Sea level rise (SLR) will affect millions of people living in coastal areas.
According to the IPCC Fifth Assessment Report, in the “worst-case” Representative Concentration Pathways (RCP) scenario, RCP 8.5, where greenhouse gas emissions continue to rise throughout the 21st century, a global mean sea level (GMSL) rise between 0.52 to 0.98 meters (m) is likely by 2100  . Other estimates, using statistical instead of process based models of GMSL, project a rise in the range of 0.75 m to 1.9 m by 2100
. Other estimates, using statistical instead of process based models of GMSL, project a rise in the range of 0.75 m to 1.9 m by 2100. Recent research from the National Oceanic and Atmospheric Administration (NOAA), however, has suggested a 2.5 m upper bound of GMSL rise by 2100 for an ‘extreme’ sea level rise scenario, and a 2 m GMSL rise for a ‘high’ scenario .
The impacts of sea level rise are potentially catastrophic. About 30% of the urban land on earth was located in high-frequency flood zones in 2000, and it is projected to increase to 40% by 2030 taking urban growth and sea level rise into account . In the United States alone, 123.3 million people, or 39% of the total population, lived in coastal counties in 2010, with a predicted 8% increase by the year 2020 . By the year 2100, a projected 13.1 million people in the United States alone would be living on land that will be considered flooded with a SLR of 6 feet (1.8 m) .
Human migration is a natural response to this climatic pressure, and is one of many adaptation measures that people will take in response to climate change [7, 8, 9, 10]. As oceans expand and encroach into previously habitable land, affected people - climate migrants - will move towards locations further inland, looking for food and shelter in areas that are less susceptible to increased flooding or extreme weather events. In this paper, we argue that the comprehensive impacts of sea level rise on human populations, when considering migration, expand far beyond the coastal areas.
Sea level rise impacts are a combination of two effects. The direct effects of SLR capture the amount of land that will be flooded and the number of people that will be displaced and forced to relocate as an ultimate result of the loss of habitable land. The indirect effects of SLR are more nuanced and are the results of aggregate changes in population distributions across the land. These indirect effects will cause accelerated changes for inland areas, particularly urban areas, that will observe much higher levels of incoming migrants than they would have absent SLR. These changes can in turn take the form of tighter labor markets  and increased housing prices , with broader effects on income inequality in the coastal areas . Of course, migration to other cities can also have positive impacts; new migrants can improve productivity as they bring with them human capital accumulated elsewhere .
Discussions regarding sea level rise impacts on human populations are often constrained to regions directly experiencing SLR-driven flooding [14, 15, 6]. Several theoretical frameworks use qualitative case studies to motivate models that might represent the reasoning behind migration choices due to sea level rise, but are not grounded in statistical methods [7, 16, 17]. There are many complex interactions between demographic driven migration and climate change driven migration, and the scope and scale of the impacts of climate change on migration will be significant [8, 18]. One example of these impacts that has been studied considers the political ramifications that will come with the eventual migrants from Pacific island of Kiribati, which will most likely become completely flooded under a 3 meter SLR in the coming centuries . Another example is the projected widening demographic differentials in countries that will be especially impacted by sea level rise [18, 20], similar to demographic consequences seen after the 1970s droughts in Africa [21, 22]. The foundation of both of these concerns is in people’s destination locations, therefore it is prudent to weigh the question of ‘where’ people will go equally with ‘how many’ people will be initially affected .
There are few empirical studies that link climate change with human migration patterns. Feng et al. show that the negative impacts of climate change on crop-yields has driven increased emigration from Mexico to the United States , while Thiede and Gray examine the effects of changing climate variables on the timing of migration in Indonesia . The only empirical works that examine the effects of SLR on human migration do so by coupling population projections with sea level rise and migration models to estimate how population distributions might change in future scenarios [25, 26]. In the US, small area population projections for the year 2100 have been combined with spatially explicit estimates of SLR  and an unobserved component regression model to estimate the destinations of populations that could be forced to migrate through coastal flooding. In , approximately 56% of counties in the US are found to be affected by larger migrant influxes under 1.8 m of SLR. Similarly, in Bangladesh, gridded population projections have been combined with a bathtub type model of SLR and the radiation model of human migration to estimate how population distributions may change . This coupled model has minimal data requirements, forecasts large quantities of immigrations to the division of Dhaka in Bangladesh, and highlights the broader potential impacts of these migrants including an increased demand for housing, food, and jobs.
These empirical studies make the critical simplifying assumption that climate driven migration will follow the same patterns as historic migration. Additionally,  assumes that migrations will happen only between locations for which there are historically observed migrations. However, human migration is a function of push and pull factors, and where increased climate stress will affect both  . As such, the patterns of climate migrants will not necessarily follow patterns observed in historical migration data. Indeed, “climate migrants resulting from press stressors will probably constitute ‘enhanced’, or extra, normal out-migration.”
. As such, the patterns of climate migrants will not necessarily follow patterns observed in historical migration data. Indeed, “climate migrants resulting from press stressors will probably constitute ‘enhanced’, or extra, normal out-migration.”.
In this work we aim to address the simplifying assumptions made in previous empirical analyzes. First, we derive a general framework for coupling models of sea level rise with dynamic models of human migration so that future innovations in both human migration modeling and sea level rise modeling can easily be coupled to produce more precise estimates of changing population distributions. Second, we design our framework with separate human migration models for affected and unaffected populations in order to capture the different dynamics of these processes. Specifically we implement our framework with small area population projections , the NOAA’s Digital Coast Sea Level Rise estimates  , and a recent machine learning (ML) method for modeling human migration
, and a recent machine learning (ML) method for modeling human migration. We model migrations made from flooded areas and from unflooded areas separately by fitting one ML migration model using “business-as-usual” migration data and one model with migration data following Hurricanes Katrina and Rita. Furthermore, our general framework also separates flooded and unflooded zones at a conceptual level to ensure simulated migrations will not end in flooded areas.
In our analysis, we compare simulated migration patterns under two sea level rise scenarios (1.8m SLR in 2100, and 0.9m SLR in 2100) to the baseline scenario of no SLR. We examine the aforementioned direct and indirect effects of SLR through its impact on human migration, and show results that highlight the importance of treating the dynamics of climate-induced migrants separately from business-as-usual migrations. Our analysis aims to answer the question of how the population distribution will change under different amounts of SLR, i.e. “where” populations displaced by SLR will go, and further, how SLR will affect the broader dynamics of human migration.
Current state-of-the-art models of human migration include the family of radiation models [29, 30], gravity models [31, 32], and machine learning models . Yet, SLR-driven human migration poses some specific challenges to traditional strategies for modelling human migration:
First, human migration induced by SLR might not follow historic migration patterns. In fact, using one year of county-to-county migration data from the IRS U.S. migration data sets, Simini et al.  showed that a fixed proportion ( 3%) of the population of a U.S. county will migrate under normal circumstances. This will not hold under sea level rise, as the entire population in flooded areas will have to move or adapt in other ways. Importantly, in addition to direct inundation due to sea level rise, climate migrants will be forced to move as climate change effects become more pronounced, directly through the exposure to “high-magnitude events” such as large scale flooding from hurricanes, or indirectly through the “cumulative contribution of ongoing localized events across regions” . The dynamics of these environmentally induced migrations will not necessarily follow those of previously observed migrations. We expect that as social scientists gather more data and knowledge, more refined and informed models of human migration will emerge.
Second, the spatial resolution of the migration model must be carefully considered. Climate migrants will not necessarily move large distances as they adapt to changing conditions in inundated areas. Indeed most migrations are made to nearby locations. This phenomenon can be seen in the migrations following Hurricane Katrina in the US, where a majority of destinations were within Louisiana . Joint SLR/migration models must capture the situations whereby migrants can choose to move to the unflooded portions of partially flooded zones, and must guarantee that no migrants are assigned to a flooded area.
Finally, SLR will not happen instantaneously and population projections need to account for the cumulative effects of SLR induced migration. The SLR influenced population distribution of a location will diverge from that of a “business as usual” scenario as the indirect effects of SLR compound; as more climate migrants settle inland, they will change the migrations patterns of future migrants and so on. Current population projections account for the direct effects of SLR where projected populations are made with respect to potentially flooded land , however these indirect effects must also be considered.
General Modeling Framework
Consider an amount of SLR in meters, , a list of spatial zones, and , which includes the spatial distribution of population in each zone, and, optionally, other features associated with each zone. Using this information, we want to compute a migration matrix , where an entry represents the number of migrants that travel from zone to under the given amount of SLR. We propose a general modeling framework for handling this problem which consists of two modules, shown in Fig 1: a SLR module and a MIGRATION module.
SLR module. This module uses a sea level rise model to partition each input zone into two new zones: the flooded portion and the unflooded portion. Using the best available data, this module should divide the features from the original zone () between the flooded-portion zone () and the unflooded-portion zone (). For example, if we have high-resolution spatial population data, then we can split population between the two partitions based on the spatial extent of the flooding. Using this module, we estimate the direct effects of SLR in terms of flooded area and number of people living in such an area.
MIGRATION module. This module calculates using the two sets of zones from the SLR module. Specifically, this module uses two migration models: 1.) a model for migrations from flooded zones to unflooded zones with the function , where migration is a forced process; and 2.) a model of migrations from unflooded zones to unflooded zones with the function , where migration happens due to usual drivers. Finally, this module should aggregate migrant flows from the two migration functions, . Using this module, we estimate the indirect effects of SLR in terms of how the population distribution changes relative to no SLR.
By separating SLR driven migration from standard migrations, our framework forces these dynamics to be considered independently, explicitly bringing up the issue from the first conceptual challenge mentioned in the previous section. Implementations of our framework can use different models for these dynamics if available, or, if such models are not available, fall back to using a simpler model where the simplifying assumption is clear. Our framework also addresses the second conceptual challenge by excluding flooded areas as destinations for all migrants by simply not considering migrant flows with destinations in the set of flooded portions. Note that within-zone migrations in partially flooded zones are handled by presenting the neighboring unflooded portions of those zones as possible destinations. Furthermore, by separating the functionality of the SLR module from that of the MIGRATION module, the framework allows ablation studies to measure how much results depend on the specific behaviors of each. The third conceptual challenge revolves around how SLR and migration are both temporal processes that form a feedback loop (i.e. SLR will affect migration decisions, which will in turn affect how many people are affected by further SLR, etc.). This is not explicitly taken into account in our framework, however should be addressed in further research as each process is further understood. In Section 5 of the Supplementary Information we provide a more formal definition of our Joint Model.
Implementation of Joint SLR/Migration Model
We implement our proposed framework with 1.) small area population projections for 2100 under different amounts of SLR, following the methodology in  - which uses the NOAA’s Digital Coast Sea Level Rise estimates  - and 2.) a recent machine learning (ML) approach for modeling human migration . An implementation of the Joint Model requires us to define the SLR function, the manner in which the SLR function splits features associated with the zones that are affected by SLR, and the two MIGRATION functions. All three of these steps are discussed in the next two sections. In Section 2 of the Supplementary Information we show a similar implementation using the Extended Radiation Model  to implement the MIGRATION functions. In Section 3 of the Supplementary Information we describe our ML model and give validation results comparing it to other human migration models on the task of predicting inter-county migrations in the US.
Sea Level Rise Modeling
First, we follow the methodology proposed in Hauer 2016  to create population projections for every Census Block Group in the US () for two SLR scenarios, medium, where 0.9m (3ft) of SLR is experienced by 2100, and high, where 1.8m (6ft) of SLR is experienced by 2100. These SLR scenarios are also proposed in Hauer 2016, based on methods from the US National Climate Assessment, and use the NOAA’s Digital Coast spatial estimates of areas affected by SLR in 1ft (0.3m) increments [27, 35]. The medium SLR scenario expects SLR to reach the 0.3m, 0.6m, and 0.9m thresholds in the years 2055, 2080, and 2100 respectively. The high scenario reaches similar increasing 0.3m SLR increments in the years 2042, 2059, 2071, 2082, 2091, and 2100. The Digital Coast model provides SLR estimates that address many of the shortcomings of a naive bathtub calculation of SLR (i.e. thresholding a digital elevation map with expected SLR amounts) by taking tidal variability, hydroconnectivity, probable flooding, and federal leveed areas into account.
With this data, we define the function as taking an input county, , and amount of SLR under either the medium or high SLR scenario, . A given county corresponds to a set of census block groups while a given SLR amount, under either scenario, corresponds to population projections for the census block groups, including an estimate of the number of people affected by flooding in each block group. We split the county population into the affected and unaffected block groups, which directly results in and . Here, is a “new” county equivalent zone, for the purposes of modeling migration, with a population equal to the sum of the unaffected populations over all the associated block groups. Similarly, , represents the innundated portion of the original county, and will contain a population equal to the sum of affected populations in the associated block groups. We can run for all to get the and sets. Population is the only feature required by the MIGRATION module, however a similar splitting technique could be used for other block group level features if they can be reliably projected into future scenarios.
Human Migration Modeling
We model human migration between counties in the USA with a recently proposed artificial neural network (ANN) based method
We model human migration between counties in the USA with a recently proposed artificial neural network (ANN) based method that is fit with historic county-to-county migration data from the IRS . This method is similar in functionality to traditional models of human mobility and migration, such as the radiation or gravity models [29, 37, 31], as it will estimate the probability of a migration between a given origin and destination based on population and distance features .
More specifically, our ANN models estimate , the probability that a migrant which leaves an origin county, , will travel to a destination county, , using the following input features: origin population, , destination population, , distance between the two, , and the “intervening opprtunities” between the two, (this is the total population in the circle centered at with radius , not including or ). These features are the same features used by traditional radiation and gravity models, and depend solely on population and distance.
To compute , the number of migrants that travel from to , we need to know the number of migrants that are attempting to leave . If we say that the number of migrants leaving zone is of the form , where is some coefficient that specifies the fraction of the total population that will migrate, then . This function is called the production function. Now we can define the MIGRATION functions, and , which represent the climate migrants and standard migrants respectively, by training two instances of our ANN model, and forming respective production functions and by choosing and .
We fit the model by finding hurricane affected counties from the IRS migration data from 2004-2011 and 2011-2014. Specifically, we search for migration data points (i.e. pairs of counties) in which the origin county was a coastal county that observed an over 100% increase in outgoing migrations with over 1,000 total outgoing migrations222The reporting methodology in the IRS migration dataset changed between the 2010-2011 data and 2011-2012 data, therefore we cannot measure percent increase in outgoing migrations between them.. This “filter” highlights counties that have potentially been affected by hurricanes or other natural disasters and indeed finds seven counties from 2005 that were heavily impacted by hurricanes Katrina and Rita: St Bernard, Orleans, Cameron, Plaquemines, Hancock, Jefferson, and Harrison (which matches literature estimates of the most damaged counties ), as well as Liberty County, GA from 2006. The only historical explanation we can find for a sudden increase in outgoing migration in Liberty County is the deactivation of a large US military division stationed within the county that year. Considering this, we fit our model using the data from the seven counties that were most seriously affected by hurricanes Katrina and Rita. As background, Hurricane Katrina struck the city of New Orleans and the broader Louisiana and Mississippi coastline on August 29, 2005 causing widespread flooding and wind damage. Less than a month later, on September 25, Hurricane Rita also struck the Louisiana coast, exacerbating damage in New Orleans and causing extensive damage to counties in the western portions of the state. Over 1500 people were killed and over 80% of the city of New Orleans was flooded as a result of these hurricanes. Followup studies and Census estimates showed that New Orleans only contained around half of its pre-hurricane population within a year of the storms. By training our ANN with these counties we allow the model to pick up on the dynamics of migrations after extreme flooding events.
We train an ANN, , using all pairs of counties from the 2005-2006 IRS data that include one of the seven previously mentioned affected counties as an origin and an unaffected county as a destination. Similarly, we fit another ANN using the rest of the IRS migration data, . Due to our assumption that all people in flooded areas will have to migrate, the production function for climate migrants is given as the identity, . This forces the entire population of the affected portions of counties to become migrants. For standard migrants, we use the production function, , due to the observation by Simini et al.  that 3% of a county’s population will migrate under normal conditions each year. Given these: , and . With these definitions we can build and by running the climate migration ANN and standard migration ANN for all pairs of counties. In Section 3 of the Supplementary Information we evaluate the performance of these models compared to other migration models in a cross validation experimental setup.
We categorize the effects of SLR into two types: direct effects, which are a direct consequence of SLR, and indirect effects, which are a consequence of changing migration patterns due to SLR. We present the spatial distribution and magnitude of these effects in Figs 2 and 3. People that live on flooded land who will have to move away are accounted for in the direct effects of SLR. People that live in counties that experience a larger number of incoming migrants in the flooding scenario relative to the baseline scenario with no SLR are accounted for in the indirect effects of SLR.
In Fig 2 we show the spatial distribution of changes in migration patterns. In the top panel, counties experiencing any flooding (i.e. that are directly affected by SLR) are highlighted in blue, while the remaining counties are colored according to how many additional migrants they receive in the 1.8m SLR scenario. The bottom two panels of Fig 2 show the difference in the number of incoming migrants between the SLR scenario and the baseline scenario for incoming migrants from unaffected counties and affected counties. The top panel is the sum of these two maps, and shows this difference for incoming migrants from all counties. From these maps we can see that the primary destination of climate migrants are counties just inland of their origin, but climate migrants also move farther towards large cities that offer more opportunities.
In Fig 3 we show the magnitude of the direct and indirect effects as well as the spatial distribution of the indirectly affected counties. Formally, a county is marked as indirectly affected if the difference between the number of incoming migrants in the SLR scenario and the baseline scenario is greater than a percentage of the population of that county. By varying we can see different intensities of indirect effects. On average, 3% of a county’s population migrates each year . Thus, if , we would observe twice as much migration into a particular county than the average migration rate of the US. We assume that as increases, the effects will be stronger as there will be a significant strain on the resources in that particular county.
The graph in the bottom panel of Fig 3 shows the direct and indirect effects of SLR in terms of number of people affected for amounts of SLR in the range from 0.3m to 1.8m in 0.3m increments. The map in the top panel shows which counties in the United States are indirectly affected at different threshold values of . In both plots the indirect effects are shown for five different values of : 0.5% 1%, 3%, 6%, and 9%.
From the graph in Fig 3 we can see that the indirect impacts of SLR grow at much faster rate than the direct impacts. In the high SLR scenario by the year 2100 there are 13 million people directly affected, in 50 thousand km of flooded land, however there are almost twice as many, 25 million people, indirectly affected at the 9% threshold due to changing migration patterns and magnitudes. This 9% threshold indicates that these people live in areas which will experience three times as many migrants as they would compared to a baseline scenario. Even under the moderate assumption of 0.9m SLR by 2100 there will be 24 million people that live in counties considered indirectly affected at a 3% threshold. Under the same threshold with a SLR of 1.8m by 2100, there will be 120 million people, over of the population of US, living in counties that will see a doubling in the number of annual incoming migrants.
The map in Fig 3 shows that these indirect effects relative to county population will be distributed unevenly over the US. Most effects are seen in the Eastern US, where there are more vulnerable coastal populations. Of particular note are southern Mississippi and southeastern Georgia, where large groups of counties are estimated to see indirect effects in the category. The Midwest is also projected to see large indirect effects, even though the magnitudes of incoming migrants are smaller than counties closer to the coast. This can be explained by the relatively small populations and baseline levels of incoming migrants. The greater magnitudes of migrations from higher population areas causes some migrants to select these midwestern areas as destination, which could cause disproportionally larger indirect effects.
Our results show that the effect of SLR on human populations could be more pervasive and widespread than anticipated, with almost all counties receiving some number of additional migrants due to SLR induced flooding. We identified two possible channels through which SLR can affect migration. First, the “direct effect” shows the amount of people that are forced to migrate away from flooded areas. The “indirect effect” consists of changes in the magnitude and pattern of migration across all populated areas due to the impact of SLR. The areas immediately adjacent to coastal counties will experience the most dramatic impacts as many migrants will simply move slightly further inland. These counties are predominantly rural and may not have the infrastructure capacity to serve several times the number of average annual incoming migrants. Increased competition for scarce resources, tighter housing and labor markets and more congested roads and diminished access to amenities can deteriorate the living conditions in the counties that receive more migrants. It is of course possible that the new influx of migrants could stimulate the economy thus creating new opportunities for growth in the local economy. This can be the case, not only if migrants flow from more affluent communities, but also because of increased human capital that can spur innovation and improve productivity. The purpose of our study is not to determine whether or not new influx of people are good or bad for a local economy, but to highlight the range of migration changes that can occur because of sea level rise. The overall socio-economic impacts of climate driven migration, of which our results are the first piece, need to be further studied as more data becomes available.
In general, we find that previously “unpopular” destinations would be more popular solely due to their close proximity to counties that experience “direct effects”. The East Coast will experience larger effects than the West coast because of the large coastal population centers and shallower coastlines. Existing urban areas will receive the largest magnitudes of migrants, as they represent the most attractive destinations, which will accelerate the existing trends of urbanization. We find that the southeast portion of the United States will experience disproportionately high effects from SLR-driven flooding due to the large vulnerable populations in New Orleans and Miami. These results show that by driving human migration, the impacts of SLR have the potential to be much farther reaching than the coastal areas which they will flood.
We find similar conclusions to previously published estimates of human migration under SLR in the USA  - inland areas immediately adjacent to the coast, and urban areas in the southeast US will observe the largest effects from SLR driven migration. Our method for modeling human migration reveals several notable differences. According to Hauer 2017, the Austin, Texas Core Based Statistical Area is expected to observe the largest effects out of all destinations, with over 800 thousand incoming migrants due to SLR. This result happens because Austin has consistently been one of the fastest growing US cities over the past decade, which is captured and projected by a time series based migration model. Our migration model instead captures the dynamics of human migration between US counties based on population and distance features, and uses this to predict flows between counties without regard to potential short term historic trends. This approach has the benefit of allowing our model to predict flows between pairs of counties for which there are no historical flows, but can also result in potentially underpredicting flows to areas growing at faster-than-average rates. Indeed, in Texas, our results show more incoming migrants to Houston and Dallas - two larger cities closer to affected coastal areas.
Our analysis extends to how “standard” migration patterns between unaffected counties can change due to changes in viable destinations. The bottom right panel of Fig 2 shows how the incoming migrant distribution from unaffected counties changes in the High 2100 scenario. We observe that migrants from unaffected areas, that would previously move to coastal areas, will especially relocate to larger population centers. The counties surrounding Los Angeles in particular could see tens of thousands of migrants that are not coming from affected areas, but must choose a different location as a result of coastal flooding.
Because we rely on machine learning techniques, we forfeit the explanatory power of our model in favor of a more accurate prediction. This approach is suitable for the purposes of our research question and conceives a much more flexible methodology to analyze future migration. This black-box approach can be further calibrated as more data on similar temporal and spatial scales for empirical studies to explain migration behaviors becomes available .
In the meantime, as various aspects of human migration are better understood, especially ones related to environmental pressures, and better models of human migration are created, our flexible analytical framework will easily support new improved implementations and produce more accurate results. Similarly, as SLR flooding estimates are improved - with finer resolution population projections, uncertainty estimates, and models of the potential spatial effects of SLR such as expected flood frequency - the results given by our framework can be refined.
J.M-C was supported in part by the National Science Foundation of the United States of America (Grant no. 1510510) and the Canada Research Chairs program. B.D. was supported in part by NSF grants CCF-1522054 (COMPUSTNET: Expanding Horizons of Computational Sustainability) and BCS-1638268 (CRISP: Sustainable and Resilient Design of Interdependent Water and Energy Systems at the Infrastructure-Human-Resource Nexus).
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