The magnetic network extending from the photosphere (solar radius $simeq R_odot$) to lower corona ($R_odot + 10$ Mm) plays an important role in the heating mechanisms of the solar atmosphere. Here we further develop the models with realistic open magnetic flux tubes of the authors in order to model more complicated configurations. Closed magnetic loops, and combinations of closed and open magnetic flux tubes are modelled. These are embedded within a stratified atmosphere, derived from observationally motivated semi-empirical and data-driven models subject to solar gravity and capable of spanning from the photosphere up into the chromosphere and lower corona. Constructing a magnetic field comprising self-similar magnetic flux tubes, an analytic solution for the kinetic pressure and plasma density is derived. Combining flux tubes of opposite polarity it is possible to create a steady background magnetic field configuration modelling a solar atmosphere exhibiting realistic stratification. The result can be applied to SOHO/MDI and SDO/HMI and other magnetograms from the solar surface, upon which photospheric motions can be simulated to explore the mechanism of energy transport. We demonstrate this powerful and versatile method with an application to Helioseismic and Magnetic Imager data.
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