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Table 1 Forecast error (in nT) over recent periods for different forecasting strategies, and using two classes of input models. The forecast error is expressed as the root-mean-squared difference between the true geomagnetic field vector, defined by an update of the CHAOS-6 field model (Finlay et al. 2016), and the forecast at the terminal epoch. The forecast error is computed for a spherical harmonic truncation equal to either 8 or 13, to conform with the IGRF framework on the one hand and to enable comparison with our previously published results on the other hand. Nocast assumes that the field does not change. Linear extrapolation assumes a linear variation whose slope is specified by the secular variation up to degree and order 8 / 13 at the start of the forecast period, as specified by the input model fed to the inverse geodynamo modelling framework: “1-year SV” means that the input model is determined based on one year of satellite data prior to the forecast; “Seq. SV” implies that the full set of satellite data available before the beginning of the forecast is used to compute the input model, using a sequential Kalman filter with analysis steps every 12 months. “Coupled Earth, ensemble, QG-MAC” indicates that the full coupled Earth dynamo model is integrated for an ensemble comprising 100 members, with the median defining the forecast, and an initialization where the QG-MAC constraint is mildly enforced for the flow at the core surface. In the bottom five rows, “steady flow” implies that the sole three-dimensional induction equation (with magnetic diffusion) is integrated, with or without an ensemble approach, and with or without the mild imposition of the QG-MAC constraint. If an ensemble approach is adopted, it is the median that defines the forecast. All non-“Seq. SV” entries for SH truncation at degree 13 taken from Fournier et al. (2021, Tab. 2)

From: Physics-based secular variation candidate models for the IGRF

Period 2005.0-2010.0 2009.0-2014.0 2015.0-2019.3
Spherical harmonic truncation used to compute error 8 13 8 13 8 13
Nocast 399.8 400.2 438.9 439.4 382.6 383.0
Linear extrapolation, 1-year SV 70.7 72.2 57.2 58.2 63.8 64.6
Linear extrapolation, Seq. SV 71.6 71.9 57.6 58.1 64.5 65.1
Coupled Earth, ensemble, QG-MAC, 1-year SV 74.5 75.4 77.3 77.8 62.2 62.9
Steady flow, ensemble, QG-MAC, 1-year SV 67.9 68.8 60.1 60.7 60.0 60.7
Steady flow, ensemble, QG-MAC, Seq. SV 64.5 64.8 59.8 60.2 62.7 63.2
Steady flow, no ensemble, QG-MAC, 1-year SV 70.8 71.7 62.7 63.3 60.5 61.4
Steady flow, ensemble, no QG-MAC, 1-year SV 66.2 67.3 60.8 61.5 64.5 65.1
Steady flow, no ensemble, no QG-MAC, 1-year SV 71.7 72.7 65.9 66.5 65.6 66.2