Update develop-ref after #2820 (#2821)

* Feature #2395 wdir (#2820)

* Per #2395, add new columns to VL1L2, VAL1L2, and VCNT line types for wind direction statistics. Work still in progress.

* Per #2395, write the new VCNT columns to the output and document the additions to the VL1L2, VAL1L2, and VCNT columns.

* Per #2395, add the definition of new statistics to Appendix G.

* Per #2395, update file version history.

* Per #2395, tweak warning message about zero wind vectors and update grid-stat and point-stat to log calls to the do_vl1l2() function.

* Per #2395, refine the weights for wind direction stats, ignoring the undefined directions.

* Update src/tools/core/stat_analysis/aggr_stat_line.cc

* Update src/tools/core/stat_analysis/parse_stat_line.cc

* Update src/tools/core/stat_analysis/aggr_stat_line.cc

* Recent changes to branch protection rules for the develop branch have broken the logic of the update_truth.yml GHA workflow. Instead of submitting a PR to merge develop into develop-ref directly, use an intermediate update_truth_for_develop branch.

---------

Co-authored-by: John Halley Gotway <johnhg@ucar.edu>
Co-authored-by: metplus-bot <97135045+metplus-bot@users.noreply.github.com>

.github/workflows/update_truth.yml

@@ -45,10 +45,12 @@ jobs:
           git config --global user.email "97135045+metplus-bot@users.noreply.github.com"
           echo git checkout ${branch_name}
           git checkout ${branch_name}
+          echo git checkout -b update_truth_for_${branch_name}
+          git checkout -b update_truth_for_${branch_name}
           echo git merge -s ours origin/${branch_name}-ref
           git merge -s ours origin/${branch_name}-ref
-          echo git push origin ${branch_name}
-          git push origin ${branch_name}
+          echo git push origin update_truth_for_${branch_name}
+          git push origin update_truth_for_${branch_name}
 
       - name: Create Pull Request
         run: gh pr create --base $BASE --body "$BODY" --title "$TITLE"

data/table_files/met_header_columns_V12.0.txt

@@ -27,9 +27,9 @@ V12.0 : STAT : RELP     : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID
 V12.0 : STAT : SAL1L2   : 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 FABAR OABAR FOABAR FFABAR OOABAR MAE
 V12.0 : STAT : SL1L2    : 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 FBAR OBAR FOBAR FFBAR OOBAR MAE
 V12.0 : STAT : SSVAR    : 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_BIN BIN_i BIN_N VAR_MIN VAR_MAX VAR_MEAN FBAR OBAR FOBAR FFBAR OOBAR FBAR_NCL FBAR_NCU FSTDEV FSTDEV_NCL FSTDEV_NCU OBAR_NCL OBAR_NCU OSTDEV OSTDEV_NCL OSTDEV_NCU PR_CORR PR_CORR_NCL PR_CORR_NCU ME ME_NCL ME_NCU ESTDEV ESTDEV_NCL ESTDEV_NCU MBIAS MSE BCMSE RMSE
-V12.0 : STAT : VAL1L2   : 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 UFABAR VFABAR UOABAR VOABAR UVFOABAR UVFFABAR UVOOABAR FA_SPEED_BAR OA_SPEED_BAR
-V12.0 : STAT : VL1L2    : 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 UFBAR VFBAR UOBAR VOBAR UVFOBAR UVFFBAR UVOOBAR F_SPEED_BAR O_SPEED_BAR
-V12.0 : STAT : VCNT     : 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 FBAR FBAR_BCL FBAR_BCU OBAR OBAR_BCL OBAR_BCU FS_RMS FS_RMS_BCL FS_RMS_BCU OS_RMS OS_RMS_BCL OS_RMS_BCU MSVE MSVE_BCL MSVE_BCU RMSVE RMSVE_BCL RMSVE_BCU FSTDEV FSTDEV_BCL FSTDEV_BCU OSTDEV OSTDEV_BCL OSTDEV_BCU FDIR FDIR_BCL FDIR_BCU ODIR ODIR_BCL ODIR_BCU FBAR_SPEED FBAR_SPEED_BCL FBAR_SPEED_BCU OBAR_SPEED OBAR_SPEED_BCL OBAR_SPEED_BCU VDIFF_SPEED VDIFF_SPEED_BCL VDIFF_SPEED_BCU VDIFF_DIR VDIFF_DIR_BCL VDIFF_DIR_BCU SPEED_ERR SPEED_ERR_BCL SPEED_ERR_BCU SPEED_ABSERR SPEED_ABSERR_BCL SPEED_ABSERR_BCU DIR_ERR DIR_ERR_BCL DIR_ERR_BCU DIR_ABSERR DIR_ABSERR_BCL DIR_ABSERR_BCU ANOM_CORR ANOM_CORR_NCL ANOM_CORR_NCU ANOM_CORR_BCL ANOM_CORR_BCU ANOM_CORR_UNCNTR ANOM_CORR_UNCNTR_BCL ANOM_CORR_UNCNTR_BCU
+V12.0 : STAT : VAL1L2   : 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 UFABAR VFABAR UOABAR VOABAR UVFOABAR UVFFABAR UVOOABAR FA_SPEED_BAR OA_SPEED_BAR DIRA_ME DIRA_MAE DIRA_MSE
+V12.0 : STAT : VL1L2    : 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 UFBAR VFBAR UOBAR VOBAR UVFOBAR UVFFBAR UVOOBAR F_SPEED_BAR O_SPEED_BAR DIR_ME DIR_MAE DIR_MSE
+V12.0 : STAT : VCNT     : 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 FBAR FBAR_BCL FBAR_BCU OBAR OBAR_BCL OBAR_BCU FS_RMS FS_RMS_BCL FS_RMS_BCU OS_RMS OS_RMS_BCL OS_RMS_BCU MSVE MSVE_BCL MSVE_BCU RMSVE RMSVE_BCL RMSVE_BCU FSTDEV FSTDEV_BCL FSTDEV_BCU OSTDEV OSTDEV_BCL OSTDEV_BCU FDIR FDIR_BCL FDIR_BCU ODIR ODIR_BCL ODIR_BCU FBAR_SPEED FBAR_SPEED_BCL FBAR_SPEED_BCU OBAR_SPEED OBAR_SPEED_BCL OBAR_SPEED_BCU VDIFF_SPEED VDIFF_SPEED_BCL VDIFF_SPEED_BCU VDIFF_DIR VDIFF_DIR_BCL VDIFF_DIR_BCU SPEED_ERR SPEED_ERR_BCL SPEED_ERR_BCU SPEED_ABSERR SPEED_ABSERR_BCL SPEED_ABSERR_BCU DIR_ERR DIR_ERR_BCL DIR_ERR_BCU DIR_ABSERR DIR_ABSERR_BCL DIR_ABSERR_BCU ANOM_CORR ANOM_CORR_NCL ANOM_CORR_NCU ANOM_CORR_BCL ANOM_CORR_BCU ANOM_CORR_UNCNTR ANOM_CORR_UNCNTR_BCL ANOM_CORR_UNCNTR_BCU DIR_ME DIR_ME_BCL DIR_ME_BCU DIR_MAE DIR_MAE_BCL DIR_MAE_BCU DIR_MSE DIR_MSE_BCL DIR_MSE_BCU DIR_RMSE DIR_RMSE_BCL DIR_RMSE_BCU
 V12.0 : STAT : GENMPR   : 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 STORM_ID PROB_LEAD PROB_VAL AGEN_INIT AGEN_FHR AGEN_LAT AGEN_LON AGEN_DLAND BGEN_LAT BGEN_LON BGEN_DLAND GEN_DIST GEN_TDIFF INIT_TDIFF DEV_CAT OPS_CAT
 V12.0 : STAT : SSIDX    : 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 FCST_MODEL REF_MODEL N_INIT N_TERM N_VLD SS_INDEX
 

docs/Users_Guide/appendixG.rst

@@ -46,7 +46,6 @@ In the same manner, we can compare the directions of two different nonzero vecto
 
 __________________________
 
-
 Now let us specialize this discussion of vectors to verification of wind vector data. We will denote the forecast wind vector by :math:`\mathbf{F}`, and the observed wind vector by **O**. These are two-dimensional horizontal vectors with *u* and *v* components as follows:
 
 .. math:: \mathbf{F} = (u_f,v_f) \text{ and } \mathbf{O} = (u_o,v_o)
@@ -71,49 +70,46 @@ Now let us look at the definitions of the vector statistics produced by MET:
 
 _________________________
 
-
 FBAR and OBAR are the average values of the forecast and observed wind speed.
 
 .. math:: 
 
-	\text{FBAR} = \frac{1}{N} \sum_i s_{fi}
-	  
-	\text{OBAR} = {1 \over N} \sum_i s_{oi}
+   \text{FBAR} = \frac{1}{N} \sum_i s_{fi}
 
-_________________________
+   \text{OBAR} = {1 \over N} \sum_i s_{oi}
 
+_________________________
 
 FS_RMS and OS_RMS are the root-mean-square values of the forecast and observed wind speeds.
 
 .. only:: latex
 
-	.. math:: 
-	
-		\text{FS\_RMS} = [ \frac{1}{N} \sum_i s_{fi}^2]^{1/2}
+   .. math::
+
+      \text{FS\_RMS} = [ \frac{1}{N} \sum_i s_{fi}^2]^{1/2}
 
-		\text{OS\_RMS} = [\frac{1}{N} \sum_i s_{oi}^2]^{1/2}
+      \text{OS\_RMS} = [\frac{1}{N} \sum_i s_{oi}^2]^{1/2}
 
 .. only:: html
 
-	.. math:: 
-		
-		\text{FS_RMS} = [ \frac{1}{N} \sum_i s_{fi}^2]^{1/2}
+   .. math::
 
-		\text{OS_RMS} = [\frac{1}{N} \sum_i s_{oi}^2]^{1/2}
+      \text{FS_RMS} = [ \frac{1}{N} \sum_i s_{fi}^2]^{1/2}
+
+      \text{OS_RMS} = [\frac{1}{N} \sum_i s_{oi}^2]^{1/2}
 
 ___________________________
 
 MSVE and RMSVE are, respectively, the mean squared, and root mean squared, lengths of the vector difference between the forecast and observed wind vectors.
 
 .. math:: 
 
-	\text{MSVE} = \frac{1}{N} \sum_i | \mathbf{F}_i - \mathbf{O}_i|^2
+   \text{MSVE} = \frac{1}{N} \sum_i | \mathbf{F}_i - \mathbf{O}_i|^2
 
-	\text{RMSVE} = \sqrt{MSVE}
+   \text{RMSVE} = \sqrt{MSVE}
 
 ____________________________
 
-
 FSTDEV and OSTDEV are the standard deviations of the forecast and observed wind speeds.
 
 .. math:: \text{FSTDEV } = \frac{1}{N} \sum_i (s_{fi} - \text{FBAR})^2 = \frac{1}{N} \sum_i s_{fi}^2 - \text{FBAR}^2
@@ -125,112 +121,181 @@ ___________________________
 FDIR and ODIR are the direction (angle) of :math:`\mathbf{F}_a \text{ and } \mathbf{O}_a` with respect to the grid directions.
 
 .. math:: \text{FDIR } = \text{ direction angle of } \mathbf{F}_a
-
-	  \text{ODIR} = \text{ direction angle of } \mathbf{O}_a
 
-________________________
+     \text{ODIR} = \text{ direction angle of } \mathbf{O}_a
 
+________________________
 
 FBAR_SPEED and OBAR_SPEED are the lengths of the average forecast and observed wind vectors. Note that this is *not* the same as the average forecast and observed wind speeds (*ie.,* the length of an average vector :math:`\neq` the average length of the vector).
 
 .. only:: latex
 
-	.. math:: 
-		
-		\text{FBAR\_SPEED } = | \mathbf{F}_a |
-		
-		\text{OBAR\_SPEED } = | \mathbf{O}_a |
+   .. math::
+
+      \text{FBAR\_SPEED } = | \mathbf{F}_a |
+
+      \text{OBAR\_SPEED } = | \mathbf{O}_a |
 
 .. only:: html
 
-	.. math:: 
-		
-		\text{FBAR_SPEED } = | \mathbf{F}_a |
-		
-		\text{OBAR_SPEED } = | \mathbf{O}_a |
+   .. math::
 
+      \text{FBAR_SPEED } = | \mathbf{F}_a |
 
-________________________
+      \text{OBAR_SPEED } = | \mathbf{O}_a |
 
+________________________
 
 VDIFF_SPEED is the length (*ie. speed*) of the vector difference between the average forecast and average observed wind vectors.
 
 .. only:: latex
 
-	.. math:: \text{VDIFF\_SPEED } = | \mathbf{F}_a - \mathbf{O}_a |
+   .. math:: \text{VDIFF\_SPEED } = | \mathbf{F}_a - \mathbf{O}_a |
 
 .. only:: html
 
-	.. math:: \text{VDIFF_SPEED } = | \mathbf{F}_a - \mathbf{O}_a |
+   .. math:: \text{VDIFF_SPEED } = | \mathbf{F}_a - \mathbf{O}_a |
 
 .. only:: latex
 
-	Note that this is *not* the same as the difference in lengths (speeds) of the average forecast and observed wind vectors. That quantity is called SPEED_ERR (see below). There is a relationship between these two statistics however: using some of the results obtained in the introduction to this appendix, we can say that :math:`| | \mathbf{F}_a | - | \mathbf{O}_a | | \leq | \mathbf{F}_a - \mathbf{O}_a |` or, equivalently, that :math:`\vert \text{SPEED\_ERR } \vert \leq \text{VDIFF\_SPEED. }`
+   Note that this is *not* the same as the difference in lengths (speeds) of the average forecast and observed wind vectors. That quantity is called SPEED_ERR (see below). There is a relationship between these two statistics however: using some of the results obtained in the introduction to this appendix, we can say that :math:`| | \mathbf{F}_a | - | \mathbf{O}_a | | \leq | \mathbf{F}_a - \mathbf{O}_a |` or, equivalently, that :math:`\vert \text{SPEED\_ERR } \vert \leq \text{VDIFF\_SPEED. }`
 
 .. only:: html
 
-	Note that this is *not* the same as the difference in lengths (speeds) of the average forecast and observed wind vectors. That quantity is called SPEED_ERR (see below). There is a relationship between these two statistics however: using some of the results obtained in the introduction to this appendix, we can say that :math:`| | \mathbf{F}_a | - | \mathbf{O}_a | | \leq | \mathbf{F}_a - \mathbf{O}_a |` or, equivalently, that	:math:`\vert \text{SPEED_ERR } \vert \leq \text{VDIFF_SPEED. }`
+   Note that this is *not* the same as the difference in lengths (speeds) of the average forecast and observed wind vectors. That quantity is called SPEED_ERR (see below). There is a relationship between these two statistics however: using some of the results obtained in the introduction to this appendix, we can say that :math:`| | \mathbf{F}_a | - | \mathbf{O}_a | | \leq | \mathbf{F}_a - \mathbf{O}_a |` or, equivalently, that   :math:`\vert \text{SPEED_ERR } \vert \leq \text{VDIFF_SPEED. }`
 
 _________________________
 
-
-VDIFF_DIR is the direction of the vector difference of the average forecast and average observed wind vectors. Note that this is {\it not} the same as the difference in direction of the average forecast and average observed wind vectors. This latter quantity would be FDIR :math:`-` ODIR.
+VDIFF_DIR is the direction of the vector difference of the average forecast and average observed wind vectors. Note that this is *not* the same as the difference in direction of the average forecast and average observed wind vectors. This latter quantity would be FDIR :math:`-` ODIR.
 
 .. only:: latex
 
-	.. math:: \text{VDIFF\_DIR } = \text{ direction of } (\mathbf{F}_a - \mathbf{O}_a)
+   .. math:: \text{VDIFF\_DIR } = \text{ direction of } (\mathbf{F}_a - \mathbf{O}_a)
 
 .. only:: html
 
-	.. math:: \text{VDIFF_DIR } = \text{ direction of } (\mathbf{F}_a - \mathbf{O}_a)
+   .. math:: \text{VDIFF_DIR } = \text{ direction of } (\mathbf{F}_a - \mathbf{O}_a)
 
 _________________________
 
-
 SPEED_ERR is the difference in the lengths (speeds) of the average forecast and average observed wind vectors. (See the discussion of VDIFF_SPEED above.)
 
 .. only:: latex
 
-	.. math:: \text{SPEED\_ERR } = | \mathbf{F}_a | - | \mathbf{O}_a | = \text{ FBAR\_SPEED } - \text{ OBAR\_SPEED }
+   .. math:: \text{SPEED\_ERR } = | \mathbf{F}_a | - | \mathbf{O}_a | = \text{ FBAR\_SPEED } - \text{ OBAR\_SPEED }
 
 .. only:: html
 
-	.. math:: \text{SPEED_ERR } = | \mathbf{F}_a | - | \mathbf{O}_a | = \text{ FBAR_SPEED } - \text{ OBAR_SPEED }
-
+   .. math:: \text{SPEED_ERR } = | \mathbf{F}_a | - | \mathbf{O}_a | = \text{ FBAR_SPEED } - \text{ OBAR_SPEED }
 
 ___________________________
 
-
 SPEED_ABSERR is the absolute value of SPEED_ERR. Note that we have SPEED_ABSERR :math:`\leq` VDIFF_SPEED (see the discussion of VDIFF_SPEED above).
 
 .. only:: latex
 
-	.. math:: \text{SPEED\_ABSERR } = \vert \text{SPEED\_ERR } \vert
+   .. math:: \text{SPEED\_ABSERR } = \vert \text{SPEED\_ERR } \vert
 
 .. only:: html
 
-	.. math:: \text{SPEED_ABSERR } = \vert \text{SPEED_ERR } \vert
+   .. math:: \text{SPEED_ABSERR } = \vert \text{SPEED_ERR } \vert
 
 __________________________
 
 DIR_ERR is the signed angle between the directions of the average forecast and average observed wind vectors. Positive if the forecast vector is counterclockwise from the observed vector.
 
 .. only:: latex
 
-	.. math:: \text{DIR\_ERR } = \text{ direction between } N(\mathbf{F}_a) \text{ and } N(\mathbf{O}_a) 
+   .. math:: \text{DIR\_ERR } = \text{ direction between } N(\mathbf{F}_a) \text{ and } N(\mathbf{O}_a)
 
 .. only:: html
 
-	.. math:: \text{DIR_ERR } = \text{ direction between } N(\mathbf{F}_a) \text{ and } N(\mathbf{O}_a) 
+   .. math:: \text{DIR_ERR } = \text{ direction between } N(\mathbf{F}_a) \text{ and } N(\mathbf{O}_a)
 
 __________________________
-	  
+
 DIR_ABSERR is the absolute value of DIR_ERR. In other words, it's an unsigned angle rather than a signed angle.
 
 .. only:: latex
 
-	.. math:: \text{DIR\_ABSERR } = \vert \text{DIR\_ERR } \vert
+   .. math:: \text{DIR\_ABSERR } = \vert \text{DIR\_ERR } \vert
+
+.. only:: html
+
+   .. math:: \text{DIR_ABSERR } = \vert \text{DIR_ERR } \vert
+
+__________________________
+
+The following statistics are computed by comparing the forecast and observed wind directions for each individual matched pair.
+
+For each point, the directed angle difference in degrees is computed between the forecast and observed wind vectors and rescaled to the range from -180, exclusive, to 180, inclusive.
+
+.. math::
+
+   N(\mathbf{F}_i) - N(\mathbf{O}_i) \in (-180, 180]
+
+Note however that the direction of the zero vector is undefined. Points for which the forecast or observed wind direction is undefined are excluded from the analysis and result in a warning message being printed. The "wind_thresh" and "wind_logic" configuration options, described in :numref:`config_options`, can be used to filter the wind vectors down to a subset that meet the specified wind speed threshold.
+
+__________________________
+
+DIR_ME is the average of the signed difference between the forecast and observed wind directions.
+
+.. only:: latex
+
+   .. math::
+
+      \text{DIR\_ME} = \frac{1}{N} \sum_i (N(\mathbf{F}_i) - N(\mathbf{O}_i))
 
 .. only:: html
 
-	.. math:: \text{DIR_ABSERR } = \vert \text{DIR_ERR } \vert
+   .. math::
+
+      \text{DIR_ME} = \frac{1}{N} \sum_i (N(\mathbf{F}_i) - N(\mathbf{O}_i))
+
+__________________________
+
+DIR_MAE is the average of the absolute value of the difference between the forecast and observed wind directions.
+
+.. only:: latex
+
+   .. math::
+
+      \text{DIR\_MAE} = \frac{1}{N} \sum_i | N(\mathbf{F}_i) - N(\mathbf{O}_i) |
+
+.. only:: html
+
+   .. math::
+
+      \text{DIR_MAE} = \frac{1}{N} \sum_i | N(\mathbf{F}_i) - N(\mathbf{O}_i) |
+
+__________________________
+
+DIR_MSE is the average of the squared difference between the forecast and observed wind directions.
+
+.. only:: latex
+
+   .. math::
+
+      \text{DIR\_MSE} = \frac{1}{N} \sum_i (N(\mathbf{F}_i) - N(\mathbf{O}_i))^2
+
+.. only:: html
+
+   .. math::
+
+      \text{DIR_MSE} = \frac{1}{N} \sum_i (N(\mathbf{F}_i) - N(\mathbf{O}_i))^2
+
+__________________________
+
+DIR_RMSE is the square root of the average squared difference between the forecast and observed wind directions.
+
+.. only:: latex
+
+   .. math::
+
+      \text{DIR\_RMSE} = \sqrt{DIR\_MSE}
+
+.. only:: html
+
+   .. math::
+
+      \text{DIR_RMSE} = \sqrt{DIR\_MSE}

docs/Users_Guide/point-stat.rst

@@ -1285,6 +1285,15 @@ The first set of header columns are common to all of the output files generated
   * - 34
     - O_SPEED_BAR
     - Mean observed wind speed
+  * - 35
+    - DIR_ME
+    - Mean wind direction difference, from -180 to 180 degrees
+  * - 36
+    - DIR_MAE
+    - Mean absolute wind direction difference
+  * - 37
+    - DIR_MSE
+    - Mean squared wind direction difference
 
 .. _table_PS_format_info_VAL1L2:
 
@@ -1331,6 +1340,15 @@ The first set of header columns are common to all of the output files generated
   * - 34
     - OA_SPEED_BAR
     - Mean observed wind speed anomaly
+  * - 35
+    - DIRA_ME
+    - Mean wind direction anomaly difference, from -180 to 180 degrees
+  * - 36
+    - DIRA_MAE
+    - Mean absolute wind direction anomaly difference
+  * - 37
+    - DIRA_MSE
+    - Mean squared wind direction anomaly difference
 
 .. _table_PS_format_info_VCNT:
 
@@ -1410,6 +1428,18 @@ The first set of header columns are common to all of the output files generated
   * - 85-87
     - ANOM_CORR_UNCNTR, :raw-html:`<br />` ANOM_CORR_UNCNTR_BCL, :raw-html:`<br />` ANOM_CORR_UNCNTR_BCU
     - Uncentered vector Anomaly Correlation excluding mean error including bootstrap upper and lower confidence limits
+  * - 88-90
+    - DIR_ME, :raw-html:`<br />` DIR_ME_BCL, :raw-html:`<br />` DIR_ME_BCU
+    - Mean direction difference, from -180 to 180 degrees, including bootstrap upper and lower confidence limits
+  * - 91-93
+    - DIR_MAE, :raw-html:`<br />` DIR_MAE_BCL, :raw-html:`<br />` DIR_MAE_BCU
+    - Mean absolute direction difference including bootstrap upper and lower confidence limits
+  * - 94-96
+    - DIR_MSE, :raw-html:`<br />` DIR_MSE_BCL, :raw-html:`<br />` DIR_MSE_BCU
+    - Mean squared direction difference including bootstrap upper and lower confidence limits
+  * - 97-99
+    - DIR_RMSE, :raw-html:`<br />` DIR_RMSE_BCL, :raw-html:`<br />` DIR_RMSE_BCU
+    - Root mean squared direction difference including bootstrap upper and lower confidence limits
 
 .. _table_PS_format_info_MPR: