Abstract 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 ( β ) 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 ( e p ), potential evapotranspiration ( e ET p ), temperature ( e T ) and the total elasticity ( e 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, ( β 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, ( β > 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, ( β > 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.

中文翻译：

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尼罗河流域径流对气候变化的敏感性

摘要 在数据稀缺的流域，例如非洲的尼罗河流域 (NRB)，与数据可用性、质量和访问相关的限制常常使使用传统方法估计径流敏感性的尝试复杂化。在本文中，我们表明，通过整合干旱指数 (AI)（源自 Budyko 曲线）和气候弹性的概念，我们可以使用最少的数据输入和建模专业知识或经验获得径流敏感性的一阶响应。径流弹性的概念依赖于这样一个事实，即可用于蒸发蒸腾的能量在确定流域内接收的降水是否产生径流方面起着重要作用。该方法没有考虑人类对径流修改和/或改道的影响。通过利用免费可用的降水、温度、径流和潜在蒸散量校正卫星数据，我们推导出了灵敏度指标 (β) 来确定 NRB 四个气候带的径流对降水和温度变化的响应，即、热带、亚热带、半干旱和干旱区。建议的敏感性指标可以划分为不同的弹性分量，即：降水量 (ep)、潜在蒸散量 (e ET p )、温度 (e T ) 和总弹性 (e tot )。这些弹性允许高度准确地对径流对降水和温度的潜在变化的响应进行可靠的量化。结果表明，热带地区能量受限，灵敏度低， ( β 1.0 ) ，这意味着输入降水超过了在可用能量的情况下可以蒸发的量。亚热带分为两个不同的区域，低地（马查尔和苏德沼泽）和高地（青尼罗河流域），每个区域都有独特的敏感性。低地地区灵敏度高，(β>1.0)。亚热带高地地区在不同敏感度的干湿期期间在能量受限到水受限的条件之间移动。半干旱区和干旱区缺水，灵敏度高，(β > 1.0)。计算出的径流弹性表明，降水减少 10% 会导致热带地区径流减少 19%，干旱地区减少 30%。另一方面，降水增加 10% 会导致热带地区径流增加 14%，干旱地区增加 22%。估计的径流变化与使用其他方法获得的结果一致。因此，弹性方法结合了数据简洁性和分析简单性，以产生对大多数目的实际有用的结果，同时促进与具有不同科学知识水平的利益相关者的沟通。需要更多的研究来扩展该方法的应用，以纳入人类活动和土地利用变化的影响。弹性方法结合了数据的简洁性和分析的简单性，以产生对大多数目的实用的结果，同时促进与具有不同科学知识水平的利益攸关方的交流。需要更多的研究来扩展该方法的应用，以纳入人类活动和土地利用变化的影响。弹性方法结合了数据的简洁性和分析的简单性，以产生对大多数目的实用的结果，同时促进与具有不同科学知识水平的利益攸关方的交流。需要更多的研究来扩展该方法的应用，以纳入人类活动和土地利用变化的影响。