Lab #3: Stability and Dispersion. Fall 2014 Due Tuesday, November 25, 2014

Transcription

1 NAME ID number Disc. Day and Time Lab #3: Stability and Dispersion Atmospheric Sciences 2L Fall 2014 Due Tuesday, November 25, 2014 In this lab, we will test the stability of a simulated atmospheric environment by pushing around an air parcel that is at equilibrium. We will also set up typical cases of positively buoyant air parcels and see how well they convect under different environmental conditions. Finally, we will study a case of a temperature inversion aloft and how afternoon heating of the ground affects dispersion in this type of atmosphere. You will be plotting graphs of environmental temperature vs. altitude, called temperature soundings. These soundings can represent environmental temperature profiles with a single lapse rate (environmental lapse rate, ELR or Γ e or γ) or multiple lapse rates. On these plots, you will also be plotting the temperature inside a rising air parcel as a function of altitude. These plot lines will represent temperature trajectories of the air parcels, and will have a fixed, common slope that corresponds to the dry adiabatic lapse rate (ALR or Γ d or just Γ). The stability of the atmosphere describes states of equilibrium. A system at equilibrium is stable if it resists a disturbance (restores itself to its original configuration), unstable if it accelerates away from its equilibrium configuration when disturbed, and neutral if it simply establishes a new equilibrium configuration when disturbed. In the atmosphere, vertical displacements ( nudges ) of air parcels can demonstrate these stability states, where an air parcel is some defined volume of air. What we are really seeing, though, is a behavior of an air parcel that has become warmer, colder, or has the same temperature as the surrounding environment. This is because an air parcel that is warmer than its environment is positively buoyant, meaning there is net upward buoyancy force on the air parcel, which causes the air parcel to rise upward. Meanwhile, an air parcel that is colder than the surrounding air is negatively buoyant, as there is a net downward buoyancy force making the air parcel sink. The buoyancy forces are a result of the density of the air inside the parcel being different from the density of the air outside with warm air tending to be less dense than colder air. An air parcel with the same temperature as the surrounding air is neutrally buoyant, and there is no net force upward or downward on the parcel. It simply floats in place. While we can make air parcels warmer or colder than their surroundings by adding or taking away heat, the more common scenario is for the air parcel to lose temperature while it is rising or forced upward via adiabatic expansion. A rising air parcel encounters decreasing atmospheric pressure, so its internal pressure must also decrease. This occurs by having the parcel expand in size. The expansion, however, uses up energy inside the parcel, which results in the loss of temperature. No heat actually enters or leaves the parcel, thus the term adiabatic is applied. The opposite occurs when an air parcel sinks it compresses adiabatically and gains temperature. A rising air parcel in the troposphere loses 10 C of temperature for every kilometer it rises (to be more precise, it s 9.8 C). This is referred to as the Adiabatic Lapse Rate, where a lapse rate is the rate at which temperature decreases as altitude increases. A temperature loss like this, which is 10 C/km, comes out as a positive lapse rate (> 0). If the temperature had increased with increasing altitude, the lapse rate would be negative (< 0).

2 # The lapse rate inside the rising or sinking air parcel is fixed. However, the environment can have a lapse rate; it s based on the temperature readings at various altitudes and is a result of the different parts of the atmosphere being heated differently (the troposphere, for example, is heated at the ground but not aloft, so the temperature decreases with increasing altitude). Since this heating is not the same from place to place and time to time, the Environmental Lapse Rate is not a fixed value. It can be negative (which would be a temperature inversion), 0 C/km, or positive (the average tropospheric lapse rate is about 6.5 C/km). Lapse rate is computed for a temperature sounding (a vertical profile of temperature in the atmosphere) between two points, (T 1, z 1 ) and (T 2, z 2 ) as follows: γ = T T 2 1 = ΔT z 2 z 1 Δz This looks similar to a mathematical slope calculation. In fact, there is a correlation between the slope of the vertical temperature plot and the lapse rate. Note that there is a minus sign in front of the fraction. This is so that the lapse rate has the proper sign for temperatures that decrease with increasing altitude. The fact that the Environmental Lapse Rate γ can be different from the Adiabatic Lapse Rate Γ means that an air parcel can be at a different temperature from the environment when it is rising or is forced to rise, since the temperatures inside and outside the parcel are changing at different rates. Thus, an air parcel that initially had the same temperature as the environment can have a different temperature after it is nudged upward a short distance. A more typical case is where the air parcel is already rising due to it being heated up by the hot ground, but its temperature is decreasing more rapidly than the surrounding air (this is where Γ is larger than γ), so the inside and outside temperatures converge and the parcel stops rising due to the loss of positive buoyancy. For a first estimate, we note that stable environmental conditions suppress vertical displacements of air, so this would inhibit the convective dispersion of air pollutants, while unstable conditions would tend to encourage convective dispersion. Neutral conditions would not inhibit convection, but they would not encourage convective dispersion either. The place above the ground where air parcels stop rising tells us how high the concentration of air pollutants near the ground will be. Using box model concepts, we note that as the volume available for mixing air pollutants increases, the concentration of pollution decreases. The stopping height of warmed air parcels defines the mixing height, or the depth of the mixed layer. The higher air parcels can go upward, the larger the mixing volume, which means the smaller the pollution concentration, assuming the air pollution is released at the ground. In lecture, we will also investigate the case of air pollution released at some point above the ground (an elevated source), which causes the dispersion behavior to be different from the case of ground sources. In the case of a temperature inversion aloft, which refers to a layer of air above the ground where the environmental temperature increases with altitude instead of decreases, the mixing height is fairly easy to estimate. The nominal mixing height is simply the altitude of the base of the inversion, which is the bottom of the layer with the temperature inversion.

3 1. Basic stability of systems in equilibrium A. Plot on the graph below the following vertical temperature soundings (the format is (altitude, temperature)): Sounding 1: (0 km, 4 C), (2 km, 8 C); Sounding 2: (0 km, 8 C), (2 km, 2 C); Sounding 3: (0 km, 12 C), (2 km, 24 C) # B. For each sounding, compute the lapse rate (show your work for one of the calculations) γ1 = C/km γ2 = C/km γ3 = C/km Note the direction the plot lines slope for positive and negative lapse rates, and how much they slope away from a vertical line versus the absolute value of the lapse rate. Based on your plots, write a statement that describes how the numerical value of the lapse rate varies with the slope of the sounding (be sure to specify the direction of the slope). C. In the next experiment, we will initialize a parcel in equilibrium, then plot its temperature trajectory as if the air parcel was pushed upward and/or downward from its initial position. By comparing the parcel temperature to the environmental temperature outside the parcel, we will be able to evaluate whether the parcel becomes positively, negatively, or neutrally buoyant (corresponding to the conditions of the parcel being warmer, cooler, or the same temperature as the environment, respectively). The parcel will then have to rise, sink, or stay in at its new altitude, respectively. This experiment therefore corresponds to a test of stability: if something in equilibrium is disturbed (in our case, pushing the air parcel upward or downward), then its subsequent behavior corresponds to either stable, unstable, or neutral equilibrium. From lecture, if we push an air parcel that is in equilibrium upward and then release it, then the parcel will:

4 #, if it was in stable equilibrium;, if it was in unstable equilibrium;, if it was in neutral equilibrium. On the following graph, plot an environmental sounding where the temperature at the ground is 20 C and the temperature at 2 km is 4 C. What is the environmental lapse rate? Plot a point for an air parcel at equilibrium at an altitude of 1.0 km. The parcelʼs temperature should be C. Now plot a dashed line that represents the parcelʼs temperature (an adiabat) if the parcel was pushed upward (to 2 km altitude). Remember, the parcelʼs temperature plot should represent a lapse rate of 10 C/km. The parcelʼs temperature at an altitude of 1.6 km would be C while the environmental temperature at that altitude is C. The air parcel is pushed upward and released. How does its temperature compare to the temperature outside the parcel, what is its buoyancy condition, and how does it subsequently behave? Based on this information, what was the original stability condition of the parcel, when it was in equilibrium with the environment? D. Write down the three possible stability cases and the corresponding relationships between the environmental lapse rate and the adiabatic lapse rate. Verify that the case we just did has the correct environmental lapse rate vs. adiabatic lapse rate relationship for the stability case we got in the previous question.

5 # 2. Starting with positively buoyant air parcels A. A more common scenario has an air parcel sitting atop a very hot patch of ground. This makes the air parcel warmer than the surrounding air. Such a positively buoyant air parcel will probably rise by itself. Plot following environmental soundings on the graph below. The parcel surface temperature is the starting point of the parcel s adiabat (at altitude 0 km). Note that the parcel starts out being 3 C warmer than the environment; it will therefore rise by itself. Plot the adiabat for the given parcel surface temperature. Environmental Lapse Rate (γ, C/km) Environmental Surface Temperature (T Parcel Surface Temperature (T Final parcel height (km) Stability rank (1 = most, 3 = least stable

6 Since there is only one parcel surface temperature, the same adiabat applies to each environmental lapse rate case. Note that this adiabat intersects each of the soundings. These intersection points represent the points at which the parcel s temperature is equal to the environmental temperature. If an air parcel was rising (along the adiabat shown) and it reached an intersection point, what happens to the air parcel s buoyancy and what will it do next? For each environmental lapse rate case, fill in the table above with the altitude at which the air parcels will stop rising. Consider that as the strength of the stability increases, the suppression of vertical parcel motion is greater (i.e., a positively buoyant air parcel will not be able to rise as high). In the last column of the table, rank the strength of the atmospheric stability, based on the final parcel heights. Write a statement relating the strength of the stability of an atmosphere vs. how much the environmental lapse rates is less than the adiabatic lapse rate. B. Repeat for the following table, except there will only be one environmental sounding and three adiabats (use dashed lines for the adiabats) Environmental Lapse Rate (γ, C/km) Environmental Surface Temperature (T Parcel Surface Temperature (T Final parcel height (km)

7 # In this experiment, there was only one environmental condition: a stable atmosphere (actually, a temperature inversion). So we already know that the positively buoyant air parcels will stop rising at some point, depending on the strength of the inversion. In this experiment, however, varying the initial temperature of the parcel varies the initial buoyancy the hotter the parcel is initially, the more buoyant it is. Based on the data you generated here, write a statement relating the initial buoyancy of an air parcel and how high it rises within an inversion. Then, write a statement that relates the concentrations of pollutants in the air to the initial buoyancy of the air parcels, if the final parcel heights are inversely related to concentration (as we had noted in class regarding mixing heights, which is a similar concept). 3. Inversions in Los Angeles A. In the previous part, your analysis essentially invoked the concept of the mixing height, which corresponds to the depth that air parcels can readily rise up and mix air pollutants with cleaner environmental air. In this part, you will set up an actual scenario where there is an inversion aloft and an actual mixing height value to contend with. Go to the CCLE site for AOS 2L and launch the Build your own inversion application in the

8 section, Lab 3 simulations. Drag the sounding handles to the following points, representing (altitude z in km, temperature T in C): (0, 15), (1, 5), (2.5, 10), (5, 15) The resulting plot should resemble a sounding with an inversion layer aloft. This inversion is an example of a summer-time inversion in Los Angeles. B. The base of the inversion is at km. This will also be the mixing height. The depth of the inversion layer (the distance between the bottom and top of the inversion layer) is km. C. In the space below, calculate the lapse rate in the region below the inversion base. Is this region, unstable, or neutral? D. In the space below, calculate the lapse rate in the region above the inversion top. Is this region stable, unstable, or neutral? E. Drag the air parcel point (red circle) to a surface temperature that is 5 C higher than the environmental surface temperature (i.e., new Tps = 200 C). Run the simulation by clicking the Start button and watch it plot an adiabat for this parcel. How high does the parcel rise? km F. Try this again and again with slightly higher parcel surface temperatures. To run the new simulations, just drag the red circle back down to z = 0 km and the new parcel surface temperature. Keep increasing the parcel surface temperature by a couple of degrees until it appears that an adiabat will fail to intersect the environmental sounding, which allows the parcel to continue rising right past the top of the inversion layer. What is the minimum parcel surface temperature where the parcel s adiabat will just intersect the environmental sounding (any higher parcel surface temperature will result in the parcel passing all the way through the inversion layer without stopping)? C G. In this last case, the air parcel would not be stopped by the inversion layer, because the lack of an intersection between the plots means the parcel s temperature will remain greater than the

9 environmental temperature. This demonstrates a phenomenon called popping the inversion. When air parcels at the ground have been sufficiently heated so they can rise past the inversion, the inversion pops and the pollution concentration drops dramatically because the mixing height suddenly becomes infinite, essentially. By how much did we have to warm the parcel to pop the inversion (compute the difference between environmental surface temperature and surface temperature of the parcel that just pops the inversion)? C H. We will now do a similar analysis of a typical winter-time inversion. Set up the following sounding by setting the plot handles to: (0, 10), (1, 15), (2.5, 0), (4, 25 ) Note how the inversion layer looks less prominent but closer to the ground than the summer case we just completed. In fact, the inversion layer is sitting on the ground. I. Run the simulation like we did previously to plot parcel adiabats, find the minimum parcel surface temperature that will pop this inversion: C. What is the difference between this temperature and the environmental surface temperature? C L. The mixing height for this sounding is 0 km, because the inversion layer is sitting on the ground. This implies that the pollution concentration should be very high, because the inversion prevents convective dispersion. However, the air quality during winter afternoons is usually better than on a summer afternoon. Considering that the air quality improves after the ground warms up and causes the inversions to be popped, use the data you found for the heating requirements for inversion popping to make a statement about why the winter air quality is better than in summer.