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Revisit the notation
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The subscripts are awkward, but I think this is consistent.
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kwinkunks authored Jan 4, 2024
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6 changes: 3 additions & 3 deletions docs/reference/configuration/keywords.rst
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Expand Up @@ -1378,14 +1378,14 @@ Keywords controlling the ES algorithm
Including outliers in the Smoother algorithm can dramatically increase the
coupling between the ensemble members. It is therefore important to filter out
these outliers prior to data assimilation. An observation,
:math:`\mathbf{d}^o_i`, will be classified as an outlier if
:math:`d^o_i`, will be classified as an outlier if

:math:`|\mathbf{d}^o_i - \bar{\mathbf{d}}_i| > \mathrm{ENKF\_ALPHA} \left(\mathbf{s}_{\mathbf{d}_i} + \mathbf{s}^o_{\mathbf{d}_i}\right)`
:math:`|d^o_i - \mathbf{\bar{d}}| > \mathrm{ENKF\_ALPHA} \left( s_{d_i} + s^o_{d_i} \right)`

where :math:`\mathbf{d}^o` is the vector of observed data,
:math:`\mathbf{\bar{d}}` is the average of the forecasted data ensemble,
:math:`\mathbf{s}_\mathbf{d}` is the vector of estimated standard deviations
for the forecasted data ensemble, and :math:`\mathbf{s}^o_{\mathbf{d}_i}` is the
for the forecasted data ensemble, and :math:`\mathbf{s}^o_\mathbf{d}` is the
vector of standard deviations for the observation error (specified a priori).

Observe that for the updates many settings should be applied on the analysis
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