Breaking Rossby waves drive extreme precipitation in the world’s arid regions

Breaking Rossby waves drive extreme precipitation in the world’s arid regions | Communications Earth & Environment

Abstract

More than a third of the world’s population lives in drylands and is disproportionately at risk from hydrometeorological hazards such as drought and flooding. While weather systems governing precipitation formation in humid regions have been widely explored, our understanding of the atmospheric processes generating precipitation in arid regions remains fragmented at best. Here we show, using a variety of precipitation datasets, that Rossby wave breaking is a key atmospheric driver of precipitation in arid regions worldwide. Rossby wave breaking contributes up to 90% of daily precipitation extremes and up to 80% of total precipitation amounts in arid regions equatorward and downstream of the midlatitude storm tracks. The relevance of Rossby wave breaking for precipitation increases with increasing land aridity. Contributions of wave breaking to precipitation dominate in the poleward and westward portions of arid subtropical regions during the cool season. Our findings imply that Rossby wave breaking plays a crucial role in projections and uncertainties of future precipitation changes in societally vulnerable regions that are exposed to both freshwater shortages and flood hazards.

Introduction

Drylands cover more than 40% of the Earth’s land surface and host more than two billion people. These dry regions are projected to expand in a warming climate 1 along with an expected doubling of the number of people living in these regions by the end of the 21st century 2. The population in these regions is disproportionately exposed to hydrometeorological hazards such as drought 3 and flooding 4 as developing countries, which are common in these regions, often have limited resources to mitigate freshwater shortages 5 and flood hazards. A horrific example is the destructive flooding that unfolded in Libya in September 2023 and left more than 12,000 people dead according to the Emergency Event Database (EM-DAT). On the other hand, precipitation in arid regions can also replenish scarce freshwater resources on which food security and ecosystems rely 6, 7. Precipitation deficits and severe droughts in already water-scarce regions, amplified by climate change, have been suggested to foster armed conflict 8, 9 and migration 10. Further increased stress on water resources in the future will likely put societies that are already affected by political and economic instability, civil unrest, and armed conflict under even larger pressure.

Under global warming, climate models generally project a decline in precipitation amounts in much of the dry subtropics 11, 12, while the intensities of the most severe precipitation extremes are anticipated to increase 13, 14, 15, 16, exacerbating the dual impacts of precipitation in these regions. However, projected changes in precipitation in these regions are subject to large uncertainties that stem from the regionally varying response of the atmospheric circulation to climate change, model bias, and internal climate variability 17. Whereas atmospheric thermodynamics leads to a spatially homogenous and robust increase in extreme precipitation intensity globally, atmospheric dynamics can modify the extreme precipitation response to global warming at a regional level, particularly in the dry subtropics 18. Understanding the atmospheric dynamics that govern precipitation formation in these dry regions is thus a prerequisite for developing plausible storylines of hydrometeorological hazards in arid regions in a future climate as well as for a process-based climate model evaluation regarding these hazards.

Weather systems at synoptic scales (~1000 km and one to several days) that govern precipitation formation in humid tropical and extratropical regions have been widely studied from a global perspective. In humid extratropical regions, precipitation largely results from extratropical cyclones 19, 20 and associated warm conveyor belts 21, fronts 22, 23, and atmospheric rivers 24, 25. In humid (sub)tropical regions, precipitation is often associated with tropical cyclones 26, monsoon lows 27, and tropical easterly waves 28. However, synoptic-scale weather systems leading to precipitation in arid regions have virtually only been studied at the regional scale, pointing to a variety of atmospheric processes at play 29, 30, 31, 32, 33, 34, 35. These processes often include upper-level troughs 36, 37 and cutoff lows 38, 39, 40, 41, 42 of midlatitude origin, suggesting a key role of extratropical wave breaking into low latitudes for the formation of precipitation in arid regions.

Rossby waves in the extratropical atmospheric circulation owe their existence to the rotation and spherical shape of the Earth 43 and are of central importance for midlatitude weather and extreme events 44, 45. Rossby waves can amplify in the meridional direction, leading to the overturning and breaking of these waves and vigorous mixing of air masses between higher and lower latitudes 46, 47. Rossby wave breaking (RWB) can support the formation of precipitation by providing both atmospheric moisture advection and forcing for ascent. The influence of the upper tropospheric forcing associated with the breaking waves can extend toward the lower troposphere, inducing enhanced moisture transport and dynamically forced ascent ahead of the breaking waves, and reducing the static stability underneath, making the atmosphere conducive to deep moist convection 48, 49. Existing studies have linked RWB to observed precipitation extremes in several regions, including North America 50, the Alpine region 51, and the Middle East 52 as well as to reanalysis-based precipitation in subtropical and extratropical regions globally 53, 54.

Here, we quantify the contribution of RWB to both precipitation extremes and total precipitation amounts in arid regions worldwide. We identify RWB by combining diagnostics for potential vorticity (PV) streamers and cutoffs (see Methods) and applying these diagnostics to atmospheric reanalysis data. Given that precipitation is a challenging variable to measure, we quantify the contribution of wave breaking to precipitation using precipitation data from different sources, including reanalysis, satellite-based estimates, station-based observations, and a product that combines these three different data sources (see Methods). We examine the contribution of RWB to precipitation over land with different degrees of aridity and provide a detailed regional and seasonal analysis focused on the world’s largest arid regions.

Results

Contribution of RWB to precipitation globally

We first demonstrate the role of RWB as a driver of extreme precipitation by 8 catastrophic flood events that caused fatalities and damages in different arid regions around the world (Fig. 1 and Table 48, 54.

Eight extreme precipitation events, associated with RWB, causing flooding with catastrophic societal impacts in (a) southwest North America, (b) central North America, (c) North Africa, (d) central Asia, (e) the Atacama region, (f) Patagonia, (g) South Africa, and (h) Australia. The vertical depth of potential vorticity streamers and cutoffs is shown in blue shading (each isentropic surface with a PV structure represents a vertical depth of 5 K) for the timestep indicated in the panel titles. Black contours demarcate the daily fields used to attribute the daily precipitation to RWB based on the spatially extended PV structures (see Methods). Orange and gray dots depict the MSWEP daily extreme precipitation attributed and not attributed to RWB, respectively. Red vectors show the standardized anomalies of vertically integrated horizontal water vapor transport, gray contours the quasi-geostrophic omega at 0.1, 0.2, 0.3, and 0.4 Pa s−1 with negative (positive) values in solid (dashed) corresponding to ascent (descent), and the green diagonal and crossed hatching the convective available potential energy values exceeding the 95th and 99th percentile thresholds, respectively, for the timestep indicated in the panel titles (see Methods).

Next, we proceed from demonstrative case studies to a climatological analysis. To quantify the portion of precipitation that forms under the influence of RWB, we compute the fractions of daily extreme precipitation occurrences and precipitation amounts that coincide with RWB in a year-round analysis and examine where this relation has a significant or non-significant positive or negative association (see Methods). A positive (negative) association indicates that precipitation is more (less) likely to co-occur with wave breaking than under locally climatological conditions. RWB is significantly associated with precipitation in subtropical and extratropical regions equatorward and downstream of the midlatitude storm tracks (Fig. 2a and Supplementary Figs. 1a, c, e and 2a, c, e, g), where wave breaking occurs relatively frequently compared to other regions (Supplementary Fig. 3). Fractions of daily precipitation extremes significantly associated with RWB exceed 80–90% in southwest and central North America, the entire Mediterranean Basin and adjacent parts of North Africa, the Middle East and eastern Europe, the Atacama region, Patagonia, and the southern flanks of southern Africa and Australia (Fig. 2a). In the same regions, up to 70–80% of the total annual precipitation amounts occur under the influence of RWB (Supplementary Fig. 1a, c, e and 2a, c, e, g).

Fractions of year-round MSWEP daily extreme precipitation occurrences associated with RWB (a) and daily extreme precipitation occurrence surplus due to RWB (b). Crossed hatching and stippling in black (gray) in (a) indicate regions where the relationship between extreme precipitation and RWB has a significant (nonsignificant) positive and negative association, respectively (see Methods). Orange contours in (a) and purple contours in (b) denote the midlatitude storm tracks based on annual mean eddy kinetic energy (EKE; see Methods) at 0.7, 0.85, and 1.1 MJ m−2 intervals.

In contrast to the aforementioned regions, RWB has a significant negative association with precipitation (i.e., significantly less precipitation occurs during RWB than under locally climatological conditions) in humid low- and high-latitude regions where other weather systems are primarily responsible for precipitation formation (Fig. 2a and Supplementary Figs. 1a, c, e and 2a, c, e, g). Prominent regions are found over the eastern parts of the North American and Asian continents and adjacent western parts of the North Pacific and North Atlantic Ocean basins, where tropical cyclones 26, extratropical cyclones 19, 20, and fronts 22, 23 govern much of the precipitation formation. Other regions where precipitation has a significant negative association with RWB can be found over the extratropical west coasts of North America, Europe, southern South America, and New Zealand, where landfalling atmospheric rivers dominate precipitation generation 24, 25.

The relevance of RWB for precipitation is further examined using an estimate of how much precipitation is enhanced or reduced due to RWB, referred to as precipitation surplus (see Methods). Positive and negative values (precipitation surplus and deficit) indicate how much precipitation would differ in a hypothetical world without RWB. Over the aforementioned subtropical and extratropical regions equatorward and downstream of the midlatitude storm tracks, daily extreme precipitation occurrences due to RWB attain a 60–80% surplus (Fig. 2b), and annual precipitation amounts reach a 40–60% surplus (Supplementary Fig. 1b, d, f and 2b, d, f, h), albeit somewhat lower fractions are found based on GPM IMERG precipitation data compared to the other three precipitation datasets (see Methods).

The relevance of RWB for precipitation follows the seasonality of the large-scale circulation (Fig. 3 and Supplementary Figs. 4 and 5). In winter, RWB contributions to precipitation reach the largest values over lower latitudes when the midlatitude storm tracks attain their strongest intensity and most equatorward influence 55. For example, hotspots of winter extreme precipitation attributed to wave breaking emerge over southwestern North America and the Mediterranean in the Northern Hemisphere (Fig. 3a, c) and the Atacama region, southern Africa, and southern Australia in the Southern Hemisphere (Fig. 3b, d). In summer, large RWB contributions to extreme precipitation are evident at higher latitudes over central North America and Europe (Fig. 3a, c). In several regions, the sign of the association reverses between the winter and summer seasons. For example, in the Southern Hemisphere, a negative association over the larger parts of the Atacama region, southern Africa, and Australia in austral summer (Fig. 3b, d), showing that wave breaking contributes to precipitation formation in these regions primarily during winter. Seasonal precipitation amounts attributed to RWB follow a very similar pattern compared to those of extreme precipitation, albeit fractions remain somewhat lower (Fig. 3 and Supplementary Figs. 4 and 5). Across all four precipitation datasets, RWB contributions to seasonal precipitation extremes and total amounts show overall similar patterns and fractions (Fig. 3 and Supplementary Figs. 4– 11), strengthening the confidence in this study’s results.

Fractions of MSWEP daily extreme precipitation occurrences associated with RWB (a, b) and daily extreme precipitation occurrence surplus due to RWB (c, d) in DJF (a, c) and JJA (b, d). Regions where extreme precipitation occurrences fall below 5% of the year-round extreme precipitation occurrences are masked in gray. Crossed hatching and stippling in black and gray in (a, b) denote associations as in Fig. 2, but for the respective seasons. Orange contours in (a, b) and purple contours in (c, d) denote the midlatitude storm tracks based on the seasonal mean EKE at 0.5, 0.7, 0.9, and 1.1 MJ m−2 intervals.

Relevance of RWB for precipitation increases with land aridity

The analysis above shows that RWB substantially contributes to precipitation equatorward and downstream of the midlatitude storm tracks, where most of the world’s arid regions are located. In a next step, we link the relevance of RWB for precipitation to land with different degrees of aridity (see Methods). Much of the arid land, here defined by a dry sub-humid to a hyper-arid climate (i.e., drylands), features a significant positive association between precipitation and wave breaking, specifically across their poleward and westward flanks (Fig. 4a, b and Supplementary Fig. 12). In contrast, the equatorward and eastward flanks of these arid regions show to a varying extent a significant negative association, most prevalent over central Asia, the Atacama region, southern Africa, and Australia. This diagonally oriented dipole pattern over several prominent arid regions shows that the extratropical forcing through RWB into low latitudes is a key driver of precipitation in the poleward and westward portions of arid regions and suggests that weather systems of tropical origin control much of the precipitation in the equatorward and eastward parts of arid regions.

Global aridity index categories, Antarctica excluded, and the associations between MSWEP year-round daily extreme precipitation occurrences (a) and total annual precipitation amounts (b) and RWB. As in Fig. 2a, black (gray) hatching and stippling indicate regions where precipitation has a significant (nonsignificant) positive and negative association with RWB, respectively, and green contours denote the midlatitude storm tracks. Bar segments represent fractions of land surface where precipitation has a positive (crossed hatching) or negative (stippling) association with RWB, considered significant in black and nonsignificant in gray, for the five aridity index categories for extreme precipitation occurrences (c) and total precipitation amounts (d). In (c, d) the colors and numbers indicate the distribution and spatially aggregated precipitation surplus due to RWB (see Methods) as a fraction of precipitation totals over land from the different aridity index categories based on precipitation from, left to right, MSWEP, ERA5, CPC, and GPM IMERG. Gray shaded parts of the bar denote the fraction of land surface where precipitation datasets have missing values for >50% of all days.

Portions of land surface where precipitation has a positive association with RWB increase with land aridity. Across the four evaluated precipitation datasets, fractions of land surface where extreme precipitation occurrences have a positive association with RWB reach from 17 to 41% in the world’s humid regions up to 64–79% in regions with a hyper-arid climate (Fig. 4c). Similarly, land surface fractions where total annual precipitation amounts have a positive association with RWB increase from 24 to 54% in humid regions up to 71–83% in hyper-arid regions (Fig. 4d). Turning our attention to spatially aggregated contributions of RWB to precipitation, we note that the extreme precipitation occurrence surplus ranges from a 2% surplus to a 7% deficit in humid regions to a 7–14% surplus in hyper-arid regions for extreme precipitation occurrences (Fig. 4c). Likewise, the total precipitation amount surplus reaches from a 1% surplus to a 4% deficit in humid regions to a 5–13% surplus in hyper-arid regions (Fig. 4d). Thus, from a spatially aggregated and year-round perspective, RWB tends to suppress precipitation in humid regions and supports precipitation in arid regions. While the relatively low spatially aggregated precipitation surplus values can be expected given the strong regionally and seasonally varying relationship between precipitation and RWB, this analysis shows that wave breaking contributions to precipitation increase with increasing land aridity.

Conceptually, we can interpret the increasing relevance of wave breaking for precipitation with increasing land aridity as follows (Fig. 5). Precipitation in humid subtropical and extratropical regions occurs primarily under the influence of weather systems other than RWB, leading to primarily negative precipitation-RWB associations and a precipitation deficit due to RWB in these regions. Humid tropical regions reside largely beyond the reach of the extratropical forcing, resulting in near-neutral precipitation-RWB associations in these regions. In dry sub-humid to arid regions poleward and westward of hyper-arid core regions, RWB strongly contributes to precipitation, partially offset by negative precipitation-RWB associations in the dry sub-humid to arid regions equatorward and eastward of these hyper-arid regions where RWB tends to suppress precipitation. The positive association patterns poleward and westward of the hyper-arid core regions reach to a large extent across these hyper-arid regions, leading to the largest contributions of RWB to precipitation in these very dry regions.

Schematic depiction of land with different degrees of aridity (aridity index categories), the climate zones and associated general circulation patterns (black text), and prevailing synoptic weather systems (green text and arrows). The relevance of RWB for precipitation is shown by positive and negative associations, and by precipitation surplus and deficit due to RWB, as indicated in the legend.

A regional and seasonal perspective

To further understand the regionally and seasonally varying relevance of RWB for precipitation formation in arid regions, we further explore their relationship in eight prominent arid regions during traditionally defined seasons. These regions are (1) southwest North America, (2) central North America, (3) the southern Mediterranean, North Africa, and the Middle East, (4) central Asia, (5) the Atacama, (6) Patagonia, (7) southern Africa, and (8) Australia (Fig. 4a, b). Figure 6 and Supplementary Fig. 13 show the spatially aggregated precipitation characteristics attributed to RWB in the same fashion as in Fig. 4c, d, but based on seasonally partitioned precipitation (heights of the bars) over the dry sub-humid to hyper-arid portions of these eight regions only.

Seasonal distribution of daily extreme precipitation occurrences in eight selected arid regions, indicated by the gray boxes in Fig. 4a, b, considering their portions with a dry sub-humid to hyper-arid climate only: southwest North America; 123–95°W, 20–40°N (a), central North America; 123–95°W, 40–60°N (b), the southern Mediterranean, North Africa, and the Middle East; 20°W–75°E, 15–40°N (c), central Asia; 40–85°E, 40–55°N and 75–120°E, 35–50°N (d), the Atacama region; 75–65°W, 15–35°S (e), Patagonia; 72.5–62.5°W, 35–55°S (f), southern Africa; 10–40°E, 15–35°S (g), and Australia; 110–155°W, 15–40°S (h). The bar height denotes the fraction of the seasonal extreme precipitation occurrences from the total annual occurrences, and the bar segments with crossed hatching and stippling reflect the fraction of arid land surface where the relationship between extreme precipitation and RWB has a positive or negative association, respectively, significant in black and nonsignificant in gray. The color in the bars indicate the distribution of extreme precipitation occurrence surplus due to RWB based on precipitation from, left to right, MSWEP, ERA5, CPC, and GPM IMERG, while the numbers above the bars show the minima and maxima of spatially aggregated extreme precipitation occurrence surplus across the four evaluated precipitation datasets. Gray shaded parts of the bar denote the fraction of land surface without any extreme precipitation occurrences during that season or where the precipitation dataset has >50% missing values for all days during that season.

In subtropical arid regions (southwest North America, the Mediterranean - North Africa - Middle East, the Atacama, southern Africa, and Australia), RWB contributes to much of the precipitation during the transition seasons and winter (Fig. 6 and Supplementary Fig. 13). Apart from Australia in MAM, RWB substantially enhances precipitation in these regions and seasons, with the spatially aggregated extreme precipitation surplus reaching from 4 to 11% in southwest North America in boreal autumn to 54–68% in southern Africa during austral winter (Fig. 6a, g; numbers above the bars). Fractions of land surface where extreme precipitation has a positive association with RWB reach from nearly half to the entire land surface (Fig. 6a, c, e, g, h; hatched parts of the bars), showing that RWB widely governs precipitation formation in the arid subtropics during the transition seasons and winter, whether being the wetter (Mediterranean - North Africa - Middle East) or the drier (the Atacama, southern Africa, and Australia) seasons of the year. In contrast, during summer, extreme precipitation has a systematic negative association with wave breaking in much of the arid land surface, except for the Mediterranean - North Africa - Middle East region, and spatially aggregated precipitation surplus due to RWB show a 7 to 19% deficit over southwest North America, southern Africa and Australia (Fig. 6). Among these regions, southern Africa and Australia receive most of their precipitation during summer (Fig. 6g, h), consistent with the significant negative association across a large part of these regions in the year-round analysis (Fig. 4a, b and Supplementary Fig. 12). These findings demonstrate that arid subtropical regions receive much of their precipitation during the transition seasons and winter under the influence of extratropical forcing through wave breaking into low latitudes and suggest that weather systems of tropical origin control much of the precipitation in these regions during the warm season when the tropical circulation exerts its most poleward influence.

Arid regions at extratropical latitudes receive precipitation under the influence of RWB during varying seasons throughout the year (Fig. 6b, d, f and Supplementary Fig. 13b, d, f). Central North America and Patagonia receive enhanced precipitation due to RWB during the transition seasons and summer, while precipitation is suppressed by RWB over central North America during winter. Over Central Asia, spatially aggregated precipitation surplus ranges from a weak deficit to moderate surplus across all seasons. Thus, extratropical arid regions differ from their subtropical counterparts, as breaking Rossby waves contribute to precipitation formation in extratropical arid regions during varying seasons throughout the year, while this is confined to the transition seasons and winter for subtropical arid regions, consistent with the seasonality of the large-scale circulation.

Discussion

This study shows that RWB significantly contributes to a large fraction of precipitation extremes and total amounts in subtropical and extratropical regions equatorward and downstream of the midlatitude storm tracks. Our results corroborate findings from previous studies that linked RWB to deep convection and precipitation in specific regions in the tropics 48, 56, 57, subtropics 36, 52, 58, 59, 60, 61, and midlatitudes 49, 50, 51, 62, 63, and to reanalysis-based precipitation 53 and larger-scale extreme precipitation events 54 globally. The present study substantially extends previous work by adopting a more complete diagnostic for the identification of RWB through combining PV streamers and cutoffs, by using precipitation from various datasets, by introducing a measure of how much precipitation is enhanced or reduced due to RWB, by explicitly quantifying the contributions of RWB to precipitation in arid regions globally, and by providing a detailed regional and seasonal analysis focused on the world’s major arid regions. Our results also seem to contradict previous studies that suggested an important role of RWB for extreme precipitation over the eastern United States 50 and convection over the Intra-Americas during the warm season 64. Our findings show mostly a suppression of precipitation by RWB in these regions and seasons, which may stem from the dynamically forced descent upstream (at the western flank) of the breaking waves, and RWB hindering the formation of other types of weather systems being relevant for precipitation in these regions, such as tropical cyclones 65.

Previous studies showed several mechanism through which RWB can lead to precipitation, including (i) a strengthening of the low-tropospheric moisture transport at the eastern flank of the breaking wave toward the region of precipitation, (ii) the influence of topography on the circulation through slowing down the motion of the upper tropospheric PV anomaly and orienting the low-tropospheric moist air flow against the mountain barrier leading to orographic lifting of the moist air flow, (iii) dynamically forced ascent on the eastern flank of the breaking wave, and (iv) reduced static stability underneath the upper-tropospheric PV anomaly, based on case studies 48, 49, 60 and climatological analyses 50, 51, 52, 54. Our demonstrative case studies confirm that RWB can support the formation of extreme precipitation through inducing anomalous moisture transport and dynamically forced ascent at the eastern flank of the breaking waves, generating a tropospheric environment that is conducive to deep moist convection.

We show that RWB is responsible for much of the precipitation in arid regions around the world. The importance of RWB for precipitation is particularly strong in the poleward and westward portions of subtropical arid regions, including those with a Mediterranean-type climate 12, where the extratropical forcing governs precipitation formation during the cool season through wave breaking into low latitudes (Fig. 5). In contrast, the equatorward and eastward flanks of several prominent arid regions display a negative association between precipitation and RWB, suggesting that tropical weather systems regulate much of the precipitation generation during the warm season in these regions. Subtropical arid regions are typically situated at the transition between extratropical and tropical circulation regimes. As a result, these regions experience a strong seasonally alternating and geographically varying influence of both types of circulation regimes, making these regions likely very sensitive to climatic changes. In some regions, changes have been observed, or are projected to occur in the future, toward increased precipitation during the warm season and reductions in cool season precipitation 66 along with a ceasing of extratropical weather systems 67, 68, 69.

The findings of this study have important societal and scientific implications for understanding and predicting extremes and climatic changes in the water cycle in arid regions around the world. Applying RWB diagnostics to operational model forecasts has the potential to assist medium-range to (sub)seasonal prediction of hydrometeorological hazards in arid regions based on the demonstrated predictability of RWB variability arising from sea surface temperature forcing 70. In the context of climate change, we note that wave breaking contributions to precipitation are particularly large in arid subtropical regions where climate models project a future decline in precipitation amounts 17 and where projected changes in precipitation extremes suffer from large uncertainties 18. This implies that the response of RWB to a warming climate is of direct relevance to the projected precipitation decline in these regions and that robust projections of future changes in precipitation extremes critically depend on climate models’ ability to accurately simulate this atmospheric process and associated precipitation generation. Earlier studies demonstrated that climate models tend to simulate wave breaking reasonably well, but they also reported substantial biases in RWB frequencies in subtropical regions 71 and in the latitudinal distribution of RWB characteristics across models 72. Extending our analysis to climate model simulations in future studies will thus help clarify the role of atmospheric dynamics in projections and uncertainties of future precipitation changes in societally vulnerable regions exposed to both flood hazards and freshwater shortages.

Methods

Precipitation

Precipitation is challenging to measure due to its very high spatiotemporal variability, specifically in arid regions 73. To obtain well-informed estimates of precipitation attributed to RWB, we use 4 precipitation products based on 3 different types of data sources: (1) the ERA5 reanalysis 74 of the European Centre for Medium-Range Weather Forecasts for 1979–2021, (2) the Integrated Multi-satellitE Retrievals of the Global Precipitation Measurement (GPM) Mission (IMERG) 75, final version 6, for 2001–2020, (3) the Climate Prediction Center (CPC) global unified gauge-based analysis of daily precipitation 76 of the National Oceanic and Atmospheric Administration (NOAA) for 1979–2021, and (4) the Multi-Source Weighted-Ensemble Precipitation (MSWEP) 77 version V280 for 1979–2020. Each of these data sources has its own strengths and limitations 78. Precipitation from reanalysis has a full coverage across space and time, and is generated by a physically consistent model, but stems from a short-range model forecast at a relatively coarse resolution and relies on parameterization for convective precipitation. The GPM IMERG product has a very high spatiotemporal resolution and provides measurements for regions with limited station coverage, but has deteriorated accuracy over mountains 79 and arid regions 80, reduced coverage toward higher latitudes 81. The MSWEP product is based on the combination of these three different data sources to leverage their respective strengths 77. Daily precipitation fields from each dataset are interpolated using first-order conservative remapping on a 0.5-degree regular grid to facilitate the attribution to RWB at the grid scale. Extreme precipitation days are defined by days on which precipitation amounts exceed the 99th percentile of all days throughout the period under consideration (Supplement Fig. 14). For the seasonal analysis, we use the same selection of year-round defined extreme precipitation days and partition these across the corresponding seasons.

Identification of RWB

Data are retrieved from the ERA5 reanalysis on a global 0.5-degree regular grid at 6-h time intervals. Potential vorticity (PV) is computed from data on model levels and then interpolated onto isentropic surfaces between 275 and 360 K with 5 K intervals. PV fields are smoothed using a 9-point local smoothing to reduce excessive small-scale PV structures. For the detection of RWB we combine the object-based identification methods of PV streamers and cutoffs, first introduced by ref. 82, and using some of the newer adaptations from refs. 52, 54, 83 for PV streamers, and from refs. 84, 85 for PV cutoffs. Other studies have used other indicators of RWB, such as PV contour advection 86, meridional reversal of PV 87, and meridionally overturning contours of PV 88, 89, potential temperature 90, 91, or absolute vorticity 72. Here we briefly summarize the applied identification method in this study and refer for more details, motivations for specific choices, and sensitivity analyses to refs. 52, 54, 82, 83, 84, 85.

The detection of PV streamers and cutoffs is based on PV fields on single isentropic surfaces and follows three steps. First, we define in each hemisphere the stratospheric reservoir by the +2 potential vorticity unit (PVU; 1 PVU = 10−6 kg K−1 m2 s−1) contour (−2 PVU contour in the Southern Hemisphere) - representing the dynamical tropopause - at the lowest latitude that encircles the Pole. If no circumglobal PV contour is present, the longest ±2 PVU contour is designated as the stratospheric reservoir, provided it spans more than 180° in the zonal direction and reaches at least partly poleward of ±80° N. Assigned stratospheric reservoirs are evaluated on their vertical connection up to the 360 K isentropic surface to avoid erroneous classification of large-scale high PV air masses near the Earth’s surface over the Poles as stratospheric reservoir. Additionally, stratospheric reservoirs that intersect with the Earth’s surface as a result of the interpolation of PV fields from model levels to isentropic surfaces are removed.

Second, PV streamers are defined by elongated structures in the ±2 PVU contours that encircle the stratospheric reservoir. Each combination of contour points (A and B), obtained by the get_isolines function of NCL version 6.6.2 92, on the ±2 PVU contour is evaluated on the four following geometric criteria (see also ref. 52, their Fig. 1): (1) the width (the great-circle distance between points A and B) <1500 km, (2) the length (the largest great circle distance of any contour point between points A and B, and the great circle of points A and B) >1000 km, (3) the ratio length over width >1, after refs. 52, 54, and (4) the length along the contour between points A and B <15,000 km, after ref. 83. If more than 50% of the stratospheric reservoirs’ surface is classified as streamer, all streamers are removed on that isentropic surface.

Third, all remaining >2 PVU (<- 2 PVU in the Southern Hemisphere) air masses that are not part of the stratospheric reservoir are considered as potential PV cutoffs. PV cutoffs are scrutinized on their vertical connection to the stratospheric reservoir aloft and low moisture content (specific humidity <0.1 g kg-1 and relative humidity <70% for at least 50% of the PV cutoff surface area) to remove PV structures with an orographic frictional and diabatic origin, respectively, after refs. 84, 85. Only PV cutoffs with a surface area <5 × 106 km2, after ref.

Atmospheric moisture transport and forcing for ascent

To provide insight into the mechanisms through which RWB can bring about (extreme) precipitation, we depict anomalous atmospheric moisture transport, quasi-geostrophic omega, and an index of environmental conditions favorable for deep moist convection in Fig. 1, all based on ERA5 data. More specifically, we compute standardized anomalies of the zonal and meridional components of vertically integrated horizontal water vapor transport, after refs. 52, 54. The standardized anomalies are based on a 21-day running window of the mean and standard deviation with reference to period of 1979–2022. Quasi-geostrophic vertical motion is computed through the inversion of the quasi-geostrophic omega equation in Q-vector form 93 using ERA5 coarse grained data at a 1.5-degree grid. We use quasi-geostrophic omega at 500 hPa based on the forcing from levels above 550 hPa to focus on the upper tropospheric forcing (i.e., wave breaking) for ascent 94. Finally, we retrieved convective available potential energy as a measure of the tropospheric environmental conditions conducive to the occurrence of deep moist convection and we signify values exceeding the 95th and 99th percentile thresholds based on a 21-day running window for the period of 1979–2022.

Attribution of precipitation to RWB

Precipitation occurring under the influence of wave breaking typically forms at the downstream flank of the breaking waves (Fig. 1). The upper-level forcing and associated cyclonic circulation of the breaking waves induces enhanced moisture transport and dynamical lifting at this location 48, 49, 50, 51, 54. Therefore, to attribute precipitation to wave breaking, we provide the PV structures with an extended area around their circumference using a fixed distance of 500 km, adjusted from refs. 53, 54. Precipitation is attributed to wave breaking based on the following spatiotemporal criteria. Daily precipitation extremes as well as daily precipitation amounts are attributed to RWB if PV structures, including their extended area, overlap with precipitation at the grid scale on at least 3 of the 5 time intervals during daily precipitation (00, 06, 12, and 18 UTC of the same day and 00 UTC of the next day) on at least 2 isentropic surfaces as a proxy of wave breaking with a vertical depth of approximately 10 K or more. Figure 1 demonstrates the attribution of extreme precipitation to PV structures based on eight extreme precipitation events in different arid parts of the world.

Positive and negative associations and statistical significance testing

To examine the relationship between precipitation and RWB, we determine where this relationship has a positive or negative association and where this association can be considered significant. To this end, we follow the following procedure, which includes the testing of the null hypothesis that precipitation and RWB occur independently, and this hypothesis is rejected in regions where precipitation co-occurs with RWB significantly more or less than expected under independence (i.e., a two-sided test).

First, we perform a Monte Carlo test whereby the dates of PV streamers and cutoffs are shuffled by taking a random day in the same month of a different year, while the dates of precipitation are kept as in reality. In this way, the seasonal influence on the relationship between precipitation and wave breaking is accounted for. This procedure is repeated 100 times for the entire period under consideration. At each grid cell, the Monte Carlo test results in 100 computed fractions of precipitation attributed to wave breaking assuming an independent relationship. The p-value is then determined based on the ranking of the observed fraction of precipitation attributed to RWB as in reality within the distribution of 100 fractions based on random matching.

Second, we control the number of false rejections of the null hypothesis by using the false discovery rate (FDR) test 95 with alpha = 0.1. Grid points with >50% missing values are not included in the FDR test. This procedure yields global fields with information at each grid point indicating whether the relationship between precipitation and RWB has a significant positive, nonsignificant, or significant negative association. A significant positive association indicates that precipitation is significantly more likely to occur in the presence of RWB than under climatology (i.e., normal conditions). A significant negative association indicates that precipitation is significantly less likely to occur in the presence of wave breaking than under climatology, suggesting the dominance of other weather systems for precipitation generation that tend to not co-occur with wave breaking. This procedure is repeated for both precipitation extremes and total amounts, for the year-round and seasonal analyses, and for each precipitation dataset.

The results from the significance testing inherently depend on the sample size, i.e., the length of the datasets that differ among the used precipitation products. To obtain consistent indications of spatially aggregated land surface where RWB favors precipitation formation, we define in addition to the significant associations, also nonsignificant positive and negative associations between precipitation and RWB at grid points where the observed fraction is larger and smaller, respectively, than the median of the fractions from the Monte Carlo samples. While positive and negative associations do not indicate statistical significance, the sign of the association is much less dependent on the length of the respective data records and is thus more easily compared across datasets with different lengths.

Precipitation surplus

Fractions of precipitation associated with RWB can be large even in regions where there is a significant negative association between precipitation and RWB, for example, in much of the humid extratropics, where wave breaking occurs relatively frequently. To obtain estimates of how much precipitation is enhanced or reduced due to RWB (note the difference to “precipitation associated with RWB”), we introduce a measure termed the precipitation surplus, denoted \(S\). First, we compute the daily precipitation rate conditional to days without RWB, \({R}_{{noRWB}}\), and derive the total precipitation that would have formed throughout the period under consideration assuming the absence of RWB, by multiplying \({R}_{{noRWB}}\) by the number of days in the considered time period (i.e., the length of the respective precipitation datasets, days with missing values excluded), yielding \({P}_{{noRWB}}\). The difference between the observed total precipitation, denoted \(P\), and the hypothetical total precipitation in absence of RWB yields the so-called precipitation surplus, i.e., \(S=P-{P}_{{noRWB}}\,(1)\). We compute the precipitation surplus \(S\) for all months separately to account for the seasonality in the relationship between precipitation and RWB and then sum it across the year or seasons, corresponding to the respective analyses in this study. Fractions of precipitation surplus are expressed relative to total precipitation at the grid scale (Figs. 2 and 3, and Supplementary Figs. 1, 2, 4– 11) or based on spatially aggregated quantities (Figs. 4c, d, 6 and Supplementary Fig. 13). Spatial aggregations of precipitation surplus are area-weighted based on the surface area that each grid point represents. Identical computations are performed for both the extreme precipitation occurrences and precipitation amounts. This approach provides an ad hoc estimate of the precipitation that forms due to (surplus) or is suppressed by (deficit) RWB and supports an adequate comparison of RWB contributions to precipitation across regions with a spatially varying RWB climatology and precipitation from various datasets.

Differences in results from the varying precipitation datasets

All analyses in this study, from global to regional scales and from year-round to seasonal timescales, show generally robust results across the four evaluated precipitation datasets, providing confidence in the results. However, we note a systematic lower contribution of RWB to precipitation based on GPM IMERG compared to the other three datasets (ERA5, CPC, and MSWEP) in terms of local associations and surplus (Figs. 2 and 3, Supplementary Figs. 1, 2, 4– 11) and land surface with a positive association and spatially aggregated precipitation surplus (Figs. 4c, d and 6, Supplementary Fig. 13). Although well beyond the scope of this paper to investigate this further, we speculate that these differences stem from the abovementioned strengths and limitations of the different precipitation products. Local convective precipitation, for which synoptic-scale processes such as RWB can be of reduced relevance compared to larger-scale precipitation events, may be better represented in GPM IMERG than in the relatively coarse resolution precipitation forecasts from reanalysis, while these storms may be missed by stations due to the low-density network in arid regions. On the other hand, precipitation from GPM IMERG has reduced accuracy over mountains and arid regions 79, 80, and for winter precipitation and snowfall 79, 80, which may contribute to the differences between the datasets, particularly the large differences for winter precipitation in the midlatitudes (Fig. 6 and Supplementary Fig. 13).

Eddy kinetic energy

To illustrate the location and intensity of the midlatitude storm tracks, we compute the eddy kinetic energy (EKE) using the 10-day high-pass filtered (fast Fourier transform) horizontal wind of ERA5 at a regular 2-degree grid at 6-h time steps and vertically integrate the mass-weighted EKE across 37 pressure levels between 1 and 1000 hPa, adjusted from ref. 55.

Aridity index

We retrieved monthly precipitation and potential evapotranspiration from the Climate Research Unit (CRU) dataset 96 for the period 1979–2021. The data have a global coverage over land except for Antarctica. The aridity index (AI) is computed as the ratio of precipitation over potential evapotranspiration: \({{\rm{AI}}}=\,\frac{{{\rm{precipitation}}}}{{{\rm{potential\; evapotranspiration}}}}\,(2)\), and the AI categories are defined as follows, following refs. 73, 97: humid (AI ≥ 0.65); dry sub-humid (0.5 ≤ AI < 0.65); semi-arid (0.2 ≤ AI < 0.5); arid (0.05 ≤ AI < 0.2); and hyper-arid (AI < 0.05).

Data availability

All datasets used in this study are freely available from the respective data providers. ERA5 reanalysis data from the ECWMF were obtained via the MARS archive and are also available from the Climate Data Store ( https://cds.climate.copernicus.eu). Other datasets used for precipitation were accessed from NASA for GPM-IMERG, from NOAA for CPC, and from GloH2O ( https://www.gloh2o.org) for MSWEP, while monthly data from CRU were obtained via https://data.ceda.ac.uk/badc/cru/. Societal impacts from 8 demonstrative extreme precipitation events driven by RWB were obtained from the Emergency event database (EM-DAT) via https://www.emdat.be, accessed on 24-10-2023. All figures have been produced using the NCAR Command Language (NCL) version 6.6.2 software. The source data for producing the figures are available under 10.5281/zenodo.12775438.

Code availability

All computer codes used for the analyses are available from the authors upon request.

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Acknowledgements

The authors thank Michael Sprenger (ETH Zurich) for generously providing quasi-geostrophic omega and Heini Wernli (ETH Zurich) for commenting on an earlier version of the manuscript. The authors appreciate the constructive comments from three reviewers that helped to improve the presentation of the results and the quality of the manuscript. M.A. was supported by an ETH Zurich Postdoctoral Fellowship (Project No. 21-1 FEL-67), by the Stiftung für Naturwissenschaftliche und Technische Forschung, the ETH Zurich Foundation, and by the Swiss National Science Foundation (grant #TMPFP2_216989). K.K. received funding from the Max Planck Graduate Center in Mainz, the MaxWater Initiative of the Max Planck Society, and the European Union’s Horizon Europe programme under grant agreement 856612 (EMME-CARE). M.R. acknowledges funding of the INTEXseas project form the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement no. 787652). Support from the Swiss National Science Foundation through project PP00PP2_198896 to D.D. is gratefully acknowledged.

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de Vries, A.J., Armon, M., Klingmüller, K. et al. Breaking Rossby waves drive extreme precipitation in the world’s arid regions. Commun Earth Environ 5, 493 (2024). https://doi.org/10.1038/s43247-024-01633-y

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DOI: https://doi.org/10.1038/s43247-024-01633-y

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