How does 'building land' fit into economic modeling? According to the ONS National Accounts 2018 &amp; RICS land valuations and ...

Land that is built on has a value that makes it half of the UK's wealth.
The rest of the land has a value less than 3% of UK wealth.
Building land is created when planning permission is granted.

Another question asked "Why is Land not considered as a fixed capital?".

The top answer said ....


  Physical capital is reproducible, and does have a finite lifetime.
  
  Hence, almost all land is not physical capital.
  
  There are corner cases, where land is reproducible, and may appear and
  then disappear again in less than a handful of human lifetimes: in
  those very rare cases, that particular land behaves more like physical
  capital rather than how land generally behaves, and so could be
  classed as such.


Building land can appear and disappear(e.g. post war prefab sites which have reverted to open space) and planning schemes can change building land into something else.

How would this very large asset, building land, fit into economic models?

I can't see how it would fit into a Cobb_Douglas function.
Land would fit into production functions or many economic models the same/similar way as other factors of production.

An example of general Cobb-Douglas function with land would be:

$$Y(K,L,T) = A K^{\alpha}L^{\beta}T^{1-\alpha-\beta}$$

Where $K$ is capital, $L$ labor, and $T$ land. Into most economic models land can be integrated rather easily as the example above shows. The land improvements necessary to clear land for building can be in principle modeled as capital accumulation with depreciation but for some general production functions there is not that much difference made between the inputs.