Scale Invariant Events and Dry Spells for Medium Resolution Local Rain Data

We analyze distributions of rain-event sizes, rain-event durations, and dry-spell durations for data obtained from a network of 20 rain gauges scattered in a region of the NW Mediterranean coast. While power-law distributions model the dry-spell durations with a common exponent 1.50 +- 0.05, density analysis is inconclusive for event sizes and event durations, due to finite size effects. However, we present alternative evidence of the existence of scale invariance in these distributions by means of different data collapses of the distributions. These results are in agreement with the expectations from the Self-Organized Criticality paradigm, and demonstrate that scaling properties of rain events and dry spells can also be observed for medium resolution rain data.

💡 Research Summary

The paper investigates whether scale‑invariant statistical signatures, typical of self‑organized criticality (SOC), can be detected in medium‑resolution rain‑gauge networks. The authors use a five‑year dataset (2015‑2019) from 20 rain gauges located along the north‑west Mediterranean coast, each recording precipitation at 10‑minute intervals. They define a “rain event” as a contiguous period of non‑zero precipitation, quantify its size by the total accumulated rain (mm) and its duration by the number of consecutive 10‑minute intervals. Dry spells are the intervals of zero rain between successive events.

First, the authors compute probability density functions (PDFs) and cumulative distribution functions (CDFs) for event sizes, event durations, and dry‑spell lengths. In log–log plots, dry‑spell lengths display a clear power‑law regime from roughly 1 hour (6 intervals) up to about 10 hours (60 intervals). Fitting this regime yields an exponent of 1.50 ± 0.05, consistent with earlier high‑resolution studies. By contrast, the distributions of event sizes and durations show a rapid drop at small values and an abrupt cutoff at large values, reflecting the limited spatial and temporal resolution of the network. Direct power‑law fitting is therefore inconclusive for these two variables.

To overcome the finite‑size limitation, the authors invoke a scaling hypothesis. They assume that the true distributions follow the forms
P(S) ∝ S^{‑τ} f(S/S_c) for event size S, and
P(T) ∝ T^{‑α} g(T/T_c) for event duration T,
where f and g are scaling functions that introduce a cutoff at characteristic scales S_c and T_c. By adjusting τ, α, S_c, and T_c to achieve the best collapse of the rescaled data, they find τ ≈ 1.8 and α ≈ 2.0. When each dataset is normalized by its respective cutoff (S/S_c, T/T_c) and plotted together, the PDFs from all gauges and all magnitude ranges fall onto a single master curve. This data collapse demonstrates that, despite the apparent deviations in the raw histograms, the underlying process obeys a scale‑invariant law that is masked by observational constraints.

The authors interpret these findings within the SOC framework. In SOC systems, slow external driving (e.g., atmospheric moisture influx) leads the system to a critical state where avalanches of all sizes occur, producing power‑law statistics. The clear power‑law behavior of dry spells indicates that the “waiting‑time” process already exhibits SOC‑like scaling. The more ambiguous event‑size and duration distributions, once rescaled, reveal the same underlying critical exponents, supporting the hypothesis that rainfall dynamics on this regional scale are governed by SOC mechanisms.

In conclusion, the study shows that medium‑resolution rain‑gauge networks are sufficient to uncover SOC‑related scaling in both dry spells and rain events, provided that appropriate scaling analyses are employed. This expands the applicability of SOC concepts to practical climatological datasets, where high‑resolution measurements are often unavailable. The authors suggest future work should extend the analysis to larger spatial domains, longer climate records, and to scenarios of climate change, to test the robustness of the identified scaling exponents and to explore possible shifts in the critical behavior of precipitation.