11. GridStat Tool
11.1. Introduction
The GridStat tool provides verification statistics for a matched forecast and observation grid. All of the forecast grid points in the region of interest are matched to observation grid points on the same grid. All the matched grid points are used to compute the verification statistics. The GridStat tool functions in much the same way as the PointStat tool, except that no interpolation is required because the forecasts and observations are on the same grid. However, the interpolation parameters may be used to perform a smoothing operation on the forecast and observation fields prior to verification. In addition to traditional verification approaches, the GridStat tool includes Fourier decompositions, gradient statistics, distance metrics, and neighborhood methods, designed to examine forecast performance as a function of spatial scale.
Scientific and statistical aspects of the GridStat tool are briefly described in this section, followed by practical details regarding usage and output from the tool.
11.2. Scientific and statistical aspects
11.2.1. Statistical measures
The GridStat tool computes a wide variety of verification statistics. Broadly speaking, these statistics can be subdivided into three types of statistics: measures for categorical variables, measures for continuous variables, and measures for probabilistic forecasts. Further, when a climatology file is included, reference statistics for the forecasts compared to the climatology can be calculated. These categories of measures are briefly described here; specific descriptions of all measures are provided in Appendix C, Section 32. Additional information can be found in Wilks (2011) and Jolliffe and Stephenson (2012), and on the Collaboration for Australian Weather and Climate Research Forecast Verification  Issues, Methods and FAQ web page.
In addition to these verification measures, the GridStat tool also computes partial sums and other FHO statistics that are produced by the NCEP verification system. These statistics are also described in Appendix C, Section 32.
11.2.1.1. Measures for categorical variables
Categorical verification statistics are used to evaluate forecasts that are in the form of a discrete set of categories rather than on a continuous scale. GridStat computes both 2x2 and multicategory contingency tables and their associated statistics, similar to PointStat. See Appendix C, Section 32 for more information.
11.2.1.2. Measures for continuous variables
For continuous variables, many verification measures are based on the forecast error (i.e., f  o). However, it also is of interest to investigate characteristics of the forecasts, and the observations, as well as their relationship. These concepts are consistent with the general framework for verification outlined by Murphy and Winkler (1987). The statistics produced by MET for continuous forecasts represent this philosophy of verification, which focuses on a variety of aspects of performance rather than a single measure. See Appendix C, Section 32 for specific information.
A user may wish to eliminate certain values of the forecasts from the calculation of statistics, a process referred to here as “conditional verification”. For example, a user may eliminate all temperatures above freezing and then calculate the error statistics only for those forecasts of below freezing temperatures. Another common example involves verification of wind forecasts. Since wind direction is indeterminate at very low wind speeds, the user may wish to set a minimum wind speed threshold prior to calculating error statistics for wind direction. The user may specify these thresholds in the configuration file to specify the conditional verification. Thresholds can be specified using the usual Fortran conventions (<, <=, ==, !, >=, or >) followed by a numeric value. The threshold type may also be specified using two letter abbreviations (lt, le, eq, ne, ge, gt). Further, more complex thresholds can be achieved by defining multiple thresholds and using && or  to string together event definition logic. The forecast and observation threshold can be used together according to user preference by specifying one of: UNION, INTERSECTION, or SYMDIFF (symmetric difference).
11.2.1.3. Measures for probabilistic forecasts and dichotomous outcomes
For probabilistic forecasts, many verification measures are based on reliability, accuracy and bias. However, it also is of interest to investigate joint and conditional distributions of the forecasts and the observations, as in Wilks (2011). See Appendix C, Section 32 for specific information.
Probabilistic forecast values are assumed to have a range of either 0 to 1 or 0 to 100. If the max data value is > 1, we assume the data range is 0 to 100, and divide all the values by 100. If the max data value is <= 1, then we use the values as is. Further, thresholds are applied to the probabilities with equality on the lower end. For example, with a forecast probability p, and thresholds t1 and t2, the range is defined as: t1 <= p < t2. The exception is for the highest set of thresholds, when the range includes 1: t1 <= p <= 1. To make configuration easier, since METv6.0, these probabilities may be specified in the configuration file as a list (>0.00,>0.25,>0.50,>0.75,>1.00) or using shorthand notation (==0.25) for bins of equal width.
Since METv6.0, when the “prob” entry is set as a dictionary to define the field of interest, setting “prob_as_scalar = TRUE” indicates that this data should be processed as regular scalars rather than probabilities.For example, this option can be used to compute traditional 2x2 contingency tables and neighborhood verification statistics for probability data. It can also be used to compare two probability fields directly.
11.2.1.4. Use of a climatology field for comparative verification
The GridStat tool allows evaluation of model forecasts compared with a usersupplied climatology. Prior to calculation of statistics, the climatology must be put on the same grid as the forecasts and observations. In particular, the anomaly correlation and mean squared error skill score provide a measure of the forecast skill versus the climatology. For more details about climatological comparisons and reference forecasts, see the relevant section in the PointStat Chapter: Section 10.2.3.4.
11.2.1.5. Use of analysis fields for verification
The GridStat tool allows evaluation of model forecasts using model analysis fields. However, users are cautioned that an analysis field is not independent of its parent model; for this reason verification of model output using an analysis field from the same model is generally not recommended and is not likely to yield meaningful information about model performance.
11.2.2. Statistical confidence intervals
The confidence intervals for the GridStat tool are the same as those provided for the PointStat tool except that the scores are based on pairing grid points with grid points so that there are likely more values for each field making any assumptions based on the central limit theorem more likely to be valid. However, it should be noted that spatial (and temporal) correlations are not presently taken into account in the confidence interval calculations. Therefore, confidence intervals reported may be somewhat too narrow (e.g., Efron, 2007). See Appendix D, Section 33 for details regarding confidence intervals provided by MET.
11.2.3. Grid weighting
When computing continuous statistics on a regular large scale or global latitudelongitude grid, weighting may be applied in order to compensate for the meridian convergence toward higher latitudes. Grid square area weighting or weighting based on the cosine of the latitude are two configuration options in both pointstat and gridstat. See Section 4 for more information.
11.2.4. Neighborhood methods
MET also incorporates several neighborhood methods to give credit to forecasts that are close to the observations, but not necessarily exactly matched up in space. Also referred to as “fuzzy” verification methods, these methods do not just compare a single forecast at each grid point to a single observation at each grid point; they compare the forecasts and observations in a neighborhood surrounding the point of interest. With the neighborhood method, the user chooses a distance within which the forecast event can fall from the observed event and still be considered a hit. In MET this is implemented by defining a square search window around each grid point. Within the search window, the number of observed events is compared to the number of forecast events. In this way, credit is given to forecasts that are close to the observations without requiring a strict match between forecasted events and observed events at any particular grid point. The neighborhood methods allow the user to see how forecast skill varies with neighborhood size and can help determine the smallest neighborhood size that can be used to give sufficiently accurate forecasts.
There are several ways to present the results of the neighborhood approaches, such as the Fractions Skill Score (FSS) or the Fractions Brier Score (FBS). These scores are presented in Appendix C, Section 32. One can also simply upscale the information on the forecast verification grid by smoothing or resampling within a specified neighborhood around each grid point and recalculate the traditional verification metrics on the coarser grid. The MET output includes traditional contingency table statistics for each threshold and neighborhood window size.
The user must specify several parameters in the grid_stat configuration file to utilize the neighborhood approach, such as the interpolation method, size of the smoothing window, and required fraction of valid data points within the smoothing window. For FSSspecific results, the user must specify the size of the neighborhood window, the required fraction of valid data points within the window, and the fractional coverage threshold from which the contingency tables are defined. These parameters are described further in the practical information section below.
11.2.5. Fourier Decomposition
The MET software will compute the full onedimensional Fourier transform, then do a partial inverse transform based on the two userdefined wave numbers. These two wave numbers define a band pass filter in the Fourier domain. This process is conceptually similar to the operation of projecting onto subspace in linear algebra. If one were to sum up all possible wave numbers the result would be to simply reproduce the raw data.
Decomposition via Fourier transform allows the user to evaluate the model separately at each spatial frequency. As an example, the Fourier analysis allows users to examine the “dieoff”, or reduction, in anomaly correlation of geopotential height at various levels for bands of waves. A band of low wave numbers, say 0  3, represent larger frequency components, while a band of higher wave numbers, for example 70  72, represent smaller frequency components. Generally, anomaly correlation should be higher for frequencies with low wave numbers than for frequencies with high wave numbers, hence the “dieoff”.
Wavelets, and in particular the MET wavelet tool, can also be used to define a band pass filter (Casati et al., 2004; Weniger et al., 2016). Both the Fourier and wavelet methods can be used to look at different spatial scales.
11.2.6. Gradient Statistics
The S1 score has been in historical use for verification of forecasts, particularly for variables such as pressure and geopotential height. This score compares differences between adjacent grid points in the forecast and observed fields. When the adjacent points in both forecast and observed fields exhibit the same differences, the S1 score will be the perfect value of 0. Larger differences will result in a larger score.
Differences are computed in both of the horizontal grid directions and is not a true mathematical gradient. Because the S1 score focuses on differences only, any bias in the forecast will not be measured. Further, the score depends on the domain and spacing of the grid, so can only be compared on forecasts with identical grids.
11.2.7. Distance Maps
The following methods can all be computed efficiently by utilizing fast algorithms developed for calculating distance maps. A distance map results from calculating the shortest distance from every grid point, s=(x,y), in the domain, D, to the nearest onevalued grid point. In each of the following, it is understood that they are calculated between event areas A, from one field and observation event areas B from another. If the measure is applied to a feature within a field, then the distance map is still calculated over the entire original domain. Some of the distance map statistics are computed over the entire distance map, while others use only parts of it.
Because these methods rely on the distance map, it is helpful to understand precisely what such maps do. Figure 11.1 demonstrates the path of the shortest distance to the nearest event point in the event area A marked by the gray rectangle in the diagram. Note that the arrows all point to a grid point on the boundary of the event area A as it would be a longer distance to any point in its interior. Figure 11.2 demonstrates the shortest distances from every grid point inside a second event area marked by the gray circle labeled B to the same event area A as in Figure 11.1. Note that all of the distances are to points on a small subsection (indicated by the yellow stretch) of the subset A.
While Figure 11.1 and Figure 11.2 are helpful in illustrating the idea of a distance map, Figure 11.3 shows an actual distance map calculated for binary fields consisting of circular event areas, where one field has two circular event areas labeled A, and the second has one circular event area labeled B. Notice that the values of the distance map inside the event areas are all zero (dark blue) and the distances grow larger in the pattern of concentric circles around these event areas as grid cells move further away. Finally, Figure 11.4 depicts special situations from which the distance map measures to be discussed are calculated. In particular, the top left panel shows the absolute difference between the two distance maps presented in the bottom row of Figure 11.3. The top right panel shows the portion of the distance map for A that falls within the event area of B, and the bottom left depicts the portion of the distance map for B that falls within the event area A. That is, the first shows the shortest distances from every grid point in the set B to the nearest grid point in the event area A, and the latter shows the shortest distance from every grid point in A to the nearest grid point in B.
The statistics derived from these distance maps are described in Appendix C, Section 32.7. To make fair comparisons, any grid point containing bad data in either the forecast or observation field is set to bad data in both fields. For each combination of input field and categorical threshold requested in the configuration file, GridStat applies that threshold to define events in the forecast and observation fields and computes distance maps for those binary fields. Statistics for all requested masking regions are derived from those distance maps. Note that the distance maps are computed only once over the full verification domain, not separately for each masking region. Events occurring outside of a masking region can affect the distance map values inside that masking region and, therefore, can also affect the distance maps statistics for that region.
11.2.8. \(\beta\) and \(G_\beta\)
See Section 32.7.5 for the \(G\) and \(G_\beta\) equations.
\(G_\beta\) provides a summary measure of forecast quality for each userdefined threshold chosen. It falls into a range from zero to one where one is a perfect forecast and zero is considered to be a very poor forecast as determined by the user through the value of \(\beta\). Values of \(G_\beta\) closer to one represent better forecasts and worse forecasts as it decreases toward zero. Although a particular value cannot be universally compared against any forecast, when applied with the same choice of \(\beta\) for the same variable and on the same domain, it is highly effective at ranking such forecasts.
\(G_\beta\) is sensitive to the choice of \(\beta\), which depends on the (i) specific domain, (ii) variable, and (iii) user’s needs. Smaller values make \(G_\beta\) more stringent and larger values make it more lenient. Figure 11.5 shows an example of applying \(G_\beta\) over a range of \(\beta\) values to a precipitation verification set where the binary fields are created by applying a threshold of \(2.1 mmh^{1}\). Color choice and human bias can make it difficult to determine the quality of the forecast for a human observer looking at the raw images in the top row of the figure (Ahijevych et al., 2009). The bottom left panel of the figure displays the differences in their binary fields, which highlights that the forecast captured the overall shapes of the observed rain areas but suffers from a spatial displacement error (perhaps really a timing error).
Whether or not the forecast from Figure 11.5 is “good” or not depends on the specific user. Is it sufficient that the forecast came as close as it did to the observation field? If the answer is yes for the user, then a higher choice of \(\beta\), such as \(N/2\), with \(N\) equal to the number of points in the domain, will correctly inform this user that it is a “good” forecast as it will lead to a \(G_\beta\) value near one. If the user requires the forecast to be much better aligned spatially with the observation field, then a lower choice, perhaps \(\beta = N\), will correctly inform that the forecast suffers from spatial displacement errors that are too large for this user to be pleased. If the goal is to rank a series of ensemble forecasts, for example, then a choice of \(\beta\) that falls in the steep part of the curve shown in the lower right panel of the figure should be preferred, say somewhere between \(\beta = N\) and \(\beta = N^2/2\). Such a choice will ensure that each member is differentiated by the measure.
In some cases, a user may be interested in a much higher threshold than \(2.1 mmh^{1}\) of the above example. Gilleland, 2021 (Fig. 4), for example, shows this same forecast using a threshold of \(40 mmh^{1}\). Only a small area in Mississippi has such extreme rain predicted at this valid time; yet none was observed. Small spatial areas of extreme rain in the observed field, however, did occur in a location far away from Mississippi that was not predicted. Generally, for this type of verification, the Hausdorff metric is a good choice of measure. However, a small choice of \(\beta\) will provide similar results as the Hausdorff distance (Gilleland, 2021). The user should think about the average size of storm areas and multiply this value by the displacement distance they are comfortable with in order to get a good initial choice for \(\beta\), and may have to increase or decrease its value by trialanderror using one or two example cases from their verification set.
Since \(G_\beta\) is so sensitive to the choice of \(\beta\), which is defined relative to the number of points in the verification domain, \(G_\beta\) is only computed for the full verification domain. \(G_\beta\) is reported as a bad data value for any masking region subsets of the full verification domain.
11.3. Practical information
This section contains information about configuring and running the GridStat tool. The GridStat tool verifies gridded model data using gridded observations. The input gridded model and observation datasets must be in one of the MET supported file formats. The requirement of having all gridded fields using the same grid specification was removed in METv5.1. There is a regrid option in the configuration file that allows the user to define the grid upon which the scores will be computed. The gridded observation data may be a gridded analysis based on observations such as Stage II or Stage IV data for verifying accumulated precipitation, or a model analysis field may be used.
The GridStat tool provides the capability of verifying one or more model variables/levels using multiple thresholds for each model variable/level. The GridStat tool performs no interpolation when the input model, observation, and climatology datasets must be on a common grid. MET will interpolate these files to a common grid if one is specified. The interpolation parameters may be used to perform a smoothing operation on the forecast field prior to verifying it to investigate how the scale of the forecast affects the verification statistics. The GridStat tool computes a number of continuous statistics for the forecast minus observation differences, discrete statistics once the data have been thresholded, or statistics for probabilistic forecasts. All types of statistics can incorporate a climatological reference.
11.3.1. grid_stat usage
The usage statement for the GridStat tool is listed below:
Usage: grid_stat
fcst_file
obs_file
config_file
[outdir path]
[log file]
[v level]
[compress level]
grid_stat has three required arguments and accepts several optional ones.
11.3.1.1. Required arguments for grid_stat
The fcst_file argument indicates the gridded file containing the model data to be verified.
The obs_file argument indicates the gridded file containing the gridded observations to be used for the verification of the model.
The config_file argument indicates the name of the configuration file to be used. The contents of the configuration file are discussed below.
11.3.1.2. Optional arguments for grid_stat
The outdir path indicates the directory where output files should be written.
The log file option directs output and errors to the specified log file. All messages will be written to that file as well as standard out and error. Thus, users can save the messages without having to redirect the output on the command line. The default behavior is no log file.
The v level option indicates the desired level of verbosity. The contents of “level” will override the default setting of 2. Setting the verbosity to 0 will make the tool run with no log messages, while increasing the verbosity above 1 will increase the amount of logging.
The compress level option indicates the desired level of compression (deflate level) for NetCDF variables. The valid level is between 0 and 9. The value of “level” will override the default setting of 0 from the configuration file or the environment variable MET_NC_COMPRESS. Setting the compression level to 0 will make no compression for the NetCDF output. Lower number is for fast compression and higher number is for better compression.
An example of the grid_stat calling sequence is listed below:
Example 1:
grid_stat sample_fcst.grb \
sample_obs.grb \
GridStatConfig
In Example 1, the GridStat tool will verify the model data in the sample_fcst.grb GRIB file using the observations in the sample_obs.grb GRIB file applying the configuration options specified in the GridStatConfig file.
A second example of the grid_stat calling sequence is listed below:
Example 2:
grid_stat sample_fcst.nc
sample_obs.nc
GridStatConfig
In the second example, the GridStat tool will verify the model data in the sample_fcst.nc NetCDF output of pcp_combine, using the observations in the sample_obs.nc NetCDF output of pcp_combine, and applying the configuration options specified in the GridStatConfig file. Because the model and observation files contain only a single field of accumulated precipitation, the GridStatConfig file should be configured to specify that only accumulated precipitation be verified.
11.3.2. grid_stat configuration file
The default configuration file for the GridStat tool, named GridStatConfig_default, can be found in the installed share/met/config directory. Other versions of the configuration file are included in scripts/config. We recommend that users make a copy of the default (or other) configuration file prior to modifying it. The contents are described in more detail below.
Note that environment variables may be used when editing configuration files, as described in Section 6.1.2 for the PB2NC tool.
model = "WRF";
desc = "NA";
obtype = "ANALYS";
fcst = { ... }
obs = { ... }
regrid = { ... }
climo_mean = { ... }
climo_stdev = { ... }
climo_cdf = { ... }
mask = { grid = [ "FULL" ]; poly = []; }
ci_alpha = [ 0.05 ];
boot = { interval = PCTILE; rep_prop = 1.0; n_rep = 1000;
rng = "mt19937"; seed = ""; }
interp = { field = BOTH; vld_thresh = 1.0; shape = SQUARE;
type = [ { method = NEAREST; width = 1; } ]; }
censor_thresh = [];
censor_val = [];
mpr_column = [];
mpr_thresh = [];
eclv_points = 0.05;
hss_ec_value = NA;
rank_corr_flag = TRUE;
tmp_dir = "/tmp";
output_prefix = "";
version = "VN.N";
The configuration options listed above are common to multiple MET tools and are described in Section 4.
nbrhd = {
field = BOTH;
vld_thresh = 1.0;
shape = SQUARE;
width = [ 1 ];
cov_thresh = [ >=0.5 ];
}
The nbrhd dictionary contains a list of values to be used in defining the neighborhood to be used when computing neighborhood verification statistics. The neighborhood shape is a SQUARE or CIRCLE centered on the current point, and the width value specifies the width of the square or diameter of the circle as an odd integer.
The field entry is set to BOTH, FCST, OBS, or NONE to indicate the fields to which the fractional coverage derivation logic should be applied. This should always be set to BOTH unless you have already computed the fractional coverage field(s) with numbers between 0 and 1 outside of MET.
The vld_thresh entry contains a number between 0 and 1. When performing neighborhood verification over some neighborhood of points the ratio of the number of valid data points to the total number of points in the neighborhood is computed. If that ratio is greater than this threshold, that value is included in the neighborhood verification. Setting this threshold to 1, which is the default, requires that the entire neighborhood must contain valid data. This variable will typically come into play only along the boundaries of the verification region chosen.
The cov_thresh entry contains a comma separated list of thresholds to be applied to the neighborhood coverage field. The coverage is the proportion of forecast points in the neighborhood that exceed the forecast threshold. For example, if 10 of the 25 forecast grid points contain values larger than a threshold of 2, then the coverage is 10/25 = 0.4. If the coverage threshold is set to 0.5, then this neighborhood is considered to be a “No” forecast.
fourier = {
wave_1d_beg = [ 0, 4, 10 ];
wave_1d_end = [ 3, 9, 20 ];
}
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_03 for waves 0 to 3 or WV1_10 for only wave 10). This 1dimensional Fourier decomposition is computed along the Ydimension only (i.e. the columns of data). It is applied to the forecast and observation fields as well as the climatological mean field, if specified. It is only defined when each grid point contains valid data. If any 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 Xdimension 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.
gradient = {
dx = [ 1 ];
dy = [ 1 ];
}
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.
distance_map = {
baddeley_p = 2;
baddeley_max_dist = NA;
fom_alpha = 0.1;
zhu_weight = 0.5;
beta_value(n) = n * n / 2.0;
}
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 Lpnorm 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 meanerror distance (MED). The default value of 0.5 gives equal weighting. This configuration option may be set separately in each obs.field entry. The beta_value entry is defined as a function of n, where n is the total number of grid points in the full verification domain containing valid data in both the forecast and observation fields. The resulting beta_value is used to compute the \(G_\beta\) statistic. The default function, \(N^2 / 2\), is recommended in Gilleland, 2021 but can be modified as needed.
output_flag = {
fho = BOTH;
ctc = BOTH;
cts = BOTH;
mctc = BOTH;
mcts = BOTH;
cnt = BOTH;
sl1l2 = BOTH;
sal1l2 = NONE;
vl1l2 = BOTH;
val1l2 = NONE;
vcnt = BOTH;
pct = BOTH;
pstd = BOTH;
pjc = BOTH;
prc = BOTH;
eclv = BOTH;
nbrctc = BOTH;
nbrcts = BOTH;
nbrcnt = BOTH;
grad = BOTH;
dmap = BOTH;
}
The output_flag array controls the type of output that the GridStat tool generates. Each flag corresponds to an output line type in the STAT file. Setting the flag to NONE indicates that the line type should not be generated. Setting the flag to STAT indicates that the line type should be written to the STAT file only. Setting the flag to BOTH indicates that the line type should be written to the STAT file as well as a separate ASCII file where the data are grouped by line type. These output flags correspond to the following types of output line types:
FHO for Forecast, Hit, Observation Rates
CTC for Contingency Table Counts
CTS for Contingency Table Statistics
MCTC for MultiCategory Contingency Table Counts
MCTS for MultiCategory Contingency Table Statistics
CNT for Continuous Statistics
SL1L2 for Scalar L1L2 Partial Sums
SAL1L2 for Scalar Anomaly L1L2 Partial Sums when climatological data is supplied
VL1L2 for Vector L1L2 Partial Sums
VAL1L2 for Vector Anomaly L1L2 Partial Sums when climatological data is supplied
VCNT for Vector Continuous Statistics
PCT for Contingency Table Counts for Probabilistic forecasts
PSTD for Contingency Table Statistics for Probabilistic forecasts
PJC for Joint and Conditional factorization for Probabilistic forecasts
PRC for Receiver Operating Characteristic for Probabilistic forecasts
ECLV for Cost/Loss Ratio Relative Value
NBRCTC for Neighborhood Contingency Table Counts
NBRCTS for Neighborhood Contingency Table Statistics
NBRCNT for Neighborhood Continuous Statistics
GRAD for Gradient Statistics
DMAP for Distance Map Statistics
Note that the first two line types are easily derived from one another. The user is free to choose which measure is most desired. The output line types are described in more detail in Section 11.3.3.
nc_pairs_flag = {
latlon = TRUE;
raw = TRUE;
diff = TRUE;
climo = TRUE;
climo_cdp = TRUE;
weight = FALSE;
nbrhd = FALSE;
gradient = FALSE;
distance_map = FALSE;
apply_mask = TRUE;
}
The nc_pairs_flag entry may either be set to a boolean value or a dictionary specifying which fields should be written. Setting it to TRUE indicates the output NetCDF matched pairs file should be created with all available output fields, while setting all to FALSE disables its creation. This is done regardless of if output_flag dictionary indicates any statistics should be computed. The latlon, raw, and diff entries control the creation of output variables for the latitude and longitude, the forecast and observed fields after they have been modified by any userdefined regridding, censoring, and conversion, and the forecast minus observation difference fields, respectively. The climo, weight, and nbrhd entries control the creation of output variables for the climatological mean and standard deviation fields, the grid area weights applied, and the fractional coverage fields computed for neighborhood verification methods. Setting these entries to TRUE indicates that they should be written, while setting them to FALSE disables their creation.
Setting the climo_cdp entry to TRUE enables the creation of an output variable for each climatological distribution percentile (CDP) threshold requested in the configuration file. Note that enabling nbrhd output may lead to very large output files. The gradient entry controls the creation of output variables for the FCST and OBS gradients in the gridx and gridy directions. The distance_map entry controls the creation of output variables for the FCST and OBS distance maps for each categorical threshold. The apply_mask entry controls whether to create the FCST, OBS, and DIFF output variables for all defined masking regions. Setting this to TRUE will create the FCST, OBS, and DIFF output variables for all defined masking regions. Setting this to FALSE will create the FCST, OBS, and DIFF output variables for only the FULL verification domain.
nc_pairs_var_name = "";
The nc_pairs_var_name entry specifies a string for each verification task. This string is parsed from each obs.field dictionary entry and is used to construct variable names for the NetCDF matched pairs output file. The default value of an empty string indicates that the name and level strings of the input data should be used. If the input data level string changes for each run of GridStat, using this option to define a constant string may make downstream processing more convenient.
nc_pairs_var_suffix = "";
The nc_pairs_var_suffix entry is similar to the nc_pairs_var_name entry. It is also parsed from each obs.field dictionary entry. However, it defines a suffix to be appended to the output variable name. This enables the output variable names to be made unique. For example, when verifying height for multiple level types but all with the same level value, use this option to customize the output variable names. This option was previously named nc_pairs_var_str which is now deprecated.
11.3.3. grid_stat output
grid_stat produces output in STAT and, optionally, ASCII and NetCDF formats. The ASCII output duplicates the STAT output but has the data organized by line type. The output files are written to the default output directory or the directory specified by the outdir command line option.
The output STAT file is named using the following naming convention:
grid_stat_PREFIX_HHMMSSL_YYYYMMDD_HHMMSSV.stat where PREFIX indicates the userdefined output prefix, HHMMSSL indicates the forecast lead time and YYYYMMDD_HHMMSSV indicates the forecast valid time.
The output ASCII files are named similarly:
grid_stat_PREFIX_HHMMSSL_YYYYMMDD_HHMMSSV_TYPE.txt where TYPE is one of fho, ctc, cts, mctc, mcts, cnt, sl1l2, vl1l2, vcnt, pct, pstd, pjc, prc, eclv, nbrctc, nbrcts, nbrcnt, dmap, or grad to indicate the line type it contains.
The format of the STAT and ASCII output of the GridStat tool are the same as the format of the STAT and ASCII output of the PointStat tool with the exception of the five additional line types. Please refer to the tables in Section 10.3.3 for a description of the common output STAT and optional ASCII file line types. The formats of the five additional line types for grid_stat are explained in the following tables.
HEADER 


Column Number 
Header Column Name 
Description 
1 
VERSION 
Version number 
2 
MODEL 
User provided text string designating model name 
3 
DESC 
User provided text string describing the verification task 
4 
FCST_LEAD 
Forecast lead time in HHMMSS format 
5 
FCST_VALID_BEG 
Forecast valid start time in YYYYMMDD_HHMMSS format 
6 
FCST_VALID_END 
Forecast valid end time in YYYYMMDD_HHMMSS format 
7 
OBS_LEAD 
Observation lead time in HHMMSS format 
8 
OBS_VALID_BEG 
Observation valid start time in YYYYMMDD_HHMMSS format 
9 
OBS_VALID_END 
Observation valid end time in YYYYMMDD_HHMMSS format 
10 
FCST_VAR 
Model variable 
11 
FCST_UNITS 
Units for model variable 
12 
FCST_LEV 
Selected Vertical level for forecast 
13 
OBS_VAR 
Observation variable 
14 
OBS_UNITS 
Units for observation variable 
15 
OBS_LEV 
Selected Vertical level for observations 
16 
OBTYPE 
User provided text string designating the observation type 
17 
VX_MASK 
Verifying masking region indicating the masking grid or polyline region applied 
18 
INTERP_MTHD 
Interpolation method applied to forecast field 
19 
INTERP_PNTS 
Number of points used by interpolation method 
20 
FCST_THRESH 
The threshold applied to the forecast 
21 
OBS_THRESH 
The threshold applied to the observations 
22 
COV_THRESH 
Proportion of observations in specified neighborhood which must exceed obs_thresh 
23 
ALPHA 
Error percent value used in confidence intervals 
24 
LINE_TYPE 
Various line type options, refer to Section 10.3.3 and the tables below. 
NBRCTC OUTPUT FORMAT 


Column Number 
NBRCTC Column Name 
Description 
24 
NBRCTC 
Neighborhood Contingency Table Counts line type 
25 
TOTAL 
Total number of matched pairs 
26 
FY_OY 
Number of forecast yes and observation yes 
27 
FY_ON 
Number of forecast yes and observation no 
28 
FN_OY 
Number of forecast no and observation yes 
29 
FN_ON 
Number of forecast no and observation no 
NBRCTS OUTPUT FORMAT 


Column Number 
NBRCTS Column Name 
Description 
24 
NBRCTS 
Neighborhood Contingency Table Statistics line type 
25 
TOTAL 
Total number of matched pairs 
2630 
BASER, 
Base rate including normal and bootstrap upper and lower confidence limits 
3135 
FMEAN, 
Forecast mean including normal and bootstrap upper and lower confidence limits 
3640 
ACC, 
Accuracy including normal and bootstrap upper and lower confidence limits 
4143 
FBIAS, 
Frequency Bias including bootstrap upper and lower confidence limits 
4448 
PODY, 
Probability of detecting yes including normal and bootstrap upper and lower confidence limits 
4953 
PODN, 
Probability of detecting no including normal and bootstrap upper and lower confidence limits 
5458 
POFD, 
Probability of false detection including normal and bootstrap upper and lower confidence limits 
5963 
FAR, 
False alarm ratio including normal and bootstrap upper and lower confidence limits 
6468 
CSI, 
Critical Success Index including normal and bootstrap upper and lower confidence limits 
6971 
GSS, 
Gilbert Skill Score including bootstrap upper and lower confidence limits 
Column Number 
NBRCTS Column Name 
Description 

7276 
HK, 
HanssenKuipers Discriminant including normal and bootstrap upper and lower confidence limits 
7779 
HSS, 
Heidke Skill Score including bootstrap upper and lower confidence limits 
8084 
ODDS, 
Odds Ratio including normal and bootstrap upper and lower confidence limits 
8589 
LODDS, 
Logarithm of the Odds Ratio including normal and bootstrap upper and lower confidence limits 
9094 
ORSS, 
Odds Ratio Skill Score including normal and bootstrap upper and lower confidence limits 
9599 
EDS, 
Extreme Dependency Score including normal and bootstrap upper and lower confidence limits 
100104 
SEDS, 
Symmetric Extreme Dependency Score including normal and bootstrap upper and lower confidence limits 
105109 
EDI, 
Extreme Dependency Index including normal and bootstrap upper and lower confidence limits 
110114 
SEDI, 
Symmetric Extremal Dependency Index including normal and bootstrap upper and lower confidence limits 
115117 
BAGSS, 
Bias Adjusted Gilbert Skill Score including bootstrap upper and lower confidence limits 
NBRCNT OUTPUT FORMAT 


Column Number 
NBRCNT Column Name 
Description 
24 
NBRCNT 
Neighborhood Continuous statistics line type 
25 
TOTAL 
Total number of matched pairs 
2628 
FBS, 
Fractions Brier Score including bootstrap upper and lower confidence limits 
2931 
FSS, 
Fractions Skill Score including bootstrap upper and lower confidence limits 
3234 
AFSS, 
Asymptotic Fractions Skill Score including bootstrap upper and lower confidence limits 
3537 
UFSS, 
Uniform Fractions Skill Score including bootstrap upper and lower confidence limits 
3840 
F_RATE, 
Forecast event frequency including bootstrap upper and lower confidence limits 
4143 
O_RATE, 
Observed event frequency including bootstrap upper and lower confidence limits 
GRAD OUTPUT FORMAT 


Column Number 
GRAD Column Name 
Description 
24 
GRAD 
Gradient Statistics line type 
25 
TOTAL 
Total number of matched pairs 
26 
FGBAR 
Mean of absolute value of forecast gradients 
27 
OGBAR 
Mean of absolute value of observed gradients 
28 
MGBAR 
Mean of maximum of absolute values of forecast and observed gradients 
29 
EGBAR 
Mean of absolute value of forecast minus observed gradients 
30 
S1 
S1 score 
31 
S1_OG 
S1 score with respect to observed gradient 
32 
FGOG_RATIO 
Ratio of forecast and observed gradients 
33 
DX 
Gradient size in the Xdirection 
34 
DY 
Gradient size in the Ydirection 
DMAP OUTPUT FORMAT 


Column Number 
DMAP Column Name 
Description 
24 
DMAP 
Distance Map line type 
25 
TOTAL 
Total number of matched pairs 
26 
FY 
Number of forecast events 
27 
OY 
Number of observation events 
28 
FBIAS 
Frequency Bias 
29 
BADDELEY 
Baddeley’s \(\Delta\) Metric 
30 
HAUSDORFF 
Hausdorff Distance 
31 
MED_FO 
Meanerror Distance from observation to forecast 
32 
MED_OF 
Meanerror Distance from forecast to observation 
33 
MED_MIN 
Minimum of MED_FO and MED_OF 
34 
MED_MAX 
Maximum of MED_FO and MED_OF 
35 
MED_MEAN 
Mean of MED_FO and MED_OF 
36 
FOM_FO 
Pratt’s Figure of Merit from observation to forecast 
37 
FOM_OF 
Pratt’s Figure of Merit from forecast to observation 
38 
FOM_MIN 
Minimum of FOM_FO and FOM_OF 
39 
FOM_MAX 
Maximum of FOM_FO and FOM_OF 
40 
FOM_MEAN 
Mean of FOM_FO and FOM_OF 
41 
ZHU_FO 
Zhu’s Measure from observation to forecast 
42 
ZHU_OF 
Zhu’s Measure from forecast to observation 
43 
ZHU_MIN 
Minimum of ZHU_FO and ZHU_OF 
44 
ZHU_MAX 
Maximum of ZHU_FO and ZHU_OF 
45 
ZHU_MEAN 
Mean of ZHU_FO and ZHU_OF 
46 
G 
\(G\) distance measure 
47 
GBETA 
\(G_\beta\) distance measure 
48 
BETA_VALUE 
Beta value used to compute \(G_\beta\) 
If requested using the nc_pairs_flag dictionary in the configuration file, a NetCDF file containing the matched pair and forecast minus observation difference fields for each combination of variable type/level and masking region applied will be generated. The contents of this file are determined by the contents of the nc_pairs_flag dictionary. The output NetCDF file is named similarly to the other output files: grid_stat_PREFIX_ HHMMSSL_YYYYMMDD_HHMMSSV_pairs.nc. Commonly available NetCDF utilities such as ncdump or ncview may be used to view the contents of the output file.
The output NetCDF file contains the dimensions and variables shown in Table 11.8 and Table 11.9.
grid_stat NETCDF DIMENSIONS 


NetCDF Dimension 
Description 
Lat 
Dimension of the latitude (i.e. Number of grid points in the NorthSouth direction) 
Lon 
Dimension of the longitude (i.e. Number of grid points in the EastWest direction) 
grid_stat NETCDF VARIABLES 


NetCDF Variable 
Dimension 
Description 
FCST_VAR_LVL_MASK _INTERP_MTHD _INTERP_PNTS 
lat, lon 
For each model variable (VAR), vertical level (LVL), masking region (MASK), and, if applicable, smoothing operation (INTERP_MTHD and INTERP_PNTS), the forecast value is listed for each point in the mask. 
OBS_VAR_LVL_MASK DIFF_FCSTVAR 
lat, lon 
For each model variable (VAR), vertical level (LVL), and masking region (MASK), the observation value is listed for each point in the mask . 
DIFF_FCSTVAR 
lat, lon 
For each model variable (VAR), vertical level (LVL), masking region (MASK), and, if applicable, smoothing operation (INTERP_MTHD and INTERP_PNTS), the difference (forecast  observation) is computed for each point in the mask. 
FCST_XGRAD_DX FCST_YGRAD_DX OBS_XGRAD_DY OBS_YGRAD_DY 
lat, lon 
List the gradient of the forecast and observation fields computed in the gridx and gridy directions where DX and DY indicate the gradient direction and size. 
The STAT output files described for grid_stat may be used as inputs to the StatAnalysis tool. For more information on using the StatAnalysis tool to create stratifications and aggregations of the STAT files produced by grid_stat, please see Section 15.