Drought is a recurrent extreme climate event with tremendous hazard for every specter of natural environment and human lives. Drought analysis usually involves characterizing drought severity, duration and intensity. Similar to most of the hydrological problems, such characteristic variables are usually not independent. Copula, as a model of multivariate distribution, widely used in finance, actuarial analysis, has won increasingly popularity in hydrological study. Here, the study has two major focuses: (1) fit drought characteristics from Streamflow Drought Index (SDI) or Standardized Runoff Index (SRI) to appropriate copulas, then using fitted copulas to estimate conditional drought severity distribution and joint return periods for both historical time period 1920-2009 and future time period 2020-2090. SDI is calculated based on long term observed streamflow while SRI is based on simulated future runoff. Parameters estimation of marginal distribution and copulas are provided, with goodness fit measures as well; (2) investigate the effects of climate change on the frequency and severity of droughts. In order to quantify the impact, three drought indices have been proposed for this study to characterize the drought duration, severity and intensity changes under the climate change in Upper Klamath River Basin. Since drought can be defined as different types, such as meteorological drought, agricultural drought, hydrological drought and social economical drought, this study chooses Standardized Precipitation Index (SPI), Palmer Drought Severity Index (PDSI) and Surface Water Supply Index (SWSI) to estimate the meteorological, agricultural and hydrological drought, respectively. Climate change effects come from three sources: the inherent reason, the human activity and the GCMs uncertainties. Therefore, the results show the long term drought condition by calculating yearly drought indices, and compared in three ways: First, compare drought characteristics of future time periods with base period; second, show the uncertainties of three greenhouse gas emission scenarios; third, present the uncertainties of six General Circulation Models (GCMs).