Multifractal singularity to bridge the scale gap between various rainfall measurement devices

Rainfall is known to exhibit extreme variability over wide range of space and time scale, which makes it challenging to characterize, model and even measure. Rainfall measurement devices have observation scales very different from one another ranging from roughly 20 cm in space and few tens seconds (or few minutes) in time for punctual measurement such as disdrometers (or rain gauge), to few hundreds meters in space and few minutes in time for operational weather radars, and up to few kilometres in space and few tens of minutes for satellite data. This very significant observation scale gap between these devices creates a challenge in the comparion simply because of the intrinsic variability of rainfall, even without considering instrumental biases associated to each device.

This work focuses on the impact of the intrinsic rainfall variability on the comparison between punctual (disdrometer or rain gauge) and weather radar rainfall measurement. In order to achieve this, the physically based and mathematically robust framework of Universal Multifractals will be used. It relies on the assumption that rainfall is generated through an underlying multiplicative process. In such framework, the rain rate field can be written as the resolution (defined as the ratio between the outer scale of the phenomenon and the observation scale) to the power of a singularity. This singularity is preserved through scales.

Rainfall data collected in UK and Taiwan are used. These include high-resolution radar composite products and ground gauge records. In the UK, C-band radar composite, Nimrod, at 5-min and 1-km resolutions is used to compare with 1-min rainfall records derived from tipping bucket gauge records, while, in Taiwan, S-band radar composite, QPESUM, at 10-min and 1-km resolutions is used to compare with 10-second disdrometer rainfall records.

The concept of singularity is used to suggest an innovative comparison approach between rainfall measurement devices. More precisely, the local singularity along with the associated uncertainty is assessed using radar data on the range of available space time scales and then compared with the one of disdrometer or rain gauge accounting for the ratio between the observation scales. Results and interpretation of this novel comparison method on the available data will be discussed.

Authors acknowledge the France-Taiwan Ra2DW project (supported by the French National Research Agency – ANR-23-CE01-0019-01 and Taiwan’s National Science and Technology Council – 113-2923-M-002-001-MY4) for partial financial support.