2.5 Evaluation metrics
With respect to the corresponding observations \(y_{i}\), the
performance of \({\hat{y}}_{i}\), simulations in model calibration and
validation or updated simulations in DA, was evaluated by the
coefficient of determination (R 2), the root
mean square error (RMSE ) and the normalized RMSE(NRMSE ):
\(R^{2}=1-\frac{\sum_{i\ =\ 1}^{n}{(y_{i}-{\hat{y}}_{i})}^{2}}{\sum_{i\ =\ 1}^{n}{(y_{i}-\overset{\overline{}}{y})}^{2}}\)(18)
\(RMSE=\sqrt{\sum_{i\ =\ 1}^{n}{(y_{i}-{\hat{y}}_{i})}^{2}/\left(n-1\right)}\)(19)
\(NRMSE=\frac{\text{RMSE}}{\overset{\overline{}}{y}}\) (20)
where \(n\) represents the number of evaluated data points, and\(\overset{\overline{}}{y}\) is the mean value of observations across
the whole growing season.
Moreover, to assess the filter behavior of EnKF, we introducedf rc, which represents the relative change of the
states after and before updating compared with the measured \(y_{i}\),
\(f_{\text{rc}}=\frac{{\overset{\overline{}}{Y}}_{i}^{a}-y_{i}}{{\overset{\overline{}}{Y}}_{i}^{f}-y_{i}}\)(21)
in which \({\overset{\overline{}}{Y}}_{i}^{a}\) is calculated as\(\frac{\left(\sum_{j=1}^{N_{\text{ens}}}Y_{t,j}^{a}\right)}{N_{\text{ens}}}\).
The closer f rc is to one, the more likely does
filter divergence occur.