## METplus Solutions for Probabilistic Forecast Verification

If you utilize METplus verification capabilities to evaluate probabilistic forecasts, you may find that your final statistical values are not exactly the same as when you compute the same statistic by pencil and paper or in a separate statistical program. These very slight differences are due to how METplus handles probabilistic information.

MET is coded to utilize categorical forecasts, creating contingency tables and using the counts in each of the contingency table cells (hits, misses, false alarms, and correct rejections) to calculate the desired verification statistics. This use extends to probabilistic forecasts as well and aids in the decomposition of statistics such as Brier Score (BS) into reliability, resolution, and uncertainty (more information on that decomposition can be found here).

MET requires users to provide three conditions for probabilistic forecasts. The first of these conditions is an observation variable that is either a 0 or 1 and a forecast variable that is defined on a scale from 0 to 1. In MET, this boolean is **prob** and METplus Wrappers utilizes the variable FCST_IS_PROB. In MET **prob** can also be defined as a dictionary with more information on how to process the probabilistic field; please review this section of the User’s Guide for information.

The second condition is the thresholds to evaluate the probabilistic forecasts across. Essentially this is where METplus turns the forecast probabilities into a binned, categorical evaluation. At its most basic usage in a MET configuration file, this looks like

cat_thresh = ==0.1;

which would create 10 bins of equal width. Users have multiple options for setting this threshold and should review this section of the User’s Guide for more information. It’s important to note that when it comes to evaluating a statistic like BS, METplus does not actually use the forecasts’ probability value; instead, it will use the midpoint of the bin width between the thresholds for the probabilistic forecasts. To understand what this looks like in METplus, let's use the previous example where 10 bins of equal width were created. When calculating BS, METplus will evaluate the first probability bin as 0.05, the midway point between the first bin (0.0 to 0.1). The next probability value would be 0.15 (the midway point between 0.1 and 0.2), and so on. MET utilizes an equation of BS that is described in more detail in the MET Appendix which evaluates to the same result as the BS equation provided in the Verification Statistics for Probabilistic Forecasts section of this guide {provide link to previous section here} if the midpoints of the bins are used as the probability forecast values. All of this is to stress that a proper selection of bin width (and the accompanying mid-point of those bins) will ultimately determine how meaningful your resulting BS value is; after all, what would the result be if the midpoint of a bin was 0.1 and many of the forecasts values were 0.1? What contingency table bin will they count towards?

The final condition users need to provide to MET for probabilistic forecasts is a threshold for the observations. As alluded to in the second condition, users can create any number of thresholds to evaluate the probabilistic forecasts. Combined with the observation threshold which determines an event observation from non-event observation, an Nx2 contingency table will be created, where N is the number of probabilistic bins for the forecasts and 2 is the event, non-event threshold set on the observations.

Now that you know a bit more about probabilistic forecasts and the related statistics as well as how MET will process them, it’s time to show how you can access those same statistics in METplus!

In order to better understand the delineation between METplus, MET, and METplus wrappers which are used frequently throughout this tutorial but are NOT interchangeable, the following definitions are provided for clarity:

- METplus is best visualized as an overarching framework with individual components. It encapsulates all of the repositories: MET, METplus wrappers, METdataio, METcalcpy, and METplotpy.
- MET serves as the core statistical component that ingests the provided fields and commands to compute user-requested statistics and diagnostics.
- METplus wrappers is a suite of Python wrappers that provide low-level automation of MET tools and plotting capability. While there are examples of calling METplus wrappers without any underlying MET usage, these are the exception rather than the rule.

### MET solutions

The MET User’s Guide provides an Appendix that dives into statistical measures that it calculates, as well as the line type it is a part of. Statistics are grouped together by application and type and are available to METplus users in line types. For the probabilistic-related statistics discussed in this section of the tutorial, MET provides the Contingency Table Counts for Probabilistic forecasts (PCT) line type, and the Contingency Table Statistics for Probabilistic forecasts (PSTD) line types. The PCT line type is critical for checking if the thresholds for the probabilistic forecasts and observations produced contingency table counts that reflect what the user is looking for in probabilistic verification. Remember that these counts are ultimately what determine the statistical values found in the PSTD line type.

As for the statistics that were discussed in the Verification Statistics section, the following are links to the User’s Guide Appendix entry that discusses their use in MET. Note that Continuous Ranked Probability Score (CRPS) and Continuous Ranked Probability Skill Score (CRPSS) appear in the Ensemble Continuous Statistics (ECNT) line type and can only be calculated from the Ensemble-Stat tool, while Ranked Probability Score (RPS) and Ranked Probability Skill Score (RPSS) appear in their own Ranked Probability Score (RPS) line type output that is also only accessible from Ensemble-Stat. RPSS is not discussed in the MET USer’s Guide Appendix and is not linked below, while discussion of CRPSS is provided to users in the existing documentation in the MET User’s Guide Appendix:

### METplus Wrapper Solutions

The same statistics that are available in MET are also available with the METplus wrappers. To better understand how MET configuration options for statistics translate to METplus wrapper configuration options, you can utilize the Statistics and Diagnostics Section of the METplus wrappers User’s Guide, which lists all of the available statistics through the wrappers, including what tools can output what statistics. To access the line type through the tool, find your desired tool in the list of available commands for that tool. Once you do, you’ll see the tool will have several options that contain _OUTPUT_FLAG_. These will exhibit the same behavior and accept the same settings as the line types in MET’s output_flag dictionary, so be sure to review the available settings to get the line type output you want.