Global land drought hubs confounded by teleconnection hotspots in equatorial oceans

doi:10.21203/rs.3.rs-3236478/v1

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Global land drought hubs confounded by teleconnection hotspots in equatorial oceans

https://doi.org/10.21203/rs.3.rs-3236478/v1

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published 10 Jan, 2024

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Emerging data-driven techniques, such as Complex Networks (CNs), can identify spatial linkages between droughts on a global scale and, subsequently, drought propagation, which can improve early warning systems. Recent studies used CNs to identify hotspots of global drought teleconnections as land drought hubs; however, these studies excluded the ocean regions in CN, an oversight that can upend the insights gained thus far. Here, using a comprehensive global CN analysis on drought onsets, we show that oceanic regions harbor significantly larger drought hubs than land regions. The Indo-Pacific Warm pool (IPWP) in the Maritime continent emerges as the most significant drought hub having the farthest teleconnections. We show that IPWP, together with a few sub-tropical land and ocean regions, exhibit a ‘rich club phenomenon’ in CN. Further, using a causal network learning algorithm, we demonstrate the confounding role of oceans in modulating drought onsets on land regions indicating earlier studies might have overestimated the teleconnections of land drought hubs. Our study reveals novel insights on the spatiotemporal linkages of global drought onsets and highlights the role of oceans in driving global drought teleconnections and their potential role in drought propagation.

Earth and environmental sciences/Climate sciences

Earth and environmental sciences/Climate sciences/Atmospheric science

With their large spatiotemporal scales and high intensities, droughts leave an indelible mark on the global socioeconomy and are thus regarded as one of the most devastating natural disasters¹. Persistent droughts have profound impacts on water availability^2,3, plant health^4,5, wildfires⁶, and human well-being^7–9, the repercussions from which can cascade into critical areas such as water resources management¹⁰, agricultural and food security^11–14, ecosystem services^15–17, and the global economy^18–20. The sixth Assessment Report (AR6) by the Intergovernmental Panel on Climate Change (IPCC) projects an increase in the intensity and frequency of droughts across the globe, fuelled by global warming, potentially reducing agricultural yields by up to 20% per decade^14,21,22. Human-induced climate change has intensified agricultural and ecological droughts across the globe, which threatens a global food crisis^19,23. Globally, around 55 million people are impacted by droughts every year²⁴, and in the past century, droughts were responsible for the deaths of around 10 million people and have left multiple economies in dire straits²⁵. According to United Nations, around 129 countries are projected to have increased exposure to droughts within the next few decades²⁵.

While spatial variability of droughts is projected to increase²⁶, our knowledge about the dynamics of droughts, their prediction, and their propagation in a warming world is limited^27–29. Droughts are complex phenomena driven by both local processes and large-scale circulation of the atmosphere; hence, onsets, intensity, spatial extent, and propagation of large-scale droughts have significant distant teleconnections and local dependence. Once set up, a large-scale drought inhibits precipitation due to land-atmosphere feedback^30,31 and thus can persist for longer durations. This internal feedback is not completely known in earth systems, and increasing anthropogenic perturbations make predicting drought onsets, durations, and intensities challenging.

Complex network (CN) analysis has gained prominence in many domains, including earth science^32–38 as it can help delineate internal feedback and external teleconnections from the observed earth science data. Due to its ability to capture novel insights on the spatial embedding of physical processes that current models do not completely resolve, many attempts have been made to understand the onsets and propagation of climate extremes (droughts and precipitation extremes) using network-based approaches^39–46. For example, Mondal et al 2023⁴² delineated CN between onsets of droughts on land to identify regions across the globe with very high connectivity called ‘drought hubs’. These regions were argued to be directly linked to multiple droughts across the globe as hotspots of global drought teleconnections through their links observed in spatially embedded CN. However, they have overlooked the influence of external confounders in the CN framework, a known cause of spurious links in network analysis^47–53. It is widely recognized that network delineation approaches can produce misleading links when variables have common drivers^52,53. In this study, we contend that the exclusion of oceanic sources in CN analysis on drought onsets can give rise to two critical oversights.

First, droughts in the ocean regions may exhibit a higher degree of connectivity compared to land regions and hence, may hold higher predictive information for droughts across the globe. The presence of ocean regions in a CN can profoundly modify the existence and characteristics of these hubs. This insight can fundamentally alter the identification of "drought hubs" and “Rich Club Phenomenon”, as previously reported in the literature⁴². Second, since ocean-atmosphere dynamics predominantly drive droughts, the degree of connectivity between drought onsets on land regions might be overestimated due to the absence of confounding factors, specifically the oceans, from the analysis. By incorporating ocean nodes into our global CN analysis, we can better capture the true extent of connectivity of drought onsets.

In this study, by including droughts in ocean regions as nodes in CN, we address these caveats and generate novel insights which can better our understanding of drought teleconnections across the globe. We conducted a comprehensive global CN analysis on drought onsets that incorporates nodes on the ocean surface in addition to land. We use the Standardized Precipitation Index (SPI) and the self-calibrating Palmer Drought Severity Index (sc-PDSI) to classify droughts. We employ the event synchronization technique and a causal network learning algorithm – PCMCI (see methods) – to demonstrate that oceans have a significantly higher number of connections across the globe than land regions; hence, oceans have bigger ‘drought hubs’ than on land.

Figure 1(a) shows the degree centrality (DC) of each grid from a complex network (CN) generated using event synchronization (ES) technique (methods) between onsets of droughts on land grids. Here, the DC of any grid in CN measures the number of grids on which a 12-month drought (measured by SPI-12 from ERA-5 data, hereafter called SPI, see methods for details) can occur within a lag (or lead time) of up to 6 months. Hence, drought onsets between any two grids can be synchronized in either direction (up to six months, see methods for details), leading to an undirected link between each grid pair. While computing DC, we consider only those links of the network on which ES was found statistically significant at 95% confidence. Hence, computed DC gives a robust estimate of the degree of connectivity of each grid. Drought onsets in a few land regions – namely Sahel, South Africa, the Middle East, western North America, South America, and northern Australia – have a very high DC (Fig. 1(a)). A higher DC of a region indicates that the drought onsets in the region are connected to many drought onsets across the globe. Hence, these regions might be experiencing simultaneous droughts or might serve as an intermediary in drought propagation. Using various CN metrics on the synchronized grids across the globe, these regions are declared as ‘drought hubs’ in the literature⁴² which are argued to be hotspots of global teleconnections of droughts.

The DC estimated in this study has been corrected against error caused by the projection system (see methods), a vital correction that is missing in many previous studies using CN on spatial datasets^{39–42, 45}. Polar regions have significantly more nodes per unit area than the equator. Hence, we get an increasing number of links for the same physical area as we move from the equator to the poles, which can lead to an overestimation of network measures and misleading inferences, as shown in supplementary figure S1 (also in literature⁴²). Figure S1(a) shows DC generated using sc-PDSI on land-only grids as done in the literature⁴², while figure S1(b) shows the same plot after correcting for the projection system. It can be clearly seen that applying correction (methods) reduces the estimated degree of extratropics. The amount of overestimation of the degree will be directly proportional to the resolution of the data. A higher resolution data will have a higher number of nodes to penalize as we move away from the equator. Hence, we used the corrected plots of DC for further analysis.

We have also generated Fig. 1(a) using SPI and sc-PDSI indices from the CRU dataset (methods), and DC from these datasets is shown in supplementary Figure S1(b, c). We observe similar regions of high DC using multiple datasets and drought metrics, though they differ slightly in the estimates of DC of these regions. Results from all the datasets point towards similar highly connected drought regions over land and are also similar to that reported in the previous studies⁴².

Drought hubs in ocean

Droughts on land are primarily driven by ocean-atmosphere interaction⁵⁴. This leads to a hypothesis that droughts on the ocean can also be synchronized with land droughts. Since many land regions are far from each other (especially in the southern hemisphere), the propagation of droughts from one land region to another can contain the ocean regions as intermediaries or confounders (one ocean region being a simultaneous driver of droughts in two land regions). Hence, the oceans can also be hotspot regions for drought propagation or regions that drive global land droughts simultaneously. To address this issue, we generate the CN by including drought onsets over the oceans, and the updated DC is shown in Fig. 1(b). In Fig. 1(b), oceanic regions in the tropics have higher DC than land regions. While the regions with high connectivity remain apparent on land (Fig. 1(b)), the DC on the ocean surface – primarily the Indo-Pacific warm pool (IPWP) in the Maritime continent, the central Pacific, and the Atlantic Ocean – is manifold higher than the DC of land regions. These regions of extremely high connectivity in the ocean might contain more predictive information for droughts on land than the land drought hubs from Fig. 1(a).

From Fig. 1, we can see that the inclusion of the ocean region reveals teleconnection hotpots in equatorial oceans. The betweenness centrality (BC), which indicates the importance of a node as an intermediary for the propagation of information, is shown in supplementary Figure S2. We observe the highest BC in the Pacific Ocean and the IPWP followed by the Atlantic Ocean, Western Indian Ocean, and some parts of the Middle East and South Africa. These regions can play a role in drought propagation across the globe. It should be noted here that we haven’t corrected BC for the errors due to the projection system, and this correction is out of the scope of the current study. The regions in the equatorial ocean regions with high DC and BC than land regions indicate the presence of manifold bigger drought hubs in the ocean than on land. This result is also intuitively related to the dependence of all major droughts on ocean-atmosphere dynamics⁴³.

To investigate further, we plot the spatial extent of synchronization of drought onsets in the two most major ocean hubs observed in Fig. 1(b) – the IPWP and the Pacific Ocean. The results are shown in supplementary Figure S3 (a) and (b), respectively. We observe that the droughts in IPWP (spatial extent considered marked in Figure S3(a)) have synchronization with South Asia, South Africa, South America, and Australia, whereas the Pacific Ocean is connected to the Middle East, East Africa and Western North America in addition to various oceanic regions. The occurrence of the largest connected drought hubs over these regions shouldn’t come as a surprise because, El-Nino southern oscillation in the Pacific Ocean, which changes the precipitation pattern over the IPWP, is known to alter global precipitation patterns by atmospheric and oceanic teleconnections^55,56. Hence, the connections between land regions might be an impression of lagged associations of these regions to a common driver in the ocean with no relation to drought propagation at all.

To demonstrate this, we show the connections of drought onsets on land regions using CNs with and without considering ocean regions in supplementary Figure S4. Figure S4 (a-d) shows connections of land drought hubs without considering ocean regions, and Figure S4 (e-h) shows the connections of the same regions after considering ocean grids as nodes in CN analysis. Drought onsets in western North America and the Middle East are connected to each other in land-only analysis (Figure S4 a, b); however when oceans are included (Figure S4 e, f), we observe that both are synchronized with the central Pacific Ocean. This pattern is due to the dependence of droughts in the Middle East and Southwest Asia on ENSO^57,58. Similarly, drought onsets over South Africa and Australia are linked to each other and are also connected to the IPWP (Figure S4(c,g)), as both are driven by ENSO^59,60. Sahel region (Figure S4(d)) shows some connections with drought onsets in south Asia and shows very limited synchronization with the IPWP region. These results prove that the existence and role of global land drought hubs are overestimated in literature due to the CN model artifact of not considering oceanic regions. The global hubs that drive global drought onsets and, potentially, drought propagation are in ocean regions instead of land regions.

Revisiting the Rich Club Phenomenon of drought hubs

To quantify the spatial extent of teleconnections of droughts hubs found in the ocean, we compute the mean synchronization distance (MSD, methods) of each node in CN. For every node, MSD measures the average spatial distance of all nodes which are connected to it. If the connectivity of a node or its spatial scale of synchronization is assumed to be its wealth in a network, the existence of a small fraction of nodes with a large degree of connectivity or MSD is analogous to a ‘rich club’ and has been argued to be a prominent topological characteristic of networks⁴². Figure 2 and supplementary figure S5 show MSD computed using links that were found statistically significant at 90% and 95% confidence, respectively. Since nearby grids are expected to be highly connected, we generate MSD considering links with distances more than 1000km (Fig. 2(a), Figure S5(a)) and 10000km (Fig. 2(b), Figure S5(b)).

We find that with a threshold of 1000 km (Fig. 2(a), S5(a)), extratropical regions (30N-60N and 30S-60S) have higher MSD than the equatorial regions with an exception in the equatorial Indian Ocean, northern South America and the Atlantic Ocean, which also have high MSDs. Among land regions, the Middle East, northern South America, South Africa, western North America, and Australia are the regions with the farthest connectivity. IPWP and the central Pacific Ocean have low MSD values, reflecting a high number of local connections. All the grids in the Pacific Ocean interact with each other increasing the number of links at around a distance of 1000–5000 km, leading to a reduction in the mean value.

The Zonal Mean of MSD, shown on the right panel of Fig. 2(a), decreases from the north to the south, with a dip at the equator, when oceanic regions are considered. On the contrary, Mondal et al. 2023⁴² from their analysis, excluding the oceanic regions, reported an increasing MSD of land regions from the northern to the southern hemisphere, concluding that drought hubs in the southern hemisphere constitute a ‘rich club’ in the CN. We performed the CN analysis with land-only grids without any threshold of distance to reproduce the results of Mondal et al. 2023⁴² in supplementary figure S6(a). The right panel (Figure S6(a)) shows the latitude variation of average MSD (blue) and percentage land area (red). It is clearly visible that the variation in MSD with latitude is opposite to the variation in the percentage of land with latitude. The southern hemisphere has fewer land areas, which are far from each other. Many of these land regions can also be connected to a common oceanic source, leading to overestimating MSD in the southern hemisphere. After considering the ocean regions in CN, the steep north-to-south increase in the average MSD of land regions vanishes, and we observe a slight increase in the MSD of land regions (Figure S6(b), showing only land regions from a CN which includes nodes on oceans as well) from north to south. Hence, we conclude that the tagging of the southern hemisphere as a “rich club” in the previous study⁴² resulted from a statistical artifact due to the asymmetrical distribution of land in both hemispheres and the non-inclusion of oceans in the analysis.

Since MSD in Fig. 2(a) can be influenced by a high number of local connections, we increase the threshold to 10000 km (Fig. 2(b) and Figure S6(b)) to reveal average spatial scales of only distant teleconnections. We observe a significant increase in the MSD of the equatorial region, with the IPWP emerging as the biggest hub with the farthest teleconnections. Apart from the IPWP, eastern portions of the Atlantic and the Indian oceans also have high MSD values. The importance of the above-mentioned oceanic regions in facilitating drought propagations is also supported by high BC values (Figure S3). High DC with high BC indicates that these nodes are important for information propagation between all other nodes. Combined with the high MSD found in Fig. 2 (b), we conclude that the ‘rich club’ of global drought hubs lies in the equatorial region, with the IPWP in the Maritime Continent being the most significant among them, having farthest teleconnections. Supplementary figures S7 (a) and (b) show the distribution of MSD from each land drought hub along with regions in the Atlantic Ocean, maritime continent, and the Pacific Ocean (all regions shown in Fig. 4(f)) considering thresholds of 1000km and 1000km respectively. Figure S7 shows that the fat-tailed nature of MSD becomes prominent after considering a threshold of 10000 km, with the region in the Maritime continent (IPWP) containing the heaviest tail followed by the Pacific Ocean, Atlantic Ocean, and the Middle East. The fat-tailed distributions of ocean regions support the hypothesis that ocean regions are the drivers of most of the drought onsets on land regions.

Drought hubs in the ocean confound drought hubs on land

The above-mentioned results demand further investigation into the possibility of land drought hubs being statistical artifacts induced by the ocean-atmosphere processes, like ENSO, acting as a confounder. Figure 3 shows the annual precipitation anomaly of major drought hubs along with the state of ENSO. El Nino and La Nina years are marked as red and blue circles at the end of each bar. The right panel shows the correlation of the annual rainfall anomaly with the Oceanic Nino Index (ONI). The Middle East and western North America have a statistically significant (p < 0.05) positive correlation with ONI and Australia, and South America has a statistically significant (p < 0.05) negative correlation with ONI. The Sahel and South Africa had a negative correlation; however, it was not statistically significant. These results indicate that the interannual variability in precipitation of all the drought hubs is significantly driven by ENSO, which clearly indicates that multiple regions can experience simultaneous or lagged droughts based on the ENSO state and their time scales of interaction with ENSO. Figure S8 shows the precipitation anomaly across the globe during El Nino and La Nina years for the summer (June, July, August (JJA)), and winter seasons (October, November, December (OND)) of the northern hemisphere. During El Nino years, the composite of summer precipitation (Figure S8(a)) shows a simultaneous reduction of precipitation over IPWP, South Asia, East Africa, Some parts of Australia, and northern South America. Hence, drought onsets in these regions can potentially be synchronized. During La Nina years, JJA precipitation (Figure S8(c)) shows opposite behavior where the above-mentioned regions receive surplus rainfall with small deficits in southern South America and northern North America, which are synchronized mainly with the reduced precipitation of central Pacific. Similarly, for winter months, during El Nino years (Figure S8(b)), the reduction in precipitation in IPWP is synchronized with South Africa, Australia, and South America. During La Nina years, OND months receive a simultaneous reduction in precipitation in East Africa, the Middle east, North America, and Southern South America, which are synchronized with a reduction in precipitation in the central Pacific. The above results show that ocean sources are the confounders of drought onsets on land. For example, in Fig. 1(a), links originating from regions South Africa or South America might not be because of drought propagation to other regions but because droughts in these regions are simultaneously modulated by teleconnections from the IPWP as shown in Figure S8(b).

ES cannot separate a direct causal association from a confounding effect. Any two drought regions on land, if modulated by the same ocean source, will be delineated as synchronized unless the influence of oceanic confounder is removed. Hence, to test for the confounding behavior of oceans, we apply a causal network learning algorithm – PCMCI – to delineate causal graphs from the monthly time series of SPI on land and ocean regions. The results are shown in Fig. 4. Nodes are various land drought hubs (regions shown in Fig. 4(f)), and their links indicate a causal connection between monthly SPI at different nodes. A link is only shown if found statistically significant at a 95% confidence level. Link labels, if present, indicate the lag at which the connection was found on a monthly scale; else, the absence of link labels means that the link was found at zero lag. Figure 4(a) contains connections between land regions when no ocean regions are considered. Figure 4 (b) adds SPI from the Atlantic Ocean (AO) to the network, Fig. 4(c) adds the Maritime Continent (MC) in addition to the AO, which is followed by Fig. 4(d), which adds a region from the central Pacific Ocean (PO). The incremental addition is done to add more ocean regions to the conditioning set one by one and observe the linkages between the land drought hubs, which are kept constant throughout the experiments. If the included ocean regions are common drivers of these drought regions, their inclusion in the conditioning set should reduce the links between land drought hubs.

Figure 4 (e) shows the number of links observed between land variables after the consecutive addition of ocean sources. We observe a continuous reduction in the number of links between land drought hubs as more ocean sources are added to the network, which conclusively validates our hypothesis that oceans are co-founders of droughts over different land regions. When no ocean sources are present (Fig. 4(a)), we observe 4 links between land variables showing the Middle East as the most connected node with an incoming connection from western North America and Australia, and an outgoing link to South America. In addition, we also get a link from Australia to South Africa. When we add the Atlantic Ocean, all the links get conditioned on an ocean source which leads to the removal of the link between the Middle East and South America and a reversal of the link between the Middle East and Australia. On adding the Maritime continent as a node (Fig. 4(b)), the link between the Middle East and Australia vanishes, and we see observe links from the Maritime continent to both Australia and the Middle East which demonstrates the confounding behavior of Ocean. Further, on adding the Pacific Ocean as a node, we don’t get a reduction in the number of links, and we observe a link towards the Pacific Ocean from the Maritime continent. This experiment conclusively identifies the confounding behavior of the oceans in modulating droughts on land regions and indicates that the ‘drought hubs’ on land reported in the literature can merely reflect large-scale drought hubs located in the oceans.

Droughts have historically been one of the greatest adversaries to mankind, primarily because of their large spatial scales and persistence over many years. They affect the health and well-being of billions of people and slow down economic growth. Propelled by global warming and climate change, droughts are projected to increase human migration by up to 500 percent⁶¹. Hence, the prediction of drought is a topic of utmost relevance to the global socioeconomy. Given the availability of large observed data, Complex network (CN) based approaches present a promising tool to understand the teleconnections, dominant drivers, spatial embedding, and propagation of droughts. These insights can be used to improve the prediction of droughts or generate robust early warning systems.

While previous studies have used CN techniques to find associations between droughts on land regions and inferred an ‘information flow’ between land drought hubs, they have failed to consider the influences of external confounders – a well-known problem in network analysis. Failure to include all necessary variables in a complex network analysis can violate the sufficiency assumption leading to spurious links while inferring causation from any data⁶². We argue that failing to incorporate ocean sources in CN can lead to two critical caveats, ultimately resulting in potentially misleading inferences from CN. First, ocean regions might possess a higher degree of connectivity than land regions which can completely modify the existence of ‘drought hubs’ and related inferences on their spatial scales as estimated in the literature. Second, the notion of information flow between drought onsets of different land regions in the literature might be a statistical artifact because of the failure to include confounders – i.e., oceans – in the analysis. In addition, previous studies have failed to acknowledge inflation in network estimates caused by the projection system. The projection systems have increasing grids per unit physical area as we move to higher latitudes. This leads to a significantly higher number of nodes near poles, which consequently generates misleading estimates of node importance measures.

We address the above-mentioned caveats in this study and, in doing so, generate novel insights into global teleconnections of droughts. We employ event synchronization (ES) to compute a global CN of drought onsets, including the oceanic nodes in addition to land regions. We also address the problem caused by the projection system by penalizing the links from extratropical regions. After including the droughts in ocean regions as nodes in CN analysis, we found regions of high DC in oceans than on land and an increase in the DC around the coastal land regions. We show that after including ocean regions in CN analysis, the rich club phenomenon of the southern hemisphere, as reported in the literature⁴² vanishes, and the equatorial regions, particularly the Indo-Pacific Warm Pool (IPWP) in the Maritime Continent, the Western Indian Ocean, and the Atlantic Ocean with some equatorial land regions in Africa and South America emerge as a ‘Rich Club’. We also found that among all oceanic regions, the Maritime continent has the farthest teleconnections, and we contend that it can be considered the biggest drought hub on Earth. This addresses the above-mentioned oversights that ocean regions contain manyfold bigger drought hubs than land drought hubs reported in the literature. Next, we use a causal network learning algorithm, PCMCI, to show that ocean regions confound global drought onsets and cause simultaneous droughts in multiple regions. Hence, links found between land drought regions can be spurious and exist only because of the confounding behavior of the ocean. We found that the number of links between SPI from land drought hubs consistently decreased upon incremental addition of SPI on ocean regions which conclusively demonstrates the confounding role of oceanic sources in driving droughts on land regions.

Our results significantly advance our understanding of global teleconnections of drought onsets and highlight the role of oceanic regions as global drought hubs. Since ocean regions can modulate multiple droughts simultaneously, identification of drought hubs in the ocean is critical for improving early warning systems of global droughts. Consequently, it holds great importance for the global socio-economy and can significantly contribute to policy formulation worldwide. The utility of drought hubs in the Maritime Continent, western Indian Ocean, and Atlantic Ocean in improving the prediction of drought onsets on land regions is the potential future extension of this study.

Data

We used gridded monthly precipitation data from European Centre for Medium-Range Weather Forecast Reanalysis Version 5 (ECMWF, ERA-5)⁶³ from 1959 to 2022. We also used gridded monthly precipitation data and monthly sc-PDSI data from 1901 to 2021 obtained from Climate Research Unit (CRU). All gridded data were aggregated to 2°x 2° spatial resolution. Oceanic Nino Index (ONI) was provided by the Physical Sciences Laboratory (PSL), National Oceanic and Atmospheric Administration (NOAA) and is publicly available at http://www.cpc.ncep.noaa.gov/data/indices/oni.ascii.txt.

Drought Onset and Characteristics

This study classifies drought onsets based on the Standardized Precipitation Index (SPI) and self-calibrating Palmer Drought Severity Index (sc-PDSI). Both indices are popular and have widely been used in the literature to estimate the onset, duration, and intensity of droughts^42,43. SPI can be computed for rainfall at various time scales, and in this study, we have used 12-month precipitation to compute SPI-12 (hereafter called SPI). SPI values below − 1 are considered a drought and sc-PDSI values below − 2 are classified as a drought. This study tries to find synchronization between drought onsets and hence the time series of SPI and sc-PDSI are converted to binary time series with drought onsets marked as 1 and the rest all values zero. Whenever the time series of SPI (sc-PDSI) goes below − 1 (-2), it is declared as drought onset.

Event Synchronisation (ES)

Droughts are driven by atmospheric processes, ocean teleconnections, and local feedbacks, which bring spatial variability in their onsets across the globe. Explaining this variability can shed light on the drought co-occurrence which can ultimately improve drought prediction. Hence, attempts have been made in the literature to understand the spatiotemporal variability of drought onsets using multiple statistical tools. Event Synchronisation (ES)^40,41, is one such tool that has gained popularity in earth science because of its computational efficiency and ability to delineate non-linear associations from data. ES is a non-parametric similarity measure that delineates temporal dependencies as well as delays between time series of various events (drought onsets in this case). In this study, ES is calculated for gridded data of drought onsets as follows:

We compute the varying time delay, ${\tau }_{l,m}^{i,j}$, between onsets at any two grid locations $i, j$ in an $m \text{x }n$ grid, having a total of ${s}_{i}$ and ${s}_{j}$onsets, respectively, as

$${\tau }_{l,m}^{i,j}=min\left\{\frac{{t}_{l+1}^{i}{- t}_{l}^{i}, {t}_{l}^{i}-{t}_{l-1}^{i},{ t}_{m+1}^{i}{- t}_{m}^{i}, {t}_{m}^{i}-{t}_{m-1}^{i}}{2}\right\}$$

Where ${ t}_{l}^{i}$(${ t}_{m}^{i})$represents ${l}^{th} \left({m}^{th}\right)$event occurring at grid location $i \left(j\right)$, with $l=1, 2, 3, \dots ,{s}_{i}$and $m=1, 2, 3, \dots ,{s}_{j}$. ${\tau }_{l,m}^{i,j}$ provides the maximum permitted time delay between drought onsets to call them synchronised. In this study, we have added an upper limit of 6 months to ${\tau }_{l,m}^{i,j}$, hence, no delays exceeding 6 months shall be considered as synchronised.

Next, ES is estimated between each grid pair by counting the temporally coinciding events, under a condition that for each pair of grids, the absolute value of the temporal delay between any two synchronous events must not exceed ${\tau }_{l,m}^{i,j}$(or 6 months, whichever is smaller).

$${ES}_{i,j}=\frac{c\left(i|j\right)+c\left(j\right|i)}{\sqrt{{s}_{i}{s}_{j}}}$$

Where $c\left(i|j\right)$ measures number of times drought onset at $i$ succeeds onset at $j$. Hence,

$$c\left(i|j\right)= \sum _{l=1}^{{s}_{i}}\sum _{m=1}^{{s}_{j}}{J}_{i,j}$$

And,

$${J}_{i,j}= \left\{\begin{array}{c}1 if 0<{t}_{l}^{i}- {t}_{m}^{i}<{\tau }_{l,m}^{i,j}\\ 0.5 if {t}_{l}^{i}= {t}_{m}^{i}\\ 0 otherwise\end{array}\right.$$

In this study, we use gridded monthly SPI-12 from ERA-5 reanalysis product at a spatial resolution of 2° x 2° within latitudes 60°S and 85°N including both land and ocean regions. This gives us a total number of grids as 13140 (73 x 180). Hence, the final ES matrix generated is of size 13140 x 13140, which represents the strength of synchronisation between drought onsets across the globe. We also apply ES to drought onsets over only land regions classified using SPI-12 and sc-PDSI data from CRU, both at a spatial resolution of 2° x 2° within latitudes 60°S and 85°N. In this case, the total number of grids are 3846 (only land grids between latitudes 60°S and 85°N) and hence, the ES matrix generated is of size 3846 x 3846, which represents the strength of synchronisation between drought onsets among land regions of the globe.

Complex Network (CN) analysis

The ES matrix can be converted to a CN adjacency matrix $\left({A}_{i,j} \right)$ where nodes $\left(i, j \right)$are the grid locations and the links between them represent the presence of pairwise synchronisation between the drought onsets on the grids. The ES matrix is symmetric because while estimating ES in Eq. (2), we count the events in both the direction $(i to j, and j to i)$. Hence, it does not provide any information about the direction of synchronisation. In this study, we test each ${ES}_{i,j}$ for statistical significance using method of shuffled surrogates as suggested by Boers et al 2019⁴¹. We randomly reshuffle the time series of events (onsets) and compute $ES$ 10000 times to generate a null distribution of ${ES}_{i,j}$ and perform hypothesis testing at 90% and 95% confidence. Hence the Adjacency matrix thus generated contains only strongest and most reliable links in the global connections between drought onsets.

$${A}_{i,j}= \left\{\begin{array}{c}1 if {ES}_{i,j} statistically significant \\ 0 otherwise\end{array}\right.$$

From the network generated above, we analyse the importance of nodes and their spatial embedding using node importance measures, namely Degree Centrality (DC), Betweenness Centrality (BC), and Mean synchronisation Distance (MSD), as explained below.

Correction for errors due to projection system

Most projection systems used by CN literature in earth science have increasing number of grids per unit area from equator to either pole. Due to this, a greater number of links will be generated from higher latitudes than on the equator for the same physical area. This can lead to overestimation of network measures which include links from higher latitudes, which if not corrected, can cause misleading inferences. In this study, we address this problem by converting the binary adjacency matrix to a weighted matrix which uses cosine of the latitude of source node as a weight.

$${A}_{ij\_corrected}= \left\{\begin{array}{c}\text{cos}\left(\phi \right) if {ES}_{i,j}is statistically significant\\ 0 otherwise\end{array}\right.$$

Where, $\phi$ is the latitude of node $j$. Hence, while computing the measures of node importance in CNs, the nodes at higher latitudes get penalised. In this study, we compute DC and MSD using ${A}_{ij\_corrected}$.

Measures of Node importance in CNs

For a network having a total N number of nodes, Degree Centrality (DC) is the simplest measure of node importance which measures the number of connections of a node.

$${DC}_{j}=\frac{\sum _{i=1}^{N-1}{A}_{i,j}}{N-1}$$

Hence, any grid having a high degree of connectivity means that drought onsets on the location (represented by the grid) are synchronised with a large number of droughts onsets across the globe.

Betweenness Centrality (BC) is a measure of node importance which quantifies the extent to which a node acts as a bridge or intermediary, facilitating the flow of information, resources, or interactions between other nodes in the network. It is calculated by determining the proportion of shortest paths in the network that pass through a particular node. BC is calculated as follows:

$${BC}_{j}= \sum _{l\ne m\ne j\in V}\frac{{n}_{l,m}\left(j\right)}{{N}_{l,m}}$$

Where, ${n}_{l,m}\left(j\right)$ is the count of all possible shortest paths from node $l$ to $m$ that pass-through node $j$. ${N}_{l,m}$ is the total number of shortest paths from node $l$ to $m$. Hence, drought onsets on grids with higher BC scores can be considered to have greater control or influence over the propagation of droughts within the network.

Spatial embedding of a network can be interpreted by analysing the actual geographical distances between the nodes in the network. We estimate the mean synchronisation distance (MSD) of a grid as an average of all the distances the grid is connected to weighted as per the strength of synchronisation (ES).

$$MSD= \frac{\sum _{i=1}^{N-1}{ES}_{ij}{A}_{ij}{d}_{ij}}{\sum _{i=1}^{N-1}{ES}_{ij}{A}_{ij}}$$

Where ${d}_{ij}$ is the physical distance between points i and j.

PCMCI

Identifying causal relationships within complex systems is a fundamental challenge across various scientific disciplines and has also gained prominence in earth science in recent past. PCMCI⁶⁴ is a causal discovery algorithm which builds on the principles of conditional independence to delineate causal associations from observations while accounting for temporal delays. It is able to remove spurious links even in presence of high dimensional datasets^50,51,64,65 – a well-known problem in conditional independence based causal discovery approaches. PCMCI⁵¹ achieves it by reducing the dimensions of the conditioning set prior to estimation of conditional independence based causal discovery. A brief description of PCMCI is as follows (for detailed algorithm please refer Runge et al 2019⁶⁴).

The first step uses a modified PC algorithm (named after the inventors, Peter and Clark⁶⁶) to generate the reduced conditioning set for each variable – called “Parents”. From a set of variables ${\overline{X}}_{t}= {X}_{t}^{1}, {X}_{t}^{2},\dots ,{X}_{t}^{N}$, for each variable ${\overline{X}}_{t}^{j}$, the PC stage starts with initialising preliminary parents $\overline{\mathcal{P}}\left({X}_{t}^{j}\right) = \left({\overline{X}}_{t-1},{\overline{X}}_{t-2},\dots ,{\overline{X}}_{t-{\tau }_{max}}\right)$ and iteratively removes variables which are redundant and add no unique information when present in the conditioning set. The first iteration removes uncorrelated variables from $\overline{\mathcal{P}}\left({X}_{t}^{j}\right)$, and the second iteration removes independent variables found after conditioning on the most correlated variables in first iteration. Next, variables which are found independent after conditioning on two strongest drivers from the previous iteration are removed from $\overline{\mathcal{P}}\left({X}_{t}^{j}\right)$. This is done until no variables are left to condition on. As recommended by Runge et al^50,51,64,65, we take an alpha level of 0.02 for hypothesis testing at this stage to not lose any true links from the $\overline{\mathcal{P}}\left({X}_{t}^{j}\right)$.

The second stage, called the MCI stage uses the above-generated parents $\overline{\mathcal{P}}\left({X}_{t}^{j} \right)$ for each variable ${X}_{t}^{j}$ and tests the following null hypothesis at α = 0.05 to find causal relationship between all variable pairs ${X}_{t-\tau }^{i}\to {X}_{t}^{j}$ at multiple lags $\tau =\left\{\text{1,2},\dots ,{\tau }_{max}\right\}$:

$$MCI: {X}_{t-\tau }^{i} ⫫ {X}_{t}^{j} \mid \overline{\mathcal{P}}\left({X}_{t}^{j} \right) \setminus \left\{ {X}_{t-\tau }^{i} \right\},\overline{\mathcal{P}}\left({X}_{t-\tau }^{i} \right) \forall {X}_{t-\tau }^{i}\in {X}_{t}^{-}$$

where, ${X}_{t}^{-} = \left({X}_{t-1},{X}_{t-1},\dots ,{X}_{t-{\tau }_{max}}\right)$. In this study, we have used a maximum lag ${\tau }_{max}$ of 6 months and a partial correlation based conditional independence within PCMCI called ‘ParCorr’.

We apply PCMCI on monthly SPI generated from ERA-5 reanalysis product to test for the presence of confounding behaviour of ocean regions. We first use PCMCI on monthly SPI of drought hubs on land and then perform three incremental addition of ocean variables. The first experiment contains SPI from land drought hubs only, the second experiment adds SPI from the Atlantic Ocean (AO), the third experiment adds the Maritime Continent (MC) in addition to the AO and the last experiment adds the Pacific Ocean (PO).

Data Availability

All the datasets used in this study are publicly available. ERA 5 reanalysis can be downloaded from https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-land. CRU sc-PDSI, and precipitation data can be downloaded from https://crudata.uea.ac.uk/cru/data/drought/ and https://crudata.uea.ac.uk/cru/data/hrg/, respectively. Oceanic Nino Index (ONI) values are taken from http://www.cpc.ncep.noaa.gov/data/indices/.

Code Availability

ES was performed using methodology provided by Boers et al 2019⁴¹ and codes can be made available upon request. To perform PCMCI, a publicly available python package ‘tigramite’ (https://github.com/jakobrunge/tigramite) was used.

Acknowledgements

The work is financially supported by the Department of Science and Technology Swarnajayanti Fellowship Scheme, through project no. DST/ SJF/ E&ASA-01/2018-19; SB/SJF/2019-20/11, and Strategic Programs, Large Initiatives and Coordinated Action Enabler (SPLICE) and Climate Change Program through project no. DST/CCP/CoE/140/2018. TC acknowledges the support from Prime Minister’s Research Fellowship (PMRF), Ministry of Education, Government of India, for his PhD scholarship.

Author Contributions

Competing interests

The authors declare no competing interests.

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Global land drought hubs confounded by teleconnection hotspots in equatorial oceans

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Abstract

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Main

Results and Discussions

Drought hubs in ocean

Revisiting the Rich Club Phenomenon of drought hubs

Drought hubs in the ocean confound drought hubs on land

Conclusion

Methods

Data

Drought Onset and Characteristics

Event Synchronisation (ES)

Complex Network (CN) analysis

Correction for errors due to projection system

Measures of Node importance in CNs

PCMCI

Declarations

Data Availability

Code Availability

Acknowledgements

Author Contributions

Competing interests

References

Additional Declarations

Supplementary Files

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