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:
That is, precipitation intensity or rate R(S,T) is by its very definition a genuinely scale-dependent random variable,
with respect to a spatio-temporal scale of aggregation determined by the geometry of the region S and the interval T of its "observation".
The accuracy of rain rate measurements is much greater when made locally on the ground by a single rain-gauge instrument
collecting actual raindrops as they land on its orifice, but it suffers by substantial error when rain rate is retrieved from echoes of radio or laser or microwave signals
reflected by interraction with probed populations of raindrops (or just cloud) via remote sensing technologies (e.g. grounded RADAR and LIDAR or space-borne satellite instruments).
Retrieval methods and algorithms rely partly on merely empirically understood relationships between high order moments (3-6 or higher) of drop size distributions (DSD's)
and various types of echoes generated by different electromagnetic radiation signals; e.g. power-law Z-R relationship between Z(S,T) radar reflectivity
(proportional to 6th moment of DSD) and R(S,T) rain rate (proportional to 3rd moment of DSD). Ultimately, modelling and inference of DSD's is typically based on
information/data collected by Disdrometers (DD), instruments on the ground probing populations of raindrops (i.e. counting raindrops in different bins of size/diameter
as they fall through a fixed chamber, measuring also their terminal velocity).
Duration of Wet and Dry "spells" along time at a given location/region,
Coverage by Wet and Dry "patches" across space at a given instant/interval.
Wet/Dry "spells" (along time) and "patches" (across space) are configured with respect to a given ô-threshold intensity,
so that "wetness" is associated with intensity values exceeding that (naturally non-negative) threshold level ô,
rendering intermittency of precipitation (across space as well as along time) with respect to that ô-threshold.
Usually intermittency is addressed only with respect to the threshold level ô = 0 (i.e. the lowest possible value of intensity,
naturally associated with total abscence of landed raindrops), attained with positive probability (unlike every other possible value ô > 0) to
suggest that precipitation intensities follow probability distributions of mixed type at any scale of aggregation actually (despite any scale-dependence
of such probability distributions).
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).
Intensity defined as spatio-temporal average rain rate (STARR),
by the ratio R(S,T) = ÄV/(ÄS*ÄÔ) of (random) total water volume ÄV, fractionally carried/contributed/accumulated by a population of individual raindrops
(with randomly varying diameters) landing in a given region (S) of area ÄS > 0 during a given interval (T) of
length ÄÔ > 0. The randomness of the numerator ÄV (but also the intermittency of its positive values by 0),
stems from the size of the population of raindrops and the probability distribution of their diameter size.
In the case of rainfields, scaling properties appropriately diagnosed through analyses of spatio-temporal data:
May serve as diagnostic tools for potential validation of spatial, temporal, and spatio-temporal models, being either purely stochastic (e.g. multiplicative cascades, point process models, diffusion models, hidden Markov models, etc.) or physical models (e.g. General Circulation Models, Climate Prediction Models, etc.) or hybrid models.
May facilitate parsimonious modelling of rainfields, by potentially rescaling just a few key parameters, but otherwise maintain the same stochastic model structure across the range of scales where such scaling is diagnosed to be statistically significant.
May facilitate to control bias and error in rainfall estimates produced by retrieval methods/algorithms from probes of rainfields via remote sensing technologies.
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 ìm - 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: