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From the principles for the description of operating rules it is evident that a discharge can be dependent on the storage content as well as on other system states. Thus, a one-dimensional dependency - only on the storage content - is no longer given. In such a case, a two- or multi-dimensional relationship exists for the unambiguous determination of a dischrage. If a time dependency is added, the problem is extended by one more dimension. A graphically simple representation is no longer feasible. Likewise the solution described above is not sufficient, since further ones are added to the dependence on the reservoir contents. Both for reasons of clarity and a suitable mathematical formulation, it is desirable to convert all dependencies back into a one-dimensional relationship without loss of information. This is achieved by scaling the ''discharge functions'' relationship. A scaling is possible for the discharge (y-axis) as well as for the reservoir content (x-axis).
The principles in the description of operating rules illustrate that discharges depend on storage volumes as well as on other system states. Thus, a one-dimensional dependency no longer exists but rather a two- or multi-dimensional relation. Considering also a time dependency the problem is extended by one more dimension. Therefore, the solution from above, and respectively a simple depiction in a diagram, are no longer possible. For clarity and adequate mathematical formulation, a conversion from multiple dependencies to a one-dimensional relation needs to be undertaken without a loss of information. Scaling the discharge functions relation achieves said conversion. It is possible for the discharge (y-axis) as well as for the reservoir volumes (x-axis).
Version vom 16. März 2021, 11:47 Uhr
The principles in the description of operating rules illustrate that discharges depend on storage volumes as well as on other system states. Thus, a one-dimensional dependency no longer exists but rather a two- or multi-dimensional relation. Considering also a time dependency the problem is extended by one more dimension. Therefore, the solution from above, and respectively a simple depiction in a diagram, are no longer possible. For clarity and adequate mathematical formulation, a conversion from multiple dependencies to a one-dimensional relation needs to be undertaken without a loss of information. Scaling the discharge functions relation achieves said conversion. It is possible for the discharge (y-axis) as well as for the reservoir volumes (x-axis).