Filters

The filters implemented in EMPIRE can be divided into two categories, particle filters and Ensemble Kalman filters

Particle filters

SIR Filter (Sequential Importance Resampling)

See file sir_filter
Gordon, Salmond and Smith (1993).
Model specific operations required:

qhalf
h
solve_r
The SIR filter has no parameters to be chosen.

To select the SIR filter, in empire.nml set the following variables:

filter = 'SI'

Equivalent Weights Particle Filter

See files proposal_filter equivalent_weights_filter
Van Leeuwen (2010).
Model specific operations required:

The Equivalent Weights particle filter has a number of free parameters to be chosen.

To select the EWPF, in empire.nml set the following variables:

filter = 'EW'

The Zhu and Van Leeuwen Equivalent Weights Particle Filter

See files proposal_filter equivalent_weights_filter_zhu
Model specific operations required:

The Zhu Equivalent Weights particle filter has a number of free parameters to be chosen.

To select the EZPF, in empire.nml set the following variables:

filter = 'EZ'

Ensemble Kalman filters

LETKF (The Localised Ensemble Transform Kalman Filter)

See file letkf_analysis
Hunt, Kostelich and Szunyogh (2007).
Model specific operations required:

The LETKF has a number of free parameters to be chosen.

rho
len

To select the LETKF, in empire.nml set the following variables:

filter = 'LE' or 'LD' with LE including model error but LD being deterministic

Smoothers

Coming at some point in the future: LETKS (Please contact us if you want us to develop this sooner rather than later)

Variational Methods

3DVar

See files threedvar_fcn
Model specific operations required:

3DVar can be used as a filter in a sequential run. Each particle uses its current forecast as a background guess for an independent 3DVar minimization.

4dEnVar

See files fourdenvar fourdenvar_fcn
Liu, Xian and Wang (2008).
Model specific operations required:

h
solve_r

Currently there is the basic functionality to do 4dEnVar so long as the optional reverse communication is used. This is work in progress.

Todo:: Finish the following description.

The following is a stream of consciousness about how to use 4dEnVar.

Firstly note that 4dEnVar is built into a different executable: empire-4denvar. Make sure to launch that along with the models.

In order to solve the 4DEnVar problem, we have one ensemble member representing the desired analysis, and the others representing the perturbations. Hence to use N ensemble members to calculate the gradient, one must launch the code with N+1 ensemble members in total.

The main program, FourDEnVar is located in src/4dEnVar/4dEnVar.f90.

The first thing it does is read from vardata.nml or empire.nml a namelist called var_params, that contains the options for the optimization method. See var_data::parse_vardata for information on this.

The next important thing to specify is the observation window, specifically when and how many observations there will be throughout the window. This is currently done with the hard-coded var_data::read_observation_numbers subroutine. What is needed is for the array vardata%ny to contain a list of the number of observations at each timestep throughout the window. As an example, suppose the observation window was 10 timesteps long, and we had 8 observations at timestep 3, 2 observations at timestep 5 and 43 observations at timestep 9, then the array vardata%ny should contain the numbers [0 0 8 0 2 0 0 0 43 0]. How this is implemented should probably change. This isn't done well as we have had no users who have contacted us saying they wish to use this method - hence we do not know what format would work best for them. Please get in touch if you want to use it!

Todo:: Put in a form of localisation into 4DEnVar