Per #2583, fix new equations with embedded underscores for PDF by def…

…ining both html and pdf formatting options.

docs/Users_Guide/appendixC.rst

@@ -976,7 +976,7 @@ RPS
 
 Called "RPS" in RPS output :numref:`table_ES_header_info_es_out_ECNT`
 
-While the above probabilistic verification measures utilize dichotomous observations, the Ranked Probability Score (RPS, :ref:`Epstein, 1969 <Epstein-1969>`, :ref:`Murphy, 1969 <Murphy-1969>`) is the only probabilistic verification measure for discrete multiple-category events available in MET. It is assumed that the categories are ordinal as nominal categorical variables can be collapsed into sequences of binary predictands, which can in turn be evaluated with the above measures for dichotomous variables (:ref:`Wilks, 2011 <Wilks-2011>`). The RPS is the multi-category extension of the Brier score (:ref:`Tödter and Ahrens, 2012 <Todter-2012>`), and is a proper score (:ref:`Mason, 2008 <Mason-2008>`).
+While the above probabilistic verification measures utilize dichotomous observations, the Ranked Probability Score (RPS, :ref:`Epstein, 1969 <Epstein-1969>`, :ref:`Murphy, 1969 <Murphy-1969>`) is the only probabilistic verification measure for discrete multiple-category events available in MET. It is assumed that the categories are ordinal as nominal categorical variables can be collapsed into sequences of binary predictands, which can in turn be evaluated with the above measures for dichotomous variables (:ref:`Wilks, 2011 <Wilks-2011>`). The RPS is the multi-category extension of the Brier score (:ref:`Tödter and Ahrens, 2012 <Tödter-2012>`), and is a proper score (:ref:`Mason, 2008 <Mason-2008>`).
 
 Let :math:`\text{J}` be the number of categories, then both the forecast, :math:`\text{f} = (f_1,…,f_J)`, and observation, :math:`\text{o} = (o_1,…,o_J)`, are length-:math:`\text{J}` vectors, where the components of :math:`\text{f}` include the probabilities forecast for each category :math:`\text{1,…,J}` and :math:`\text{o}` contains 1 in the category that is realized and zero everywhere else. The cumulative forecasts, :math:`F_m`, and observations, :math:`O_m`, are defined to be:
 
@@ -987,7 +987,7 @@ To clarify, :math:`F_1 = f_1` is the first component of :math:`F_m`, :math:`F_2
 
 .. math:: \text{RPS} = \sum_{m=1}^J (F_m - O_m)^2 = \sum_{m=1}^J BS_m,
 
-where :math:`BS_m` is the Brier score for the m-th category (:ref:`Tödter and Ahrens, 2012 <Todter-2012>`). Subsequently, the RPS lends itself to a decomposition into reliability, resolution and uncertainty components, noting that each component is aggregated over the different categories; these are written to the columns named "RPS_REL", "RPS_RES" and "RPS_UNC" in RPS output :numref:`table_ES_header_info_es_out_ECNT`.
+where :math:`BS_m` is the Brier score for the m-th category (:ref:`Tödter and Ahrens, 2012 <Tödter-2012>`). Subsequently, the RPS lends itself to a decomposition into reliability, resolution and uncertainty components, noting that each component is aggregated over the different categories; these are written to the columns named "RPS_REL", "RPS_RES" and "RPS_UNC" in RPS output :numref:`table_ES_header_info_es_out_ECNT`.
 
 CRPS
 ----
@@ -1112,19 +1112,27 @@ Called "IGN_CONV_OERR" and "IGN_CORR_OERR" in ECNT output :numref:`table_ES_head
 
 One approach that is used to take observation error into account in a summary measure is to add error to the forecast by a convolution with the observation model (e.g., :ref:`Anderson, 1996 <Andersen-1996>`; :ref:`Hamill, 2001 <Hamill-2001>`; :ref:`Saetra et. al., 2004 <Saetra-2004>`; :ref:`Bröcker and Smith, 2007 <Bröcker-2007>`; :ref:`Candille et al., 2007 <Candille-2007>`; :ref:`Candille and Talagrand, 2008 <Candille-2008>`; :ref:`Röpnack et al., 2013 <Röpnack-2013>`). Specifically, suppose :math:`y=x+w`, where :math:`y` is the observed value, :math:`x` is the true value, and :math:`w` is the error. Then, if :math:`f` is the density forecast for :math:`x` and :math:`\nu` is the observation model, then the implied density forecast for :math:`y` is given by the convolution:
 
-.. math:: (f*\nu)(y)=\int\nu(y|x)f(x)dx
+.. math:: (f*\nu)(y) = \int\nu(y|x)f(x)dx
 
 :ref:`Ferro, 2017 <Ferro-2017>` gives the error-convolved version of the ignorance scoring rule (referred to therein as the error-convolved logarithmic scoring rule), which is proper under the model where :math:`w\sim N(0,c^2)`) when the forecast for :math:`x` is :math:`N(\mu,\sigma^2)` with density function :math:`f`, by
 
-.. math:: \text{IGN_CONV_OERR} =
-          s(f,y)=\frac{1}{2}\log(\sigma^2+c^2) +
-          \frac{(y-\mu)^2}{2(\sigma^2+c^2)}
+.. only:: latex
+
+  .. math:: \text{IGN\_CONV\_OERR} = s(f,y) = \frac{1}{2}\log(\sigma^2 + c^2) + \frac{{y - \mu}^2}{2{\sigma^2 + c^2}}
+
+.. only:: html
+
+  .. math:: \text{IGN_CONV_OERR} = s(f,y) = \frac{1}{2}\log(\sigma^2 + c^2) + \frac{{y - \mu}^2}{2{\sigma^2 + c^2}}
 
 Another approach to incorporation of observation uncertainty into a measure is the error-correction approach. The approach merely ensures that the scoring rule, :math:`s`, is unbiased for a scoring rule :math:`s_0` if they have the same expected value. :ref:`Ferro, 2017 <Ferro-2017>` gives the error-corrected ignorance scoring rule (which is also proposer when :math:`w\sim N(0,c^2)`) as
 
-.. math:: \text{IGN_CORR_OERR} =
-          s(f,y) = \log\sigma +
-          \frac{(y-\mu)^2-c^2}{2\sigma^2}
+.. only:: latex
+
+  .. math:: \text{IGN\_CORR\_OERR} = s(f,y) = \log\sigma + \frac{{y - \mu}^2 - c^2}{2\sigma^2}
+
+.. only:: html
+
+  .. math:: \text{IGN_CORR_OERR} = s(f,y) = \log\sigma + \frac{{y - \mu}^2 - c^2}{2\sigma^2}
 
 The expected score for the error-convolved ignorance scoring rule typically differs from the expected score that would be achieved if there were no observation error. The error-corrected score, on the other hand, has the same expectation.
 

docs/Users_Guide/refs.rst

@@ -21,13 +21,12 @@ References
 .. _Andersen-1996:
 
 | Anderson JL., 1996: A method for producing and evaluating probabilistic forecasts
-|   from ensemble model integrations. *J. Clim.* 9: 1518–1530.
+|   from ensemble model integrations. *J. Clim.* 9: 1518-1530.
 |   doi: `https://doi.org/10.1175/1520-0442(1996)009<1518:AMFPAE>2.0.CO;2 <https://doi.org/10.1175/1520-0442(1996)009\<1518:AMFPAE\>2.0.CO;2>`_
 |
 
 .. _Barker-1991:
 
-
 | Barker, T. W., 1991: The relationship between spread and forecast error in
 |   extended-range forecasts. *Journal of Climate*, 4, 733-742.
 |
@@ -37,14 +36,14 @@ References
 | Bradley, A.A., S.S. Schwartz, and T. Hashino, 2008: Sampling Uncertainty
 |   and Confidence Intervals for the Brier Score and Brier Skill Score.
 |   *Weather and Forecasting*, 23, 992-1006.
-| 
+|
 
 .. _Brill-2009:
 
 | Brill, K. F., and F. Mesinger, 2009: Applying a general analytic method
 |   for assessing bias sensitivity to bias-adjusted threat and equitable
 |   threat scores. *Weather and Forecasting*, 24, 1748-1754.
-| 
+|
 
 .. _Brown-2007:
 
@@ -60,7 +59,7 @@ References
 .. _Bröcker-2007:
 
 | Bröcker J, Smith LA., 2007: Scoring probabilistic forecasts: The importance
-|   of being proper. *Weather Forecasting*, 22, 382–388.
+|   of being proper. *Weather Forecasting*, 22, 382-388.
 |   doi: https://doi.org/10.1175/WAF966.1
 |
 
@@ -69,13 +68,13 @@ References
 | Buizza, R., 1997: Potential forecast skill of ensemble prediction and spread
 |   and skill distributions of the ECMWF ensemble prediction system. *Monthly*
 |   *Weather Review*, 125, 99-119.
-| 
+|
 
 .. _Bullock-2016:
 
 | Bullock, R., T. Fowler, and B. Brown, 2016: Method for Object-Based
 |   Diagnostic Evaluation. *NCAR Technical Note* NCAR/TN-532+STR, 66 pp.
-| 
+|
 
 .. _Candille-2007:
 
@@ -90,14 +89,14 @@ References
 | Candille, G., and O. Talagrand, 2008: Impact of observational error on the
 |   validation of ensemble prediction systems. *Quarterly Journal of the Royal*
 |   *Meteorological Society* 134: 959-971.
-| 
+|
 
 .. _Casati-2004:
 
 | Casati, B., G. Ross, and D. Stephenson, 2004: A new intensity-scale approach
 |   for the verification of spatial precipitation forecasts. *Meteorological*
 |   *Applications* 11, 141-154.
-| 
+|
 
 .. _Davis-2006:
 
@@ -109,19 +108,19 @@ References
 | Davis, C.A., B.G. Brown, and R.G. Bullock, 2006b: Object-based verification
 |   of precipitation forecasts, Part II: Application to convective rain systems.
 |   *Monthly Weather Review*, 134, 1785-1795.
-| 
+|
 
 .. _Dawid-1984:
 
 | Dawid, A.P., 1984: Statistical theory: The prequential approach. *Journal of*
 |   *the Royal Statistical Society* A147, 278-292.
-| 
+|
 
 .. _Ebert-2008:
 
 | Ebert, E.E., 2008: Fuzzy verification of high-resolution gridded forecasts:
 |   a review and proposed framework. *Meteorological Applications*, 15, 51-64.
-| 
+|
 
 .. _Eckel-2012:
 
@@ -146,7 +145,7 @@ References
 .. _Ferro-2017:
 
 | Ferro C. A. T., 2017: Measuring forecast performance in the presence of observation error.
-|   *Q. J. R. Meteorol. Soc.*, 143 (708), 2665−2676.
+|   *Q. J. R. Meteorol. Soc.*, 143 (708), 2665-2676.
 |   doi: https://doi.org/10.1002/qj.3115
 |
 
@@ -195,7 +194,7 @@ References
 |   *Minimum CRPS Estimation*. Technical Report no. 449, Department of
 |   Statistics, University of Washington. Available at
 |   http://www.stat.washington.edu/www/research/reports/
-| 
+|
 
 .. _Haiden-2012:
 
@@ -209,33 +208,33 @@ References
 
 | Hamill, T. M., 2001: Interpretation of rank histograms for verifying ensemble
 |   forecasts. *Monthly Weather Review*, 129, 550-560.
-| 
+|
 
 .. _Hersbach-2000:
 
 | Hersbach, H., 2000: Decomposition of the Continuous Ranked Probability Score
 | for Ensemble Prediction Systems. *Weather and Forecasting*, 15, 559-570.
-| 
+|
 
 .. _Jolliffe-2012:
 
 | Jolliffe, I.T., and D.B. Stephenson, 2012: *Forecast verification. A*
 |   *practitioner's guide in atmospheric science.* Wiley and Sons Ltd, 240 pp.
-| 
+|
 
 .. _Knaff-2003:
 
 | Knaff, J.A., M. DeMaria, C.R. Sampson, and J.M. Gross, 2003: Statistical,
 |   Five-Day Tropical Cyclone Intensity Forecasts Derived from Climatology
 |   and Persistence. *Weather and Forecasting*, Vol. 18 Issue 2, p. 80-92.
-| 
+|
 
 .. _Mason-2004:
 
 | Mason, S. J., 2004: On Using "Climatology" as a Reference Strategy
 |   in the Brier and Ranked Probability Skill Scores. *Monthly Weather Review*,
 |   132, 1891-1895.
-| 
+|
 
 .. _Mason-2008:
 
@@ -244,7 +243,6 @@ References
 |   doi: https://doi.org/10.1002/met.51
 |
 
-
 .. _Mittermaier-2014:
 
 | Mittermaier, M., 2014: A strategy for verifying near-convection-resolving
@@ -255,7 +253,7 @@ References
 
 | Mood, A. M., F. A. Graybill and D. C. Boes, 1974: *Introduction to the*
 |   *Theory of Statistics*, McGraw-Hill, 299-338.
-| 
+|
 
 .. _Murphy-1969:
 
@@ -268,7 +266,7 @@ References
 
 | Murphy, A.H., and R.L. Winkler, 1987: A general framework for forecast
 |   verification. *Monthly Weather Review*, 115, 1330-1338.
-| 
+|
 
 .. _North-2022:
 
@@ -290,7 +288,7 @@ References
 | Roberts, N.M., and H.W. Lean, 2008: Scale-selective verification of rainfall
 |   accumulations from high-resolution forecasts of convective events.
 |   *Monthly Weather Review*, 136, 78-97.
-| 
+|
 
 .. _Rodwell-2010:
 
@@ -326,7 +324,7 @@ References
 | Santos C. and A. Ghelli, 2012: Observational probability method to assess
 |   ensemble precipitation forecasts. *Quarterly Journal of the Royal*
 |   *Meteorological Society* 138: 209-221.
-| 
+|
 
 .. _Schwartz-2017:
 
@@ -339,16 +337,16 @@ References
 
 | Stephenson, D.B., 2000: Use of the "Odds Ratio" for diagnosing
 |   forecast skill. *Weather and Forecasting*, 15, 221-232.
-| 
+|
 
 .. _Stephenson-2008:
 
 | Stephenson, D.B., B. Casati, C.A.T. Ferro, and C.A. Wilson, 2008: The extreme
 |   dependency score: A non-vanishing measure for forecasts of rare events.
 |   *Meteorological Applications* 15, 41-50.
-| 
+|
 
-.. _Todter-2012:
+.. _Tödter-2012:
 
 | Tödter, J. and B. Ahrens, 2012: Generalization of the Ignorance Score:
 |   Continuous ranked version and its decomposition. *Monthly Weather Review*,
@@ -361,18 +359,18 @@ References
 | Weniger, M., F. Kapp, and P. Friederichs, 2016: Spatial Verification Using
 |   Wavelet Transforms: A Review. *Quarterly Journal of the Royal*
 |   *Meteorological Society*, 143, 120-136.
-| 
+|
 
 .. _Wilks-2010:
 
 | Wilks, D.S. 2010: Sampling distributions of the Brier score and Brier skill
 |   score under serial dependence. *Quarterly Journal of the Royal*
 |   *Meteorological Society*, 136, 2109-2118.
 |   doi: https://doi.org/10.1002/qj.709
-| 
+|
 
 .. _Wilks-2011:
 
 | Wilks, D., 2011: *Statistical methods in the atmospheric sciences.*
 |   Elsevier, San Diego.
-| 
+|