For a K3 surface \(X\) defined over a global field \(K\) of characteristic $0$ or $p \geq 3$ (assumed ordinary when $K$ is a global function field) we provide an exact formula for the density of primes \(p\) corresponding to each Picard rank jump \[\mathrm{NS}(\overline{X_p}) = \mathrm{NS}(\overline{X}) + c. \] More generally, under some suitable genericity conditions, we prove that a density 0 set of reductions carries an algebraic cycle representing a fixed squareclass under the intersection pairing.