  We study the impact of time-dependent solar cycles in the atmospheric
neutrino rate at DUNE and Hyper-Kamiokande (HK), focusing in particular on the
flux below 1 GeV. Including the effect of neutrino oscillations for the
upward-going component that travels through the Earth, we find that across the
solar cycle the amplitude of time variation is about $\pm5\%$ at DUNE, and $\pm
1\%$ at HK. At DUNE, the ratio of up/down-going events ranges from 0.45 to
0.85, while at HK, it ranges from 0.75 to 1.5. Over the 11-year solar cycle, we
find that the estimated statistical significance for observing time modulation
of atmospheric neutrinos is $4.8\sigma$ for DUNE and $2.0\sigma$ for HK. Flux
measurements at both DUNE and HK will be important for understanding
systematics in the low-energy atmospheric flux as well as for understanding the
effect of oscillations in low-energy atmospheric neutrinos.
