Assessing precipitation elasticity of streamflow based on the strength of the precipitation-streamflow relationship

Water resource management increasingly seeks to incorporate the impacts of global climate change in the planning of future water supplies. Studies across numerous regions have documented the sensitivity of streamflow to climate change using the precipitation elasticity of streamflow, defined as the proportional change in streamflow to a change in precipitation. This study shows that calculating precipitation elasticity of streamflow without first assessing the strength of the precipitation-streamflow relationship can produce misleading and unrealistic results. For example, the Spokane river basin precipitation elasticity of streamflow is 0.90 by using annual precipitation and streamflow accumulated on a January-December calendar year basis. This indicates that a 10% change in annual precipitation would produce an annual streamflow change of 9.0%. However, using water year (Oct-Sep, in this case) precipitation and streamflow data gives an elasticity of 1.65, indicating a 10% change in annual precipitation would result in a 16.5% change in annual streamflow. Further analysis shows that the water year data has a much stronger precipitation-streamflow relationship (R 2 =0.72) compared with the calendar year data (R 2 =0.23). From this we infer that the precipitation elasticity of streamflow should be calculated using the seasonality that produces the strongest precipitation-streamflow relationship, as the precipitation elasticity of streamflow is sensitive to the strength of the precipitation-streamflow relationship. A useful practice is to use water year data series - with annual cycles starting from the beginning of the dry season or from just before the snowmelt period. The results of the temporal variations of precipitation elasticity of streamflow for 30 and 50 year blocks indicate that 50-yr-block time series generate less temporal variation, as expected given the longer time period used. These results have implications for the use of elasticity as a rule of thumb under changing climate and climate change and variability impact studies. It can be argued that it is better to use as long a record as possible to estimate elasticity as this captures the range of observed variability. However, with potential climate change and variability, there may be good reason to use only the most recent record (e.g., the most recent 30-50 years) to estimate the elasticity, or use dry or wet periods that are similar to future projections to quantify the climatic change impacts on streamflow. The relationships between the elasticity values and annual rainfall, annual streamflow, and the runoff coefficient (ratio of annual streamflow to annual precipitation) for the Murray-Darling Basin indicate that the elasticity values are generally negatively correlated to these streamflow and runoff coefficient , i.e., a low flow period in general results in a larger elasticity value. Moreover, the relationship between elasticity and the runoff coefficient is stronger than that between elasticity and rainfall, with correlation coefficients of - 0.423 and 0.089 respectively. The relationship between elasticity and streamflow is in-between at -0.260. This implies that annual rainfall is not the only driving force causing larger elasticities in recent years. These research results can be used to guide the application of elasticity methods to quantify hydrological responses to climatic change that inform long-term water management strategies.