Kirkby (1997) argues that a move away from the exponential treatment of the relation between discharge and soil moisture may mean that spatially explicit solutions to the equations for TOPMODEL become necessary.
Based on the framework presented here, it may be possible to construct the same argument from a different starting point. Unless one uses the logarithmic form of the index, you are implying a slow mixing of an appropriate intensive quantity of the hydrological system. The associated complexity introduced by this slow mixing implies a spatially explicit solution.
M.J. 1997. TOPMODEL: A personal view. Hydrological Processes 11, 1087-97.