Statistically Self‐Consistent and Accurate Errors for SuperDARN Data

The Super Dual Auroral Radar Network (SuperDARN)‐fitted data products (e.g., spectral width and velocity) are produced using weighted least squares fitting. We present a new First‐Principles Fitting Methodology (FPFM) that utilizes the first‐principles approach of Reimer et al. (2016) to estimate the variance of the real and imaginary components of the mean autocorrelation functions (ACFs) lags. SuperDARN ACFs fitted by the FPFM do not use ad hoc or empirical criteria. Currently, the weighting used to fit the ACF lags is derived from ad hoc estimates of the ACF lag variance. Additionally, an overcautious lag filtering criterion is used that sometimes discards data that contains useful information. In low signal‐to‐noise (SNR) and/or low signal‐to‐clutter regimes the ad hoc variance and empirical criterion lead to underestimated errors for the fitted parameter because the relative contributions of signal, noise, and clutter to the ACF variance is not taken into consideration. The FPFM variance expressions include contributions of signal, noise, and clutter. The clutter is estimated using the maximal power‐based self‐clutter estimator derived by Reimer and Hussey (2015). The FPFM was successfully implemented and tested using synthetic ACFs generated with the radar data simulator of Ribeiro, Ponomarenko, et al. (2013). The fitted parameters and the fitted‐parameter errors produced by the FPFM are compared with the current SuperDARN fitting software, FITACF. Using self‐consistent statistical analysis, the FPFM produces reliable or trustworthy quantitative measures of the errors of the fitted parameters. For an SNR in excess of 3 dB and velocity error below 100 m/s, the FPFM produces 52% more data points than FITACF.