Browsing by Author "Frieler, K."
Now showing 1 - 15 of 15
Results Per Page
Sort Options
- ItemAdaptation required to preserve future high-end river flood risk at present levels(Washington : American Association for the Advancement of Science (A A A S), 2018) Willner, S.N.; Levermann, A.; Zhao, F.; Frieler, K.Earth’s surface temperature will continue to rise for another 20 to 30 years even with the strongest carbon emission reduction currently considered. The associated changes in rainfall patterns can result in an increased flood risk worldwide. We compute the required increase in flood protection to keep high-end fluvial flood risk at present levels. The analysis is carried out worldwide for subnational administrative units. Most of the United States, Central Europe, and Northeast and West Africa, as well as large parts of India and Indonesia, require the strongest adaptation effort. More than half of the United States needs to at least double their protection within the next two decades. Thus, the need for adaptation to increased river flood is a global problem affecting industrialized regions as much as developing countries.
- ItemClimate impact research: Beyond patchwork(München : European Geopyhsical Union, 2014) Huber, V.; Schellnhuber, H.J.; Arnell, N.W.; Frieler, K.; Gerten, D.; Haddeland, I.; Kabat, P.; Lotze-Campen, H.; Lucht, W.; Parry, M.; Piontek, F.; Rosenzweig, C.; Schewe, J.; Warszawski, L.Despite significant progress in climate impact research, the narratives that science can presently piece together of a 2, 3, 4, or 5 °C warmer world remain fragmentary. Here we briefly review past undertakings to characterise comprehensively and quantify climate impacts based on multi-model approaches. We then report on the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP), a community-driven effort to compare impact models across sectors and scales systematically, and to quantify the uncertainties along the chain from greenhouse gas emissions and climate input data to the modelling of climate impacts themselves. We show how ISI-MIP and similar efforts can substantially advance the science relevant to impacts, adaptation and vulnerability, and we outline the steps that need to be taken in order to make the most of the available modelling tools. We discuss pertinent limitations of these methods and how they could be tackled. We argue that it is time to consolidate the current patchwork of impact knowledge through integrated cross-sectoral assessments, and that the climate impact community is now in a favourable position to do so.
- ItemConsistent increase in Indian monsoon rainfall and its variability across CMIP-5 models(München : European Geopyhsical Union, 2013) Menon, A.; Levermann, A.; Schewe, J.; Lehmann, J.; Frieler, K.The possibility of an impact of global warming on the Indian monsoon is of critical importance for the large population of this region. Future projections within the Coupled Model Intercomparison Project Phase 3 (CMIP-3) showed a wide range of trends with varying magnitude and sign across models. Here the Indian summer monsoon rainfall is evaluated in 20 CMIP-5 models for the period 1850 to 2100. In the new generation of climate models, a consistent increase in seasonal mean rainfall during the summer monsoon periods arises. All models simulate stronger seasonal mean rainfall in the future compared to the historic period under the strongest warming scenario RCP-8.5. Increase in seasonal mean rainfall is the largest for the RCP-8.5 scenario compared to other RCPs. Most of the models show a northward shift in monsoon circulation by the end of the 21st century compared to the historic period under the RCP-8.5 scenario. The interannual variability of the Indian monsoon rainfall also shows a consistent positive trend under unabated global warming. Since both the long-term increase in monsoon rainfall as well as the increase in interannual variability in the future is robust across a wide range of models, some confidence can be attributed to these projected trends.
- ItemConsistent negative response of US crops to high temperatures in observations and crop models(London : Nature Publishing Group, 2017) Schauberger, B.; Archontoulis, S.; Arneth, A.; Balkovic, J.; Ciais, P.; Deryng, D.; Elliott, J.; Folberth, C.; Khabarov, N.; Müller, C.; Pugh, T.A.M.; Rolinski, S.; Schaphoff, S.; Schmid, E.; Wang, X.; Schlenker, W.; Frieler, K.High temperatures are detrimental to crop yields and could lead to global warming-driven reductions in agricultural productivity. To assess future threats, the majority of studies used process-based crop models, but their ability to represent effects of high temperature has been questioned. Here we show that an ensemble of nine crop models reproduces the observed average temperature responses of US maize, soybean and wheat yields. Each day >30 °C diminishes maize and soybean yields by up to 6% under rainfed conditions. Declines observed in irrigated areas, or simulated assuming full irrigation, are weak. This supports the hypothesis that water stress induced by high temperatures causes the decline. For wheat a negative response to high temperature is neither observed nor simulated under historical conditions, since critical temperatures are rarely exceeded during the growing season. In the future, yields are modelled to decline for all three crops at temperatures >30 °C. Elevated CO 2 can only weakly reduce these yield losses, in contrast to irrigation.
- ItemDelaying future sea-level rise by storing water in Antarctica(München : European Geopyhsical Union, 2016) Frieler, K.; Mengel, M.; Levermann, A.Even if greenhouse gas emissions were stopped today, sea level would continue to rise for centuries, with the long-term sea-level commitment of a 2 °C warmer world significantly exceeding 2 m. In view of the potential implications for coastal populations and ecosystems worldwide, we investigate, from an ice-dynamic perspective, the possibility of delaying sea-level rise by pumping ocean water onto the surface of the Antarctic ice sheet. We find that due to wave propagation ice is discharged much faster back into the ocean than would be expected from a pure advection with surface velocities. The delay time depends strongly on the distance from the coastline at which the additional mass is placed and less strongly on the rate of sea-level rise that is mitigated. A millennium-scale storage of at least 80 % of the additional ice requires placing it at a distance of at least 700 km from the coastline. The pumping energy required to elevate the potential energy of ocean water to mitigate the currently observed 3 mm yr−1 will exceed 7 % of the current global primary energy supply. At the same time, the approach offers a comprehensive protection for entire coastlines particularly including regions that cannot be protected by dikes.
- ItemEmulating Atlantic overturning strength for low emission scenarios: Consequences for sea-level rise along the North American east coast(München : European Geopyhsical Union, 2011) Schleussner, C.F.; Frieler, K.; Meinshausen, M.; Yin, J.; Levermann, A.In order to provide probabilistic projections of the future evolution of the Atlantic Meridional Overturning Circulation (AMOC), we calibrated a simple Stommeltype box model to emulate the output of fully coupled threedimensional atmosphere-ocean general circulation models (AOGCMs) of the Coupled Model Intercomparison Project (CMIP). Based on this calibration to idealised global warming scenarios with and without interactive atmosphere-ocean fluxes and freshwater perturbation simulations, we project the future evolution of the AMOC mean strength within the covered calibration range for the lower two Representative Concentration Pathways (RCPs) until 2100 obtained from the reduced complexity carbon cycle-climate model MAGICC 6. For RCP3-PD with a global mean temperature median below 1.0 C warming relative to the year 2000, we project an ensemble median weakening of up to 11% compared to 22% under RCP4.5 with a warming median up to 1.9 C over the 21st century. Additional Greenland meltwater of 10 and 20 cm of global sea-level rise equivalent further weakens the AMOC by about 4.5 and 10 %, respectively. By combining our outcome with a multi-model sea-level rise study we project a dynamic sea-level rise along the New York City coastline of 4 cm for the RCP3-PD and of 8 cm for the RCP4.5 scenario over the 21st century. We estimate the total steric and dynamic sea-level rise for New York City to be about 24 cm until 2100 for the RCP3-PD scenario, which can hold as a lower bound for sea-level rise projections in this region, as it does not include ice sheet and mountain glacier contributions.
- ItemEstimating the near-surface permafrost-carbon feedback on global warming(München : European Geopyhsical Union, 2012) Schneider von Deimling, T.; Meinshausen, M.; Levermann, A.; Huber, V.; Frieler, K.; Lawrence, D.M.; Brovkin, V.Thawing of permafrost and the associated release of carbon constitutes a positive feedback in the climate system, elevating the effect of anthropogenic GHG emissions on global-mean temperatures. Multiple factors have hindered the quantification of this feedback, which was not included in climate carbon-cycle models which participated in recent model intercomparisons (such as the Coupled Carbon Cycle Climate Model Intercomparison Project – C4MIP) . There are considerable uncertainties in the rate and extent of permafrost thaw, the hydrological and vegetation response to permafrost thaw, the decomposition timescales of freshly thawed organic material, the proportion of soil carbon that might be emitted as carbon dioxide via aerobic decomposition or as methane via anaerobic decomposition, and in the magnitude of the high latitude amplification of global warming that will drive permafrost degradation. Additionally, there are extensive and poorly characterized regional heterogeneities in soil properties, carbon content, and hydrology. Here, we couple a new permafrost module to a reduced complexity carbon-cycle climate model, which allows us to perform a large ensemble of simulations. The ensemble is designed to span the uncertainties listed above and thereby the results provide an estimate of the potential strength of the feedback from newly thawed permafrost carbon. For the high CO2 concentration scenario (RCP8.5), 33–114 GtC (giga tons of Carbon) are released by 2100 (68 % uncertainty range). This leads to an additional warming of 0.04–0.23 °C. Though projected 21st century permafrost carbon emissions are relatively modest, ongoing permafrost thaw and slow but steady soil carbon decomposition means that, by 2300, about half of the potentially vulnerable permafrost carbon stock in the upper 3 m of soil layer (600–1000 GtC) could be released as CO2, with an extra 1–4 % being released as methane. Our results also suggest that mitigation action in line with the lower scenario RCP3-PD could contain Arctic temperature increase sufficiently that thawing of the permafrost area is limited to 9–23 % and the permafrost-carbon induced temperature increase does not exceed 0.04–0.16 °C by 2300.
- ItemA framework for the cross-sectoral integration of multi-model impact projections: Land use decisions under climate impacts uncertainties(München : European Geopyhsical Union, 2015) Frieler, K.; Levermann, A.; Elliott, J.; Heinke, J.; Arneth, A.; Bierkens, M.F.P.; Ciais, P.; Clark, D.B.; Deryng, D.; Döll, P.; Falloon, P.; Fekete, B.; Folberth, C.; Friend, A.D.; Gellhorn, C.; Gosling, S.N.; Haddeland, I.; Khabarov, N.; Lomas, M.; Masaki, Y.; Nishina, K.; Neumann, K.; Oki, T.; Pavlick, R.; Ruane, A.C.; Schmid, E.; Schmitz, C.; Stacke, T.; Stehfest, E.; Tang, Q.; Wisser, D.; Huber, V.; Piontek, F.; Warszawski, L.; Schewe, J.; Lotze-Campen, H.; Schellnhuber, H.J.Climate change and its impacts already pose considerable challenges for societies that will further increase with global warming (IPCC, 2014a, b). Uncertainties of the climatic response to greenhouse gas emissions include the potential passing of large-scale tipping points (e.g. Lenton et al., 2008; Levermann et al., 2012; Schellnhuber, 2010) and changes in extreme meteorological events (Field et al., 2012) with complex impacts on societies (Hallegatte et al., 2013). Thus climate change mitigation is considered a necessary societal response for avoiding uncontrollable impacts (Conference of the Parties, 2010). On the other hand, large-scale climate change mitigation itself implies fundamental changes in, for example, the global energy system. The associated challenges come on top of others that derive from equally important ethical imperatives like the fulfilment of increasing food demand that may draw on the same resources. For example, ensuring food security for a growing population may require an expansion of cropland, thereby reducing natural carbon sinks or the area available for bio-energy production. So far, available studies addressing this problem have relied on individual impact models, ignoring uncertainty in crop model and biome model projections. Here, we propose a probabilistic decision framework that allows for an evaluation of agricultural management and mitigation options in a multi-impact-model setting. Based on simulations generated within the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP), we outline how cross-sectorally consistent multi-model impact simulations could be used to generate the information required for robust decision making. Using an illustrative future land use pattern, we discuss the trade-off between potential gains in crop production and associated losses in natural carbon sinks in the new multiple crop- and biome-model setting. In addition, crop and water model simulations are combined to explore irrigation increases as one possible measure of agricultural intensification that could limit the expansion of cropland required in response to climate change and growing food demand. This example shows that current impact model uncertainties pose an important challenge to long-term mitigation planning and must not be ignored in long-term strategic decision making.
- ItemFuture changes in extratropical storm tracks and baroclinicity under climate change(Bristol : IOP, 2014) Lehmann, J.; Coumou, D.; Frieler, K.; Eliseev, A.V.; Levermann, A.The weather in Eurasia, Australia, and North and South America is largely controlled by the strength and position of extratropical storm tracks. Future climate change will likely affect these storm tracks and the associated transport of energy, momentum, and water vapour. Many recent studies have analyzed how storm tracks will change under climate change, and how these changes are related to atmospheric dynamics. However, there are still discrepancies between different studies on how storm tracks will change under future climate scenarios. Here, we show that under global warming the CMIP5 ensemble of coupled climate models projects only little relative changes in vertically averaged mid-latitude mean storm track activity during the northern winter, but agree in projecting a substantial decrease during summer. Seasonal changes in the Southern Hemisphere show the opposite behaviour, with an intensification in winter and no change during summer. These distinct seasonal changes in northern summer and southern winter storm tracks lead to an amplified seasonal cycle in a future climate. Similar changes are seen in the mid-latitude mean Eady growth rate maximum, a measure that combines changes in vertical shear and static stability based on baroclinic instability theory. Regression analysis between changes in the storm tracks and changes in the maximum Eady growth rate reveal that most models agree in a positive association between the two quantities over mid-latitude regions.
- ItemA new climate dataset for systematic assessments of climate change impacts as a function of global warming(München : European Geopyhsical Union, 2012) Heinke, J.; Ostberg, S.; Schaphoff, S.; Frieler, K.; Müller, C.; Gerten, D.; Meinshausen, M.; Lucht, W.Interactions between food demand, biomass energy and forest preservation are driving both food prices and land-use changes, regionally and globally. This study presents a new model called Nexus Land-Use version 1.0 which describes these interactions through a generic representation of agricultural intensification mechanisms within agricultural lands. The Nexus Land-Use model equations combine biophysics and economics into a single coherent framework to calculate crop yields, food prices, and resulting pasture and cropland areas within 12 regions inter-connected with each other by international trade. The representation of cropland and livestock production systems in each region relies on three components: (i) a biomass production function derived from the crop yield response function to inputs such as industrial fertilisers; (ii) a detailed representation of the livestock production system subdivided into an intensive and an extensive component, and (iii) a spatially explicit distribution of potential (maximal) crop yields prescribed from the Lund-Postdam-Jena global vegetation model for managed Land (LPJmL). The economic principles governing decisions about land-use and intensification are adapted from the Ricardian rent theory, assuming cost minimisation for farmers. In contrast to the other land-use models linking economy and biophysics, crops are aggregated as a representative product in calories and intensification for the representative crop is a non-linear function of chemical inputs. The model equations and parameter values are first described in details. Then, idealised scenarios exploring the impact of forest preservation policies or rising energy price on agricultural intensification are described, and their impacts on pasture and cropland areas are investigated.
- ItemProjecting Antarctic ice discharge using response functions from SeaRISE ice-sheet models(München : European Geopyhsical Union, 2014) Levermann, A.; Winkelmann, R.; Nowicki, S.; Fastook, J.L.; Frieler, K.; Greve, R.; Hellmer, H.H.; Martin, M.A.; Meinshausen, M.; Mengel, M.; Payne, A.J.; Pollard, D.; Sato, T.; Timmermann, R.; Wang, W.L.; Bindschadler, R.A.The largest uncertainty in projections of future sea-level change results from the potentially changing dynamical ice discharge from Antarctica. Basal ice-shelf melting induced by a warming ocean has been identified as a major cause for additional ice flow across the grounding line. Here we attempt to estimate the uncertainty range of future ice discharge from Antarctica by combining uncertainty in the climatic forcing, the oceanic response and the ice-sheet model response. The uncertainty in the global mean temperature increase is obtained from historically constrained emulations with the MAGICC-6.0 (Model for the Assessment of Greenhouse gas Induced Climate Change) model. The oceanic forcing is derived from scaling of the subsurface with the atmospheric warming from 19 comprehensive climate models of the Coupled Model Intercomparison Project (CMIP-5) and two ocean models from the EU-project Ice2Sea. The dynamic ice-sheet response is derived from linear response functions for basal ice-shelf melting for four different Antarctic drainage regions using experiments from the Sea-level Response to Ice Sheet Evolution (SeaRISE) intercomparison project with five different Antarctic ice-sheet models. The resulting uncertainty range for the historic Antarctic contribution to global sea-level rise from 1992 to 2011 agrees with the observed contribution for this period if we use the three ice-sheet models with an explicit representation of ice-shelf dynamics and account for the time-delayed warming of the oceanic subsurface compared to the surface air temperature. The median of the additional ice loss for the 21st century is computed to 0.07 m (66% range: 0.02–0.14 m; 90% range: 0.0–0.23 m) of global sea-level equivalent for the low-emission RCP-2.6 (Representative Concentration Pathway) scenario and 0.09 m (66% range: 0.04–0.21 m; 90% range: 0.01–0.37 m) for the strongest RCP-8.5. Assuming no time delay between the atmospheric warming and the oceanic subsurface, these values increase to 0.09 m (66% range: 0.04–0.17 m; 90% range: 0.02–0.25 m) for RCP-2.6 and 0.15 m (66% range: 0.07–0.28 m; 90% range: 0.04–0.43 m) for RCP-8.5. All probability distributions are highly skewed towards high values. The applied ice-sheet models are coarse resolution with limitations in the representation of grounding-line motion. Within the constraints of the applied methods, the uncertainty induced from different ice-sheet models is smaller than that induced by the external forcing to the ice sheets.
- ItemRetrievals of chlorine chemistry kinetic parameters from Antarctic ClO microwave radiometer measurements(München : European Geopyhsical Union, 2011) Kremser, S.; Schofield, R.; Bodeker, G.E.; Connor, B.J.; Rex, M.; Barret, J.; Mooney, T.; Salawitch, R.J.; Canty, T.; Frieler, K.; Chipperfield, M.P.; Langematz, U.; Feng, W.Key kinetic parameters governing the partitioning of chlorine species in the Antarctic polar stratosphere were retrieved from 28 days of chlorine monoxide (ClO) microwave radiometer measurements made during the late winter/early spring of 2005 at Scott Base (77.85° S, 166.75° E). During day-time the loss of the ClO dimer chlorine peroxide (ClOOCl) occurs mainly by photolysis. Some time after sunrise, a photochemical equilibrium is established and the ClO/ClOOCl partitioning is determined by the ratio of the photolysis frequency, J, and the dimer formation rate, kf. The values of J and kf from laboratory studies remain uncertain to a considerable extent, and as a complement to these ongoing studies, the goal of this work is to provide a constraint on that uncertainty based on observations of ClO profiles in the Antarctic. First an optimal estimation technique was used to derive J/kf ratios for a range of Keq values. The optimal estimation forward model was a photochemical box model that takes J, kf, and Keq as inputs, together with a priori profiles of activated chlorine (ClOx = ClO+2×ClOOCl), profiles of ozone, temperature, and pressure. JPL06 kinetics are used as a priori in the optimal estimation and for all other chemistry in the forward model. Using the more recent JPL09 kinetics results in insignificant differences in the retrieved value of J/kf. A complementary approach was used to derive the optimal kinetic parameters; the full parameter space of J, kf, Keq and ClOx was sampled to find the minimum in differences between measured and modelled ClO profiles. Furthermore, values of Keq up to 2.0 times larger than recommended by JPL06 were explored to test the sensitivity of the J/kf ratio to changes in Keq. The results show that the retrieved J/kf ratios bracket the range of 1.23 to 1.97 times the J/kf value recommended by JPL06 over the range of Keq values considered. The retrieved J/kf ratios lie in the lower half of the large uncertainty range of J/kf recommended by JPL06 and towards the upper portion of the smaller uncertainty range recommended by JPL09.
- ItemA scaling approach to project regional sea level rise and its uncertainties(München : European Geopyhsical Union, 2013) Perrette, M.; Landerer, F.; Riva, R.; Frieler, K.; Meinshausen, M.Climate change causes global mean sea level to rise due to thermal expansion of seawater and loss of land ice from mountain glaciers, ice caps and ice sheets. Locally, sea level can strongly deviate from the global mean rise due to changes in wind and ocean currents. In addition, gravitational adjustments redistribute seawater away from shrinking ice masses. However, the land ice contribution to sea level rise (SLR) remains very challenging to model, and comprehensive regional sea level projections, which include appropriate gravitational adjustments, are still a nascent field (Katsman et al., 2011; Slangen et al., 2011). Here, we present an alternative approach to derive regional sea level changes for a range of emission and land ice melt scenarios, combining probabilistic forecasts of a simple climate model (MAGICC6) with the new CMIP5 general circulation models. The contribution from ice sheets varies considerably depending on the assumptions for the ice sheet projections, and thus represents sizeable uncertainties for future sea level rise. However, several consistent and robust patterns emerge from our analysis: at low latitudes, especially in the Indian Ocean and Western Pacific, sea level will likely rise more than the global mean (mostly by 10–20%). Around the northeastern Atlantic and the northeastern Pacific coasts, sea level will rise less than the global average or, in some rare cases, even fall. In the northwestern Atlantic, along the American coast, a strong dynamic sea level rise is counteracted by gravitational depression due to Greenland ice melt; whether sea level will be above- or below-average will depend on the relative contribution of these two factors. Our regional sea level projections and the diagnosed uncertainties provide an improved basis for coastal impact analysis and infrastructure planning for adaptation to climate change.
- ItemSensitivity of polar stratospheric ozone loss to uncertainties in chemical reaction kinetics(Göttingen : Copernicus GmbH, 2009) Kawa, S.R.; Stolarski, R.S.; Newman, P.A.; Douglass, A.R.; Rex, M.; Hofmann, D.J.; Santee, M.L.; Frieler, K.The impact and significance of uncertainties in model calculations of stratospheric ozone loss resulting from known uncertainty in chemical kinetics parameters is evaluated in trajectory chemistry simulations for the Antarctic and Arctic polar vortices. The uncertainty in modeled ozone loss is derived from Monte Carlo scenario simulations varying the kinetic (reaction and photolysis rate) parameters within their estimated uncertainty bounds. Simulations of a typical winter/spring Antarctic vortex scenario and Match scenarios in the Arctic produce large uncertainty in ozone loss rates and integrated seasonal loss. The simulations clearly indicate that the dominant source of model uncertainty in polar ozone loss is uncertainty in the Cl2O 2 photolysis reaction, which arises from uncertainty in laboratory-measured molecular cross sections at atmospherically important wavelengths. This estimated uncertainty in JCl 2O2 from laboratory measurements seriously hinders our ability to model polar ozone loss within useful quantitative error limits. Atmospheric observations, however, suggest that the Cl2O2 photolysis uncertainty may be less than that derived from the lab data. Comparisons to Match, South Pole ozonesonde, and Aura Microwave Limb Sounder (MLS) data all show that the nominal recommended rate simulations agree with data within uncertainties when the Cl2O2 photolysis error is reduced by a factor of two, in line with previous in situ ClOx measurements. Comparisons to simulations using recent cross sections from Pope et al. (2007) are outside the constrained error bounds in each case. Other reactions producing significant sensitivity in polar ozone loss include BrO + ClO and its branching ratios. These uncertainties challenge our confidence in modeling polar ozone depletion and projecting future changes in response to changing halogen emissions and climate. Further laboratory, theoretical, and possibly atmospheric studies are needed.
- ItemA trend-preserving bias correction – The ISI-MIP approach(München : European Geopyhsical Union, 2013) Hempel, S.; Frieler, K.; Warszawski, L.; Schewe, J.; Piontek, F.Statistical bias correction is commonly applied within climate impact modelling to correct climate model data for systematic deviations of the simulated historical data from observations. Methods are based on transfer functions generated to map the distribution of the simulated historical data to that of the observations. Those are subsequently applied to correct the future projections. Here, we present the bias correction method that was developed within ISI-MIP, the first Inter-Sectoral Impact Model Intercomparison Project. ISI-MIP is designed to synthesise impact projections in the agriculture, water, biome, health, and infrastructure sectors at different levels of global warming. Bias-corrected climate data that are used as input for the impact simulations could be only provided over land areas. To ensure consistency with the global (land + ocean) temperature information the bias correction method has to preserve the warming signal. Here we present the applied method that preserves the absolute changes in monthly temperature, and relative changes in monthly values of precipitation and the other variables needed for ISI-MIP. The proposed methodology represents a modification of the transfer function approach applied in the Water Model Intercomparison Project (Water-MIP). Correction of the monthly mean is followed by correction of the daily variability about the monthly mean. Besides the general idea and technical details of the ISI-MIP method, we show and discuss the potential and limitations of the applied bias correction. In particular, while the trend and the long-term mean are well represented, limitations with regards to the adjustment of the variability persist which may affect, e.g. small scale features or extremes.