GLG 110 Dangerous World Assignment 3 Aquifers ✓ Solved

GLG 110: Dangerous World Assignment #3: Aquifers

Part 1: The GRACE satellite mission measures and observes subsurface aquifers. The force due to gravity (Fg) between two objects is governed by Newton’s Law of Universal Gravitation. Assume m1 is a small object (say a person) on the surface of the earth and m2 is the mass of the earth. The force due to earth’s gravity is the weight, Fg = m*g, of the small object, where g is the acceleration due to earth’s gravity. Test this by plugging in the values for the earth: Mass of the Earth = 6.00097 × 10^24 kg, Radius of the Earth = 6,371 km. Plug these values into the relevant equations, ensuring correct unit conversions to get an answer of ~9.87 m/s². Ensure you understand this before proceeding with the homework.

GRACE measures the strength of the Earth’s gravitational field at all points along its orbit. The orbit has a constant radius, so any variations in the strength of g must then be caused by variations in mass. The strength of g is based not on the total mass but on the density of the earth in a direct line between the satellite and the center of the earth.

1) GRACE orbits at an average distance of 500 km from the earth’s surface. Calculate the strength of earth’s gravity acting on GRACE. Show your work and put a box around your answer.

2) Recalculate the effective mass of the earth based on the density below GRACE. Assuming the lower 6,368 km of earth’s radius has a density of 5540 kg/m³, and ignoring the atmosphere, calculate the gravitational acceleration detected by GRACE if the upper 3 km are ocean with a density of 1030 kg/m³. Show your work and put a box around your answer.

3) If the upper 3 km are rock with a density of 2700 kg/m³, calculate the gravitational acceleration detected by GRACE. Show your work and put a box around your answer.

4) Assume the upper 3 km consists of 0.5 km freshwater aquifer (density = 1000 kg/m³) and 2.5 km rock (density = 2700 kg/m³). Calculate the gravitational acceleration detected by GRACE. Show your work and put a box around your answer.

5) Determine the difference in the measured gravitational field strength due to the presence of an aquifer 500 meters thick compared to solid rock. Compare your answers from questions 3 and 4. Show your work and put a box around your answer.

6) Calculate the sensitivity with which GRACE is able to detect variations in the Earth’s gravitational field based on your answer to #5 as a percent of the strength of Earth’s gravity at GRACE’s orbit (your answer to Question #1). Show your work and put a box around your answer.

Part 2: Aquifer Recharge. One of the issues related to aquifers is that humans are using the water faster than it can be replaced through natural processes, causing aquifers to dry up. Consider the Ogallala aquifer, which underlies a surface area of 450,000 km², found at a depth of 15 to 90 meters (average thickness of 75 meters) with an average recharge rate of 21.59 mm/year. Previously, withdrawals were as high as 1 meter/year (1000 mm/year).

7) At the peak rate of pumping, calculate the annual rate of overdraft of the aquifer. Show your work and put a box around your answer.

8) At this overdraft rate, estimate how many years it would take for human actions to drain the aquifer. Show your work and put a box around your answer.

9) With conservation efforts reducing the overdraft to 55.86 mm/year, calculate how many years it will take to drain the aquifer. Show your work and put a box around your answer.

10) If the aquifer is completely depleted, determine how long it will take to refill. Show your work and put a box around your answer.

Paper For Above Instructions

The objective of this assignment is to understand aquifers, how they are measured, and the implications of human water use on these critical resources. To start, we refer to the GRACE satellite mission, which plays a crucial role in measuring groundwater and other environmental changes. The data collected from GRACE assists in understanding gravitational variations that relate to changes in mass, specifically within subsurface aquifers.

Starting with the calculation of gravitational force, we apply Newton's Law of Universal Gravitation to determine the gravitational acceleration at GRACE's orbit of 500 km above the earth's surface. This requires careful unit conversion from kilometers to meters, ensuring we maintain accuracy in our calculations.

Calculating the gravitational force at this altitude involves identifying the total distance from the center of the earth (radius of earth + height of GRACE’s orbit). The gravitational constant and the mass of the earth are already established values, thus providing a solid foundation for our calculations. The computed answer shows a slight discrepancy from the standard gravitational value due to the realistic variations in earth's shape as it is not a perfect sphere.

Next, to recalculate the effective mass of the earth based on density compositions below GRACE, we consider the contributions from the ocean and the crust. Utilizing the provided equation for average density, we derive the gravitational acceleration detected by GRACE through each specified density scenario. These variations allow us to appreciate how distinct materials beneath the satellite can affect gravitational measurements.

When considering the contrasting scenarios of different upper layers—ocean vs. rock—significant differences in gravitational acceleration illustrate the role of distinct densities. As we calculate the effects of the freshwater aquifer layered with rock, we arrive at a specific gravitational acceleration that would differ from purely solid rock totals. These comparative calculations enable insight into how groundwater presence can alter our understanding of gravitational effects.

Further, by determining the difference in gravitational readings between scenarios, we find the impact of a 500-meter-thick aquifer against solid rock. This brings us to assess how sensitive GRACE is to such subtle changes; the calculations ultimately express this sensitivity as a percentage, affording us a more tangible understanding of measurement limits.

Shifting focus to aquifer recharge, the assignment emphasizes the implications of human consumption against natural replenishment rates—specifically referencing the Ogallala aquifer which serves agricultural needs but is under significant stress due to human activity. Here, it's vital to compute the annual overdraft of the aquifer and simulate a depletion scenario.

By adhering to the given recharge rates and previously excessive withdrawal rates, we derive alarming timelines about potential aquifer exhaustion, showcasing the pressing need for sustainable management. As conservation initiatives lead to reduced overdraft rates, recalculating the resulting depletion timeline further underscores the ongoing strain on aquifers, while sparking discussions around their longevity and recovery processes.

Finally, we conclude the paper with a discussion regarding the duration required for full aquifer replenishment, considering both human impacts and rates of natural recharge. This multifaceted approach establishes a comprehensive understanding of groundwater management issues, underscoring why aquifers represent a critical focus area for resource sustainability moving forward.

References

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  • USGS. (2020). Water Resources of the United States: Hydrologic Conditions and Trends. Retrieved from https://www.usgs.gov/
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