Global increase in extreme events

We first estimate the long-term trend during 1929–2017 for annual extremes, i.e., 99th and 95th percentile daily total precipitation, daily average runoff and corresponding daily mean temperature (T mean ), daily maximum temperature (T max ) and daily minimum temperature (T min ). As expected, we find an overall positive trend of temperature at the global scale20,21,22, except in the midwestern US and north-western Europe, which exhibit distinct cooling trends (Fig. 1a and Supplementary Fig. 2). A recent regional study23 revealed that this cooling phenomenon might be attributed to intense agriculture and land management practices (Supplementary Fig. 3). Observational and modelling studies have demonstrated the ability of intense agriculture and irrigation to cool surface temperatures through increased evapotranspiration24,25. This cooling trend is attenuated when we use only temperatures on wet (i.e., rainy) days (Supplementary Fig. 4), because agriculture has larger cooling impacts on dry days when evapotranspiration is large.

Fig. 1 Global trend results for annual 99th percentile daily extremes during 1929–2017. a–c Trend of T mean (a), precipitation (b) and runoff (c), respectively. White indicates grids with insufficient data or that the trend is insignificant at a 0.05 level Full size image

Most rainfall stations outside of Russia show positive trends for precipitation extremes (Fig. 1b). Large increases are present in the midwestern US due to the increased moisture supply from irrigation23 and changes in mesoscale convective system (MCS) activity26. Agricultural intensification increases soil moisture and evapotranspiration23,24,25, leading to greater atmospheric moisture availability and is in line with the increasing trends of relative humidity (RH), specific humidity and moisture flux convergence in the midwestern US (Supplementary Fig. 5). A significant increase of the convective available potential energy in this region also makes the environment more favourable for convection and allows MCSs to grow larger26,27, thus resulting in a significant increase in the MCS rainfall volume28. A decreasing trend in precipitation dominates Russia, particularly a strong decreasing signal during 1961–1980, because moisture advection from the ocean is limited29,30, and decreased as a result of lower wind speeds and reduced specific humidity over Eurasia (Supplementary Fig. 6). The strong increase of precipitation, which prevails over Southeast Asia is consistent with previous findings, highlighting the change in regional atmospheric convergence there31. Most of global runoff stations show positive trends, although these are accompanied by large spatial variability in magnitude. The American continent indicates an overall increasing trend, while runoff extremes over the Sahel areas in Africa have declined (Fig. 1c); the fast flow extremes show similar changes (Supplementary Fig. 7). These changes in global extremes are more severe when we focus only on the more recent years, 1980–2017 (Supplementary Figs. 7–9). A more significant cooling trend is observed over the midwestern US and north-western European regions, and precipitation and runoff extremes show more distinct intensification over America, implying a stronger climate change impact in recent decades.

Hook structure of extremes-temperature scaling

Both fast flow and precipitation extremes exhibit three types of behaviour with temperature (Fig. 2c, d and Supplementary Fig. 10): (i) a monotonic increase with temperature, (ii) a monotonic decrease with temperature or (iii) a hook-like structure32,33, where extremes increase with temperature up to a threshold (hereafter called peak point temperature) and then decrease with a warming temperature. As examples, we examine more closely the three typical structures in four sample areas (see Fig. 2b). Region #3 indicates a hook-like structure, and the other three regions indicate a monotonic (increasing or decreasing) scaling structure. To have a better understanding of the scaling robustness, we also present scaling curves, all significant at a 0.05 level, of different stations from the four example regions (see Methods, Supplementary Fig. 11). We attempt to understand the extreme decline characteristics under high temperature by evaluating RH data on wet days (i.e., on days with precipitation over 0.1 mm/d) against temperature (Fig. 2e–h). The change in RH tends to coincide with the scaling relationship, i.e., although Region #1 and Region #2 both indicate monotonically increasing scaling behaviour, Region #1 shows an overall increase in RH with warming and has a super C–C scaling for precipitation–temperature relation, while Region #2 shows a RH decrease and sub-C–C scaling (Fig. 2e, f). The discrepancy over Region #1 and Region #2 implies that RH changes weaken or strengthen the C–C scaling, emphasising the role of atmospheric dynamics in addition to thermodynamics for extremes. The thermodynamics for extremes hinges on the assumption that precipitation intensity should be proportional to changes in the saturation vapour pressure, neglecting moisture limitation and energy constraints34. Atmospheric dynamics by affecting large-scale subsidence, advection and atmospheric humidity can also modify precipitation and its extremes in response to a changing climate. For instance, over land regions, RH tends to decrease under high temperatures, and reduced moisture availability could partially account for an offset of precipitation intensities due to increased saturation vapour pressure35. Importantly, a hook-like structure of RH as a function of temperature is found in Region #3, where RH begins to decline sharply near the peak point temperature in the scaling of precipitation and fast flow extremes, while the steep RH drop occurring in Region #4 coincides with a negative scaling (Fig. 2g, h). The above conclusions also hold when we evaluate RH data one day prior to rain (Supplementary Fig. 12).

Fig. 2 Peak point temperature for percentile 99th extreme with daily mean temperature and extremes and relative humidity varying with temperature over four example regions. a, b Peak point temperature of precipitation extremes (a), and fast flow extremes (b). c, d Relationship between T mean with precipitation extremes (c), and fast flow extremes (d). e–h Relative humidity on wet day varying with T mean over four example regions, i.e., Region #1 (e), Region #2 (f), Region #3 (g) and Region #4 (h). Region #1 in north Japan (139°E–145°E, 41°N–47°N), Region #2 in western Asia (64°E–70°E, 35°N–41°N), Region #3 in southeastern China (113°E–119°E, 27°N–33°N) and Region #4 in Central America (81°W–87°W, 8°N–14°N). The solid curves in c, d are fitted with extreme-temperature scatters using the LOWESS method, while the solid lines are fitted by linear regression method (p value < 0.05). Dashed lines are C–C scaling Full size image

As a metric for precipitation intensity–temperature relationship, C–C scaling is thought to be applicable only when there is no moisture limitation or when RH is fairly steady36,37. This may not be the case over land, however, where very warm temperatures may imply a large saturation deficit and increased aridity in the absence of sufficient evaporation or moisture advection37. Indeed, RH over land regions is decreasing with global warming compared to the ocean where it is relatively steady35,36,37. This is due to a constraint in nearly equal equivalent potential temperature changes over the ocean and land. As land regions have higher Bowen ratios, this implies higher absolute temperature changes and lower RH over continents38. This continental moisture limitation would then inhibit the development of convection and extreme precipitation and result in less intense rainfall and storm runoff response39.

The monotonic increase of precipitation extremes with temperature is the dominant phenomenon at high latitudes such as in northern Europe, western Asia, southern Australia and Russia, while most areas over the midlatitudes (e.g., the US, southern Europe, eastern Asia and eastern Australia) typically exhibit a hook-like structure (Fig. 2a). A monotonic decrease is dominant over the tropics, particularly in Southeast Asia, the Indian subcontinent and Central America. Compared with the precipitation–temperature scaling, the hook-like structure of fast flow-temperature scaling prevails over major areas of globe. The negative scaling still dominates the tropical regions except for the Indochina Peninsula (Fig. 2b), where land use change and human activities (Supplementary Figs. 13, 14) have likely impacted the scaling relationships40,41,42. The above findings are robust to the use of different quantiles of extremes, to the same-day versus previous-day local temperature, and to other means of deriving the fast flow extreme (e.g., a baseline of 25th percentile runoff for non-extreme conditions, Supplementary Figs. 15–17).

The negative scaling of extremes at very high temperatures may raise questions about the existence of a potential upper bound for future extremes; however, the decreasing scaling of extremes at high temperatures does not imply such a limit. During extreme precipitation events, the shortwave reflectance of thick cloud, strong surface latent heat fluxes and rain evaporative cooling all contribute to surface cooling, resulting in same-day observation bias towards cooler temperatures. The limitation of the sample size of surface observations at high temperatures might also be an artefact for the occurrence of breakdown in scaling relationships10,43. Our work shows that the mean temperatures are colder than the peak point temperature for both precipitation and fast flow over most regions of the globe (Supplementary Fig. 18). Most local temperatures in the regions characterised by a hook-like curve are still described by its ascending branch, suggesting potential intensification of precipitation and runoff extremes with warmer conditions. More importantly, previous work has employed climate models to project that the peak point temperature will increase with warming, shifting the hook curve to warmer temperatures in the future and resulting in a significant increase in precipitation extremes that occur at the peak point temperature37.

Scaling rates of extremes with local temperatures

To gain further insight into the temperature dependence of extremes, we estimate the spatial distribution of scaling rates of both precipitation–temperature and fast flow-temperature relationships by binning44,45,46; if a hook-like structure was observed, regression fitting was applied only up to the peak point temperature47,48,49. For the precipitation–temperature relationship, a limited region of the globe exhibits a near C–C rate (i.e., between 5 and 9%/°C), dominant over eastern Asia, southeastern Australia, northern Russia, south-western Canada and inner Europe (Fig. 3a). The tropics commonly exhibit negative scaling rates with large scaling variability, from −40%/°C all the way up to 40%/°C (Fig. 3d). This is likely due to the lack of data over the tropics so that the observations do not uniformly sample the conditions there (Fig. 3g). Most regions of the globe indicate sub-C–C rates (i.e., below 5%/°C), such as the eastern US, eastern Europe, southern Russia, southeastern China and Middle Eastern regions. A very super C–C rate (i.e., over 20%/°C) is observed over coastal regions, such as the coastal South China Sea, north-eastern Australia, coastal regions of Africa, and islands (Fig. 3a). Given the importance of oceans in contributing approximately 85% of the moisture to the atmosphere50 and the limited role of soil moisture recycling in those regions51, the oceans play a dominant role in supplying the moisture needed to generate intense precipitation extremes. In coastal regions, the land–sea breeze is an essential means of moisture advection over land and hence coastal precipitation52.

Fig. 3 Global scaling results for 99th percentile precipitation and fast flow extremes with local temperature. a Scaling results of precipitation extremes with T mean . b Scaling results of fast flow extremes with T mean . c Ratio of fast flow to precipitation scaling with T mean . d–f Zonal results based on precipitation scaling, fast flow scaling and ratio, respectively. g–i Used stations for precipitation scaling, fast flow scaling and ratio analysis, respectively. Solid blue lines indicate the median scaling rate or ratio in each latitude band, and the shading shows the associated 90% confidence intervals. Dashed blue lines indicate the global average values, and dashed red lines in d, e indicate C–C scaling Full size image

Similarly to precipitation, the negative C–C scaling of fast flow prevails over tropical regions except for the Indochina peninsula (Fig. 3b), this inconsistency may be due to agriculture, human activities and dam construction (Supplementary Figs. 3, 13, 14 and 19), which have affected runoff. Super C–C rates of storm runoff dominate most observed areas of the globe, while very large super C–C scaling prevails over coastal regions (Fig. 3b), such as the western US, southeastern Africa, northern Europe and the coastal regions of Australia, implying that coastal MCSs and land–sea circulations contribute to storm runoff intensification52,53. In contrast with precipitation, the sub-C–C scaling rates are mainly observed over the eastern US and over a few limited regions in southern Europe (Fig. 3b), implying that warming climate and anthropogenic changes during the same period, have higher impacts on storm runoff than on daily precipitation extremes. Conducting scaling analysis using T max or T min in lieu of T mean , does not alter the conclusions presented here (Supplementary Fig. 20). The runoff-temperature scaling results are globally significant at a 0.05 level, except for a few stations with small scaling rates. The precipitation–temperature scaling is also significant throughout the extra-tropics and only insignificant in regions with low scaling rate (Supplementary Figs. 21, 22). Using local previous-day temperatures produced larger scaling rates than same-day (wet-day) temperatures (Supplementary Fig. 23 and Supplementary Table 1) because of rain evaporative cooling. Rain also reduces same-day temperature via lower surface sensible heat fluxes, so that the previous-day temperature should generally be a better indicator of atmospheric moisture availability.

How does the scaling of fast flow extremes compare to that of precipitation? In the extra-tropics, fast flow usually exhibits higher temperature scaling compared with precipitation, while over certain limited regions in the tropics the fast flow-temperature scaling is opposite that of precipitation–temperature, for example, over the Indochina Peninsula and north-western Australia (Fig. 3c). If we use the 95th percentile extremes or derive the fast flow extreme using other methods such as a baseline of 25th percentile runoff for non-extreme conditions, the above conclusions still hold (Supplementary Figs. 24–26). The runoff without separating base flow has slightly lower temperature-scaling rates than fast flow and the relative scaling with precipitation does not change much (Supplementary Table 1 and Supplementary Fig. 27).

To closely investigate the zonal distribution of scaling rates and ratios, we derive the zonal values in each 10° latitude bin (Fig. 3d–f). The scaling rates for precipitation and fast flow both indicate strong zonal variability, slightly more so for the fast flow. In the tropics, the zonal median scaling rates of precipitation–temperature are almost always below zero and range from −11.1 to 7.4%/°C, while the fast flow-temperature scaling rates show large fluctuations, ranging from −12.6 to 20.1%/°C. Notwithstanding spatial and zonal variation, the zonal median temperature scaling rates for fast flow over the extra-tropics usually falls between 5.4 and 24.8%/°C, which is much larger than that of precipitation scaling (ranging from 3.6 and 7.1%/°C). The zonal median ratios of fast flow scaling rate to precipitation rate are above one at major latitude bands of the globe, although with large variability, especially over the tropics where there are fewer stations (Fig. 3g–i).

The different responses of precipitation and storm runoff to temperature can be attributed not only to warming, but also to factors like land use land cover changes, water and land management and vegetation changes that have altered the underlying surface conditions and hydrological feedbacks and hence storm runoff generation. Fast runoff is generated through infiltration excess and saturation-excess mechanisms, largely impacted by soil condition and storm events in terms of intensity and duration. Rainfall intensifies with warming, until the precipitation intensity becomes larger than the infiltration rate capacity and generates runoff54. Such a discrepancy in precipitation and infiltration-excess generated runoff suggests a difference of scaling rate at the ponding point also holds at higher temperatures (Supplementary Fig. 28a, b). Moreover, soil pores fill up sooner with higher-intensity rains, generating more saturation-excess runoff. Those soil condition changes contribute to the nonlinear increase in runoff coefficient (i.e., ratio of excess runoff to total rain) with rain intensity increase (Supplementary Fig. 28b), supported by numerous theoretical considerations and observational studies54,55. A larger runoff coefficient suggests a higher scaling rate of runoff than precipitation with temperature (see Methods and Supplementary Fig. 28c).

The hydrologic effects of forest degradation, especially in the tropics, can also increase storm runoff generation56. Emerging evidence has been provided for the “infiltration–evapotranspiration trade-off hypothesis”, which states that forest removal reduces the infiltration capacity of soil and the water losses through quick flow are larger than the gains from reduced evapotranspiration57. The deforestation impairs the maintenance of base flow, which changes the storm runoff pathway and contributes to larger infiltration-excess runoff yields58. All these mechanisms contribute to a stronger storm runoff response to climate and anthropogenic changes than for precipitation.

Decadal variability of extremes-temperature scaling

Despite the strong evidence for climate and anthropogenic influence on storm runoff extremes increase that we have presented so far, it is important to consider the potential confounding effect of decadal variability on these results. We evaluate the influence of decadal variability in the scaling of both precipitation and fast flow extremes, by splitting the total period into eight consecutive time period bins instead of one (Fig. 4a, b, Supplementary Figs. 29, 30). Precipitation and storm runoff scaling in different time period bins show similar zonal characteristics, i.e., tropical regions indicate negative scaling rates with large variability (ranging from −30 to +40%/°C rate) probably due to a lack of stations (Supplementary Fig. 31), while extra-tropic areas mainly show positive scaling rates. Even though it exhibits decadal variability, fast flow mostly exhibits a super C–C scaling whereas precipitation usually exhibits a sub-C–C scaling over the extra-tropics, and the zonal median ratio between these two scaling rates is still almost always greater than one over the extra-tropic region (Fig. 4c). The results for previous-day temperature with extremes show qualitatively similar and quantitatively larger scaling rates. The relative change between precipitation and storm runoff are consistent with the above findings (Fig. 4d–f, Supplementary Figs. 32, 33), implying that the fundamental conclusions that a warming climate has important impacts on extreme storm runoff is robust.