Univariate drought indicators are insufficient for characterizing the complicated effects and conditions of droughts. Accordingly, this study aimed to introduce and assess a composite drought index called the Integrated Drought Index (IDI), composed of the most important water balance variables including, temperature, precipitation, streamflow, and soil moisture to simultaneously monitor hydrological, agricultural, and meteorological drought. To this end, four widely used linear and non-linear combination approaches—namely the kernel mean component analysis (KMCA), copula function (CF), entropy weighting (EW), and the principal component analysis (PCA)—were used here, whose products are called IDI-KMCA, IDI-CF, IDI-EW, and IDI-PCA, respectively. The research data were extracted from ERA5 (ECMWF Reanalysis v5) datasets on a monthly scale for the 1979–2020 period. According to the findings, all proposed composite indices exhibited a mostly similar variation pattern as the individual indices and performed well in monitoring drought conditions—except for IDI-CF, which slightly deviated from the pattern during the 1989–1990 period. High values of the index of agreement (with the average values ranging between 0.5 and 0.9) and correlation coefficient (with the average values ranging between 0.7 and 0.9) also suggested a good agreement among the proposed composite indices. Since climate and hydrologic conditions in the region were not complex, they evaluated the same drought conditions through linear and non-linear approaches. In addition, Frank functions were selected to derive the joint distribution functions of drought characteristics for bi-variate and tri-variate functions. Finally, considering the spatial distribution of the drought return period, the probability of mild droughts remained the same under bi-variate and tri-variate conditions, whereas the occurrence probability of extreme drought changed (increasing and decreasing in the case of "and" and "or").
