Abstract
Eleven coupled model intercomparison project 3 based global climate models are evaluated for the case study of Upper Malaprabha catchment, India for precipitation rate. Correlation coefficient, normalised root mean square deviation, and skill score are considered as performance indicators for evaluation in fuzzy environment and assumed to have equal impact on the global climate models. Fuzzy technique for order preference by similarity to an ideal solution is used to rank global climate models. Top three positions are occupied by MIROC3, GFDL2.1 and GISS with relative closeness of 0.7867, 0.7070, and 0.7068. IPSL-CM4, NCAR-PCMI occupied the tenth and eleventh positions with relative closeness of 0.4959 and 0.4562.
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Present research work is supported by Council of Scientific and Industrial Research, New Delhi vide project number 23(0023)/12/EMR-II dated 15.10.2012.
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Appendix
Appendix
1.1 Sample Calculation for Computation Of D + i , D − i , C i
Chosen global climate model: GISS
Values of indicators in triangular membership environment:
Correlation coefficient (CC) = (0.670, 0.828, 0.985)
Normalised root mean square deviation (NRMSD) = (0.436, 0.534, 0.687)
Skill Score (SS) = (0.704, 0.778, 0.853)
Ideal values of indicators = (1, 1, 1)
Anti-ideal values of indicators = (0, 0, 0)
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(i)
Separation measure of GISS from ideal solution (Eq. 1):
\(D_{GISS}^{+} = \sqrt {\frac{{\left[(p_{ij} - p_{j}^{*} )^{2} + (q_{ij} - q_{j}^{*} )^{2} + (r_{ij} - r_{j}^{*} )^{2} \right]}}{3}} \) = \( \sqrt {\frac{{[(0.670 - 1)^{2} + (0.828 - 1)^{2} + (0.985 - 1)^{2} ]}}{3}} \) for correlation coefficient + \( \sqrt {\frac{{[(0.436 - 1)^{2} + (0.534 - 1)^{2} + (0.687 - 1)^{2} ]}}{3}} \) for normalised root mean square deviation + \( \sqrt {\frac{{[(0.704 - 1)^{2} + (0.778 - 1)^{2} + (0.853 - 1)^{2} ]}}{3}} \) for skill score
= 0.2150 + 0.4594 + 0.2299 = 0.9043
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(ii)
Separation measure of GISS from anti-ideal solution (Eq. 2):
\(D_{Giss}^{-} = \sqrt {\frac{{\left[(p_{ij} - p_{j}^{**} )^{2} + (q_{ij} - q_{j}^{**} )^{2} + (r_{ij} - r_{j}^{**} )^{2} \right]}}{3}} \) = \( \sqrt {\frac{{[(0.670 - 0)^{2} + (0.828 - 0)^{2} + (0.985 - 0)^{2} ]}}{3}} \) for correlation coefficient + \( \sqrt {\frac{{[(0.436 - 0)^{2} + (0.534 - 0)^{2} + (0.687 - 0)^{2} ]}}{3}} \) for normalised root mean square deviation + \( \sqrt {\frac{{[(0.704 - 0)^{2} + (0.778 - 0)^{2} + (0.853 - 0)^{2} ]}}{3}} \) for skill score
= 0.8376 + 0.5619 + 0.7807 = 2.1802
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(iii)
Relative closeness of GISS with reference to anti-ideal measure (Eq. 3):
\( C_{GISS} = \frac{{D_{GISS}^{ - } }}{{(D_{GISS}^{ - } + D_{GISS}^{ + } )}} \) = \( \frac{2.1802}{(2.1802 + 0.9043)} \) = 0.7068
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Srinivasa Raju, K., Nagesh Kumar, D. (2015). Fuzzy Approach to Rank Global Climate Models. In: Ravi, V., Panigrahi, B., Das, S., Suganthan, P. (eds) Proceedings of the Fifth International Conference on Fuzzy and Neuro Computing (FANCCO - 2015). Advances in Intelligent Systems and Computing, vol 415. Springer, Cham. https://doi.org/10.1007/978-3-319-27212-2_5
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