Measuring galaxy morphology at $z>1$. I - calibration of automated proxies

[abridged] New near-infrared surveys, using the HST, offer an unprecedented opportunity to study rest-frame optical galaxy morphologies at z>1 and to calibrate automated morphological parameters that will play a key role in classifying future massive datasets like EUCLID or LSST. We study automated parameters (e.g. CAS, Gini, M20) of massive galaxies at 1<z<3, measure their dependence on wavelength and evolution with redshift and quantify the reliability of these parameters in discriminating between visually-determined morphologies, using machine learning algorithms. We find that the relative trends between morphological types observed in the low-redshift literature are preserved at z>1: bulge-dominated systems have systematically higher concentration and Gini coefficients and are less asymmetric and rounder than disk-dominated galaxies. However, at z>1, galaxies are, on average, 50% more asymmetric and have Gini and M20 values that are 10% higher and 20% lower respectively. In bulge-dominated galaxies, morphological parameters derived from the rest-frame UV and optical wavelengths are well correlated; however late-type galaxies exhibit higher asymmetry and clumpiness when measured in the rest-frame UV. We find that broad morphological classes (e.g. bulge vs. disk dominated) can be distinguished using parameters with high (80%) purity and completeness of 80%. In a similar vein, irregular disks and mergers can also be distinguished from bulges and regular disks with a contamination lower than 20%. However, mergers cannot be differentiated from the irregular morphological class using these parameters, due to increasingly asymmetry of non-interacting late-type galaxies at z>1. Our automated procedure is applied to the CANDELS GOODS-S field and compared with the visual classification recently released on the same area getting similar results.