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Water Pollution Model MGTS7523 (System Dynamics) System Dynamics Modelling Assignment Name: Student number: Background Information Tanning leather has been conducted around the world for over 5,000 years. The leather produced was used to make sandals and boots, water containers, harnesses, bags, armour, quivers, boats, etc. The old tanning process was accomplished by using materials that were noxious and produced very unpleasant smells. Consequently, the process was usually relegated to locations some distance from most small villages and towns. The process of tanning also requires a significant amount of water, so tanning production had to be established near larger bodies of water (which is also where towns tend to be established). Leather tanning is a billion-dollar industry today. The process of tanning today still requires a significant amount of water. During the process, chemical biocides are added to the soaking skins to prevent bacterial growth. The polluted water used in the process is generally dumped back into the water system. With strict environmental regulations in developed countries causing greater costs to complete the tanning process, much of the actual tanning process is accomplished by shipping the hides to developing countries, where environmental regulations are much weaker and labour is much cheaper. Your task is to use Stella Architect to create a stock and flow model of a small city that is dependent upon a tanning industry for many of its jobs An assumption is that the city is situated near a large river that runs into a lake a few miles away. The city was chosen because of the abundance of water needed for the tanning process. But is it possible for the city to support a tanning industry and still keep water pollution to a pre-determined safe level? Utilise your knowledge from exercises in the classroom to help you with constructing your stock and flow model. Figure 1 shows the dynamic relationship between the sub-systems of ‘population” and ‘water pollution’. This is a high-level feedback loop that reflects the interdependent behaviour of these two sub-systems (i.e. population and water pollution) — do not use this diagram to answer question 24. At this point there are only two sub-sectors to consider for this problem: the population of the city and the water pollution produced by the tanning industry that provides jobs for some of the people in the city.

Your stock and flow model will therefore consist of two modules: one to represent the population of the city, and the other to represent the water pollution produced from the tanning process that is discharged into nearby rivers. Population Figure 1. Sub-system view of the dynamic relationship between population and water pollution It seems reasonable to expect that as the population grows, the pollution in the water will increase. The water pollution will probably increase the death rate of the population at some point in time.

Model # 1 Population sub-system Step 1 - Build the Base Model for Population In Stella Architect construct a standard population stock and flow model, including the names, as shown in Figure 3. Population —5—>0 births deaths birth rate normal death rate Figure 3. Stock and flow structure for the Population sub-system Use the following information, parameterise your model: - The initial population is 100,000 people - The ‘birth rate’ is 0.01 people/people/year - The ‘normal death rate’ is 0.01 people/people/year Step 2 — Set the Equations Q1. Write the equation for the ‘Births’ flow in the box below. Make sure to include the units for each variable in your answer (1 mark) births (people/year) = Q2. Write the equation for the ‘Deaths’ flow in the box below. Make sure to include the units for each variable in your equation (1 mark) deaths (people/year) = Add these two (2) equations to your stock and flow model.

Water Pollution Sub-system Step 1 - Build the Base Model for Pollution (in the same Stella Architect file that you have built your Population sub-system model) - Add a stock and rename it as ‘Water Pollution Level’. Assume an initial value of 2,500 mg for this stock - Add an inflow to this and rename it as ‘pollution added from tanning’ - Add three new converters and give them the following names: - Tanning industry population - Fraction of population in the tanning industry - Annual pollution produced by one person in the tanning industry - Connect ‘Population’ and ‘Fraction of population in the tanning industry’ to ‘Tanning industry population’ - Connect ‘Tanning industry population’ and ‘Annual pollution produced by one person in the tanning industry’ to ‘pollution added from tanning’ The following fraction of the population works in the tanning industry: 16 people in every 100 people. Each year, each person who works in the tanning industry adds 0.155 mg of pollution to the river. You will need to use this information to parameterise your model. - Add an outflow from ‘Water Pollution Level’ called ‘normal pollution absorption’ to represent the pollution absorbed by the river - Add two new converters and rename them as: - Natural pollution absorbed by river - Time to absorb pollution Connect ‘Natural pollution absorbed by river’ and ‘Time to absorb pollution’ to the outflow of the Water Pollution Level stock. 2,480 mg of pollution can be absorbed by the river naturally each year (i.e. time to absorb = 1 year). You will need to use this information to parameterise your model (ensure you set the units). Step 2 — Set the Equations Q3. Write the equation for ‘Tanning industry population’in the box below. Make sure to include the units for each variable in your equation (1 mark) Tanning industry population (people) =

Step 2 - Set the Equations Q6. Write the new equation for the ‘deaths’ flow in the box below. Make sure to include the units for each variable in your equation (1 mark) Deaths (people/year) = The ‘Effect of pollution on death rate’ is a dimensionless multiplier and therefore its units will be ‘dimensionless’. It adjusts the ‘Normal death rate’ to produce the ‘Actual death rate’. Q7. Write the equation for the ‘Actual Death Rate’ in the box below. Make sure to include the units for each variable in your equation (1 mark) Actual Death Rate (people/people/year) = Add these two (2) equations to your stock and flow model. Step 3 — Define the Dimensionless Multiplier The ‘Effect of pollution on death rate’ depends upon a ratio comparing the water pollution and the initial water pollution. The actual water pollution is the ‘Water Pollution Level’ stock. Add a new converter called ‘Initial water pollution level’ and set its value to 2,500 mg. 7 Connect ‘Water Pollution Level’ and ‘Initial water pollution level’ to ‘Effect of pollution on death rate so that this part of the model looks like Figure 5. Effect of pollution Initial water pollution level on death rate Water Pollution Lével + Figure 5. Model showing inputs to ‘Effect of pollution on death rate’ Q8. Write the equation for the ‘Effect of pollution on death rate’ in the box below. Make sure to include the units for each variable in your equation (1 mark) Effect of Pollution on Death Rate (dimensionless) = Step 4 — Set up the Graphical Function The ‘Effect of pollution on death rate’ converter is a dimensionless multiplier defined as a graphical function - hence the output value will change based on the ratio of ‘Water Pollution Level and ‘Initial water pollution level’. We anticipate that the water pollution could rise as high as 10 times the initial water pollution.

Make the ‘Effect of pollution on death rate’ converter a graphical function. To do this, double click on this converter, and select ‘Graphical Function’ from the panel on the right-hand side (Figure 6) and check the box titled ‘Graphical’ at the top of the panel (Figure 7). < QI H#IQIBIT SSv Figure 6. Graphical Function selected (O Effect of pollution on death rate Q@ Graphical Figure 7. Check the box titled ‘Graphical’ - Set the number of data points to 11. (Hint: Graphical Function Editor — Points) - Set the lower value of the horizontal axis to 0 and the upper value to 10 - Set the lower value of the vertical axis to 0 and the upper value to 12 When the ‘Water Pollution Level’ / ‘Initial water pollution level’ ratio is equal to or less than 1, the ‘Effect of pollution on death rate’ multiplier should equal 1. When the ‘Water Pollution Level is greater than the ‘Initial water pollution level’, we expect the actual death rate to increase according to an S-shaped growth pattern. To capture this dynamic, use the following table (Table 1) to define the graphical function for the ‘Effect of pollution on death rate’ (you will need to change the view from ‘Graph’ to ‘Points’). Table 1. Data for the ‘Effect of pollution on death rate’ graphical function Water Pollution Level / Initial water pollution | Effect of pollution on death rate level 0.00 1.00 1.00 1.00 2.00 1.80 3.00 3.50 4.00 6.80 5.00 9.00 6.00 10.15 7.00 11.20 8.00 11.75 9.00 11.90 10.00 12.00

Step 2 — Update the ‘birth rate’ variable Change the ‘birth rate’ so that it steps up from 0.01 to 0.012 (people/people/year) in the year 1982. Use the STEP function to do this. Define the ‘birth rate’ as STEP (amount, time of change). - Rerun the simulation Q11. Insert a picture of your model at this stage in the box below. Below your model, insert a graph that shows: Population; Water Pollution Level (5 marks)

Model #2 Knowing that the tanning industry would be dumping pollutants into the nearby river, the city council built a water treatment plant to remove some of the pollution from the water before it is dumped into the river. Step 1 - Update the Water Pollution Sector - Rename the ‘Water Pollution Level’ stock to ‘Treatment Plant Water Pollution Level’ The treatment plant creates a material delay between receiving the pollutants and dumping the pollutants into the river. - Add a new stock called ‘Treated Water Remaining Pollution’ This stock will have an initial value of 2,500 mg. (It is good practice to use the ‘Initial Water Pollution level’ converter as the initial value for both the ‘Treated Water Remaining Pollution’ and ‘Treatment Plant Water Pollution Level’ stocks). Water will flow between the ‘Treatment Plant Water Pollution Level’ stock and the ‘Treated Water Remaining Pollution’ stock. - Add this flow connecting these two stocks and name it ‘Pollutant discharged flow’ The ‘Treated Water Remaining Pollution’ stock should have ‘normal pollution absorption’ as an outflow. - Disconnect the ‘normal pollution absorption’ flow from the ‘Treatment Plant Water Pollution Level’ stock and connect it as an outflow to the ‘Treated Water Remaining Pollution’ stock You will also have to change another connection in the model to correctly incorporate the ‘Treated Water Remaining Pollution’ stock, since the ‘Treated Water Remaining Pollution” (not ‘Treatment Plant Water Pollution Level') will now affect the ‘normal death rate’. - Disconnect the ‘Effect of pollution on death rate’ from ‘Treatment Plant Water Pollution Level’ stock - Connect the ‘Treated Water Remaining Pollution’ stock to the ‘Effect of pollution on death rate’ Q12. Write the new equation for the ‘Effect of pollution on death rate’’ in the box below. Make sure to include the units for each variable in your equation (1 mark) Effect of Pollution on Death Rate (dimensionless) =

Treated Water Pollutant discharged flow Remaining Pollution D Treatment Plant Water Pollution Level + ax | time to remove pollution pollutiory water pollution level maximum acceptable Figure 8. Update model section for Model#2 Step 3 — Set the Equations Q13. If the ‘pollution removed’ is determined by the ‘pollution level gap’ and the ‘time to remove pollution’, write the equation for the ‘pollution removed’ flow in the box below. Make sure to include the units for each variable in your equation (1 mark) Pollution Removed (mg/year) = Q14. If the ‘Pollutant discharged flow’ is the difference between ‘Treatment Plant Water Pollution Level’ and ‘pollution removed’, write the equation for the ‘Pollutant discharged flow’ in the box below (Hint: the units for the stock and flow are different. Use the ‘time to remove pollution’ in your equation to convert ‘Treatment Plant Water Pollution Level’ to the same units as ‘pollution removed’). Make sure to include the units for each variable in your equation (1 mark) Pollutant discharged flow (mg/year) = Add these equations to your stock and flow model. Step 4 — Produce a Graph We are interested in the behaviour of population, water pollution in the treatment plant and pollution remaining in the treated water over the 150 year period (i.e. 1980 — 2130). - Create a graph and add: ‘Population’, ‘Treatment Plant Water Pollution Level’ and ‘Treated Water Remaining Pollution’ - Set the scale for ‘Population’ from 80,000 to 110,000 - Set the scale for ‘Treatment Plant Water Pollution Level’ from 1,400 to 4,000 - Set the scale for ‘Treated Water Remaining Pollution’ from 1,400 to 4,000

Hint: remember to select Multiscale in the Graph settings. Ensure that ‘Keep zero visible’ is unchecked for all three variables. Step 5 — Show the Model and Graph Q15. Insert a picture of your model at this stage in the box below. Below your model, insert a graph that shows: Population, Treatment Plant Water Pollution Level, Treated Water Remaining Pollution’ (5 marks)

Model # 3 Part A Actual data from health records indicate that the number of deaths in the city are different from the model results. This indicates that something has been left out of the model. Currently, the model assumes all information about pollution is immediately available. Realistically, data has to be collected from the polluted river to determine how much pollution needs to be removed by the treatment plant. It is also necessary to obtain permission from the city council and obtain funding to support the data collection, a process that can take one year. Another 0.5 years are needed to collect water quality samples from various parts of the river to determine the gap between the maximum acceptable water pollution level and the amount of pollution remaining in the treated water. Step 1 — Add Information Delays To include this delay in the model, we will use a first order information delay (total of 1.5 years). We will use a converter to model this information delay rather than using a normal information delay structure. Add a new converter called ‘Delay in Collecting Pollution Data’. - Disconnect ‘Treated Water Remaining Pollution’ from the ‘pollution level gap’ - Connect ‘Treated Water Remaining Pollution’ to ‘Delay in collecting pollution data’ - Connect ‘Delay in collecting pollution data’ to the ‘pollution level gap’ The new model section should look like Figure 9. Treated Water Remaining Pollution + Deky in collecting pollution data level gap water pollution level maximum acceptable Figure 9. Updated section for Model #3 (part A)

Use the SMTH1 function from Stella’s built-in library to represent the information delay. Define the ‘Delay in collecting pollution data’ as SMTH1 (Treated Water Remaining Pollution, 1.5). Q17. Write the new equation for the ‘pollution level gap’ in the box below. Make sure to include the units for each variable in your equation (1 mark) pollution level gap (mg) = Step 2 — Produce a Graph showing the three (3) stocks Update your graph of ‘Population’, ‘Treatment Plant Water Pollution Level’ and ‘Treated Water Remaining Pollution’ with your new simulation results.

Q19. Create two (2) charts — one showing ‘Treated Water Remaining Pollution’ for Model #2 and one showing Treated Water Remaining Pollution’ for Model #3 Part A. Paste these two (2) charts in the box below. Explain how the behaviour changed for ‘Treated Water Remaining Pollution’ between Model #2 and Model #3 Part A. Also explain why the behaviour changed if it did (5 marks)

Part B Step 1 — Incorporate a Reporting Delay In addition to the 1.5 years required to secure funding and collect water quality samples from the river, it takes another 0.5 years for the report to be written about the current level of pollution in the river. - Add a new converter called ‘pollution reporting delay’ - Disconnect the ‘pollution level gap’ from the ‘pollution removed’ outflow - Connect the ‘pollution level gap’ to ‘pollution reporting delay’ - Connect the ‘pollution reporting delay” to the ‘pollution removed’ outflow This is what this new model section should look like Figure 10. in collecting ollution data [ pollutionf femoved pollution reporting delay pollution favel gap S Figure 10. Updated model section for Model #3 (part B) water pollution level maximum acceptable Use the SMTH1 function to represent the information delay. Define the ‘pollution reporting delay’ as SMTH1 (pollution level gap, 0.5) with units of mg. Update the equation for the ‘pollution removed’ flow to accommodate this change in model structure. Step 2 — Produce a Table We are interested in comparing values for pollution remaining in treated water between Model #3 Part A and Model #3 Part B. - For each of Model #3 Part A and Model #3 Part B, create a table and add ‘Treated Water Remaining Pollution’