A refined index of model performance: a rejoinder
Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology, forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance (dr) that they purport to be superior to other methods. Their refined inde...
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| Vydáno v: | International journal of climatology Ročník 33; číslo 4; s. 1053 - 1056 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Chichester, UK
John Wiley & Sons, Ltd
30.03.2013
Wiley Wiley Subscription Services, Inc |
| Témata: | |
| ISSN: | 0899-8418, 1097-0088 |
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| Abstract | Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology, forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance (dr) 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 (E1) over the positive portion of the domain of dr. We disagree with Willmott et al. (2012) that dr provides a better interpretation; rather, E1 is more easily interpreted such that a value of E1 = 1.0 indicates a perfect model (no errors) while E1 = 0.0 indicates a model that is no better than the baseline comparison (usually the observed mean). Negative values of E1 (and, for that matter, dr < 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 dr is piecewise continuous, it is not continuous through the second and higher derivatives. We explain why the coefficient of efficiency (E or E2) and its modified form (E1) are superior and preferable to many other statistics, including dr, because of intuitive interpretability and because these indices have a fundamental meaning at zero.
We also expand on the discussion begun by Garrick et al. [Garrick M, Cunnane C, Nash JE. 1978. A criterion of efficiency for rainfall‐runoff models. Journal of Hydrology 36: 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. Water Resources Research 35(1): 233‐241.] and Schaefli and Gupta [Schaefli B, Gupta HV. 2007. Do Nash values have value? Hydrological Processes 21: 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. Copyright © 2012 Royal Meteorological Society |
|---|---|
| AbstractList | Willmott
et al.
[Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance.
International Journal of Climatology
, forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance (
d
r
) 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 (
E
1
) over the positive portion of the domain of
d
r
. We disagree with Willmott
et al.
(
2012
) that
d
r
provides a better interpretation; rather,
E
1
is more easily interpreted such that a value of
E
1
= 1.0 indicates a perfect model (no errors) while
E
1
= 0.0 indicates a model that is no better than the baseline comparison (usually the observed mean). Negative values of
E
1
(and, for that matter,
d
r
< 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
d
r
is piecewise continuous, it is not continuous through the second and higher derivatives. We explain why the coefficient of efficiency (
E
or
E
2
) and its modified form (
E
1
) are superior and preferable to many other statistics, including
d
r
, because of intuitive interpretability and because these indices have a fundamental meaning at zero.
We also expand on the discussion begun by Garrick
et al.
[Garrick M, Cunnane C, Nash JE. 1978. A criterion of efficiency for rainfall‐runoff models.
Journal of Hydrology
36
: 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.
Water Resources Research
35
(1): 233‐241.] and Schaefli and Gupta [Schaefli B, Gupta HV. 2007. Do Nash values have value?
Hydrological Processes
21
: 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. Copyright © 2012 Royal Meteorological Society Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology, forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance (dr) 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 (E1) over the positive portion of the domain of dr. We disagree with Willmott et al. (2012) that dr provides a better interpretation; rather, E1 is more easily interpreted such that a value of E1 = 1.0 indicates a perfect model (no errors) while E1 = 0.0 indicates a model that is no better than the baseline comparison (usually the observed mean). Negative values of E1 (and, for that matter, dr < 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 dr is piecewise continuous, it is not continuous through the second and higher derivatives. We explain why the coefficient of efficiency (E or E2) and its modified form (E1) are superior and preferable to many other statistics, including dr, because of intuitive interpretability and because these indices have a fundamental meaning at zero. We also expand on the discussion begun by Garrick et al. [Garrick M, Cunnane C, Nash JE. 1978. A criterion of efficiency for rainfall-runoff models. Journal of Hydrology 36: 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. Water Resources Research 35(1): 233-241.] and Schaefli and Gupta [Schaefli B, Gupta HV. 2007. Do Nash values have value? Hydrological Processes 21: 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. Copyright © 2012 Royal Meteorological Society [PUBLICATION ABSTRACT] Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology, forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance (dr) 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 (E1) over the positive portion of the domain of dr. We disagree with Willmott et al. (2012) that dr provides a better interpretation; rather, E1 is more easily interpreted such that a value of E1 = 1.0 indicates a perfect model (no errors) while E1 = 0.0 indicates a model that is no better than the baseline comparison (usually the observed mean). Negative values of E1 (and, for that matter, dr < 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 dr is piecewise continuous, it is not continuous through the second and higher derivatives. We explain why the coefficient of efficiency (E or E2) and its modified form (E1) are superior and preferable to many other statistics, including dr, because of intuitive interpretability and because these indices have a fundamental meaning at zero. We also expand on the discussion begun by Garrick et al. [Garrick M, Cunnane C, Nash JE. 1978. A criterion of efficiency for rainfall‐runoff models. Journal of Hydrology 36: 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. Water Resources Research 35(1): 233‐241.] and Schaefli and Gupta [Schaefli B, Gupta HV. 2007. Do Nash values have value? Hydrological Processes 21: 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. Copyright © 2012 Royal Meteorological Society Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology, forthcoming. DOI:10.1002/joc.2419.] recently suggest a refined index of model performance (d sub(r)) 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 (E sub(1)) over the positive portion of the domain of d sub(r). We disagree with Willmott et al. (2012) that d sub(r) provides a better interpretation; rather, E sub(1) is more easily interpreted such that a value of E sub(1) = 1.0 indicates a perfect model (no errors) while E sub(1) = 0.0 indicates a model that is no better than the baseline comparison (usually the observed mean). Negative values of E sub(1) (and, for that matter, d sub(r) < 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 d sub(r) is piecewise continuous, it is not continuous through the second and higher derivatives. We explain why the coefficient of efficiency (E or E sub(2)) and its modified form (E sub(1)) are superior and preferable to many other statistics, including d sub(r), because of intuitive interpretability and because these indices have a fundamental meaning at zero. We also expand on the discussion begun by Garrick et al. [Garrick M, Cunnane C, Nash JE. 1978. A criterion of efficiency for rainfall-runoff models. Journal of Hydrology 36: 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. Water Resources Research 35(1): 233-241.] and Schaefli and Gupta [Schaefli B, Gupta HV. 2007. Do Nash values have value? Hydrological Processes 21: 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. |
| Author | Legates, David R. McCabe, Gregory J. |
| Author_xml | – sequence: 1 givenname: David R. surname: Legates fullname: Legates, David R. email: legates@udel.edu. – sequence: 2 givenname: Gregory J. surname: McCabe fullname: McCabe, Gregory J. |
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| Cites_doi | 10.1002/hyp.6825 10.3354/cr030079 10.1029/JC090iC05p08995 10.1002/joc.2419 10.1016/0022-1694(78)90155-5 10.1029/2005WR004820 10.1029/1998WR900018 10.1016/0022-1694(70)90255-6 |
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| References | 1999; 35 2005; 30 1970; 10 1985; 90 2006; 42 1978; 36 2012 2007; 21 e_1_2_6_9_1 e_1_2_6_8_1 e_1_2_6_5_1 e_1_2_6_4_1 e_1_2_6_7_1 e_1_2_6_6_1 e_1_2_6_3_1 e_1_2_6_2_1 |
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| Snippet | Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology, forthcoming.... Willmott et al. [Willmott CJ, Robeson SM, Matsuura K. 2012. A refined index of model performance. International Journal of Climatology , forthcoming.... |
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| SubjectTerms | accuracy indices coefficient of efficiency Earth, ocean, space Exact sciences and technology External geophysics Geophysics. Techniques, methods, instrumentation and models goodness‐of‐fit Meteorology model evaluation model‐performance statistics Other topics in atmospheric geophysics |
| Title | A refined index of model performance: a rejoinder |
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