Update develop-ref after dtcenter/MET#2942

.github/workflows/testing.yml

@@ -360,6 +360,8 @@ jobs:
           - jobid: 'job3'
             tests: 'climatology_2.5deg'
           - jobid: 'job4'
+            tests: 'climatology_mixed'
+          - jobid: 'job5'
             tests: 'python point2grid plot_data_plane mode mode_analysis perc_thresh hira plot_point_obs quality_filter obs_summary duplicate_flag'
       fail-fast: false
     steps:

data/table_files/met_header_columns_V12.0.txt

@@ -5,15 +5,15 @@ V12.0 : STAT : FHO      : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID
 V12.0 : STAT : ISC      : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL TILE_DIM TILE_XLL TILE_YLL NSCALE ISCALE MSE ISC FENERGY2 OENERGY2 BASER FBIAS
 V12.0 : STAT : MCTC     : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL (N_CAT) F[0-9]*_O[0-9]* EC_VALUE
 V12.0 : STAT : MCTS     : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL N_CAT ACC ACC_NCL ACC_NCU ACC_BCL ACC_BCU HK HK_BCL HK_BCU HSS HSS_BCL HSS_BCU GER GER_BCL GER_BCU HSS_EC HSS_EC_BCL HSS_EC_BCU EC_VALUE
-V12.0 : STAT : MPR      : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL INDEX OBS_SID OBS_LAT OBS_LON OBS_LVL OBS_ELV FCST OBS OBS_QC CLIMO_MEAN CLIMO_STDEV CLIMO_CDF
+V12.0 : STAT : MPR      : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL INDEX OBS_SID OBS_LAT OBS_LON OBS_LVL OBS_ELV FCST OBS OBS_QC OBS_CLIMO_MEAN OBS_CLIMO_STDEV OBS_CLIMO_CDF FCST_CLIMO_MEAN FCST_CLIMO_STDEV
 V12.0 : STAT : SEEPS    : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL S12 S13 S21 S23 S31 S32 PF1 PF2 PF3 PV1 PV2 PV3 MEAN_FCST MEAN_OBS SEEPS
 V12.0 : STAT : SEEPS_MPR    : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE OBS_SID OBS_LAT OBS_LON FCST OBS OBS_QC FCST_CAT OBS_CAT P1 P2 T1 T2 SEEPS
 V12.0 : STAT : NBRCNT   : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL FBS FBS_BCL FBS_BCU FSS FSS_BCL FSS_BCU AFSS AFSS_BCL AFSS_BCU UFSS UFSS_BCL UFSS_BCU F_RATE F_RATE_BCL F_RATE_BCU O_RATE O_RATE_BCL O_RATE_BCU
 V12.0 : STAT : NBRCTC   : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL FY_OY FY_ON FN_OY FN_ON
 V12.0 : STAT : NBRCTS   : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL BASER BASER_NCL BASER_NCU BASER_BCL BASER_BCU FMEAN FMEAN_NCL FMEAN_NCU FMEAN_BCL FMEAN_BCU ACC ACC_NCL ACC_NCU ACC_BCL ACC_BCU FBIAS FBIAS_BCL FBIAS_BCU PODY PODY_NCL PODY_NCU PODY_BCL PODY_BCU PODN PODN_NCL PODN_NCU PODN_BCL PODN_BCU POFD POFD_NCL POFD_NCU POFD_BCL POFD_BCU FAR FAR_NCL FAR_NCU FAR_BCL FAR_BCU CSI CSI_NCL CSI_NCU CSI_BCL CSI_BCU GSS GSS_BCL GSS_BCU HK HK_NCL HK_NCU HK_BCL HK_BCU HSS HSS_BCL HSS_BCU ODDS ODDS_NCL ODDS_NCU ODDS_BCL ODDS_BCU LODDS LODDS_NCL LODDS_NCU LODDS_BCL LODDS_BCU ORSS ORSS_NCL ORSS_NCU ORSS_BCL ORSS_BCU EDS EDS_NCL EDS_NCU EDS_BCL EDS_BCU SEDS SEDS_NCL SEDS_NCU SEDS_BCL SEDS_BCU EDI EDI_NCL EDI_NCU EDI_BCL EDI_BCU SEDI SEDI_NCL SEDI_NCU SEDI_BCL SEDI_BCU BAGSS BAGSS_BCL BAGSS_BCU
 V12.0 : STAT : GRAD     : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL FGBAR OGBAR MGBAR EGBAR S1 S1_OG FGOG_RATIO DX DY
 V12.0 : STAT : DMAP     : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL FY OY FBIAS BADDELEY HAUSDORFF MED_FO MED_OF MED_MIN MED_MAX MED_MEAN FOM_FO FOM_OF FOM_MIN FOM_MAX FOM_MEAN ZHU_FO ZHU_OF ZHU_MIN ZHU_MAX ZHU_MEAN G GBETA BETA_VALUE 
-V12.0 : STAT : ORANK    : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL INDEX OBS_SID OBS_LAT OBS_LON OBS_LVL OBS_ELV OBS PIT RANK N_ENS_VLD (N_ENS) ENS_[0-9]* OBS_QC ENS_MEAN CLIMO_MEAN SPREAD ENS_MEAN_OERR SPREAD_OERR SPREAD_PLUS_OERR CLIMO_STDEV 
+V12.0 : STAT : ORANK    : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL INDEX OBS_SID OBS_LAT OBS_LON OBS_LVL OBS_ELV OBS PIT RANK N_ENS_VLD (N_ENS) ENS_[0-9]* OBS_QC ENS_MEAN OBS_CLIMO_MEAN SPREAD ENS_MEAN_OERR SPREAD_OERR SPREAD_PLUS_OERR OBS_CLIMO_STDEV FCST_CLIMO_MEAN FCST_CLIMO_STDEV
 V12.0 : STAT : PCT      : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL (N_THRESH) THRESH_[0-9]* OY_[0-9]* ON_[0-9]*
 V12.0 : STAT : PJC      : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL (N_THRESH) THRESH_[0-9]* OY_TP_[0-9]* ON_TP_[0-9]* CALIBRATION_[0-9]* REFINEMENT_[0-9]* LIKELIHOOD_[0-9]* BASER_[0-9]*
 V12.0 : STAT : PRC      : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID_END OBS_LEAD OBS_VALID_BEG OBS_VALID_END FCST_VAR FCST_UNITS FCST_LEV OBS_VAR OBS_UNITS OBS_LEV OBTYPE VX_MASK INTERP_MTHD INTERP_PNTS FCST_THRESH OBS_THRESH COV_THRESH ALPHA LINE_TYPE TOTAL (N_THRESH) THRESH_[0-9]* PODY_[0-9]* POFD_[0-9]*

docs/Users_Guide/appendixA.rst

@@ -1801,8 +1801,11 @@ Q. What are MET's conventions for latitude, longitude, azimuth and bearing angle
 
   .. dropdown:: Answer
 
-     MET considers north latitude and east longitude positive. Latitudes
-     have range from :math:`-90^\circ` to :math:`+90^\circ`. Longitudes have
+     MET considers north latitude and east longitude positive. However,
+     internally MET considers east longitude negative so users may encounter
+     DEBUG statements with longitude of a different sign than they provided
+     (e.g. for observation locations or grid metadata). Latitudes have
+     range from :math:`-90^\circ` to :math:`+90^\circ`. Longitudes have
      range from :math:`-180^\circ` to :math:`+180^\circ`. Plane angles such
      as azimuths and bearing (example: horizontal wind direction) have
      range :math:`0^\circ` to :math:`360^\circ` and are measured clockwise

docs/Users_Guide/appendixC.rst

@@ -616,23 +616,23 @@ Anomaly Correlation Coefficient
 
 Called "ANOM_CORR" and "ANOM_CORR_UNCNTR" for centered and uncentered versions in CNT output :numref:`table_PS_format_info_CNT`
 
-The anomaly correlation coefficient is equivalent to the Pearson correlation coefficient, except that both the forecasts and observations are first adjusted according to a climatology value. The anomaly is the difference between the individual forecast or observation and the typical situation, as measured by a climatology (**c**) of some variety. It measures the strength of linear association between the forecast anomalies and observed anomalies. The anomaly correlation coefficient is defined as: 
+The anomaly correlation coefficient is equivalent to the Pearson correlation coefficient, except that both the forecasts and observations are first adjusted by subtracting their corresponding climatology value. The anomaly is the difference between the individual forecast or observation and the typical situation, as measured by a forecast climatology (:math:`c_f`) and observation climatology (:math:`c_o`). It measures the strength of linear association between the forecast anomalies and observed anomalies. The anomaly correlation coefficient is defined as:
 
-.. math:: \text{Anomaly Correlation} = \frac{\sum(f_i - c)(o_i - c)}{\sqrt{\sum(f_i - c)^2} \sqrt{\sum(o_i -c)^2}} .
+.. math:: \text{Anomaly Correlation} = \frac{\sum(f_i - {c_f}_i)(o_i - {c_o}_i)}{\sqrt{\sum(f_i - {c_f}_i)^2} \sqrt{\sum(o_i - {c_o}_i)^2}} .
 
 The centered anomaly correlation coefficient (ANOM_CORR) which includes the mean error is defined as: 
 
 .. only:: latex
 
-  .. math:: \text{ANOM\_CORR } = \frac{ \overline{[(f - c) - \overline{(f - c)}][(a - c) - \overline{(a - c)}]}}{ \sqrt{ \overline{( (f - c) - \overline{(f - c)})^2} \overline{( (a - c) - \overline{(a - c)})^2}}}
+  .. math:: \text{ANOM\_CORR } = \frac{ \overline{[(f - c_f) - \overline{(f - c_f)}][(o - c_o) - \overline{(o - c_o)}]}}{ \sqrt{ \overline{( (f - c_f) - \overline{(f - c_f)})^2} \overline{( (o - c_o) - \overline{(o - c_o)})^2}}}
 
 .. only:: html
 
-  .. math:: \text{ANOM_CORR } = \frac{ \overline{[(f - c) - \overline{(f - c)}][(a - c) - \overline{(a - c)}]}}{ \sqrt{ \overline{( (f - c) - \overline{(f - c)})^2} \overline{( (a - c) - \overline{(a - c)})^2}}}
+  .. math:: \text{ANOM_CORR } = \frac{ \overline{[(f - c_f) - \overline{(f - c_f)}][(o - c_o) - \overline{(o - c_o)}]}}{ \sqrt{ \overline{( (f - c_f) - \overline{(f - c_f)})^2} \overline{( (o - c_o) - \overline{(o - c_o)})^2}}}
 
 The uncentered anomaly correlation coefficient (ANOM_CORR_UNCNTR) which does not include the mean errors is defined as: 
 
-.. math:: \text{Anomaly Correlation Raw } = \frac{ \overline{(f - c)(a - c)}}{ \sqrt{\overline{(f - c)^2} \overline{(a - c)^2}}}
+.. math:: \text{Anomaly Correlation Raw } = \frac{ \overline{(f - c_f)(o - c_o)}}{ \sqrt{\overline{(f - c_f)^2} \overline{(o - c_o)^2}}}
 
 Anomaly correlation can range between -1 and 1; a value of 1 indicates perfect correlation and a value of -1 indicates perfect negative correlation. A value of 0 indicates that the forecast and observed anomalies are not correlated.
 
@@ -650,56 +650,60 @@ The partial sums can be accumulated over individual cases to produce statistics
 Scalar L1 and L2 Values
 -----------------------
 
-Called "FBAR", "OBAR", "FOBAR", "FFBAR", and "OOBAR" in SL1L2 output :numref:`table_PS_format_info_SL1L2`
+Called "FBAR", "OBAR", "FOBAR", "FFBAR", "OOBAR", and "MAE" in SL1L2 output :numref:`table_PS_format_info_SL1L2`
 
 These statistics are simply the 1st and 2nd moments of the forecasts, observations and errors:
 
 .. math:: 
-  \text{FBAR} = \text{Mean}(f) = \bar{f} = \frac{1}{n} \sum_{i=1}^n f_i
+  \text{FBAR} = \text{Mean}(f) = \frac{1}{n} \sum_{i=1}^n f_i
 
-  \text{OBAR} = \text{Mean}(o) = \bar{o} = \frac{1}{n} \sum_{i=1}^n o_i
+  \text{OBAR} = \text{Mean}(o) = \frac{1}{n} \sum_{i=1}^n o_i
 
-  \text{FOBAR} = \text{Mean}(fo) = \bar{fo} = \frac{1}{n} \sum_{i=1}^n f_i o_i
+  \text{FOBAR} = \text{Mean}(fo) = \frac{1}{n} \sum_{i=1}^n f_i o_i
 
-  \text{FFBAR} = \text{Mean}(f^2) = \bar{f}^2 = \frac{1}{n} \sum_{i=1}^n f_i^2
+  \text{FFBAR} = \text{Mean}(f^2) = \frac{1}{n} \sum_{i=1}^n f_i^2
 
-  \text{OOBAR} = \text{Mean}(o^2) = \bar{o}^2 = \frac{1}{n} \sum_{i=1}^n o_i^2
+  \text{OOBAR} = \text{Mean}(o^2) = \frac{1}{n} \sum_{i=1}^n o_i^2
+
+  \text{MAE} = \text{Mean}(|f - o|) = \frac{1}{n} \sum_{i=1}^n |f_i - o_i|
 
 Some of the other statistics for continuous forecasts (e.g., RMSE) can be derived from these moments.
 
 Scalar Anomaly L1 and L2 Values
 -------------------------------
 
-Called "FABAR", "OABAR", "FOABAR", "FFABAR", "OOABAR" in SAL1L2 output :numref:`table_PS_format_info_SAL1L2`
+Called "FABAR", "OABAR", "FOABAR", "FFABAR", "OOABAR", and "MAE" in SAL1L2 output :numref:`table_PS_format_info_SAL1L2`
 
-Computation of these statistics requires a climatological value, c. These statistics are the 1st and 2nd moments of the scalar anomalies. The moments are defined as:
+Computation of these statistics requires climatological values, where :math:`c_f` is the forecast climatology value and :math:`c_o` is the observation climatology value. These statistics are the 1st and 2nd moments of the scalar anomalies. The moments are defined as:
 
 .. math:: 
-  \text{FABAR} = \text{Mean}(f - c) = \bar{f - c} = \frac{1}{n} \sum_{i=1}^n (f_i - c)
+  \text{FABAR} = \text{Mean}(f - c_f) = \frac{1}{n} \sum_{i=1}^n (f_i - {c_f}_i)
+
+  \text{OABAR} = \text{Mean}(o - c_o) = \frac{1}{n} \sum_{i=1}^n (o_i - {c_o}_i)
 
-  \text{OABAR} = \text{Mean}(o - c) = \bar{o - c} = \frac{1}{n} \sum_{i=1}^n (o_i - c)
+  \text{FOABAR} = \text{Mean}[(f - c_f)(o - c_o)] = \frac{1}{n} \sum_{i=1}^n (f_i - {c_f}_i)(o_i - {c_o}_i)
 
-  \text{FOABAR} = \text{Mean}[(f - c)(o - c)] = \bar{(f - c)(o - c)} = \frac{1}{n} \sum_{i=1}^n (f_i - c)(o_i - c)
+  \text{FFABAR} = \text{Mean}[(f - c_f)^2] = \frac{1}{n} \sum_{i=1}^n (f_i - {c_f}_i)^2
 
-  \text{FFABAR} = \text{Mean}[(f - c)^2] = \bar{(f - c)}^2 = \frac{1}{n} \sum_{i=1}^n (f_i - c)^2
+  \text{OOABAR} = \text{Mean}[(o - c_o)^2] = \frac{1}{n} \sum_{i=1}^n (o_i - {c_o}_i)^2
 
-  \text{OOABAR} = \text{Mean}[(o - c)^2] = \bar{(o - c)}^2 = \frac{1}{n} \sum_{i=1}^n (o_i - c)^2
+  \text{MAE} = \text{Mean}(|(f - c_f) - (o - c_o)|) = \frac{1}{n} \sum_{i=1}^n |(f_i - {c_f}_i) - (o_i - {c_o}_i)|
 
 Vector L1 and L2 Values
 -----------------------
 
-Called "UFBAR", "VFBAR", "UOBAR", "VOBAR", "UVFOBAR", "UVFFBAR", "UVOOBAR" in VL1L2 output :numref:`table_PS_format_info_VL1L2`
+Called "UFBAR", "VFBAR", "UOBAR", "VOBAR", "UVFOBAR", "UVFFBAR", and "UVOOBAR" in VL1L2 output :numref:`table_PS_format_info_VL1L2`
 
-These statistics are the moments for wind vector values, where **u** is the E-W wind component and **v** is the N-S wind component ( :math:`u_f` is the forecast E-W wind component; :math:`u_o` is the observed E-W wind component; :math:`v_f` is the forecast N-S wind component; and :math:`v_o` is the observed N-S wind component). The following measures are computed:
+These statistics are the moments for wind vector values, where :math:`u` is the E-W wind component and :math:`v` is the N-S wind component ( :math:`u_f` is the forecast E-W wind component; :math:`u_o` is the observed E-W wind component; :math:`v_f` is the forecast N-S wind component; and :math:`v_o` is the observed N-S wind component). The following measures are computed:
 
 .. math:: 
-  \text{UFBAR} = \text{Mean}(u_f) = \bar{u}_f = \frac{1}{n} \sum_{i=1}^n u_{fi}
+  \text{UFBAR} = \text{Mean}(u_f) = \frac{1}{n} \sum_{i=1}^n u_{fi}
 
-  \text{VFBAR} = \text{Mean}(v_f) = \bar{v}_f = \frac{1}{n} \sum_{i=1}^n v_{fi}
+  \text{VFBAR} = \text{Mean}(v_f) = \frac{1}{n} \sum_{i=1}^n v_{fi}
 
-  \text{UOBAR} = \text{Mean}(u_o) = \bar{u}_o = \frac{1}{n} \sum_{i=1}^n u_{oi}
+  \text{UOBAR} = \text{Mean}(u_o) = \frac{1}{n} \sum_{i=1}^n u_{oi}
 
-  \text{VOBAR} = \text{Mean}(v_o) = \bar{v}_o = \frac{1}{n} \sum_{i=1}^n v_{oi}
+  \text{VOBAR} = \text{Mean}(v_o) = \frac{1}{n} \sum_{i=1}^n v_{oi}
 
   \text{UVFOBAR} = \text{Mean}(u_f u_o + v_f v_o) = \frac{1}{n} \sum_{i=1}^n (u_{fi} u_{oi} + v_{fi} v_{oi})
 
@@ -710,25 +714,27 @@ These statistics are the moments for wind vector values, where **u** is the E-W
 Vector Anomaly L1 and L2 Values
 -------------------------------
 
-Called "UFABAR", "VFABAR", "UOABAR", "VOABAR", "UVFOABAR", "UVFFABAR", "UVOOABAR" in VAL1L2 output :numref:`table_PS_format_info_VAL1L2`
+Called "UFABAR", "VFABAR", "UOABAR", "VOABAR", "UVFOABAR", "UVFFABAR", and "UVOOABAR" in VAL1L2 output :numref:`table_PS_format_info_VAL1L2`
 
-These statistics require climatological values for the wind vector components, :math:`u_c \text{ and } v_c`. The measures are defined below:
+These statistics require climatological values for the wind vector components, where :math:`{u_c}_f` and :math:`{v_c}_f` are the forecast climatology vectors and :math:`{u_c}_o` and :math:`{v_c}_o` are the observation climatology vectors. The measures are defined below:
 
 .. math:: 
-  \text{UFABAR} = \text{Mean}(u_f - u_c) = \frac{1}{n} \sum_{i=1}^n (u_{fi} - u_c)
+  \text{UFABAR} = \text{Mean}(u_f - {u_c}_f) = \frac{1}{n} \sum_{i=1}^n ({u_f}_i - {{u_c}_f}_i)
 
-  \text{VFBAR} = \text{Mean}(v_f - v_c) = \frac{1}{n} \sum_{i=1}^n (v_{fi} - v_c)
+  \text{VFBAR} = \text{Mean}(v_f - {v_c}_f) = \frac{1}{n} \sum_{i=1}^n ({v_f}_i - {{v_c}_f}_i)
 
-  \text{UOABAR} = \text{Mean}(u_o - u_c) = \frac{1}{n} \sum_{i=1}^n (u_{oi} - u_c)
+  \text{UOABAR} = \text{Mean}(u_o - {u_c}_o) = \frac{1}{n} \sum_{i=1}^n ({u_o}_i - {{u_c}_o}_i)
 
-  \text{VOABAR} = \text{Mean}(v_o - v_c) = \frac{1}{n} \sum_{i=1}^n (v_{oi} - v_c)
+  \text{VOABAR} = \text{Mean}(v_o - {v_c}_o) = \frac{1}{n} \sum_{i=1}^n ({v_o}_i - {{v_c}_o}_i)
 
-  \text{UVFOABAR} &= \text{Mean}[(u_f - u_c)(u_o - u_c) + (v_f - v_c)(v_o - v_c)] \\
-                  &= \frac{1}{n} \sum_{i=1}^n (u_{fi} - u_c) + (u_{oi} - u_c) + (v_{fi} - v_c)(v_{oi} - v_c)
+  \text{UVFOABAR} &= \text{Mean}[(u_f - {u_c}_f)(u_o - {u_c}_o) + (v_f - {v_c}_f)(v_o - {v_c}_o)] \\
+                  &= \frac{1}{n} \sum_{i=1}^n ({u_f}_i - {{u_c}_f}_i) + ({u_o}_i - {{u_c}_o}_i) + ({v_f}_i - {{v_c}_f}_i)({v_o}_i - {{v_c}_o}_i)
 
-  \text{UVFFABAR} = \text{Mean}[(u_f - u_c)^2 + (v_f - v_c)^2] = \frac{1}{n} \sum_{i=1}^n ((u_{fi} - u_c)^2 + (v_{fi} - v_c)^2)
+  \text{UVFFABAR} &= \text{Mean}[(u_f - {u_c}_f)^2 + (v_f - {v_c}_f)^2] \\
+                  &= \frac{1}{n} \sum_{i=1}^n (({u_f}_i - {{u_c}_f}_i)^2 + ({v_f}_i - {{v_c}_f}_i)^2)
 
-  \text{UVOOABAR} = \text{Mean}[(u_o - u_c)^2 + (v_o - v_c)^2] = \frac{1}{n} \sum_{i=1}^n ((u_{oi} - u_c)^2 + (v_{oi} - v_c)^2)
+  \text{UVOOABAR} &= \text{Mean}[(u_o - {u_c}_o)^2 + (v_o - {v_c}_o)^2] \\
+                  &= \frac{1}{n} \sum_{i=1}^n (({u_o}_i - {{u_c}_o}_i)^2 + ({v_o}_i - {{v_c}_o}_i)^2)
 
 Gradient Values
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