Derivation and use of core surface flows for forecasting secular variation

Improving forecasts of the temporal and spatial changes of the Earth's main magnetic field over periods of less than 5 years has important scientific and economic benefits. Various methods for forecasting the rate of change, or secular variation, have been tried over the past few decades, ranging from the extrapolation of trends in ground observatory measurements to computational geodynamo modeling with data assimilation from historical magnetic field models. We examine the utility of an intermediate approach, using temporally varying core surface flow models derived from relatively short periods of magnetic field data to produce, by advection, secular variation estimates valid for the Earth's surface. We describe a new method to compute a core flow changing linearly with time from magnetic secular variation and acceleration data. We invert a combination of data from the CHAMP satellite mission and ground observatories over the period 2001.0 to 2010.0 for a series of such models. We assess their ability to forecast magnetic field changes by comparing them to CHAOS-4, a state-of-the-art model using data from 1997 to 2014.5. We show that the magnetic field predictions tend to have a lower root-mean-square difference from CHAOS-4 than the International Geomagnetic Reference Field or World Magnetic Map series of secular variation models.