Developed by Francesco Cappelli, Salvatore Grimaldi, Andrea Petroselli, and Emanuele Santinami of Tuscia University in Viterbo, Italy, Virtual Rain v1.0 does not invent new rainfall mathematics. Instead, its novelty lies in integration. For the first time, two previously separate and validated methodologies, the CoSMoS-2s daily rainfall generator and the Multifractal Random Cascade disaggregation model, are available together in a single, reproducible software environment, implemented through Python and R routines and mirrored on an interactive web platform that requires no programming skills.

The problem the toolkit addresses is structural. Hydrologists typically have access to long daily precipitation time series, often spanning several decades, plus fragmentary observations of short, intense storms used to build intensity-duration-frequency curves, the workhorse charts of infrastructure design. What they lack is continuous sub-daily data, which stochastic precipitation models need in abundance to capture the multiscale structure of rainfall. Existing generators and disaggregation techniques abound in the literature, but choosing and wiring together an appropriate combination has remained a genuine obstacle for practitioners, particularly in data-sparse regions.

Virtual Rain’s first module tackles daily simulation using CoSMoS-2s, a two-state stochastic framework that explicitly separates rainfall occurrence from rainfall intensity. In the first state, the observed record is transformed into a binary wet-or-dry process, with seasonally varying occurrence probabilities and autocorrelation structures mapped into a Gaussian autoregressive model and converted back through thresholds. In the second state, wet-day rainfall amounts are fitted with parametric distributions, including Gamma, Generalized Gamma, Burr, and Weibull families, while their persistence is reproduced through parametric or empirical autocorrelation functions. The two components are then recombined, allowing the synthetic series to preserve intermittency, seasonal cycles, marginal distributions, and temporal dependence simultaneously.

The second module performs the disaggregation. It assumes that rainfall intensity evolves as a multiplicative cascade, a multifractal process in which the mean intensity at each timescale is redistributed through random weights following a beta-lognormal distribution. Three parameters govern the cascade: one controlling intermittency and the share of dry intervals, one governing the intensity fluctuations, and an outer-scale parameter defining the range of the multifractal behaviour. Crucially, rather than demanding high-resolution observations for calibration, the model derives these parameters from IDF curves, matching theoretical multifractal intensity-duration relationships to the target curves through numerical optimization. Because IDF information is widely available even where fine-scale gauges are not, this dramatically broadens the framework’s reach.

The toolkit guides users through a structured workflow. On the simulation side, routines handle exploratory plotting, fitting of seven candidate marginal distributions using the Nelder-Mead algorithm, estimation of autocorrelation structures for both the binary and continuous processes, ensemble generation of synthetic series, and diagnostic comparison of observed versus simulated statistics, from dry-day probability to extreme percentiles. On the disaggregation side, routines extract annual maxima, fit generalized extreme value distributions by maximum likelihood, probability weighted moments, or L-moments, calibrate the cascade parameters against IDF targets, and finally break daily totals down to resolutions as fine as one minute, with an option to preserve daily rainfall volumes exactly.

To demonstrate the software, the authors applied the complete workflow to a rain gauge in the Arno River Basin in Tuscany, one of Italy’s longest river systems, using a 20-year daily record from a network of more than 70 gauges with continuous 15-minute observations. The Gamma distribution emerged as the best overall fit for wet-day intensities, and an ensemble of 50 synthetic series successfully reproduced the observed dry frequency, seasonal cycle, autocorrelation, and ranked annual maxima, with only a slight overestimation in the upper tail that the authors attribute to the limited sample of wet days in a record that is nearly 70 percent dry. The imposed IDF scaling exponent, estimated at 0.251 from the observed sub-daily data, and the dry-day frequency were both recovered exactly in the disaggregated output, confirming that the integrated pipeline preserves the statistical properties it is calibrated to reproduce.

The authors are careful about what the case study does and does not show. Because the same observational record serves for calibration and diagnostics, the comparison verifies the software implementation rather than validating predictive performance on independent data, and the methodological validation of the underlying models rests on earlier publications. They also flag honest limitations: parameter uncertainty is not yet propagated through the full simulation-disaggregation chain, some combinations of cascade parameters can fit equally well, and short or incomplete records can produce unstable estimates. Diagnostic outputs, they stress, should be treated as an integral part of model configuration, not an afterthought.

What makes Virtual Rain potentially transformative is accessibility. Beyond the Python and R routines, an interactive web platform walks users step by step from data upload through seasonal partitioning, distribution fitting, ensemble diagnostics, cascade calibration, and final disaggregation, with both interfaces implementing identical formulations and parameterizations. The software is archived on Zenodo under a GPL-3.0 licence, and the Tuscan rainfall data are openly available under a Creative Commons licence. For engineers designing drainage systems, researchers assessing flood risk under climate change, or teachers demonstrating stochastic hydrology, the toolkit lowers a barrier that has long separated sophisticated rainfall theory from everyday practice, turning decades of ordinary daily rain gauges into a window on the violent, minute-scale storms that matter most.

Subject of Research: Stochastic simulation and temporal disaggregation of rainfall time series for hydrological modelling

Article Title: Virtual Rain v1.0: a unified toolkit for high-resolution rainfall simulation and disaggregation

Article References: Cappelli, F., Grimaldi, S., Petroselli, A., & Santinami, E. (2026). Virtual Rain v1.0: a unified toolkit for high-resolution rainfall simulation and disaggregation. Geoscientific Model Development, 19(19), 9489-9518. https://doi.org/10.5194/gmd-19-9489-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-9489-2026

Keywords: rainfall simulation, stochastic modelling, disaggregation, CoSMoS-2s, multifractal random cascade, IDF curves, flood risk, hydrology, open-source software, time series generation, Geoscientific Model Development, Tuscia University