Industrial Problems II(5482)-(spring 2002)----- Yong Jung Kim -----

Research Project 1 : Air pollution in Far East Asia

What to do : Pretend that you are submitting a research proposal to the Korean or Japanese government. So the people who are going to read your proposal is not an expert in air quality modeling, but have lots of money.

You are supposed to include some numerical computations of model cases (1-D and 2-d) to show that this research is promising. So you need to set up the situation of numerical computation to show the importance of the research. You need to explain the meaning of the result to those people who are not experts. You also have to explain the scheme you have used in plain English. You also have to present the future research if the government provides the fund you want.

Your project will be graded from 2 view points.
1. The quality of computation results (40%)
2. Analysis of the results (30 %)
3. The way you persuade the people. (30 %)

(If you use your own coding or other computational tools, then you will get extra 10%)

The outline is given at http://www.math.umn.edu/~yongkim/airpollution.html

AN EXAMPLE AND OUTLINE

Introduction and Goals : China is now the most rapidly developing country in the world with the biggest population. Most of their industries has been built along their east coast which are close to Korea and Japan. Air pollution produced from such a mega developing country causes serious problems to Korea, Japan and China. The effects strong depends on the previous weather of 5-15 days. This project is to simulate such a phenomenon.

Applicability of this project : The direct objective of this project is to forecast the air pollution with from 1 to 10 days interval. If the data is accumulated, seasonal forecast will be possible. The effect of Yellow Dust produced in the central China or other effects which are adverted by the wind in macroscopic scale can be easily adapted.

Mathematical Model : Let $(U(x,y,z,t),V(x,y,z,t),W(x,y,z,t))$ be the wind vector, $g(x,y,t)$ be the air pollution source function and $k_{i,j}(x,y,z,t), i,j,=x,y,z$ be the diffusion matrix. Then the air pollution concentration $c(x,y,z,t)$ satisfies $$c_t+(Uc)_x+(Vc)_y+(Wc)_z=g(x,y,z,t)+(k_{i,j}c_i)_j. $$ Note that in this example we assume that there is no air pollution melted in the sea when it crosses over the sea. But, for some cases we need to consider it.

Properties of functions: The air pollution source function can be considered as a function of three variables $x,y,t$, i.e., $g=g(x,y,t)$. The quantity of the air pollution may increase as the industry grows and may increase as new techniques are used which produce less air pollution. However, it changes slowly in compare with other factors. So we may consider it as a function of $x,y$ only, i.e., $g=g(x,y)$. The diffusion matrix $k_{i,j}$ mostly depends on the property of air and pollution particles. We may consider it as a constant matrix. The biggest factor is the wind velocity. It may changes daily basis and it may make big seasonal difference. So it is required to have good data of previous days and good wind forecast to predict the air pollution.

An example of wind velocity : In the following figure an Asia Wind Forecast is given. The direction of wind varies all over the places. So it is very important to monitor the wind to study the advection of air pollution. We can find couple of things. First, wind is usually faster in ocean than in land. The main direction of the wind in the upper hemisphere is heading toward east.

Asia Wind Forecast (24 hr) (current time : Tue Mar 12 16:15:39 CST 2002)

Wind Forecast The wind maps display expected surface wind speed and direction 24 hours after the time indicated on the map. The colors on the map represent different wind speeds. The red, orange and purple family of colors represent stronger winds, while the blues depict weaker winds (see map key). The arrows represent wind direction. Winds less than 13 miles per hour (20 km/h) are not plotted on the map.

The area we are modeling : We are interested in the following area in the Far East Asia.

The portion of the map we consider (Far East Asia)

Simplified Geometry : The present goal is to demonstrate in a simplified situation. First we consider a simplified geometry of the following. The orange, blue and black portion of the map represents the land, ocean and pollution source respectively.

The simplified map we use (Far East Asia)

1-D case : (C++ source file) Here we consider 1-dimensional example. Suppose that China is in the range of $x$ less than $200$, Korea is between $x=700$ and $x=1000$ and Japan is between $x=1700$ and $x=2000$. Let the pollution source function is given by $g(x)=100$ if $x$ is between $x=100$ and $x=102$ and $g(x)=0$ otherwise. Suppose that the wind velocity is given differently over the land and sea. Assume $U=20$ over the sea and $U=5$ over the land. Under these assumptions we may obtain following figure of air pollution concentration.

2-D case : ( C++ source file, This file is not complete. You need to complete and modify variables and functions.) For 2 dimensional case, the situation is a lot different. One of the worst scenario is the case that the wind blows from the pollution source to Korea (or Japan if you are submitting your proposal to Japanese government) for several days.

The following figure, which is one of my computation results, is exactly the case. You may observe the accumulation of air pollution near the Korea and Japan.

Air Pollution after 10(?) days

Further research we want to pursue : The modeling results we are presenting in this proposal are actually over simplified ones. For more detailed results and to build up accurate air pollution forecasting system followings are needed.