What can we learn from long hydrological time-series? The case of rainfall data at Collegio Romano, Rome, Italy

In this work, we explore the statistical behavior of one of the longest rainfall time-series in Italy and in the world, covering the period 1782–2017. Some standard and innovative statistical tools are applied to test the variability and change of the process across all values (in average, but also in terms of extremes) and scales (from days to years). An oscillation pattern occurs across all the time scales, from years to decades, limited by the sample length. It implies that there are no particular periods of variability, apart from seasonality, and no statistically significant trends, such that the process can be fully characterized in terms of the Hurst coefficient. Despite its exceptional length, the dataset is still insufficient to adequately capture the complex behavior of rainfall over the time scales, especially with regards to extremes, and to separate anthropogenically induced change from natural variability based on the data alone. Our findings suggest that samples of limited length do not allow robust statistical predictions, raising concerns about statistical analyses based on a limited dataset, even a relatively large one.