## 5 Variability of QBIE Temperature Events
### Internannual Variability and Predictability
The above ARIMA analysis indicates that the interannual variability of QBIE temperature events in Hong Kong is generally not autocorrelated and suggests that it is almost not feasible to conduct short-term climate prediction on QBIE temperature events based on its past evolution patterns. Hence, we further explore the potential for predicting interannual variability of Hong Kong's QBIE heat waves and cold surges from the several dominant climate variability, including the Arctic Oscillation (AO), North Atlantic Oscillation (NAO), El Nino-Southern Oscillation (ENSO), and Indian Ocean Dipole (IOD). Specifically, we examine the correlations of the variability in annual event counts with the indices of these climate systems. Two key aspects are discussed below. First, since state-of-the-art climate models are able to partly capture the future states of these dominant climate systems, a high correlation coefficient between QBIE event counts and climate variability would help climatologists to predict interannual variability QBIE temperature events based on climate simulation products. Second, if a lead-lag correlation exists between QBIE event count and one of the dominant climate variability indices, it may be possible to predict QBIE activity based on the state of the climate system in the previous year. Thus, we particularly examine the 0-year and 1-year lead-lag correlation in the following analysis. The analysis results show that no meaningful correlations are observed between Hong Kong's QBIE temperature events with the above-mentioned climate variability. Although prior research has shown that tropical intraseasonal oscillations are closely related to climate systems such as AO and ENSO [37; 38], we find that nearly all types of QBIE temperature events do not correlate with AO, NAO, ENSO, or IOD. The only exceptions are the relationships between IOD and the interannual variability of WNT QBIE heat waves, with a statistically significant correlation coefficient of \(-0.24\), and between boreal winter ENSO and SDT heat waves, with a significant correlation coefficient of \(-0.40\) (Figure 9a). Similar results are observed in the 1-year lead-lag correlation analyses, where climate variability leads QBIE event counts by 1 year. Namely, most correlation coefficients are statistically insignificant. A few statistically significant correlations are observed, such as between SDT QBIE heat waves and ENSO and between SDT QBIE cold surges and NAO; however, the highest correlation coefficient only reaches 0.34. The relatively low \begin{table}
\begin{tabular}{l l l} \hline \hline
**QBIE Events** & **ARIMA Fitting Model** & **Description** \\ \hline ALL heat waves & & White noise series \\ \hline ALL cold surges & ARIMA((14),0,0) & The variance of the residuals is 2.42 \\ \hline CDN heat waves & ARIMA(0,0,(11,28)) & The variance of the residuals is 0.47 \\ \hline CDN cold surges & & White noise series \\ \hline WNT heat waves & & White noise series \\ \hline WNT cold surges & & White noise series \\ \hline SNT heat waves & & White noise series \\ \hline SNT cold surges & ARIMA((4),0,0) & The variance of the residuals is 0.36 \\ \hline WDT heat waves & & White noise series \\ \hline WDT cold surges & & White noise series \\ \hline SDT heat waves & & White noise series \\ \hline SDT cold surges & ARIMA((4,6,7),0,0) & The variance of the residuals is 0.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ARIMA modeling results for different types of QBIE count events. correlations between QBIE event counts and climate variability suggest that it is challenging to build a valid statistical model to predict the interannual variability of QBIE events in Hong Kong. Together with the findings from the ARIMA analyses, these results indicate a relatively low predictability for the interannual variability of long-lived heat waves and cold surges in Hong Kong.