Feature 1673 gbeta

met/data/config/GridStatConfig_default

@@ -202,6 +202,7 @@ distance_map = {
    baddeley_max_dist = NA;
    fom_alpha         = 0.1;
    zhu_weight        = 0.5;
+   beta_value(n)     = n * n / 2.0;
 }
 
 ////////////////////////////////////////////////////////////////////////////////

met/data/table_files/met_header_columns_V10.1.txt

@@ -10,7 +10,7 @@ V10.1 : STAT : NBRCNT   : VERSION MODEL DESC FCST_LEAD FCST_VALID_BEG FCST_VALID
 V10.1 : 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
 V10.1 : 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
 V10.1 : 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
-V10.1 : 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 
+V10.1 : 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 
 V10.1 : 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 
 V10.1 : 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]*
 V10.1 : 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]*

met/docs/Users_Guide/appendixC.rst

@@ -1134,7 +1134,7 @@ A mathematical metric, :math:`m(A,B)\geq 0`, must have the following three prope
 
 The first establishes that a perfect score is zero and that the only way to obtain a perfect score is if the two sets are identical according to the metric. The second requirement ensures that the order by which the two sets are evaluated will not change the result. The third property ensures that if *C* is closer to *A* than *B* is to *A*, then :math:`m(A,C) < m(A,B)`.
 
-It has been argued in :ref:`Gilleland (2019) <Gilleland-2019>` that the second property of symmetry is not necessarily an important quality to have for a summary measure for verification purposes because lack of symmetry allows for information about false alarms and misses.
+It has been argued in :ref:`Gilleland (2017) <Gilleland-2017>` that the second property of symmetry is not necessarily an important quality to have for a summary measure for verification purposes because lack of symmetry allows for information about false alarms and misses.
 
 The results of the distance map verification approaches that are included in the Grid-Stat tool are summarized using a variety of measures. These measures include Baddeley's :math:`\Delta` Metric, the Hausdorff Distance, the Mean-error Distance, Pratt's Figure of Merit, and Zhu's Measure. Their equations are listed below.
 
@@ -1205,6 +1205,29 @@ where MED *(A,B)* is as in the Mean-error distance, *N* is the total number of g
 
 The range for ZHU is 0 to infinity, with a score of 0 indicating a perfect forecast.
 
+.. _App_C-gbeta:
+
+:math:`G` and :math:`G_\beta`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Called "G" and "GBETA" in the DMAP output :numref:`table_GS_format_info_DMAP`
+
+See :numref:`grid-stat_gbeta` for a description.
+
+Let :math:`y = {y_1}{y_2}` where :math:`y_1 = n_A + n_B - 2n_{AB}`, and :math:`y_2 = MED(A,B) \cdot n_B + MED(B,A) \cdot n_A`, with the mean-error distance (:math:`MED`) as described above, and where :math:`n_{A}`, :math:`n_{B}`, and :math:`n_{AB}` are the number of events within event areas *A*, *B*, and the intersection of *A* and *B*, respectively.
+
+The :math:`G` performance measure is given by
+
+.. math:: G(A,B) = y^{1/3}
+
+and the :math:`G_\beta` performance measure is given by
+
+.. math:: G_\beta(A,B) = max\{1-\frac{y}{\beta}, 0\}
+
+where :math:`\beta > 0` is a user-chosen parameter with a default value of :math:`n^2 / 2.0` with :math:`n` equal to the number of points in the domain. The square-root of :math:`G` will give units of grid points, where :math:`y^{1/3}` gives units of grid points squared.
+
+The range for :math:`G_\beta` is 0 to 1, with a score of 1 indicating a perfect forecast.
+
 Calculating Percentiles
 _______________________
 

met/docs/Users_Guide/appendixD.rst

@@ -77,8 +77,9 @@ All other verification scores with CIs in MET must be obtained through bootstrap
 
 5. Calculate CIs for the parameters directly from the sample (see text below for more details)
 
-Typically, a simple random sample is taken for step 2, and that is how it is done in MET. As an example of what happens in this step, suppose our sample is :math:`X_1,X_2,X_3,X_4`. Then, one possible replicate might be :math:`X_2,X_2,X_2,X_4`. Usually one samples :math:`m = n` points in this step, but there are cases where one should use :math:`m < n`. For example, when the underlying distribution is heavy-tailed, one should use a smaller size m than n (e.g., the closest integer value to the square root of the original sample size).
+Typically, a simple random sample is taken for step 2, and that is how it is done in MET. As an example of what happens in this step, suppose our sample is :math:`X_1,X_2,X_3,X_4`. Then, one possible replicate might be :math:`X_2,X_2,X_2,X_4`. Usually one samples :math:`m = n` points in this step, but there are cases where one should use :math:`m < n`. For example, when the underlying distribution is heavy-tailed, one should use a smaller size m than n (e.g., the closest integer value to the square root of the original sample size).  See :ref:`Gilleland (2020, part II) <Gilleland_PartII-2020>` for considerably more information about the issues with estimators that follow a heavy tailed distribution and the closely related issue of bootstrapping extreme-valued estimators, such as the maximum, in the atmospheric science domain.
 
 There are numerous ways to construct CIs from the sample obtained in step 4. MET allows for two of these procedures: the percentile and the BCa. The percentile is the most commonly known method, and the simplest to understand. It is merely the :math:`\alpha / 2` and :math:`1 - \alpha / 2` percentiles from the sample of statistics. Unfortunately, however, it has been shown that this interval is too optimistic in practice (i.e., it doesn't have accurate coverage). One solution is to use the BCa method, which is very accurate, but it is also computationally intensive. This method adjusts for bias and non-constant variance, and yields the percentile interval in the event that the sample is unbiased with constant variance.
 
-If there is dependency in the sample, then it is prudent to account for this dependency in some way. One method that does not make a lot of assumptions is circular block bootstrapping. This is not currently implemented in MET, but will be available in a future release. At that time, the method will be explained more fully here, but until then consult :ref:`Gilleland (2010) <Gilleland-2010>` for more details.
+If there is dependency in the sample, then it is prudent to account for this dependency in some way. :ref:`Gilleland (2010) <Gilleland-2010>` describes the bootstrap procedure, along with the above-mentioned parametric methods, in more detail specifically for the verification application. If there is dependency in the sample, then it is prudent to account for this dependency in some way (see :ref:`Gilleland (2020, part I) <Gilleland_PartI-2020>` part I for an in-depth discussion of bootstrapping in the competing forecast verification domain). One method that is particularly appropriate for serially dependent data is the circular block resampling procedure for step 2.
+

met/docs/Users_Guide/config_options.rst

@@ -413,7 +413,7 @@ e.g. model = "GFS";
 
   model = "WRF";
 
-.._desc:
+.. _desc:
 
 :ref:`desc <desc>`
 
@@ -1615,136 +1615,6 @@ This dictionary may include the following entries:
      ];
   }
 
-.. _nbrhd:
-
-:ref:`nbrhd <nbrhd>`
-
-The "nbrhd" entry is a dictionary that is very similar to the "interp"
-entry. It specifies information for computing neighborhood statistics in
-Grid-Stat. This dictionary may include the following entries:
-
-* The "field" entry specifies to which field(s) the computation of
-  fractional coverage should be applied. Grid-Stat processes each
-  combination of categorical threshold and neighborhood width to
-  derive the fractional coverage fields from which neighborhood
-  statistics are calculated. Users who have computed fractional
-  coverage fields outside of MET can use this option to disable
-  these computations. Instead, the raw input values will be
-  used directly to compute neighborhood statistics:
-
-  * "BOTH" to compute fractional coverage for both the forecast
-    and the observation fields (default).
-
-  * "FCST" to only process the forecast field.
-
-  * "OBS"  to only process the observation field.
-
-  * "NONE" to process neither field.
-
-* The "vld_thresh" entry is described above.
-
-* The "shape" entry defines the shape of the neighborhood.
-  Valid values are "SQUARE" or "CIRCLE"
-
-* The "width" entry is as described above, and must be odd.
-
-* The "cov_thresh" entry is an array of thresholds to be used when
-  computing categorical statistics for the neighborhood fractional
-  coverage field.
-
-.. code-block:: none
-
-  nbrhd = {
-     field      = BOTH;
-     vld_thresh = 1.0;
-     shape      = SQUARE;
-     width      = [ 1 ];
-     cov_thresh = [ >=0.5 ];
-  }
-
-.. _fourier:
-
-:ref:`fourier <fourier>`
-
-The "fourier" entry is a dictionary which specifies the application of the
-Fourier decomposition method. It consists of two arrays of the same length
-which define the beginning and ending wave numbers to be included. If the
-arrays have length zero, no Fourier decomposition is applied. For each array
-entry, the requested Fourier decomposition is applied to the forecast and
-observation fields. The beginning and ending wave numbers are indicated in
-the MET ASCII output files by the INTERP_MTHD column (e.g. WV1_0-3 for waves
-0 to 3 or WV1_10 for only wave 10). This 1-dimensional Fourier decomposition
-is computed along the Y-dimension only (i.e. the columns of data). It is only
-defined when each grid point contains valid data. If either input field
-contains missing data, no Fourier decomposition is computed.
-
-The available wave numbers start at 0 (the mean across each row of data)
-and end at (Nx+1)/2 (the finest level of detail), where Nx is the X-dimension
-of the verification grid:
-
-* The "wave_1d_beg" entry is an array of integers specifying the first
-  wave number to be included.
-
-* The "wave_1d_end" entry is an array of integers specifying the last
-  wave number to be included.
-
-.. code-block:: none
-
-  fourier = {
-     wave_1d_beg = [ 0, 4, 10 ];
-     wave_1d_end = [ 3, 9, 20 ];
-  }
-
-.. _gradient:
-
-:ref:`gradient <gradient>`
-
-The "gradient" entry is a dictionary which specifies the number and size of
-gradients to be computed. The "dx" and "dy" entries specify the size of the
-gradients in grid units in the X and Y dimensions, respectively. dx and dy
-are arrays of integers (positive or negative) which must have the same
-length, and the GRAD output line type will be computed separately for each
-entry. When computing gradients, the value at the (x, y) grid point is
-replaced by the value at the (x+dx, y+dy) grid point minus the value at
-(x, y).
-
-This configuration option may be set separately in each "obs.field" entry.
-
-.. code-block:: none
-
-  gradient = {
-     dx = [ 1 ];
-     dy = [ 1 ];
-  }
-
-.. _distance_map:
-
-:ref:`distance_map <distance_map>`
-
-The "distance_map" entry is a dictionary containing options related to the
-distance map statistics in the DMAP output line type. The "baddeley_p" entry
-is an integer specifying the exponent used in the Lp-norm when computing the
-Baddeley Delta metric. The "baddeley_max_dist" entry is a floating point
-number specifying the maximum allowable distance for each distance map. Any
-distances larger than this number will be reset to this constant. A value of
-NA indicates that no maximum distance value should be used. The "fom_alpha"
-entry is a floating point number specifying the scaling constant to be used
-when computing Pratt's Figure of Merit. The "zhu_weight" specifies a value
-between 0 and 1 to define the importance of the RMSE of the binary fields
-(i.e. amount of overlap) versus the mean-error distance (MED). The default
-value of 0.5 gives equal weighting.
-
-This configuration option may be set separately in each "obs.field" entry.
-
-.. code-block:: none
-
-  distance_map = {
-     baddeley_p        = 2;
-     baddeley_max_dist = NA;
-     fom_alpha         = 0.1;
-     zhu_weight        = 0.5;
-  }
-
 .. _land_mask:
 
 :ref:`land_mask <land_mask>`