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The analysis of irregularly sampled time series remains a challenging task requiring methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases. The edit-distance is an effective metric to quantitatively compare time series segments of unequal length by computing the cost of transforming one segment into the other. We show that transformation costs generally exhibit a non-trivial relationship with local sampling rate. If the sampling resolution undergoes strong variations, this effect impedes unbiased comparison between different time episodes. We study the impact of this effect on recurrence quantification analysis, a framework that is well-suited for identifying regime shifts in nonlinear time series. A constrained randomization approach is put forward to correct for the biased recurrence quantification measures. This strategy involves the generation of a novel type of time series and time axis surrogates which we call sampling rate constrained (SRC) surrogates. We demonstrate the effectiveness of the proposed approach with a synthetic example and an irregularly sampled speleothem proxy record from Niue island in the central tropical Pacific. Application of the proposed correction scheme identifies a spurious transition that is solely imposed by an abrupt shift in sampling rate and uncovers periods of reduced seasonal rainfall predictability associated with enhanced ENSO and tropical cyclone activity.

Stalagmites are an extraordinarily powerful resource for the reconstruction of climatological palaeoseasonality. Here, we provide a comprehensive review of different types of seasonality preserved by stalagmites and methods for extracting this information. A new drip classification scheme is introduced, which facilitates the identification of stalagmites fed by seasonally responsive drips and which highlights the wide variability in drip types feeding stalagmites. This hydrological variability, combined with seasonality in Earth atmospheric processes, meteoric precipitation, biological processes within the soil, and cave atmosphere composition means that every stalagmite retains a different and distinct (but correct) record of environmental conditions. Replication of a record is extremely useful but should not be expected unless comparing stalagmites affected by the same processes in the same proportion. A short overview of common microanalytical techniques is presented, and suggested best practice discussed. In addition to geochemical methods, a new modelling technique for extracting meteoric precipitation and temperature palaeoseasonality from stalagmite d18O data is discussed and tested with both synthetic and real-world datasets. Finally, world maps of temperature, meteoric precipitation amount, and meteoric precipitation oxygen isotope ratio seasonality are presented and discussed, with an aim of helping to identify regions most sensitive to shifts in seasonality.