Geoscience Reference
In-Depth Information
The dimension of the contingency tables can be as small as 22 (tetrachoric) or larger
(polychoric) depending on the number of thresholds used in the classification scheme.
Obviously, in our wet-versus-dry hourly values discrimination, we are dealing with
tetrachoric tables, since just one discrete value (namely 0.4 mm/h) is used to divide the
two categories. On the one hand, the properties of a set of observations can be condensed
and clearly displayed through such tables; on the other hand, to satisfy needs of specific
users, even for a simple tetrachoric table, several different scores have been introduced.
Here, we will use two scores that can be applied to both tetrachoric and polychoric
tables:
the Heidke Skill Score (HSS), also known as Kappa Index of Agreement (KIA), Khat, …
the Hanssen-Kuipers (HK) score also known as True Skill Score (TSS), …
Details regarding these two scores can be found in literature; the interested reader may
refer, among others, to the paper by Tartaglione [2010] regarding HK and to the work by
Hogan et al. [2009] regarding HSS. In particular, the Appendix of this last paper interestingly
aims at estimating confidence intervals in the HSS.
G  0.4 mm/h
G < 0.4 mm/h
R  0.4 mm/h
38
4
42
R < 0.4 mm/h
10
92
102
48
96
144
Table 2. Contingency table between the Palermo radar estimates and the Altofonte rain
gauge measurements.
From Table 2, it is straightforward to derive the Probability Of Detection (POD), which is
38/48= 0.79 and the False Alarm Ratio (FAR), which is 4/42= 0.095.
Regarding the two above mentioned multi-categorical scores selected, HSS results to be
0.774 ; HK is slightly smaller: 0.750.
4.2.2 Quantitative agreement between gauge and radar-derived hourly rain rates
During the 48 “Wet-Gauge” hours, the total rainfall amount according to the Altofonte
Gauge was 72.4 mm. According the Palermo Radar, the total rainfall amount was 55.9 mm,
which means a residual “Wet-Gauge Mean Field Bias” of 1.1 dB (radar underestimation).
Based on these 48 “ Wet-Gauge ” hourly amounts, which are shown in Fig. 7, the Scatter
results to be 2.38 dB , as can also be seen from the 48 values displayed in Fig. 8.
Using only the 38 hours where BOTH the Radar AND the Gauge amounts were larger or
equal to 0.4 mm/h, the total Gauge (Radar) amount was 64.6 (54.7) mm. Consequently, the
“wet-wet” Mean Field Bias is 0.7 dB. As expected, also the “wet-wet” Scatter improves:
based on such 38 “wet-wet” hourly amounts, it results to be 1.97 dB, as can be seen from Fig.
9. The 0.4 dB decrease in the value of the Scatter is a clue of the not-negligible rain amount
missed by the radar during the 10 “Missing Detection hours”.
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