Identification of dry and rainy periods using telecommunication ...

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12 nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011 R [mm/h]; Residuals [dBm]; RSL [dBm]; B [dBm] 24 0 -24 -48 Measured rain intensity [mm/h] Residual (dBm) of: - only fast model (upper, dark grey line) - the combination of fast and slow model (lower, black line) B ± threshold for only the fast model (grey lines) or the combination of the fast and slow model (black lines) [dBm] RSL (dBm) -72 17.07. 12:00 17.07. 16:00 17.07. 20:00 18.07. 00:00 18.07. 04:00 Page 6 of 12 Timestamp of the connection between the two sub-models Figure 4 Signal decomposition of MWL No. 8 with a Gaussian Factor graph. (Bottom) RSL and baseline model, (Top) Fast and slow baseline components, Residual attenuation and Measured rain intensities. Type I errors: dry class error (false rainfall alert) = False Positives / n_dry (3) Type II errors: wet class error (missed rain) = False Negatives / n_wet (4) RESULTS AND DISCUSSION Moving window algorithms The results for period A demonstrate that the original algorithm (S1a and S1b) is prone to 25.4 - 64.9% of type II errors ( Figure 5, left), which is unsatisfactory. It is remarkable that type II errors of the MWL with a 0.1 dBm quantization were about half of those with a coarse quantization. For the coarse quantization MWL, we found that the wet class errors decreased with increasing �Wt. In contrast, our modified algorithm, S2, presented lower wet class errors and higher dry class errors. Furthermore, S2 showed a superior performance regarding the true detections of dry and wet periods for all the investigated MWL in our study area ( Figure 5, right). Period B included events with snowfall and ice particles, which have a different influence on millimeter microwave attenuation (Brussaard and Watson, 1994). Therefore, the wet Figure 5 (Left) Class errors for S1a, S1b and S2 for ten MWL with a fine (0.1 dBm) and four with a coarse (1.0 dBm) quantization for period A. (Right) Proportion of the RSL measurements that were classified as wet by a rain gauge for the methods S1a, S1b and S2 for period A (mean over all 14 links). The class errors were calculated without offset.
12 nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011 class error for S1a and S1b increased to approximately 45% (coarse quantization: 75%). In contrast, the wet class error for S2 only increased to 20 % (coarse quantization: 30%). As expected, the dry class error did not experience important changes. Regressive classification trees and random forests Similar to the above algorithms, we developed individual classifiers for the 14 MWL based on Random forests and the various attributes computed from period A data. As described above, we classified dry (D) and rainy periods, split into light (L) and strong (W). The direct comparison with S1-S2 shows rather favourable results for the random forest algorithms RF1- RF6, because less than 5% of all rainy cases {L,W} were misclassified as dry (results not shown). We found that the mean class errors for RF1- RF6 (averaged over all 14 links) for class W were about 20%, with 30-50% errors for L, light rains, which means that many light rains are wrongly classified as strong and vice versa. Also, the online algorithms perform competitively against the offline algorithm, because the class error for W is very similar and errors for the two other classes only increase slightly (e.g., D: RF1/RF2 = 19.9%/22.2%). For period B, the class errors (averaged over all links and over RF1-RF6) showed an increase of 9.9 % (D), 3.9 % (L) and 8.5 % (W) (absolute values). Figure 6 shows the average �Gini for the offline algorithm RF1, which indicates the potential of the different attributes to identify dry or wet periods. First of all, we found that the important attributes depend on the quantization of the MWL. Second, min(RSL) (for �Wt= {15,30}) and the RSL itself are very informative for the MWL with 0.1 dBm resolution. Third, for the coarse MWL, the by far most informative attribute is the radar rainfall (RTS_past) and the attributes calculated based on the RSL unfortunately do not contain much information. Interestingly, attributes computed from �Wt=120min are very informative for the coarse MWL, but not for the fine ones. The online algorithms (RF2, RF4 and RF6) which only use past information show similar patterns. Gaussian factor graphs For the data from period A, we found that, for the fine (coarse) MWL, the factor graph produces 2% (7%) of type I errors, and misclassifies about 35% (32%) of the W class (Figure 7). For period B, this is about 1% (5%) higher (absolute values). Nevertheless, the Factor Graph is a very elegant algorithm, because it can cope very well with pronounced signal fluctuations and even large gaps of missing data (Reller et al., 2011). In addition, the available MATLAB implementation is very fast compared to current implementations of the other algorithms. The classification performance could be further optimized by tuning, eventually also accompanied by a post-processing to filter out unrealistically frequent and small rain events. �Gini 180 160 140 120 100 80 60 40 20 0 min15_fut min30_past min15_past min30_fut RSL RTS_past min120_past std120_past std30_past min120_fut std30_fut std120_fut max15_fut q10_120_fut q10_120_past std15_past std15_fut max15_past autocor120_past slope30_fut Page 7 of 12 slope120_fut slope30_past max30_fut autocor120_fut slope120_past max30_past slope15_past 0.1 dB-Links 1 dB-Links slope15_fut q90_120_past rain_10_40_past autocor30_past autocor30_fut max120_fut max120_past autocor15_past autocor15_fut Figure 6 Mean Gini-decrease for algorithm RF1. �Gini is the average decrease over ten 0.1 dBm and four 1.0 dBm links.
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