We determine the dependence of the initial helium abundance and the
present-day helium abundance in the convective envelope of solar models (\yim
and \ysm respectively) on the parameters that are used to construct the
models. We do so by using reference standard solar models to compute the
power-law coefficients of the dependence of \yim and \ysm on the input
parameters. We use these dependencies to determine the correlation between
\yim and \ysm and use this correlation to eliminate uncertainties in \yim
from all solar model input parameters except the microscopic diffusion rate. We
find an expression for \yim that depends only on \ysm and the diffusion
rate. By adopting the helioseismic determination of solar surface helium
abundance, \ysms= 0.2485\pm0.0035, and an uncertainty of 20% for the
diffusion rate, we find that the initial solar helium abundance, \yims, is
0.278±0.006 independently of the reference standard solar models (and
particularly on adopted the solar abundances) used in the derivation of the
correlation between \yim and \ysm. When non-standard solar models with
extra mixing are used, then we derive \yims = 0.273 \pm 0.006. In both cases,
the derived \yims value is higher than that directly derived from solar model
calibrations when the low metalicity solar abundances (e.g. by Asplund et al.)
are adopted in the models.Comment: 18 pages, including 3 figures and 2 tables. Accepted for publication
in Ap