The importance of internal climate variability in climate impact projections
Edited by Timothy Palmer, University of Oxford, Oxford, United Kingdom; received May 10, 2022; accepted August 18, 2022
Significance
Statistical projections of the socioeconomic impacts of climate change are increasingly used in policy, development, and the private sector to understand and prepare for climate risks. Climate uncertainty is the dominant source of uncertainty in many of these projections. Such studies increasingly account for some sources of climate uncertainty, including differences between climate models and emissions scenarios. However, uncertainty due to internal climate variability is generally ignored. We show that internal variability substantially boosts the uncertainty by 38% on average for near-term mortality, corn yields, and gross domestic product projections in the continental United States. Omitting uncertainty due to internal variability could lead to an underestimation of worst-case impacts and/or a misallocation of resources in climate mitigation and adaptation efforts.
Abstract
Uncertainty in climate projections is driven by three components: scenario uncertainty, intermodel uncertainty, and internal variability. Although socioeconomic climate impact studies increasingly take into account the first two components, little attention has been paid to the role of internal variability, although underestimating this uncertainty may lead to underestimating the socioeconomic costs of climate change. Using large ensembles from seven coupled general circulation models with a total of 414 model runs, we partition the climate uncertainty in classic dose–response models relating county-level corn yield, mortality, and per-capita gross domestic product to temperature in the continental United States. The partitioning of uncertainty depends on the time frame of projection, the impact model, and the geographic region. Internal variability represents more than 50% of the total climate uncertainty in certain projections, including mortality projections for the early 21st century, although its relative influence decreases over time. We recommend including uncertainty due to internal variability for many projections of temperature-driven impacts, including early-century and midcentury projections, projections in regions with high internal variability such as the Upper Midwest United States, and impacts driven by nonlinear relationships.
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Studies on the socioeconomic impacts of climate change have historically underestimated climate uncertainty, leading to overconfident projections of the resulting impacts (1, 2). Uncertainty in simulations of the future climate may arise from three major sources: 1) scenario uncertainty, representing differences in plausible future greenhouse gas emissions trajectories; 2) (climate) model uncertainty, representing differences in model responses to the same scenario inputs; and 3) internal variability (3). Currently, state-of-the-art analyses of future climate impacts account for scenario uncertainty by using projections from multiple future scenarios and model uncertainty by using a multimodel ensemble of projections from coupled general circulation models (CGCMs) (1, 2, 4–6). However, uncertainty due to internal variability is rarely taken into account despite the evidence that internal variability is an important component of total climate uncertainty for at least the first 50 y of projections (3, 7–9).
Internal variability consists of the naturally occurring variations in climate on timescales from daily weather to multidecadal processes due to interactions between various components of the Earth system. Internal variability is made up of components that are predictable, such as the El Niño–Southern Oscillation (10), as well as irreducible uncertainty due to the chaotic nature of the system (11). In the continental United States (CONUS), for example, increased likelihood of droughts and higher temperatures occurs during and following El Niño events in the Pacific Northwest (12, 13), following La Niña events in the Midwest (14, 15), and during the positive phase of the Atlantic Multidecadal Oscillation (16–18). In addition, internal variability leads to variability in trends of temperature, particularly over the northern and eastern CONUS (19, 20). The current best available estimates of the true internal variability of the Earth’s climate system come from multimodel ensembles of initial-condition large ensembles (LEs), where a CGCM is run multiple times with slight perturbations to the initial conditions to sample the distribution of its possible climate outcomes, conditioned on the same emissions scenario (21). The LEs used in this study provide generally realistic simulations of historical temperature variability over CONUS (22).
While much of the attention in climate impact studies is on end-of-century projections, policymakers generally respond to short-term challenges on time horizons of days to decades (23, 24), when internal variability is most prominent in projections of climate variables. It is particularly important to properly characterize the uncertainty of an impact when determining worst-case scenarios (25, 26), especially since the frequency of threshold-defined extremes often used in impact studies is more affected by changes in the variability than the mean (27, 28). Underestimating uncertainty of an impact leads to underestimation of the socioeconomic costs of climate change (26). Following the findings of ref. 2 that climate model uncertainty must be accounted for to fully understand climate uncertainty in end-of-century impact projections, we suggest that a proper representation of internal variability is critical to properly represent the total climate uncertainty of shorter-term projections. The recent availability of LE climate model experiments makes it possible to determine the uncertainty added by internal variability in projected socioeconomic impacts of climate change.
In this study, we quantify the climate uncertainty due to scenario, model, and internal variability uncertainties of future projections of mortality, gross domestic product (GDP) per capita, and corn yields. Each of these impacts is assumed to be driven by temperature changes at the county level over the CONUS. By comparing the relative magnitude of variance contributed by each source of uncertainty, we identify the conditions where the inclusion of internal variability is critical to accurately representing the uncertainty of a future climate impact.
Partitioning Climate Uncertainty in Climate Impact Projections
In this study, we quantify and partition the climate uncertainty in socioeconomic studies that use statistical models to link observed weather and climate to an impact of interest; that is, we determine what share of their climate uncertainty comes from scenario, model, or internal sources. In such impact studies, the relationship between an observed or projected climate variable (Fig. 1 D and H) and socioeconomic outcomes (Fig. 1 A–C) is represented through a dose–response function (Fig. 1 E–G), estimated through the historical relationship between a climate variable and a socioeconomic impact (4). With the relationship between climate and an impact established through the dose–response function, future impacts are determined by 1) estimating the projected change in climate using CGCM simulations and 2) using the dose–response function to calculate the future change in the impact of interest. Other approaches to modeling future climate impacts, such as process-based or top-down models, may use climate projections at different stages of the projection of damages (29); climate uncertainty may therefore propagate differently than through dose–response functions. In process-based crop models in particular, recent studies have shown substantial influences of internal variability in projections of future crop yields in Sub-Saharan Africa (30) and Canada (31).
Fig. 1.
We investigate the importance of internal variability by revisiting three classic dose–response functions. We selected studies with three different common shapes of dose–response functions, providing a broad survey of the possible effects of internal variability on impact uncertainty. For ease of comparison, we chose dose–response functions that all relate an impact variable to temperature over CONUS, calculated at the county level. While the current state-of-the-art dose–response functions often use multiple climate variables as inputs and evolve in time to account for changes in adaptation (4, 6), focusing on simple, stationary functions of temperature applied to a constant population distribution allows for clear interpretation of the decomposed climate uncertainty. Specifically, we selected the U-shaped relationship between mortality and temperature of ref. 32 (Fig. 1E); the roughly decreasing relationship between GDP per capita and temperature of ref. 33 (Fig. 1F); and the cutoff-style relationship between corn yield and temperature, where yield rapidly decreases with temperature after a threshold temperature is exceeded, of ref. 34 (Fig. 1G).
Using the LE multimodel archive, we construct early (2010 to 2039), middle (2040 to 2069), and late (2070 to 2099) 21st century projections of daily temperature by adding the relative change in monthly mean temperature from the LE simulations to 30 y of daily ERA-Interim reanalysis data (1980 to 2009) (35). This projection method accounts for annual mean temperature change as well as any changes to the seasonal cycle but not changes in the distribution of daily temperature within a month (36, 37). The changes to the daily temperature distribution are not explored here as not all LEs in the study provide daily temperature projections. Incorporating the daily temperature distribution changes will likely not affect the CONUS results presented here as internal variability is dominated by longer-term trend uncertainty (20). However, these changes may be more important to include in regions of lower trend internal variability.
To construct impact projections of mortality, per capita GDP, and corn yield changes, we input the differences between future temperature projections and historical temperature records into the dose–response functions of (32–34), respectively. A CONUS-wide impact is calculated for each ensemble member by the weighted average over all counties where the weighting is by county population for mortality and per capita GDP and by historical average corn yield for corn yield. Internal variability is estimated as the mean of the impact variances for each model, while the intermodel uncertainty is estimated as the variance of the ensemble means of each calculated impact.
Since most of the models in the LE archive were only run using a single future greenhouse gas scenario—the Representative Concentration Pathway 8.5 (RCP8.5) high baseline emissions scenario (38)—another method must be used to determine the scenario uncertainty of the projected impacts. Following current best practices in LE studies, we estimate the scenario uncertainty as the variance across scenarios of the multimodel mean across models from the fifth phase of the Coupled Model Intercomparison Project (CMIP5), using all CMIP5 models which have data for the RCP2.6, RCP4.5, RCP6.0, and RCP8.5 scenarios (39). Following ref. 40, we alternatively calculate scenario uncertainty using the Max Planck Institute’s (MPI) Earth System Model (MPI-ESM), the only LE in the sample with data from RCP2.6 and RCP4.5 in addition to RCP8.5 and the LE best replicating CONUS internal variability (41), and highlight results where relevant.
Results
Our projections of mortality, GDP, and corn yield changes due to climate change are similar in magnitude to the original estimates of refs. 32–34. Each of these studies originally underestimated the full uncertainty in their projections, by using only one run from one model and therefore ignoring all three sources of uncertainty (32), by incorporating scenario but not model or internal uncertainty (34), and by incorporating model but not scenario or internal uncertainty (33).
The total climate uncertainty in each aggregated impact over CONUS grows throughout the 21st century (Fig. 1 L–N), as would be expected as greenhouse gas emissions scenarios diverge, increasing scenario uncertainty, and growing differences in inputs from historical baselines enhance the differentiation between models, increasing model uncertainty. We see an increase in the variance of climate uncertainty from early to late 21st century by a factor of 35 for mortality, 16 for GDP, and 14 for corn yield. This growth in uncertainty is largely due to increases in model and scenario uncertainties, with uncertainty due to internal variability remaining approximately constant over time for projections of each of the three impacts.
Internal variability is particularly important in projections of strongly nonlinear impacts over 2010 to 2039 such as mortality (57% of climate uncertainty; Fig. 1I and SI Appendix, Table S1, top three rows) and corn yields (37% of climate uncertainty; Fig. 1K and SI Appendix, Table S1, bottom three rows). Even for a relatively linear dose–response function such as GDP, internal variability plays a considerable role in early-century projections, underscoring the need to account for internal variability for projections made on scales of years to a few decades. Conditioned on the RCP8.5 scenario that forced the LE runs, internal variability continues to make up 6 to 13% of the joint model–internal uncertainty by midcentury and 4 to 7% by the end of the century.
The climate uncertainty partitioning is different for each of the three impact projections. By the end of the 21st century, impact projection uncertainty is largely driven by model and scenario uncertainty. The relative weight of the three sources of uncertainty in impact projections is determined by the shape of the dose–response function, despite uncertainty in mean CONUS temperature change projections being dominated by scenario uncertainty (SI Appendix, Fig. S1). The mortality dose–response function, which features a turning point toward the middle of the historical temperature distribution (Fig. 1E), is particularly affected by model uncertainty well into the 21st century. Small differences in exposure to temperatures on either side of the turning point in any scenario can have large consequences in the CONUS average for the balance between counties with expected increases and those with expected decreases in mortality.
The climate uncertainty partitioning of each impact projection is different from the climate uncertainty partitioning in mean temperature (SI Appendix, Fig. S1). In particular, uncertainty due to internal variability is greater in each of the three impact projections than in temperature, demonstrating how a small contribution of internal variability to total climate variability for raw temperature does not imply that internal variability can be ignored in an impact projection that depends on temperature.
The projection of climate impacts interacts with internal variability in complex and often nonintuitive ways. This is illustrated through the ensemble members of the Community Earth System Model version 1 and Community Atmosphere Model version 5 (CESM1-CAM5) that project the highest and lowest mortality change between the historical and midcentury time periods (Fig. 2). Both ensemble members have similar changes in CONUS mean temperature (Fig. 2A). However, geographic (Fig. 2 C and D) and seasonal (SI Appendix, Fig. S2) variability in trends produce nearly opposite patterns of changes in mortality rates compared to the ensemble mean change (Fig. 2 F and G), with the greatest variability found in the Upper Midwest and Texas in this model (SI Appendix, Fig. S3). The ensemble member with the highest mortality change has particularly high increases in mortality rates in eastern CONUS, while the member with the lowest change projects particularly low midcentury mortality rates in south-central and eastern CONUS. When accounting for the spatial distribution of population, we project 7,900 additional annual heat-related deaths in the highest mortality ensemble member by midcentury compared to the 1980 to 2009 average and 4,300 fewer deaths in the ensemble member with lowest projected mortality. These represent an increase of 0.3% and a decrease of 0.2%, respectively, relative to 2.7 million total deaths in CONUS in 2015 (42) (data are from the Multiple Cause of Death files, 1999–2020, as compiled from data provided by the 57 vital statistics jurisdictions through the Vital Statistics Cooperative Program). Thus, the dominant sources of climate uncertainty in a projected impact depend on both the dominant source of climate uncertainty in each county-level impact as well as the spatial distribution of the population affected. Critically, this population distribution may not overlap with the areas of greatest climate uncertainty.
Fig. 2.
A large portion of model uncertainty, particularly in projections of mortality, is due to the outlier Geophysical Fluid Dynamics Laboratory CM3 model (GFDL-CM3) (Fig. 3 and SI Appendix, Fig. S4), which projects particularly strong warming during the summer over much of CONUS. That is, GFDL-CM3 projects a substantial shift in the shape of the average seasonal cycle not found in other models (SI Appendix, Figs. S5 and S6). These differences are less pronounced when mean temperature is weighted by historical corn yields, explaining the lower discrepancy between variability calculations with or without GFDL-CM3 in corn yield projections (SI Appendix, Figs. S4 and S5). Although the global warming response to increased greenhouse gas concentrations in GFDL-CM3 falls within the limit of plausible climate sensitivities based on our current understanding of historical and paleoclimate records and emergent constraints (43), many aspects of the model’s performance over CONUS have not yet been evaluated. Removing GFDL-CM3 from the variability partitioning calculation increases the relative importance of internal variability in all three impact projections (SI Appendix, Fig. S7 G–I). Further subsetting to the four models that best replicate the internal and forced response over North America [MPI-ESM, CESM1-CAM5, the Canadian Earth System Model, version 2 (CanESM2), and the GFDL-ES2M model (41)] does not substantially change the absolute magnitude of internal variability but further decreases the relative importance of model uncertainty (SI Appendix, Fig. S7 J–L), as would be expected from selecting models based on a common, observational target.
Fig. 3.
The partitioning of climate uncertainty in each impact is robust to ensemble size as shown by repeating the calculation with 16 ensemble members per model, the number of runs in the smallest ensemble (SI Appendix, Fig. S7 D–F). This suggests that 16 ensemble members are sufficient to sample the internal variability of relevance to these dose–response functions over CONUS. Similar results have been found in projections of trends of climate variables alone; ref. 44, for example, showed that 10 ensemble members may be enough to sample the spread of mean temperatures in the middle of the CONUS region. Note that substantially more ensemble members may be needed to fully sample internal variability in regions with larger and more complex patterns of internal variability.
Since most LEs in the sample only have output from the RCP8.5 scenario, scenario uncertainty is calculated using output from CMIP5 models (39). However, scenario uncertainty is similar when calculated using MPI-ESM, the one LE in the sample with data from multiple scenarios (SI Appendix, Fig. S2 M–O).
Decomposing the projected mortality uncertainty spatially shows that internal variability is more substantial in certain regions of CONUS (Fig. 4 A–C and SI Appendix, Fig. S8). Notably, internal variability accounts for around 50% of the total climate uncertainty in the midcentury projection of mortality in the northern Midwest, a region known to exhibit large uncertainty due to internal variability in temperature trends (20). The GDP (Fig. 4 D–F and SI Appendix, Fig. S9) and corn yield (Fig. 4 G–I and SI Appendix, Fig. S10) impacts show similar spatial inhomogeneities but with less contribution from internal variability, as expected from their CONUS-average values. In general, regional differences in variability may be masked by spatial averages of impact estimates.
Fig. 4.
The spatial distribution of uncertainty also highlights why scenario uncertainty is less important in end-of-century projections of mortality than in projections of corn yields or GDP per capita. The dose–response function has a turning point close to the middle of the temperature distribution, and the various scenarios are approximately centered on this turning point. As a result, in each projection scenario, some counties are expected to experience decreases in mortality due to a reduction in exposure to extreme cold that outweighs the increase in exposure to extreme heat, and vice versa. The geographic area where both effects cancel each other out is visible as the counties with nearly no relative contribution to uncertainty from scenario uncertainty in Fig. 4C.
We note that the dose–response functions themselves have uncertainty arising from drawing a statistical relationship between climate and socioeconomic outcome. Each of the three dose–response functions used in this study was published with statistical uncertainty estimates. As this study focuses on the role of internal variability in total climate uncertainty, the additional uncertainty added by the dose–response uncertainty was not investigated. However, climate uncertainty tends to be a substantial, if not the dominant source of uncertainty in many impact projections (see, e.g., ref. 2 or figure S7 in ref. 5).
Discussion
We have investigated the sources of climate uncertainty in projections of mortality, GDP per capita, and corn yields over CONUS using dose–response functions from the literature and have found that previously unaccounted for internal variability can have a substantial influence on uncertainty in future climate impact projections. While results will differ based on timescale, shape of dose–response function, and location as shown, internal variability is particularly impactful in 1) early-century to midcentury impacts, 2) impacts with dose–response functions that exhibit turning points close to the center of the historical climate distribution, and 3) impact studies in regions where natural variability in historical climate patterns or trends is a bigger component of the climate signal.
We have focused specifically on climate impact studies based on the estimation of dose–response functions using historical data. Internal variability is likely to also be relevant to other methods of estimating the impacts of climate change, such as process-based models, Integrated Assessment Models, or top-down approaches, although given their different relationship with climate inputs, more research may be needed to fully understand how climate uncertainty propagates through their impact projection processes. Furthermore, this study is limited to simple functions of temperature in CONUS. Studies focusing on other regions or the impacts of different climate variables may be affected by a different partitioning of the three sources of climate uncertainty. Other regions may see a lower contribution from internal variability as CONUS is a known region of high internal variability in temperature (20, 21). Uncertainty in precipitation trends is known to depend more on internal variability than temperature trends in many regions of the world (45, 46); future studies should investigate the relative role internal variability plays in these other domains as well. The impact projections that we investigated also do not account for future changes in adaptation behavior or geographical shifts in population or cropped areas; climate uncertainty would interact with these changes in complex ways since future changes in distributions of impact variability depend in turn on future climate states.
In the three projections evaluated here, the relative contribution of internal variability to impact climate uncertainty is generally greater than the corresponding relative contribution of internal variability to uncertainty in temperature. Therefore, decompositions of climate uncertainty in mean temperature and precipitation projections such as refs. 3, 39 may not be sufficient to justify excluding climate variability uncertainty from impact projection studies.
Uncertainty in the future impacts of climate change is not necessarily reduced by CGCM improvements alone (3). For projections on near-term, decision-relevant timescales that involve climate impacts with strongly nonlinear relationships with climate variables or impacts in parts of the world with significant present-day climate variability, the most important source of uncertainty may be unrelated to climate change but instead arise from the internal, existing variability of the climate system. Conversely, for end-of-century projections, involving variables with fairly linear relationships with climate variables, and for impacts in parts of the world with low existing variability, the most important source of uncertainty may be scenario uncertainty, i.e., uncertainties in human collective decision-making.
Generally, impact projection studies should account for uncertainty due to internal variability when at least one of the three conditions above is met. Including internal variability is increasingly feasible with the larger size of CMIP6 historical and projection ensembles, in addition to the multimodel LE archive used in this study. However, the additional computational and software development costs to include internal variability can be substantial, which may be inefficient if the climate uncertainty of an impact is dominated by model and/or scenario uncertainty at the timescales or location of interest. By including all relevant sources of climate uncertainty, impact projections better represent worst-case outcomes that can be prepared for or prevented through climate adaptation and mitigation.
Materials and Methods
Climate Data.
Multimodel LE archive.
We use all seven models that provide output from 1950 to 2100 and contain ensembles of at least 16 members from the multimodel LE archive (SI Appendix, Table S3, and table 1 of ref. 21). Each model is forced with historical forcings from 1950 to 2005 and RCP8.5 forcings from 2006 to 2100. We use monthly near-surface air temperature from each ensemble member of each model. We use monthly data since not all models saved output at a higher temporal resolution.
CMIP5 models.
To characterize scenario uncertainty, we use 14 models from CMIP5 (47) (SI Appendix, Table S4). We use every model that had available near-surface monthly temperature output for all four 21st-century scenarios [RCP2.6, RCP4.5, RCP6.0, and RCP8.5 (38)]. Note that this selection of models includes several which have LE configurations that are included in this study (GFDL-CM3, GFDL-ESM2M, and the Commonwealth Scientific and Industrial Research Organization’s [CSIRO] Mk3.6 model [CSIRO-Mk3.6.0].
Historical climate data.
We use daily mean, maximum, and minimum near-surface air temperature data from “ERA-Interim” (35) from 1980 to 2009 to characterize historical temperature over CONUS. Mean temperature is used for calculating mortality and GDP impacts, and maximum and minimum temperature are used to calculate corn yield impacts.
Building Climate Projections.
We develop a series of climate projections for each climate model and ensemble member to quantify the uncertainty in future projections of climate impacts. Daily temperature projections are made with the delta method (48, 49) (sometimes also known as the change factor method), which assumes that model changes are less biased in absolute terms than model mean states. All calculations occur for each pixel separately. First, 1980 to 2009 “ERA-Interim” daily temperature at all pixels covering CONUS are regridded to each model’s grid to create , the base period temperature time series for day d in month m for a particular model. Then, temperature projections Tf are constructed as follows for each future time period :where is a given model run’s 1980 to 2009 average temperature for month m across all years and is a given model’s average temperature for month m across all years in time period f. Then Tf is a 30-y time series of daily temperature, projected from the historical time period by changes in monthly average temperatures taken from a particular run from an LE or a CMIP5 model. These projections are repeated for each run in each LE and for each CMIP5 model, creating an ensemble of future temperature projections over CONUS.
[1]
Using the method above, we create future projections of the mean, minimum, and maximum daily near-surface air temperature. Since most LEs used in this study did not save minimum or maximum air temperature, we project both of these variables by the change in the mean daily temperature.
This projection method accounts for annual mean temperature change as well as any changes to the seasonal cycle. However, it ignores well-known changes in the shape of the daily temperature distributions (36, 37), which are not considered here as many of the CGCM LEs used in this study only published monthly data.
Dose–Response Functions.
The dose–response functions used are the estimates as given in the studies on mortality (32), GDP per capita (33), and corn yield (34). We use the methodologies of each original dose–response function project to convert differences in temperature time series into projections of climate impacts; a summary of these methodologies is reproduced here for convenience.
Mortality.
The mortality dose–response function of ref. 32 is based on 10 F-wide temperature bins from less than 10 F to more than 90 F. For each pixel, the change in the number of days per year in each temperature bin between the historical and a given future time period is dotted into the dose–response function to get the change in annual mortality rate/100,000. After this change in mortality rate is aggregated to the county level, the total CONUS mortality change is calculated as the sum across counties of the product of the change in mortality rate and the population in each county. We use the total population in each county in 2015 from the SEER database (50).
GDP per Capita.
The GDP per capita dose–response of ref. 33 is based on 3 C-wide temperature bins from less than C to more than 30 C. For each pixel, the change in the number of days per year in each temperature bin between the historical and a given future time period is dotted into the dose–response function to get the log change in annual GDP per capita. After this change is aggregated to the county level, the total CONUS GDP per capita change is calculated as the population-weighted average of each county’s GDP change across all counties.
We use 2015 GDP per capita for counties from the Bureau of Economic Analysis’s County-Level GDP estimates (51).
Corn Yields.
We use the piecewise linear formulation of the corn yield–temperature dose–response function of ref. 34 (e.g., the red line in figure 1A of ref. 34). As in that study, we model the progression of daily temperature by fitting a sinusoidal between the minimum and maximum temperature (discretized using 15 points per day). The impact calculation is similar to that of mortality and GDP above, although additionally scaled by the number of points used to discretize daily temperature distributions.
We use corn yields from the US Department of Agriculture’s National Agricultural Statistical Service’s county-level corn yields database (52) and take the average corn yield per county from 1979 to 2010.
We report the average change in county-level corn yields for CONUS by aggregating across counties with corn production in the sample and weighting by this county-level corn production. We follow ref. 34 and report results in percent change over the historical period.
Projecting Impacts.
Each impact projection is calculated at the pixel level before aggregating to counties; e.g., we create projections of changes in mortality rate for each pixel. This is done to minimize distortions that may occur upon geographical aggregation and to preserve the within-county temperature variation.
We then aggregate changes in mortality rate, GDP per capita, and corn yield to the county level by, for each county, area-averaging all pixels that overlap with the given county, weighted by the area overlapping between each pixel and the county. CONUS-wide estimates of changes in mortality, GDP per capita, and corn yields are then calculated by aggregating results across all counties, weighting by county-level population (for mortality and GDP per capita) or corn yields.
A single estimate for the change in an impact variable is calculated for each run in each model for the entire CONUS by aggregating county-level results.
Partitioning Climate Uncertainty in Impact Projections.
Climate uncertainty is calculated as the variance across estimates for total CONUS mortality, GDP per capita, and corn yield changes, following the partitioning methodology of ref. 3. Estimates are calculated for each run in each LE (RCP8.5) and for each CMIP5 model in the sample for each scenario (RCP2.6, RCP4.5, RCP6.0, and RCP8.5).
Internal Uncertainty.
Internal uncertainty is calculated as the mean across LEs of each LE’s variance of outcomes across runs.
Model Uncertainty.
Model uncertainty is calculated as the variance across LEs of each LE’s mean of outcomes across runs.
Scenario Uncertainty.
Since most LEs were only run on one scenario due to computational constraints, we follow refs. 3, 39 and estimate scenario uncertainty using a range of CMIP5 models. Many of the LEs used in this sample are versions of the models submitted to the CMIP5 project; CMIP5 models therefore provide a reasonable estimate of the scenario uncertainty that LEs would show. Scenario uncertainty is calculated as the variance across scenarios of the mean outcome across CMIP5 models for each scenario. In SI Appendix, Fig. S7 M–O, we alternatively show scenario uncertainty calculated using the MPI-ESM LE, which had saved output for the RCP2.6 and RCP4.5 scenarios in addition to RCP8.5, as was done by, e.g., ref. 40. In this case, scenario uncertainty is calculated as the variance across scenarios of the mean outcome across MPI-ESM ensemble members.
Data, Materials, and Software Availability
Source code and raw data has been deposited to Mendeley (https://data.mendeley.com/datasets/48m4scp8jx/1) (53). The most up-to-date code is available on GitHub at https://github.com/ks905383/iv_impacts (54).
Acknowledgments
We thank the editor and two anonymous reviewers for their constructive comments that improved the presentation of this work. We are grateful for thoughtful comments from James Rising, Mingfang Ting, Kate Marvel, Tom Bearpark, Corey Lesk, Gernot Wagner, and the Large Ensemble community. We also thank the US Climate and Ocean: Variability, Preditability, and Change (US CLIVAR) Working Group on Large Ensembles for coordinating the multimodel LE experiment and making the data public.
Supporting Information
Appendix 01 (PDF)
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L. Suarez-Gutierrez, S. Milinski, N. Maher, Exploiting large ensembles for a better yet simpler climate model evaluation. Clim. Dyn. 57, 2557–2580 (2021).
23
H. Nissan et al., On the use and misuse of climate change projections in international development. Wiley Interdiscip. Rev. Clim. Change 10, e579 (2019).
24
S. Hallegatte, Strategies to adapt to an uncertain climate change. Glob. Environ. Change 19, 240–247 (2009).
25
S. Hallegatte, A. Shah, R. Lempert, C. Brown, S. Gill, “Investment decision making under deep uncertainty—Application to climate change” (Policy Research Working Papers, The World Bank, 2012). https://ssrn.com/abstract=2143067. Accessed 23 September 2022.
26
C. Proistosescu, G. Wagner, Uncertainties in climate and weather extremes increase the cost of carbon. One Earth 2, 515–517 (2020).
27
R. W. Katz, B. G. Brown, Extreme events in a changing climate: Variability is more important than averages. Clim. Change 21, 289–302 (1992).
28
R. L. Revesz et al., Global warming: Improve economic models of climate change. Nature 508, 173–175 (2014).
29
F. Piontek et al., Integrated perspective on translating biophysical to economic impacts of climate change. Nat. Clim. Chang. 11, 563–572 (2021).
30
A. Dale, C. Fant, K. Strzepek, M. Lickley, S. Solomon, Climate model uncertainty in impact assessments for agriculture: A multi-ensemble case study on maize in sub-Saharan Africa. Earths Future 5, 337–353 (2017).
31
B. Qian et al., Quantifying the uncertainty introduced by internal climate variability in projections of Canadian crop production. Environ. Res. Lett. 15, 074032 (2020).
32
O. Deschênes, M. Greenstone, Climate change, mortality, and adaptation: Evidence from annual fluctuations in weather in the US. Am. Econ. J. Appl. Econ. 3, 152–185 (2011).
33
T. Deryugina, S. M. Hsiang, “Does the environment still matter? Daily temperature and income in the United States” (National Bureau of Economic Research, Working Paper 20750, 2014). https://www.nber.org/papers/w20750. Accessed 23 September 2022.
34
W. Schlenker, M. J. Roberts, Nonlinear temperature effects indicate severe damages to U.S. crop yields under climate change. Proc. Natl. Acad. Sci. U.S.A. 106, 15594–15598 (2009).
35
D. P. Dee et al., The ERA-Interim Reanalysis: Configuration and Performance of the Data Assimilation System. Q. J. R. Meteorol. Soc. 137, 553–97 (2011).
36
M. A. Haugen, M. L. Stein, E. J. Moyer, R. L. Sriver, Estimating changes in temperature distributions in a large ensemble of climate simulations using quantile regression. J. Clim. 31, 8573–8588 (2018).
37
M. A. Haugen, M. L. Stein, R. L. Sriver, E. J. Moyer, Future climate emulations using quantile regressions on large ensembles. Adv. Stat. Climatol. Meteorol. Oceanogr. 5, 37–55 (2019).
38
D. P. van Vuuren et al., The representative concentration pathways: An overview. Clim. Change 109, 5–31 (2011).
39
F. Lehner et al., Partitioning climate projection uncertainty with multiple large ensembles and CMIP5/6. Earth Syst. Dyn. 11, 491–508 (2020).
40
N. Maher, F. Lehner, J. Marotzke, Quantifying the role of internal variability in the temperature we expect to observe in the coming decades. Environ. Res. Lett. 15, 054014 (2020).
41
L. Suarez-Gutierrez, N. Maher, S. Milinski, Evaluating the internal variability and forced response in Large Ensembles. US CLIVAR Var. 18, 27–35 (2020).
42
Centers for Disease Control and Prevention, National Center for Health Statistics, National Vital Statistics System, Mortality 1999–2020, CDC WONDER Online Database (2021). https://wonder.cdc.gov/. Accessed 4 August 2022.
43
S. C. Sherwood et al., Aln assessment of Earth’s climate sensitivity using multiple lines of evidence. Rev. Geophys. 58, e2019RG000678 (2020).
44
S. Milinski, N. Maher, D. Olonscheck, How large does a large ensemble need to be? Earth Syst. Dyn. 11, 885–901 (2020).
45
A. Dai, C. E. Bloecker, Impacts of internal variability on temperature and precipitation trends in large ensemble simulations by two climate models. Clim. Dyn. 52, 289–306 (2019).
46
R. R. Wood, F. Lehner, A. G. Pendergrass, S. Schlunegger, Changes in precipitation variability across time scales in multiple global climate model large ensembles. Environ. Res. Lett. 16, 084022 (2021).
47
K. E. Taylor, R. J. Stouffer, G. A. Meehl, An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93, 485–498 (2011).
48
E. Hawkins, T. M. Osborne, C. K. Ho, A. J. Challinor, Calibration and bias correction of climate projections for crop modelling: An idealised case study over Europe. Agric. For. Meteorol. 170, 19–31 (2013).
49
J. Diaz-Nieto, R. L. Wilby, A comparison of statistical downscaling and climate change factor methods: Impacts on low flows in the River Thames, United Kingdom. Clim. Change 69, 245–268 (2005).
50
National Cancer Institute, Surveillance, Epidemiology, and End Results (SEER) program populations (1969–2019) (2021). https://seer.cancer.gov/. Accessed 22 March 2022.
51
US Bureau of Economic Analysis, CAGDP1 gross domestic product (GDP) summary by county and metropolitan area (2021). https://apps.bea.gov/itable/iTable.cfm?ReqID=70&step=1&acrdn=5. Accessed 28 February 2022.
52
National Agricultural Statistics Service, USDA, 1979–2010 NASS corn yields (2019). https://quickstats.nass.usda.gov. Accessed 27 July 2021.
53
K. Schwarzwald, N. Lenssen, Dataset - Climate uncertainty in climate impact studies. Mendeley Data. V1. https://data.mendeley.com/datasets/48m4scp8jx/1. Deposited 19 September 2022.
54
K. Schwarzwald, IV Impacts. GitHub. https://github.com/ks905383/iv_impacts. Deposited 5 August 2022.
Information & Authors
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Copyright © 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
Data, Materials, and Software Availability
Source code and raw data has been deposited to Mendeley (https://data.mendeley.com/datasets/48m4scp8jx/1) (53). The most up-to-date code is available on GitHub at https://github.com/ks905383/iv_impacts (54).
Submission history
Received: May 10, 2022
Accepted: August 18, 2022
Published online: October 10, 2022
Published in issue: October 18, 2022
Keywords
Acknowledgments
We thank the editor and two anonymous reviewers for their constructive comments that improved the presentation of this work. We are grateful for thoughtful comments from James Rising, Mingfang Ting, Kate Marvel, Tom Bearpark, Corey Lesk, Gernot Wagner, and the Large Ensemble community. We also thank the US Climate and Ocean: Variability, Preditability, and Change (US CLIVAR) Working Group on Large Ensembles for coordinating the multimodel LE experiment and making the data public.
Notes
This article is a PNAS Direct Submission.
Authors
Competing Interests
The authors declare no competing interest.
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The importance of internal climate variability in climate impact projections, Proc. Natl. Acad. Sci. U.S.A.
119 (42) e2208095119,
https://doi.org/10.1073/pnas.2208095119
(2022).
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Figures
Fig. 1.
Climate uncertainty in the projections of climate impacts. (A–H) Dose–response functions (E–G) relate a variable of societal interest to historical climate distributions (D and H, showing the 1980 to 2009 county-level population-weighted and corn yield–weighted temperature distributions, respectively), thereby estimating an exposure to the impact (A–C, blue line). Future projections of impact variables are constructed by inputting future temperature projections (D and H, red line, representing the average distribution across all LE runs), leading to exposure to a future impact distribution (A–C, red line, representing the average impact across all LE runs). However, future temperatures are uncertain (D and H, red filled region showing range of future temperature distributions across all runs of all LEs, representing internal and model uncertainty), leading to uncertainty in impacts projections (A–C, red filled region). (I–N) This climate uncertainty can be decomposed into contributions from internal (orange), scenario (green), and model (blue) uncertainty, which are shown as relative (I–K; values in SI Appendix, Table S1) and absolute variances (L–N; values in SI Appendix, Table S2). Internal variability is substantial in the early 21st century (I–K, left column), especially for projections of mortality and corn yields, while model (for mortality) or scenario (for GDP per capita and corn yields) uncertainty dominates by the end of century (I–K, right column). Internal variability remains roughly constant in absolute terms throughout the century, while model and scenario uncertainty increase over time (L–N).
Fig. 2.
Example of how internal uncertainty propagates through projections of changes in heat-related mortality CESM1-CAM5. This figure shows the ensemble mean change in temperature (black line in A and B) and mortality rate (E; 1,300 additional annual deaths vs. historical average), the same for the ensemble member projecting the highest mortality in midcentury (7,900 additional annual deaths vs. historical average; red in A, shown in C and F), and the same for the ensemble member projecting the lowest mortality in midcentury (4,300 fewer annual deaths vs. historical average; blue in A, shown in D and G). Note the different ranges on the color bar between the ensemble mean (B and E) and the relative changes (C, D, F, and G). Variability in trends is produced by both seasonal (SI Appendix, Fig. S2) and geographic (C and D; SI Appendix, Fig. S3) differences.
Fig. 3.
Histogram of projections of heat-related mortality changes in CONUS across LEs by the (A) early (2010 to 2039), (B) middle (2040 to 2069), and (C) late (2070 to 2099) 21st century, compared to the 1980 to 2009 period. Each dot represents a projection constructed from a single LE run, colored by model. Figure shows internal variability as the spread of dots of a single color and intermodel variability as the spread between dots of different colors. Internal variability dominates at the start of the century, i.e., the spread of dots of a given color is similar to the spread of all runs (A), while intermodel variability dominates by the end of the century. GFDL-CM3 is an outlier due to its unique shifts in its seasonal cycle in CONUS (SI Appendix, Figs. S5 and S6).
Fig. 4.
A spatial decomposition of the three sources of climate uncertainty on (A–C) mortality, (D–F) per capita GDP, and (G–I) corn yield impacts for 30-y periods in early (A, D, and G), middle (B, E, and H), and late (C, F, and I) 21st century projections. The band of counties in end-of-century mortality projections dominated by model uncertainty reflect the turning point in the dose–response function of ref. 32; in counties north of this band, mortality is expected to decrease, while in counties south of this strip, mortality is expected to increase. Blank counties in G–I had no corn production reported in the National Agricultural Statistics Service database from 1979 to 2010. See SI Appendix, Figs. S8–S10, for maps showing the magnitude of each individual source of uncertainty.
Tables
Media
References
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S. Hallegatte, Strategies to adapt to an uncertain climate change. Glob. Environ. Change 19, 240–247 (2009).
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S. Hallegatte, A. Shah, R. Lempert, C. Brown, S. Gill, “Investment decision making under deep uncertainty—Application to climate change” (Policy Research Working Papers, The World Bank, 2012). https://ssrn.com/abstract=2143067. Accessed 23 September 2022.
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C. Proistosescu, G. Wagner, Uncertainties in climate and weather extremes increase the cost of carbon. One Earth 2, 515–517 (2020).
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R. W. Katz, B. G. Brown, Extreme events in a changing climate: Variability is more important than averages. Clim. Change 21, 289–302 (1992).
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R. L. Revesz et al., Global warming: Improve economic models of climate change. Nature 508, 173–175 (2014).
29
F. Piontek et al., Integrated perspective on translating biophysical to economic impacts of climate change. Nat. Clim. Chang. 11, 563–572 (2021).
30
A. Dale, C. Fant, K. Strzepek, M. Lickley, S. Solomon, Climate model uncertainty in impact assessments for agriculture: A multi-ensemble case study on maize in sub-Saharan Africa. Earths Future 5, 337–353 (2017).
31
B. Qian et al., Quantifying the uncertainty introduced by internal climate variability in projections of Canadian crop production. Environ. Res. Lett. 15, 074032 (2020).
32
O. Deschênes, M. Greenstone, Climate change, mortality, and adaptation: Evidence from annual fluctuations in weather in the US. Am. Econ. J. Appl. Econ. 3, 152–185 (2011).
33
T. Deryugina, S. M. Hsiang, “Does the environment still matter? Daily temperature and income in the United States” (National Bureau of Economic Research, Working Paper 20750, 2014). https://www.nber.org/papers/w20750. Accessed 23 September 2022.
34
W. Schlenker, M. J. Roberts, Nonlinear temperature effects indicate severe damages to U.S. crop yields under climate change. Proc. Natl. Acad. Sci. U.S.A. 106, 15594–15598 (2009).
35
D. P. Dee et al., The ERA-Interim Reanalysis: Configuration and Performance of the Data Assimilation System. Q. J. R. Meteorol. Soc. 137, 553–97 (2011).
36
M. A. Haugen, M. L. Stein, E. J. Moyer, R. L. Sriver, Estimating changes in temperature distributions in a large ensemble of climate simulations using quantile regression. J. Clim. 31, 8573–8588 (2018).
37
M. A. Haugen, M. L. Stein, R. L. Sriver, E. J. Moyer, Future climate emulations using quantile regressions on large ensembles. Adv. Stat. Climatol. Meteorol. Oceanogr. 5, 37–55 (2019).
38
D. P. van Vuuren et al., The representative concentration pathways: An overview. Clim. Change 109, 5–31 (2011).
39
F. Lehner et al., Partitioning climate projection uncertainty with multiple large ensembles and CMIP5/6. Earth Syst. Dyn. 11, 491–508 (2020).
40
N. Maher, F. Lehner, J. Marotzke, Quantifying the role of internal variability in the temperature we expect to observe in the coming decades. Environ. Res. Lett. 15, 054014 (2020).
41
L. Suarez-Gutierrez, N. Maher, S. Milinski, Evaluating the internal variability and forced response in Large Ensembles. US CLIVAR Var. 18, 27–35 (2020).
42
Centers for Disease Control and Prevention, National Center for Health Statistics, National Vital Statistics System, Mortality 1999–2020, CDC WONDER Online Database (2021). https://wonder.cdc.gov/. Accessed 4 August 2022.
43
S. C. Sherwood et al., Aln assessment of Earth’s climate sensitivity using multiple lines of evidence. Rev. Geophys. 58, e2019RG000678 (2020).
44
S. Milinski, N. Maher, D. Olonscheck, How large does a large ensemble need to be? Earth Syst. Dyn. 11, 885–901 (2020).
45
A. Dai, C. E. Bloecker, Impacts of internal variability on temperature and precipitation trends in large ensemble simulations by two climate models. Clim. Dyn. 52, 289–306 (2019).
46
R. R. Wood, F. Lehner, A. G. Pendergrass, S. Schlunegger, Changes in precipitation variability across time scales in multiple global climate model large ensembles. Environ. Res. Lett. 16, 084022 (2021).
47
K. E. Taylor, R. J. Stouffer, G. A. Meehl, An overview of CMIP5 and the experiment design. Bull. Am. Meteorol. Soc. 93, 485–498 (2011).
48
E. Hawkins, T. M. Osborne, C. K. Ho, A. J. Challinor, Calibration and bias correction of climate projections for crop modelling: An idealised case study over Europe. Agric. For. Meteorol. 170, 19–31 (2013).
49
J. Diaz-Nieto, R. L. Wilby, A comparison of statistical downscaling and climate change factor methods: Impacts on low flows in the River Thames, United Kingdom. Clim. Change 69, 245–268 (2005).
50
National Cancer Institute, Surveillance, Epidemiology, and End Results (SEER) program populations (1969–2019) (2021). https://seer.cancer.gov/. Accessed 22 March 2022.
51
US Bureau of Economic Analysis, CAGDP1 gross domestic product (GDP) summary by county and metropolitan area (2021). https://apps.bea.gov/itable/iTable.cfm?ReqID=70&step=1&acrdn=5. Accessed 28 February 2022.
52
National Agricultural Statistics Service, USDA, 1979–2010 NASS corn yields (2019). https://quickstats.nass.usda.gov. Accessed 27 July 2021.
53
K. Schwarzwald, N. Lenssen, Dataset - Climate uncertainty in climate impact studies. Mendeley Data. V1. https://data.mendeley.com/datasets/48m4scp8jx/1. Deposited 19 September 2022.
54
K. Schwarzwald, IV Impacts. GitHub. https://github.com/ks905383/iv_impacts. Deposited 5 August 2022.
