Uncertainties are present in virtually all observational (geoscientific) time series, stemming from different origins such as the measurement process itself, spatial aggregation, or the dating process as in paleoclimatic research. In particular for measurement uncertainties, a plethora of methods exists to quantify them and incorporate them into the actual analysis of the time series. Quite generally, time series uncertainties are treated by considering measurement outcomes as mean or median values in combination with a set of errors, thereby dividing the analysis into two steps: first, the analysis of the time series of mean (or median) values, and second, thereafter, the analysis of the errors. However, a complete assessment of how these uncertainties propagate to the final results of modern data analysis techniques is often highly non-trivial, and the described two-step approach is not suitable in many situations.

In this short course, we aim to put forward the idea of considering the temporal evolution of an observed system not as sequences of pointwise estimates like the mean, but as sequences of probability density functions that reflect the inherent uncertainties. Such probability density functions describe the system in much greater detail than simple point estimates.

We will first briefly introduce the elements of probability theory and statistics that are relevant for an accurate description of uncertainties in time series analysis. Thereafter, we will walk the audience through some real-world examples, where we demonstrate the advantages of considering the temporal evolution of a system in terms of a sequence of probability density functions rather than as a sequence of points (and error bars). These examples will cover paleoclimatic applications, where the uncertainties mainly result from the dating processes, but also applications investigating the evolution of the El Nino Southern Oscillation, where the uncertainties stem from the spatial aggregation of the data. Furthermore, we will provide explicit examples of how to generalize traditional time series analysis methods to the analysis of probability density sequences. The final part of the course is planned as an open discussion, where we hope to learn about similar problems that people in the audience face in their research, and discuss further methodological developments needed for a more thorough treatment of uncertainties in geoscientific time series.

To register your interest in the course, simply send an email to: goswami(at)pik-potsdam(dot)de