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AOSS/GeoSci 321: Earth System Dynamics 1 Homework 6 (80 total pts - all homeworks have equal weight) Due Thursday 18 March 2010 Q1: (12 total pts) a)...

How do I do question 1 and 2 on the attached homework assignment?
AOSS/GeoSci 321: Earth System Dynamics 1 Homework 6 (80 total pts – all homeworks have equal weight) Due Thursday 18 March 2010 Q1: (12 total pts) a) (4 pts; Problem 1a in chapter 9 of Marshall & Plumb.) Consider an ocean of uniform density, ρ ref = 10 3 kg/m 3 , from the hydrostatic relation- ship, determine the pressure at a depth of 1 km and at 5 km. Express your answer in units of atmospheric pressure, p s = 1000 mbar = 10 5 Pa. b) (4 pts) At what depth in the ocean is the pressure due to overlying water equal to the pressure at the sea-surface? c) (4 pts) At what depth in the ocean is atmospheric pressure negligible? Assume atmospheric pressure is negligible when the pressure in the ocean is 100 times the pressure above the sea-surface. Q2: (30 total pts) Assume ρ ref = 10 3 kg / m 3 . a) (4 pts) Using the figure, what is your best estimate of σ at: i) T = 0 C, S = 36 psu ii) T = 0 C, S = 33 psu iii) T = 30 C, S = 36 psu iv) T = 30 C, S = 33 psu
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AOSS/GeoSci 321: Earth System Dynamics 2 b) (4 pts) Using the full non-linear equation of state of seawater, see http://www.phys.ocean.dal.ca/~kelley/seawater/density.html at the surface, what is the density of seawater at: i) T = 0 C, S = 36 psu ii) T = 0 C, S = 33 psu iii) T = 30 C, S = 36 psu iv) T = 30 C, S = 33 psu c) (6 pts) Using the linear approximation of the equation of state of sea- water, and assuming σ o = σ (30 C , 33psu) (use σ o in the answer to a-iv, and assume α T = 2 × 10 - 4 1 / C, β S = 7 . 6 × 10 - 4 1 / psu), calculate σ and ρ at: i) T = 0 C, S = 36 psu ii) T = 0 C, S = 33 psu iii) T = 30 C, S = 36 psu d) (8 pts) Using α T and β S corresponding to σ o = σ (15 C , 38 psu) at the surface (see Table 9.4 in Marshall & Plumb), use the linear approximation of the sea-water equation of state to calculate: i) T = 0 C, S = 36 psu ii) T = 0 C, S = 33 psu iii) T = 30 C, S = 36 psu iv) T = 30 C, S = 33 psu e) (6 pts) What is the difference in the linear approximations in parts (c) and (d)? Based on this exercise, what can you conclude about the accuracy of the linear approximation of the equation of state? g) (2 pts) Using the full non-linear equation of state of seawater, see http://www.phys.ocean.dal.ca/~kelley/seawater/density.html What is the density of seawater at typical abyss temperature and salinity ( T = 2 C, S = 34 . 75 psu) at the depth of 1km, and 5km? (HINT: use your solution to Q1, and 1 decibar = 0.1bar = 100 mbar.)
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