Figure P3.16 shows a schematic description of the global carbon cycle (Li, ). In the figure, m
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Figure P3.16 shows a schematic description of the global carbon cycle (Li, ). In the figure, mA(t) represents the amount of carbon in gigatons (GtC) present in the atmosphere of earth; mV(t) the amount in vegetation; ms(t) the amount in soil; mSO(t) the amount in surface ocean; and mIDO(t) the amount in intermediate and deep ocean reservoirs. Let uE(t) stand for the human generated CO2 emissions (GtC/yr). Fromthe figure, the atmospheric mass balance in the atmosphere can be expressed as:
where the k’s are exchange coefficients (yr-1).
a. Write the remaining reservoir mass balances. Namely, write equations for dmSO(t)/dt ; dmIDO(t)/dt ; dmV (t)/dt ; and dmS(t)/dt
b. Express the system in state-space form.
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