diff --git a/doc/src/dfs.md b/doc/src/dfs.md index 0964c7c..4038659 100644 --- a/doc/src/dfs.md +++ b/doc/src/dfs.md @@ -6,11 +6,13 @@ ### 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.