Investigating the radar-rain gauge observation-scale gap through local multifractal singularity

Abstract. Rain gauges and weather radars observe rainfall at substantially different spatial supports, from near-point gauge measurements to kilometre-scale radar pixels. Given the strong spatial variability of rainfall, this observational-support mismatch contributes to radar-gauge differences independently of instrumental and retrieval errors. Here, we investigate this scale effect using local rainfall singularity, which describes how rainfall intensity changes with observational scale through a locally estimated power-law exponent. The approach is applied to radar and rain-gauge observations for 10 rainfall events over the United Kingdom. Locally identifiable scaling behaviour is found for a substantial proportion of the observations, with scaling over 1–16 km being more consistent than over larger spatial ranges. The retrieved singularities are then used to extrapolate radar rainfall towards a pragmatic finer support of 50 m. Accounting for local scale dependence substantially modifies radar rainfall estimates but does not systematically improve their agreement with gauges; instead, conventional verification scores generally deteriorate. These results show that observational-support mismatch is only one component of radar-gauge disagreement, alongside radar retrieval errors, gauge uncertainty, and unresolved rainfall variability. Local singularity therefore provides a scale-aware diagnostic for investigating radar-gauge differences, rather than a direct correction towards point-scale rainfall.