Reconstructing representative runoff coefficients in small basins using limited historical data

Flood events can be highly localized in both time and space. Many of the most severe events observed in recent years have occurred in small catchments, where high flow velocities and the rapid development of floods substantially limit the effectiveness of monitoring and hydrometeorological forecasting. When reconstructing the characteristics of such events, together with the analysis of catchment response times, attention is commonly given to soil infiltration and retention processes. In engineering applications, the runoff coefficient is often used to describe the proportion of rainfall that becomes runoff during an event.

For a given watershed, the runoff coefficient is not a fixed parameter; it varies considerably with event intensity and the physical and hydrological characteristics of the catchment. This study proposes a practical methodology for estimating a representative catchment runoff coefficient where high-resolution rainfall and streamflow time series are lacking. Leveraging more than 1,000 historical events from 60 small to medium-sized catchments in diverse climatic regions of Italy, sourced from national Hydrological Yearbooks, we reconstruct annual runoff coefficients from historical hydrological extremes and compare two estimation methods: an event-based and a frequency-based approach.

A key element of the event-based method is the development of a procedure to associate discharge maxima with their corresponding rainfall maxima in time, which was necessary because, in many cases, the dates of occurrence of extremes (day/month) were not recorded. On the other hand, a frequency-based pairing of rainfall and discharge extremes was shown to provide runoff coefficient estimates that are comparably robust to those obtained with the event-based approach.

Further investigation of case studies characterized by unusually low (below 0.1) or high (above 1) runoff coefficients highlighted several sources of data inconsistency that can compromise estimate reliability. The most common issues include spatial mismatches between rain gauge locations and catchment boundaries, transcription errors in historical datasets, and additional runoff contributions, such as snowmelt in Alpine regions. Recognizing and accounting for these factors allowed for a more consistent and reliable estimation of runoff coefficients.