A monitoring and prediction system for compound dry and hot events

The SCEI was used as the predictand for predicting the severity based on antecedent SCEI and SNINO, which represents the persistence and external forcing, respectively (Hao et al 2019). Specifically, the 1 month lead prediction of SCEI for a period t (W_t+1) can be achieved based on the conditional distribution given two predictors W_t and X_t (SNINO) which can be expressed as:

$$\begin{eqnarray}&&P({W}_{t+1}| {W}_{t},{X}_{t}).\end{eqnarray} \tag{ 5 }$$

By assuming a multivariate normal distribution of the three standardized variables (SPI, STI, and SNINO), the conditional distribution in equation (5) is essentially a normal distribution with mean μ and variance σ² (Wilks 2011, Hao et al 2019). The conditional mean μ can be regarded as the predicted severity of the compound event. The Pearson correlation coefficient between observed and predicted SCEI was used to evaluate the prediction skill of the conditional distribution model.

For the prediction of occurrences of compound events (Z = 1), the logistic regression model was employed and can be expressed as (Hao et al 2018a):

$$\begin{eqnarray}&&\,\begin{array}{c}\mathrm{ln}\left[\displaystyle \frac{\pi }{1-\pi }\right]\end{array}=\alpha +\beta \,x,\end{eqnarray} \tag{ 6 }$$

where π is the probability of occurrence P(Z = 1x); $\alpha$ is the constant and $\beta$ is the regression coefficient; x is the predictor (i.e. NINO34). The 1 month lead prediction of the probability of occurrences of a compound dry and hot event (i.e. Z = 1) can then be expressed as:

$$\begin{eqnarray}&&P({Z}_{t+1}=1| x)=\displaystyle \frac{1}{1+\exp \left[-\left(\alpha +\beta {x}_{t}\right)\right]}.\end{eqnarray} \tag{ 7 }$$

The Brier Skill Score (BSS) was used to evaluate the probabilistic prediction skill of the logistic regression model, which was defined as (Wilks 2011, Lepore et al 2017):

$$\begin{eqnarray}&&{\rm{B}}{\rm{S}}{\rm{S}}=1-\displaystyle \frac{\displaystyle {\sum }_{{i}=1}^{n}{({P}_{{i}}-{O}_{{i}})}^{2}}{\displaystyle {\sum }_{{i}={\rm{1}}}^{n}{({R}_{{i}}-{O}_{{i}})}^{2}},\end{eqnarray} \tag{ 8 }$$

where n is the number of periods (or instances) of prediction; P_i is the predicted probability for period i; O_i = 1 if the compound event in observations occurs and O_i = 0 otherwise; R_i is the reference prediction, which is defined as the climatology frequency of occurrences of compound dry and hot events during the period 1980–2018. The BSS ranges from −∞ to 1 with a positive value indicating skillful prediction (i.e. better prediction performance than the reference prediction).

ENSO is a commonly used predictor for precipitation and temperature extremes across the globe and it tends to peak in boreal winter (Neelin et al 2000, Wang et al 2012, Yeh et al 2018). Thus, we focused on the prediction of compound dry and hot events during DJF. In this section, we assessed the validity of ENSO as the predictor by investigating its impact on compound dry and hot events during DJF. The lag 1 month and 3 month correlation coefficient (r) between SCEI of DJF and NINO34 in previous seasons (i.e. November–December–January (NDJ), September–October–November (SON)) is shown in figures 3(a), (b). Significant (and negative) correlation coefficients (at the 0.05 significance level) were found in large regions, including northern North America, northern South America, southern Africa, southeast Asia, and parts of Australia. This implies that lower SCEI values (or more severe compound event conditions) are associated with higher values of SNINO during DJF (or El Niño).

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We used the threshold P₅₀/T₅₀ to define the occurrence of compound dry and hot events. This setting enables the extraction of a relatively large number of occurrences for statistical modeling of compound events. Significant (and positive) regression coefficients β (at the 0.05 significance level) of lag 1 month and 3 month in equation (6) were used to assess the relationship between occurrences of compound events during DJF and NINO34 in previous seasons (NDJ and SON), which is shown in figures 3(c), (d). Similar to figures 3(a), (b), regions with significant (and positive) β mainly located in northern South America, southern Africa, southeast Asia, and parts of Australia. The positive values of β imply more occurrences of compound dry and hot events with higher values of NINO34 during DJF (or during El Niño years) in these regions.

For certain limited regions (e.g. southern North America), the opposite pattern of relationships between ENSO and compound events is shown (i.e. significant positive r and negative β). This indicates that La Niña (or low NINO34 values) is associated with increased occurrences of compound dry and hot events in southern North America. The main reason is that during La Niña, the Pacific jet stream often tends to shift northward, leading to dry and hot conditions in southern United States (Cook and Schaefer, 2008).

In previous sections, only 39 years of monthly precipitation and temperature data from MERRA-2 (i.e. 1980–2018) were used to evaluate the predictor. The number of compound dry and hot events extracted from historical records may not be sufficient for statistical modeling in certain regions. To address the potential uncertainty of datasets, we used the CRU data with a longer record (1951–2016) to assess ENSO impacts. The correlation coefficient (r) between SCEI and NINO34 and the regression coefficient (β) from the logistic regression model of lag 1 month and 3 month based on the CRU data are shown in figure S2. Overall, similar pattern of impacts of ENSO on compound dry and hot events is shown (negative r and positive β in regions such as northern South America and southern Africa). These results indicate that ENSO provides a good predictor for the prediction of compound events in these regions.

To assess the prediction skill of the two prediction models, the leave-one-out cross validation (LOOCV) was used for the period from 1980 to 2018 (n = 39), in which the fitting procedure is repeated n times, each time with a sample of size n−1 by leaving out one sample for prediction and evaluation (Wilks 2011). For the prediction of SCEI, the positive correlation (significant at the 0.05 significance level) between observed and predicted SCEI values (1 month and 3 month lead time) of DJF during 1980–2018 based on LOOCV is shown in figure S3. Due to the persistence of SCEI, correlation coefficients between observations and 1 month lead predictions is high for large land areas. When the lead time increases to 3 month, high correlation coefficients between observations and predictions are mainly shown in southern US, northern South America, southern Africa, southeast Asia and parts of Australia. For the probabilistic prediction of occurrences, the BSS for the 1 month and 3 month lead prediction is shown in figure S4. Skillful predictions are shown in regions with significant relationships between ENSO and occurrences of compound dry and hot events (e.g. positive BSS values in northern South America and southern Africa). Overall, these results show that ENSO provides skillful prediction of compound events during DJF for 1 month and 3 month lead time for regions including southern US, northern South America, southern Africa, southeast Asia and parts of Australia.

Based on the analysis of the predictor and prediction skill above, we then applied the two models to predict compound events during DJF 2015–2016 as a case study. The monitoring of the compound event for this period is shown in figures 4(a), (b). From figure 4(a), the SCEI is particularly low in regions including northern South America, northern and southern Africa, southeast Asia, parts of Australia, and northern Russia. From figure 4(b), the occurrence of different categories of compound events resides in similar regions (e.g. occurrences in northern South America and southern Africa based on the threshold P₁₀/T₉₀). These patterns of compound events are generally consistent with previous studies showing both drought and hot conditions for this period in these regions (Herring et al 2018), such as northern South America, southern Africa (Yuan et al 2018), and southeast Asia (King et al 2016, Christidis et al 2018).

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The prediction of the SCEI and occurrence is first illustrated at one grid to show the application of the two models. The observed SCEI values and occurrences of compound events during DJF from 1980 to 2018 for one grid in southern Africa (longitude: 22.5, latitude: −20) are shown in figure 5, which indicates historical compound dry and hot events during certain periods, such as DJF 2015–2016. The 1 month and 3 month lead prediction of the SCEI and occurrence from the two models based on LOOCV is shown in figures 5(a) and (b), respectively. In figure 5(a), the correlation between observations and predictions of SCEI values is significant and relatively high (0.76 and 0.46 for 1 month and 3 month lead prediction, respectively). For the predicted probability of occurrences in figure 5(b), if 0.5 is selected as the threshold to define the occurrence, the probabilistic prediction from the logistic regression model performs well in identifying a large number of historical occurrences of compound events (e.g. during DJF 2015–2016). For example, the 1 month and 3 month lead prediction of the probability of occurrences of compound dry and hot events during DJF 2015–2016 is 0.91 and 0.90, respectively, indicating high likelihoods of occurrences during this period.

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The 1 month and 3 month lead prediction of SCEI over global land areas is shown in figures 4(c), (e). The low SCEI values from the prediction generally resemble observations in figure 4(a) for large regions (e.g. northern South America, southern Africa, southeast Asia). In addition, the 1 month and 3 month lead prediction of occurrences is shown in figures 4(d), (f). Higher probability of occurrences of compound dry and hot events is predicted in similar regions to those with low SCEI values from the prediction in figures 4(c), (e), which is consistent with observed occurrences in figure 4(b). The relatively good prediction performance of compound dry and hot events for this period in these regions mainly results from the strong impact of ENSO (Hao et al 2019). However, the prediction model based on ENSO fails to predict compound dry and hot events in certain regions, such as northern Russia, where no significant impact of ENSO is shown from figure 3. These results highlight the useful early warning information of compound dry and hot events from this system for regions with significant impacts from ENSO. Meanwhile, improved understanding and modeling of compound events beyond the region significantly affected by ENSO is a pressing need to improve the system.