Climate migration amplifies demographic change and population aging

Edited by William N. Adger, University of Exeter, Exeter, Devon, United Kingdom; received April 11, 2022; accepted October 16, 2022 by Editorial Board Member William C. Clark.
January 8, 2024
121 (3) e2206192119

Significance

We project climate migration driven by sea-level rise through 2100 in the United States, incorporating fertility and gravity effects to capture secondary population processes, which we call “demographic amplification.” Failure to include these indirect effects underestimates the demographic impact of climate migration. The demographic amplification of climate migrants results in 5.3 and 18 times the number of migrants. Because migration is most likely to occur in more youthful populations, areas experiencing accelerated climate out-migration could face accelerated population aging. In both origins and destinations, policies addressing sustainable growth management such as access to affordable housing, aging services, future public health needs, and infrastructure planning should incorporate demographic amplification to fully anticipate population changes and build a more sustainable future.

Abstract

The warnings of potential climate migration first appeared in the scientific literature in the late 1970s when increased recognition that disintegrating ice sheets could drive people to migrate from coastal cities. Since that time, scientists have modeled potential climate migration without integrating other population processes, potentially obscuring the demographic amplification of this migration. Climate migration could amplify demographic change—enhancing migration to destinations and suppressing migration to origins. Additionally, older populations are the least likely to migrate, and climate migration could accelerate population aging in origin areas. Here, we investigate climate migration under sea-level rise (SLR), a single climatic hazard, and examine both the potential demographic amplification effect and population aging by combining matrix population models, flood hazard models, and a migration model built on 40 y of environmental migration in the United States to project the US population distribution of US counties. We find that the demographic amplification of SLR for all feasible Representative Concentration Pathway-Shared Socioeconomic Pathway (RCP–SSP) scenarios in 2100 ranges between 8.6–28 M [5.7–53 M]—5.3 and 18 times the number of migrants (0.4–10 M). We also project significant aging of coastal areas as youthful populations migrate but older populations remain, accelerating population aging in origin areas. As the percentage of the population lost due to climate migration increases, the median age also increases—up to 10+ y older in some highly impacted coastal counties. Additionally, our population projection approach can be easily adapted to investigate additional or multiple climate hazards.
Thirty years ago, the Intergovernmental Panel on Climate Change (IPCC) raised concerns that climate change could “initiate large migrations of people” (1). Projections suggest that these large migrations could be more than 140 million people by 2050 (2), and up to 3 billion people could be left outside the human climate niche (3). The potential for widespread human migration in the face of climate change continues to be an adaptation policy priority (4).
Despite the importance of climate migration as an adaptation strategy (5), relatively few studies have attempted to model the demographic impact of climate migration. Previous attempts eschew two key considerations in modeling climate migration.
First, scientists generally model climate migrants as age-less and sex-less individuals (2, 68), omitting the well-established relationship between migration propensity and demographic characteristics (5, 9, 10). In particular, the near-universal age schedule of migration, with older populations being the least likely age groups to migrate and young adults the most likely (see Fig. 1 for the classic migration schedule), suggests that climate migration is most likely to occur among working-age adults. Significant climate migration literature focuses on migration among young, working-age adults (1114). Origin areas could experience accelerated population aging as younger populations migrate in response to climate change and older populations remain. For example, after Hurricane Katrina, those aged 70+ y were the least likely to evacuate New Orleans (15), and after Hurricane Maria, out-migration among working-age adults from Puerto Rico is rapidly aging the island (16). By omitting these well-established demographic relationships, the extent to which highly vulnerable communities could experience accelerated population aging from climate migration as more youthful populations migrate away remains underexplored.
Fig. 1.
The classic probability of migrating by age and median age in 2020 and 2100 for the whole United States. Dashed vertical lines are median ages in 2020 and 2100. Median age is based on Shared Socioeconomic Pathway 2 (20). The figure is generated using IPUMS-USA data (21). Barring any additional information, this curve suggests that migration will lessen as the US population ages this century.
Second, climate migration models lack the crucial demographic feedback loop whereby climate migrants alter the population trajectory in both their origin and destination. If climate change forces people to migrate, a potential domino effect could result, enhancing population growth in destination areas and suppressing population growth in hazardous origin areas (1719). Scientists rarely model this population compounding (see ref. 2 for a notable exception), and the extent to which climate migration will alter demographic futures remains unknown.
We call this demographic feedback loop “demographic amplification” or just “amplification” for short. Climate migration directly alters population growth rates and demographic characteristics by virtue of the migration itself. But these potential migrants further alter both growth rates and demographic characteristics by interacting and amplifying other demographic processes. For example, young migrants could start families in their new destinations (i.e., a fertility effect), shifting potential offspring from origins to destinations. Migrants could also shift additional nonclimate-related migrants from origins to destinations by virtue of population aggregation (i.e., a gravity effect). This shift in population necessitates changes in ancillary services such as doctors, construction workers, waiters, engineers, etc., making some locations more attractive and some locations less attractive. Thus, a complete accounting of climate migration captures the direct effect of climate migration itself, the indirect effect of potential family formation, and the indirect effect of population gravity. Taken together, climate migration amplifies the underlying demographic trajectories in origins and destinations both in the aggregate (population totals) and in characteristics (age, sex, etc.).
Sea-level rise (SLR) emerged as a potential driver of climate migration more than 40 y ago (22) due to the potential disintegration of antarctic ice sheets. Since those early warnings, SLR has remained one of the most costly and visible impacts of global climate change (2325). With the global coastal population projected to eclipse one billion people this century (26), SLR is expected to affect and, in many cases, displace hundreds of millions of people (6, 24), making it one of the largest potential sources of climate migration by the end of the century.
In this paper, we combine matrix population models, flood hazard models, and a migration model built on 40 y of environmental migration to project the United States’ county-level population distribution, accounting for anticipated demographic change, migration probabilities, and SLR. Many US geographies are redrawn with each decennial Census, making long-range projections difficult, except in areas with stable geographic boundaries. We use counties as our unit of analysis as these are the smallest spatial units with generally consistent geographic boundaries in the United States. This approach allows us to investigate the potential compounding or amplification of demographic change in both origin and destination communities and accelerated aging in coastal communities due to SLR.
To investigate climate migration, we produce three population projections using multiregional Leslie matrices that take the following general forms:
Base:Pt+1Base=StPtBase,Displacement:Pt+1Disp=MtyStPtBase,Amplification:Pt+1Amp=MtyStPtAmp,
[1]
where Pt + 1 is the population at time t + 1, St is a Leslie matrix containing the age–sex-specific probabilities of fertility and survival, and Mty is a matrix containing the proportion migrating from county to county under y amount of SLR. See Methods and SI Appendix for details.
Our “Base” population projection represents a projection agnostic to climate change or one without SLR impacts. “Displacement” represents a similar projection to those undertaken in the broader literature (e.g., refs. (6, 7) and (27)). This projection renders the displaced climate migrants demographically inert, preventing climate migrants from demographically interacting in their destinations.
Our Amplification population projection accounts for integrated population dynamics in origins and destinations. In this projection, we model climate migrants by age and sex within a demographically integrated projection model, allowing us to address the two limitations related to demographic compounding and potential aging effects in climate migration models.
We populate our matrices from multiple data sources. Pt comes from the National Vital Statistics System (NVSS) US Census Populations with Bridged Race Categories Dataset (https://seer.cancer.gov/popdata/download.html). St is populated with cohort-change ratios (CCRs) from the NVSS population data. Finally, migration research suggests that “climate migration” is likely to follow preexisting migration flows (28, 29), leveraging embedded social capital and kin networks in destination decision-making (5). Thus, Mty contains the proportion migrating from each county to each county based on the IRS county-to-county migration data (30) and adjusted to account for the h proportion of each county inundated by y SLR.
Mty reflects the percentage of population we anticipate will be displaced by SLR from a parsimonious displacement model. We arrive at this reduction with a simple, parsimonious model fit with US counties between 1980 and 2019 with verified large (>4σ) population declines (n = 48 such county-years). We use the Spatial Hazard Events and Losses Database for the United States (SHELDUS)—a county-level hazard dataset containing information about the direct losses (property and crop losses, injuries, and fatalities) caused by a hazard event (thunderstorms, hurricanes, floods, wildfires, tornadoes, flash floods, earthquakes, etc.)—to verify these large population declines. We estimate exposure to SLR as a percentage of the population in each county using a bathtub model of inundation based on the population-weighted area under Representative Concentration Pathways (RCPs) 2.6, 4.5, and 8.5 (for 2100 SLR amounts of 0.5 m [0.29–0.82], 0.59 [0.36–0.93], and 0.79 [0.52–1.2] 90th percentile prediction intervals). For simplicity and clarity, we report most results using RCP4.5.
Finally, Mty and St are projected using ARIMA(0,1,1) (St) and ETS (error, trend, seasonal models; Mty) to capture potential changes in demographic rates.

Results

We find that SLR could spur 0.4–10 M* people (Displacement model) to migrate between 2020 and 2100 under all feasible Representative Concentration Pathway-Shared Socioeconomic Pathway (RCP–SSP) scenarios (Figs. 2A and 3). The potential migration of 0.4–10 M people (Amplification model) leads to a demographic amplification of 5.7–53 M people. To illustrate the demographic amplification of SLR, RCP4.5–SSP2 manifests as 1.5 M people migrating to other places for a net demographic change of 1.5 M people (Displacement model). However, accounting for population dynamics under RCP4.5–SSP2 (Amplification model), the actual demographic impact of 1.5 M migrants is 15 M. This is due to two interacting effects: 1) a compounding or “domino effect” where destination counties attract more people over time and origin counties attract less and the interaction of migrants with the other demographic component processes of fertility and mortality. 2) This total demographic effect or amplification is considerably more pronounced than the simple displacement effect—10 times larger under RCP4.5–SSP2 and between 5.3 and 18 times larger under all feasible RCP–SSP combinations. Under all plausible RCP–SSP scenarios except RCP4.5–SSP3, SLR leads to a demographic amplification of at least 10 million persons (Table 1).
Fig. 2.
A comparison of Base, Displacement, and Amplification projections for all US coastal counties impacted by sea-level rise and other example counties over the next century. These projections use RCP4.5. Uncertainty reflects the 90th percentile prediction interval and the minimum/maximum SSP. We adopt the general climate migration typology as proposed by Marandi and Main (19) for the seven example counties. (A) compares the population trajectories for all US coastal counties impacted by SLR. Here, we can see the amplification effect of population processes and migration, driving the population much lower than what a simple displacement model suggests. (BD) are example destination counties using the framework of Marandi and Main (19). (E, F) are example vulnerable counties, showing significant declines earlier in the century. (G, H) are example recipient counties. The integrated demographic model (Amplification) exhibits significant amplification of the demographic trajectories, depending on the timing and extent of inundation.
Fig. 3.
Projected numeric change in population due to displacement (A) and amplified population processes (B) under the SSP2–RCP4.5 50th percentile in 2100. Counties in white have no projected change in population due to displacement or amplified population processes. These maps highlight the domino effect where climate migration further enhances migration to destinations and suppresses migration to origins.
Table 1.
RCP–SSP matrix for 2100 showing all feasible RCP–SSP combinations (31).
RCP SSP1SSP2SSP3SSP4SSP5
8.5SLR amount (meters)  0.79 [0.52–1.2]  
 Migrants (millions)    3.4 [1.3–10]
 Demographic amplification (millions)    28 [17–53]
4.5SLR amount (meters)  0.59 [0.36–0.93]  
 Migrants (millions)1.5 [0.65–4.2]1.5 [0.63–4.1]0.84 [0.36–2.3]1.2 [0.51–3.3]2.2 [0.96–6.2]
 Demographic amplification (millions)15 [10–27]15 [10–26]8.6 [5.7–15]12 [8–21]23 [15–41]
2.6SLR amount (meters)  0.5 [0.29–0.82]  
 Migrants (millions)1.2 [0.55–3.5]1.2 [0.54–3.4] 0.96 [0.44–2.8]1.8 [0.82–5.1]
 Demographic amplification (millions)14 [9.7–24]14 [9.5–24] 11 [7.6–19]21 [15–37]

Here, we compare the expected number of migrants with the demographic amplification for all reasonable RCP–SSP combinations. All numbers in parentheses are the 90th percentile prediction interval. Regardless of the RCP-SSP combination, matrix population models suggest that millions of people will shift in the United States due to sea-level rise.

Furthermore, Fig. 2 shows this population compounding effect for seven example counties following the general typology of climate migration put forth by Marandi and Main (19)—“vulnerable” to climate impacts with significant population losses, “recipient” counties that could receive some migrants, and “climate destinations” that might receive many migrants. Here, Fig. 2E and F are counties experiencing significant population declines over the entire time horizon (vulnerable counties). Our results for Miami-Dade, FL, under RCP4.5 suggest 28.3 K [4.4–204.2 K] migrants by 2100 but a total demographic impact of 243.9 K [72.9 K–1.1 M] fewer people. We see similar results for Dare, NC, as well (8.5 K [1.5–22.9 K] migrants and a 39.8 K [14.6–70.0 K] total demographic impact). Relatively small displacements can cascade into considerably larger demographic changes.
Fig. 2G and H are counties close to heavily threatened areas. We see two separate population trajectories and demonstrate the amplification of population change. McIntosh, GA, is initially a recipient county, as people from nearby heavily affected areas migrate into nearby counties. But as the century wears on, this recipient county turns into a vulnerable county, and out-migration begins to turn into negative population growth. The difference between the simple, Displacement model and the demographically integrated Amplification model suggests markedly different population growth trajectories. The Displacement model suggests that SLR migration in McIntosh will yield more population than the climate agnostic Base projection into the end of the century. Conversely, the Amplification model has the population greatly increasing before population growth turns negative after 2070.
These results suggest that many people and their descendants could find themselves exposed and displaced by SLR as presently safe areas become increasingly vulnerable over time. Climate migration is often nonlinear due to multiple competing processes (demographic, ecologic, topographic, etc.). In the case of New York, NY, SLR initially takes people away from the county as highly exposed populations initially migrate, but population growth turns positive in the tail end of the century, as other nearby counties are more exposed and contain more potential climate migrants. New York thus transitions from a vulnerable county to a potential recipient county as the century progresses. These results highlight the nonlinearity that climate migration is likely to take this century.
Finally, Fig. 2BD are examples of climate destinations (counties considered “climate havens”). We see a similar, though reversed, pattern of population trajectories to vulnerable counties. Here, Rutherford, TN (245.1 K [78.5–852.3 K] amplified demographic change versus 34.9 K [8.2–197.5 K] displaced migrants), Douglas, CO (377.7 K [117.8–1.6 M] vs. 32.3 K [5.2–230.3 K]), and Washington, OR (131.9 K [50.9–377.8 K] vs. 12.9 K [3.8–55.1 K]), exhibit considerably larger demographic impacts when accounting for population dynamics compared to just the Displacement model. These results echo suggestions of emerging climate havens in “safer” areas (19). If cities prepare solely for climate migrants, they are likely to underprepare for the demographic change associated with climate in-migration.
Because our demographic model is stratified by age, we can investigate the impact of climate migration on demographic age structures and potential population aging. Fig. 4 shows the impact of population processes on aging related to climate migration. We find that as the percentage of the population lost due to climate migration-related population processes increases, the median age in the population also increases (Fig. 4). Conversely, counties receiving the greatest increase in population actually exhibit more youthful populations. This effect is particularly pronounced in some counties where the increase in median age can approach 10+ y in some highly impacted coastal counties due to climate migration.
Fig. 4.
Population Aging and climate migration. Here, we show the relationship between population change due to SLR and aging by 2100. The more an area experiences climate out-migration, the greater the population aging. Conversely, the more an area experiences climate in-migration, the younger the area becomes. Results shown are under the SSP2–RCP4.5 50th percentile.

Discussion

Climate migration continues to receive both policy and scientific focus. But projections of climate migration that do not account for other population processes fail to describe compounding population effects or accelerated population aging in origins. When population processes are fully integrated within a climate migration model, we see dramatic impacts on both origin and destination communities, particularly in their changing age structures.
Given our results, vulnerable areas experiencing climate out-migration could face a future where more youthful age groups exercise “migration as adaptation” but the oldest populations remain in vulnerable areas. Climate migration could place an enormous burden on those communities that might face the triple challenges of climate change, dwindling populations, and rapid population aging. Adaptation costs continue to rise (32), but communities could struggle to afford the necessary adaptation strategies to protect their remaining residents as prime-age income earners migrate away, potentially eroding local tax bases.
Furthermore, given the accelerated population aging in origin communities, maladaptation could easily result if adaptation strategies are aimed at more youthful populations who are less likely to remain in these areas—especially as the century progresses. Some adaptation strategies to build resiliency to SLR call for raising first-floor elevations (33), yet elevating homes and adding steps might result in maladaptation in communities facing accelerated aging due to climate migration. Origin communities should consider the potential impact of adaptation strategies and policies on older populations in order to better build resilient communities for all age groups.
Destination communities also face challenges due to climate migration. Destination communities that consider only climate migrants underestimate the population change likely to occur due to demographic compounding effects. Larger and closer places tend to attract more people, much like gravity. Climate destinations are likely to become even more attractive as additional gravity-driven migration effects play a crucial factor for additional migration streams, beyond just climate migrants. For some climate destinations already struggling with growth management and sustainability goals, climate migration poses significant challenges. The total demographic impact of climate migration could further burden these communities if growth is managed haphazardly. Destination communities for climate migrants should consider these other demographic forces in their sustainability plans and address challenges sooner rather than later.
Climate migration has been broadly conceptualized as simply a rearrangement of people across space. Our results show that this conceptualization underestimates the total demographic impact in two main ways: climate migration is likely to accelerate population aging in origins and accelerate population growth in destinations. We also demonstrate that climate migration in isolation is unlikely to significantly alter population distributions but climate migration in combination with other population processes will produce significant demographic shifts in the future. The 8.6–28 M potential demographic amplification is considerably larger than the expected number of migrants here (0.8–3.4 M) and elsewhere in the literature (2426). This work offers a glimpse of these demographic shifts.
We model RCPs 2.6, 4.5, and 8.5, which imply a maximum 2100 SLR amount of 1.2 m under RCP8.5 (35). While these SLR amounts are in line with recent IPCC projections, other SLR projections suggest that 2100 SLR could greatly exceed 1.2 m (3638). It is possible that the demographic amplification that we find is likely conservative. We also choose to model migration resulting from complete inundation, yet it is possible that migration begins sooner than complete inundation (18, 39). Thus, the direct migration we model could also be considered conservative. If people migrate sooner, in a more anticipatory manner or due to other related hazards such as storm surge, the demographic amplification and population aging we find would be underestimated.
Additionally, vulnerability to SLR is not limited to only elevation, but economic, political, social, and other factors render some people and places more vulnerable than others (40) and thus more or less likely to migrate in the face of environmental change (5). We primarily model migration based on exposure, but the combination of exposure, sensitivity, and adaptive capacity could create more or less uneven vulnerability than we model. Such differential vulnerability could exacerbate or dampen our results.
The uncertainty in our results arises primarily from the demographic uncertainty inherent in long-range population projections and the uncertainty in future SLR. The SSP projections in 2100 for the United States range from a low of 250 M under SSP3 to a high of 700 M under SSP5 (20). Similarly, SLR in 2100 could be as small as 0.3 m under the lower bound of RCP2.6 to as high as 1.2 m under the upper bound of RCP8.5 (38, 41). Without taking into account significant population processes, such a large variation in anticipated SLR translates into considerable differences in population exposure (34). These two uncertainties interact to drive relatively large uncertainties in our results.
Future outcomes are not always predicated on past tendencies. Future demographic trajectories may change as a result of socioeconomic changes, population growth limits, local growth restrictions, adaptive behavior and infrastructure, and climate change itself. Climate change could alter future fertility and mortality rates, and new migration destinations could emerge in reaction to the host of social and environmental changes anticipated this century. The COVID-19 pandemic also taught us that “black swan” events could profoundly alter projections of any kind. Although we base our results on historical trends and estimates and take care to account for demographic patterns, uncertainty, and model accuracy, our results may not accurately reflect future populations, especially considering the long time horizons involved.
The approach for modeling the demographic implications of climate migration shown here allows for modeling demographic change in concert with other climate stressors—not just SLR. Our parsimonious, one-dimensional Displacement model (Eq. 2) requires minimal translation of climate hazards into age-specific displacement. Future scientists could implement extreme heat/humidity combinations, tropical cyclones, or water availability as either singular climate hazards or in a multihazard model. To our knowledge, few, if any, demographic projection models account for climate change impacts. This type of modeling approach has great potential to better understand the integration of population processes and climate change.

Materials and Methods

We employ the use of multiregional Leslie matrices (42) to project climate migration in the United States. Eq. 1 is the general form for our projections.
To answer our research questions, we employ three main modules and describe them here. The first is the development of a parsimonious, one-dimensional, age-specific Displacement model. The second is a SLR exposure model. The third is a multiregional Leslie matrix specification.

Parsimonious, One-Dimensional, Age-Specific Displacement Model.

Our Displacement model makes use of a statistical time series outlier detection technique to first identify anomalous demographic behavior in a time series and then verify that this anomalous behavior is associated with an environmental event.
We use a statistical time series outlier detection algorithm (43), implemented in the R programming language (44) via the tsoutliers package (45).
This algorithm iteratively uses autoregressive integrated moving average (ARIMA) models to 1) identify potential outliers and 2) refit the ARIMA with the outliers removed to produce a counterfactual time series. First, an ARIMA model is fit to the time series using the “forecast” package in R (46, 47) where the best-performing ARIMA model is selected based on the Bayesian information criterion (BIC). Finally, the residuals from the forecast are checked for their significance where only outliers above a critical t-static are considered “true” outliers (|τ|≥4; P-value < 0.000063). We chose this threshold to minimize the probability of committing a type I error (or claiming that an outlier is true when it is, in fact, not).
We use this outlier detection algorithm to search over county population totals for the time period 1980–2019. We use the NVSS US Census Populations with Bridged Race Categories dataset. The NVSS Bridged Race Categories dataset harmonizes racial classifications and county boundaries across disparate time periods to allow population estimates to be sufficiently comparable across space and time. Importantly, all county boundaries are rectified to be geographically consistent across all time periods. We use the 1969–2019 dataset, but the historical population estimates prior to 1980 display unusual volatility, so we consider only the time periods 1980–2019. We also consider only counties created prior to year 2000 and contained in the NVSS data.
We search all US counties for negative statistical outliers (indicating population losses) between 1980 and 2019. We detect 53 county-years with population losses of magnitude 4σ or greater. We then use the SHELDUS (48), a county-level hazard dataset for the United States which contains information about the direct losses (property and crop losses, injuries, and fatalities) caused by a hazard event (thunderstorms, hurricanes, floods, wildfires, tornadoes, flash floods, earthquakes, etc.) for the period 1960 to the present. We use SHELDUS to ensure that the county time periods we identify as statistical outliers with population losses experienced an environmental hazard in that county-year with per capita hazardous losses in excess of the 50th percentile. This is to ensure that the outlier population losses that we detect are associated with a hazard rather than other forces, such as economic forces.
Four county-periods either were not in the SHELDUS database or experienced per capita hazard losses below the 50th percentile. Additionally, one county-period contained age–sex groups with 0 people, necessitating exclusion. The remaining 48 environmental events include tornadoes, wind damage, winter weather, earthquakes, flooding, tropical cyclones, hail, and other environmental hazards. Using this universe of 48 county-periods exhibiting large population declines after verified hazard losses, across over 40 y and across a wide variety of environmental hazards, we then build a flexible, one-dimensional, age-specific Displacement model.
To link population displacement with age-specific population changes, we calculate CCRs in each county using the NVSS population data for the period 1969–2019. CCRs take the following general form (see refs. (49) and (50) for a more detailed description):
CCRx,t=nPx,tnPxk,tk,
where nPx, t is the population aged x to x + n in time t, and nPxk, t is the population aged xk to x + nk in time t, where k refers to the time difference between time periods. Since mortality must decrement a population, any CCR above 1.0 implies a net-migration rate in excess of the mortality rate and a growing population. There is special consideration for both the initial age group without a preceding age group and the final, open-ended age interval without a proceeding age group (see (49) for additional details).
We build the following model based on the relationship between the change in CCRs at age x, ΔCCRx = CCRx, t/CCRx, t − 1, and the percentage decline in the total population compared to the counterfactual in the outlier detection method, ΔPt=Pt̂/Pt:
log(ΔCCRx)=ax+bxh+cxh2.
Here, h is the log(ΔPt) and shows a quadratic relationship with the logarithm of the change in CCRs by age. x refers to five-year age groups: 0–4, 5–9,…, 85+. This is a similar model and approach to Wilmoth et al.’s (51) flexible, one-dimensional mortality model based on the similarity between age-specific mortality rates and infant mortality. SI Appendix, Table S1 depicts the r-squared values between log(ΔCCRx) and log(ΔPt). The age groups with the lowest r-squared values are young adult males aged 20–39 and those in the open-ended age interval (80+), suggesting that these age/sex groups react to environmental signals the least predictably.
Using hty = log(ΔPty), we can estimate age-specific changes in CCRs after an environmental event by simply applying the following formula:
CCR^xy,t=CCRx,t1·eβ^xhty+c^xhty2,
[2]
where eβ̂xhty+ĉxhty2 provides the percentage change in CCRxt based on the log(ΔPty) under SLR amount y. In this case, we drop the intercept (ax) from the estimation procedure to ensure that a 0% decline in population yields a corresponding 0% change in the CCR. Multiplying the result from the model with the CCR in the year prior yields the anticipated change in the CCR. These changes in CCRs can then be applied to any time series of population values to generate an anticipated population.
We estimate the predicted population using the equation outlined above and then compare it against the observed population. SI Appendix, Figs. S1 and S2, and SI Appendix, Table S1 show the accuracy of our fitted, one-dimensional model. Regarding the total population in our 48 counties, our model performs well with an r2 value of 0.996 and performs well regardless of population size. Regarding each individual Px group, our model still performs quite well with an r2 of 0.995. Just like with the total population, the accuracy of our model does not depend on population size.

Sea-Level Rise Exposure.

To estimate the populations at risk to SLR and thus the value h in Eq. 2, we employ inundation modeling (25), which assumes that people who are underwater 100% of the time must migrate. We estimate these populations using airborne lidar-derived digital elevation models (DEMs) produced by National Oceanic and Atmospheric Administration (NOAA) and supplemented with both the US Geological Survey (USGS) Northern Gulf of Mexico Topobathymetric DEM in Louisiana and the USGS National Elevation Dataset in the fraction of land not covered by other sources (see ref. 52 for details on the construction of the DEMs).
Using a bathtub model of inundation, we calculate the land area under a given water height to generate binary inundation surfaces. SLR exposure is hyperlocalized, and we generate this inundation area in the Census Block Groups (CBG; n = 81,815) located in coastal counties (n = 406) expected to experience any probability of flooding. We use probabilistic SLR projections (35, 38) that are closely aligned with the IPCC for our water heights. To calculate the land area under a given water height, we simply threshold the DEM to find pixels below SLRyt, where y is the projected height of SLR in a given year t. For each CBG, we simply calculate the percentage of its pixels on dry land (defined in the National Wetland Inventory (53)) covered by the inundation surface and multiply this percentage by the total population in the CBG in year t to produce the total number of people at risk to a given amount of SLR in a given year. We then aggregate these CBGs to the county level to calculate the percentage of people in a given county at risk of inundation.
To account for potential subcounty shifts in population, we use a specification of subcounty demographic projections (34). Specifically, we use a subcounty demographic projection to produce spatiotemporally consistent CBG boundaries for the period 1940–2010 and project these populations forward using a mixed, linear/exponential projection for the period 2010–2100. CBGs expected to increase use a linear projection, and CBGs expected to decrease use an exponential projection. This creates a time-varying, population-weighted estimate of exposure to SLR.
The percentage of the population at risk to SLR in each county, in essence, represents the ΔPt from our Eq. 2 above, where ΔPt = Pt, y/Pt. In this case, Pt, y/Pt is the percentage of the population in any county at risk of inundation under a given water height y. Such a calculation allows us to seamlessly combine our parsimonious Displacement model with our matrix population model.

Matrix Population Models.

We employ the use of multiregional Leslie matrices in our population projections (42).
where Pt refers to the population matrix containing x age groups and St contains the age-specific fertility (F) and mortality rates (S), where Sx refers to the survival probabilities for age group x and Fx refers to the fertility rates.
We populate our Leslie matrices with the 3,143 US counties, 18 five-year age groups, and two sex groups; thus, Pt is a vector of length 113,148, and St and Mty are 113,148 × 113,148 matrices. We use CCRs to populate our Sx values in each matrix and child–woman ratios to populate our Fx values. The values come from the NVSS Bridged Race Categories dataset. To project the CCRs, we employ an ARIMA model for forecasting equally spaced univariate time series data. We use an ARIMA(0,1,1) model, which produces forecasts equivalent to simple exponential smoothing. All projections were undertaken in R (44) using the forecast package (46).
We use the NVSS data for the period 1969–2019 for county c, age group x, sex s in an ARIMA(0,1,1) to create CCRcxst for time periods t + 1. The initial P1 and St matrices use the 2019 NVSS data.
We also calculate the probability of migrating from each county to each county and use this to populate the Mty matrix. These data come from the Internal Revenue Service (IRS) county-to-county migration files for 1990–2018 (see refs. (54) and (55) for descriptions of this data). We populate Mty as Mt·(1eβ̂xhty+ĉxhty2) and where i = j as eβ̂xhty+ĉxhty2. Mt is a vector containing the proportion migrating from county i to county j in the IRS migration data, thus ensuring the columns of Mty sum to 1.0.
To capture changes in the migration system, we employ an ETS model (error, trend, seasonal), a univariate time series forecasting model (56). We use an ETS model for migration instead of an ARIMA(0,1,1) as we do for the CCRs because the CCRs are subject to multiplication during a drift, whereas the migration system is not. A CCR that drifts from 1.1 → 1.3 represents more than a 10-fold increase in a projected population over our time horizons (1.117 = 5x, 1.317 = 86x). Projecting the migration system itself is not subject to such exponential drift.
We fit individual ETS models for each county’s numeric migrants between each origin–destination dyadic pair using the forecast package in R (46). This approach allows the underlying migration system to evolve and change over the projection horizon, allowing dyadic pairs to wax or wane. We convert the numeric projections to fractions of the total projected migrants to populate the diagonal in the M matrix above where nonmigrants (i.e., those migrating from ii) are included. The result is the fraction of individuals surviving from age group x who migrate from ij.
We control all population projections to the Shared Socioeconomic Pathways (20), and we use RCPs 2.6, 4.5, and 8.5 for our inundation scenario (35).
We provide a narrative description of the matrix population modeling with an accompanying simplified model in SI Appendix.

Data, Materials, and Software Availability

The underlying data that support the findings of this study are available from Climate Central, but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Climate Central. The complete computer code that supports our findings and the data resulting from this study are deposited at (https://doi.org/10.5281/zenodo.7041806) (57).

Acknowledgments

This work was supported by the State of Louisiana, the American Society of Adaptation Professionals, the New York State Energy Research & Development Authority, and the Great Lakes Integrated Sciences & Assessment. We would like to thank T. Gill, N. Nagle, A. Moulton, S. Bohon, C. Schmertmann, and E. Fenimore, for their early feedback and assistance.

Author contributions

M.E.H. and S.A.J. designed research; M.E.H., S.A.J., and S.A.K. performed research; M.E.H. and S.A.K. contributed new reagents/analytic tools; M.E.H., S.A.J., and S.A.K. analyzed data; and M.E.H., S.A.J., and S.A.K. wrote the paper.

Competing interests

The authors declare no competing interest.

Supporting Information

Appendix 01 (PDF)

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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 121 | No. 3
January 16, 2024
PubMed: 38190539

Classifications

Data, Materials, and Software Availability

The underlying data that support the findings of this study are available from Climate Central, but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Climate Central. The complete computer code that supports our findings and the data resulting from this study are deposited at (https://doi.org/10.5281/zenodo.7041806) (57).

Submission history

Received: April 11, 2022
Accepted: October 16, 2022
Published online: January 8, 2024
Published in issue: January 16, 2024

Keywords

  1. climate migration
  2. sea-level rise
  3. multiregional population projections
  4. demographic amplification
  5. population aging

Acknowledgments

This work was supported by the State of Louisiana, the American Society of Adaptation Professionals, the New York State Energy Research & Development Authority, and the Great Lakes Integrated Sciences & Assessment. We would like to thank T. Gill, N. Nagle, A. Moulton, S. Bohon, C. Schmertmann, and E. Fenimore, for their early feedback and assistance.
Author Contributions
M.E.H. and S.A.J. designed research; M.E.H., S.A.J., and S.A.K. performed research; M.E.H. and S.A.K. contributed new reagents/analytic tools; M.E.H., S.A.J., and S.A.K. analyzed data; and M.E.H., S.A.J., and S.A.K. wrote the paper.
Competing Interests
The authors declare no competing interest.

Notes

This article is a PNAS Direct Submission. W.N.A. is a guest editor invited by the Editorial Board.
*
Unless otherwise stated, uncertainty intervals in parentheses relate to the SSP3–RCP2.6 5th percentile and SSP5–RCP8.5 95th percentile.

Authors

Affiliations

Department of Sociology, Florida State University, Tallahassee, FL 32306
Center for Demography and Population Health, Florida State University, Tallahassee, FL 32306
Department of Sociology, Florida State University, Tallahassee, FL 32306
Center for Demography and Population Health, Florida State University, Tallahassee, FL 32306
Climate Central, Princeton, NJ 08542

Notes

1
To whom correspondence may be addressed. Email: [email protected].

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Climate migration amplifies demographic change and population aging
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