Editing IPCC:AR6/WGI/Chapter-8 (section)

=== 8.5.3 Non-linearities Across Global Warming Levels ===

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The AR5 concluded that annual and seasonal mean precipitation changes can be estimated by linear pattern-scaling techniques ( [[#Santer--1990|Santer and Wigley, 1990]] ; [[#Arnell--2016|Arnell and Gosling, 2016]] ; [[#Greve--2018|Greve et al., 2018]] ), which represent regional changes in precipitation as a linear function of global mean temperature change. However, there are a number of caveats when pattern-scaling is applied to low-emissions scenarios or to scenarios where localized forcing (e.g., anthropogenic aerosols) are significant and vary in time ( [[#Collins--2013|Collins et al., 2013]] ). Here the focus is in on non-linear water cycle responses to increasing global warming levels, as estimated for instance from the difference between the first 2°C of global warming, and the next 2°C of warming (Figure 8.25), and their possible underlying mechanisms.

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[[File:9324edb0441675e3d1c9de729b4087f7 IPCC_AR6_WGI_Figure_8_25.png]]

'''Figure 8.25 |''' '''Effect of first versus second 2°C of global warming relative to the 1850–1900 base period on seasonal mean precipitation (mm day''' ''–1'' ''').''' CMIP6 multi-model ensemble mean December–January–February (left panels) and June–July–August (right panels) precipitation difference for '''(a, b)''' SSP5-8.5 at +2°C '''(c, d)''' SSP5-8.5 at +4°C minus SSP5-8.5 at +2°C (second 2°C warming); '''(e, f)''' second minus first 2°C fast warming (c–a and d–b). Only models reaching the +4°C warming levels in SSP5-8.5 are considered. Differences are computed based on 21-year time windows centred on the first year reaching or exceeding the selected global warming level using a 21-year running mean global surface atmospheric temperature criterion. Uncertainty is represented using the simple approach. No overlay indicates regions with high model agreement, where ≥80% of models agree on sign of change. Diagonal lines indicate regions with low model agreement, where &lt;80% of models agree on sign of change. For more information on the simple approach, please refer to the Cross-Chapter Box Atlas.1. Further details on data sources and processing are available in the chapter data table (Table 8.SM.1).

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==== 8.5.3.1 Non-linearities in Large-scale Atmospheric Circulation and Precipitation ====

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Since AR5, there is further evidence that the pattern-scaling technique has limitations ( [[#Lopez--2014|Lopez et al., 2014]] ; [[#Wartenburger--2017|Wartenburger et al., 2017]] ; [[#Tachiiri--2019|Tachiiri et al., 2019]] ), and that alternative approaches, such as multiple regressions using the land–sea warming contrast as an additional predictor, offer added value ( [[#Joshi--2013|Joshi et al., 2013]] ). The simplest traditional pattern-scaling approach approximates future changes by the product of a time-evolving global surface temperature change and a pattern that varies spatially but is constant across time, scenarios, and models. This technique was shown to be more robust across scenarios rather than across models, with better results for temperature compared with precipitation ( [[#Tebaldi--2014|Tebaldi and Arblaster, 2014]] ; see also [[IPCC:Wg1:Chapter:Chapter-4#4.2.4|Section 4.2.4]] ). One approach which avoids scaling is to consider a period in a different scenario with the same global surface temperature change ( [[#Herger--2015|Herger et al., 2015]] ). It is attractive as it provides patterns of any temporal resolution that are consistent across variables. Nonetheless, this technique is still only based on global surface temperature and is not necessarily suitable for precipitation changes projected in stabilized versus transient scenarios (at the same global warming level) given the fast-atmospheric adjustment to GHG radiative forcing (Sections 8.2.1 and 8.4.1.1).

Even in a theoretical climate system governed by linear processes, pattern-scaling assumptions can fail because the different forcing time response of different parts of the Earth system cause evolving spatial warming patterns ( [[#Good--2016a|Good et al., 2016a]] ). This occurs primarily because different feedbacks occur at different time scales ( [[#Armour--2013|Armour et al., 2013]] ; [[#Andrews--2015|Andrews et al., 2015]] ), which in turn implies that the atmospheric circulation and water cycle is dependent both on the level of warming and the rate of change ( [[#Ceppi--2018|Ceppi et al., 2018]] ). The usual distinction between the fast adjustment to increased GHG concentrations and the slower response to SST warming ( [[#8.2.2.2|Section 8.2.2.2]] ) may, however, not be sufficient to explain the time evolution of the hydroclimatic response at the regional scale, especially in subtropical land areas where this response critically depends on shifts in atmospheric circulation associated with distinct ‘fast’ (typically five to ten years, that is however much slower than the atmospheric adjustment assessed in [[#8.2.1|Section 8.2.1]] ) and slow SST warming patterns ( [[#Zappa--2020|Zappa et al., 2020]] ). The changing balance between the water cycle response to anthropogenic GHG and aerosol forcings is another source of non-linearity across time and global warming levels (Ishizaki et al. , 2013; Rowell et al. , 2015; Y. Liu et al. , 2019b; Wilcox et al., 2020) .

Non-linearities in the climate response are thought to arise from multiple factors. These include state-dependent ice-albedo feedback and its potential influence on Northern Hemisphere (NH) storm tracks (Peings and Magnusdottir, 2014; [[#Semenov--2015|Semenov and Latif, 2015]] ; see also Cross-Chapter Box 10.1 and [[#8.6.1|Section 8.6.1.2]] ); a state-dependent sensitivity of tropical precipitation to increased SST ( [[#Schewe--2017|Schewe and Levermann, 2017]] ; [[#He--2018|He et al., 2018]] ); a complex response of the Atlantic meridional overturning circulation (AMOC; Sections 9.2.4.1 and 8.6.1.1) and its model- and magnitude dependent teleconnections with regional temperature and precipitation (Kageyama et al., 2013; [[#Jackson--2015|Jackson et al., 2015]] ; [[#Qasmi--2017|Qasmi et al., 2017]] , 2020); and other atmospheric and terrestrial ( [[#8.5.3.2|Section 8.5.3.2]] ) processes such as cloud and land surface feedbacks (Ceppi and Gregory, 2017; [[#King--2019|King, 2019]] ). The response of convective precipitation may exhibit non-linearities because it is itself modulated by both dynamics and atmospheric water content, each responding independently to warming (Chadwick and Good, 2013; [[#Neupane--2013|Neupane and Cook, 2013]] ).

Based on a simple model, it was also suggested that the Indian summer monsoon may exhibit a moisture-advection feedback which allows multiple stable states as boundary conditions change (Zickfeld et al., 2005). However, limitations of this theory and comprehensive GCMs suggest a near-linear monsoon response to a broad range of radiative forcings (Boos and Storelvmo, 2016). Non-linear precipitation responses to global warming have been reported in the Indo-Pacific, where a linear increase in SSTs can trigger non-linear changes in precipitation and a shift in the ITCZ depending on the relative amplitudes of uniform and structured SST anomalies ( C.T.Y. [[#Chung--2014|]] [[#Chung--2014|Chung et al., 2014]] ; [[#Toda--2018|Toda and Watanabe, 2018]] ).

Compared to atmospheric circulation and seasonal mean precipitation, extreme precipitation has been found to scale more accurately with local and global mean temperature (Chou et al., 2012; [[#Pendergrass--2015|Pendergrass et al., 2015]] ). The projected increase in the magnitude of extreme precipitation is generally proportional to the global warming level, with an increase of around 7% per 1°C warming ( [[IPCC:Wg1:Chapter:Chapter-11#11.4.5|Section 11.4.5]] ) although this rate shows seasonal and geographical variations and is slightly less for five-day than for one-day precipitation maxima. Projected changes in extreme precipitation are the result of both thermodynamical and more model-dependent and potentially less linear dynamical contributions ( [[#Pfahl--2017|Pfahl et al., 2017]] ). Projected changes in precipitation extremes are also potentially sensitive to a non-linear response of spatial convective organization (Pendergrass et al., 2016), and can exhibit a quadratic rather than linear response to global warming (Pendergrass et al., 2019).

Within CMIP6, the linearity to CO <sub>2</sub> forcing can be assessed through the comparison of the model response to abrupt doubling compared with abrupt quadrupling of atmospheric CO <sub>2</sub> ( [[#Webb--2017|Webb et al., 2017]] ). Preliminary analyses based on CMIP5 models showed that annual precipitation changes following a doubling step change in CO <sub>2</sub> from pre-industrial levels are not necessarily consistent with the response to the step from doubling to quadrupling despite a similar change in radiative forcings ( [[#Good--2016a|Good et al., 2016a]] ; [[#Ceppi--2017|Ceppi and Shepherd, 2017]] ). Beyond the visual comparison of the climate response at various global warming levels (e.g., Figure 4.35), the linearity across global warming levels can be assessed by using the highest emissions scenario and comparing seasonal mean relative precipitation changes at +2°C versus +4°C above pre-industrial (1850–1900) temperatures (Figure 8.25). The results support the previous finding ( [[#Good--2016b|Good et al., 2016b]] ) that a second 2°C warming does not necessarily lead to the same precipitation anomaly pattern as the first 2°C, especially in the tropics where regional differences can be large but not necessarily consistent among different models. They are also consistent with a recent analysis of CMIP5 models showing that the projected drying in the Mediterranean and in Chile is substantially faster than the increase in GSAT, and therefore does not scale linearly with global warming ( [[#Zappa--2020|Zappa et al., 2020]] ).

In summary, there is ''high confidence'' that continued global warming will further amplify GHG-induced changes in large-scale atmospheric circulation and precipitation. Nonetheless, there are cases where regional water cycle changes are not linearly related to global warming due to the interaction of multiple forcings, feedbacks and time scales ( ''medium confidence'' , see also Sections 4.2.4, 7.4.3 and 8.2.1). Aridity in subtropical regions is highly sensitive to fast shifts in large-scale atmospheric circulation so are particularly susceptible to such non-linearities.

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==== 8.5.3.2 Non-linearities in Land Surface Processes and Feedbacks ====

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Land surface responses and feedbacks represent a potential source of non-linearity for the water cycle response, at least at regional and local scales. The forced response of soil moisture and freshwater resources not only depends on precipitation, but also on evaporation ( [[#Laîné--2014|Laîné et al., 2014]] ), snowmelt ( [[#Thackeray--2016|Thackeray et al., 2016]] ), and runoff(X. [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|Zhang et al., 2018]] ) which are intrinsically non-linear processes depending on soil moisture or temperature thresholds. Bare ground evaporation is, for instance, usually estimated as a non-linear function of surface soil moisture ( [[#Jefferson--2015|Jefferson and Maxwell, 2015]] ). Plant transpiration requires more complex formulations with non-linear dependencies on multiple environmental factors including root-zone soil moisture and atmospheric CO <sub>2</sub> concentration ( [[#Franks--2017|Franks et al., 2017]] ). Globally, land surface evaporation is both energy and soil-moisture limited, but one of these limitations can become dominant depending on regions and seasons. Non-linearities may be particularly strong in transitional regimes where and when soil moisture limitation plays a major role ( [[#Berg--2018b|Berg and Sheffield, 2018b]] ).

Snowmelt is a nonl-inear process and projected changes in snowfall are also a non-linear combination of changes in total precipitation and in the fraction of solid precipitation. In cold regions, snowfall may first increase because of the increased water capacity of a warmer atmosphere and then decrease because snow falls as rain in an even warmer atmosphere. Such non-linearities can contribute to elevation, latitudinal and seasonal contrasts in the observed and projected retreat of the Northern Hemisphere (NH) snow cover ( [[#Shi--2015|Shi and Wang, 2015]] ; [[#Thackeray--2016|Thackeray et al., 2016]] ). Mountain glaciers also represent source of non-linear runoff responses since the annual runoff can first increase due to additional melting and then decrease as the glaciers shrink ( [[#Kraaijenbrink--2017|Kraaijenbrink et al., 2017]] ; [[#Shannon--2019|Shannon et al., 2019]] ). [[IPCC:Wg1:Chapter:Chapter-9#9.5.1.3|Section 9.5.1.3]] concludes with ''high confidence'' that the average annual runoff from glaciers will generally reach a peak at the latest by the end of the 21st century, and decline thereafter. This peak may have already occurred for small catchments with little ice cover, but tends to occur later in basins with large glaciers. Permafrost thawing is another mechanism which can trigger a non-linear hydrological response in the high latitudes of the NH( [[#Walvoord--2016|Walvoord and Kurylyk, 2016]] ), whose magnitude and potential abruptness is assessed in [[IPCC:Wg1:Chapter:Chapter-5#5.4.3.3|Section 5.4.3.3]] .

Land surface runoff and groundwater recharge are highly non-linear process, depending for instance on rainfall intensity, soil infiltration capacity, vertical profile of soil moisture and water table depth. A non-linear relationship between rainfall and groundwater recharge was observed in the tropics where intense seasonal rainfalls associated with internal climate variability contribute disproportionately to recharge (R.G. Taylor et al. , 2013a; Cuthbert et al. , 2019a) . Groundwater fluxes in arid regions are generally less responsive to climate variability than in humid regions, which can temporarily buffer climate change impacts on water resources or lead to a long, initially hidden, hydrological responses to global warming ( [[#Cuthbert--2019a|Cuthbert et al., 2019a]] ). Hydrological model simulations driven by individual and combined forcing show that decreased precipitation can cause larger deficits in soil moisture, streamflow and water table depth than other forcings, but also that these factors are not linearly cumulative when applied in combination ( [[#Hein--2019|Hein et al., 2019]] ). Surface runoff was found to scale only approximately with global warming ( [[#Tanaka--2017|Tanaka et al., 2017]] ). Significant non-linearities were found in the projected annual mean runoff response to global warming in CMIP5 projections, which could not be entirely explained by precipitation changes(X. [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|]] [[#Zhang--2018|Zhang et al., 2018]] ). Similar non-linear behaviours are found in CMIP6 models over the Amazon, Yangtze, Niger, Euphrates and Mississippi river basins (Figure 8.26), highlighting the need to reassess the assumption of linearity when estimating regional water cycle changes.

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'''Figure 8.26 |''' '''Rate of change in basin-scale annual mean runoff with increasing global warming levels.''' Relative changes (%) in basin-averaged annual mean runoff estimated as multi-model ensemble median from a variable subset of CMIP6 models for each SSP over nine major river basins: '''(a)''' Mississippi, '''(b)''' Danube, '''(c)''' Lena, '''(d)''' Amazon, '''(e)''' Euphrates, '''(f)''' Yangtze, '''(g)''' Niger, '''(h)''' Indus, and '''(i)''' Murray. The basin averages have been estimated after a first-order conservative remapping of the model outputs on the 0.5° by 0.5° river network of [[#Decharme--2019|Decharme et al. (2019)]] . The shaded area indicates the 5–95% confidence interval of the ensemble values across all SSPs. Note that the y-axis range differs across basins and is particularly large for Niger and Murray (panels g and i). The number of models considered is specified for each scenario in the legend located inside panel b. Further details on data sources and processing are available in the chapter data table (Table 8.SM.1).

Beyond changes in land surface water fluxes, non-linearities in the response of soil moisture and freshwater reservoirs have not been well documented in global climate projections but deserve further attention given the complex interactions between the water, energy and carbon cycles ( [[#Berg--2018a|Berg and Sheffield, 2018a]] ), the growing direct human influence on rivers and groundwater ( [[#Abbott--2019|Abbott et al., 2019]] ), and a possible offset between the linear components of changes in precipitation and evapotranspiration. Significant non-linearities were found in water scarcity projections, as seen by the stronger sensitivity to the first 2°C increase in global warming ( [[#Gosling--2016|Gosling and Arnell, 2016]] ).

In summary, there is both numerical and process-based evidence that terrestrial water cycle changes can be non-linear at the regional scale ( ''high confidence'' ). Non-linear regional responses of runoff, groundwater recharge and water scarcity have been documented based on both CMIP5 and CMIP6 models, and highlight the limitations of simple pattern-scaling techniques ( ''medium confidence'' ). Water resources fed by melting glaciers are particularly exposed to such non-linearities ( ''high co'' ''nfidence'' ).

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