A systematic method of parameterisation estimation using data assimilation

Figures & data

Fig. 1 A single timestep from the data assimilation trajectory from timestep t−1 to t. Step 3 defines as a single model timestep from the data assimilation trajectory at timestep t−1 using the model f with the prior parameterisation G ^b .

Fig. 2 Estimated parameter values from state augmentation, for the parameters described in eq. (38).

Table 1. Analysis parameterisations from parameterisation estimation method for different observation densities

Observations at all space-time points
Observations at every three gridpoints and every timestep
Observations at every gridpoint and every three timesteps
Observations at every three gridpoints and every three timesteps

Table 2. Analysis parameterisations from parameterisation estimation method for different magnitudes of observation error relative to model error

R=0.005^2 I such that Q=4R
R=0.01^2 I such that Q=R
R=0.02^2 I such that Q = 0.25R