Record-breaking Events Research Articles

Causes on the 2018 record-breaking heatwave in South Korea: compound impacts from recurrent large-scale atmospheric teleconnections

Abstract This study analyzed the causes of the extreme heatwave in East Asia in 2018, which brought a record-breaking event in South Korea in terms of the number of hot days and the intensity in history. Long-lasting atmospheric patterns were observed during the 2018 heatwave, and the patterns were similar to those known as the Pacific–Japan (PJ), circum-global teleconnection (CGT), and Arctic Oscillation (AO) patterns identified in a previous study. In 2018, all three patterns appeared to exhibit a strong positive phase. In particular, the PJ and AO Indices showed the highest values within the analysis period, having a major impact on the heatwave. According to a quantitative analysis through multi-linear regression (MLR) of how much each of the three patterns affects the heatwave, all three patterns of PJ, CGT, and AO have significant effects on the heatwave in Korea. The statistically reconstructed heatwave days (HWD) time series with the three indices by MLR account for 51% of the total variability at the interannual timescale. Especially in 2018, most of the occurred HWD could be restored using the three indices. Also, in 1994, when the three indices had a high peak, the number of HWDs was the second-longest ever, while in 1993, when all three indices had a low peak, the heatwave was the lowest. This study quantitatively examined whether the large-scale extreme heatwave in 2018 greatly increased because of PJ, CGT, and AO. This study suggests that extreme heatwave can occur again if three apparently independent atmospheric patterns appear at once in the future.

Role of warming trend in occurrence of record‐breaking high‐temperature events in China during the past 40 years

AbstractRecord high temperatures and heatwaves are increasingly being reported worldwide, sparking significant public concern. In a stable climate, occurrences of record‐breaking events (RBEs) should naturally decrease over time. Therefore, the increasing occurrence of record high temperatures signifies significant instability in the current climate change, potentially attributed to global warming. In this study, we aim to quantitatively investigate the impact of the warming trend on RBE occurrence by examining high‐temperature RBEs based on observations in China over the past 40 years. Additionally, we introduce statistical theory based on random processes to assess its applicability to real‐world scenarios. By comparing the frequency, intensity, and waiting time for RBEs derived from the original and detrended high‐temperature series‐, we find that approximately 10% of RBE frequency in Nanjing station over the past 40 years can be linked to the warming trend. Furthermore, the intensity of RBEs weakens and the occurrence time advances for the same reason. Especially, the increase in high‐temperature RBE frequency attributed to the upward temperature trend in the southwest region of China is estimated to be around 10%–20%, significantly surpassing that in other regions. Meanwhile, the observed RBE occurrence probability and intensity align with the theoretical results, while notable discrepancies exist in RBE prediction, highlighting the need for improvement in theory and skill for RBE forecasting given its complexity and uncertainty.

Global record-breaking recurrence rates indicate more widespread and intense surface air temperature and precipitation extremes.

We analyzed the evolution of extreme annual surface air temperature and rainfall on Earth, based on the recurrence rate of record-breaking events, and found the highest recurrence rates for record-high annual temperatures in the tropics, as opposed to the polar regions with the fastest warming. Both recurrence rates and the global surface area fraction with daily mean surface air temperatures exceeding 30° and 40°C provide further evidence for extremely hot years becoming more common and widespread. A similar analysis for precipitation highlighted some regions with more record-high annual total precipitation and others with record-low annual precipitation typically associated with drought. A multimodel ensemble of 306 runs with global climate models [Coupled Model Intercomparison Project phase 6 (CMIP) Shared Socioeconomic Pathways 2-45 (SSP2-45)] reproduced the statistics of record-breaking high temperatures, but there were some differences for the reanalysis precipitation record-breaking recurrence rates. The global climate model simulations suggested a slightly altered geographical pattern for record-breaking annual precipitation recurrence rates.

A case study of the “21.7” Henan extremely rainfall event: From the perspective of water vapor monitored with GNSS tomography

Water vapor plays a vital role in the development of heavy rainfall system. The “21.7” Henan rainfall event, a record-breaking event, was investigated from the perspective of water vapor based on in-situ measurements, namely the 220 continuously operating GNSS ground stations in Henan Province, with GNSS tomography technique. Results showed that during and after the heavy rainfall, the error RMS of water vapor density from tomography was 21 % lower than that of GFS prediction data at the height of about 1450 m by comparing with radiosonde data. Taking ERA5 as the reference, the average relative error of tomographic water vapor density at the height below 4 km was within 10 % before and during the rainfall. The analyses of spatiotemporal variations of water vapor illustrated that tomographic products can, compared to ERA5 reanalysis data, more distinctly reflect the formation and convergence process of low-level water vapor bands before the occurrence of the extreme rainfall, as well as the fracture of the water vapor bands before the end of the rainfall. By combining the tomographic water vapor and GFS wind field data, the water vapor flux divergence can be calculated to further elucidate the movement of water vapor where significant variations of water vapor at the height of 10 to12 km (near the tropopause) and 1 to 4 km in both the vertical and horizontal directions were found before the extreme precipitation.

Frequency of Italian Record-Breaking Floods over the Last Century (1911–2020)

This study provides an in-depth analysis of the frequency of extreme streamflow in Italy, adopting the innovative perspective of the theory of records, and focusing on record-breaking floods. (i.e., annual maximum series, AMS) observed in Italy between 1911 and 2020. Our research employs an extensive dataset of 522 annual maximum series (AMS) of streamflow observed across Italy between 1911 and 2020. We consider three time intervals (1911–2020, 1911–1970, and 1971–2020), and we define pooling-groups of AMSs based on (a) hydrological (e.g., catchment size, mean annual precipitation, etc.) and (b) spatial proximities of the gauged sites. First, within each group and for each time period, we compute the regional average number of record-breaking events (NRbins). Second, with a series of resampling experiments that preserve the spatial correlation among the AMSs, we test the hypothesis that NRbins result from a group of stationary sequences. Our results show spatially coherent patterns of an increasing number of record-breaking floods in central and in northeastern Italy over the last 50 years. In the same time interval, significant deviations in the regional number of record-breaking events from what would be expected for stationary flood sequences seem to be more common in drier climates or at higher altitudes, while the catchment size does not seem to be a meaningful descriptor.

Reaching New Heights

The global aerospace and defence sectors will gather at the Farnborough International Airshow 2024 from 22-26 July. The organisers are forecasting it will be a record-breaking event

Long-term trend and variability in surface temperatures over Emilia-Romagna from 1962 to 2022

Scientific interest is increasingly drawn towards regional meteorological extremes, given their impacts on populations, infrastructure, and ecosystems. These extremes are shaped by complex interactions between internal climate variability and long-term trends. The aim of the present work is to evaluate changes in high-frequency variability and the influence of long-term trends on the frequency of occurrences of extremes, with a focus on surface temperatures over the period from 1962 to 2022 in Emilia-Romagna, a region of Northern Italy. Daily data of 2 m air temperatures averaged over the region are retrieved from ERACLITO, a high-resolution climate analysis. The distributions of daily temperature anomalies show a general broadening in 1992–2022 with respect to 1962–1991. This is true for maximum, minimum, and mean daily surface temperatures, especially during the summer and spring seasons. A significant warming trend of 0.37 °C/decade is detected in annual mean surface temperatures over the period considered. The study is completed with a comparison between the observed frequency of record-breaking annual temperature events, a hypothetical stationary climate distribution and a theoretical derivation that accounts for changes in trends and variability. During the last decade, the theoretical count of extreme events is 1.26, which yields a likelihood of 86% that this is owed to the trend rather than interannual variability. Idealized experiments demonstrate that the expected occurrences of record-breaking events in future decades depend on the warming rate rather than the warming level. Finally, an analysis performed at seasonal level shows that the majority (minority) of record events are occurring in the summer (spring) seasons.

Boost to early spring compound heatwaves over South Asia from anomalous Tibetan Plateau atmospheric heat source

In the early spring of 2022, South Asia (SA) experienced an unprecedented and prolonged episode of compound extreme heatwaves (EHWs), which pose significant risks to both human society and ecosystems. This exceptional event broke historical records for both frequency and intensity anomalies since 1981 and could be attributed to a barotropic atmospheric regime characterized by an anomalous anticyclone. This study ascribed this record-breaking event to an exceptionally warm Tibetan Plateau (TP) atmospheric apparent heat source (TPAHS). Both the observations and the numerical experiments conducted with a linear baroclinic model revealed that the unusual TPAHS acted as an “air pump”, driving the vigorous lower-level convergence and ascending motion around the TP. Abnormal TPAHS led to an increase in air temperature, subsequently elevating the height of the tropopause. This, in turn, induced a cooler upper-level and warmer lower-level thermal structure over the TP, resulting in a negative potential vorticity (PV) source near 200 hPa. As the TPAHS continued to intensify, the anomalous anticyclone strengthened and extended westward, facilitating the advection of negative PV anomalies from the TP to upstream regions. This resulted in negative PV anomalies and increased geopotential height over the SA. Furthermore, the triggered zonal circulation significantly enhanced descending motion and reduced relative vorticity, thereby strengthening the barotropic atmospheric regime over the SA. Consequently, clear skies prevailed, amplifying the solar shortwave radiation reaching the ground. This increase in surface thermal radiation warmed the near-surface air temperatures, ultimately resulting in compound EHWs on an interannual timescale.

Nonparametric tests of extremes of daily maximum temperatures based on the breaking records: A case study in Seoul and Busan during 1961-2022

An observation in a time series is called an upper record if it is greater than all previous observations in the series. Also it is called a lower record than all previous observations in the series. Therefore, the analysis of record-breaking events is of interest in fields such as climatology, economics and sports. As an alternative to the classical extreme value theory, which are based on the fit of generalized extreme value (GEV) distribution, generalized Pareto (GP) distribution and Poisson processes, this work is based on the study of record-breaking events to analyze non-stationarity in the extremes. The contribution of this work is the use of the statistical tools developed by Castillo-Mateo et al. (2023) to assess and analyze the effect of global warming in the extreme and record breaking events using daily maximum temperature series in Seoul and Busan over 1961-2022. These test statistics consider the information based on the four different types of record, that is, forward upper, forward lower, backward upper and backward lower. Also, change point detection is implemented based on records.

The patterns, magnitude, and drivers of unprecedented 2022 mega-drought in the Yangtze River Basin, China

The Yangtze River Basin in China was hit by an unprecedented extreme drought in 2022. Such a record-breaking event is jointly driven by a few outlier factors and shows abnormal phenomena. The exceptionality of this drought event cannot be fully described by any individual indicator. Therefore, we performed this comprehensive study to highlight the exceptionality of 2022 Yangtze River Basin drought. We evaluated three drought characteristics: onset period (the time interval of moisture condition from normal to extreme), intensity, and affected area and their compound features. Additionally, historical climatology (1950–2022) and four past severe events are used as references. Lastly, we investigated the driving mechanisms of this event from synoptic perspective. Our results indicate the 2022 drought ranked as the most severe event in history. The recurrence interval of the 2022 Yangtze River drought is estimated to be 120–400 years by considering individual and combined drought characteristics. Behind the scenes, the synoptic environment triggered the abnormally high temperatures and abrupt alteration of precipitation, which is the main driver of the event. The 2022 Yangtze River drought is an archetype of an event characterized by both rapid intensification over time and space, which is indicative for drought monitoring and early warning in a warming climate.

Quantitative rainfall analysis of the 2021 mid-July flood event in Belgium

Abstract. The exceptional flood of July 2021 in central Europe impacted Belgium severely. As rainfall was the triggering factor of this event, this study aims to characterize rainfall amounts in Belgium from 13 to 16 July 2021 based on two types of observational data. First, observations recorded by high-quality rain gauges operated by weather and hydrological services in Belgium have been compiled and quality checked. Second, a radar-based rainfall product has been improved to provide a reliable estimation of quantitative precipitation at high spatial and temporal resolutions over Belgium. Several analyses of these data are performed here to describe the spatial and temporal distribution of rainfall during the event. These analyses indicate that the rainfall accumulations during the event reached unprecedented levels over large areas. Accumulations over durations from 1 to 3 d significantly exceeded the 200-year return level in several places, with up to 90 % of exceedance over the 200-year return level for 2 and 3 d values locally in the Vesdre Basin. Such a record-breaking event needs to be documented as much as possible, and available observational data must be shared with the scientific community for further studies in hydrology, in urban planning and, more generally, in all multi-disciplinary studies aiming to identify and understand factors leading to such disaster. The corresponding rainfall data are therefore provided freely in a supplement (Journée et al., 2023; Goudenhoofdt et al., 2023).

Dramatic increase in the probability of 2006-like compound dry and hot events over Southwest China under future global warming

Compound dry and hot events, the combination of high temperature and scarce rainfall, are receiving attention in recent times due to their devastating stress on ecosystems, agricultural production, and public health worldwide. Knowing the risk of compound dry and hot events, particularly for the severe ones on record, is essential for developing effective measures to mitigate the negative impacts. However, most of the existing investigations only focus on the long-term trend of compound dry and hot events during the past decades, and future changes in those record-breaking events remain sparsely reported, especially in China. With a focus on the typical severe compound dry and hot event over Southwest China in summer 2006, this study quantifies the future probability of such compound extreme under various emission and societal development scenarios. Results show that the compound dry and hot event in 2006 is the most severe during 1901–2020, with widespread spatial extent in Southwest China. The observed change in temperature plays a dominant role in the variation of compound severity. Based on Coupled Model Intercomparison Project phase 6 (CMIP6) multi-model simulations, we further show that the maximum ratio of the increase in the area affected by compound dry and hot events to that of 2006 is projected to probably be about twofold under the Shared Socioeconomic Pathway (SSP) 1–2.6 scenario in about 2040, while it would likely climb to nearly triple for the other two scenarios SSP2-4.5 and SSP5-8.5 in about 2060 and 2050, respectively. These findings could provide a support for urgent adaptation and mitigation efforts against compound dry and hot events to mitigate the impact.

En echelon faults reactivated by wastewater disposal near Musreau Lake, Alberta

SUMMARY We use machine-learning and cross-correlation techniques to enhance earthquake detectability by two magnitude units for the earthquake sequence near Musreau Lake, Alberta, which is induced by wastewater disposal. This deep catalogue reveals a series of en echelon ∼N–S oriented strike-slip faults that are favourably oriented for reactivation. These faults require only ∼0.6 MPa overpressure for triggering to occur. Earthquake activity occurs in bursts, or episodes; episodes restricted to the largest fault tend to have earthquakes starting near the southern end (distant from injectors) and progressing northwards (towards the injectors). While most events are concentrated along these ∼N–S oriented faults, we also delineate smaller faults. Together, these findings suggest pore pressure as the triggering mechanism, where a time-dependent increase in pore pressure likely caused these faults to progressively reawaken. Analysis of the ‘next record-breaking event’, a statistical model that forecasts the sequencing of earthquake magnitudes, suggests that the next largest event would be ML ∼4.3. The seismically illuminated length of the largest fault indicates potential magnitudes as large as Mw 5.3.

The temporal evolution of induced seismicity sequences generated by low-pressure, long-term fluid injection

Traffic light schemes (TLSs) are commonly used to mitigate induced seismicity caused by subsurface fluid injection. Verdon and Bommer (J Seismol 25:301–326, 2021a) investigated the validity of the implicit assumptions that underpin the successful functioning of TLSs. In particular, they examined the extent to which magnitude jumps (sudden increases in event magnitudes from any preceding seismicity) and trailing events (continued increases in seismicity levels after the end of injection) took place in hydraulic fracturing (HF) induced seismicity sequences. Other technologies such as carbon capture and storage (CCS), wastewater disposal (WWD) and natural gas storage (NGS) involve the gradual but long-term injection of large fluid volumes at low pressure. Hence, we might expect to see a different spatial and temporal evolution of magnitudes for seismicity induced by low-pressure, long-term (LPLT) injections compared to HF. In this study, we compile cases of LPLT injection-induced seismicity in order to examine their temporal evolution. We examine the occurrence of magnitude jumps, trailing events and onset times for seismicity after the initiation of injection. We find that few LPLT injections have produced trailing events, and that magnitude jumps are typically below 1.5 magnitude units. The timescale of event occurrence (relative to the onset of injection) is highly variable, likely reflecting site-specific conditions. For long-term injection, we observe a trend for the largest events to occur within the earlier part of each sequence, with magnitudes then stabilising, or even reducing, as injection continues. Finally, we evaluate the performance of the next record breaking event (NRBE) model as a method for forecasting induced event magnitudes, finding that this method performs reasonably well in most cases, but that in some cases the largest event significantly exceeds this model.

Variability conceals emerging trend in 100yr projections of UK local hourly rainfall extremes

Extreme precipitation is projected to intensify with warming, but how this will manifest locally through time is uncertain. Here, we exploit an ensemble of convection-permitting transient simulations to examine the emerging signal in local hourly rainfall extremes over 100-years. We show rainfall events in the UK exceeding 20 mm/h that can cause flash floods are 4-times as frequent by 2070s under high emissions; in contrast, a coarser resolution regional model shows only a 2.6x increase. With every degree of regional warming, the intensity of extreme downpours increases by 5-15%. Regional records of local hourly rainfall occur 40% more often than in the absence of warming. However, these changes are not realised as a smooth trend. Instead, as a result of internal variability, extreme years with record-breaking events may be followed by multiple decades with no new local rainfall records. The tendency for extreme years to cluster poses key challenges for communities trying to adapt.

Statistics of Weibull Record-Breaking Events

The statistics of record-breaking events plays an important role in the analysis of natural physical systems. It can provide an additional insight into the mechanisms and the occurrence of extreme events. In this work, the statistical aspects of the record-breaking events drawn from the Weibull distribution are considered and analyzed in detail. It is assumed that the underlying sequences of events are independent and identically distributed (i.i.d.). Several statistical measures of record-breaking events are analyzed. Exact analytical expressions are derived for the statistics of records. Particularly, the distributions of record magnitudes and the corresponding average magnitudes of records in case of Weibull distributed events are derived exactly for any specific record order and time step. In addition, a convolution operation is used to derive a recursive formula for the distribution of times of the occurrence of records. The analytical results are compared with the Monte Carlo simulations and their validity is confirmed. The numerical simulations also reveal that the finite-size effects strongly affect the statistics of records and need to be considered during the analysis of numerical experiments or empirical data.

Distribution-free changepoint detection tests based on the breaking of records

The analysis of record-breaking events is of interest in fields such as climatology, hydrology or anthropology. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem. They are CUSUM-type statistics based on the upper and/or lower record indicators observed in a series. Using a version of the functional central limit theorem, we show that the CUSUM-type statistics are asymptotically Kolmogorov distributed. The main results under the null hypothesis are based on series of independent and identically distributed random variables, but a statistic to deal with series with seasonal component and serial correlation is also proposed. A Monte Carlo study of size, power and changepoint estimate has been performed. Finally, the methods are illustrated by analyzing the time series of temperatures at Madrid, Spain. The R package RecordTest publicly available on CRAN implements the proposed methods.

Australian wildfire smoke in the stratosphere: the decay phase in 2020/2021 and impact on ozone depletion

Abstract. Record-breaking wildfires raged in southeastern Australia in late December 2019 and early January 2020. Rather strong pyrocumulonimbus (pyroCb) convection developed over the fire areas and lofted enormous amounts of biomass burning smoke into the tropopause region and caused the strongest wildfire-related stratospheric aerosol perturbation ever observed around the globe. We discuss the geometrical, optical, and microphysical properties of the stratospheric smoke layers and the decay of this major stratospheric perturbation. A multiwavelength polarization Raman lidar at Punta Arenas (53.2∘ S, 70.9∘ W), southern Chile, and an elastic backscatter Raman lidar at Río Grande (53.8∘ S, 67.7∘ W) in southern Argentina, were operated to monitor the major record-breaking event until the end of 2021. These lidar measurements can be regarded as representative for mid to high latitudes in the Southern Hemisphere. A unique dynamical feature, an anticyclonic, smoke-filled vortex with 1000 km horizontal width and 5 km vertical extent, which ascended by about 500 m d−1, was observed over the full last week of January 2020. The key results of the long-term study are as follows. The smoke layers extended, on average, from 9 to 24 km in height. The smoke partly ascended to more than 30 km height as a result of self-lofting processes. Clear signs of a smoke impact on the record-breaking ozone hole over Antarctica in September–November 2020 were found. A slow decay of the stratospheric perturbation detected by means of the 532 nm aerosol optical thickness (AOT) yielded an e-folding decay time of 19–20 months. The maximum smoke AOT was around 1.0 over Punta Arenas in January 2020 and thus 2 to 3 orders of magnitude above the stratospheric aerosol background of 0.005. After 2 months with strongly varying smoke conditions, the 532 nm AOT decreased to 0.03-0.06 from March–December 2020 and to 0.015–0.03 throughout 2021. The particle extinction coefficients at 532 nm were in the range of 10–75 Mm−1 in January 2020 and, later on, mostly between 1 and 5 Mm−1. Combined lidar–photometer retrievals revealed typical smoke extinction-to-backscatter ratios of 69 ± 19 sr (at 355 nm), 91 ± 17 sr (at 532 nm), and 120 ± 22 sr (at 1064 nm). An ozone reduction of 20 %–25 % in the 15–22 km height range was observed over Antarctica and New Zealand ozonesonde stations in the smoke-polluted air, with particle surface area concentrations of 1–5 µm2 cm−3.

On the Local Rain-Rate Extreme Associated with a Mesovortex over South China: Observational Structures, Characteristics, and Evolution

Abstract Extreme short-term hourly rainfall accumulations are shown to be commonly attendant with rotation-featured mesovortices. This study aims to document the detailed aspects of mesovortex-related extreme rain rates in a record-breaking event that occurred over South China on 7 May 2017 through high-resolution observations, and to reveal how the mesoscale storm contributes to the extreme rain rates, with special attention given to the minute rain-rate enhancement episode (MREE). The event accumulation possesses highly local distribution, with a spatial rainfall core. Extreme rain rates are dictated by a meso-γ-scale storm, and it is found that the observed rain rate is well correlated to storm-related maximum reflectivity in the lowest 2 km above ground level (AGL) as well as its reflectivity centroid (i.e., reflectivity factor exceeding 50 dBZ) depth. The cross section reveals that the storm structure evolves progressively into a single centroid, which subsequently descends to the near surface, resulting in the rain-rate peak (4.8 mm min−1). Extremely weak environmental mean flow interacts with the near-opposite storm propagation that determines the slow storm movement, prolonging local rainfall. Rainfall-induced cold outflow surges ahead unevenly, leading to an inhomogeneous mesoscale outflow boundary (IMOB) at low levels. A mesovortex subsequently develops along the IMOB in the lowest ∼5.5 km AGL, with a horizontal radius of 1.5–3 km. A mesoscale low-level jet observed over the upstream of the storm increases the low-level shear despite short duration, which provide potential dynamics for the storm and mesovortex development. These results help us better understand the generation of extreme rain rates in small spatiotemporal scale. Significance Statement Despite many extreme short-duration rainfall events linking to low-level rotation phenomenon, we are still exploring how these rotations develop within extreme-rainfall-producing storms. While past studies have found that these low-level rotations within such storms are conducive to enhancing rainfall, rotation characteristics are less understood. In this study, we examine how the rotations develop during an episode of observed-rainfall rise. The results reveal that the cold airflows resulted from the storm-inducing rainfall impinge unevenly on warm moist southerly wind, leading to such low-level rotation. The rainfall observed per minute is found to associate well with low-level rotation that develops upward. These results further motivate exploration of extreme short-duration rainfall and storm-related rotation.

Statistical properties of avalanches via the c-record process.

We study the statistics of avalanches, as a response to an applied force, undergone by a particle hopping on a one-dimensional lattice where the pinning forces at each site are independent and identically distributed (i.i.d.), each drawn from a continuous f(x). The avalanches in this model correspond to the interrecord intervals in a modified record process of i.i.d. variables, defined by a single parameter c>0. This parameter characterizes the record formation via the recursive process R_{k}>R_{k-1}-c, where R_{k} denotes the value of the kth record. We show that for c>0, if f(x) decays slower than an exponential for large x, the record process is nonstationary as in the standard c=0 case. In contrast, if f(x) has a faster than exponential tail, the record process becomes stationary and the avalanche size distribution π(n) has a decay faster than 1/n^{2} for large n. The marginal case where f(x) decays exponentially for large x exhibits a phase transition from a nonstationary phase to a stationary phase as c increases through a critical value c_{crit}. Focusing on f(x)=e^{-x} (with x≥0), we show that c_{crit}=1 and for c<1, the record statistics is nonstationary. However, for c>1, the record statistics is stationary with avalanche size distribution π(n)∼n^{-1-λ(c)} for large n. Consequently, for c>1, the mean number of records up to N steps grows algebraically ∼N^{λ(c)} for large N. Remarkably, the exponent λ(c) depends continuously on c for c>1 and is given by the unique positive root of c=-ln(1-λ)/λ. We also unveil the presence of nontrivial correlations between avalanches in the stationary phase that resemble earthquake sequences.