An early-warning indicator for Amazon droughts exclusively based on tropical Atlantic sea surface temperatures

We utilize monthly SST data retrieved from the Extended Reconstructed Sea Surface Temperature data set (ERSST Version 3b) [32] with a resolution of $2^{\circ} \times 2^{\circ}$. For the continental precipitation the Climate Hazard Group InfraRed Precipitation with Station (CHIRPS) data [33] is used at a monthly resolution. The data is interpolated from the native $0.05^{\circ} \times 0.05^{\circ}$ grid to $2^{\circ} \times 2^{\circ}$ to match the resolution of the SST data and to reduce computational efforts. Both data sets are considered for their common time period from 1981 to 2016. We compute monthly anomalies with respect to the long-term mean annual cycle by subtracting the respective mean values for each month (Supplementary Notes section S1 (available at stacks.iop.org/ERL/15/094087/mmedia)).

As a drought indicator, we use the standardized precipitation index for a three-month period (SPI-3) [34], averaged over the central Amazon basin. Here, server droughts correspond to SPI values below −1.5. SPI-3 has been shown to provide similar drought characteristics as more complex multi-variable integrated indices like the Palmer Drought Severity Index (PDSI) [10], so that we restrict our attention here to this conceptually simpler index exclusively based on rainfall sums.

In order to conveniently represent the strongest negative and positive correlations between SST and rainfall time series at different locations, we construct unweighted two-variable coupled networks [30]. This approach allows simultaneously investigating the dominating correlation patterns within the individual climate fields as well as between them. Here, we restrict ourselves to the analysis of cross-linkages between two spatially distinct sub-networks, representing the oceanic SST and continental rainfall anomalies, respectively.

For measuring the association between each pair of time series, Spearman's rank-order correlation coefficient is applied. To obtain a coupled network representation, each grid point is identified with a node of a spatially embedded network, and only those pairs of grid points with the strongest correlations are represented as links. Thereby, statistical associations below a certain threshold are not taken into account. Here, we choose this threshold such as to represent the 10% strongest positive and negative correlations as links in two distinct networks. A detailed discussion of this choice, along with the robustness of the obtained results for different values, is provided in the Supplementary Notes section S2. In general, we find that the overall spatial patterns of links remain very similar even when the employed link density of 10% is substantially modified. The resulting network structure is fully described by the unweighted adjacency matrix

$$\begin{align} A^{\mathrm{unweighted}}_{ij} = \begin{cases} 0 \rho_{ij} \lt \rho_{th} \\ 1 \rho_{ij} \geq \rho_{th} \end{cases} \,, \end{align} \tag{ 1 }$$

where ρ_ij denotes Spearman's rank-order correlation coefficient between the time series at node i and node j, and ρ_th the correlation threshold. To identify the strength of cross correlations between a specific grid cell and the other sub-network (variable), the local cross degree [30]

$$\begin{align} k_i^{lm} = \sum_{j \in V_m} A_{ij}, i \in V_l \end{align} \tag{ 2 }$$

is used, where V_l and V_m denote the node sets of the two respective sub-networks.

While the previous static network approach allows identifying regions with SST anomalies markedly co-varying with central Amazon basin rainfall anomalies, the inter-dependency between the observed (rainfall or SST) variability in those different regions requires further study. For this purpose, weighted two-variable coupled networks are constructed. Unlike for the unweighted network representation as described above, the correlation coefficients between each pair of nodes are used here as coefficients of the weighted adjacency matrix $A^{\mathrm{weighted}}$

$$\begin{align} A^{\mathrm{weighted}}_{ij} = \begin{cases} 0 \rho_{ij} \lt \rho_{th} \\ \rho_{ij} \rho_{ij} \geq \rho_{th} \end{cases} \,, \end{align} \tag{ 3 }$$

and analogously using absolute values for negative correlations.

For studying the temporal evolution of the correlations between different regions, a sliding window approach is applied. Here, for each month within the observation period, except for the first two years, an individual network is constructed based on the data of the previous 24 months. To quantify the magnitude of connectivity between two regions of choice, we employ the average cross correlation $\mathrm{ACC} = \left< \rho_{ij} \right>$ with i ∈ V_l and j ∈ V_m. Note that this measure takes the entire cross-correlation matrix between the two fields into account, i.e. no correlation threshold is needed. We associate each ACC value with the end point of the time window for which it has been computed. Thus, only data from the past enter each particular value.

We finally examine the capability of ACC values between SST anomalies in the NTAO and STAO to provide a binary (yes/no) early-warning indicator of incipient Amazon droughts. For this purpose, the monthly ACC data are smoothed using a Chebyshev type-I low-pass filter with a cutoff at 24 months, since we are only interested in longer time-scale variations of these correlations. Then, a threshold to the filtered ACC values is chosen such that the obtained threshold crossing events coincide as much as possible with the observed Amazon droughts. To quantify the skill of the proposed forecasting scheme, we use the Heidke Skill Score (HSS) [35, 36]

$$\begin{align} \mathrm{HSS} = \frac{2(tt \cdot ff-ft \cdot tf)}{ft^2+tf^2+2 \cdot tt \cdot ff+(ft+tf) \cdot (tt+ff)} \,, \end{align} \tag{ 4 }$$

which compares the performance of our scheme with that of a random forecast. Here tt represents the number of cases with a correct forecast of a subsequent event, ff the number of instances of no forecast and no event, ft stands for the number of times where no forecast was issued but an event occurred (missed hits), and tf stands for the number of forecasts with no following event (false alarms). A value of $\mathrm{HSS} = 0$ corresponds to the skill of a random forecast, while a score of 1 indicates a perfect forecast.

We first construct two unweighted static two-variable coupled network representations of strong positive and negative correlation patterns between monthly SST and continental rainfall anomalies. This allows identifying continental and oceanic regions with high cross degree (Supplementary figure S2), which represent coherent spatial patterns of relevant correlations between rainfall and SST that on average persist on inter-annual time scales and beyond.

Instead of exploiting the full cross degree patterns, we focus on rainfall anomalies in the central Amazon basin (0^°–10^°S, 55^°–70^°W, see figure 2(a)), neglecting regions north of the equator because of their opposite seasonality. This restriction identifies four distinct ocean regions comprising the highest 20% of all cross degree values in the SST field, among which two regions are positively and two negatively correlated with rainfall anomalies in the central Amazon. For positive correlations, the highest cross degrees are observed around the equator in the southern tropical Atlantic (STAO) and in the southern Pacific ocean (SPO) (figure 2(a)). The highest values for negative correlations are found in the tropical Atlantic north of the equator (NTAO), as well as in the equatorial central Pacific ocean (CPO) most likely related with ENSO (figure 2(b)). In what follows, we will restrict our attention to these four regions regions and their relationship with rainfall variability in the central Amazon basin.

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In order to further study the mutual dependency between SST anomalies in the four identified ocean regions and the rainfall anomalies in the central Amazon basin as a function of time, we generate weighted complex networks between the corresponding variables shrinked to the respective pairs of regions for sliding 24-month windows (see Supplementary Notes section S3 for detailed results and a corresponding in-depth discussion). The temporal variability of the respective ACC values between the two Pacific regions and the central Amazon basin indicates no significant correlations during most of the times. In turn, the temporal evolution of the ACC between the NTAO and central Amazon rainfall exhibits generally negative values, especially during periods with marked water shortages. The ACC between the STAO and the central Amazon, on the contrary, is mainly close to zero. However, it exhibits markedly negative correlations during drought conditions. This dynamical correlation structure is consistent with previous findings based on a different approach for detecting SST-rainfall coupling [37].

The above results, along with other several other studies [9, 10, 37], demonstrate that droughts in the central Amazon and strong SST anomalies in the tropical Atlantic ocean can be expected to often occur simultaneously (see also Supplementary figure S3). This supports recent suggestions that droughts in the Amazon basin are triggered by an emerging gradient between the northern and southern tropical Atlantic (see Supplementary figure S4) [2]. Instead of just looking at the instantaneous SST gradient between NTAO and STAO, we follow the highly non-stationary nature of correlations as reported above and study the mutual relationship between the SST anomalies in both tropical Atlantic regions in more detail. We again construct evolving weighted coupled climate networks; this time, however, between the SST anomalies in the two mentioned regions. The temporal evolution of the resulting ACC (figure 3) reveals generally positive values, indicating that the SST anomalies in both Atlantic regions proceed largely in phase. However, prior to drought events, the ACC typically decreases and becomes negative, indicating that SST anomalies in the NTAO and STAO develop a dipolar relationship. This signal precedes the SPI of the central Amazon basin by, on average, about one year.

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Along with the occurrence of a drought in the Central Amazon, the ACC reaches a minimum before increasing again. During a drought in the central Amazon, the dipole between NTAO and STAO thus reaches its maximum strength, before diminishing again in the aftermath. We emphasize that the dipole between these two regions—with maximum strength indicated by the minimum in the ACC between the SSTs of NTAO and STAO—is associated with, but should not be considered the same as, the SST gradient between the two Atlantic regions that has been proposed to cause droughts in former studies [2, 20]: During the development of the dipole, SST anomalies in the two regions evolve in opposite directions, leading to an increased gradient between them (Supplementary figure S4).

To establish an early warning method for droughts in the central Amazon basin, we therefore focus on the emergence of the SST dipole pattern between the NTAO and the STAO. Specifically, we expect a shortage in rainfall within the following one and a half years whenever the ACC between the NTAO and the STAO becomes significantly negative, with the peak of the drought occurring around the time when this correlation reaches its minimum. Empirically, crossing a threshold at −0.06 from above is found to provide an optimal early-warning signal of a drought event based on the considered study period and data sets (see Supplementary figure S5). For the time period between 1981 and 2016, in which high quality rainfall data are available, the SPI indicates seven severely dry periods (i.e. SPI $\lt-1.5$) in the Amazon basin. Out of these seven droughts, our method is able to correctly hindcast six (all but the one taking place in 2005), while we would have also issued one false alarm in 2002 (for possible reasons of the false alarm and missed hit see Discussion section). This leads to a HSS of 0.82 (equation (4)). Extensive robustness tests of this hindcast are provided in the Supplementary Notes section S4. Because it occurred at the very beginning of the study period, we did not include the drought of 1983 in our analysis (as we do not know whether the ACC had crossed the threshold before). Note that to comply with the size of our sliding windows, droughts which occur in close succession are counted as one, e.g. 1991 − 1992 and 2009 − 2010. Furthermore, all droughts except the one in 1995 occurred within one year after the threshold was crossed, while the one in 1995 occurred only after one and a half years.

During very wet periods in the central Amazon basin, we often observe a positive SST gradient between NTAO and STAO (Supplementary figure S4). Accordingly, the ACC between these two Atlantic regions is close to zero or even positive during such periods (Supplementary figure S6). In this spirit, we find indications that shortly before very wet anomalies, the dipole diminishes and the SST anomalies of the two Atlantic regions rather vary in phase. The fact that this behavior appears less regular and—taken alone—more unreliable for establishing a robust early warning suggests that the mechanisms leading to the occurrences of very wet conditions are more complex and depend on additional parameters associated with the formation of extensive positive rainfall anomalies, such as orography, ENSO, or other atmospheric processes. Given that the relationship is more concise for dry conditions in the Amazon, we focus on the prediction of droughts in this study.

While we have only presented here the results for the filtered ACC time series, corresponding findings for the non-filtered data, shown in Supplementary figure S7, indicate that the high forecast skill of our method does not critically depend on the smoothing. Details on the corresponding analysis can be found in the Supplementary Notes section S5.