Abstract
Changes in heavy precipitation frequency can be viewed as a change in the event return period, a common metric of risk. Compared with intensity, frequency changes are less well-studied and past work has largely been constrained to analysis of well-instrumented regions. We exploit the latest ERA5 reanalysis and its global hourly accumulations at 1/4° spatial resolution and apply a metric that captures frequency changes across both wet and dry regions. According to ERA5 and in a global average sense, during 1989–2018, hourly events that occurred once per year in 1979–1988 increased in frequency by 71 (53–93, 95% range) %, while the one day per year heavy event frequency increased by 44 (37–54) %. Thus, hourly events that occurred once per year in the baseline decade are on track to double in frequency by 2021–2030, and the daily events by 2047–2056. Furthermore, our results replicate prior findings that relative frequency increases are larger for increasingly rare events, and for the first time we quantify that mean frequency increases have been greater over ocean than land. Ocean increases are larger by factors of 3.0 and 2.1 for the hourly and daily events that occurred once per year in 1979–1988, respectively.
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1. Introduction
In a warming climate, global precipitation is expected to increase at ∼2% K−1 following atmospheric energy balance constraints (Allen and Ingram 2002), whereas heavy precipitation increases at ∼7% K−1 where moisture is available (Trenberth 1999) based on the Clausius–Clapeyron relationship, or even more in the presence of dynamic changes (Bhattacharya et al 2017, Pfahl et al 2017). Such disproportionality means that extreme events increase at the expense of moderate and light events (Trenberth 1999, Fischer and Knutti 2016). Indeed, observational and modeling studies have reported regional increases in the frequency and intensity of heavy precipitation (e.g. Groisman et al 2005, Donat et al 2013, Westra et al 2013, Alexander 2016, Wong and Teixeira 2016, Prein et al 2017, Kirchmeier-Young and Zhang 2020). The spatial distribution of these changes is highly heterogeneous, with some regions showing opposite trends (Donat et al 2013, Alexander 2016). This is explained by the lack of moisture availability over land, natural climate variability and dynamics. Furthermore, research also suggests that sub-daily heavy precipitation may increase more than daily heavy precipitation (Lenderink et al 2008, Westra et al 2014, Yu et al 2016, Barbero et al 2017, Guerreiro et al 2018). Primarily, this is attributed to latent heat release invigorating short-term convective precipitation (Lenderink et al 2017). Changing extreme events on different timescales may be policy-relevant, for example a greater increase in sub-daily extremes may result in additional flash flooding beyond that expected from daily statistics (Milly et al 2002, Trenberth 2011).
Intensification of heavy precipitation has been identified using several common metrics (Zhang et al 2011), but large-scale changes in frequency are less well studied. Reported metrics include trends in the frequency of extreme precipitation events that exceed a base period percentile (Zhai et al 2005, Papalexiou and Montanari 2019) or a predefined threshold (Goswami et al 2006, Roxy et al 2017). Here, we adopt an approach similar to that used in recently published studies (Fischer and Knutti 2016, Myhre et al 2019) of European precipitation extremes, where frequency changes are spatially aggregated. This aggregation can be performed over any arbitrary region, but here we only analyze global, and then separately global land and ocean.
We used hourly precipitation at 1/4° spatial resolution from the new European Reanalysis—ERA5 (Hersbach et al 2020), to assess changes in the frequency of hourly and daily heavy precipitation events during 1989–2018 relative to 1979–1988. This is, to our knowledge, the first global analysis of changes in heavy precipitation frequency using an observation-based product that also allows a comparison between hourly and daily events. Our results are derived for ERA5 only, and trends may be susceptible to time-dependent biases in the reanalysis, such as those related to changes in assimilated observations. These issues are addressed by selecting an approach that is less sensitive to constant absolute biases, and by validating trends over land against a dataset built from continuous long-term precipitation gauge records. However, the conclusions remain conditional on possible, but undetected by our analysis, temporal biases in ERA5 that affect the ranking of heavy precipitation events.
We select a local-percentile-based method to define 'heavy' precipitation frequency and to account for changes in all regions. Gauge-based studies of heavy precipitation often adopt a fixed threshold (e.g. Goswami et al 2006, Ma et al 2015), such as intensities >50 mm d−1. This is appropriate for climatologically homogeneous regions but when averaged over large areas, only changes in regions that experience such intense precipitation would contribute to the derived statistics. While rare events over dry regions are less intense than those in deep convective regions, local systems (e.g. ecological, social or economic) are most likely adapted to those drier conditions and might be sensitive to increased frequency of rare events. Our metric captures such changes, and also mitigates any time-constant inter-product biases in precipitation rates. For example, if one product consistently retrieves X % more precipitation than another, they will both count the same events as heavy precipitation when using their own thresholds.
We report maps of the interdecadal changes, along with annual time series for the globe, land and ocean, plus sensitivities in terms of % change in frequency per K global-mean warming. We also inspect changes in daily and hourly extremes to determine whether the conclusions of previous studies—as cited above, are supported in reanalysis at a global scale.
2. Materials and methods
2.1. ERA5 hourly precipitation
Uncertainty sources in precipitation datasets can introduce mean-state biases, discontinuities or spurious trends. Reanalyses such as ERA5 can mitigate these uncertainties by assimilating multiple data sources and using a physics-based model to reduce the occurrence of unrealistic values. However, discontinuities in reanalyses can still occur when present in the source data or when datasets are added to or removed from the assimilation. To test for discontinuities, we compare ERA5 output against datasets from the Frequent Rainfall Observations on GridS (FROGS) database (Roca et al 2019). Because we use our methodology for this comparison, ERA5 and the statistical methods are introduced before describing the FROGS products (section 2.3) and the validation results (section 4.1).
ERA5 features improvements over the prior ERA-Interim, such as an updated model and data assimilation system, higher spatial and temporal resolutions (31 km horizontally, 137 vertical levels and hourly output), and more assimilated observations including ground-based radar precipitation retrievals since 2009 (Hersbach et al 2020). Among reanalyses it showed the smallest discrepancy relative to ground-based observations of daily US precipitation (Beck et al 2019). Nevertheless, simulation of convective precipitation is particularly challenging and has large uncertainties. ERA5 assimilates observations that constrain properties like large scale moisture convergence, and we argue that this likely reduces uncertainty in calculated heavy precipitation frequency relative to intensity. Provided that heavy event frequency is defined with reference to ranking within the reanalysis, any consistent biases in precipitation intensity will not change the ranking and so frequency calculations will be less sensitive to these errors. Additionally, our metric was designed to be more robust to errors in absolute precipitation amount than the widely used frequency metric Rxmm (i.e. number of heavy precipitation days that exceeded e.g. 20 mm d−1)—section 2.2.
ERA5 hourly precipitation output was downloaded for 1979–2018 from the Copernicus Climate Change Service (https://cds.climate.copernicus.eu/). ERA5 will be extended over 1950–1978 but this was not available at processing time. Daily accumulation is from time steps 1–00 UTC, i.e. 00 UTC corresponds to accumulation between 23 and 24 UTC, thus the daily precipitation of 1 January 1980 is the accumulation of the timesteps 1–23 UTC of the 1 January and 00 UTC timestep of 2 January.
2.2. Calculation of frequency changes
2.2.1. Calculation of baseline precipitation thresholds
Precipitation intensities generally follow a Gamma distribution (Martinez-Villalobos and Neelin 2019), and a common characterization involves evaluating the Gamma distribution parameters (Semenov and Bengtsson 2002). Changes in extremes can be estimated by assessing how these distribution parameters change with time (Groisman et al 1999), but small errors in derived parameters can result in large errors in the estimated frequency at the high tail of the distribution (Zhang et al 2005). By adopting a percentile-based index we avoid distributional assumptions and provide a more intuitive estimate.
We derive heavy precipitation event frequency relative to a percentile-based index defined at each grid cell during a reference period, including both wet and dry timesteps to avoid known biases (Schär et al 2016). We refer to these in terms of event frequency, e.g. 3.6525 events per year is the intensity exceeded once per 100 days on average, and is equal to the annual 99th percentile for daily data or approximately the 99.96th percentile for hourly data. This is equivalent to a 'top X event' metric used in a recent study of extremes with gauge data (Guerreiro et al 2018), but here expressed in natural time units. An alternative view is that it is the change in frequency of events that exceed the commonly used Rxday or Rxhour calculated from a baseline period (Zhang et al 2011).
For every grid cell, we take all hours or days during our baseline period 1979–1988, then select the 10–200 highest precipitation amounts as local thresholds associated with each respective event rarity. That is, the tenth highest ranked event in the baseline decade defines our 1 event per year threshold.
Note that while we associate our rankings to percentiles, different empirical percentile definitions may affect results. For example, Python's numpy.percentile and MATLAB's prctile default functions are biased relative to the empirical percentiles derived from order statistics (see section S1 (available online at stacks.iop.org/ERL/16/074035/mmedia)). The widely used Climate Data Operators (CDO) toolbox timeselpctl default method is also strongly biased at extremely high percentiles of precipitation distributions. This is because, to reduce memory requirements, the data are converted into a histogram of 101 uniform width bins. More accurate calculations require user modification of this default.
2.2.2. Calculation of annual frequency time series from precipitation thresholds
For every year from 1989 to 2018, and for every grid cell, the number of timesteps whose precipitation exceed the locally derived threshold are summed, generating maps of hour or day counts. We require precipitation > threshold because for some grid cells and frequency occurrences, the threshold intensity is zero—this is common over the Sahara where it precipitates fewer than 10 d yr−1, and if we required precipitation ⩾ threshold, then all timesteps at these locations would be counted since their accumulation ⩾ 0 mm d−1. The subsequent count maps are area-weighted to generate global, and ocean and land mean frequency time series using the ERA5 land-sea mask.
Due to the unknown bias in derived frequencies between the baseline and out-of-baseline periods (figure S1 and Zhang et al 2005), any percentage change outside the baseline period must be calculated relative to an out-of-baseline reference. Therefore, we converted area-mean frequency series to percentage change relative to 1989. Supplementary analysis using CanESM2 climate model output (Arora et al 2011, Kirchmeier-Young et al 2017), supports this choice (see figure S1). Zhang et al (2005) suggested a bootstrapping procedure to correct the baseline frequencies and remove the discontinuity, but this would be prohibitively computationally expensive with the large ERA5 dataset and has not been demonstrated to work for our very high percentiles. Lastly, we limit ourselves to one event per year trends, but no rarer.
2.2.3. Frequency trends and sensitivities to global temperature
Analysis of the CanESM2 large ensemble suggests that historical frequency changes should be well-captured by linear trends (figure S4). Thus, we obtain frequency trends in % decade−1 relative to 1989 using the nonparametric Theil–Sen estimator with the 95% confidence interval following equation (2.6) in Sen (1968) (see table S1 for justification).
We also estimate the decade by which some extremes will double in frequency relative to 1989. For this, we calculated how many years of the derived trends would be required to produce a 100% increase, resulting in implied doubling times of 68 years (1 d yr−1) and 42 years (1 h yr−1) (section 3.3). These were rounded to the nearest year and added to 1979 to determine the first year of the decade during which event frequency would double, assuming continuation of our best estimate linear trend.
Finally, the 1989–2018 annual global, land and ocean frequency series are regressed against the annual mean global temperature anomaly from Berkeley Earth (Rohde et al 2013). Fits used optimized least squares (OLS) since tests did not reject normality. Berkeley Earth was selected due to its use of more temperature stations, spatial kriging and handling of temperature anomalies when sea ice extent changes, all of which reduce biases in recent trends relative to some other datasets (Richardson et al 2018). Results are similar when using Theil–Sen instead of OLS, and two other global temperature datasets (Cowtan and Way 2014, Lenssen et al 2019) (table S2).
2.3. Inter-product comparison
ERA5 may have discontinuities or trend biases in heavy precipitation frequency. This well-known problem is typically addressed in observational studies by using subsets of rain gauges with strict quality control and methods to account for changes in properties of the station network.
Reanalysis output is gridded, while rain gauges provide point estimates, and satellite data may have nonuniform spatiotemporal sampling. We therefore consider gridded products where developers have already attempted to account for these issues, and select daily precipitation datasets from the FROGS database on a common 1° × 1° latitude-longitude grid. The FROGS database contains several ground-based, satellite and reanalysis products of daily precipitation, all gridded to a common 1° × 1° latitude-longitude grid, and it aims to promote the usage of multiple datasets in research, and allow for easier inter-product comparisons.
Two sources provide 1979–2016 coverage: Rainfall Estimates on a Gridded Network (REGEN, Contractor et al 2020) and NOAA Climate Prediction Center (CPC, Xie et al 2007). Both are gauge-based and cover land from 60° S–90° N but only REGEN-LONG uses exclusively long-term stations with a record length ⩾40 years, which minimizes discontinuities as stations are added or removed. We therefore select REGEN-LONG as our primary target comparison. We repeat the 1979–1988 threshold and annual area-weighted annual frequency calculations for ERA5 and the FROGS products on a 1° × 1° grid with a common 60° S–90° N land mask. These results are discussed in section 4.1, which also refers to a supplementary analysis over 1998–2016 to allow consideration of more FROGS products.
3. Results
3.1. Spatial changes in frequency of heavy precipitation from 1989 to 2018
Figures 1(a) and (b) maps hourly and daily precipitation intensity with a one event per year baseline occurrence, i.e. the tenth heaviest event in 1979–1988. The hourly and daily extremes are spatially similar. Figures 1(c) and (d) show the spatial changes in frequency of the baseline one event per year from 1979–1988 to 2009–2018, while figures 1(e) and (f) only show the areas with changes that are significant at approximately 2
according to Monte Carlo confidence interval estimates (section S6). The greatest changes are over the tropical oceans, with a stronger fractional increase for the hourly data in which the event frequency more than tripled, i.e. the heaviest annual event during 1979–1988 was exceeded roughly three times per year during 2009–2018. On the other hand, a decrease is visible over the subtropical Eastern Pacific possibly related to the mean precipitation decrease owing to the Hadley cell expansion and the direct radiative response to CO2 increase (Pfahl et al
2017). Over land, increases are evident over the Amazon basin, Maritime Continent, India, Sub-Saharan Africa, Northern Europe and Eastern North America. Moreover, these increases are more pronounced for hourly precipitation, except over the Amazon basin and Southern Africa. In contrast, a frequency decrease is discernible in Western North America especially for hourly precipitation and in East China for daily precipitation.
Figure 1. (a), (b) Hourly and daily precipitation intensity thresholds defined locally as the tenth heaviest event during the baseline period 1979–1988 (BP). (c), (d) Frequency of events that exceeded the baseline thresholds (BT) displayed in (a) and (b) during 2009–2018, shown as changes (%) relative to the BP frequency. FOC denotes frequency of occurrence. (e), (f) Same as (c) and (d) only for statistically significant areas at approximately p < 0.05 according to Monte Carlo confidence interval estimates (section S6).
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Standard image High-resolution image3.2. Annual mean frequency series
Figure 2, representing annual spatially aggregated results, shows a consistent increase in the annual average frequency of one and three events per year daily and hourly precipitation relative to 1989, with larger increases over ocean than land. The most striking interannual variability is in hourly ocean events during the strong El Niño years of 1997/98 and 2015/16. Moreover, ERA5 suggests that the occurrence of heavy events is increasing faster for the hourly data. For instance, hourly and daily ocean precipitation totals associated with the heaviest three event per year in the base period were on average exceeded more than five and four times per year, respectively, during the last decade. Overall, land frequency changes are smaller, partly because of opposite local trends as illustrated in figures 1(c) and (d).
Figure 2. Annual area-weighted mean frequency of hourly and daily events that exceeded the local intensity thresholds associated with one and three events per year during 1979–1988, presented as percentage differences relative to 1989. The light and dark grey shading marks moderate and strong El Niño episodes. (a), (b) Global, (c), (d) global ocean, and (e), (f) global land.
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Standard image High-resolution image3.3. Frequency trends by event rarity and sensitivity to global-mean temperature
Theil–Sen derived frequency trends in % decade−1 for global, land and ocean surfaces are shown in figure 3 for event rarities ranging from 1 to 20 events per year (equivalent to 10–200 events per decade as shown in the x-axis). In agreement with figure 2 and prior literature (Fischer and Knutti 2016, Myhre et al 2019), the frequency changes are stronger for the most intense events. Global frequency changes for hourly events are generally higher than for daily, e.g. 1 h yr−1 events increased by 23.7 (17.7–31.1, all ranges 2σ) % decade−1, while 1 d yr−1 events increased by 14.7 (12.3–17.9) % decade−1. The global hourly and daily frequency trend disparities are driven by a larger difference over oceans, since over land the one event per year hourly trend is 9.3 (4.9–13.8) % decade−1 and daily is 7.8 (4.6–11.4) % decade−1. The land trends are overall smaller and only significant (p < 0.05) for events rarer than 15 h yr−1 and 7 d yr−1. If continued, current global trends would result in events that occurred 1 h yr−1 during 1979–1988 doubling in frequency by 2021–2030, and 1 d yr−1 events doubling by 2047–2056.
Figure 3. Theil–Sen trends (% decade−1) with 95% confidence intervals of annual mean frequency of events that exceeded the local 1979–1988 intensity thresholds from 10 to 200 events per decade. Lines show the best estimate and the shading spans the 95% confidence intervals. (a) Global, (b) global ocean, and (c) global land.
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Standard image High-resolution imageRegarding temperature sensitivity, for one event per year baseline occurrence, these trends are equivalent to 1989–2018 sensitivities of: 138 ± 36% K−1 (±2σ) and 39 ± 17% K−1 over ocean and land for the hourly data; and 78 ± 17% K−1 and 30 ± 15% K−1 for the daily data (table S2). These numbers represent changes in the frequency at the tails of the distribution, which are small in absolute size but are proportionally very large. They are not comparable to intensity changes predicted from physical constraints, such as Clausius–Clapeyron.
4. Discussion
4.1. Limitations and interpretation of heavy precipitation in reanalysis
We detected noticeable changes in the frequency of heavy precipitation reported by ERA5 at a global scale. This supports the conclusions of other studies using gauge data, but extends the results to wider spatial scales, includes the ocean and distinguishes between hourly and daily heavy precipitation.
One concern is that ERA5 outputs are on a uniform latitude–longitude grid, which yields smaller physical cell sizes away from the equator. If results are sensitive to physical grid cell size then this would introduce a latitudinally varying bias. However, our results are robust to regridding so this factor is unlikely to matter (figures S2 and S3).
The largest concerns with using reanalysis output relate to the fundamental limitations of reanalysis, including the representation of physical processes such as convection and changes in assimilated data. These are genuine issues, but alternative observation-based approaches similarly have limits. Gauge-based analyses have non-representative space-time sampling and require careful adjustments. Heavy precipitation shows weaker spatial covariance than temperature, so standard methods to adjust data such as pairwise homogenization (Williams et al 2012) are not plausible, resulting in large dataset uncertainties. Satellite-only precipitation datasets all have some combination of short data records (e.g. the active sensor on TRMM), large retrieval uncertainties (e.g. most passive sensors (Prakash et al 2016, Asong et al 2017)), calibration drift, and in the case of the instruments used in one study substantial diurnal drift in measurement time (Wentz et al 2007).
Figure 4 compares ERA5 and FROGS products 1989–2016 frequencies over land from 60° S–90° N. As discussed in section 2.3, REGEN-LONG is the dataset which most likely avoids spurious trends related to station network changes, and for 1 and 3 d yr−1, trends are statistically indistinguishable between ERA5 and REGEN-LONG. These results give us confidence to extend the ERA5 analysis to other event rarities and from daily to hourly precipitation. Both CPC and REGEN-ALL show larger trends, with CPC's difference relative to ERA5 significant at p< 0.05, however these products are likely less reliable for long-term trends than REGEN-LONG due to larger discontinuities in their source data.
Figure 4. Annual area-weighted mean frequency of events exceeding (a) 1 d yr−1 and (b) 3 d yr−1 base period thresholds, as in figure 2, but 60° S–90° N land only. Theil–Sen trends with 95% confidence intervals are listed in the caption. REGEN-LONG has the most stable station network, making it the most appropriate comparison for long-term trends.
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During 1998–2016, comparison against more products including those using satellite data with ocean coverage is possible, albeit using a different methodology (section S7). We find no clear evidence of ERA5 discontinuities, although they appear in other products; for example, the widely used Global Precipitation Climatology Project (GPCP, Huffman et al 2001) has a discontinuity coinciding with a 2008–2009 switch in microwave instruments (figure S5). This analysis is not directly comparable with our main results due to differences in period and baseline methodology, but there is large inter-product spread. Excluding GPCP over ocean, the inter-product difference in trends relative to ERA5 is as extreme as ±2.5% yr−1 (figure S6), however, we anticipate that the largest outliers are due to individual dataset issues such as station network changes in CPC and potential satellite calibration drift or inter-mission changes in other products that lack the correction methods inherent to reanalysis. The standard deviation between ERA5 and gauge-based products tends to be of order 0.06–0.12 d yr−1 (i.e. 6%–12% of the mean) and between ERA5 and satellite-based products it approximately spans 0.1–0.2 d yr−1.
Recently, Alexander et al (2020) showed that reanalyses and satellite products have a substantially larger spread than gauge-based products for the frequency metric R20mm (ERA5 was not included in their analysis.) Yet, figures 4 and S5 show an overall smaller inter-product spread supporting the argument that our metric by design is more robust than Rxmm, likely resulting in more reliable frequency change estimates, and that the product performance is metric-dependent.
4.2. Historical and future changes in heavy precipitation frequency
Our reported increases in daily events over Eastern North America, and North and Central Europe are in agreement with previous studies (Fischer and Knutti 2016, Martinez‐Villalobos and Neelin 2018, Myhre et al 2019, Papalexiou and Montanari 2019), yet ERA5 suggests an even greater increase for hourly events, as in the daily and sub-daily analysis of Yu et al (2016) over Eastern North America.
At one event per year there are particularly large increases over both land and ocean convective regions (figure 1). Our analysis cannot distinguish between forced and unforced patterns, but modern approaches could allow an attempted detection and attribution of anthropogenic contributions (e.g. Fischer and Knutti 2015, Kirchmeier-Young and Zhang 2020). However, given the characteristic multidecadal timescales of some internal variability such as the Pacific Decadal Oscillation, which are known to affect spatial patterns of precipitation (e.g. DeFlorio et al 2013), a large contribution from internal variability seems likely at regional scales over 30 years. For example, recent spatial temperature patterns have been demonstrated to drive changes in cloudiness and Earth's global-mean energy budget (Zhou et al 2016). The ocean series show particularly large frequency increases of heavy precipitation during El Niño years, indicating the existence of such a 'pattern effect' in global-ocean heavy precipitation frequency.
5. Conclusions
The new ERA5 is the current state-of-the-art reanalysis and adds new, spatially complete information on hourly and daily heavy precipitation. According to ERA5, in a global average sense, during 1989–2018, hourly events that occurred once per year in ERA5 in 1979–1988 increased in frequency by 71 (53–93, 2σ range) %, while the one day per year extreme event frequency increased by 44 (37–54) %. Moreover, the mean frequency increases are three-times greater for hourly precipitation over land compared with ocean, and two-times greater for daily precipitation.
Although frequency changes are highly spatially heterogenous, our robust metrics capture changes in the frequency of locally heavy precipitation and show larger trends for hourly rather than daily data, and for increasingly rare events. This could mean that changes in even more extreme events, for which our statistics are not yet reliable, may be larger than those reported here.
Acknowledgments
Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. We acknowledge the support of the NASA MAP Program, the Department of Energy (DE-SC0019242) and the National Science Foundation (AGS 1916619). MR was supported by the CloudSat project 80NM0018F0631. PM was supported by the Portuguese Foundation for Science and Technology (FCT) project UIDB/50019/2020—Instituto Dom Luiz. We thank Gunnar Myhre for explaining technical issues related to his work.
Data availability statement
The ERA5 reanalysis dataset that support the findings of this study are publicly available online at the Copernicus Climate Change Service Climate Date Store in https://cds.climate.copernicus.eu/.
The Berkeley Earth temperature dataset is available in http://berkeleyearth.org/data-new/. The CanESM2 piControl simulation is available in the Earth System Grid Federation node at the Lawrence Livermore National Laboratory website: https://esgf-node.llnl.gov/projects/esgf-llnl/.
The CanESM2 large ensemble data from Environment and Climate Change Canada is available in https://open.canada.ca/data/en/dataset/aa7b6823-fd1e-49ff-a6fb-68076a4a477c.
Conflict of interest
The authors declare no conflict of interest.