A Methodology to Predict the Geomagnetic Field with Confirmatory Evidence from the Polar Region in Canada

It is well established that solar activity can give rise to geomagnetic storms that are harmful to communications, Global Positioning System, and electric power systems located in mid to high latitudes. Consistent with this assessment, during solar cycle 22, a very intense geomagnetic storm on March 13, 1989 contributed to large perturbance in the field in the vicinity of Ontario and Quebec Canada which in turn contributed to the collapse of the Hydro Quebec electric power system. Accurate space weather forecasts would have enabled protective actions to be undertaken. Unfortunately, while significant progress has been made in understanding the solar drivers of the geomagnetic activity, there is room for improvement in prediction. This paper presents a machine learning time-series approach that may ameliorate matters. The modeling approach employed in this paper is distinct from other forms of machine learning because it presumes that the data has a time-based dimension. For example, the well-known “Random Forest” machine learning method presumes that the data can be resorted without any loss in information. The view here is that resorting a time-series data set can have adverse modeling consequences when the outcome in period t is correlated with the outcomes in previous periods.

The starting point of this paper is the observation that the data representing the geomagnetic field, while significantly volatile at times, has a diurnal pattern. As a result, the value of the horizontal component of the geomagnetic field in hour t will be correlated with its prior values in hours t-1, t-2, t-3.... t-24, t-48, t-72 etc. Since the past values of the geomagnetic field are known at hour t, modeling this nature of the data can significantly enhance its short-term predictability. Predictability is also enhanced by explicitly modeling the volatility in the data. The overall goal of improved predictability is accomplished by using an autoregressive conditional heteroskedasticity/ autoregressive–moving-average model with exogenous inputs (hereafter, an ARCH/ARMAX model) where the ARCH component models the autoregressive nature of the volatility in geomagnetism, the ARMA component models the more “ordinary” autoregressive process, and X reflects the exogenous explanatory inputs. This approach has proven to be invaluable in modeling any time-series variable that is autoregressive that also exhibits periods of turbulence followed by a relative calm at some point.

The analysis uses hourly data corresponding to the horizontal component of the geomagnetic field from the Resolute Geomagnetic Observatory in Canada’s polar region (74.690° N, 265.105° E). Hourly data from January 1, 1983, through December 31, 1999, are used to estimate the model. The model is evaluated using hourly data from January 1, 2000, to December 31, 2017. The preliminary out-of-sample results indicate that the horizontal component of the geomagnetic field’s hourly average (H) can be predicted with moderate to high accuracy, as illustrated in Figure 1. Consistent with the figure, the weighted mean absolute percent error (WMAPE) corresponding to the predictions is approximately 1 %. The only obvious shortcoming is that the extreme spikes in the field are underestimated, a deficiency that is currently being addressed.