a. Precipitation difference and biases
When simulating the CP-WRF events, the average total precipitation in all synoptic-related events exceeded the raw ECMWF precipitation. Among the extratropical events (Fig. 4), the total precipitation notably increased at lead time W1 over the west coast of the AP, just north of Jeddah and the Zagros Mountains east of the Persian Gulf (also known as the Arabian Gulf) (see the difference plot in Fig. 4g). The precipitation was notably increased over the central AP where the raw ECMWF generates drier conditions. At W2, the CP-WRF precipitation was again higher over Jeddah, the central Red Sea, and the Zagros Mountains than the raw ECMWF precipitation (Fig. 4b and e) as shown in the difference plots (Fig. 4h). However, the CP-WRF produced drier conditions over the central AP than the raw ECMWF. Similarly to W2, the CP-WRF at W3 obtained higher total precipitation over the central Red Sea, near Jeddah, and the Zagros Mountains than the raw ECMWF (Fig. 4c, f, and i). Over the Red Sea, where the raw ECMWF barely generated precipitation at W3, the precipitation increase was notable.
Among the tropical events (Fig. 5), the average total precipitation of the CP-WRF at W1 was also higher than the raw ECMWF precipitation, especially over the central AP (see difference plot in Fig. 5g). Interestingly the CP-WRF produced two separate precipitation maxima: one southwest of Jeddah, the other southeast of Jeddah. The city of Jeddah was drier in the CP-WRF model than in the raw ECMWF. At W2 in the raw ECMWF, the precipitation exceeded 8 mm over a large area of the central Red Sea (Fig. 5e), whereas in the CP-WRF, the precipitation was concentrated over the high terrain southeast of Jeddah to the central AP and the east coast of Sudan, exceeding 18 mm precipitation in total (Fig. 5b). In contrast, the central Red Sea was almost dry. Similar patterns were found at W3, but the precipitation signatures were weaker than at W2 (Fig. 5c). These high average precipitations at W1, W2, and W3 in the CP-WRF were likely attributable to convective organization at the meso-γ scale, particularly over the complex terrain southeast of Jeddah, which could be resolved in this model but not in the raw ECMWF.
Figure 6 shows the average accumulated precipitations of GPMF and KAUST-RA and the precipitation biases of the CP-WRF at W1, W2, and W3 in the extratropical events. The GPMF clearly gave more precipitation (> 20 mm) in the central AP than the KAUST-RA (Fig. 6a, b, c, g, h, i). The CP-WRF precipitation exhibited a dry bias (indicated by the blue shading) relative to the GPMF precipitation at W1, W2, and W3 (Fig. 6d to f) in the north of Jeddah, the central AP, and the Zagros Mountains. Conversely, it showed a wet bias (< 15 mm) (indicated by the red shading) in the central Red Sea at W2 and W3. Compared to the KAUST-RA precipitation, the CP-WRF consistently exhibited a dry bias over Jeddah and the Zagros Mountains at all lead times (Fig. 6j to l).
Figure 7 shows the observed precipitation and the CP-WRF biases during the tropical events. The KAUST-RA generated more precipitation (> 18 mm) than the GPMF, especially over the central AP (Fig. 7a, b, c, g, h, i). Compared to the GPMF, the CP-WRF exhibited a dry bias over Jeddah and the central AP that increased from W1 to W3 (Fig. 7d to f). Interestingly, wet biases were notable over the east coast of Sudan and the southwestern tip of the AP (Fig. 7d to f). The dry bias of the CP-WRF was more pronounced relative to the KAUST-RA precipitation than relative to the GPMF, especially over the central AP (Fig. 7k, l). This result was expected, because the KAUST-RA generated more precipitation than the GPMF.
In summary, the CP-WRF generated more precipitation in the extratropical events than the raw ECMWF at W1, W2, and W3. This is shown in the differences, which were dominated by positive values over the central Red Sea, the central AP, and the Zagros Mountains. In the tropical events, the CP-WRF generated notable precipitation only in the southwest of Jeddah, the east coast of Sudan, and the central AP at W1. The raw ECMWF generated more precipitation over the central Red Sea at W2 and W3 than the CP-WRF. In general, the CP-WRF precipitation was lower than the GPMF and KAUST-RA precipitations, but higher than the raw ECMWF precipitation.
b. Precipitation categorical statistics
Figure 8 displays the differences between the CSI, POD, and FAR of the CP-WRF and raw ECMWF precipitations relative to the GPMF precipitation for the extratropical events. Consistent with the average CP-WRF precipitation, the precipitation forecast skills were consistently higher in the CP-WRF than in the raw ECMWF when domain-averaging was applied, irrespective of the forecast timescale. The CSI and POD differences were also field-significant (> 90%) from W1 to W3. At W1, the precipitation forecast skill was high (blue shading) over the entire Red Sea, the central AP, and the Zagros Mountains. At W2 and W3, the forecast skill was notably high over the central Red Sea including Jeddah and areas along the west coast of the AP, and also over the Zagros Mountains. The FAR results (here plotted as 1 – FAR) were consistent with the CSI and POD results but were not field-significant.
Figure 9 displays the differences between the three verification metrics of the CP-WRF and raw ECMWF precipitations relative to the GPMF for the tropical events. These results confirm the average CP-WRF precipitations during the tropical events in the previous subsection. At W1, the CP-WRF better forecasted the precipitation than the raw ECMWF (blue shading) over the central AP and a small part of the Red Sea, but underperformed around Jeddah and the central Red Sea (red shading). At W2, the forecast skill of the CP-WRF was higher only over the areas east of Jeddah, the central and northern AP, and the east coast of Sudan. Over this area, the raw ECMWF generally outperformed the CP-WRF, possibly because the CP-WRF inadequately resolves the precipitation over the central Red Sea. As mentioned earlier, the persistent SST might reduce the forecasting ability of the CP-WRF. Finally, at W3, the CP-WRF better forecasted the precipitation than the raw ECMWF in the central Red Sea, Jeddah, and the Zagros Mountains.
Similar results were obtained using KAUST-RA as the ground reference. Figure 10 shows the CSI, POD, and FAR differences between the CP-WRF and raw ECMWF for the extratropical events. The CSI and POD differences were field-significant. At W1, the CP-WRF outperformed the raw ECMWF in the Red Sea, the central AP including the Jeddah area, and the Zagros Mountains. At W2 and W3, the enhanced precipitation forecast skill of the CP-WRF was notable in the central Red Sea, Jeddah, the west coast of AP, and the Zagros Mountains
For the tropical events (see Fig. 11), the difference plots of the CP-WRF and raw ECMWF again indicate a higher precipitation forecast skill of the CP-WRF than of ECMWF, and field significance of the CSI and POD results. At W1, the CP-WRF outperformed the ECMWF over the area east of Jeddah and the central AP, and northwest of the Persian Gulf. At W2, the enhanced forecast skill was notable over east of Jeddah, some parts of the central and northern AP, and along the east coast of Sudan. In contrast, the forecast skill of CP-WRF was reduced in the central Red Sea. At W3, the CP-WRF outperformed the ECMWF in the central Red Sea and the west coast of AP, including Jeddah.
Figures 12 and 13 show the frequency distributions of the POD relative to the GPMF for all week lead times in the extratropical and tropical events, respectively. In both sets of events and at all lead times, PODs above 0.8 appeared more frequently in the CP-WRF than in the raw ECMWF. At W2, the differences between CP-WRF and ECMWF were statistically significant (marked by yellow stars) only for PODs greater than 0.9, but at W1 and W3, they were statistically significant for PODs greater than 0.8. Among the tropical events (Fig. 13), PODs greater than 0.3 appeared more frequently in the CP-WRF than in the raw ECMWF at W2 and W3. The same results were found in the frequency distributions of POD relative to KAUST-RA (not shown).
In summary, the CSI, POD, and FAR difference results were very similar for two different data sources of observed precipitation. Therefore, the value added by the CP-WRF is not a function of any particular observational precipitation product. The CP-WRF can better predict both extratropical and tropical precipitation events than the driving raw ECMWF model, up to three weeks ahead of the events. More importantly, the CP-WRF demonstrated higher forecast skill than the raw ECMWF around the area of Jeddah, the central Red Sea, and the high terrain in the west coast of AP, suggesting that the CP-WRF can improve the forecast of extratropical-driven extreme precipitation events. Moreover, these extreme precipitation events occurred at sub-seasonal time scales at the original raw ECMWF resolution, but the overall precipitation amounts were lower than the observed amounts (see subsection 3.1).
c. ROC curves and AUC of precipitation
A 20-mm precipitation threshold was applied to each event in the ROC analysis. Figure 14 shows the ROC curves of the individual extratropical event relative to the GPMF precipitation for W1, W2, and W3. At W1, the raw ECMWF exhibited a high forecast skill in most of the events, but was outperformed by CP-WRF in five events (with AUC values > 0.8). The higher forecast skill of the CP-WRF is consistent with the verification metrics analyzed in the previous subsection. At W2, the AUCs of the CP-WRF exceeded 0.5 for nearly all events, again outperforming the raw ECMWF. Most importantly, the AUCs of more than 90% of the events at W3 were higher in the CP-WRF than in the raw ECMWF. Most of the AUCs in CP-WRF were slightly above 0.5. The AUCs below 0.5 in the CP-WRF (two events) were higher than their counterpart AUCs in the raw ECMWF.
Figure 15 shows the ROC curves of the individual tropical events for all lead times. Similarly to the extratropical events, the tropical events were well forecasted by the CP-WRF. At W1, the AUCs of all events were higher in CP-WRF than in the raw ECMWF, although the AUC of one ROC was lower than 0.5 in the CP-WRF model. At W2, the AUCs of the ROC curves of all events exceeded 0.5 in the CP-WRF, but were below 0.5 in the raw ECMWF. At W3, the CP-WRF and raw ECMWF again yielded notably different ROC curves. The AUCs of the ROCs exceeded 0.5 for almost all events in the CP-WRF (for the two exceptions, the AUC was ~ 0.4). In contrasts, all events in the raw ECMWF yielded AUC values around 0.4.
Figures 16 and 17 show the ROC curves of the individual extratropical and tropical events, respectively, relative to the KAUST-RA precipitation for all lead times. Again, the precipitation prediction accuracy was higher in CP-WRF (AUC > 0.5) than in raw ECMWF at W1, W2, and W3. These results are consistent with the ROC curve analysis relative to the GPMF precipitation.
The average differences between the AUCs of the CP-WRF and raw ECMWF analyses relative to the GPMF and KAUST-RA precipitation data are shown in Tables 4 and 5, respectively. All differences are positive, confirming the higher precipitation forecast skill of CP-WRF than of raw ECMWF at W1, W2, and W3 in both extratropical and tropical events. Although the differences were slightly higher for the tropical events than for the extratropical events, whether the tropical events are more predictable than the extratropical events should not be decided from this ROC curve analysis alone, because the number of samples was statistically constrained and the ROC curve analysis covers the whole domain rather than regional areas such as Jeddah and the central Red Sea.
Table 4
Difference between the average AUCs of the CP-WRF precipitation events and those of the raw ECMWF precipitation events relative to GPMF precipitation
|
W1
|
W2
|
W3
|
Extratropical events
|
0.13
|
0.23
|
0.12
|
Tropical events
|
0.16
|
0.26
|
0.21
|
Table 5
Difference between the average AUCs of the CP-WRF precipitation events and those of the raw ECMWF precipitation events relative to KAUST-RA precipitation
|
W1
|
W2
|
W3
|
Extratropical events
|
0.10
|
0.19
|
0.12
|
Tropical events
|
0.17
|
0.23
|
0.20
|
In summary, the precipitation forecast skill of CP-WRF was high at W1, W2, and W3 for both extratropical and tropical events, whereas the driving raw ECMWF exhibited almost no skill at W2 and W3. At W1, the raw ECMWF showed some forecast skill for many events (i.e., AUC > 0.5), but was consistently outperformed by the CP-WRF (see Tables 4 and 5). Therefore, we concluded that the CP-WRF improves the predictability of extreme precipitation events (> 20 mm), up to three weeks ahead of the events on sub-seasonal forecast time scales. According to the categorical statistics (CSI, POD, and FAR) in subsection 3.2, the precipitation forecast skill over Jeddah and the central Red Sea is higher in the extratropical events than in the tropical events. Therefore, the extratropical events provide the forecast opportunity of CP-WRF at these sub-seasonal time scales.
Geopotential heights
Luong et al. (2020a) attempted to identify the dominant synoptic patterns underlying convective extremes over the AP. They found that the interaction between the 500- and 850-hPa geopotential height fields closely influences the positioning of the RST and AA and convective organization over the AP. Therefore, we assessed the predictability of the precipitation forecasts by evaluating the synoptic-scale geopotential heights in the ERA-Interim and raw ECMWF at different lead times of the forecasting. Figure 18 displays the Pearson’s correlation-coefficient contours (color-coded shading) between the ERA-Interim and the raw ECMWF 500-hPa geopotential heights, overlaid with the 500-hPa geopotential heights from the Luong–SOM analysis (solid lines) and the daily means of the 500-hPa geopotential heights extracted from the raw ECMWF (dashed lines). The correlation coefficients at W1, W2, and W3 were consistently higher for the extratropical events (Fig. 18a, c, e) than for the tropical events, as shown by both the color-coded shading and the average correlation coefficients (Rs) across the domain. The difference was notable at W3 (Fig. 18e and f) over Jeddah and along the west coast of the AP, where R > 0.7 for the extratropical events and R < 0.5 for the tropical events.
The 500-hPa geopotential height contours were also consistent with the correlation coefficients. At W1 (Fig. 18a), the raw ECMWF afforded extratropical 500-hPa geopotential contours that almost matched those of the Luong–SOM analysis, but its tropical 500-hPa geopotential contours (Fig. 18b) notably differed from those of the Luong–SOM analysis. At W2 and W3, the differences between the contours of the tropical events became more pronounced because the trough over the east coast of Africa was not developed (Fig. 18d, f). In contrast, the extratropical 500-hPa geopotential contours of the raw ECMWF almost matched those of the Luong–SOM analysis. The raw ECMWF did forecast the trough at W2 and W3, but at a weaker magnitude than that in the ERA-Interim.
Interestingly, the 850-hPa geopotential height contours presented higher correlations at W2 and W3 in the tropical events than in the extratropical events (Fig. 19c, d, e, f), whereas at W1, the correlation coefficients of both types of events were almost identical. The correlation-coefficient difference was large at W3 (0.05 for the extratropical events versus 0.32 for the tropical events, also evidenced by the shading). In the tropical events, the raw ECMWF at W2 and W3 (Fig. 19d, f) apparently predicted the RST that closely matched both the ERA-Interim and the Luong–SOM analysis. The AA was also predicted (albeit weakly, with R < 0.5) at W2 and W3. However, in the extratropical events, the raw ECMWF poorly predicted the dominant extratropical trough over the Red Sea at W2 and W3 (Fig. 19c, e). Instead, it presented a weak signature of RST over the east coast of Sudan, probably because the SST is warmer in the raw ECMWF than in the ERA-Interim.
The correlation coefficients of the extratropical and tropical 500-hPa geopotential heights were compared by Student’s t-test. The differences at W1, W2, and W3 were statistically significant at the \(pcript>\) significance level. However, when the correlation coefficients of the 850-hPa geopotential heights results were analyzed by the same test, the differences were statistically significant only at W2 and W3. The non-significant difference at W1 was consistent with the similar correlation coefficients at W1.
Whether extratropical events over the AP are more predictable at sub-seasonal time scales than tropical events is difficult to conclude from the above results. We hypothesize that the 850-hPa geopotential height is more directly affected by the rapid changes of near-surface variables such as the SST, moisture fluxes, and near-surface temperature, than the 500-hPa geopotential heights. Therefore, at this height, the forecast contains more uncertainty at sub-seasonal time scales than at 500 hPa. Consequently, the predictability of the 850-hPa geopotential heights disagreed with those of the 500-hPa geopotential heights based on the event classification. An investigation with more extreme event samples is needed. However, previous studies (e.g., Hafez and Almazroui, 2016; Christidis and Stott, 2015) have heavily relied on the 500-hPa geopotential heights for diagnosing extreme events because 500 hPa is the level of non-divergence and is commonly assumed in extreme weather and climate diagnostics. Therefore, considering only the predictability of the 500 hPa geopotential heights, the categorical statistics (CSI, POD, FAR), and the ROC analysis, we conclude that extreme precipitation at sub-seasonal time scales (W1 to W3) is more predictable in the extratropical synoptic regime than in the tropical synoptic regime.