From 58cb282c7a273093f01e93f5bfd50e4e11e1c8ed Mon Sep 17 00:00:00 2001
From: Tracy <tracy.hertneky@noaa.gov>
Date: Thu, 26 Oct 2023 14:27:49 -0600
Subject: [PATCH] move algorithm documentation out and instead include links

---
 .../UserScript_fcstGEFS_Difficulty_Index.py   | 32 +++----------------
 1 file changed, 4 insertions(+), 28 deletions(-)

diff --git a/docs/use_cases/model_applications/medium_range/UserScript_fcstGEFS_Difficulty_Index.py b/docs/use_cases/model_applications/medium_range/UserScript_fcstGEFS_Difficulty_Index.py
index 7e30de35d6..653081aaa5 100644
--- a/docs/use_cases/model_applications/medium_range/UserScript_fcstGEFS_Difficulty_Index.py
+++ b/docs/use_cases/model_applications/medium_range/UserScript_fcstGEFS_Difficulty_Index.py
@@ -32,8 +32,10 @@
 # error, which adds uncertainty in a similar way to ensemble spread.) The challenge is combining 
 # these factors into a continuous function that allows the user to assess relative risk.
 #
-# Additional details on the computation of the Difficulty Index can be found in the Python
-# Embedding section.
+# Additional details on the computation of the Difficulty Index can be found in the `METcalcpy 
+# documentation<https://metcalcpy.readthedocs.io/en/latest/Users_Guide/difficulty_index.html>`_ 
+# and more information on plotting difficulty index can be found in the `METplotpy documentation
+# <https://metplotpy.readthedocs.io/en/latest/Users_Guide/difficulty_index.html>`_.
 
 ##############################################################################
 # Datasets
@@ -115,32 +117,6 @@
 # .. highlight:: python
 # .. literalinclude:: ../../../../parm/use_cases/model_applications/medium_range/UserScript_fcstGEFS_Difficulty_Index/wind_difficulty_index.py
 #
-# Consider the following formulation of a forecast decision difficulty index:
-#
-# .. math :: \text{d_{i,j}} = \frac{A(\bar{x}_{i,j})}{2}(\frac{(sigma/\bar{x})_{i,j}{(sigma/\bar{x})_{ref}}}+[1-\frac{1}{2}|P(x_{i,j}\geq\text{thresh})-P(x_{i,j}<thresh)|])
-#
-# where :math:`\sigma` is the ensemble standard deviation, :math:`\bar{x}` is the ensemble mean, 
-# :math:`P(x_{i,j}\geq thresh)` is the ensemble (sample) probability of being greater than or equal 
-# to the threshold, and  :math:`P(x_{i,j}<thresh)` is the ensemble probability of being less than 
-# the threshold. The :math:`(\sigma/\bar{x})` expression is a measure of spread normalized by the 
-# mean, and it allows one to identify situations of truly significant uncertainty. Because the 
-# difficulty index is defined only for positive definite quantities such as significant wave height, 
-# division by zero is avoided. :math:`(\sigma/\bar{x})_{ref}` is a (scalar) reference value, for 
-# example the maximum value of :math:`(\sigma/\bar{x})` obtained over the last 5 days as a function 
-# of geographic region.
-#
-# The first term in the outer brackets is large when the uncertainty in the current forecast is 
-# large relative to a reference. The second term is minimum when all the probability is either 
-# above or below the threshold, and maximum when the probability is evenly distributed about the 
-# threshold. So it penalizes the split case, where the ensemble members are close to evenly split on 
-# either side of the threshold. The A term outside the brackets is a weighting to account for 
-# heuristic forecast difficulty situations. Its values for winds are given below.
-#
-# .. math :: A = 0 if \bar{x} is above 50kt
-# .. math :: A = 0 if \bar{x} is below 5kt
-# .. math :: A = 1.5 if \bar{x} is between 28kt and 34kt
-# .. math :: \text{A} = 1.5 - 1.5[\frac{\bar{x}(kt)-34kt}{16kt}] for 34kt\leq\bar{x}\leq 50kt
-# .. math :: \text{A} = 1.5[\frac{\bar{x}(kt)-5kt}{23kt}] for 5kt\leq\bar{x}\leq 28kt
 
 ##############################################################################
 # Running METplus