  The future space missions Euclid and WFIRST-AFTA will use the Halpha emission
line to measure the redshifts of tens of millions of galaxies. The Halpha
luminosity function at z>0.7 is one of the major sources of uncertainty in
forecasting cosmological constraints from these missions. We construct unified
empirical models of the Halpha luminosity function spanning the range of
redshifts and line luminosities relevant to the redshift surveys proposed with
Euclid and WFIRST-AFTA. By fitting to observed luminosity functions from Halpha
surveys, we build three models for its evolution. Different fitting
methodologies, functional forms for the luminosity function, subsets of the
empirical input data, and treatment of systematic errors are considered to
explore the robustness of the results. Functional forms and model parameters
are provided for all three models, along with the counts and redshift
distributions up to z~2.5 for a range of limiting fluxes (F_Halpha>0.5 - 3 x
10^-16 erg cm^-2 s^-1) that are relevant for future space missions. For
instance, in the redshift range 0.90<z<1.8, our models predict an available
galaxy density in the range 7700--13300 and 2000--4800 deg^-2 respectively at
fluxes above F_Halpha>1 and 2 x 10^-16 erg cm^-2 s^-1, and 32000--48000 for
F_Halpha>0.5 x 10^-16 erg cm^-2 s^-1 in the extended redshift range 0.40<z<1.8.
We also consider the implications of our empirical models for the total Halpha
luminosity density of the Universe, and the closely related cosmic star
formation history.
