The general box model with forcing terms

One way of circumventing the difficulties encountered for systems with widely different time constants is to split the reservoirs into two categories. The first category will comprise the reservoirs with short residence times which will be explicitly required to satisfy the constraints of mass conservation. Reservoirs with long residence times will make up the second category which we will treat as source and sinks. Equation (7.3.8) will be transformed into 

If b does not depend explicitly on the M decoupling reservoirs introduces a forcing term without affecting the short-term relaxation behavior.The diagonal decomposition of A as UAU 1 gives 

Two oceanic basins noted A and B contain initially a mass of sodium MA° and Mb°. Sodium residence time in each basin is rA and rB. Sodium exchange takes place 

Let us first calculate steady-state concentrations when all Na weathered from evaporites has been transported to the sea and all the parameters become time-invariant. At steady-state, fluxes between reservoirs must be equal 

Inserting numerical values gives MA°° = 12.5 and MB°° = 2.5 in the same units as the 

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