Research Interests

My research activity is driven by an interest to explore and analyze scaling properties of precipitation in a space-time framework, pertaining to statistical characteristics (i.e. probability distributions their moments and spectral distributions) of three basic quantifiers of precipitation phenomena:

This research aims several intermediate targets, ranging from developing statistical diagnostics (based on appropriate linear or non-linear regression) for various scaling properties, to stochastic modelling, leading ultimately to spatial reconstruction and tempopral prediction of rainfields by stochastic spatial down-scaling of STARR time series "observed" with high sampling frequency (e.g. hourly or sub-hourly intervals of aggregation and/or lag) over large enough regions of reference (~1000km diameter). Such down-scaling is actually feasible by implementation of (discrete) dynamic multiplicative cascades, driven by time-and-scale dependent stochastic generators shaped on the basis of suitable scaling properties. The postulate of spectral multiscaling (SMS) constitutes tangible paradigm of a scaling property suitable for that very purpose, actually being diagnosed as statistically significant in observed (as radar images) and in simulated (by spatio-temporal Random Pulse Models (RPM) fitted to radar images) rainfields. Although the idea of developing a stochastic framework for spatial down-scaling of time series representing spectrally multiscaling spatial or spatio-temporal aggregates is relatively new, it is a rather promising one, reaching beyond rainfall research to the broader realm of Geophysical and Environmental Sciences, where spatio-temporal data gathered via remote sensing technologies are instrumental to resolving pending problems (e.g. Problem of Ungauged Basins (PUB) in Surface Hydrology). 

In the case of rainfields, scaling properties appropriately diagnosed through analyses of spatio-temporal data:

In a "nutshell", exploration and statistical analysis of scaling properties plays a key role in stochastic modelling of both intermittency and variability of precipitation across wide ranges of scales, usually discerned to micro-scales (1 m - 1 km) , meso-scales (1 km - 1000 km), and synoptic or macro-scales (greater than 1000 km), while scaling properties of precipitation may be viewed as statistical links between the (non-linear) physics and the (multifractal) geometry of the phenomenon.

The typical format of data used for this research is that of regular time series (hourly or sub-hourly sampling frequency) of 2D-images, in short referred to as "map-series", usually produced from probes of rainfields via remote sensing (e.g. GATE, TOGA-COARE), although some products may be based on spatial smoothing of measurements from a dense network of rain-gauges (e.g. CPC-NOAA) or even on assimilation of different remote sensing probes (e.g. TRMM-GPM) possibly inclusive of "ground truth" measured by rain-gauges too.

Each map in the series represents a 2D-spatial distribution of the observed rainfield in terms of rain-rate values over a lattice (usually regular) of pixels (usually squares; 2km x 2km or 4km x 4km or coarser). Each 2D-spatial distribution could be (practically) instantaneous or cumulative over a time interval of length equal to the regular sampling frequency of the series, but without overlaps of time intervals of accumulation between successive maps in the series. This type of data is most appropriate for concurrent investigation of spatial and spatio-temporal aspects of rainfall at multiple scales of aggregation in a statistically comprehensive manner. Moreover, map-series rainfall data facilitate the exploration of relationships between a variety of statistics among Intensity, Duration, and Coverage, such as the well known "Optimal Threshold Method" (OTM) for estimation/prediction of rain rate spatial averages over a large enough region, using as linear predictor the fraction of that region where pixel rain rate values exceed a certain optimal threshold level (i.e. wet coverage with respect to the optimal threshold intensity).

The above described research interests and activity meet with several areas of Statistical Science, feeding back renewed interests on:

 

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