https://www.talsim.de/docs/index.php?action=history&feed=atom&title=Berechnungsschema%2F_Implementierung_der_Betriebsregeln%2Fen 2026-05-05T05:59:59Z Versionsgeschichte dieser Seite in TALSIM Docs MediaWiki 1.38.4 https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12841&oldid=prev 2021-08-30T09:27:26Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:27 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l83">Zeile 83:</td> <td colspan="2" class="diff-lineno">Zeile 83:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The computation of a section-by-section linear memory with arbitrary many inputs and outputs has been described by Ostrowski (1992)&lt;ref name=&quot;Ostrowski_1992&quot;&gt;&#039;&#039;&#039;Ostrowski, M.&#039;&#039;&#039; (1992): Ein universeller Baustein zur Simulation hydrologischer Prozesse, Wasser und Boden, Heft 11&lt;/ref&gt;. This solution was extended to include scaling of both the x-axis and y-axis by Ostrowski (1999)&lt;ref name=&quot;Ostrowski_1999&quot;&gt;&#039;&#039;&#039;Ostrowski, M. et al.&#039;&#039;&#039; (1999): Ein universeller, nicht linearer Speicherbaustein zur Simulation hydrologischer Systeme. Institutseigene Modell- und Anwendungsbeschreibung, Institut für Wasserbau und Wasserwirtschaft, TU Darmstadt, unveröffentlicht&lt;/ref&gt;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The computation of a section-by-section linear memory with arbitrary many inputs and outputs has been described by Ostrowski (1992)&lt;ref name=&quot;Ostrowski_1992&quot;&gt;&#039;&#039;&#039;Ostrowski, M.&#039;&#039;&#039; (1992): Ein universeller Baustein zur Simulation hydrologischer Prozesse, Wasser und Boden, Heft 11&lt;/ref&gt;. This solution was extended to include scaling of both the x-axis and y-axis by Ostrowski (1999)&lt;ref name=&quot;Ostrowski_1999&quot;&gt;&#039;&#039;&#039;Ostrowski, M. et al.&#039;&#039;&#039; (1999): Ein universeller, nicht linearer Speicherbaustein zur Simulation hydrologischer Systeme. Institutseigene Modell- und Anwendungsbeschreibung, Institut für Wasserbau und Wasserwirtschaft, TU Darmstadt, unveröffentlicht&lt;/ref&gt;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In summary, a <del style="font-weight: bold; text-decoration: none;">reservoir </del>can have multiple uses. For each use, there is a function depending on the <del style="font-weight: bold; text-decoration: none;">reservoir </del>volume, which must remain constant within an outer time step, but is changeable from time step to time step (time dependency). Besides, scaling the functions differently for each time step accounts for external dependencies via factors. Prerequisites for the scaling are constant factors during the time step. The calculation process is independent of the time step, as it is split according to section changes into an arbitrary number of inner time steps. As a result, the method is suitable for a wide variety of time intervals and produces results that are true to the volume. The method facilitates its use for diverse time intervals, e.g. it is suitable for a flood event with a time step of a few minutes but as well for a long-term simulation with daily values or even larger time intervals. For this purpose, it is critical, to define discharge functions with a sufficient number of supporting points.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In summary, a <ins style="font-weight: bold; text-decoration: none;">storage </ins>can have multiple uses. For each use, there is a function depending on the <ins style="font-weight: bold; text-decoration: none;">storage </ins>volume, which must remain constant within an outer time step, but is changeable from time step to time step (time dependency). Besides, scaling the functions differently for each time step accounts for external dependencies via factors. Prerequisites for the scaling are constant factors during the time step. The calculation process is independent of the time step, as it is split according to section changes into an arbitrary number of inner time steps. As a result, the method is suitable for a wide variety of time intervals and produces results that are true to the volume. The method facilitates its use for diverse time intervals, e.g. it is suitable for a flood event with a time step of a few minutes but as well for a long-term simulation with daily values or even larger time intervals. For this purpose, it is critical, to define discharge functions with a sufficient number of supporting points.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12839&oldid=prev 2021-08-30T09:26:11Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:26 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l76">Zeile 76:</td> <td colspan="2" class="diff-lineno">Zeile 76:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;y_{(t)}^s = y_{i-1}^s + k_i^s \cdot \left ( S_{(t)}^s - S_{i-1}^s \right )&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;y_{(t)}^s = y_{i-1}^s + k_i^s \cdot \left ( S_{(t)}^s - S_{i-1}^s \right )&lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>To calculate the delivery function scaled with external system states, proceed analogously to the above method. Here, &lt;code&gt;x&lt;sub&gt;factor&lt;/sub&gt;&lt;/code&gt; corresponds to the maximum <del style="font-weight: bold; text-decoration: none;">reservoir </del>volume and &lt;code&gt;y&lt;sub&gt;factor&lt;/sub&gt;&lt;/code&gt; corresponds to the scaling factor from the external system state or state group. It is assumed that the factors remain constant during the outer time interval. The sum of the integrations over the internal time loop divided by the outer time step provides the final output value.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>To calculate the delivery function scaled with external system states, proceed analogously to the above method. Here, &lt;code&gt;x&lt;sub&gt;factor&lt;/sub&gt;&lt;/code&gt; corresponds to the maximum <ins style="font-weight: bold; text-decoration: none;">storage </ins>volume and &lt;code&gt;y&lt;sub&gt;factor&lt;/sub&gt;&lt;/code&gt; corresponds to the scaling factor from the external system state or state group. It is assumed that the factors remain constant during the outer time interval. The sum of the integrations over the internal time loop divided by the outer time step provides the final output value.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-8)&lt;/div&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-8)&lt;/div&gt;</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12837&oldid=prev 2021-08-30T09:25:55Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:25 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44">Zeile 44:</td> <td colspan="2" class="diff-lineno">Zeile 44:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;S(t) = \frac{C_1}{C_2} \cdot \left [ 1 - e^{-C_2} \cdot (t-t_0) \right ]&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;S(t) = \frac{C_1}{C_2} \cdot \left [ 1 - e^{-C_2} \cdot (t-t_0) \right ]&lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>If at least one discharge function exceeds the viewed section, respective changes to the <del style="font-weight: bold; text-decoration: none;">reservoir </del>volumes and to the discharges must be identified up to that point and &lt;code&gt;C&lt;sub&gt;1&lt;/sub&gt;&lt;/code&gt; and &lt;code&gt;C&lt;sub&gt;2&lt;/sub&gt;&lt;/code&gt; recalculated. With this method, the used time interval - the outer time step - is processed by an arbitrary number of inner time steps, depending on the closeness of the supporting points. The time it takes to undertake a section change can be determined by solving the following equation for &lt;code&gt;t&lt;/code&gt;:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>If at least one discharge function exceeds the viewed section, respective changes to the <ins style="font-weight: bold; text-decoration: none;">storage </ins>volumes and to the discharges must be identified up to that point and &lt;code&gt;C&lt;sub&gt;1&lt;/sub&gt;&lt;/code&gt; and &lt;code&gt;C&lt;sub&gt;2&lt;/sub&gt;&lt;/code&gt; recalculated. With this method, the used time interval - the outer time step - is processed by an arbitrary number of inner time steps, depending on the closeness of the supporting points. The time it takes to undertake a section change can be determined by solving the following equation for &lt;code&gt;t&lt;/code&gt;:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-5)&lt;/div&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-5)&lt;/div&gt;</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12835&oldid=prev 2021-08-30T09:25:38Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:25 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l67">Zeile 67:</td> <td colspan="2" class="diff-lineno">Zeile 67:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Bild:Theorie_Abb25.png|thumb|Figure 25: Linearization of a scaled discharge function - section by section]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Bild:Theorie_Abb25.png|thumb|Figure 25: Linearization of a scaled discharge function - section by section]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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 <del style="font-weight: bold; text-decoration: none;">reservoir </del>volumes (x-axis).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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 <ins style="font-weight: bold; text-decoration: none;">storage </ins>volumes (x-axis).</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After introducing the scaling factors, the result for a scaled section of a function is:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>After introducing the scaling factors, the result for a scaled section of a function is:</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12833&oldid=prev 2021-08-30T09:25:13Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:25 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l56">Zeile 56:</td> <td colspan="2" class="diff-lineno">Zeile 56:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>#: After the time &lt;code&gt;t&lt;sub&gt;1&lt;/sub&gt;&lt;/code&gt;, there is a section change . The span between &lt;code&gt;t&lt;sub&gt;0&lt;/sub&gt;&lt;/code&gt; and &lt;code&gt;t&lt;sub&gt;1&lt;/sub&gt;&lt;/code&gt; represents the length of the inner time step.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>#: After the time &lt;code&gt;t&lt;sub&gt;1&lt;/sub&gt;&lt;/code&gt;, there is a section change . The span between &lt;code&gt;t&lt;sub&gt;0&lt;/sub&gt;&lt;/code&gt; and &lt;code&gt;t&lt;sub&gt;1&lt;/sub&gt;&lt;/code&gt; represents the length of the inner time step.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># &lt;math&gt;t_1 &lt; 0 \,&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># &lt;math&gt;t_1 &lt; 0 \,&lt;/math&gt;</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>#: There is no <del style="font-weight: bold; text-decoration: none;">reservoir </del>content increase but a decrease. Instead of the upper section boundary, the lower section boundary must be used and the calculation repeated.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>#: There is no <ins style="font-weight: bold; text-decoration: none;">storage </ins>content increase but a decrease. Instead of the upper section boundary, the lower section boundary must be used and the calculation repeated.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If section changes are observed, the storage volume is known at every time &lt;code&gt;t&lt;/code&gt;. Consequently, processes depending on the storage volumes are also known. In general, the development of the curve over time is not required but rather the mean value within one time interval. If equation 2-4 is inserted into equation 2-1 and integrated over the inner time step length, the average process rate in the relevant time interval is obtained.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If section changes are observed, the storage volume is known at every time &lt;code&gt;t&lt;/code&gt;. Consequently, processes depending on the storage volumes are also known. In general, the development of the curve over time is not required but rather the mean value within one time interval. If equation 2-4 is inserted into equation 2-1 and integrated over the inner time step length, the average process rate in the relevant time interval is obtained.</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12831&oldid=prev 2021-08-30T09:24:49Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:24 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l39">Zeile 39:</td> <td colspan="2" class="diff-lineno">Zeile 39:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;\frac{dS}{dt} = C_1 - C_2 \cdot S_{(t)} &lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;\frac{dS}{dt} = C_1 - C_2 \cdot S_{(t)} &lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>As long as the <del style="font-weight: bold; text-decoration: none;">reservoir </del>volumes are within one section &lt;code&gt;S&lt;sub&gt;i-1&lt;/sub&gt;&lt;/code&gt; to &lt;code&gt;S&lt;sub&gt;i&lt;/sub&gt;&lt;/code&gt;, the solution to the differential equation is:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>As long as the <ins style="font-weight: bold; text-decoration: none;">storage </ins>volumes are within one section &lt;code&gt;S&lt;sub&gt;i-1&lt;/sub&gt;&lt;/code&gt; to &lt;code&gt;S&lt;sub&gt;i&lt;/sub&gt;&lt;/code&gt;, the solution to the differential equation is:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-4)&lt;/div&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-4)&lt;/div&gt;</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12829&oldid=prev 2021-08-30T09:24:36Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:24 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32">Zeile 32:</td> <td colspan="2" class="diff-lineno">Zeile 32:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t : Time</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:t : Time</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>After dividing the equation into a constant part and a part depending on the storage volume S, the known and solvable equation of the linear single <del style="font-weight: bold; text-decoration: none;">reservoir </del>is obtained.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>After dividing the equation into a constant part and a part depending on the storage volume S, the known and solvable equation of the linear single <ins style="font-weight: bold; text-decoration: none;">storage </ins>is obtained.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-3)&lt;/div&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-3)&lt;/div&gt;</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12827&oldid=prev 2021-08-30T09:24:23Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:24 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Zeile 19:</td> <td colspan="2" class="diff-lineno">Zeile 19:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;S_i &lt; S_{(t)} \le S_{i+1}&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;S_i &lt; S_{(t)} \le S_{i+1}&lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For any number of discharge functions, the equation of a linear single <del style="font-weight: bold; text-decoration: none;">reservoir </del>for a section is:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>For any number of discharge functions, the equation of a linear single <ins style="font-weight: bold; text-decoration: none;">storage </ins>for a section is:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-2)&lt;/div&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div style=&quot;float:right&quot;&gt;(2-2)&lt;/div&gt;</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=12825&oldid=prev 2021-08-30T09:23:56Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. August 2021, 11:23 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Zeile 5:</td> <td colspan="2" class="diff-lineno">Zeile 5:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>To operationalize principles for simulation, it is required to devise mathematical relations.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>To operationalize principles for simulation, it is required to devise mathematical relations.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The previously given order of principles already indicates a useful structure for the mathematical formulation. The storage volume poses the most essential dependency. In system hydrology, this type of dependency is known as a linear single <del style="font-weight: bold; text-decoration: none;">reservoir </del>and can be thoroughly solved. Its principle is based on the assumption that the discharge is always proportional to the amount of water present in the <del style="font-weight: bold; text-decoration: none;">reservoir </del>(storage volume). The proportionality factor k is referred to as the <del style="font-weight: bold; text-decoration: none;">reservoir </del>constant. Taking into account the continuity equation and the <del style="font-weight: bold; text-decoration: none;">reservoir </del>constant gives the differential equation of the linear single <del style="font-weight: bold; text-decoration: none;">reservoir</del>. However, the <del style="font-weight: bold; text-decoration: none;">reservoir </del>equation is inapplicable to storage systems influenced by controls and operation rules. In this case, the discharges are not proportional to the storage volume, and therefore, an extension of the equation to any number of discharges is necessary.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The previously given order of principles already indicates a useful structure for the mathematical formulation. The storage volume poses the most essential dependency. In system hydrology, this type of dependency is known as a linear single <ins style="font-weight: bold; text-decoration: none;">stroage </ins>and can be thoroughly solved. Its principle is based on the assumption that the discharge is always proportional to the amount of water present in the <ins style="font-weight: bold; text-decoration: none;">storage </ins>(storage volume). The proportionality factor k is referred to as the <ins style="font-weight: bold; text-decoration: none;">storage </ins>constant. Taking into account the continuity equation and the <ins style="font-weight: bold; text-decoration: none;">storage </ins>constant gives the differential equation of the linear single <ins style="font-weight: bold; text-decoration: none;">storage</ins>. However, the <ins style="font-weight: bold; text-decoration: none;">storage </ins>equation is inapplicable to storage systems influenced by controls and operation rules. In this case, the discharges are not proportional to the storage volume, and therefore, an extension of the equation to any number of discharges is necessary.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Bild:Theorie_Abb24.png|thumb|Figure 24: Linearization of a function - section by section ]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Bild:Theorie_Abb24.png|thumb|Figure 24: Linearization of a function - section by section ]]</div></td></tr> </table>

Haghani https://www.talsim.de/docs/index.php?title=Berechnungsschema/_Implementierung_der_Betriebsregeln/en&diff=11946&oldid=prev 2021-03-16T10:29:22Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. März 2021, 12:29 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l63">Zeile 63:</td> <td colspan="2" class="diff-lineno">Zeile 63:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;\bar{y} = y_{p,i-1} - k_{p,i} \cdot S_{p,i-1} + k_{p,i} \cdot \left [ \frac{C_1}{C_2} + \left ( 1-e^{-C_2} \cdot (t_1-t_0) \right ) \cdot \left ( \frac{S_0}{(t_1-t_0) \cdot C_2} - \frac{C_1}{(t_1-t_0) \cdot C_2^2} \right ) \right ] &lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:&lt;math&gt;\bar{y} = y_{p,i-1} - k_{p,i} \cdot S_{p,i-1} + k_{p,i} \cdot \left [ \frac{C_1}{C_2} + \left ( 1-e^{-C_2} \cdot (t_1-t_0) \right ) \cdot \left ( \frac{S_0}{(t_1-t_0) \cdot C_2} - \frac{C_1}{(t_1-t_0) \cdot C_2^2} \right ) \right ] &lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>After <del style="font-weight: bold; text-decoration: none;">building the sum of </del>the inner time step values, the average process rate over the entire outer time interval is obtained.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>After <ins style="font-weight: bold; text-decoration: none;">summing up </ins>the inner time step values, the average process rate over the entire outer time interval is obtained.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Bild:Theorie_Abb25.png|thumb|Figure 25: Linearization of a scaled discharge function - section by section]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Bild:Theorie_Abb25.png|thumb|Figure 25: Linearization of a scaled discharge function - section by section]]</div></td></tr> </table>

T.Schnellbach