Given an instantaneous change of mass distribution on the surface of the Earth, the shape of...

   

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Given an instantaneous change of mass distribution on the surface of the Earth, the shape of the Earth's gravity field (also known as the "Geoid") will change, causing a change in the sea level surface. If the change in mass is concentrated as the South Pole (i.e. ice melt in Antarctica), then the corresponding change in sea level is given by a convolutional integral that is purely a function of latitude (0): where pe = water. 1 2 sin(0 - 0o/2) + 10-³ S(00) = 1²₁ - (2 1 Pe Pc) e e Pw -10(0+)² de 5.5 g/cm³ is the average density of the Earth and Pw = 1 g/cm³ is the density of ocean (a) (10 pts) Calculate the expected sea level change (S) near Atlanta 00≈ 0.59 by using the Trapezoid Rule to calculate the sea level integral with n= 100 subintervals. (b) (5 pts) Calculate and plot the expected sea level change (S) near Atlanta 00≈ 0.59 as a function of n = 10, 20, ..., 500, the number of subintervals. What does the shape of this curve indicate about the numerical method? (c) (10 pts) Use the same integration algorithm to calculate and plot the expected sea level change (S) as a function of latitude over 0o = [-1.5, 1.5]. Go to Settings to activate Windows. Given an instantaneous change of mass distribution on the surface of the Earth, the shape of the Earth's gravity field (also known as the "Geoid") will change, causing a change in the sea level surface. If the change in mass is concentrated as the South Pole (i.e. ice melt in Antarctica), then the corresponding change in sea level is given by a convolutional integral that is purely a function of latitude (0): where pe = water. 1 2 sin(0 - 0o/2) + 10-³ S(00) = 1²₁ - (2 1 Pe Pc) e e Pw -10(0+)² de 5.5 g/cm³ is the average density of the Earth and Pw = 1 g/cm³ is the density of ocean (a) (10 pts) Calculate the expected sea level change (S) near Atlanta 00≈ 0.59 by using the Trapezoid Rule to calculate the sea level integral with n= 100 subintervals. (b) (5 pts) Calculate and plot the expected sea level change (S) near Atlanta 00≈ 0.59 as a function of n = 10, 20, ..., 500, the number of subintervals. What does the shape of this curve indicate about the numerical method? (c) (10 pts) Use the same integration algorithm to calculate and plot the expected sea level change (S) as a function of latitude over 0o = [-1.5, 1.5]. Go to Settings to activate Windows.

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a To calculate the expected sea level change near Atlanta at 00 059 using the Trapezoid Rule with n ... View the full answer