  The article aims to analyze a construction of charges (conserved quantities)
for the gravity field in the (3+1) decomposition. The construction is based on
(3+1) splitting of conformal Yano--Killing (CYK) two-form. The splitting leads
to charges, defined on Cauchy surface, which are combined from components of
Weyl tensor and conformal Killing vector. The relations between the conserved
quantities and its classical ADM counterparts are revisited. Asymptotic
behavior of the conserved quantities is described. The charges are analyzed for
a particular choice of initial data, among others, Bowen -- York spinning black
hole.
