A new classification of the magnitude of hydrological events and extremes using the Z value

In literature it is assumed that an extreme is a rare, high (or low) magnitude event, where the concepts of rarity and magnitude depend on
the physical and temporal contexts. A statistical approach is presented to measure and communicate the magnitude of hydrological events and identify extremes. The core of the method is the frequency analysis of time series and the transformation of any data probability distribution into a standard normal distribution, where the event magnitude is expressed by the Z value, which is dimensionless. It provides a probability-based measuring scale that is invariant from the nature and variance of the hydrological phenomena and the spatial context. The Z value has the same properties as standardized indices, such as the well-known Standardized Precipitation Index (SPI), used in drought monitoring. An “extreme” is defined as an event with magnitude Z ≥ 2 (upper tail) or ≤ –2 (lower tail), depending on the nature of the hydrological variable.

The “extreme event” definition proposed does not contain any details about the event’s impact on the ground surface. These impacts depend on both the event magnitude (e.g., rainfall intensity) and land use or anthropogenic modifications of the natural environment as well. Furthermore, any geomorphological and hydrological processes, such as landslides and floods, depend on additional hydrological factors, including the pre-event wetness conditions of the soil, which could dump or amplify the event impact on the ground surface. Thus, the association between the Z value (event magnitude) and its impacts on the Earth surface could not be direct.  

The Z value would provide a more suitable representation of the event magnitude than return period, commonly adopted to express the rarity or exceptionality of hydrological phenomena, as it represents a more stable scale, especially in the tails of the distribution. However, its use does not reduce intrinsic uncertainty and complexity of the probablity model.