Dependence of the ionization yield function Y(h) (see Eq. (9)) on the atmospheric depth h for primary protons with different kinetic energies, as indicated in the legend. Two components can be observed, viz. direct ionization by the primary particles which dominate the upper atmosphere, and the ionization by secondaries of the atmospheric cascade which dominates in the lower atmosphere. An extension of the cascade-induced ionization to the upper atmosphere is depicted by thin dashed curves.