Ensemble deep learning models for prediction and uncertainty quantification of ground magnetic perturbation

Abstract

Geomagnetically Induced Currents are one of the most hazardous effects caused by geomagnetic storms. In the past literature, the variations in ground magnetic fields over time, dB/dt were used as a proxy value for GIC. Machine Learning (ML) techniques have emerged as a preferred methodology to predict dB/dt. However, space weather data are highly dynamic in nature, and the data distribution is subject to change over time due to environmental variability. The ML models developed are prone to the uncertainty in the input data and therefore suffer from high variance. In addition, a part of an ML architecture performance is conditional on the variables used to model the system in focus. Therefore, a single algorithm may not generate the required accuracy for a given dataset. In this work, a Bayesian Ensemble ML model has been developed to predict the variations over time of the local ground magnetic horizontal component, dBH/dt. The Ensemble methodology combines multiple ML models in the prediction process to predict dBH/dt. Bayesian statistics allow the estimation of model parameters and output as probability distributions, where the variance quantifies the uncertainty. The input data consists of solar-wind data from OmniWeb for the years 2001–2010. The local ground horizontal magnetic components for the corresponding time were calculated using SuperMAG data for the Ottawa ground magnetometer station for the years mentioned above. The years 2011–2015 were selected for model testing, as it encompasses the 5 August 2011 and 17 March 2015 geomagnetic storms. Five different accuracy metrics were considered; namely, Root Mean Squared Error (RMSE), Probability of Detection (POD), Probability of False Detection (PFD), Proportion Correct (PC), and Heidke Skills Score (HSS). The parameter uncertainty of the models is quantified, and the mean predicted dBH/dt is generated with a 95% credible interval. It can be observed that different models perform better with different datasets and the ensemble model has an accuracy comparable to the models with a relatively strong performance.

Physics-Enhanced TinyML for Real- Time Detection of Ground Magnetic Anomalies

“…In a local magnetic reference frame, N is "northwards", E is "eastwards", and Z is "vertically downwards" []. As shown in Eq-1, dB H /dt is the resultant of the time derivatives of the two horizontal vectors B N , and B E , where dt represents a cadence of 1 min [15]. The ground magnetometer data were obtained from SuperMAG.…”

“…In addition, ground magnetometers are deployed on the Earth's land surface, which measures the strength and direction of the ground magnetic perturbations [48] [49] [50]. However, obtaining exact measurements of GIC data is challenging, as it requires knowledge and access to the electric power network, which tends to be proprietary information of private energy companies [15] [51]. Therefore, different magnetic indices have been used throughout the literature as a proxy measure for GIC [12] [52] [13] [15] [51].…”

“…In recent years, with the advent of Big Data, there has been a rising interest in exploring data-driven approaches, where machine learning (ML) and its variant deep learning (DL) have emerged as a preferred methodology [1] [16] [13] [51] [15]. Numerous methodologies have been utilized in forecasting geomagnetic indices and assessing solar wind parameters [1] [16] [13] [51] [15] [2].…”

“…Strategies for mitigating these risks encompass monitoring via space-borne satellites and terrestrial magnetometers and applying predictive models derived from the acquired data [10] [11] [9]. Nonetheless, the accurate quantification of GICs is challenging, attributed to proprietary restrictions imposed by energy corporations, necessitating the employment of alternative indicators such as the rate of change in the ground horizontal magnetic component (dB H /dt) [12] [13] [14] [15]. While traditional forecasting methodologies leverage physics-based simulation models, offering theoretical robustness and interpretability, they are constrained by difficulties in assimilating imprecise observational data for determining initial and boundary conditions and their substantial computational complexity [16] [17].…”

Forecasting of Geomagnetically Induced Currents using Non- Linear Autoregression with Exogenous Inputs

“…GICs hazards have socio-economic ramifications because modern civilization is becoming excessively reliant on complex electrical systems (Oughton et al, 2017). As a result, many efforts have been made to mitigate the effects of these currents through developing forecasting models that can give estimates of the levels of induced currents to expect ( e.g., Bailey et al, 2022;Keesee et al, 2020;Siddique and Mahmud, 2022). Most of these models depend on the use of the geoelectric field, which are mostly not available, necessitating the use of alternate methods to derive this information.…”