Analysis-Forecast Observation Impacts driver

[arango]

Added a new driver obs_sen_w4dpsas_forecast.h for computing observation impacts for the analysis-forecast cycle. It is activated with C-preprocessing option W4DPSAS_FCT_SENSITIVITY. It basically computes the impacts of each observation on the forecast error.

Added the tangent linear (tl_rpcg_lanczos.F) and adjoint (ad_rpcg_lanczos.F) versions of the Restricted B-preconditioned Conjugate Gradient Lanczos algorithm (known as RBLanczos or RPCG) used the 4D-Var dual formulation.

The following diagram is used to explain the forecast cycle observations impacts: For more information, check the following WikiROMS ​page. The red and blue curves show the typical configuration for the algorithm computing the analysis-forecast cycle observation impacts.

The observation impacts can be forced at the model grid points, defining the desired metrics or at the observation locations when OBS_SPACE is activated additionally.

WARNINGS:

Both the roms.in and s4dvar.in scripts were modified to add new parameters needed in them analysis-forecast cycle observation impacts configuration:

• In ocean.in, we have:

  ! Number of timesteps for computing observation impacts during the
  ! analysis-forecast cycle.
  
    NTIMES_ANA == 1440                               ! analysis interval
    NTIMES_FCT == 1440                               ! forecast interval
  
  ...
  
  ! Input adjoint forcing NetCDF filenames for computing observations
  ! impacts during the analysis-forecast cycle. If the forecast error
  ! metric is defined in state-space, then FOInameA and FOInameB should
  ! be regular adjoint forcing files just like ADSname. If the forecast
  ! error metric is defined in observation space (OBS_SPACE is activated)
  ! then the forecast is initialized OIFnameA and OIFnameB (specified in
  ! s4dva4.in input script) will have the structure of a 4D-Var observation
  ! file.
  
      FOInameA == roms_foi_a.nc
      FOInameB == roms_foi_b.nc
  
  ! Input NetCDF filenames for the forecasts initialized from the analysis
  ! of the current 4D-Var cycle (FCTnameA) and initialized from the analysis
  ! of the previous 4D-Var cycle (FCTnameB).
  
      FCTnameA == roms_fct_a.nc
      FCTnameB == roms_fct_b.nc
  

  Where NTIMES_ANA and NTIMES_FCT are the total number of timesteps to compute the observations-impacts interval during the analysis and forecast cycle, respectively, when W4DPSAS_FCT_SENSITIVITY is activated.

FOInameA and FOInameB are the input forcing NetCDF files at model grid points for computing the observation impact when the forecast is initialized with the 4D-Var analysis (red curve) or the 4D-Var background (blue curves), respectively. FCTnameA is the current 4D-Var analysis cycle (red curve) and FCTnameB is the previous 4D-Var analysis cycle (blue curve).

• In s4dvar.in, we have:

  ! Input forcing filenames at observation locations for computing observations
  ! impacts during the analysis-forecast cycle when the forecast is initialized
  ! with the 4D-Var analysis (OIFnameA) or the 4D-Var background (OIFnameB).
  
        OIFnameA == roms_oif_a.nc
        OIFnameB == roms_oif_b.nc
  

  were OIFnameA and OIFnameB are the input forcing NetCDF files at observation location for computing the observation impact when the forecast is initialized with the 4D-Var analysis (red curve) or the 4D-Var background (blue curves), respectively, when both W4DPSAS_FCT_SENSITIVITY and OBS_SPACE options are activates.

References:

Errico, R.M., 2007: Interpretations of an adjoint-derived observational impact measure, Tellus, 59A, 273-276.

Gelaro, R., Y. Zhu, R.M. Errico, 2007: Examination of various-order adjoint-based approximations of observation impact, Meteorologische Zeitschrift, 16, 685-692.

Langland, R.H. and N.Baker, 2004: Estimation of observation impact using the NRL atmospheric variational data assimilation adjoint system, Tellus, 56, 189-201.

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Many thanks to Andy Moore for his help coding and testing this complex algorithm. There are involved technical description that will be published in the near feature with realistic applications.