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Update sdr.rst to fix notation in trapping and flux equations
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changed p(i,j) to p(j,i) in trapping and flux equations, as it is meant to denote proportion of flow from pixel j to pixel i
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lmandle authored Sep 13, 2024
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4 changes: 2 additions & 2 deletions source/en/sdr.rst
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Expand Up @@ -234,12 +234,12 @@ These mechanics can be captured as a linear interpolation of the difference of p

Now we define the amount of sediment flux that is retained on any pixel in the flowpath using :math:`dT_i` as a weighted flow of upslope flux:

.. math:: T_i=dT_i\cdot\left(\sum_{j\in\{pixels\ that\ drain\ to\ i\}}F_j \cdot p(i,j)\right)
.. math:: T_i=dT_i\cdot\left(\sum_{j\in\{pixels\ that\ drain\ to\ i\}}F_j \cdot p(j,i)\right)
:label: ti

where :math:`F_i` is the amount of sediment export that does not reach the stream "flux", defined as:

.. math:: F_i=(1-dT_i)\cdot(\left(\sum_{j\in\{pixels\ that\ drain\ to\ i\}} F_j \cdot p(i,j)\right) + E'_i)
.. math:: F_i=(1-dT_i)\cdot(\left(\sum_{j\in\{pixels\ that\ drain\ to\ i\}} F_j \cdot p(j,i)\right) + E'_i)
:label: fi

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