  We assess the performance of the Taruya, Nishimichi and Saito (TNS) model for
the halo redshift space power spectrum, focusing on utilising mildly non-linear
scales to constrain the growth rate of structure f. Using simulations with
volume and number density typical of forthcoming Stage IV galaxy surveys, we
determine ranges of validity for the model at redshifts z = 0.5 and z = 1. We
proceed to perform a Bayesian MCMC analysis utilising the monopole, quadrupole,
and hexadecapole spectra, followed by an exploratory Fisher matrix analysis. As
previously noted in other forecasts as well as in real data analyses, we find
that including the hexadecapole can significantly improve the constraints.
However, a restricted range of scales is required for the hexadecapole in order
for the growth parameter estimation to remain unbiased, limiting the
improvement. We consistently quantify these effects by employing the multipole
expansion formalism in both our Fisher and MCMC forecasts.
