Circadian clocks allow the temporal compartmentalization of biological processes. In Arabidopsis, circadian rhythms display organ specificity but the underlying molecular causes have not been identified. We investigated the mechanisms responsible for the similarities and differences between the clocks of mature shoots and roots in constant conditions and in light : dark cycles. We developed an imaging system to monitor clock gene expression in shoots and light- or dark-grown roots, modified a recent mathematical model of the Arabidopsis clock and used this to simulate our new data. We showed that the shoot and root circadian clocks have different rhythmic properties (period and amplitude) and respond differently to light quality. The root clock was entrained by direct exposure to low-intensity light, even in antiphase to the illumination of shoots. Differences between the clocks were more pronounced in conditions where light was present than in constant darkness, and persisted in the presence of sucrose. We simulated the data successfully by modifying those parameters of a clock model that are related to light inputs. We conclude that differences and similarities between the shoot and root clocks can largely be explained by organ-specific light inputs. This provides mechanistic insight into the developing field of organ-specific clocks.