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In data scarce basins, such as the Nile River Basin (NRB) in Africa, constraints related to data availability, quality, and access often complicate attempts to estimate runoff sensitivity using conventional methods. In this paper, we show that by integrating the concept of the aridity index (AI) (derived from the Budyko curve) and climate elasticity, we can obtain the first order response of the runoff sensitivity using minimal data input and modeling expertise or experience. The concept of runoff elasticity relies on the fact that the energy available for evapotranspiration plays a major role in determining whether the precipitation received within a drainage basin generates runoff. The approach does not account for human impacts on runoff modification and or diversions. By making use of freely available gauge-corrected satellite data for precipitation, temperature, runoff, and potential evapotranspiration, we derived the sensitivity indicator (beta) to determine the runoff response to changes in precipitation and temperature for four climatic zones in the NRB, namely, tropical, subtropical, semiarid and arid zones. The proposed sensitivity indicator can be partitioned into different elasticity components i.e: precipitation (epsilon(p)), potential evapotranspiration (epsilon(ETp)), temperature (epsilon(T)) and the total elasticity (epsilon(tot)). These elasticities allow robust quantification of the runoff response to the potential changes in precipitation and temperature with a high degree of accuracy. Results indicate that the tropical zone is energy-constrained with low sensitivity, (beta < 1.0), implying that input precipitation exceeds the amounts that can be evaporated given the available energy. The subtropical zone is subdivided into two distinct regions, the lowland (Machar and Sudd marshes), and the highland area (Blue Nile Basin), where each area has a unique sensitivity. The lowland area has high sensitivity, (beta > 1.0). The subtropical-highland zone moves between energy-limited to water-limited conditions during periods of wet and dry spells with varying sensitivity. The semiarid and arid zones are water limited, with high sensitivity, (beta > 1.0). The calculated runoff elasticities show that a 10% decrease in precipitation leads to a decrease in runoff of between 19% in the tropical zone and 30% in the arid zones. On the other hand, a 10% precipitation increase leads to a runoff increase of 14% in the tropical zone and 22% in the arid zone. The estimated runoff changes are consistent with the result obtained using other methods. Thus, the elasticity approach combines data parsimony and analytical simplicity to produce results that are practically useful for most purposes while facilitating communication with stakeholders with different levels of scientific knowledge. More research is needed to extend the application of the method to incorporate the effects of human activities, and land use change.