diff --git a/README.md b/README.md
index 6bdb62b..c6489ac 100644
--- a/README.md
+++ b/README.md
@@ -57,7 +57,7 @@ state :
   date:  # ISO8601 datetime
   state variables: # list of the model state variables matching the `name` field above
   nemo field file: # input background data
-  variance field file: # input error data
+  nemo error field file: # input error data
 ```
 
 ## Help
diff --git a/examples/hofx3d_nc_orca1_checker_ice_mpi.yaml b/examples/hofx3d_nc_orca1_checker_ice_mpi.yaml
index 5dd403b..2ee7513 100644
--- a/examples/hofx3d_nc_orca1_checker_ice_mpi.yaml
+++ b/examples/hofx3d_nc_orca1_checker_ice_mpi.yaml
@@ -15,7 +15,7 @@ state :
   date: 2021-06-29T12:00:00Z
   state variables: [ ice_area_fraction ]
   nemo field file: your_example_data/orca1_sic.nc
-  variance field file: your_example_data/orca1_sic_err.nc
+  nemo error field file: your_example_data/orca1_sic_err.nc
 observations:
   observers:
   - obs space:
diff --git a/examples/hofx3d_odb_prof_example.yaml b/examples/hofx3d_odb_prof_example.yaml
index efed5d3..0f1435f 100644
--- a/examples/hofx3d_odb_prof_example.yaml
+++ b/examples/hofx3d_odb_prof_example.yaml
@@ -11,14 +11,14 @@ geometry :
     - name: sea_water_temperature_background_error
       nemo field name: t_tot_var
       model space: volume
-      variable type: background variance
+      variable type: background error variance
   grid name: eORCA12_T
   number levels: 75
 state :
   date: 2021-08-21T00:00:00Z
   state variables: [ sea_water_temperature, sea_water_temperature_background_error, depth ]
   nemo field file: your_example_data/eorca12_20210630.nc
-  variance field file: your_example_data/eorca12_err_20210630.nc
+  nemo error field file: your_example_data/eorca12_err_20210630.nc
 time window:
   begin: 2021-08-20T00:00:00Z
   length: P2D
diff --git a/examples/hofx_nc_ice_mpi.yaml b/examples/hofx_nc_ice_mpi.yaml
index dee39bc..99173ec 100644
--- a/examples/hofx_nc_ice_mpi.yaml
+++ b/examples/hofx_nc_ice_mpi.yaml
@@ -15,7 +15,7 @@ geometry:
     - name: ice_area_fraction_background_error
       nemo field name: seaice_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
   grid name: eORCA12_T
   source mesh halo: 0
   number levels: 2
@@ -24,7 +24,7 @@ initial condition :
   date: 2021-06-28T23:00:00Z
   state variables: [ ice_area_fraction, ice_area_fraction_background_error ]
   nemo field file: your_example_data/eorca12_20210630.nc
-  variance field file: your_example_data/eorca12_err_20210630.nc
+  nemo error field file: your_example_data/eorca12_err_20210630.nc
 model :
   name: PseudoModel
   tstep: P1D
@@ -32,15 +32,15 @@ model :
   states:
     - date: 2021-06-28T23:00:00Z
       nemo field file: your_example_data/eorca12_20210630.nc
-      variance field file: your_example_data/eorca12_err_20210630.nc
+      nemo error field file: your_example_data/eorca12_err_20210630.nc
       state variables: [ ice_area_fraction ]
     - date: 2021-06-29T23:00:00Z
       nemo field file: your_example_data/eorca12_20210630.nc
-      variance field file: your_example_data/eorca12_err_20210630.nc
+      nemo error field file: your_example_data/eorca12_err_20210630.nc
       state variables: [ ice_area_fraction ]
     - date: 2021-07-01T23:00:00Z
       nemo field file: your_example_data/eorca12_20210630.nc
-      variance field file: your_example_data/eorca12_err_20210630.nc
+      nemo error field file: your_example_data/eorca12_err_20210630.nc
       state variables: [ ice_area_fraction ]
 observations:
   observers:
diff --git a/src/orca-jedi/geometry/Geometry.cc b/src/orca-jedi/geometry/Geometry.cc
index c939e5c..bcc027a 100644
--- a/src/orca-jedi/geometry/Geometry.cc
+++ b/src/orca-jedi/geometry/Geometry.cc
@@ -226,7 +226,7 @@ const oops::Variables & Geometry::variables() const {
 }
 
 /// \brief Check if a variable's data is a member of a type (e.g if it can be
-///        sourced from the background file, variance file, or MDT file).
+///        sourced from the background file, error file, or MDT file).
 /// \param[in]     variable_name  Name of variable.
 /// \param[in]     variable_type  Type of variable.
 /// \return        Boolean for membership.
diff --git a/src/orca-jedi/geometry/GeometryParameters.h b/src/orca-jedi/geometry/GeometryParameters.h
index b845c33..10d4508 100644
--- a/src/orca-jedi/geometry/GeometryParameters.h
+++ b/src/orca-jedi/geometry/GeometryParameters.h
@@ -26,7 +26,9 @@ class NemoFieldParameters : public oops::Parameters {
   oops::RequiredParameter<std::string> nemoName {"nemo field name", this};
   oops::RequiredParameter<std::string> modelSpace {"model space", this};
   oops::Parameter<std::string> variableType {"variable type",
-    "type of variable (default is 'background' other option is 'background variance')",
+    "type of variable (default is 'background' other options are 'background error variance' and"
+    "'background error standard deviation' both are included for clarity, but both variables are"
+    " read from the error file",
     "background",
     this};
   oops::Parameter<FieldDType> fieldPrecision{"field precision",
diff --git a/src/orca-jedi/state/State.cc b/src/orca-jedi/state/State.cc
index 9334079..bd359a8 100644
--- a/src/orca-jedi/state/State.cc
+++ b/src/orca-jedi/state/State.cc
@@ -82,8 +82,10 @@ State::State(const Geometry & geom,
     nemo_file_name = params.nemoFieldFile.value();
     readFieldsFromFile(nemo_file_name, *geom_, validTime(), "background",
          stateFields_);
-    nemo_file_name = params.varianceFieldFile.value().value_or("");
-    readFieldsFromFile(nemo_file_name, *geom_, validTime(), "background variance",
+    nemo_file_name = params.errorFieldFile.value().value_or("");
+    readFieldsFromFile(nemo_file_name, *geom_, validTime(), "background error standard deviation",
+       stateFields_);
+    readFieldsFromFile(nemo_file_name, *geom_, validTime(), "background error variance",
        stateFields_);
   }
   geom_->log_status();
diff --git a/src/orca-jedi/state/StateParameters.h b/src/orca-jedi/state/StateParameters.h
index fe99117..f7b9057 100644
--- a/src/orca-jedi/state/StateParameters.h
+++ b/src/orca-jedi/state/StateParameters.h
@@ -22,8 +22,8 @@ class OrcaStateParameters : public oops::Parameters {
 
  public:
   oops::RequiredParameter<std::string> nemoFieldFile{"nemo field file", this};
-  oops::OptionalParameter<std::string> varianceFieldFile{
-    "variance field file", "", this};
+  oops::OptionalParameter<std::string> errorFieldFile{
+    "nemo error field file", "", this};
   oops::OptionalParameter<bool> analyticInit{"analytic initialisation", this};
   oops::OptionalParameter<std::string> outputNemoFieldFile{
     "output nemo field file", "", this};
diff --git a/src/tests/orca-jedi/test_geometry.cc b/src/tests/orca-jedi/test_geometry.cc
index 96c6da7..4a766e4 100644
--- a/src/tests/orca-jedi/test_geometry.cc
+++ b/src/tests/orca-jedi/test_geometry.cc
@@ -32,7 +32,7 @@ CASE("test basic geometry") {
   nemo_var_mappings[1].set("name", "sea_ice_area_fraction_error")
     .set("nemo field name", "sic_tot_var")
     .set("model space", "surface")
-    .set("variable type", "background variance");
+    .set("variable type", "background error variance");
   nemo_var_mappings[2].set("name", "sea_surface_foundation_temperature")
     .set("nemo field name", "votemper")
     .set("model space", "surface");
@@ -52,11 +52,11 @@ CASE("test basic geometry") {
     EXPECT(geometry.variable_in_variable_type("sea_ice_area_fraction",
                                               "background"));
     EXPECT(geometry.variable_in_variable_type("sea_ice_area_fraction_error",
-                                              "background variance"));
+                                              "background error variance"));
     EXPECT(!geometry.variable_in_variable_type("sea_ice_area_fraction_error",
                                                "background"));
     EXPECT(!geometry.variable_in_variable_type("sea_ice_area_fraction",
-                                               "background variance"));
+                                               "background error variance"));
   }
 
   SECTION("test geometry variable sizes") {
diff --git a/src/tests/orca-jedi/test_interpolator.cc b/src/tests/orca-jedi/test_interpolator.cc
index da32462..d99c593 100644
--- a/src/tests/orca-jedi/test_interpolator.cc
+++ b/src/tests/orca-jedi/test_interpolator.cc
@@ -65,7 +65,7 @@ CASE("test  interpolator") {
     nemo_var_mappings[1].set("name", "sea_ice_area_fraction_error")
       .set("nemo field name", "sic_tot_var")
       .set("model space", "surface")
-      .set("variable type", "background variance");
+      .set("variable type", "background error variance");
     nemo_var_mappings[2].set("name", "sea_surface_foundation_temperature")
       .set("nemo field name", "votemper")
       .set("model space", "surface");
@@ -85,7 +85,7 @@ CASE("test  interpolator") {
     settings_map["ORCA2_T"].state_config.set("state variables", state_variables);
     settings_map["ORCA2_T"].state_config.set("date", "2021-06-30T00:00:00Z");
     settings_map["ORCA2_T"].state_config.set("nemo field file", "../Data/orca2_t_nemo.nc");
-    settings_map["ORCA2_T"].state_config.set("variance field file", "../Data/orca2_t_bkg_var.nc");
+    settings_map["ORCA2_T"].state_config.set("nemo error field file", "../Data/orca2_t_bkg_var.nc");
 
     settings_map["ORCA2_T"].lons = std::vector<double>{0, 120, 270};
     settings_map["ORCA2_T"].lats = std::vector<double>{88, 0, 30};
@@ -135,7 +135,7 @@ CASE("test  interpolator") {
     settings_map["AMM1"].state_config.set("state variables", state_variables);
     settings_map["AMM1"].state_config.set("date", "2021-06-30T00:00:00Z");
     settings_map["AMM1"].state_config.set("nemo field file", "../Data/amm1_nemo.nc");
-    settings_map["AMM1"].state_config.set("variance field file", "../Data/amm1_nemo.nc");
+    settings_map["AMM1"].state_config.set("nemo error field file", "../Data/amm1_nemo.nc");
 
     settings_map["AMM1"].lons = std::vector<double>{-17.5, -6.78, -16.1};
     settings_map["AMM1"].lats = std::vector<double>{58.16, 58.91, 63.55};
diff --git a/src/tests/orca-jedi/test_interpolator_parallel.cc b/src/tests/orca-jedi/test_interpolator_parallel.cc
index 8a336f4..069323f 100644
--- a/src/tests/orca-jedi/test_interpolator_parallel.cc
+++ b/src/tests/orca-jedi/test_interpolator_parallel.cc
@@ -47,7 +47,7 @@ CASE("test serial interpolator") {
   nemo_var_mappings[1].set("name", "sea_surface_height_anomaly_error")
     .set("nemo field name", "ssh_tot_std")
     .set("model space", "surface")
-    .set("variable type", "background variance");
+    .set("variable type", "background error standard deviation");
   nemo_var_mappings[2].set("name", "sea_surface_foundation_temperature")
     .set("nemo field name", "votemper")
     .set("model space", "surface");
@@ -103,7 +103,7 @@ CASE("test serial interpolator") {
   state_config.set("date", "2021-06-30T00:00:00Z");
   state_config.set("analytic initialisation", true);
   state_config.set("nemo field file", "../Data/orca2_t_nemo.nc");
-  state_config.set("variance field file", "../Data/orca2_t_bkg_var.nc");
+  state_config.set("nemo error field file", "../Data/orca2_t_bkg_var.nc");
   OrcaStateParameters stateParams;
   stateParams.validateAndDeserialize(state_config);
   State state(geometry, stateParams);
@@ -194,7 +194,7 @@ CASE("test checkerboard interpolator") {
   nemo_var_mappings[1].set("name", "sea_surface_height_anomaly_error")
     .set("nemo field name", "ssh_tot_std")
     .set("model space", "surface")
-    .set("variable type", "background variance");
+    .set("variable type", "background error standard deviation");
   nemo_var_mappings[2].set("name", "sea_surface_foundation_temperature")
     .set("nemo field name", "votemper")
     .set("model space", "surface");
@@ -249,7 +249,7 @@ CASE("test checkerboard interpolator") {
   state_config.set("date", "2021-06-30T00:00:00Z");
   state_config.set("analytic initialisation", true);
   state_config.set("nemo field file", "../Data/orca2_t_nemo.nc");
-  state_config.set("variance field file", "../Data/orca2_t_bkg_var.nc");
+  state_config.set("nemo error field file", "../Data/orca2_t_bkg_var.nc");
   OrcaStateParameters stateParams;
   stateParams.validateAndDeserialize(state_config);
   State state(geometry, stateParams);
diff --git a/src/tests/orca-jedi/test_state.cc b/src/tests/orca-jedi/test_state.cc
index afd3217..da65300 100644
--- a/src/tests/orca-jedi/test_state.cc
+++ b/src/tests/orca-jedi/test_state.cc
@@ -39,7 +39,7 @@ CASE("test basic state") {
     .set("field precision", "double")
     .set("nemo field name", "sic_tot_var")
     .set("model space", "surface")
-    .set("variable type", "background variance");
+    .set("variable type", "background error variance");
   nemo_var_mappings[2].set("name", "sea_surface_foundation_temperature")
     .set("field precision", "double")
     .set("nemo field name", "votemper")
@@ -61,12 +61,12 @@ CASE("test basic state") {
 
   SECTION("test state parameters") {
     state_config.set("nemo field file", "../Data/orca2_t_nemo.nc");
-    state_config.set("variance field file", "../Data/orca2_t_bkg_var.nc");
+    state_config.set("nemo error field file", "../Data/orca2_t_bkg_var.nc");
     params.validateAndDeserialize(state_config);
     EXPECT(params.nemoFieldFile.value() ==
         state_config.getString("nemo field file"));
-    EXPECT(params.varianceFieldFile.value() ==
-        state_config.getString("variance field file"));
+    EXPECT(params.errorFieldFile.value() ==
+        state_config.getString("nemo error field file"));
     EXPECT(params.analyticInit.value().value_or(true));
     auto datetime = static_cast<util::DateTime>(state_config.getString("date"));
     EXPECT(params.date.value() == datetime);
@@ -105,7 +105,7 @@ CASE("test basic state") {
   }
 
   state_config.set("nemo field file", "../Data/orca2_t_nemo.nc");
-  state_config.set("variance field file", "../Data/orca2_t_bkg_var.nc");
+  state_config.set("nemo error field file", "../Data/orca2_t_bkg_var.nc");
   state_config.set("output nemo field file", "../testoutput/orca2_t_output.nc");
   params.validateAndDeserialize(state_config);
   State state(geometry, params);
diff --git a/src/tests/testinput/hofx3d_nc_potm.yaml b/src/tests/testinput/hofx3d_nc_potm.yaml
index 62bff77..53c6848 100644
--- a/src/tests/testinput/hofx3d_nc_potm.yaml
+++ b/src/tests/testinput/hofx3d_nc_potm.yaml
@@ -11,14 +11,14 @@ geometry :
     - name: sea_water_potential_temperature_background_error
       nemo field name: t_tot_var
       model space: volume
-      variable type: background variance
+      variable type: background error variance
   grid name: ORCA2_T
   number levels: 3
 state :
   date: 2021-06-30T00:00:00Z
   state variables: [ sea_water_potential_temperature, sea_water_potential_temperature_background_error, depth ]
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 time window:
   begin: 2021-06-29T12:00:00Z
   length: P1D
diff --git a/src/tests/testinput/hofx3d_nc_prof_2vars.yaml b/src/tests/testinput/hofx3d_nc_prof_2vars.yaml
index 48b8ced..1086655 100644
--- a/src/tests/testinput/hofx3d_nc_prof_2vars.yaml
+++ b/src/tests/testinput/hofx3d_nc_prof_2vars.yaml
@@ -11,14 +11,14 @@ geometry :
     - name: sea_water_potential_temperature_background_error
       nemo field name: t_tot_var
       model space: volume
-      variable type: background variance
+      variable type: background error variance
     - name: salinity
       nemo field name: vosaline
       model space: volume
     - name: salinity_background_error
       nemo field name: t_tot_var
       model space: volume
-      variable type: background variance
+      variable type: background error variance
   grid name: ORCA2_T
   number levels: 3
 state :
@@ -30,7 +30,7 @@ state :
   - salinity
   - salinity_background_error
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 time window:
   begin: 2021-06-29T12:00:00Z
   length: P1D
diff --git a/src/tests/testinput/hofx3d_nc_sic.yaml b/src/tests/testinput/hofx3d_nc_sic.yaml
index 70bfd8f..2d99c0b 100644
--- a/src/tests/testinput/hofx3d_nc_sic.yaml
+++ b/src/tests/testinput/hofx3d_nc_sic.yaml
@@ -14,14 +14,14 @@ geometry :
     - name: ice_area_fraction_background_error
       nemo field name: sic_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
   grid name: ORCA2_T
   number levels: 10
 state :
   date: 2021-06-30T00:00:00Z
   state variables: [ ice_area_fraction, ice_area_fraction_background_error ]
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 time window:
   begin: 2021-06-29T12:00:00Z
   length: P1D
diff --git a/src/tests/testinput/hofx3d_nc_ssh_amm1.yaml b/src/tests/testinput/hofx3d_nc_ssh_amm1.yaml
index 783278f..633e1f6 100644
--- a/src/tests/testinput/hofx3d_nc_ssh_amm1.yaml
+++ b/src/tests/testinput/hofx3d_nc_ssh_amm1.yaml
@@ -11,7 +11,7 @@ geometry :
     - name: sea_surface_height_anomaly_background_error
       nemo field name: sossheig
       model space: surface
-      variable type: background variance
+      variable type: background error standard deviation
   grid name: Data/amm1_atlas_grid_spec.yaml
   number levels: 1
   partitioner: serial
@@ -22,7 +22,7 @@ state :
     - sea_surface_height_anomaly
     - sea_surface_height_anomaly_background_error
   nemo field file: &field_file Data/amm1_nemo.nc
-  variance field file: *field_file
+  nemo error field file: *field_file
 observations:
   observers:
   - obs space:
diff --git a/src/tests/testinput/hofx3d_nc_ssh_amm1r.yaml b/src/tests/testinput/hofx3d_nc_ssh_amm1r.yaml
index fd60b3c..301eaa7 100644
--- a/src/tests/testinput/hofx3d_nc_ssh_amm1r.yaml
+++ b/src/tests/testinput/hofx3d_nc_ssh_amm1r.yaml
@@ -11,7 +11,7 @@ geometry :
     - name: sea_surface_height_anomaly_background_error
       nemo field name: sossheig
       model space: surface
-      variable type: background variance
+      variable type: background error variance
   grid name: Data/amm1r_atlas_grid_spec.yaml
   number levels: 1
   partitioner: serial
@@ -22,7 +22,7 @@ state :
     - sea_surface_height_anomaly
     - sea_surface_height_anomaly_background_error
   nemo field file: &field_file Data/amm1r_nemo.nc
-  variance field file: *field_file
+  nemo error field file: *field_file
 observations:
   observers:
   - obs space:
diff --git a/src/tests/testinput/hofx3d_nc_sst.yaml b/src/tests/testinput/hofx3d_nc_sst.yaml
index fa05dfe..85b32f0 100644
--- a/src/tests/testinput/hofx3d_nc_sst.yaml
+++ b/src/tests/testinput/hofx3d_nc_sst.yaml
@@ -11,18 +11,18 @@ geometry :
     - name: ice_area_fraction_background_error
       nemo field name: sic_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
     - name: sea_surface_temperature_background_error
       nemo field name: t_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
   grid name: ORCA2_T
   number levels: 1
 state :
   date: 2021-06-30T00:00:00Z
   state variables: [ sea_surface_temperature, sea_surface_temperature_background_error ]
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 time window:
   begin: 2021-06-29T12:00:00Z
   length: P1D
diff --git a/src/tests/testinput/hofx_nc_potm_amm1r.yaml b/src/tests/testinput/hofx_nc_potm_amm1r.yaml
index 87a9204..391f690 100644
--- a/src/tests/testinput/hofx_nc_potm_amm1r.yaml
+++ b/src/tests/testinput/hofx_nc_potm_amm1r.yaml
@@ -15,7 +15,7 @@ geometry :
     - name: sea_water_potential_temperature_background_error
       nemo field name: vosaline
       model space: volume
-      variable type: background variance
+      variable type: background error variance
   grid name: Data/amm1r_atlas_grid_spec.yaml
   number levels: 1
   partitioner: serial
@@ -26,18 +26,18 @@ initial condition :
     - sea_water_potential_temperature
     - sea_water_potential_temperature_background_error
   nemo field file: &field_file Data/amm1r_nemo.nc
-  variance field file: *field_file
+  nemo error field file: *field_file
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-29T23:00:00Z
       nemo field file: *field_file
-      variance field file: *field_file
+      nemo error field file: *field_file
       state variables: *state_variables
     - date: 2021-06-30T23:00:00Z
       nemo field file: *field_file
-      variance field file: *field_file
+      nemo error field file: *field_file
       state variables: *state_variables
 observations:
   observers:
diff --git a/src/tests/testinput/hofx_nc_sic.yaml b/src/tests/testinput/hofx_nc_sic.yaml
index f4cbbe7..c12b5bd 100644
--- a/src/tests/testinput/hofx_nc_sic.yaml
+++ b/src/tests/testinput/hofx_nc_sic.yaml
@@ -18,7 +18,7 @@ geometry:
     - name: ice_area_fraction_background_error
       nemo field name: sic_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
   grid name: ORCA2_T
   number levels: 2
 initial condition :
@@ -26,18 +26,18 @@ initial condition :
   state variables: [ ice_area_fraction, ice_area_fraction_background_error ]
   #analytic_init: zeroed state
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-29T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: [ ice_area_fraction ]
     - date: 2021-06-30T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: [ ice_area_fraction ]
 observations:
   observers:
diff --git a/src/tests/testinput/hofx_nc_ssh.yaml b/src/tests/testinput/hofx_nc_ssh.yaml
index 8c3c480..9714489 100644
--- a/src/tests/testinput/hofx_nc_ssh.yaml
+++ b/src/tests/testinput/hofx_nc_ssh.yaml
@@ -12,7 +12,7 @@ geometry :
     - name: sea_surface_height_anomaly_background_error
       nemo field name: ssh_tot_std
       model space: surface
-      variable type: background variance
+      variable type: background error standard deviation
   grid name: ORCA2_T
   number levels: 1
   partitioner: serial
@@ -22,18 +22,18 @@ initial condition :
     - sea_surface_height_anomaly
     - sea_surface_height_anomaly_background_error
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-29T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: &state_variables [ sea_surface_height_anomaly ]
     - date: 2021-06-30T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: *state_variables
 observations:
   observers:
diff --git a/src/tests/testinput/hofx_nc_ssh_amm1.yaml b/src/tests/testinput/hofx_nc_ssh_amm1.yaml
index 10f3d01..1008ad4 100644
--- a/src/tests/testinput/hofx_nc_ssh_amm1.yaml
+++ b/src/tests/testinput/hofx_nc_ssh_amm1.yaml
@@ -12,7 +12,7 @@ geometry :
     - name: sea_surface_height_anomaly_background_error
       nemo field name: sossheig
       model space: surface
-      variable type: background variance
+      variable type: background error standard deviation
   grid name: Data/amm1_atlas_grid_spec.yaml
   number levels: 1
   partitioner: serial
@@ -23,18 +23,18 @@ initial condition :
     - sea_surface_height_anomaly
     - sea_surface_height_anomaly_background_error
   nemo field file: &field_file Data/amm1_nemo.nc
-  variance field file: *field_file
+  nemo error field file: *field_file
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-29T23:00:00Z
       nemo field file: *field_file
-      variance field file: *field_file
+      nemo error field file: *field_file
       state variables: &state_variables [ sea_surface_height_anomaly ]
     - date: 2021-06-30T23:00:00Z
       nemo field file: *field_file
-      variance field file: *field_file
+      nemo error field file: *field_file
       state variables: *state_variables
 observations:
   observers:
diff --git a/src/tests/testinput/hofx_nc_ssh_checkerboard.yaml b/src/tests/testinput/hofx_nc_ssh_checkerboard.yaml
index 7be8e02..7afbd7b 100644
--- a/src/tests/testinput/hofx_nc_ssh_checkerboard.yaml
+++ b/src/tests/testinput/hofx_nc_ssh_checkerboard.yaml
@@ -10,7 +10,7 @@ geometry :
     - name: sea_surface_height_anomaly_background_error
       nemo field name: ssh_tot_std
       model space: surface
-      variable type: background variance
+      variable type: background error standard deviation
   grid name: ORCA2_T
   number levels: 1
   partitioner: checkerboard
@@ -20,18 +20,18 @@ initial condition :
     - sea_surface_height_anomaly
     - sea_surface_height_anomaly_background_error
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-29T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: &state_variables [ sea_surface_height_anomaly ]
     - date: 2021-06-30T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: *state_variables
 observations:
   observers:
diff --git a/src/tests/testinput/hofx_nc_ssh_eorca025.yaml b/src/tests/testinput/hofx_nc_ssh_eorca025.yaml
index 45fb4d9..fb63f53 100644
--- a/src/tests/testinput/hofx_nc_ssh_eorca025.yaml
+++ b/src/tests/testinput/hofx_nc_ssh_eorca025.yaml
@@ -12,7 +12,7 @@ geometry :
     - name: sea_surface_height_anomaly_background_error
       nemo field name: sossheig
       model space: surface
-      variable type: background variance
+      variable type: background error standard deviation
   grid name: eORCA025_T
   number levels: 1
   partitioner: checkerboard
@@ -23,18 +23,18 @@ initial condition :
     - sea_surface_height_anomaly
     - sea_surface_height_anomaly_background_error
   nemo field file: Data/eorca025_t_nemo.nc
-  variance field file: Data/eorca025_t_nemo.nc
+  nemo error field file: Data/eorca025_t_nemo.nc
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-29T23:00:00Z
       nemo field file: Data/eorca025_t_nemo.nc
-      variance field file: Data/eorca025_t_bkg_var.nc
+      nemo error field file: Data/eorca025_t_bkg_var.nc
       state variables: &state_variables [ sea_surface_height_anomaly ]
     - date: 2021-06-30T23:00:00Z
       nemo field file: Data/eorca025_t_nemo.nc
-      variance field file: Data/eorca025_t_nemo.nc
+      nemo error field file: Data/eorca025_t_nemo.nc
       state variables: *state_variables
 observations:
   observers:
diff --git a/src/tests/testinput/hofx_nc_sst.yaml b/src/tests/testinput/hofx_nc_sst.yaml
index 7cbf5b4..e78e3b2 100644
--- a/src/tests/testinput/hofx_nc_sst.yaml
+++ b/src/tests/testinput/hofx_nc_sst.yaml
@@ -15,29 +15,29 @@ geometry :
     - name: ice_area_fraction_background_error
       nemo field name: sic_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
     - name: sea_surface_temperature_background_error
       nemo field name: t_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
   grid name: ORCA2_T
   number levels: 1
 initial condition :
   date: 2021-06-28T23:00:00Z
   state variables: [ sea_surface_temperature, sea_surface_temperature_background_error ]
   nemo field file: Data/orca2_t_nemo.nc
-  variance field file: Data/orca2_t_bkg_var.nc
+  nemo error field file: Data/orca2_t_bkg_var.nc
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-29T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: &state_variables [ sea_surface_temperature ]
     - date: 2021-06-30T23:00:00Z
       nemo field file: Data/orca2_t_nemo.nc
-      variance field file: Data/orca2_t_bkg_var.nc
+      nemo error field file: Data/orca2_t_bkg_var.nc
       state variables: *state_variables
 observations:
   observers:
diff --git a/src/tests/testinput/hofx_odb_sic.yaml b/src/tests/testinput/hofx_odb_sic.yaml
index b45a286..186a783 100644
--- a/src/tests/testinput/hofx_odb_sic.yaml
+++ b/src/tests/testinput/hofx_odb_sic.yaml
@@ -18,7 +18,7 @@ geometry:
     - name: ice_area_fraction_background_error
       nemo field name: sic_tot_var
       model space: surface
-      variable type: background variance
+      variable type: background error variance
   grid name: ORCA2_T
   number levels: 2
 initial condition :
@@ -26,22 +26,22 @@ initial condition :
   state variables: [ ice_area_fraction, ice_area_fraction_background_error ]
   #analytic_init: zeroed state
   nemo field file: orca-jedi/src/tests/Data/orca2_t_nemo.nc
-  variance field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
+  nemo error field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
 model :
   name: PseudoModel
   tstep: P1D
   states:
     - date: 2021-06-28T23:00:00Z
       nemo field file: orca-jedi/src/tests/Data/orca2_t_nemo.nc
-      variance field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
+      nemo error field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
       state variables: &state_variables [ ice_area_fraction ]
     - date: 2021-06-29T23:00:00Z
       nemo field file: orca-jedi/src/tests/Data/orca2_t_nemo.nc
-      variance field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
+      nemo error field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
       state variables: *state_variables
     - date: 2021-07-01T23:00:00Z
       nemo field file: orca-jedi/src/tests/Data/orca2_t_nemo.nc
-      variance field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
+      nemo error field file: orca-jedi/src/tests/Data/orca2_t_bkg_var.nc
       state variables: *state_variables
 observations:
   observers: