Hi,
I am trying to assimilate the satellite-derived sea-ice concentration over the Arctic into the sea-ice mode (CICE) embedded in the CESM package, using DART as a data assimilation system. I am suffering from model error convergence (ensemble spread becomes quite small) in the local area in the Arctic, so finding some solutions to alleviate the model error convergence problem. In DART, two approaches are available to counteract the model error convergence: a) prior and posterior inflation and b) spread restoration.
Unfortunately, even though the adaptive inflation algorithm is turned on with the prior inflation, this approach does not contribute to alleviating the model error convergence.
In contrast, when the spread restoration algorithm is turned on and slightly modified, I found that the model error convergence is slightly improved. However, I cannot find any documents describing the concept of the spread restoration and how to define the linear relationship between the error ratio and the inflation values (the equation is below).
<assim_tools_mod.f90>
if(spread_restoration) then
! Don't use this to reduce spread at present (should revisit this line)
net_a = min(net_a_in, 1.0_r8)
! Default restoration increment is 0.0
restoration_inc = 0.0_r8
! Compute the factor by which to inflate
! These come from correl_error.f90 in system_simulation and the files ens??_pairs and
! ens_pairs_0.5 in work under system_simulation. Assume a linear reduction from 1
! as a function of the net_a. Assume that the slope of this reduction is a function of
! the reciprocal of the ensemble_size (slope = 0.80 / ens_size). These are empirical
! for now. See also README in spread_restoration_paper documentation.
factor = 1.0_r8 / (1.0_r8 + (net_a - 1.0_r8) / (-2.4711_r8 + 1.6386_r8 * ens_size)) - 1.0_r8
! Variance restoration
state_mean = sum(state) / ens_size
restoration_inc = factor * (state - state_mean)
state_inc = state_inc + restoration_inc
endif
Please let me know if you know of any documents related to the spread restoration scheme.
Many thanks,
Youngchan Noh
I am trying to assimilate the satellite-derived sea-ice concentration over the Arctic into the sea-ice mode (CICE) embedded in the CESM package, using DART as a data assimilation system. I am suffering from model error convergence (ensemble spread becomes quite small) in the local area in the Arctic, so finding some solutions to alleviate the model error convergence problem. In DART, two approaches are available to counteract the model error convergence: a) prior and posterior inflation and b) spread restoration.
Unfortunately, even though the adaptive inflation algorithm is turned on with the prior inflation, this approach does not contribute to alleviating the model error convergence.
In contrast, when the spread restoration algorithm is turned on and slightly modified, I found that the model error convergence is slightly improved. However, I cannot find any documents describing the concept of the spread restoration and how to define the linear relationship between the error ratio and the inflation values (the equation is below).
<assim_tools_mod.f90>
if(spread_restoration) then
! Don't use this to reduce spread at present (should revisit this line)
net_a = min(net_a_in, 1.0_r8)
! Default restoration increment is 0.0
restoration_inc = 0.0_r8
! Compute the factor by which to inflate
! These come from correl_error.f90 in system_simulation and the files ens??_pairs and
! ens_pairs_0.5 in work under system_simulation. Assume a linear reduction from 1
! as a function of the net_a. Assume that the slope of this reduction is a function of
! the reciprocal of the ensemble_size (slope = 0.80 / ens_size). These are empirical
! for now. See also README in spread_restoration_paper documentation.
factor = 1.0_r8 / (1.0_r8 + (net_a - 1.0_r8) / (-2.4711_r8 + 1.6386_r8 * ens_size)) - 1.0_r8
! Variance restoration
state_mean = sum(state) / ens_size
restoration_inc = factor * (state - state_mean)
state_inc = state_inc + restoration_inc
endif
Please let me know if you know of any documents related to the spread restoration scheme.
Many thanks,
Youngchan Noh
