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Systems:
We have spent the last two weeks on a very detailed physical process: F=ma. We're now going to back up to look at the larger relationships between objects and processes, wrapped up in systems dynamics. To start, we need a few definitions.
Closed system: A set of objects and their interactions on which no outside influences act; closed so that no mass and/or energy gets in or out of the system and nothing from outside can influence the system's observable behavior or properties. Example: Earth is closed to mass (the small amount of meteorites that hit Earth each year are vanishingly small, equivalent to a layer 0.1 nm thick spread out across Earth's surface accumulating each year).
Open system: A set of objects and their interactions on which outside influences act; mass and/or energy enters and/or leaves the system. Example: Earth is open to energy (it receives energy from the Sun and reradiates energy out into space).
Conservation of mass: Matter changes form, but cannot be created or destroyed. This implies that in a closed system, the mass is constant and ΔMass=0. For an open system, ΔMass=Massin-Massout. For open systems, if Massin=Massout then it follows that ΔMass=0 and the system is said to be "steady" or "in steady state."
Example 1: Is is appropriate to approximate Earth as a closed system with respect to mass?
(thickness of accumulated layer)=[(incoming mass per year)*(age of Earth)]/[(density of material)*(surface area of Earth)]
Earth receives ~1x108 kg/yr of dust from space. Let's assume a density of sedimentary rocks, 2000 kg/m3. The age of Earth is 4.5 billion years, and the surface area is 5x1014 m2. The accumulated layer would be less than 0.5 m thick, so Earth (at least now) can be assumed to be a closed system to mass.
Example 2: How do you assess the "health" of a glacier?
(mass balance)=(incoming mass per year through snowfall) - (outgoing mass per year through melting) +/- (other processes like iceberg calving)
A glacier is stable if its incoming mass through snowfall in the winter is exactly balanced by the outgoing mass through melting in the summer. A glacier changes size if there is a mismatch in the incoming and outgoing mass. This means that a glacier can shrink even if it receives more snowfall each year, as long as the melt rate goes up more. Likewise a glacier can grow even if melting increases, as long as the snowfall rate goes up more.
Most glaciers worldwide are shrinking because melt rates are increasing as a result of global warming. However, Antarctica and Greenland have experienced some growth because snowfall has gone up on these two continents as the air temperature has warmed. In fact, the history of snow accumulation and temperature in Greenland over the last 10,000 years indicates that snowfall and warming temperatures have gone hand-in-hand since the end of the last Ice Age. Overall, Greenland has shrunk because the melt rates have increased more than snowfall rates have increased.
Example 3: What is the mass balance of a particular part of a glacier?
(mass balance)=(incoming mass per year through snowfall) - (outgoing mass per year through melting) + (incoming mass per year through flowing ice) - (outgoing mass per year through flowing ice)
The highest elevations of a glacier tend to get the greatest amounts of snowfall each winter. They also tend to have the lowest amount of melting. This region of a glacier is known as the accumulation area, because it has net accumulation of snow. It stays snow-covered year-round. This part of the glacier is stable only if the amount of ice flowing downglacier balances the net snow accumulation.
The lowest elevations of a glacier tend to get the smallest amounts of snowfall each winter. They also tend to have the largest amount of melting. This region of a glacier is known as the ablation area, because it has net loss of snow and ice. It has bare ice by the end of the summer. This part of the glacier is stable only if the amount of ice flowing from upglacier balances the net ablation. If the amount of ice flowing from upglacier is less than the amount of melting, the glacier "retreats".
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