Energy dependence of flux ratio (muon type/electron type) is quite clear. Muon neutrinos are produced from pion decay as well as muon decay, whereas electron neutrinos are created only from muon decay. High energy muons reach earth's surface before they decay producing less electron neutrinos, increasing flux ratio.

Zenith angle ( θ ) dependence is seen in plots of atmospheric neutrino flux vs cos θ. The peak is seen at cos θ=0. When the flux is symmetric about the peak there is no zenith angle dependence. Otherwise if flux is not symmetric about θ=90 degree, then one says that there is zenith angle dependence, which is caused by earth's geomagnetic field. Sizable zenith angle dependence is observed for atmospheric neutrinos in sub-GeV energy range.

If θ is zenith angle then cos θ =0 is horizontal direction, -1 is upward direction, +1 is downward direction. Atmospheric neutrino flux is enhanced in horizontal direction, which is cos θ=0. On both sides of peak value, flux falls symmetrically for multi GeV events. For sub-GeV events flux curve is not symmetric about the peak at cos θ=0. This is zenith angle dependence. In cos θ negative half, atmospheric neutrinos have passed through earth's core, and so they bear imprints of earth's geomagnetic field.

Regarding L values, we notice that upward going neutrinos have to pass through earth. So for cos θ = -1, L value is largest and those with cos θ= +1 the L value is the smallest. Intermediate L values can be parametrized in terms of cos θ. This is the required dependence of L value with zenith angle.