Quantifying Uncertainty in Time Averages of the Geomagnetic Dipole

Time averages of the geomagnetic field provide insights into the state of the geodynamo, but uncertainties in these averages can compromise the interpretation. An important source of uncertainty is due to a restricted averaging duration. Short averages do not sample the full range of variability, leading to errors in the resulting estimates. Here we assess the uncertainty of finite‐time averages by assuming that stochastic models give a reasonable description of fluctuations in the axial dipole. We derive an expression for the variance of the time average as a function of the averaging duration. Averages longer than 1 Myr are required to lower the standard deviation of the average to 10% of the natural variability. We apply our theory to known differences in the axial dipole between the Brunhes and Matuyama chrons. These differences are too large to attribute to natural variability, indicating a need for refinements in the Myr‐scale models.