Computing horizontal geomagnetic field variation near the agonic line

It is important to be able to predict the impacts of geomagnetic activity at ground level, for example when it comes to estimating the effect of geomagnetically induced currents (GICs).  The rate of change of the magnetic field in the horizontal direction (dH/dt) is regularly used as a proxy or indicator for potentially hazardous space weather activity.  Most researchers tend to use one of two methods for computing the dH/dt: one is correct and the other is an approximation, with one method taking into account the difference in both the magnitude and direction of the magnetic field vector between timesteps and the other method only looking at the difference in the magnitude of the vector quantities. As the differentiation of the magnetic field in the latter method takes place after the two field directions have been combined to a scalar quantity, the relative sizes of the magnetic field in the two different directions can lead to a difference between the approaches. In particular, when either the northward or eastward magnetic field components are close to zero, such as near the agonic line, a relatively large difference in dH/dt magnitude can appear. We show using geomagnetic observatory measurements that there is an observable difference between the two methods close to the agonic line. We suggest which method for computing dH/dt should be employed.