that air sinks though as that air parcel sinks it's going to compress as more pressure is put down on it and the molecules get compressed into a smaller space so as it sinks it's going to heat by the D ALR because we're saying the air is unstable and it's in motion it is sinking and so it sinks and it heats up at a rate of 55° per th000 ft so I've already done the math conversion here for you 3.75 miles is 19,800 Ft so you can take that 19,800 divide it by 1,000 it's going to come out to 19.8 multiply it times 5.5 and remember here we're using a positive rate because we're going down and warming and so we get 108.9 de of total warming remember though we got to account for our starting temperature so -4 plus 108.9 degrees of change equals a final air temperature of roughly 105° so in areas where air is sinking from the upper levels of the atmosphere you can get major heating that occurs so this is why around the subtropical High pressure belts like the one that sits around the Sahara Desert why you get such major warming and high temperatures in those areas even though they're a little bit further away from the equator that sinking air and that heating of it matters okay so let's talk again about stable versus unstable air remember that our adiabatic include expansion or compression okay as that air parcel Rises or sinks you get expansional cooling or compressional heating okay so think about that fire extinguisher example that air in there or the the chemicals in there are not at freezing when you have them compressed but again they cool off as it expands and again you can think about blowing on your hand with your mouth open or your mouth closed for expansional or compressional cooling or heating so looking at this again in the D let's look at how it changes going up and going down so I showed you that example before of air going down like around our subtropical High belts but remember the air also cools off if we're going in the opposite direction in the opposite direction we cool off by 5 a half degrees per th feet as long as that air is not saturated now the thing we have to introduce in addition to the D and the nlr is the W or the wet [Music] adiabatic sometimes the air is saturated like when we have clouds or we've reached the D Point temperature but remember all of that energy we talked about being associated with condensation or deposition so where the air is saturated with a 100% humidity and condensation for example is occurring remember that some of that heat that was holding water as a vapor or a gas is going to be released to the atmosphere so that heat energy that was being stored by water or in water as a gas that latent heat energy is going to wind up going back out to the atmosphere and it's going to partially result in heating the atmosphere so where you have saturated air and condensation occurring the rate is going to be lower for the W than the D because that that condensation process is going to counteract some of that cooling that's occurring as you change an elevation okay so the air partial is still going to get colder as it rises it's just not going to happen as quickly as it would if the air is totally unsaturated or dry below 100% humidity so what we should remember is the walr is always always always lower than the D because of that condens ational heating or depositional heating effect okay so the wet adiabatic lapse rate is going to range somewhere around 2.8 de to 3.2 degrees usually okay so it's usually about 3 to 3.2 degrees Fahrenheit per th000 ft in class I'll probably have you just use 3 Dees Fahrenheit per th000 ft because it's a nice round number and makes the calculations easy pay attention to lab though in case they have you use the a different w because it can vary because it turns out the walr actually can be slightly different because it depends on how fast the condensation is actually occurring okay so remember walr lower than the D because that condensation heating the atmosphere that was stored again as latent heat in water as a vapor before it became a liquid or a solid depending on the temperature of the atmosphere so let's do a practice problem that relates to things that you may do in lab or in lecture okay here's the problem an air paral is going to rise when it reaches 90 degrees fhe so I'm telling you the air is rising which means we no longer have stable air conditions on this given day the dupoint temperature is reached at 8,000 fet in the atmosphere okay the air continues to be unstable and Rise until it reaches a final elevation of 12,000 ft okay so assuming that the W is 3 degrees per th000 ft what is the temperature of the air when we reach the D point and when it reaches its final elevation of 12,000 ft so to figure out the temperature change we need to take the change in elevation times the appropriate lapse rate so this is a classic two-step problem in lab they may refer to this type of problem as the mountain problem because air goes up a mountain and it comes back down and you have to use the D and walr here in lecture I'm just having you look at what's essentially happening for cloud formation just on the way up okay so let's look at that let's assume we're starting at zero feet to make the math easy the D Point again is reached at 8,000 ft and the air on this day is going to reach a final elevation of 12,000 ft our starting temperature is 90° f as I told you in the problem so remember that we use the D LR where the air is not saturated okay so before we reach the dup point which I told you is at 8,000 ft we have to use the dalr so here is where that dup point would be reached right so below that point below that point the relative humidity is less than 100% above that point the relative humidity is greater than 100% okay so that's why we're using the dry rate below 8,000 ft so you take 8,000 ft times our D rate of 52 de per th000 ft so there's 44° of Total Temperature change right remember we're going up so that's going to be cooling 44° that tells us if we're starting at 90 and we subtract 44 Dees so 90 right 90 minus 44 is going to lead to our dupoint temperature over here of 46 deges so that's coming from our starting temperature minus our dalr rate of change so our due point is 46° okay above that due point we use the W okay so from 8,000 to 12,000 ft we use the D I'm sorry above 8,000 ft we use the W the wet rate for saturated air and we take our 4,000 ft of change times 3° that I told you is the wlr rate for this problem and we get 4 * 3 is 12 so we get 12 degrees of cooling above the D point so our total temperature change is going to be our 44 from the dry rate right there it is and our 12 over here from the wet rate and so our final air temperature is going to be 90 de as our starting temperature minus our 56 degrees of change so it's going to be 34 degrees when it stops Rising so up here the temperature is 34 deges and down here at the D Point remember it's 46° right in this region where we have our flat bottom of the cloud that's how we do our two-step problem and how we integrate D and walr that's for unstable air and our adiabatic changes remember if I tell you that the air is stable then instead of using these two rates you would use the normal lapse rate or the environmental lapse rate for the problem