This paper presents a thorough and mathematically rigorous analysis of the relation between ground magnetic perturbations and ionospheric conductances measured by the EISCAT radars.  The statistics are carefully performed, and the separation of the equivalent currents into divergence-free and curl-free parts is a significant improvement over prior similar studies. 

There are several drawbacks to the model that should be addressed in more detail in the discussion section as noted in the attached annotated file. Nevertheless, the model described here can be very useful for the study of individual events localized over suitably spaced ground magnetometers.

Overall, this paper represents a significant contribution that will facilitate future studies and improved insights on auroral electrodynamic processes.  I consider the paper publishable after the comments in the attached file are addressed.

The paper introduced a new empirical model which can predict conductance based on divergence-free part of the horizontal current density. They built the model using EISCAT observations. They further introduced a method to further solve the field-aligned currents and potential. They validated the model against other empirical models and SWARM observations. Even though the validation result is not perfect, the method itself is novel. If more details about the methodology can be added, I will suggest publishing it.

Minor suggestions:

Section 3.2: More introduction to AMPS and SWIPE in the first paragraph would be helpful. For example, what is the input and output of these models. For example, is E_DF assumed to be zero in AMPS?

Introduce the name of the model at the beginning. Usage of AMPS-EISCAT is a bit confusing.

Font size in Figure 11 and 12 is too small. How are the internal and external E_DF separated?