[R-sig-ME] Time as both fixed and random term

[Lionel]

Dear List,

In my work we usually deals with measures sampled repeatedly on 
experimental units over several time points and with specific 
treatments. For example we sampled plant biomass on 100 experimental 
plots at 5 different time point (say season or year). Some people argue 
that in this context we should model time as both a fixed effect term 
(as continuous variable) and random effect term in order to compute the 
correct numbers of degrees of freedom to test our treatment effects 
(usually considered as a continuous variables).

This is how such a model would look like:

Biomass ~ Treatment + Time + (1|Plot) + (1|Time)

In my experience having the same term has both fixed and random results 
in very low estimated standard deviation for the random term, which 
makes me skeptical about this approach. But having very little knowledge 
about how to correctly estimate the numbers of degrees of freedom I 
would like to ask you:

(i) if such a model makes sense,
(ii) if the argument "we need to have time as both fixed and random term 
to get the correct number of degrees of freedom" is valid
(iii) if such an alternative model: "Biomass ~ Treatment + Time + 
(1|Plot)" would be more appropriate.

Thanks for your input,
Lionel