The Brazilian SIN data verification through the simply quality check of Benford?s Law

Código

I-EBHE0098

Autores

João Marcos Carvalho, Henrique Degraf

Tema

WG 1.13: Ensuring evidence-based findings

Resumo

Benford?s Law (or The Law of Anomalous Numbers) is a quite unintuitive and surprising relation regarding the first, or first two digits, of a natural phenomenon time series. It was published in 1938, and it says that in natural systems, lower digits are expected to appear with a higher frequency than higher digits ? but more than that, the frequency theorical frequency obeys a logarithmical curve, were the digit 1 has a frequency of 30%, while the digit 9 only appears in 5% of the time. The law has been applied with success to a multitude of different datasets, such as city populations, atomic weights, death rates, public water use, bedload motion, income measures, hydrological data etc. Given that data from natural phenomena, particularly hydrological time series, may exhibit bias and alterations, Benford?s Law can be employed to detect inconsistencies within such datasets. It is important to mention that the lack of conformity of a hydrological time series with Benford?s Law does not indicate that the measurements are incorrect; however, it may suggest some kind of artificial bias. Considering this scenario, in this article we analyze the adherence to Benford?s law of daily and monthly naturalized streamflow data of the main Brazilian Hydro Power Plants (HPP), made available by the National Electrical System Operator (ONS). The dataset analyzed comprehend streamflow data from 155 HPPs, which are widely used to estimate energy generation, update hydrological and hydraulic studies and develop research in the water resources field. In a general context the results of the test imply that the data followed the expected frequency distribution, indicating that most part of the analyzed streamflow series do not exhibit patterns or alterations. However, it was observed that 8 HPP presented a deviation greater than 20% from the theorical distribution, and 25 HPP presented a deviation greater than 15% from the expected probability. These results imply that almost 1 in 6 samples, from the dataset made available by the ONS, may not be adequately representing the HPP?s natural flows of all 155 HPP. Despite these results, it is essential to continue verifying other possible errors in the data to ensure its accuracy in representing nature.