A procedure for testing the significance of orbital tuning of the martian polar layered deposits

Layered deposits of dusty ice in the martian polar caps have been hypothesized to record climate changes driven by orbitally induced variations in the distribution of incoming solar radiation. Attempts to identify such an orbital signal by tuning a stratigraphic sequence of polar layered deposits (PLDs) to match an assumed forcing introduce a risk of identifying spurious matches between unrelated records. We present an approach for evaluating the significance of matches obtained by orbital tuning, and investigate the utility of this approach for identifying orbital signals in the Mars PLDs. Using a set of simple models for ice and dust accumulation driven by insolation, we generate synthetic PLD stratigraphic sequences with nonlinear time-depth relationships. We then use a dynamic time warping algorithm to attempt to identify an orbital signal in the modeled sequences, and apply a Monte Carlo procedure to determine whether this match is significantly better than a match to a random sequence that contains no orbital signal. For simple deposition mechanisms in which dust deposition rate is constant and ice deposition rate varies linearly with insolation, we find that an orbital signal can be confidently identified if at least 10% of the accumulation time interval is preserved as strata. Addition of noise to our models raises this minimum preservation requirement, and we expect that more complex deposition functions would generally also make identification more difficult. In light of these results, we consider the prospects for identifying an orbital signal in the actual PLD stratigraphy, and conclude that this is feasible even with a strongly nonlinear relationship between stratigraphic depth and time, provided that a sufficient fraction of time is preserved in the record and that ice and dust deposition rates vary predictably with insolation. Independent age constraints from other techniques may be necessary, for example, if an insufficient amount of time is preserved in the stratigraphy.