techniques which go beyond point-to-point pair verification. This emanated from the necessity to appropriately evaluate goodness of fit of data of fine temporal and spatial resolutions since the traditional approaches were likely to penalize small differences in location and intensities, by trying to find an exact match based on point-to-point verification (Rossa et al., 2008).
In the context of radar nowcasting (short term forecasting 1-6 hours), it is very likely that the area-based nowcasting technique used to generate the forecast will produce a forecast with seemingly realistic precipitation patterns but with intensities and locations somewhat misplaced (Mesin, 2011), and so it is unreasonable to expect a perfect match. These small errors in magnitude and displacements can potentially have significant impact on hydrological applications in urban catchments, depending on the size of the catchments.
40
Accordingly, the verification approach should give an indication of the forecast skill at different spatial scales.
Publications relating to the verification of radar based QPFs against QPEs are rare. Instead more studies have focused on the comparison of radar based QPE against rain gauge data mainly to provide information in order to improve their estimates, such as for calibration (Seo et al., 2013, Russell et al., 2010, Chumchean et al., 2006, Brown et al., 2001, Borga, 2002).
Comparing radar based QPFs against radar based QPEs gives an indication of how well the nowcasting technique performs, making the understanding of uncertainty sources a little less complex. To illustrate the verification of radar based QPFs data with radar based QPEs ,a method which is more commonly used for verifying NWP QPF against radar QPE is applied (Mittermaier et al., 2013, Zacharov and Rezacova, 2010, Roberts and Lean, 2008). In the fractions skill score (FSS) method, developed by Roberts and Lean (2008), the condition of exact match is relaxed to provide an estimate of goodness of fit at different scales for different rainfall thresholds.
The gridded observational and forecasted data sets considered covered 5 stratiform and 5 convective events during the period Nov 2012- Nov 2013, for the X-band radar. The method involves splitting the verification area into a number of neighbourhood windows of a certain spatial scale ๐ , and computing the proportions of both the observed and forecasted fractions for a particular rainfall threshold. In order to determine at which scale the neighbourhood is useful, the size of the neighbourhood is increased. The verification score, in this case, the Fractions Skill Score (FSS), is computed using:
๐น๐๐ = 1 โ 1/๐ โ [๐๐น๐ โ ๐๐๐ ] 2 ๐ 1/๐[โ ๐๐น๐ 2+ ๐ โ ๐๐๐ 2 ๐ ] (1)
where ๐ is the number of neighbourhood windows in the verification area; ๐๐น๐ and ๐๐๐ are the neighbourhood proportions at the ๐๐กโ grid box in the model forecast and observed fraction fields ๐ . This is discussed in more detail in Chapter 11.
41
The FSS values for a convective and stratiform event as a function of lead time for a rainfall threshold exceeding 0.3mm/hr are presented in Figure 3-2. As expected there is an increase in FSS as the spatial scale increases for both events. However, more encouraging results were shown for the stratiform event, plot (b) even at radar pixel scale (0.5km). The big difference in FSS scores for stratiform and convective regimes is related to their characteristic features. Stratiform events are a lot easier to forecast because of their fairly large homogenous extents. The evidence from this study suggest that the forecast are generally better for stratiform regimes, a more extensive study is required to generalize the results since the value of the FSS depends on the number of events evaluated.
Figure 3-2: Fractions skill scores for the 5 minute forecasted precipitation intensities at different spatial scales as a function of forecast lead time with the threshold of 0.3mm/hr for a convective (a) and stratiform (b) event. The model domain is 4.5x13.5km.
00 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1
Lead Time [minutes]
F S S 27-07-2013 00 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1
Lead Time [minutes]
F S S 22-05-2013 0.5km 1.5km 4.5km model domain (a) (b)
42
4 Uncertainty estimation in QPF
Precipitation is the most dominant input in flood forecasting. This is of greatest interest as precipitation is the single most uncertain variable in hydrological modelling. According to Butts et al. (2002) operational experience suggests that in many cases the forecasted and observed precipitation inputs are the most significant source of forecast uncertainty and therefore it is desirable and recommended that estimates of forecast uncertainties are made as part of the forecast.
To date, there are many methods for uncertainty estimation in NWP QPFs but less so for radar based QPFs (Dai et al., 2014, Liguori et al., 2012), despite the inherent uncertainties in the radar based QPEs. Radar based QPFs are a derivative of radar based QPEs, and as such there is an uncertainty cascade which is not limited to the uncertainty in the QPEs but also with the nowcasting technique. Nonetheless, this chapter only presents and demonstrates the applicability of a method for uncertainty estimation in NWP QPFs and relates it to current approaches. The method is developed on a case with high resolution data and a modified version is presented on a case with poor quality data. The uncertainty estimation method could also be applied to QPFs from weather radar with some modification to distribute the error spatially.