Newcomb-Benford Law characterization of solar wind magnetic field and geomagnetic indices

Abstract

<p>A. M. Benedito Nunes (co-first author), J. Gamper (co-first author), M. Friel, J. W. Gjerloev, S.C. Chapman</p> <p> </p> <p>The Newcomb-Benford Law (NBL) prescribes the probability distribution of the first digit of variables under conditions including aggregation. It will not apply where there is strong truncation or a cut-off. We apply it to space weather relevant magnetic field observations and indices for the first time. In upstream solar wind magnetic field OMNI HRO IMF observations we show that the NBL detects the improvement in data quality with the availability of the WIND and later, ACE spacecraft after 1995, in addition to IMP8. The SMR geomagnetic index averages over multiple ground magnetometer time-series and follows the NBL to a consistent high precision across changing solar activity and a ten-fold increase in the number of constituent stations. The AE and SME indices select the extremal signals from a set of stations. AE, which is mostly based on the same stations throughout its record, follows the NBL to a consistent high precision and with weak but statistically significant variation, it follows the NBL less well during relatively strong solar cycle maxima compared to solar minima. Both the number of constituent stations and the station type comprising SME has changed over the SME record. First, in 1996 the number of available stations increased tenfold, but the station type remained homogeneous. The NBL is followed to a consistent high precision through this period, up to 2006. Beyond 2006, new station types are introduced into the composition of SME and this can be seen in an approximately factor of two drop in the precision with which the NBL is followed. Subsequently, the SME record follows the NBL to varying precision which tracks the inclusion and omission of different types of magnetometer in the record. As the use of composite indices becomes more widespread across the geosciences, the NBL may therefore provide a generic 'data flag' to indicate when the constituent raw data, calibration or sampling method has changed.</p>