3) Mixing and dispersion in the atmosphere
Lab 3: Gaussian Mixing and Smokestack plumes
Download the lab and data files to your computer. Then, upload them to your JupyterHub following the instructions here.
- Lab 3-1: Gaussian Smokestack
- Lab 3-2: Wind Profiles
- Lab 3-3: Stability Classes
- Lab 3-4: Solve an Air Quality Problem
- Lab 3-5: BONUS, extra credit: Guassian Smokestack with an Inversion
- Data: Sounding Data Jan 10
- Data: Sounding Data Dec 26
- Graphic: Smokestack_gaussian_plume.png
- Graphic: Plume_reflection.png
- Graphic: Stability_classes.png
- BONUS Graphic: Smokestack_oneReflection.jpg
- BONUS Graphic: Smokestack_2reflections.jpg
- BONUS Graphic: Smokestacks_doublereflections.jpg
Homework 3:
Problem 1
On an overcast day with class C stability, the wind velocity at 10 m is 5 m/s. The emission rate of an atmospheric pollutant is 65 g/s from a stack having an effective height of 100 m. Assume rural conditions. (You will want to use the lab python notebooks to solve this problem.)
- Estimate the center-line, ground-level concentration 22 km downwind from the stack, in micrograms per cubic meter.
- Estimate the ground-level concentration 22 km downwind and 650 m from the stack center line, in micrograms per cubic meter.
- Calculate and plot the centerline ground level concentration versus distance from the stack (C(x)).
- From the plot, estimate the magnitude and location of the peak ground concentration.
- How would the location and magnitude of the peak ground concentration change if the stack height was 120 ๐? (Plot on the same axes)
Problem 2
You are asked to assess the air quality in two cities A and B. The temperature profiles over each of the cities is shown below. Note that a parcel rising from the surface will start with the surface temperature 25 ยฐC. Assume dry air.
- What is the mixing height (H) over each city?
- Based on the observed temperature profiles, estimate the stability class (A-F) for each city.
- Determine the vertically averaged velocity between z=0 and z=H. You are told that the wind speed 10 ๐ above the surface is ๐ข=5 ๐/๐ . Note: the velocity profile follows the power law and the vertical average is given by:
- What is the Dilution Rate (or ventilation coefficient) for each city?
- Which city is likely to have better air quality on this day?
- If both cities are 25 ๐๐ across, what is the residence time over each?
Problem 3
Consider an area-source box model for air pollution above a peninsula of land (see figure below). The length of the box is 30 km, its width is 100 km, and a radiation inversion restricts mixing to 100 m. Wind is blowing clean air into the long dimension of the box at 0.7 m/s. Between 4 and 6 pm there are 300,000 vehicles on the road, each being driven 25 km, and each emitting 5 g/km of CO.
W = 100 km, L = 30 km, H=100 m, u = 0.7 m/s
- Find the average rate of CO emissions during this two-hour period (g CO/s per m^2 of land).
- Estimate the concentration of CO at 6 pm if there was no CO in the air at 4 pm. Assume that CO is conservative (does not decay or change) and that there is instantaneous and complete mixing in the box.
- Assume the windspeed is 0, and use the basic equation (below) to derive a relationship between CO and time and use it to find the CO over the peninsula at 6 pm.
