Questions:
Question 2 - 3-box model of water and nutrient fluxes/residence times
A 2-Box model of the ocean does not allow examination of the process of deep water formation at high latitudes (Arctic/Antarctic) and deep mixing during cold season. Consider the 3-Box model shown here. Using the box model approach anwer the following:
2.a) Given an ocean volume of 1349930000
Km3, an ocean surface area of362000000 km2, the depths of the warm surface box and cold high latitude box shown in the figure, and the respective densities, calculate the mass of water in each control volume (Warm Surf. Ocean, Cold High Lat. Ocean and Deep Ocean). Show your calculations.
2.b) Given a global river runoff of 3.73x1016 kg water/y and a global rainfall on the ocean of 3.98x1017 (both distributed between surface boxes as shown in the graph), and water fluxes between each box due to advection (shown with thick arrows) of 6.47x1017 kg water/y calculate total inputs of water into each of the three boxes (Surface Warm, High Lat, Deep Ocean). Assume evaporation from the surface boxes balances inputs so the system is at steady state. Calculate the residence time of water relative to total inputs in the three boxes under the following scenarios:
Scenario 1 = use the fluxes and assumptions listed above.
Scenario 2 = assume global runoff and precipitation are decreased by 50% relative to conditions in Scenario 1.
Scenario 3 = assume advective fluxes (i.e. deep water formation, upwelling) are decreased by 20% relative to conditions in Scenario 1.
Describe what these results mean in terms of time scales for chemical reactions in the three boxes and their sensitivity to changes in fluvial/precipitation fluxes vs. circulation fluxes.
2.c) Measurements of total dissolved phosphorous (TDP) concentrations (in units of g/kg water) show the following values for different reservoirs: Warm Surf. Ocean = 6.75x10-6; High Lat. Ocean = 2.88x10-5; Deep Ocean = 7.25x10-5; Average River Water = 6.94x10-5; Average Rainfall Water = 7.54x10-7; Evaporated water vapor = 0.00. Given those concentrations, calculate overall mass of TDP in the three ocean reservoirs. Using the water fluxes estimated previously (and accounting for the aerial distribution of river runoff and precipitation) calculate the fluxes in and out for each of the three boxes.
2.d) Examine the TDP fluxes in and out of the Warm Surf. Ocean box. Do they balance? If not, which one is greater (inputs or outputs)? What process is responsible for this difference? Explain. Next, knowing the magnitude of the extra flux calculated above, examine the TDP fluxes in and out of the Deep Ocean box. Do they balance? If not, which one is greater (inputs or outputs)? Explain. Finally, do the same mass balance exercise for the high latitude box? Are the TDP fluxes balanced there? If not, which one is greater (inputs or outputs)? What may be responsible for this result - hint note that there is a difference in the mass balance of this box relative to those of others.
2.e) Given the newly derived estimates of total inputs (or outputs) of TDP for each box, estimate the residence time of phosphorous in each of the boxes. Compare those residence times to those of water. Explain what this means in terms cycling of this key nutrient for ocean productivity.