SYSTEMS IN SERIES
Some systems may be readily divided into a series of subsystems, so that budgets can be developed for each of the subsystems. Let us repeat Figure 1 from the previous section as a departure point:
Figure 1. Generalized diagram illustrating the calculation of water and salt budgets in coastal water bodies. Terms are defined in the text. In each diagram, green arrows indicate quantities which are assumed to be known, and red arrows and equations are quantities calculated from the budgets.
Figure 2 illustrates a more complex geometry, in which three subsystems can be budgeted. Note that the arithmetic for each system is totally analogous to the arithmetic laid out in the previous section for a single system.
Figure 2. Water and salt budgets for three linked boxes. As above, the convention is that arrows of known value are shown in green, while unknowns are shown in red.
An example of such a geometry might be two small estuaries which open out into a larger bay. Click here to see an example of such a budget. An important point is that the individual system can still be budgeted unambiguously. Both systems #1 and #2 receive material (salt, water) from land and exchange material with a single downstream system (system #3). System # 3 is more complicated, in that it exchanges with both #1 and #2, as well as with the ocean (labeled #4). However, those exchanges are readily resolved.
By contrast with this example, Figure 4 illustrates a superficially similar system, but one which involves ambiguities in flows. Because system #2 exchanges both with #3 and with the ocean (#4), a simple budget cannot resolve the relative fluxes (either exchanges or residual flows) with respect to these reservoirs. There might even be flow from #3, through #2, to #4. In the case of more complex flow patterns like this, some method of partitioning the fluxes independent of the budgets will be required. For example, there might be well described data on currents between #2 and #4. Plugging that information into the budget would allow definition of the flows between #2 and #3. An example of dealing with such an ambiguity is shown by clicking here.
Figure 4. Water and salt budgets for three linked boxes with with a more complexflow pattern, compared to Fig 3. As above, the convention is that arrows of known value are shown in green, while "standard unknowns" are shown in red. In this example, the budgets cannot be resolved explicitly, because system #2 exchanges with both #3 and the ocean (#4). These ambiguities are indicated by the question marks (?).
Some systems are vertically stratified; the classical example is so-called "estuarine circulation."
With some simplifying assumptions, such systems can also be budgeted as described here.
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Last Updated 12 May 2009 by FW