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is the vector of the n pixels in the image and
H
{}
ij
h
is the n x n matrix of the advection
operator.
Ruzanski et al. (2011) report that their approach is computationally efficient, although the
time taken to derive the motion vectors was comparable to that required for optical flow.
Furthermore, the advection algorithm was an order of magnitude slower than a simple
implementation of a semi-Lagrangian backward interpolation scheme. Both Ruzanski et al.
(2011) and Fox and Wikle (2005) demonstrated their methods using small images. The size
of the advection operator is likely to become a constraint when using this technique to
advect a large (say 10 6 pixels) image.
4.1.3 Analogues
Panziera et al. (2011) provide a good introduction on the assumptions and use of analogues
in nowcasting. Advection-based tracking techniques rely on the assumption that
precipitation fields evolve relatively slowly in Lagrangian coordinates and, therefore, their
future state can be predicted largely by extrapolation. The assumption of Lagrangian
persistence becomes a major limitation on the accuracy of nowcasts in situations where a
field evolves rapidly, for example in situations where new storms are initiated or existing
storms grow or decay. Data mining and analogue techniques seek to predict initiation,
growth and decay by matching the current weather pattern with similar, past events and
then use these past events as the basis for generating a forecast.
The first step in the use of analogues is to, either identify a set of regimes in the historical
data, or identify a set of predictors that can be used as measures of similarity. Thereafter, the
analogue that is closest to the current situation is selected and used as a basis for the
forecast. This implies that the technique must be trained for each location, and that a
significant historical record is available. Panziera et al. (2011) used predictors of mesoscale
airflow and air-mass stability to select 120 analogues, and then employed two measures
from the radar derived rainfall fields to select a set of 12 analogues to use as a forecast
ensemble. Foresti and Pozdnoukhov (2011) derived maps of where orographic enhancement
was likely to occur for a set of weather types. These could then be used to correct biases in
advection forecasts.
4.2 Errors in precipitation nowcasts
4.2.1 Error sources and attribution
Sources of forecast errors include errors in the initial quantitative precipitation estimates
(QPE), those arising from incorrect diagnosis of the field of motion, and changes in the
motion and evolution of precipitation fields during the forecast period.
Approximately half of the total forecast error in the first hour of a forecast is due to errors in
the radar derived rainfall analyses (Bellon & Austin, 1984; Fabry & Seed, 2009). This is
because radar rainfall estimation errors, arising from variations in the relationship
employed to convert the observed radar reflectivity to rainfall, have significant correlations
over about an hour in time (Lee et al., 2007) and tens of kilometres in space (Velasco-Forero
et al., 2009; Yeung et al., 2011).
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