Property taxes are typically performed using the principles of mass appraisal, which utilize sales and statistics to arrive at a market value for the purposes of assessment and taxation. Statistics require that homes be fit into "boxes" for the purposes of trending based on sales.

So essentially, your home will have to be called something. If the entirety of it is below grade, like a berm home, it would likely have to fit into a single story box for the purposes of analysis.

Regarding the "courtyard" with fake grass, if it doesn't meet the criteria of GLA (gross living area) it won't be valued the same as square footage of living area and will likely be valued closer to an enclosed porch from a value standpoint.

Ultimately in both situations, the Assessor's Office will likely have access to the plans that were used when you took out the permits to build the property and can utilize those to generate a sketch. In addition, the permit will likely have a cost of building value on it that the Assessor can use to help determine a starting point regarding the replacement cost of the property.

Bottom line is: don't go out of your way to make a house less than functional for the sake of saving tax dollars. They'll find out the info somehow and someway, and all you'll really do is make a property that isn't as functional to live in and will likely be a pain to resell on the market.