Remove m_root

Issue/feature addressed

Remove m_root to avoid possible future conflict with parallel-in-time driver. Also m_root was not used consistently. This MR was split from MR !1457 (merged)

Checklist

• [ ] Functions and classes, or changes to them, are documented.
• [ ] User guide/documentation is updated.
• Changelog is updated.
• [ ] Suitable tests added for new functionality.
• [ ] Contributed code is correctly formatted. (See the contributing guidelines).
• [ ] License added to any new files.
• [ ] No extraneous files have been added (e.g. compiler output or test data files).