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The reliability of stream flow projection under changing climate cannot be guaranteed if the General Circulation Model (GCM) used for the projection of future climate does not predict well its past climate. In this study stream flows in the Wami River sub-basin were simulated under changing climate by the skilled and non-linear bias corrected GCM using a physically based and semi distributed rainfall runoff model, SWAT. The SWAT model was setup using the terrain, land use, soil, precipitation and temperature data. The baseline water uses were used to naturalise stream flows and the SWAT model was calibrated and validated using the historical stream flows. In addressing future runoff projections the domestic, livestock, irrigation and industrial water demands in the sub-basin were projected to the year 2039 using the current irrigation area growth rates, Tanzania vision 2025 and development plans for the Wami River sub-basin. The GCMs were incorporated in the hydrological model so as to factor in the effects of climate change. Precipitation was selected as the changing climatic variable for projection because runoff is very sensitive to precipitation as compared to other climatic variables like temperature. A total of twenty four GCMs from CMIP3 database representing twentieth century precipitation were interpolated into forty five sub-catchments in the sub-basin and evaluated for their skills. The HADCM3 model was selected due to its highest skill score in predicting past climate. Then the HADCM3 precipitation signal of scenario A2, was corrected by Non-linear Bias Correction (NBC) in the forty five sub-catchments in the sub-basin and used to simulate future stream flow. The results of stream flow simulated using skilled and non-linear corrected HADCM3 precipitation signal shows that stream flow is projected to increase for the near term climatology (2010 – 2039).