1. FW364 Ecological Problem Solving Lab 1: Ecosystems / Mass Balance September 3, 2013

2. The study of stocks and flows of materials and energy through ecosystems We will use an example to explore ecosystem ecology (and review some math ): Ecosystem Ecology

3. Trash: What does the problem look like?

4. Case Study: Plastic Trash We currently recover only 5% of the plastics we produce. What happens to the rest of it? Roughly 50% is buried in landfills, some is remade into durable goods, and much of it remains “unaccounted for”, lost in the environment where it ultimately washes out to sea. Much of the plastic trash we generate on land flows into our oceans through storm drains and watersheds.

5. “Plastics: made to last forever, designed to throw away.” Plastic decays very slowly and once broken down, turns into very small confetti like pieces which can and is ingested by sea life and wildlife. http://vimeo.com/8307034 http://vimeo.com/8307034

6. there are 5 major oceanic gyres (large collections of trash, somewhat like soup) worldwide, with several smaller gyres in Alaska and Antarctica floating in the open ocean.. The trash collects in these remote areas due to trade winds that move the trash around (like jets in a hot tub). http://vimeo.com/11704000, http://vimeo.com/8350606 http://vimeo.com/11704000http://vimeo.com/8350606

7. Birds? A Dutch study in the North Sea of fulmar seabirds concluded 95 per cent of the birds had plastic in their stomachs. More than 1600 pieces were found in the stomach of one bird in Belgium. When marine animals consume plastic trash, presumably mistaking it for food, this can lead to internal blockages, dehydration, starvation, and potentially death. http://www.youtube.com/watch?feature=player_embedded&v= Dc0a4uuI1gY

8. What does this mean for wildlife? The United Nations Environment Program says plastic is accountable for the deaths of more than a million seabirds and more than 100,000 marine mammals such as whales, dolphins and seals every year. http://www.youtube.com /watch?v=wNu-MLwkva4 http://www.youtube.com /watch?v=wNu-MLwkva4

9. Now that we suspect that trash is a problem for marine wildlife, we need to quantify the problem. First, let’s come up with a model of what is going on in this system.

10. Ocean Plastic Stocks and flows model Flows Stocks These models are a general framework (general model) that we will apply in many contexts

11. Ocean Plastic Ocean example: Trash –stocks and flows What are the inputs and outputs for ocean plastic trash? Ocean Plastic Stock: Typically a “reservoir” or “compartment” In this case, the ocean is the stock Trash is incorporated into the ocean Flows:Inputs and outputs from the stock Inputs: The processes that ADD material to the stock Outputs: The processes that REMOVE material from the stock Inputs: Outputs:

12. Ocean Plastic Let’s keep building the ecosystem Class Exercise: Build a stock and flow model for Plastic in the ocean (just a conceptual model for now) Work with the people next to you – you have 3-5 minutes Flows Stocks Think about:What are your stocks? What are your flows? Hint:Include some sort of source of trash as a stock Keep the model simple

13. Ocean Trash Let’s start with just a patch of ocean This conceptual model could represent any size ecosystem as currently shown, e.g., the whole ocean or just part of the ocean Important point: Losses from one stock are additions to another stock Trash on land

14. Ocean Trash Let’s start with just a patch of ocean This conceptual model could represent any size ecosystem as currently shown, e.g., the whole ocean or just part of the ocean Important point: Losses from one stock are additions to another stock Trash on land Trash dumped from boats

15. Ocean Trash Detritus Biodegradation Let’s start with just a patch of ocean This conceptual model could represent any size ecosystem as currently shown, e.g., the whole ocean or just part of the ocean Important point: Losses from one stock are additions to another stock Trash on land Trash dumped from boats

16. Ocean Trash Detritus Biodegradation Let’s start with just a patch of ocean This conceptual model could represent any size ecosystem as currently shown, e.g., the whole ocean or just part of the ocean Note: The loop is NOT entirely closed (not a complete cycle) Trash on land Trash dumped from boats

17. Stock & Flow Equations - Definitions Stock (also called pool): S Amount of material or energy in a defined compartment Units: mass/area or mass/volume Flow (also called transfer rate or flux): F Amount of material or energy flowing into or out of stock Units: mass/area/time Turnover time (also called residence time): T Time it takes for one complete exchange of stock Units: time (days, months, years) Stock (S) Flow (F) gPlastic/m 2 / day gPlastic/m 2

18. Stock & Flow Equations - Analogy What is the stock? What are the flows? In? Out? What is the turnover time? Analogy: bathtub, faucet, & drain Amount of water in tub In: Water arriving from faucet Out: Water leaving from drain Time it takes for one complete water exchange for the tub Average time a water molecule in the tub stays in the tub (residence time)

19. Question: What is my share of the problem? How can we figure this out? Count each piece of trash as it leaves the US and divide that by the number of people in the US. Estimate how much plastic the US is contributing and divide that by the number of people in the US. Measure how much trash each of you are actually producing.

20. Let’s simplify the problem… Let’s just look at plastic. Americans use about 40 billion plastic bottles every year. Americans use more than 380 billion plastic bags and wraps each year. How many is that per person? (There are 320 million people in the US) If we recycle about a quarter of the bottles, how many still end up trashed?

21. Let’s take a break!

22. Stock & Flow Equations - Analogy What is the stock? What are the flows? In? Out? What is the turnover time? Analogy: bathtub, faucet, & drain Amount of water in tub In: Water arriving from faucet Out: Water leaving from drain Time it takes for one complete water exchange for the tub Average time a water molecule in the tub stays in the tub (residence time)

23. Stock & Flow Equations where F is total flow in OR out At this point, we know that Turnover Time depends on Stock and Flow This sounds like an equation in the making… T = S F Going to be making the assumption that flow in = flow out

24. Stock & Flow Equations - Units Some consideration of units: T = S F We said earlier: T is measured in time units S is measured as a mass/area (or mass/volume) F is measured as mass/area/time You can derive this equation by thinking about units of T, S and F! time = mass/area mass/area/time time = which reduces to: i.e., understanding units helps with remembering equations

25. Stock & Flow Equations - Units Some consideration of units: We said earlier: T is measured in time units S is measured as a mass/area (or mass/volume) F is measured as mass/area/time time = mass/area mass/area/time time = which reduces to: Remember to keep units consistent E.g., if flow is given as g/m 2 /d and stock is in kg/m 2, need to covert to same units before calculating turnover T = S F

26. Exercise 1 The number of students at Wallaby North University is constant at 1000. If the average residence time of students is 4 years, and no students drop out, how many students graduate each year? How many enroll each year?

27. Exercise 1 Stock: Students at Wallaby North Univ (known: 1000 students) Flow: Enrollment (input) OR graduation (output) rate (unknown) Turnover: Time at Wallaby North Univ (known: 4 yr) ~ Time for new students to “fill” university How many students enroll each year? Input = Output  Enrollment = Graduation = 250 students/yr T = S F F = S T F = 1000 students 4 years 250 students/yr graduate F = The number of students at Wallaby North University is constant at 1000. If the average residence time of students is 4 years, and no students drop out, how many students graduate each year? How many enroll each year?

28. Steady State What have we assumed about the stock?  The size of the student body is not changing This is called the steady-state assumption This assumption allows us to assume inputs = outputs written mathematically: ∆S = 0 or dS/dt = 0 (for those familiar with calculus) dS/dt = “instantaneous change” (more about this later) We will use the steady-state assumption many times in the course It is often violated in nature, so we must always state when we are making it in our modeling (remember for your assignments)

29. Steady State Checkbook example : balance jan = balance dec + deposits - payments re-arrange to: balance jan - balance dec = deposits - payments change in balance: ∆S = deposits - payments, if at steady-state, ∆S = 0 so deposits = payments (inputs equal outputs) Steady-state assumption implies that inputs equal outputs stocksflows

30. Exercise 2 The number of students enrolled at Wallaby South University is constant at 1000. If 50 students drop out after 1 year of residence and 200 students graduate each year, a) How many students enroll each year? b) What is the average residence time of the students? c) What is the average time it takes to get a degree (for those students that do)?

31. Exercise 2 The number of students enrolled at Wallaby South University is constant at 1000. If 50 students drop out after 1 year of residence and 200 students graduate each year, a) How many students enroll each year? Inputs = Outputs  Enrollment = # Leaving (graduate + drop out) = 200 students/yr + 50 students/yr = 250 students/yr 1000 students Enrollment? graduate 200 students/yr 50 students/yr drop out using steady-state assumption (since number of students is constant)

32. Exercise 2 The number of students enrolled at Wallaby South University is constant at 1000. If 50 students drop out after 1 year of residence and 200 students graduate each year, b) What is the average residence time of the students? Total student body of 1000 students, 200 students graduate/yr and 50 drop out after 1 year of residence T = S F T = 1000 students 250 students/yr 4 yr T = Reminder: at steady-state, can use either the input or output flows to calculate T

33. Exercise 2 The number of students enrolled at Wallaby South University is constant at 1000. If 50 students drop out after 1 year of residence and 200 students graduate each year, c) What is the average time it takes to get a degree (for those students that do)? Mental note: average time for a degree is 4 years, but many students drop out each year, so time for a degree for students that actually graduate must be more than 4 years We are interested in residence time of students that obtain degrees, so we need to redefine the stock into students who will eventually obtain degrees: 1000 students total – 50 students that drop out = 950 students that graduate T = S F T = 950 students graduate 200 students graduate/yr 4.75 yr T =

34. Exercise 2 We can now check the answer to Question 2b using this new info (Q 2b: What is the average residence time of the students?) We know the average residence time from Q 2b was 4 yr Does 4.75 yr for graduates “make sense”? We can check this quantitatively with a weighted average 200 students (graduates) have a residence time of 4.75 yr 50 students (drop-outs) have a residence time of 1 yr 200 students x 4.75 yr + 50 students x 1 yr 250 students 4 yr = weighted average # student graduates x 4.75 yr + # student drop outs x 1 yr total # students = =

35. What would this look like at MSU? The number of students enrolled at Michigan State University is constant at 37,000 a) How many students drop out each year? Inputs = Outputs  Enrollment = # Leaving (graduate + drop out+ transfer) = 4215 students graduating/yr + 3685 Students leaving/yr = 7900 students/yr 37,000 students 7900 freshman/year graduate 4215 students/yr ? students/yr drop out using steady-state assumption (since number of students is constant) ? students/yr transfer out

36. Feel Good Moment of the day… Showing up is 90% of the battle. Just by making it this far without leaving, you are on a pathway to pass about many of your classmates. The four year graduation rate at MSU is ~40%. The six year graduation rate is 65.9-77% (depending on which data source you look at)

37. Homework for this week… Data collection: Keep a trash diary for the week. Write down how many items you trashed and recycled each day. We will be using the data during next week’s lab. Reflection: Reflect on this ocean trash problem, and write a one page essay describing what, if anything, you think should be done to manage this issue.

38. So what are the options for this problem? Develop biodegradable/compostable plastics Reduce/Reuse/Recycle Stop producing trash Stop trash from getting to the ocean Go out and get the trash back from the ocean Buying less products that contain plastics or plastic packaging

39. Next Class More Stocks and Pools Excitement! (Wednesday, Sept. 4) No regular office hours this week because of Labor Day; email for appointment if needed Carbon Cycling and The Carbon Cycling Game Where you get to be the molecules…

40. Lab 2 Exercise with acid rain in Lake Ontario and how residence time affects potential for lake acidification Lab activity involving residence time of oceans