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Conventional single-variable indices fail to capture the nonlinear, asymmetric dependence between precipitation and temperature\u2014a limitation that is particularly critical in data-scarce, high-mountain catchments, where incomplete drought characterization undermines the reliability of early-warning systems. To address this, we propose a novel vine-copula-based Multivariate Drought Index (VMDI) that integrates the Standardized Precipitation Index (SPI), the Standardized Precipitation Evapotranspiration Index (SPEI), and the Standardized Precipitation Temperature Index (SPTI) within a flexible, station-adaptive dependence-modeling framework. VMDI\u2019s key novelty lies in its station-adaptive canonical vine (C-vine) copula structure in which each index is first transformed into uniform pseudo-observations via rank-based empirical CDFs. Dependence is then decomposed into unconditional (Tree 1) and conditional (Tree 2) pair-copulas with SPTI as the root variable, capturing both direct interactions and joint behavior conditioned on SPTI. Copula families are selected locally via information criteria, and Kendall\u2019s\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{\\tau }$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>\u03c4<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    values derived from the fitted vine structure yield physically consistent, station-specific index weights. Validated across six stations in the Upper Indus Basin (UIB), VMDI substantially outperforms benchmark indices for precipitation-driven drought signals, achieving agreement improvements of 15\n                    <jats:italic>\u2013<\/jats:italic>\n                    30%, MAE reductions exceeding 50%, skill-score gains of 30\n                    <jats:italic>\u2013<\/jats:italic>\n                    40%, F1-score improvements of 33\n                    <jats:italic>\u2013<\/jats:italic>\n                    37%, and lower-tail dependence coefficients above 0.70, while maintaining low conditional entropy (CE\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{&lt;} \\varvec{0.99}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mrow>\n                              <mml:mo>&lt;<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mn>0.99<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    ). For evapotranspiration-related drought conditions, JSDI outperforms VMDI relative to SPEI by about 27\n                    <jats:italic>\u2013<\/jats:italic>\n                    38%, with the greatest improvements observed at the glacier-influenced stations of Bunji and Gilgit. Overall, VMDI and JSDI offer a complementary and operationally robust framework for comprehensive drought monitoring across complex mountain catchments.\n                  <\/jats:p>","DOI":"10.1007\/s11356-026-38256-z","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T13:28:46Z","timestamp":1790861326000},"page":"16359-16379","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A novel multivariate vine-copula\u2013based drought index with application to high-elevation catchments"],"prefix":"10.1007","volume":"33","author":[{"given":"Zanib","family":"Badar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ishfaq","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2046-6268","authenticated-orcid":false,"given":"Touqeer","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ibrahim Mufrah","family":"Almanjahie","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,1]]},"reference":[{"issue":"3","key":"38256_CR1","doi-asserted-by":"publisher","first-page":"e25422","DOI":"10.1016\/j.heliyon.2024.e25422","volume":"10","author":"I Ahmad","year":"2024","unstructured":"Ahmad I, Ahmad T, Rehman SU, Mufrah Almanjahie I, Alshahrani F (2024) A detailed study on quantification and modeling of drought characteristics using different copula families. 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The analysis is based entirely on hydroclimatic observations obtained from national agencies. Therefore, ethical approval was not required for this research.","order":1,"name":"Ethics","label":"Ethical approval","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors agree with the content of the submission, and all agree to continue to support the follow-up work.","order":2,"name":"Ethics","label":"Consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This manuscript has not been submitted to or published in other journals, and all authors consent to its publication.","order":3,"name":"Ethics","label":"Consent for publication","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":4,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}]}}