Add in 3DVar FGAT (with time interpolation) for aerosol DA (#679)

* aerosol FGAT YAML template

* Linear time interpolation FGAT

parm/aero/obs/config/viirs_n20_aod.yaml

@@ -14,6 +14,7 @@ obs space:
   channels: 4
 get values:
   interpolation method: barycentric
+  time interpolation: linear
 obs operator:
   name: AodCRTM
   Absorbers: [H2O,O3]

parm/aero/obs/config/viirs_npp_aod.yaml

@@ -14,6 +14,7 @@ obs space:
   channels: 4
 get values:
   interpolation method: barycentric
+  time interpolation: linear
 obs operator:
   name: AodCRTM
   Absorbers: [H2O,O3]

parm/aero/variational/3dvar_fgat_gfs_aero.yaml

@@ -0,0 +1,112 @@
+cost function:
+  cost type: 3D-FGAT
+  window begin: '{{ AERO_WINDOW_BEGIN | to_isotime }}'
+  window length: $(AERO_WINDOW_LENGTH)
+  analysis variables: &3dvars
+                      [mass_fraction_of_sulfate_in_air,
+                       mass_fraction_of_hydrophobic_black_carbon_in_air,
+                       mass_fraction_of_hydrophilic_black_carbon_in_air,
+                       mass_fraction_of_hydrophobic_organic_carbon_in_air,
+                       mass_fraction_of_hydrophilic_organic_carbon_in_air,
+                       mass_fraction_of_dust001_in_air, mass_fraction_of_dust002_in_air,
+                       mass_fraction_of_dust003_in_air, mass_fraction_of_dust004_in_air,
+                       mass_fraction_of_dust005_in_air, mass_fraction_of_sea_salt001_in_air,
+                       mass_fraction_of_sea_salt002_in_air, mass_fraction_of_sea_salt003_in_air,
+                       mass_fraction_of_sea_salt004_in_air]
+  geometry:
+    fms initialization:
+      namelist filename: ./fv3jedi/fmsmpp.nml
+      field table filename: ./fv3jedi/field_table
+    akbk: ./fv3jedi/akbk.nc4
+    layout:
+    - $(layout_x)
+    - $(layout_y)
+    npx: $(npx_ges)
+    npy: $(npy_ges)
+    npz: $(npz_ges)
+    field metadata override: ./fv3jedi/fv3jedi_fieldmetadata_restart.yaml
+  model:
+    name: PSEUDO
+    datapath: ./bkg
+    filetype: fms restart
+    filename is datetime templated: true
+    tstep: PT3H
+    filename_core: '%yyyy%mm%dd.%hh%MM%ss.fv_core.res.nc'
+    filename_trcr: '%yyyy%mm%dd.%hh%MM%ss.fv_tracer.res.nc'
+    filename_cplr: '%yyyy%mm%dd.%hh%MM%ss.coupler.res'
+  background:
+    datapath: ./bkg
+    filetype: fms restart
+    datetime: '{{ AERO_WINDOW_BEGIN | to_isotime }}'
+    filename_core: '{{ AERO_WINDOW_BEGIN | to_fv3time }}.fv_core.res.nc'
+    filename_trcr: '{{ AERO_WINDOW_BEGIN | to_fv3time }}.fv_tracer.res.nc'
+    filename_cplr: '{{ AERO_WINDOW_BEGIN | to_fv3time }}.coupler.res'
+    state variables: [t,delp,sphum,so4,bc1,bc2,oc1,oc2,
+                      dust1,dust2,dust3,dust4,dust5,
+                      seas1,seas2,seas3,seas4]
+  background error: !INC ${BERROR_YAML}
+  observations: !INC ${OBS_LIST}
+variational:
+  minimizer:
+    algorithm: DRIPCG
+  iterations:
+  - ninner: 35
+    gradient norm reduction: 1e-10
+    test: on
+    geometry:
+      fms initialization:
+        namelist filename: ./fv3jedi/fmsmpp.nml
+        field table filename: ./fv3jedi/field_table
+      akbk: ./fv3jedi/akbk.nc4
+      layout:
+      - $(layout_x)
+      - $(layout_y)
+      npx: $(npx_anl)
+      npy: $(npy_anl)
+      npz: $(npz_anl)
+      field metadata override: ./fv3jedi/fv3jedi_fieldmetadata_restart.yaml
+    diagnostics:
+      departures: bkgmob
+  - ninner: 35
+    gradient norm reduction: 1e-10
+    test: on
+    geometry:
+      fms initialization:
+        namelist filename: ./fv3jedi/fmsmpp.nml
+        field table filename: ./fv3jedi/field_table
+      akbk: ./fv3jedi/akbk.nc4
+      layout:
+      - $(layout_x)
+      - $(layout_y)
+      npx: $(npx_anl)
+      npy: $(npy_anl)
+      npz: $(npz_anl)
+      field metadata override: ./fv3jedi/fv3jedi_fieldmetadata_restart.yaml
+    diagnostics:
+      departures: bkgmob1
+final:
+  diagnostics:
+    departures: anlmob
+  increment:
+    geometry:
+      fms initialization:
+        namelist filename: ./fv3jedi/fmsmpp.nml
+        field table filename: ./fv3jedi/field_table
+      akbk: ./fv3jedi/akbk.nc4
+      layout:
+      - $(layout_x)
+      - $(layout_y)
+      npx: $(npx_ges)
+      npy: $(npy_ges)
+      npz: $(npz_ges)
+      field metadata override: ./fv3jedi/fv3jedi_fieldmetadata_restart.yaml
+    output:
+      datapath: ./anl
+      prefix: aeroinc
+      filetype: fms restart
+      filename_core: '{{ current_cycle | to_fv3time }}.fv_core.res.nc'
+      filename_trcr: '{{ current_cycle | to_fv3time }}.fv_tracer.res.nc'
+      filename_cplr: '{{ current_cycle | to_fv3time }}.coupler.res'
+      state variables: [t,delp,sphum,so4,bc1,bc2,oc1,oc2,
+                        dust1,dust2,dust3,dust4,dust5,
+                        seas1,seas2,seas3,seas4]