Latitudinal heterogeneity and hotspots of uncertainty in projected extreme precipitation

Projected precipitation from climate models is used in a wide range of fields for climate change impact assessment. However, the spatial pattern of uncertainty across latitudes and the global uncertainty hotspots are not well understood despite their importance for regional adaptation planning. In this study, we describe uncertainties in projected extreme precipitation changes per K global warming across latitudes, and decompose the overall uncertainty into climate model and internal variability uncertainties. We then identify global uncertainty hotspots and discuss the broader implications. Our results show that both uncertainty sources are highly heterogeneous across latitudes, while climate model uncertainty exceeds internal variability uncertainty for all seasons and precipitation intensities. The largest difference between model and internal variability uncertainties is found in tropical regions where model uncertainty is thrice as large as internal variability uncertainty in June–July–August season and twice as large as that in the other seasons. Tropical and subtropical regions are identified as the global uncertainty hotspots, with the Sahara desert and the southern part of the Middle East being the local hotspots. The large uncertainty in the tropics and subtropics is primarily due to the convective nature of rainstorms which cannot be adequately represented by coarse-scale climate models, and also to sparse observation networks based on which climate models can be tuned and improved. The results highlight areas where future model development and improvement efforts should focus to reduce the overall uncertainties in projected precipitation extremes.


Introduction
The recent IPCC special report on global warming of 1.5°C states that anthropogenic global warming reached approximately 1°C in 2017 compared to preindustrial levels, which in turn, led to an increase in the intensity and frequency of extreme precipitation events at global scale (IPCC 2018). Intensified precipitation events have amplified the risk of flooding and landslide activity at regional scale (Pachauri et al 2014, Gariano and Guzzetti 2016, Blöschl et al 2017. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Collins et al 2011), carbon cycle processes (Friedlingstein et al 2006, Booth et al 2012 and gravity-wave drag and its susceptible interplay with large-scale dynamics (Shepherd 2014). The uncertainty is further expanded by natural variability (Lee et al 2006) and unknown possible future trajectories of socioeconomic changes such as population change, land use/land cover evolution, technology and economic development and energy usage (Nakicenovic et al 2000).
Knowledge on uncertainty/trustworthiness of climate projections is essential for detection and attribution studies and strategic approaches for future planning in the face of climate change by taking appropriate adaptation and mitigation measures (Deser et al 2012, Hosseinzadehtalaei et al 2018. However, to render simple, user-friendly information for policymakers and stakeholders, climate change uncertainties are often suppressed by combining climate change results from different members of a multi-model ensemble into a single projection (e.g. mean scenario) (Tabari and Willems 2018a). The uncertainty analyses are also often biased, for instance, by disregarding different sample sizes of uncertainty sources leading to an underestimation of uncertainties for the sources with smaller sample sizes (Hosseinzadehtalaei et al 2017).
A key interpretation of studies on climate change impact on extreme precipitation suggests a spatial heterogeneity (variations in the direction and magnitude over space; Kaufmann et al 2017) in the future projections (O'Gorman 2012, Chen et al 2014, Fischer and Knutti 2015. The spatial heterogeneity stems from different climate change impacts on microand macro-scale atmospheric processes controlling extreme precipitation formation in different regions. Nonetheless, the spatial pattern of total and fractional uncertainties introduced by different components has been poorly explored. In particular, it would be useful to understand whether uncertainties spatially behave in a similar fashion as extreme precipitation changes or another distinct spatial pattern is detectable, how sensitive is the spatial variation to precipitation intensities and what is the seasonal dependence of uncertainties. We endeavor to bridge this crucial knowledge gap by spatially analyzing the associated uncertainties of changes in extreme precipitation of different severities per K global warming in different seasons to identify hotspots of uncertainties where further improvement of climate modeling is required for narrowing the uncertainties through resolving different responses of climate models to forcings. The information on the geographical distribution of uncertainties in extreme precipitation changes is also of great importance for regional adaptation planning (Hawkins and Sutton 2009, 2011).

Materials and methods
Climate model simulations We use daily precipitation simulations from 25 Coupled Model Intercomparison Project Phase 5 (CMIP5) GCMs (ACCESS1-0, ACCESS1-3, CanESM2,  CMCC-CESM, CMCC-CM, CMCC-CMS, CNRM-CM5, CSIRO-Mk3-6-0, GFDL-CM3, GFDL-ESM2G,  GFDL-ESM2M, HadGEM2-AO, HadGEM2-CC, Had-GEM2-ES, inmcm4, IPSL-CM5A-LR, IPSL-CM5A-MR, IPSL-CM5B-LR, MIROC5, MIROC-ESM,  MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, MRI-CGCM3, NorESM1-M) from 1971 to 2000 for the historical period and from 2071 to 2100 for the future period under RCP8.5 scenario. Precipitation flux obtained from the CMIP5 GCMs in kg/m 2 /s is converted to daily precipitation totals in mm/day for further analyses. Monthly temperature data from the same GCMs are also used to estimate global warming. We consider the first initial condition run (r1) of each GCM, giving an equal weight to each model. In addition, 10 available runs of the CSIRO-Mk3.6.0 GCM and 5 runs of the CanESM2 GCM are used to quantify internal variability uncertainty. As these runs are initialized from starting conditions taken from different states of the pre-industrial control run, the difference between them is an indicator of precipitation variability only due to internal variability.
Climate change signals for extreme precipitation Global climate change impact analysis is performed for extreme precipitation events with different severities. Although climate model results are more consistent for less extreme events compared to more extreme ones, more extreme events are more pertinent for flood studies. We analyze the daily extreme precipitation with return periods of 2, 5 and 15 years (T year return period means expected occurrence frequency of once every T years on average). The return period for an empirical distribution is defined as the ratio of the length of the study period to the rank of precipitation values (with rank 1 corresponding to the largest value). The climate change signals are calculated as the ratio of daily extreme precipitation of a given return period for the future time period (2071-2100) under the business-as-usual scenario RCP8.5 to daily extreme precipitation of the same return period for the historical period . The extreme precipitation changes are computed as a function of global warming. To this end, global warming is estimated for each of the 25 considered GCMs as the changes in the 30 year global average annual temperature between the periods 1971-2000 and 2071-2100 under RCP8.5 scenario. Afterwards, the extreme precipitation change in individual model grid cells is divided by the warming rate of the respective model to calculate the change per K warming. In order to compare the extreme precipitation changes between different seasons, precipitation extremes are calculated separately for December-January-February (DJF), March-April-May (MAM), June-July-August (JJA) and September-October-November (SON). The significance of the signals is assessed using the signal-to-noise (S2N) ratio, which is calculated by dividing the multi-model median of extreme precipitation changes by the standard deviation of the changes across the 10-member ensemble of the CSIRO-Mk3.6.0 GCM. A signal is significant when S2N is larger than the critical Z value for the 10% level (1.645) from the standard normal distribution table.
To calculate multi-model median of the extreme precipitation changes (also for uncertainty analysis) different spatial resolutions of the CMIP5 GCMs are regridded to a common rectangular grid using the bilinear interpolation method. The common grid size is selected in this study as the average of the spatial resolutions of all the 25 GCMs, which is about 2°×2°. Our preliminary analyses show that the regridding results are not sensitive to the choice of the interpolation method and of the common grid size.

Uncertainty analysis of extreme precipitation projections
For the uncertainty analysis, the ensemble of the CMIP5 GCMs consists of 25 GCMs and 10 initial conditions of the CSIRO-Mk3.6.0 GCM respectively referring to climate model and internal variability uncertainties. Because the larger size of the GCMs can result in a larger uncertainty compared to the internal variability uncertainty component, the variance decomposition-same sample size (VD-SSS) method (Hosseinzadehtalaei et al 2017, Tabari and Willems 2018b) is used to limit the influence of a larger sample size and make a fair comparison between different uncertainty components. The VD-SSS method computes uncertainty based on the smallest sample size among the uncertainty components through a repetitive random sampling process. In the framework of the sampling-theory based bootstrapping procedure, the smallest sample size is randomly chosen from the full population of the components with larger sample sizes (here, GCMs). In our case, ten is the smallest sample size among the uncertainty }as the original dataset where N is equal to 25 for the CMIP5 GCMs. After taking the median across different initial conditions, we resample the data to obtain a bootstrap resample with the sample N* (in our case, For the uncertainty component with the smallest sample size (here, initial conditions), the conventional variance decomposition (VD) method (without any sampling) is applied. To validate the internal variability uncertainty computed by the CSIRO-Mk3.6.0 GCM, the internal variability uncertainty is also quantified using 5 runs of the CanESM2 GCM. In that case, VD is used for the CanESM2 model and VD-SSS for the CSIRO-Mk3.6.0 model (sampling 5 runs out of 10). Apart from the uncertainty decomposition analyses, the total uncertainty is estimated by calculating d across the projected changes per K global warming from the entire ensemble of the CMIP5 GCMs including all GCMs and GCM initial conditions. The global uncertainty hotspots are defined as the regions with the first spatial quintile of the climate model uncertainty. The model uncertainties at all pixels are pooled to create a time series and then the corresponding percentile for each pixel is calculated. The pixels in the first quintile of the climate model uncertainties are highlighted as the global uncertainty hotspots (red color in figure 6). Similarly, the local hotspots in the global uncertainty hotspots (see figure  S9 is available online at stacks.iop.org/ERL/14/ 124032/mmedia) are identified as the first spatial quintile of the climate model uncertainties in these regions.

Results and discussion
Latitudinal heterogeneity of climate change signals We calculate extreme precipitation changes per K global warming for 2, 5 and 15 year return periods. Our results show that global warming for the end of the 21st century for the 25 CMIP5 GCMs ranges from 2.9 to 5.7 K, with an ensemble median of 4.5 K. The global median of extreme precipitation increase per K global warming is between 4% and 5%, being largest in DJF and smallest in JJA for all return periods (figure 1). Similarly, Donat et al (2016) found a 5% increase in annual-maximum daily precipitation (Rx1day) per K global warming. The larger the return period, the larger is the change per K warming: from 4.15-4.32% K −1 for a 2 year return period to 4.79-5.03% K −1 for a 15 year return period (figure 1).
The spatial distribution and latitudinal pattern of 5 year extreme precipitation changes per K global warming in different seasons are shown in figure 2. We find a clear increasing signal in extreme precipitation throughout the world except at low latitudes between 10 and 30°(in the Northern Hemisphere for DJF and MAM and in the Southern Hemisphere for JJA and SON). With the exception of these regions, the extreme precipitation changes in the Northern and Southern Hemispheres are more or less symmetrical, with a slightly larger change in the Northern Hemisphere (figures 2(a), (c), (e), (g)). The spatial variation of extreme precipitation changes can be explained by spatially-varying dynamic effects (changes in regional large-scale atmospheric circulations), as thermodynamic mechanisms alone would lead to a spatially homogeneous extreme precipitation increase with warming (Pfahl et al 2017). Along latitudes, the extreme precipitation increase for all seasons is particularly pronounced in polar latitudes (>66.5°in both hemispheres) (figure 2), with a median increase of 8-9% K −1 in all seasons and return periods (figures 2 and S1 is available online at stacks.iop.org/ERL/14/ 124032/mmedia). The changes in polar regions are significant and S2N ratios go up to 4 for DJF 2 year extreme precipitation (figure S2). A larger extreme precipitation change per K global warming at high latitudes is attributed to a larger warming rate and an intensified local surface evaporation resulting from sea-ice retreat (Bintanja and Selten 2014).
Extreme precipitation also increases in extratropical regions (latitudes between 35°and 66.5°in both hemispheres) in all seasons and for all return periods, but at a lower rate of 4-5% K −1 compared to polar regions (figures 2 and S1). In contrast to extratropical and polar regions, seasonally-varying changes are found in tropical (latitudes between 23.5°N and 23.5°S) and subtropical (latitudes between 23.5°and 35°in both hemispheres) regions where the changes in DJF and MAM are opposite to the ones in JJA and SON (figures 2 and S1). In the Northern Hemisphere, tropical and subtropical JJA and SON extreme precipitation are expected to increase, while a decreasing signal is projected for DJF and MAM except for a 15 year return period. An opposite pattern, but without the 15 year return period exception is seen in tropical and subtropical regions in the Southern Hemisphere. However, the turning point in the tropics (i.e. equator) has always an increasing signal of 5% K −1 , independent of seasons and return periods (figure S1).
While in the mid-to-high latitudes extreme precipitation changes are mainly controlled by thermodynamics, in the tropics and subtropics the dynamic contribution strongly modifies the extreme precipitation amplification and even reverses the signal regionally by offsetting the thermodynamic wetting tendency The dynamical contribution in these regions can be partly explained by a poleward circulation shift (Pfahl et al 2017). As precipitation intensity increases, the decreasing signals in the tropics get smaller or are even converted to increasing signals (figure S1) due to a decreased fractional dynamic effect for more extreme precipitation (Norris et al 2019).
The extreme precipitation changes are compared between the ensemble median of the 10 CSIRO-Mk3.6.0 GCM runs, which is used to quantify internal uncertainty, and the ensemble median of the CMIP5 GCMs (excluding the CSIRO-Mk3.6.0 GCM). The results show that the latitudinal pattern and magnitude of extreme precipitation changes in the CSIRO-Mk3.6.0 GCM are consistent with the other CMIP5 models, with smaller JJA extreme precipitation changes in the tropics and larger MAM changes in the polar region in the Southern Hemisphere by the CSIRO-Mk3.6.0 GCM ( figure S3).

Latitudinal heterogeneity of uncertainties
Once the climate change signals are derived, the associated uncertainties are assessed. The latitudinal profile of total uncertainty in extreme precipitation changes per K global warming exhibits maxima in tropical and subtropical regions ( figure 3). The results also show that the more intense the precipitation, the larger is the uncertainty. A larger uncertainty in more extreme event (15 year return period) changes compared with less extreme events (2 and 5 year return periods) is evident for all seasons and across latitudes. This is a result of either a high spatial heterogeneity in the physical processes controlling local extreme precipitation events or a strong internal variability (Fischer et al 2014, Sillmann et al 2017). The stronger internal variability for more extreme precipitation is confirmed from our results of VD analysis.
The total uncertainty in extreme precipitation changes per K global warming is decomposed into climate model uncertainty and internal variability uncertainty (hereafter as model and internal uncertainty, respectively). The results of the VD-SSS for the global scale show that for all seasons and precipitation intensities, model uncertainty (i.e. structural differences among models) dominates the total uncertainty with 56%-62% (figure 4). Although seasonality does not much matter for the fractional model uncertainty, the absolute model uncertainty differs across seasons especially for the tropical and subtropical regions ( figure S4). The fractional model uncertainty lessens as precipitation becomes more intense. Note that although independent uncertainty magnitudes for both model and internal uncertainties increase with precipitation intensities, a lower increasing rate for model uncertainty compared to internal uncertainty leads to a decrease in its relative uncertainty. The internal uncertainty increase with precipitation intensity is consistent with recent studies underlining the role of internal variability in extreme precipitation projections at the grid point scale (Fischer and Knutti 2014, Martel et al 2018).
The latitudinal profile of the uncertainty sources in extreme precipitation projections indicates that both model and internal uncertainties are heterogeneous across latitudes (figure 5). Model uncertainty reaches its maximum in the tropics, while internal uncertainty is largest in the polar region in the Southern Hemisphere in all seasons except DJF when it is largest in the tropics. Model uncertainty exceeds internal uncertainty across all latitudes for different precipitation intensities and seasons except in the polar region in the Southern Hemisphere for MAM, JJA and SON, with the largest difference in tropical latitudes. The difference between model and internal uncertainties peaks in JJA in tropical region. The median model uncertainty over the tropics is thrice as large as internal uncertainty in JJA and twice as large as that in the other seasons. When comparing the latitudinal uncertainties among return periods, the difference decreases with return periods (figure 5). The internal uncertainty may be larger for shorter time horizons of a few decades considering the decaying contribution of internal variability with lead time (Hawkins andSutton 2009, 2011).
The geographical heterogeneity of the fractional uncertainties and particularly model uncertainty can also be seen in spatial maps (figure S5). The model uncertainty explains more than 70% of the total uncertainty in extreme precipitation changes per K warming in the tropics. Climate model results are generally less consistent for decreasing signals of extreme precipitation compared with increasing signals, having the smallest uncertainty for the increasing signals ranging between 4 and 6% K −1 (figure S6). Though following a similar pattern, the largest model uncertainty over the tropical low latitudes is more obvious for changes in JJA, whereas the spatial contrast is less marked in DJF ( figure S5).
To check the validity of the internal uncertainty derived from the CSIRO-Mk3.6.0 GCM ensemble, it is also quantified using the CanESM2 GCM ensemble. A comparison between the latitudinal distribution of the internal uncertainties derived from the CSIRO-Mk3.6.0 and CanESM2 ensembles indicates that they have a similar spatial representation of internal uncertainty (figure S7). Fischer et al (2013) also found that the internal variability uncertainty for precipitation extremes derived from the 21-member ensemble of the CESM-IC model is consistent with that from the 10-member ensemble of the CSIRO-Mk3-6-0 model. In terms of magnitude, our results show that the internal uncertainty derived from the CSIRO-Mk3.6.0 ensemble is mostly larger than that from the CanESM2 ensemble, with the largest difference in DJF extreme precipitation at 10 to 15°N latitudes.

Uncertainty hotspots
Narrowing the total uncertainty in climate change projections can primarily be achieved by reducing model uncertainty as it is the dominating component of the overall uncertainty (Smith et al 2007, Hawkins and Sutton 2009, 2011. We therefore define  A seasonal dependence analysis shows that the hotspots in tropical regions are slightly more critical in JJA, while in polar regions in the Southern Hemisphere, the uncertainty is clearly more critical in DJF (figures 6(e), (f)). This seasonal pattern is consistent with the seasonal variation of GCM bias for precipitation simulations over the 70°-90°N domain (Walsh et al 2008). Indeed, a larger bias and possibly a larger uncertainty of climate models in DJF can be due to the oversmoothing of the topography by the models to represent the orographic DJF precipitation in polar regions (Walsh et al 2008). The temperate region in the Northern Hemisphere (latitudes between 35 and 66.5) has the largest uncertainty in JJA when mesoscale convective systems are dominant.
After identifying tropical and subtropical regions as the global uncertainty hotspots, the uncertainty in the regions is further examined to detect local hotspots to which special attention must be paid by climate modeling centers. With a focus over land, the Sahara desert is in the frontline, where the uncertainty is largest in all seasons (figure S9). All-season hotspots also appear in the southern part of the Middle East (i.e. Yemen, Oman, southern Saudi Arabia and southern Pakistan). The uncertainty hotspots identified here are consistent with the results of a recent study by Donat et al (2019). They analyzed changes in precipitation totals and extremes over the world's climatic regions and highlighted that model uncertainty is largest in arid regions including the Middle East and North Africa.

Conclusions
This study detected a spatial pattern in the total and fractional uncertainties in extreme precipitation changes and identified uncertainty hotspots. Our results suggested that the total and fractional uncertainties substantially vary across latitudes. Tropical and subtropical regions were identified as the global uncertainty hotspots where future research should be focused to reduce the uncertainties. Local uncertainty hotspots in the tropics and subtropics were found in the Sahara desert and the southern part of the Middle East. The large discrepancy across models at the uncertainty hotspots needs further attention from climate modeling centers. Improvements in climate models to better represent unresolved and poorly understood processes relevant for extreme precipitation such as moist convection (O'Gorman and Schneider 2009) are necessary to reduce climate model uncertainty. Apart from a better understanding of climate systems and a more trustworthy representation of micro-scale features responsible for extreme precipitation by climate models at these hotspots, precipitation observation networks in these regions need to be updated in the future next to preserving the current network. Observations are indispensable to evaluate climate models and to improve the representation of the geophysical processes relevant for the precipitation formation in these regions (Roberts et al 2018). A sparse observational network or lack of observations hampers model tuning (calibration) during the development stage of climate models to evaluate the representation of different processes and detect shortcomings in models (Eyring et al 2019), leading to bias and possibly expanding the intermodel spread.
The larger the climate change uncertainty is the more expensive the adaptation planning will be to ensure tolerance to more extreme events. Yet, the large uncertainties at the hotspots should not hinder climate change mitigation and adaptation actions. Rather, a flexible adaptation strategy that is constantly updated with new information on future climate changes is required (Fletcher et al 2019). It enables us to reassess the decisions and planning for climate change adaptation by learning more over time. Considering the current discord among policy makers/ risk managers and climate scientists in dealing with climate change uncertainty, it is essential to reach a unified perspective on this issue for a more effective adaptation planning. The future planning in the African tropical and subtropical countries despite being uncertainty hotspots is especially important as they are poor, vulnerable countries with the least contribution to climate change, but most severe impacts (climate inequity; Green 2016, Bathiany et al 2018). It calls for financial and technological supports from richer countries, responsible for the vast bulk of current warming (Althor et al 2016), to facilitate the adaptation of the vulnerable countries to knock-on cultural, socioeconomic and environmental effects of climate change felt disproportionately.

Acknowledgments
The first author has received funding from the Flemish regional government through a contract as a FWO (Research Foundation-Flanders) post-doctoral researcher. The work has also been partially funded by the European Union's Horizon 2020 research and innovation programmes under grant agreement No 700699, project BRIGAID (BRIdges the GAp for Innovations in Disaster resilience). The first author thanks Allianz for the financial support provided through the 2018 Allianz Climate Risk Research Award.

Data availability
The CMIP5 GCM data used in this study are freely available at the website of the Earth System Grid Federation (https://esgf-index1.ceda.ac.uk).