Quantifying the Uncertainty Sources of Future Climate Projections and Narrowing Uncertainties With Bias Correction Techniques

Abstract

Decomposing the uncertainty of global climate models is highly instructive in understanding climate change. However, it remains unclear whether sources of uncertainty have changed as the models have evolved and the extents to which uncertainty in temperature and precipitation are narrowed after bias correction (BC). We quantified uncertainty in temperature and precipitation projections over global land from three sources—model uncertainty, scenario uncertainty, and internal variability—and compared results from the models participating in the 5th and 6th phases of the Coupled Model Intercomparison Project (CMIP5 and CMIP6). In addition, we investigated the potential of four BC methods for narrowing uncertainty in temperature and precipitation over the globe and individual continents. Raw projections of temperature and precipitation have greater uncertainty and lower fractional uncertainty relative to their anomalies. The largest temperature uncertainties appear in high-latitude and high-altitude regions, and the largest precipitation uncertainties are in low-latitude regions and mountainous and coastal areas. For uncertainties in CMIP6 temperatures, the contribution from model uncertainty decreases with time (from 99% to 39%), while the contribution from scenario uncertainty increases with time (from 0.01% to 61%). For precipitation projections, the contribution from model uncertainty predominates (98%), while the contributions from scenario uncertainty (1.8%) and internal variability (0.2%) are extremely low. Four BC methods have exhibited excellent ability to reduce uncertainty, and among them, BC and spatial disaggregation has the best performance. These findings can help us better understand the characteristics of the models, while also providing decision makers with more accurate information to address climate mitigation and adaptation measures.

Introduction

Global climate models (GCMs) can reproduce past climate characteristics and project future climate evolution, and they are currently one of the most effective tools for climate change research (Parsons, 2020). With the recent release of phase 6 of the Coupled Model Intercomparison Project (CMIP6), numerous climate studies have been conducted (Peng et al., 2022; Seneviratne & Hauser, 2020). However, quantitative climate projections from GCMs are subject to high uncertainty (Wu et al., 2021; Kharin et al., 2013; Tebaldi et al., 2021) due to our incomplete knowledge of climate, insufficient representation of climate system, and limited computer resources (Bennett et al., 2012; Hawkins & Sutton, 2009; Yip et al., 2011). In this context, uncertainty refers to the different expressions of the same climate change process by different models. Quantitative studies of uncertainty in the field of climate research are often conducted on the anomalies of climate variables (anomalies are commonly used to characterize deviations of climate variables from their normal values, which means they show the variables' departure from their average values over a certain period). Use of anomalies narrows the uncertainty of the original values of the model outputs by removing systematic error (Strobach & Bel, 2017) and does not reflect the true magnitude of uncertainty (Figure 1). The uncertainties (±1 standard deviation here) of global annual mean temperature and precipitation are projected to be 3.8°C and 243.8 mm (which is larger than the uncertainty of the anomalies), respectively, under a high-emissions scenario by 2100 (Figure 1). As a consequence, making reliable projections of future climate and assessing the impacts of these projections on other fields are relatively difficult.

Figure 1. Phase 6 of the Coupled Model Intercomparison Project modeled annual temperature and precipitation series over the global land (except Antarctica) during the period 1955–2099. (a) Surface air temperature anomalies (unit: °C) and (b) annual total precipitation anomalies (unit: mm) relative to the baseline period 1970–1999; (c) original temperature outputs (unit: °C); and (d) original precipitation outputs (unit: mm). The historical simulations (gray) and future projections under SSP1-2.6 (blue), SSP2-4.5 (orange), and SSP5-8.5 (red) are calculated by area-weighted averaging and then smoothed with the 10-year running mean. The solid curves and shadings denote the multi-model ensemble mean and uncertainty (±1 standard deviation across the multi-model ensembles).

Clarifying uncertainty sources can provide important scientific support for enhancing the credibility of future projection results and resolve relevant scientific questions for subsequent modeling applications (Miao et al., 2022). The evaluation and characterization of uncertainty using level of confidence and likelihood are given extensive attention in the IPCC Sixth Assessment Report (IPCC, 2021). Hawkins and Sutton (2009) proposed three main sources of projection uncertainty. The first one is the internal variability. This refers to the natural fluctuations produced by the planet without any radiative forcing (Marotzke & Forster, 2015). There are also some typical internal variability modes, such as the El Niño-Southern Oscillation (Grothe et al., 2020), North Atlantic Oscillation (Börgel et al., 2020), and Pacific Decadal Oscillation (Wu et al., 2011). Model uncertainty is the second source of uncertainty. Different models respond differently to climate change with the same radiative forcing owing to different implementations of numerical methods, varied mathematical expressions, diverse parameterization processes (X. Wang et al., 2021), and the discrepancies between the regional scales that integrate small-scale processes and the larger synoptic scales that GCMs operate at (Macilwain, 2014; Palmer, 2014). The series of Coupled Model Intercomparison Projects (CMIPs) established by World Climate Research Program is currently in its sixth phase (CMIP6). Compared to CMIP5 (Taylor et al., 2012), the models participating in CMIP6 take into account more complex chemical, physical, and biological processes, which makes the investigation of model uncertainty more complex (Eyring et al., 2016). The third source of projection uncertainty is scenario uncertainty. This is seen when a given model exhibits large differences under various future emission scenarios, which are highly uncertain due to their dependence on future population levels and pathways of economic and social development (Yu et al., 2018). As climate models evolve, so do emissions scenarios. Future climate projections under Representative Concentration Pathways (RCPs) emissions scenarios have been conducted by models participating in CMIP5 (van Vuuren et al., 2011), and Shared Socioeconomic Pathways (SSPs) in CMIP6 have been developed based on the RCPs. The RCP describes possible future levels of greenhouse gases and other factors in the atmosphere that could alter the amount of solar energy intercepted by the Earth (known as the “radiation factor” and measured in W/m²) (Meinshausen et al., 2011). Different pathways (i.e., RCP2.6, RCP4.5, and RCP8.5) are used to assess the resulting ranges of warming and climate change (Naumann et al., 2018). The SSPs are based on Integrated Assessment Models (i.e., not climate models), and they do not consider climate change alone but also pay attention to population, economic growth, education, urbanization, and the rate of technological development (Eyring et al., 2016). These SSPs can be seen as a combination of an SSP and an RCP: for example, SSP1-2.6 is a combination of SSP1 (a world of sustainability-focused growth and equality) and RCP2.6 (Liu et al., 2021).

A number of approaches to quantifying and partitioning sources of uncertainty have also been widely discussed and developed in recent years, and they use mainly the analysis of variance (ANOVA) as mathematical foundations (Finger et al., 2012; Hingray & Saïd, 2014; Yip et al., 2011; Zhuan et al., 2019). A considerable number of studies have focused on uncertainty decomposition in the last decade, including in studies looking at ocean carbon uptake (Lovenduski et al., 2016), agriculture (Vermeulen et al., 2013), soil moisture droughts (Lu et al., 2019; Chen & Yuan, 2022), agricultural drought (Lu et al., 2019), zonal wind (Strobach & Bel, 2017), climate extremes (Zhang & Chen, 2021), and water scarcity (Greve et al., 2018). There have also been studies that focused on internal variability (Chen et al., 2021; Gu et al., 2019). Uncertainty decompositions in temperature and precipitation have also received a lot of attention in recent years (Evin et al., 2019; Hingray & Saïd, 2014; Lehner et al., 2020; Woldemeskel et al., 2012; Zhou et al., 2020). Most of these studies have been performed on the anomaly values of the variables. However, in many cases, such as when driving another model, it is necessary to use the original magnitudes of the variables. Therefore, it makes sense to decompose the sources of uncertainty in the original outputs of the variables, which helps us to understand the most fundamental information about climate models and provides clarity about uncertainty for those who use climate model outputs as drivers for other models (such as hydrological or ecological models).

It is well known that climate models are generally subject to systematic bias (Zadra et al., 2018). Biases in GCMs may stem from many aspects, including limited spatial resolution; simplified physical processes in the atmosphere, land surface, ocean, and cryosphere; and incomplete understanding of the climate system (Nahar et al., 2017). The bias in original model outputs used in conducting climate change impact assessments often produces unrealistic results, thereby reducing the credibility of the study. Therefore, raw GCM outputs usually are corrected before impact studies are completed. In recent years, a range of bias correction (BC) methods have been developed, such as the delta change (DC) method, multiple linear regressions, and quantile mapping (QM) approach (Miao et al., 2016). Sometimes BC is also combined with statistical downscaling to correct for climate variables (Abatzoglou & Brown, 2012), such as bias correction and spatial disaggregation (BCSD; Wood et al., 2002, 2004). There have been some comparisons of upper air climate variables with and without BC (Eghdamirad et al., 2016). However, decomposed sources of uncertainty for temperature and precipitation after BC have seldom been quantified.

Based on the above, this paper attempts to answer the following scientific questions: (a) How much do the raw projected uncertainties of temperature and precipitation and their corresponding anomaly uncertainties differ? (b) How well does BC narrow the uncertainty in temperature and precipitation projections for different regions of globe? (c) Which of the three sources of uncertainty is narrowed most after BC?

Data and Methods Data

In this study, we used monthly mean surface air temperature and monthly total precipitation from 21 CMIP5 models (Taylor et al., 2012) and 26 CMIP6 models (Eyring et al., 2016) (Tables S1–S2 in Supporting Information S1). We used historical simulations for 1955–2005 (1955–2014) and future projections for 2006–2099 (2015–2099) from CMIP5 (CMIP6) under future scenarios. In our research, future scenarios include three RCPs (RCP2.6, RCP4.5, and RCP8.5) for CMIP5 and three SSPs (SSP1-2.6, SSP2-4.5, and SSP5-8.5) for CMIP6 for a fair comparison. Only the first realization for each involved GCM output was used. We used bilinear interpolation to standardize the resolution of model outputs to 1° × 1°.

We used global observation data of monthly mean surface air temperature and monthly total precipitation to correct the GCM output. We chose the Climatic Research Unit (CRU) Gridded Time Series Datasets (version 4.05) (Harris et al., 2020) as our observed data set. Since CRU data are missing in Antarctica, our study area is all global land north of 60°S. The spatial resolution of the data set is 0.5° × 0.5°.

Methodology Uncertainty Partitioning

In this study, the uncertainty reflects the spread among GCM projections. The decomposition of uncertainty in temperature and precipitation projections for the 21st century follows the method developed by Hawkins and Sutton (2009, 2011). Uncertainty in climate projections is decomposed into three sources: internal variability (I), model uncertainty (M), and scenario uncertainty (S). Before performing the uncertainty decomposition, we calculated a 10-year running mean for all temperature and precipitation values in CMIP5 and CMIP6 models by grid point in order to weaken the interannual variation, following Seneviratne and Hauser (2020). Each GCM simulation under each emission scenario is fitted using ordinary least squares with a fourth-order polynomial from 1955 to 2099, following Hawkins and Sutton (2009).

For the fitting of GCM projection outputs, the raw simulation $${X}_{m,s,t}$$ for each model m, scenario s, and year t is expressed as [Image Omitted. See PDF]

For the fitting of original magnitudes, the raw simulation $${X}_{m,s,t}$$ for each model m, scenario s, and year t is expressed as [Image Omitted. See PDF]

Here, $${i}_{m,s}$$ is the multi-year average temperature or precipitation in the baseline period (1970–1999), the fourth-order fit is denoted by $${x}_{m,s,t}$$, and $${\varepsilon }_{m,s,t}$$ is the residuals of the fitted equation. Past studies have shown that the choice of the baseline period has almost no effect on the uncertainty decomposition results (Zhou et al., 2020).

The internal variability of each model is considered to be the variance of the residuals from the fits: [Image Omitted. See PDF]where $${\mathrm{v}\mathrm{a}\mathrm{r}}_{s,t}\left({\varepsilon }_{m,s,t}\right)$$ denotes the variance of the model m across all scenarios and time, and $${N}_{m}$$ is the number of models (21 for CMIP5 and 26 for CMIP6). $$V$$ is a constant over time and is not affected by emissions scenarios (Thompson et al., 2015).

The model uncertainty of a certain scenario is defined as the variance among the different models under this scenario: [Image Omitted. See PDF]where $${N}_{s}$$ is the number of scenarios (which is three for both CMIP5 and CMIP6).

The scenario uncertainty is defined as the variance of the multi-model average under the three scenarios: [Image Omitted. See PDF]where $${N}_{m}$$ is the number of models.

The Fractional Uncertainty

We assume a premise that there are no interactions among different sources of uncertainty and therefore total uncertainty is equal to the sum of the uncertainties from the three sources: [Image Omitted. See PDF]

Uncertainty in the latter context refers to the above-mentioned quantities $$V$$, $$M$$, $$S$$, and $$T$$.

The mean projection of all the GCMs is calculated as multi-scenario and multi-model averages, [Image Omitted. See PDF]

We define the fractional uncertainty of a variable as the projected uncertainty divided by the mean of all predictions (Hawkins & Sutton, 2009; Zhou et al., 2020). This indicator can eliminate regional differences to a certain extent. For example, we assume that the temperature projections in the equatorial and polar regions have the same magnitude of uncertainty, but the difference in average temperatures between the two regions leads to a large discrepancy in the fractional uncertainty. The fractional uncertainty (F) at the 90% confidence level is defined as: [Image Omitted. See PDF]where 1.65 is a characteristic of the 90% confidence interval of the normal distribution. Note that all models here are equally weighted. The proportion of variance refers to the quantities $$V/T$$, $$M/T$$, and $$S/T$$. The proportion of variance is the proportion of each source of uncertainty in relation to the total uncertainty (in other words, the relative contribution of each source of uncertainty).

Bias Correction

We looked at four BC methods in this study: DC (Beyer et al., 2020), QM (Maraun et al., 2017; Maurer & Pierce, 2014), nonstationary cumulative-distribution function-matching (CNCDFm) (Miao et al., 2016), and BCSD (Figure S1 in Supporting Information S1) (Wood et al., 2002, 2004; Xu & Wang, 2019). The principles and formulas for each BC method are shown in Supporting Information S1. Note that the GCM output is corrected by month based on grid point scale. For the first three BC methods, the model outputs and observations were converted to a common grid of 1° × 1° (latitude × longitude) by bilinear interpolation. All four BC methods eventually yielded projections of 1° × 1° resolution for temperature and precipitation.

Because the CMIP6 historical simulation ends in 2014 and to ensure that there are two consecutive 30-year periods in the BC process, we choose 1955 as the start of the time period used for the fourth-order fit. And because the historical simulation for CMIP5 ends in 2005, the period 1955–2005 is divided into two periods: 1955–1980 and 1981–2005. In the above-mentioned BC methods, the specific periods for correcting historical and future GCM outputs are listed below (Table 1). We use period 1 as the reference period to correct the outputs of period 2. For further analysis, we consider the 2030s (2030–2039) to be near term, 2060s (2060–2069) medium term, and 2090s (2090–2099) long term.

Table 1 Division of the Bias Correction Periods

	Historical correction		Future correction
	Period 1	Period 2	Period 1	Period 2
CMIP5	1955–1980	1981–2005	1955–2005	2006–2099
CMIP6	1955–1984	1985–2014	1955–2014	2015–2099

Results Uncertainty of GCM Projection Anomalies

The uncertainty decomposition of the anomaly values for temperature and precipitation is presented in Figure 2. The most important source of uncertainty in temperature projections in this century has been model uncertainty. Up until about the 2030s, internal variability is the second-leading source of uncertainty for CMIP6 (fractional uncertainty: 0.07, representing 12.5% of total uncertainty in the near term), while after about the 2060s, scenario uncertainty dominates among the three sources of uncertainty (fractional uncertainty: 0.88, for 66.4% of total uncertainty in the long term). Total fractional uncertainty decreases and then increases, reaching a minimum (0.39 for CMIP6) around 2030. The relative importance of each source of uncertainty, however, varies between precipitation and temperature. Early in the 21st century, it is worth noting that internal variability in precipitation for CMIP5 becomes a major source of uncertainty (53.7%). After that, model uncertainty dominates during the 21st century, and scenario uncertainty overtakes internal variability in ∼2060. The corresponding results for CMIP5 and CMIP6 are similar.

Figure 2. The fractional uncertainty (the projected uncertainty divided by the mean projections) from different sources in the decadal mean projection anomalies for (a) temperature (Tas) and (b) precipitation (Pre) from the 5th and 6th phases of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) over the global land (except Antarctica), relative to the baseline period, 1970–1999.

Figure 3 shows the contributions of uncertainty for temperature and precipitation quantified by the proportion of variance over the globe. Over time, the contributions from model uncertainty and internal variability for CMIP6 decrease, and the contribution from scenario uncertainty increases. In general, internal variability contributes more to projection uncertainty for precipitation (39.5%) than temperature (20.8%) over the globe early in the century, and the former is almost twice as large as the latter. However, in the long term, the contribution of scenario uncertainty in temperature (82.0%) is greater than in precipitation (25.5%) over the globe. We find that for continents with small areas, like Europe and Australia, scenario uncertainty almost disappears and has a very small contribution to total uncertainty of precipitation, while the proportion of model uncertainty (93.0% for Europe and 86.1% for Australia in the long term) has been increasing. The contributions of internal variability in temperature (56.9%) and precipitation (77.9%) in Australia are greater than the contributions for other continents in the early years of this century. Results from CMIP5 are relatively consistent with those from CMIP6 (Figure S2 in Supporting Information S1), although a slight difference is that scenario uncertainty of precipitation for CMIP5 is smaller than it is for CMIP6 in the long term.

Figure 3. The proportion of variance in the decadal mean projections anomalies from the 6th phase of the Coupled Model Intercomparison Project is explained by uncertainty from different sources for temperature (Tas, left) and precipitation (Pre, right) over the global land (except Antarctica) and the continents, relative to the baseline period 1970–1999 (unit: %) (NAM: North America; SAM: South America).

Uncertainty of GCM Projections

We find a large difference between the anomalies and the raw outputs when comparing how the uncertainties of each source are decomposed (Figure 4). Raw projections of temperature and precipitation have greater uncertainty (related figure not shown) and smaller fractional uncertainty relative to their anomalies. Compared with the fractional uncertainty of anomalies (Figure 2), the most obvious difference in the CMIP6 results is that internal variability is extremely low over time for both temperature (fractional uncertainty: 0.01, representing a 6.8% contribution to total uncertainty in the near term) and precipitation (fractional uncertainty: 0.01, a 4.3% contribution to total uncertainty). Model uncertainty for CMIP6 remains a major source of uncertainty in the near term for temperature (fractional uncertainty: 0.11, which is 83.3% of total uncertainty) and precipitation (fractional uncertainty: 0.20, which is 94.7% of total uncertainty). Consistent with the anomaly results (Figure 2), scenario uncertainty of CMIP6 for temperature and precipitation overtake internal variability in ∼2030 and ∼2060, respectively. It is noteworthy that the CMIP6 model uncertainty for precipitation over time (near term: 0.20; long term: 0.21) is larger than that of CMIP5 (near term: 0.15; long term: 0.15).

Figure 4. The fractional uncertainty from different sources in decadal mean projections for (a) temperature (Tas) and (b) precipitation (Pre) from the 5th and 6th phases of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) over the global land (except Antarctica).

There are notable differences between anomalies and raw projections in the proportion of total variance (Figures 3 and 5). For temperature, model uncertainty over the global land accounts for almost 100% of total uncertainty for CMIP6 (98.4% in the near term), and the percentage goes down with time (38.7% in the long term). The contribution of scenario uncertainty for temperature over the globe increases with time (from 0.06% to 61.2%), while the proportion of internal variability remains extremely low (changing from 0.83% to 0.13%). In Australia, the proportion of internal variability and scenario uncertainty are larger than in other continents in the long term. For global precipitation, model uncertainty has dominated over time (contributing from 99.8% to 98.1%), while the contributions of scenario uncertainty (changing from 0.004% to 1.77%) and internal variability (changing from 0.22% to 0.17%) are extremely small over the globe. In North America and Asia, scenario uncertainty has a larger proportion than in other continents in the long term. The results for temperature and precipitation from CMIP5 and CMIP6 are very similar over the globe and individual continents (Figure S3 in Supporting Information S1).

Figure 5. The proportions of variance in decadal mean projection from the 6th phase of the Coupled Model Intercomparison Project is explained by uncertainty from different sources for temperature (Tas, left) and precipitation (Pre, right) over the global land (except Antarctica) and the continents (unit: %) (NAM: North America; SAM: South America).

Uncertainty After Bias Correction

To explore the changes in the uncertainty of each source after BC, we use four BC methods to correct raw model outputs. In the near term, the ability of different BC techniques to narrow uncertainty is almost identical (Figure 6). We find that the reduction of total uncertainty is primarily due to a reduction in model uncertainty, and BC narrows model uncertainty considerably for temperature (percentage reduction by 72.4% for BCSD, 72.2% for QM, 52.8% for DC, and 57.4% for CNCDFm) and precipitation (percentage reduction by 94.6% for BCSD, 93.4% for QM, 92.7% for DC, and 93.6% for CNCDFm) in the long term (Figure 6, top two rows). Scenario uncertainty is virtually unaffected by BC in the early years of this century, but it is slightly narrowed in the long term. Internal variability is always small, and most BC methods have a weak ability to narrow internal variability, except for DC, which increases it. This finding is relatively consistent across continents (Figures S4–S7 in Supporting Information S1). It is worth mentioning that the pattern of change in scenario uncertainty for precipitation appears to be more unusual for some continents (e.g., Australia, Europe, and South America), where it exhibits volatile changes. The conclusions for fractional uncertainty (Figure 6, bottom two rows) generally agree with the conclusions for uncertainty (Figure 6, top two rows). The results indicate that the ability of BC to narrow model uncertainty in temperature (percentage reduction by 70.5% for BCSD, 70.5% for QM, 61.4% for DC, and 49.5% for CNCDFm) and precipitation (percentage reduction by 88.2% for BCSD, 87.0% for QM, 85.0% for DC, and 85.9% for CNCDFm) is stronger in the near term over the globe (Figure 6). BC is not very effective for addressing scenario uncertainty and internal variability, especially using DC or CNCDFm (Figure 6 and Figures S8–S11 in Supporting Information S1). Combining the above aspects of performance, BCSD has the strongest ability to narrow uncertainty, and therefore we show only the results of BCSD in the subsequent content.

Figure 6. Uncertainties from different sources in the decadal mean projections for temperature (Tas) and precipitation (Pre) from the 6th phase of the Coupled Model Intercomparison Project over global land (except Antarctica) for four BC methods, including delta change (DC), bias correction and spatial disaggregation (BCSD), quantile mapping (QM), and nonstationary cumulative-distribution function-matching (CNCDFm). The first row shows uncertainty for temperature, the second row shows uncertainty for precipitation, the third row shows fractional uncertainty for temperature, and the fourth row shows fractional uncertainty for precipitation.

The proportions of each source of uncertainty before and after BC are shown in Figure 7. For the raw model outputs, we find that the proportions of uncertainty associated with internal variability for global temperature (0.6% in near term) and precipitation (0.2%) are extremely low. However, the contribution of internal variability becomes notably higher for temperature (5.2%) and precipitation (12.5%) after BC over the globe in the near term. For temperature, the proportion of model uncertainty after BC is highest among the three sources of uncertainty in the near term (84.9%) over the globe. In the long term, scenario uncertainty dominates (79.4%) and internal variability almost disappears (0.2%) over the globe. For precipitation, the most important source of uncertainty is derived from model uncertainty throughout the 21st century. Continental-scale findings are consistent with the global land results. It is worth noting that internal variability (47.8%) becomes a dominant contribution after BC in the near term in Australia. The results for CMIP5 and CMIP6 are highly consistent (Figure 7 and Figure S12 in Supporting Information S1). Overall, BC reduces the contribution of model uncertainty and increases those of scenario uncertainty and internal variability over time.

Figure 7. The proportion of uncertainty from different sources in the decadal mean projections for temperature (Tas: a–c) and precipitation (Pre: d–f) from the 6th phase of the Coupled Model Intercomparison Project before and after bias correction (BC) over global land (except Antarctica) and each continent (unit: %). Internal variability, scenario uncertainty, and model uncertainty are represented in orange, green, and blue, respectively. The darker colors show the results before BC, and the lighter colors show the results after BC. The results shown here use only bias correction and spatial disaggregation as the BC method. The horizontal axis of each subplot: Globe (GLO), Africa (AFR), Asia (ASI), Australia (AUS), Europe (EUR), North America (NAM), and South America (SAM).

The spatial patterns of uncertainty before and after BC are shown in Figures S13–S16 in Supporting Information S1. There are larger uncertainties in regions of high latitude and high altitude (such as the Qinghai–Tibetan Plateau) for temperature, and in low-latitude regions and mountainous and coastal areas for precipitation, suggesting that these features are not adequately represented in GCMs. In the long term, for precipitation, scenario uncertainty is larger in the tropical and boreal zones, and internal variability is larger in the low-latitude regions and near the Mediterranean Sea.

To illustrate how BC affects uncertainty spatially, we also calculated the difference between BCSD and raw simulations grid cell by grid cell (Figure 8 and Figure S17 in Supporting Information S1). We find that model uncertainty is reduced in most regions. Only certain regions show an increase in scenario uncertainty and internal variability after BC relative to raw projections, notably North Asia for temperature and near the Mediterranean Sea and the coastal regions of South America and Africa for precipitation. At the same time, we find that the ability of BC to narrow model uncertainty is more prominent in regions with larger uncertainty. In particular, a very clear line of demarcation emerges south of the Sahara Desert in Africa and north of the Qinghai–Tibetan Plateau.

Figure 8. The change due to bias correction (calculated as the results of bias correction and spatial disaggregation minus raw model outputs from the 6th phase of the Coupled Model Intercomparison Project) for uncertainty from different sources in the decadal mean projections for temperature and precipitation over global land (except Antarctica). The figure shows the near term (2030s), medium term (2060s), and long term (2090s). This graph shows four columns of uncertainty: total uncertainty (first), model uncertainty (second), scenario uncertainty (third), and internal variability (fourth).

Discussion Interpretation of the Results

A finding of our study is that raw projections of temperature and precipitation have greater uncertainty relative to projections of anomalies. This is because the use of anomalies themselves is considered to be one of the simplest BC methods by removing systematic error (Strobach & Bel, 2017), and this results in a greater fractional uncertainty (a smaller denominator in Equation 8). Scenario uncertainty for temperature is greater than it is for precipitation in the long term, probably because temperature is more sensitive to different future emission scenarios (Papalexiou et al., 2020). Notably, model uncertainty (referring to fractional uncertainty) for raw precipitation projections from CMIP6 (∼0.20) is larger than that from CMIP5 (∼0.15) over time; this could be explained by the fact that CMIP6 is more complex than CMIP5, including more models with more processes, all applied to a wider range of questions (Eyring et al., 2016). Using more models in precipitation studies tends to introduce greater uncertainty (Woldemeskel et al., 2016), while temperature is less sensitive to the choice of the number of models (Pirtle et al., 2010). At the continental scale, scenario uncertainty for precipitation from CMIP6 appears volatile for some of the continents (i.e., Australia, Europe, and South America); however, considering that the magnitude of the total uncertainty of precipitation is above the tens of thousands, the change in scenario uncertainty is negligible. Moreover, the uncertainty in precipitation outputs is greater than the uncertainty in temperature outputs. Owing to the limitations of our recognition of precipitation processes, GCMs are unable to reproduce some important phenomena (Rana et al., 2014). The complexity of precipitation formation mechanisms also directly leads to more difficulty in simulating precipitation (Ullah et al., 2021). The interactions among the elements of the climate system directly or indirectly affect the simulation of precipitation. For example, atmospheric water content is directly related to temperature (Maghrabi et al., 2019); plant transpiration and soil evaporation provide water for precipitation (Gu et al., 2021); and cloud cover influences convective precipitation by altering the amount of solar energy reaching the surface (Scaff et al., 2020).

Impact of Calculation Method on Uncertainty

Uncertainty decomposition methods differ in the calculation of internal variability. Yip et al. (2011) compared two methods to investigate whether the method of calculating internal variability would have a large effect on the results. The first method calculates the variance of the residual from the fitted equation as internal variability (Hawkins & Sutton, 2009, 2011). The second is a complete framework for estimating internal variability based on ANOVA by computing the variance of each member around the model scenario mean (Yip et al., 2011). The difference in internal variability calculated under these two methods is not significant; therefore, the main conclusions are not relevant to the method used to define internal variability (Hingray & Saïd, 2014; Reintges et al., 2017). Our research approach considers only three sources of uncertainty that are assumed to be independent of each other; however, there may be interactions among these uncertainties, which may slightly affect total uncertainty. A large number of studies have found an interaction between model uncertainty and scenario uncertainty; however, the interaction term is sufficiently small not to affect the major conclusions (Reintges et al., 2017; Yip et al., 2011). It has been found that, on average, the interaction term contributes 0%–7% of uncertainty for precipitation and 0%–10% for temperature (Woldemeskel et al., 2016).

The Potential to Narrow Uncertainty

Natural variability cannot be removed because it is inherent to the Earth system (Hawkins & Sutton, 2009, 2011). Model structural uncertainty is the primary source in GCM simulations (Woldemeskel et al., 2014), and most BC techniques (i.e., QM and BCSD) force all models to have the same attributes (mean, standard deviation, etc.) in the historical period (Woldemeskel et al., 2016), therefore, a BC technique has a greater ability to address model uncertainty. The ability of BC to narrow model uncertainty is more prominent in regions with larger uncertainty. The result that regions of high latitudes and high altitudes have larger uncertainty for temperature has been corroborated elsewhere (Woldemeskel et al., 2016). These regions have relatively few temperature observation stations due to the specifics of their geographical locations, which increases the difficulty of generating accurate climate model simulations to a certain extent, thus introducing greater uncertainty. For precipitation, regions of low latitudes and mountainous and coastal areas have larger uncertainty, because these areas receive high rainfall and high frequency of rainfall. The resolution of GCMs is too coarse to accommodate small-scale climate processes (Macilwain, 2014), and this limitation may be a source of relatively larger uncertainty.

Recently, a model weighting scheme based on own skill at successfully reproducing past changes was developed to narrow the uncertainty (Brunner et al., 2019; Lovenduski et al., 2016). In some regions, weighting the ensemble can reduce the spread between interquartiles by more than 20% (Brunner et al., 2019), thereby increasing the reliability of projection results. Previous research has also found that improved model performance and the use of highly skilled models can reduce projection uncertainty by narrowing model uncertainty (Zhou et al., 2020). This reflects the fact that model evaluation and selection can effectively enhance the robustness of climate projection results. A Bayesian model averaging approach has also been used for model evaluation (Khan et al., 2021), and it also can reduce uncertainty. Alternatively, the emergent constraint approach is a prospective way to reduce uncertainty in climate change projections that has been suggested in recent years (Hall et al., 2019). It seeks a close relationship between the uncertainty component of future climate and observable climate indicators. Emergent constraints can identify the best possible estimate of future changes in a given ensemble of GCMs (Thackeray et al., 2021). All of the methods mentioned above can reduce uncertainty to some extent, but in this study, the models are equally weighted when we perform uncertainty decomposition, because the most fundamental purpose of our research is to obtain the original uncertainty information in temperature and precipitation projections.

Limitations of the Study

Although the study has produced informative results, there are some limitations to consider. (a) Our study considers only the first realization of the simulation output of CMIP5 and CMIP6. In future studies, a wide range of GCMs with large ensembles is needed for climate adaptation and mitigation policies (Deser et al., 2020). More specifically, the use of output from multiple large initial-condition ensemble experiments, such as the CESM Large Ensemble, is key to projecting uncertainty in regional climate change (Deser et al., 2016). This is a powerful tool for assessing internal variability and scenario uncertainty in projection uncertainty. (b) It is also important to recognize that the quality of the observations determines the effectiveness of BC (J. Wang et al., 2021). Only one CRU observation data set was used in this study, which leaves room for improvement in the future. The use of multiple source observations could make our findings more robust. (c) We have here explored only uncertainties in mean temperature and precipitation, while extremes of temperature and precipitation and compound extreme events of both have profound impacts on humans (J. Wang et al., 2021; Zscheischler et al., 2020). (d) Understanding and quantifying climate projection uncertainty at regional scales is critical for regional climate adaptation. Our study is only detailed to the continental scale, and the study of smaller spatial scales, such as national scales, also deserves attention. Internal variability grows in importance for smaller regions (Hawkins & Sutton, 2009). All of these aspects are worth exploring further.

Conclusions

We quantified the uncertainty in temperature and precipitation projections from three sources—model uncertainty, scenario uncertainty, and internal variability—arising from model outputs of 21 CMIP5 and 26 CMIP6 GCMs. We also investigated the potential of four BC methods (DC, QM, CNCDFm, and BCSD) for narrowing uncertainty in temperature and precipitation projections over the globe and continents. The following conclusions were drawn:

1. Raw projections of temperature and precipitation have greater uncertainty and lower fractional uncertainty relative to their anomalies. The largest uncertainties for temperature appear in regions of high latitude and high altitude; for precipitation, the largest uncertainties are in low-latitude regions and in mountainous and coastal areas. The uncertainties from CMIP5 and CMIP6 are quite similar.

2. For uncertainties in temperature projections from CMIP6, the contribution from model uncertainty decreases with time (from 99% to 39% over global land), and likewise for internal variability (from 0.7% to 0.1%), whereas the contribution from scenario uncertainty increases with time (from 0.01% to 61%), except for in Australia and Europe. The source of uncertainty for precipitation is distinct from that of temperature, mainly in the long term, with model uncertainty dominating (contributing 98%), while contributions from scenario uncertainty (1.8%) and internal variability (0.2%) are extremely low. These results are comparable for CMIP5 and CMIP6.

3. The four BC methods have excellent ability to reduce uncertainty, and BCSD has the best performance among them. BCSD can effectively reduce model uncertainty for temperature by 72% and precipitation by 95% relative to raw simulations for CMIP6 in the long-term period, and this is more pronounced in regions with larger uncertainty; scenario uncertainty in the long term is narrowed by 32% for temperature and 54% for precipitation. Most BC techniques have poor ability to narrow internal variability, and over time they reduce the contribution of model uncertainty and increase those of internal variability and scenario uncertainty.

Where should we invest more efforts to narrow uncertainty in temperature and precipitation projections? We conclude that uncertainty is effectively narrowed mainly through the reduction of model uncertainty, and BC techniques are very effective in narrowing the model uncertainty. Meanwhile, although we believe that it is impossible to completely remove the uncertainties in climate projections, by continuously improving our understanding of geophysical processes and the representation of thermodynamic cycles and hydrological cycles in numerical models, we can narrow the uncertainty in the future. In addition, ways to more effectively narrowing uncertainty deserve further investigation.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (42041006 and 41877155), and the State Key Laboratory of Earth Surface Processes and Resource Ecology (2022-ZD-03). The authors acknowledge the World Climate Research Program, which, through its Working Group on Coupled Modeling, coordinated and promoted CMIP5 and CMIP6. The authors thank the climate modeling groups listed in Tables S1 and S2 in Supporting Information S1 for producing and making available their model output.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Data Availability Statement

The involved CMIP5 models and CMIP6 models are listed in Tables S1 and S2 in Supporting Information S1. The data from 21 CMIP5 models and 26 CMIP6 models can be accessed at https://esgf-node.llnl.gov/projects/cmip5/ and https://esgf-node.llnl.gov/projects/cmip6/. The global observation data of monthly mean surface air temperature and monthly total precipitation are obtained from the Climatic Research Unit Gridded Time Series Datasets (version 4.05) (https://data.ceda.ac.uk/badc/cru/data/cru_ts/cru_ts_4.05/data/).