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dollars to ticks (#50)
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ewhelan authored May 17, 2024
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### Definition
The DFS is defined as the trace of the product of the observation sensitivity matrix and the observation error covariance matrix. Mathematically, it can be expressed as:

$$ \text{DFS} = \text{Tr}(\mathbf{K} \mathbf{H}) $$
```math
\text{DFS} = \text{Tr}(\mathbf{K} \mathbf{H})
```

where:
- $\mathbf{K}$ is the Kalman gain matrix, which represents how much weight is given to the observations in the assimilation process.
- $\mathbf{H}$ is the observation operator, which maps the model state variables to the observed variables.
- ``\mathbf{K}`` is the Kalman gain matrix, which represents how much weight is given to the observations in the assimilation process.
- ``\mathbf{H}`` is the observation operator, which maps the model state variables to the observed variables.

### Interpretation
1. **Information Content**: DFS indicates how much the observations have influenced the analysis. A higher DFS means that the observations have a significant impact on the analysis, providing more information.
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