1. FW364 Ecological Problem Solving Residence Time of the Seas Mass Balance

2. Today we are going to practice… First as a class, then in small groups, and finally on your own…

3. Mass Balance Practice Acid rain in Lake Ontario and how residence time affects potential for lake acidification

4. Mass Balance Practice We are going to evaluate this statement: Lake Ontario has not been acidified by the highly acidic rain falling in its watershed because Lake Ontario is so large What do you think? Is this possible? Is Lake Ontario so large that the acid rain has been diluted so much as to not have an effect? We can evaluate this statement using mass balance

5. Mass Balance Practice With the verbal description, it’s not so obvious what the assumptions are Let’s be more explicit with a quantitative statement: “Acid rain has not affected Lake Ontario because total (accumulated) input of acidic water is small relative to the volume of the lake” This is a classic residence time problem: We need to compare the amount of water in the lake to how much acid rain water has entered Assumptions: 1) All water going into Lake Ontario is acid rain (i.e., all water in Lake Ontario was precipitation in the past either that fell on the lake directly or that fell in the lake’s watershed and flowed into the lake) 2)Acid rain has been falling for ~50 years 3)Steady-state

6. Mass Balance Practice With these assumptions, the question then becomes: “Is the amount of water that has been added to Lake Ontario in the past 50 years large relative to the total amount of water in the lake?” We can convert this “quantity of material” question to a time question: “Is the amount of time that acid rain has been added to the lake large relative to the residence time of the lake?” For the initial statement to be right, the residence time must be >> time acid rain has been entering lake (50 years) If residence time < 50 years, then the lake is not large enough to dilute the acid rain, and the initial statement is wrong

7. Mass Balance Practice Let’s start by looking at a map so we can develop our conceptual model (i.e., stock & flow model) What are the relevant features of Lake Ontario that should be included in our conceptual model?

8. Mass Balance Practice Lake Ontario St. Lawrence RiverNiagara Falls Many small rivers What should we use to get an idea of flow of water through the lake? Inputs or outputs? Using outputs would be easiest – only the St. Lawrence River We now know what we will use to calculate flow What will our stock be?  Volume of Lake Ontario

9. Mass Balance Practice Stock (S): Volume of Lake Ontario: ~1700 km 3 Flow (F): Discharge of St. Lawrence River: ~200,000 cfs T = S F Residence time: But first we need to get units to match 200,000 cfs = 5600 m 3 /s = 1.8 x 10 11 m 3 /yr = 180 km 3 /yr conversion factors: (1ft / 0.305 m) 3 = 1 ft 3 / 0.028 m 3 60 s/1 m * 60 min/1 hr * 24 hr/1 d * 365 d/1 y = 32000000 sec/yr 1 km 3 = 1000 m x 1000 m x 1000 m = 1,000,000,000 m = 10 9 m 3

10. Mass Balance Practice Stock (S): Volume of Lake Ontario: ~1700 km 3 Flow (F): Discharge of St. Lawrence River: ~180 km 3 /yr T = S F = 1700 km 3 180 km 3 /yr = 9 yr Residence time of ~9 yr is way shorter than time acid rain has been filling lake (50 yr) So the initial statement was wrong: The water in Lake Ontario has been exchanged many times since ~1962 If the St. Lawrence is not the only output, what will happen to our estimate?  Residence time will go down; our estimate is probably a little high Actual residence time is closer to 6 yr, but (and this is a BIG point) – our simple model did pretty well; was sufficient to address initial question

11. Small Group Work And now for today’s lab: The Global Hydrologic Cycle & Residence Time of the Oceans You have been given: Total surface area of the Earth: 5.10 x 10 8 km 2 Total surface area of oceans: 3.61 x 10 8 km 2 Total volume of oceans: 1.35 x 10 18 m 3 Average global precipitation: 1 m/year Total evapotranspiration from land: 6.2 x 10 13 m 3 /year Notes: Unlike Lake Ontario example, you will need to model precipitation explicitly Pay attention to units! (I suggest using meters)

12. Lab 1 Distill this version of the hydrological cycle to the most relevant features Body of water

14. First Real Lab Report Loch Ness Monster Ecosystems / Mass Balance

15. Notes The rest of our time is devoted to working on lab assignment The “C Residence Time in Plant-Herbivore System” example from class will be helpful to look over

16. Lab 2 How many monsters could Loch Ness support? A mass balance approach can be used to answer this question! Can use information about the productivity of Loch Ness, some assumptions about monster size, and food chain length to determine how much monster biomass can be supported … End result should be a calculation of the number of monsters (not just total biomass of monsters)

17. Lab 2 How many monsters could Loch Ness support? In your lab reports: Need to include a range of estimates for number of monsters based on different combinations of assumptions, e.g., Two different phosphorus concentrations of Loch Ness Two different food chain lengths Two different monster masses Cold-blooded vs. warm-blooded (i.e., fish vs. mammal) Based on your calculation of the number of monsters, speculate on the likelihood of a viable Loch Ness monster population

18. Lab 2 How many monsters could Loch Ness support? For today (IN CLASS), please use these assumptions: Two trophic levels between phytoplankton and the monster The monster is a fish (i.e., cold-blooded) The monster’s average mass is that of an elephant Two possible phosphorus concentrations: 10 mg/m 3 5 mg/m 3 Tips: Pay attention to units Units for equations based on empirical relationships do not need to balance e.g., Relationship of TP (mg/m 3 ) to NPP (gC/m 2 /yr)

19. Writing Lab Reports Assignment 1: Due two weeks from today (by 5pm) Reports must be typed and turned in as hard copies (not emailed) Report should include: Narrative explanation of rationale (i.e., explain your process) Assumptions Equations, calculations, and results Tables, graphs, or figures, as needed A brief discussion of the results (i.e., interpretation of results) No set page limit; 2-4 pages for most reports is sufficient