The Burak diagrams: a family of 3D diagrams for evaluation of climatological and hydrological simulations
Stochastic Environmental Research and Risk Assessment, cilt.40, sa.11, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 40 Sayı: 11
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s00477-026-03366-0
- Dergi Adı: Stochastic Environmental Research and Risk Assessment
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, Environment Index, Geobase, Index Islamicus, zbMATH, Academic Search Ultimate (EBSCO), Natural Science Collection (ProQuest), Engineering Source (EBSCO), Materials Science & Engineering Collection (ProQuest), Pharma Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Bias, Climatological and hydrological model evaluation, Taylor diagram
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
This study introduces the Burak Diagrams by incorporating an orthogonal bias axis into the Taylor Diagram (Taylor 2001), thereby enabling multiple performance metrics to be represented as analytically derived 3D surfaces. Three Burak Diagrams are developed: BD-Clim for climatological simulations, BD-HydNSE for hydrological simulations incorporating the Nash–Sutcliffe Efficiency, and BD-HydKGE for hydrological simulations incorporating the Kling–Gupta Efficiency. All three diagrams share a common theoretical foundation based on the geometric decomposition of the root-mean-square difference (or) proposed by Taylor (2001). BD-Clim extends the Taylor Diagram by incorporating bias () as a third axis while preserving the original representation of correlation (), variability, and centered root-mean-square difference (), with (or) represented as analytic surfaces. Similarly, BD-HydNSE and BD-HydKGE incorporate percent bias () as a third axis while preserving the original Taylor Diagram representation, with and represented as analytic surfaces for evaluating hydrological model performance. Interactive visualization tools for all three diagrams are developed in the R programming environment and are available on CRAN as the “burakDiagrams” package. Together, the proposed diagrams support the simultaneous interpretation of complementary performance metrics, improve insight into model behaviour, and facilitate more comprehensive intercomparison of climatological and hydrological simulations. By representing,, and as surfaces, the diagrams visually reveal how these metrics vary in response to changes in their underlying component metrics.