Application in Singapore

Similarly to the geostatistical approach discussed in section5.3, the effect of different dis-tances as well as different temporal aggregations on the spatial Spearman’s rank correlation functions are conducted but using the pairwise-based approach. Empirical investigation results are presented in Figure5.9and Figure5.10. Figure5.9and Figure5.10depict the spa-tial rank correlation functions of precipitation values at different time scales from hourly to monthly scale as well as different seasons using the pairwise approach in the region of Singa-pore. Figure5.9highlights the effect of various distances on the Spearman’s rank correlation, whereas Figure5.10emphasizes the impact of different time scales on the correlations.

66 5.4. PAIRWISE CONTEXT Effect of spatial scales The spatial Spearman’s rank correlations decline gradually as the result of the increment distances corresponding to the stations located at different locations and fit well enough using the negative exponential functions which are marked with the red lines as shown in Figure5.9. The spatial correlation behavior above is similar to those which are conducted based on the geostatistical approach.

However, the spatial correlation functions carried out based on the pairwise approach ex-hibit significantly higher values in comparison to the geostatistical approach. The correla-tion lengths based on the pairwise approach roughly range from 12-255 km, whereas the correlation lengths which are conducted based on the geostatistical approach only roughly range from 12-15 km as presented in section5.3.

Unlike the geostatistical approach, where the correlations are nearly independent of the seasons, empirical evidence proves that the spatial correlation functions conducted on the basis of the pairwise approach are influenced by the seasonal periods. For example, in the months of DJF and MAM, the correlation lengths roughly vary between 21 and 60 km, and 12 and 30 km for hourly and 12-hours scale, respectively. By contrast, in the months of JJA and SON, despite of the correlation lengths at the time scale of hourly and 12-hours presenting similar behavior for both seasons, namely, ranging from 15 to 43 km and 15 to 41 km, respectively, the values are significantly different from those which are estimated above in the seasons of DJF and MAM. For the higher temporal scales, such as from daily to monthly scales, the correlation lengths exhibit significantly different values for all different seasons, namely, ranging from 53 to 103 km, and from 46 to 110 km for the seasons of JJA and SON and roughly varying between 66 and 213 km and between 33 and 60 km for the seasons of DJF and MAM, respectively.

Another characteristic dissimilarity of the spatial rank correlation functions carried out on the basis the geostatistical and pairwise approach in term of the aspect of spatial scale is that the variability of the spatial rank correlation function based on the pairwise approach increases with the increase of distance scales. This is contradictory to the geostatistical ap-proach where the increment of distance scales brings less uncertainty of the Spearman’s rank correlation at least until a specific distance point, for example, the distance of 15 km.

Effect of time scales The impact of different temporal scales on the Spearman’s rank correlation functions which are estimated based on the pairwise approach are obviously seen in Figure5.9. Overall, the Spearman’s rank correlations increase dramatically because of the increase of temporal scales from hourly to monthly scale. This tendency is more decisive than those which are calculated by the geostatistical approach. This pattern applies not only to the specific distances of the gauge pairs which are located at different locations but also to all distances from 5 to 25 km. This increasing trend of the correlations applies for all different seasons no matter which season of the year.

The variability of the Spearman’s rank correlation function generally decreases with time scales. This is consistent with the geostatistical approach where the increment of tempo-ral scales brings less uncertainty of the correlation. However, the degree of variability is substantially small in comparison to the geostatistical approach. Outliers are found more

frequently as the temporal scales increase, which slightly differs from the geostatistical ap-proach.

Effect of anisotropic assumption Figure5.11shows isolines of spatial correlation in the two-dimensional spaces of distances at different timescales from hourly to 5-days scale and in different seasons using the pairwise approach in Singapore in order to detect spatial anisotropy correlation. Overall, the anisotropic spatial correlation functions are pronounced only for the DJF season, during which the North-East Monsoon occurs. Thus, the spatial rank correlation in the North-East to South-West direction is the largest among other direc-tions.

The Northeast Monsoon occurs from December to early March when the cooling of the air masses over Siberia and Tibet leads to a high-pressure zone over Asia generating a constant north-eastern airflow transporting moisture from the Chinese Sea into the area. This means that the correlations are higher orthogonal to the prevailing wind direction. It is an indica-tion that some of the events have a frontal character so that the staindica-tions in the North-West to the South-East configuration are on the same line relative to the flow field and thus receive precipitation within the timeBeck et al. (2015). For other seasons (MAM, JJA, and SON), the spatial correlations exhibit isotropic behavior because of the cylindrical isolines of the correlation functions implying that the rank correlations are the same in all directions for any given distance, on the whole.

68 5.4. PAIRWISE CONTEXT

Figure 5.9: The Spearman’s rank correlation functions over distances using the pairwise ap-proach in the regions of Singapore. The vertical axes represent the rank correla-tion. Panels from top to bottom represent seasons (DJF, MAM, JJA, and SON).

The horizontal axes represent distances (from 5 km to 25 km). Each panel repre-sents the time scale (hourly (1h) to monthly (1m).

Figure 5.10: The Spearman’s rank correlation functions over time scales using the pairwise approach in the region of Singapore. The vertical axes represent the rank cor-relation. The horizontal axes represent a variety of time scales from hourly to monthly. Panels from top to bottom represent seasons (DJF, MAM, JJA, and SON). Panel from left to right represent distances (5 km to 25 km).

70 5.4. PAIRWISE CONTEXT

Figure 5.11: Isocorrelation lines in the two-dimensional spaces of distances using the pair-wise approach in Singapore. The vertical axes represent the lag distances in North and South direction in km unit. The horizontal axes stand for the lag distances in East-West direction. Panels from top to bottom represent seasons (DJF, MAM, JJA, and SON). Panels from left to right represent time scales from hourly to 5-days.