<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:contributor>Gregory J. McCabe</dc:contributor>
  <dc:creator>David R. Legates</dc:creator>
  <dc:date>2013</dc:date>
  <dc:description>&lt;p&gt;Willmott&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;et al.&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;[Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance.&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;International Journal of Climatology&lt;/i&gt;, forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance (&lt;i&gt;d&lt;/i&gt;&lt;sub&gt;&lt;i&gt;r&lt;/i&gt;&lt;/sub&gt;) that they purport to be superior to other methods. Their refined index ranges from − 1.0 to 1.0 to resemble a correlation coefficient, but it is merely a linear rescaling of our modified coefficient of efficiency (&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;) over the positive portion of the domain of&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;d&lt;/i&gt;&lt;sub&gt;&lt;i&gt;r&lt;/i&gt;&lt;/sub&gt;. We disagree with Willmott&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;et al.&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;(&lt;a class="link__reference js-link__reference" title="Link to bibliographic citation" rel="references:#bib8" href="http://onlinelibrary.wiley.com/doi/10.1002/joc.3487/abstract#bib8" data-mce-href="http://onlinelibrary.wiley.com/doi/10.1002/joc.3487/abstract#bib8"&gt;2012&lt;/a&gt;) that&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;d&lt;/i&gt;&lt;sub&gt;&lt;i&gt;r&lt;/i&gt;&lt;/sub&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;provides a better interpretation; rather,&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;is more easily interpreted such that a value of&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;= 1.0 indicates a perfect model (no errors) while&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;= 0.0 indicates a model that is no better than the baseline comparison (usually the observed mean). Negative values of&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;(and, for that matter,&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;d&lt;/i&gt;&lt;sub&gt;&lt;i&gt;r&lt;/i&gt;&lt;/sub&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&amp;lt; 0.5) indicate a substantially flawed model as they simply describe a ‘level of inefficacy’ for a model that is worse than the comparison baseline. Moreover, while&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;d&lt;/i&gt;&lt;sub&gt;&lt;i&gt;r&lt;/i&gt;&lt;/sub&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;is piecewise continuous, it is not continuous through the second and higher derivatives. We explain why the coefficient of efficiency (&lt;i&gt;E&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;or&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;) and its modified form (&lt;i&gt;E&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;) are superior and preferable to many other statistics, including&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;d&lt;/i&gt;&lt;sub&gt;&lt;i&gt;r&lt;/i&gt;&lt;/sub&gt;, because of intuitive interpretability and because these indices have a fundamental meaning at zero.&lt;/p&gt;&lt;p&gt;We also expand on the discussion begun by Garrick&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;et al.&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;[Garrick M, Cunnane C, Nash JE. 1978. A criterion of efficiency for rainfall-runoff models.&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;Journal of Hydrology&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;strong&gt;36&lt;/strong&gt;: 375-381.] and continued by Legates and McCabe [Legates DR, McCabe GJ. 1999. Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation.&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;Water Resources Research&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;strong&gt;35&lt;/strong&gt;(1): 233-241.] and Schaefli and Gupta [Schaefli B, Gupta HV. 2007. Do Nash values have value?&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;Hydrological Processes&lt;/i&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;strong&gt;21&lt;/strong&gt;: 2075-2080. DOI: 10.1002/hyp.6825.]. This important discussion focuses on the appropriate baseline comparison to use, and why the observed mean often may be an inadequate choice for model evaluation and development.&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;</dc:description>
  <dc:format>application/pdf</dc:format>
  <dc:identifier>10.1002/joc.3487</dc:identifier>
  <dc:language>en</dc:language>
  <dc:publisher>Royal Meteorological Society</dc:publisher>
  <dc:title>A refined index of model performance: a rejoinder</dc:title>
  <dc:type>article</dc:type>
</oai_dc:dc>