Abstract
Hydrological time series are sometimes found to have a distinctive behavior known as long-term persistence, in which subsequent values depend on each other even under very large time scales. This implies multiyear consecutive droughts or floods. Typical models used to generate synthetic hydrological scenarios, widely used in the planning and management of water resources, fail to preserve this kind of persistence in the generated data and therefore may have a major impact on projects whose design lives span for long periods of time. This study deals with the evaluation of long-term persistence in streamflow records by means of the rescaled range analysis proposed by British engineer Harold E. Hurst, who first observed the phenomenon in the mid-twentieth century. In this paper, Hurst’s procedure is enhanced by a strategy based on statistical hypothesis testing. The case study comprises the six main hydroelectric power plants located in the São Francisco River Basin, part of the Brazilian National Grid. Historical time series of inflows to the major reservoirs of the system are investigated and 5/6 sites show significant persistence, with values for the so-called Hurst exponent near or greater than 0.7, i.e., around 40% above the value 0.5 that represents a white noise process, suggesting that decision makers should take long-term persistence into consideration when conducting water resources planning and management studies in the region.
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Notes
The t-th residual, xt − Y, is defined as the departure of the yield Y from the inflow xt at time t. The residual mass curve is, thus, the graph of the cumulative departures as a function of time.
This means that either floor(12.1) or floor(12.9) results in 12.
Here assumed to be nmin = 16 due to the fact that smaller values may produce inconsistent estimates (Krištoufek 2010).
Differences between observed and calculated values.
β is the significance level.
d is the number of data points to which the regression line is fitted.
That is the same length of the investigated SFRB time series.
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The second author acknowledges the Brazilian National Council for Scientific and Technological Development (CNPq) for the financial support.
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Araujo, M.V.O., Celeste, A.B. Rescaled range analysis of streamflow records in the São Francisco River Basin, Brazil. Theor Appl Climatol 135, 249–260 (2019). https://doi.org/10.1007/s00704-018-2375-y
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DOI: https://doi.org/10.1007/s00704-018-2375-y