  We compute a new generation of standard solar models (SSMs) that includes
recent updates on some important nuclear reaction rates and a more consistent
treatment of the equation of state. Models also include a novel and flexible
treatment of opacity uncertainties based on opacity kernels, required in the
light of recent theoretical and experimental works on radiative opacity. Two
large sets of SSMs, each based on a different canonical set of solar abundances
with high and low metallicity (Z), are computed to determine model
uncertainties and correlations among different observables. We present detailed
comparisons of high- and low-Z models against different ensembles of solar
observables including solar neutrinos, surface helium abundance, depth of
convective envelope and sound speed profile. A global comparison, including all
observables, yields a p-value of 2.7$\sigma$ for the high-Z model and
4.7$\sigma$ for the low-Z one. When the sound-speed differences in the narrow
region of $0.65 < r/R_{sun} < 0.70$ are excluded from the analysis, results are
0.9$\sigma$ and 3.0$\sigma$ for high- and low-Z models respectively. These
results show that: high-Z models agree well with solar data but have a
systematic problem right below the bottom of the convective envelope linked to
steepness of molecular weight and temperature gradients, and that low-Z models
lead to a much more general disagreement with solar data. We also show that,
while simple parametrizations of opacity uncertainties can strongly alleviate
the solar abundance problem, they are insufficient to substantially improve the
agreement of SSMs with helioseismic data beyond that obtained for high-Z models
due to the intrinsic correlations of theoretical predictions. All the detailed
information of the new solar models, can be found online:
http://www.ice.cat/personal/aldos/Solar_Data.html
