New ocean/ice B diag (#1050)

### What was done
- Variance partitioning of ice and ocean backgrounds
- Switch to using the `StdDev` saber block with the above fields as a
proxy of the background error
- Changed the obs filtering
- Removed the hybrid B, will plug it back in later
- Use Travis' script to extract the vertical decorrelation scales from
the bkg, using the mld.
- Use of jinja for the new yamls
- setting NMEM_ENS to something larger that 3 will trigger the hybrid
envar and use static or real members, depending on the status or
`DO_HYBVAR`

The results are reasonable but some of the parameters of the variance
partitioning still need to be optimized further

- fixes #982 
- fixes #927 
- fixes #939 (not exactly but good enough. It tests the hybrid envar
with static members)

---------

Co-authored-by: Cory Martin <cory.r.martin@noaa.gov>

parm/soca/berror/soca_diagb.yaml.j2

@@ -0,0 +1,59 @@
+geometry:
+  mom6_input_nml: mom_input.nml
+  fields metadata: ./fields_metadata.yaml
+
+date: '{{ ATM_WINDOW_MIDDLE }}'
+
+background:
+  date: '{{ ATM_WINDOW_MIDDLE }}'
+  basename: ./bkg/
+  ocn_filename: '{{ RUN }}.ocean.t{{ gcyc }}z.inst.f009.nc'
+  ice_filename: '{{ RUN }}.agg_ice.t{{ gcyc }}z.inst.f009.nc'
+  read_from_file: 1
+
+background error:
+  datadir: ./
+  date: '{{ ATM_WINDOW_MIDDLE }}'
+  exp: bkgerr_stddev
+  type: incr
+
+variables:
+  name: [tocn, socn, uocn, vocn, hocn, ssh, cicen, hicen, hsnon, mom6_mld]
+
+rescale: 2.0    # rescales the filtered std. dev. by "rescale"
+min sst: 0.0    # Added to sst bkg. err.
+max ssh: 0.0    # Limits the amplitude of the unbalanced bkg err
+number of halo points: 4
+number of neighbors: 16
+simple smoothing:
+  horizontal iterations: 2
+  vertical iterations: 1
+
+# TODO(G): Start using when the normalization is optional
+#diffusion:
+#   saber block name: EXPLICIT_DIFFUSION
+#   active variables: [tocn, socn, ssh, cicen, hicen, hsnon]
+#   geometry:
+#     mom6_input_nml: mom_input.nml
+#     fields metadata: ./fields_metadata.yaml
+#   group mapping:
+#   - name: ocean
+#     variables:
+#     - tocn
+#     - socn
+#     - ssh
+#   - name: ice
+#     variables:
+#     - cicen
+#     - hicen
+#     - hsnon
+#   read:
+#     groups:
+#     - name: ocean
+#       horizontal:
+#         filename: hz_ocean.nc
+#       vertical:
+#         filename: vt_ocean.nc
+#     - name: ice
+#       horizontal:
+#         filename: hz_ice.nc

parm/soca/berror/soca_hybrid_bmat.yaml

@@ -0,0 +1,92 @@
+covariance model: hybrid
+components:
+- covariance:
+    covariance model: SABER
+    saber central block:
+      saber block name: EXPLICIT_DIFFUSION
+      active variables: [tocn, socn, ssh, cicen]
+      geometry:
+        mom6_input_nml: mom_input.nml
+        fields metadata: ./fields_metadata.yaml
+      group mapping:
+      - name: ocean
+        variables:
+        - tocn
+        - socn
+        - ssh
+      - name: ice
+        variables:
+        - cicen
+      read:
+        groups:
+        - name: ocean
+          horizontal:
+            filename: hz_ocean.nc
+          vertical:
+            filename: vt_ocean.nc
+        - name: ice
+          horizontal:
+            filename: hz_ice.nc
+
+    saber outer blocks:
+    - saber block name: StdDev
+      read:
+        model file:
+          date: '{{ATM_WINDOW_MIDDLE}}'
+          basename: ./
+          ocn_filename: 'ocn.bkgerr_stddev.incr.{{ATM_WINDOW_MIDDLE}}.nc'
+          ice_filename: 'ice.bkgerr_stddev.incr.{{ATM_WINDOW_MIDDLE}}.nc'
+          read_from_file: 3
+
+    linear variable change:
+      input variables: [cicen, hicen, hsnon, socn, tocn, uocn, vocn, ssh]
+      output variables: [cicen, hicen, hsnon, socn, tocn, uocn, vocn, ssh]
+      linear variable changes:
+      - linear variable change name: BalanceSOCA
+
+  weight:
+    value: 1.00
+
+- covariance:
+    covariance model: ensemble
+    members from template:
+      template:
+        read_from_file: 1
+        date: '{{ATM_WINDOW_MIDDLE}}'
+        basename: ./static_ens/
+        ocn_filename: 'ocn.pert.steric.%mem%.nc'
+        ice_filename: 'ice.%mem%.nc'
+        state variables: [tocn, socn, ssh, uocn, vocn, cicen, hicen, hsnon]
+      pattern: '%mem%'
+      nmembers: ${ENS_SIZE}
+    localization:
+      localization method: SABER
+      saber central block:
+        saber block name: EXPLICIT_DIFFUSION
+        active variables: [tocn, socn, ssh]
+        geometry:
+          mom6_input_nml: mom_input.nml
+          fields metadata: ./fields_metadata.yaml
+        group mapping:
+        - name: ocean
+          variables: [tocn, socn, ssh, uocn, vocn]
+        - name: ice
+          variables: [cicen, hicen, hsnon]
+        read:
+          groups:
+          - name: ocean
+            multivariate strategy: duplicated
+            horizontal:
+              filename: hz_ocean.nc
+            vertical:
+              strategy: duplicated
+          - name: ice
+            horizontal:
+              filename: hz_ice.nc
+
+  weight:
+    read_from_file: 3
+    basename: ./
+    ocn_filename: 'ocn.ens_weights.incr.{{ATM_WINDOW_MIDDLE}}.nc'
+    ice_filename: 'ice.ens_weights.incr.{{ATM_WINDOW_MIDDLE}}.nc'
+    date: '{{ATM_WINDOW_MIDDLE}}'

parm/soca/berror/soca_parameters_diffusion_vt.yaml

@@ -25,6 +25,8 @@ background error:
       - name: vt_ocean
         vertical:
           as gaussian: true
-          fixed value: 5.0
+          from file:
+            filename: vt_scales.nc
+            variable name: vt
         write:
           filename: vt_ocean.nc

parm/soca/berror/soca_static_bmat.yaml

@@ -0,0 +1,42 @@
+covariance model: SABER
+saber central block:
+  saber block name: EXPLICIT_DIFFUSION
+  active variables: [tocn, socn, ssh, cicen]
+  geometry:
+    mom6_input_nml: mom_input.nml
+    fields metadata: ./fields_metadata.yaml
+  group mapping:
+  - name: ocean
+    variables:
+    - tocn
+    - socn
+    - ssh
+  - name: ice
+    variables:
+    - cicen
+  read:
+    groups:
+    - name: ocean
+      horizontal:
+        filename: hz_ocean.nc
+      vertical:
+        filename: vt_ocean.nc
+    - name: ice
+      horizontal:
+        filename: hz_ice.nc
+
+saber outer blocks:
+- saber block name: StdDev
+  read:
+    model file:
+      date: '{{ATM_WINDOW_MIDDLE}}'
+      basename: ./
+      ocn_filename: 'ocn.bkgerr_stddev.incr.{{ATM_WINDOW_MIDDLE}}.nc'
+      ice_filename: 'ice.bkgerr_stddev.incr.{{ATM_WINDOW_MIDDLE}}.nc'
+      read_from_file: 3
+
+linear variable change:
+  input variables: [cicen, hicen, hsnon, socn, tocn, uocn, vocn, ssh]
+  output variables: [cicen, hicen, hsnon, socn, tocn, uocn, vocn, ssh]
+  linear variable changes:
+  - linear variable change name: BalanceSOCA

parm/soca/berror/soca_vtscales.yaml.j2

@@ -0,0 +1,13 @@
+gridspec_filename: soca_gridspec.nc
+restart_filename: ./INPUT/MOM.res.nc
+mld_filename: 'ocn.bkgerr_stddev.incr.{{ ATM_WINDOW_MIDDLE }}.nc'
+output_filename: ./vt_scales.nc
+output_variable_vt: vt
+output_variable_hz: hz
+
+VT_MIN: 5
+VT_MAX: 15
+
+HZ_ROSSBY_MULT: 1.0
+HZ_MAX: 200e3
+HZ_MIN_GRID_MULT: 2.0