Geoscience Reference
In-Depth Information
3.6 Exploration of statistical and statistical-dynamical models of precipitation
This same period saw the development of a number of statistical (Krajewski & Georgakakos,
1985; Cox & Isham, 1988) and statistical-dynamical predictive models of precipitation
(Georgakakos & Bras, 1984a, b; Lee & Georgakakos, 1990; French & Krajewski, 1994; Bell &
Moore, 2000a). The latter were formulated to assimilate radar estimates and surface
observations of precipitation and make forecasts using a simplified treatment of the
governing atmospheric equations, focusing on the conservation of water mass. These studies
were motivated by the operational forecasting requirements of the hydrological community
and the limitations of “steady-state” nowcasting techniques and the first generation of
operational, mesoscale NWP models.
3.7 Impact of forecast uncertainties
A growing recognition of the need to account for and communicate meteorological forecast
uncertainty (Murphy & Carter, 1980; Krzysztofowicz, 1983), particularly in relation to
precipitation, led to the development of a range techniques for probabilistic precipitation
nowcasting. Andersson and Ivarsson (1991) evaluated an advection-based nowcasting
scheme in which the probability of precipitation at a given location is estimated from the
areal distribution of precipitation in a neighbourhood surrounding it (see also Schmid et al.,
2000) This approach accounts for the impact of extrapolation errors on the location of
advected precipitation. Other authors have adopted similar approaches. For example,
Germann and Zawadzki (2004) used a local Lagrangian method to produce probabilistic
extrapolation nowcasts.
The previously mentioned theoretical work on multi-fractals, and empirical studies
supporting a scaling model representation of precipitation fields, laid the foundations for
the development of a number of stochastic precipitation nowcasting schemes exploiting
scale decomposition frameworks. Seed (2003) adopted a multi-scale decomposition
framework in his S-PROG (Spectral-Prognosis) scheme to nowcast the space-time evolution
of high resolution radar derived precipitation fields (see Figure 2); he highlighted the
potential application of S-PROG to conditional simulation and design storm modelling.
In a similar vein, the McGill Algorithm for Precipitation Nowcasting by Lagrangian
Extrapolation (MAPLE; Turner et al., 2004) exploits a wavelet transform to model the
predictability of precipitation as a function of scale. The aim of the scale decomposition is to
filter out the unpredictable scales in an extrapolation nowcast, and in so doing, minimize the
Root Mean Square nowcast error (typically measured using rain gauge observations and/or
radar inferred estimates of surface precipitation rate or accumulation).
Pegram and Clothier (2001) used a power law model to filter Gaussian distributed random
numbers to generate stochastic realizations of radar precipitation fields in their String of
Beads Model (SBM). Noise generation techniques similar to these were combined with a
stochastic model of extrapolation velocity errors in the Short Term Ensemble Prediction
System (STEPS, Bowler et al., 2006) to produce operational precipitation nowcasts
quantifying uncertainties in phase as well as amplitude. In STEPS, the noise serves several
purposes: it enables ensembles of equally likely nowcast solutions to be generated by
perturbing predicted features as they lose skill; it also downscales an NWP forecast,
injecting variance at scales lacking power (variance) relative to the radar.
