Accounting for internal migration in spatial population projections—a gravity-based modeling approach using the Shared Socioeconomic Pathways

Gridded population projections constitute an essential input for climate change impacts, adaptation, and vulnerability (IAV) assessments as they allow for exploring how future changes in the spatial distribution of population drive climate change impacts. We develop such spatial population projections, using a gravity-based modeling approach that accounts for rural-urban and inland-coastal migration as well as for spatial development patterns (i.e. urban sprawl). We calibrate the model (called CONCLUDE) to the socioeconomically diverse Mediterranean region, additionally considering differences in socioeconomic development in two geographical regions: the northern Mediterranean and the southern and eastern Mediterranean. We produce high-resolution population projections (approximately 1 km) for 2020–2100 that are consistent with the Shared Socioeconomic Pathways (SSPs), both in terms of qualitative narrative assumptions as well as national-level projections. We find that future spatial population patterns differ considerably under all SSPs, with four to eight times higher urban population densities and three to 16 times higher coastal populations in southern and eastern Mediterranean countries compared to northern Mediterranean countries in 2100. In the South and East, the highest urban density (8000 people km−2) and coastal population (107 million) are projected under SSP3, while in the North, the highest urban density (1500 people km−2) is projected under SSP1 and the highest coastal population (15.2 million) under SSP5. As these projections account for internal migration processes and spatial development patterns, they can provide new insights in a wide range of IAV assessments. Furthermore, CONCLUDE can be extended to other continental or global scales due to its modest data requirements based on freely available global datasets.


Introduction
The future impacts of climate change will be driven by physical changes in climatic conditions as well as by changes in socioeconomic development (Field et al 2014). Recent studies found that socioeconomic development can be the dominant factor in driving impacts, in particular in the first half of the 21st century when climatic changes still take place at a slower pace (Marsha et al 2018, Rohat et al 2019c and in regions with rapid population growth , Rohat et al 2019a. To assess future impacts in a comprehensive manner, it is therefore important to explore the range of uncertainty regarding changes in socioeconomic conditions in locations that are exposed to climate hazards (Moss et al 2010.
The current state-of-the-art socioeconomic scenarios in climate change research, the Shared Socioeconomic Pathways (SSPs), provide a suitable basis for exploring this uncertainty . Five global-scale SSPs describe plausible alternative trends in socioeconomic development in the course of the 21st century based on societal challenges to climate change mitigation and adaptation. Each SSP has an underlying narrative that describes the socioeconomic developments of the SSP in qualitative terms SM1); furthermore, the narratives have been quantified to produce national-level projections of key variables in impacts, adaptation, and vulnerability (IAV) research (Van Ruijven et al 2014) such as population (Kc and Lutz 2017), urbanization (Jiang and O'Neill 2017), and gross domestic product (Crespo Cuaresma 2017, Dellink et al 2017, Leimbach et al 2017. However, national-level projections can be applied in IAV research to a limited degree as these assessments require spatially downscaled projections of key variables (Van Vuuren et al 2010, Van Ruijven et al 2014, with population being one of the mostused indicators for characterizing future impacts, for instance with regard to heat stress (Jones et al 2015, Rohat et al 2019a, water scarcity (Hanasaki et al 2013, Veldkamp et al 2016, Chen et al 2018, river flooding (Jongman et al 2015, Winsemius et al 2016, and coastal flooding (Hinkel et al 2014, Neumann et al 2015, Tiggeloven et al 2020. A number of previous studies have spatially downscaled population projections to the grid cell level, using the national-level SSP projections as boundary conditions, for example at global scale (Jones andO'Neill 2016, Murakami andYamagata 2019), with a focus on coastal population growth (Merkens et al 2016); at continental scale, for Africa (Boke-Olén et al 2017), Europe , based on Batista E Silva et al 2016, and the Mediterranean region (Reimann et al 2018); and at national scale, for the US O'Neill 2020a, 2020b) and China (Chen et al 2020).
Besides their different regional contexts, these gridded population projections differ in terms of spatial resolution, input data, and modeling approaches used. The spatial resolution of the projections ranges from 100 m (Chen et al 2020) to 0.5 • (Murakami and Yamagata 2019), depending on the complexity of the modeling approach, the intended application of the projections, and the regional focus of the study. Modeling approaches range from simple rescaling techniques  to more data-intensive approaches using distance measures from existing settlements, roads, and other infrastructure as modeling variables (Boke-Olén et al 2017, Murakami and Yamagata 2019, Chen et al 2020. The approach of Merkens et al (2016) (also used in Reimann et al 2018) employs a rescaling technique that differentiates population development in coastal versus inland locations. However, it does not include spatial changes in settlement patterns (i.e. urban sprawl), which are accounted for in the gravitybased approach used by Jones and O'Neill (2016) (also used in O'Neill 2020a, 2020b). The approaches of Merkens et al (2016) and Jones and O'Neill (2016) have modest data requirements, primarily relying on spatial population distributions of two time steps as model input; therefore both approaches are suitable for applications at continental to global scales where consistent input data are often lacking (Vafeidis et al 2008, Leyk et al 2019. None of the above-mentioned approaches account for both urban development patterns and inland-coastal migration, although these two processes are considered key drivers of future climate change impacts, in particular in coastal locations (Seto et al 2011, Neumann et al 2015. Historically, coastal locations have experienced high population growth, resulting in higher population densities and urbanization levels compared to inland locations (McGranahan et al 2007, Kummu et al 2016. Accordingly, the majority of megacities (>8 million inhabitants) are located in low-lying coastal areas (Brown et al 2013). With urbanization projected to increase in the course of the 21st century under all SSPs (Jiang and O'Neill 2017), these settlement patterns are expected to continue in the future , Merkens et al 2016.
We address this gap by extending the gravitybased approach of Jones and O'Neill (2016) to account for distinct changes in settlement patterns (i.e. urban sprawl) in coastal versus inland locations; we name the extended version of the model CONCLUDE 4 . For capturing inland-coastal as well as rural-urban migration processes, we refine the spatial resolution from a resolution of 7.5 arc minutes (approximately 15 km at the equator) to 30 arc seconds (approximately 1 km). We use freely available global-scale input data to calibrate the model to observed changes in spatial population patterns in coastal and inland locations, using the Mediterranean region, a socioeconomically diverse region characterized by a densely populated and highly urbanized coastal zone (European Environment Agency 2014, Lange et al 2020), as a case study.
This regional focus allows us to calibrate the model to two geographical regions based on the largest current differences in socioeconomic development across the region, the northern 5 and the southern and eastern 6 Mediterranean (Reimann et al 2018). Based on the calibrated model parameters for the two geographical regions and coastal versus inland locations, we produce gridded population projections in ten-year time steps from 2020 to 2100 for each SSP that reflect the development patterns described in the SSP narratives. These projections explore the uncertainty space regarding plausible future population patterns, and can be used in a wide range of IAV assessments.
In the methods section, we describe the modeling approach in more detail, including model calibration, validation, and modifications made to produce the population projections. In the results section, we present the spatial population patterns by SSP and geographical region, focusing particularly on developments in urban population density and in coastal population across the SSPs and the 21st century. We then critically evaluate the model for producing meaningful spatial population projections in the context of IAV research by comparing our results to previous work and by reflecting upon the model limitations. Last, we conclude with ideas of how to further refine the model in future work.

Methods
The following sections provide an overview of the extensions implemented in the gravity-based model CONCLUDE to be able to produce spatial population projections that account for spatial development patterns (i.e. urban sprawl) as well as for rural-urban and inland-coastal migration. Please consult supplementary materials 2-7 available online at stacks.iop.org/ ERL/16/074025/mmedia for further methodological detail (as referenced in the text).

Modeling approach
We used and extended the gravity-based population model INCLUDE described in Jones and O'Neill (2013), Jones and O'Neill (2016) and Rigaud et al (2018). Demographic gravity models are based on Newton's law of gravity and gravitational potential, assuming that densely populated locations are more attractive for human settlement than less densely populated locations (so-called 'population potential' (Grübler et al 2007)), and that relative attractiveness decreases with increasing distance between locations (Anderson 2011). The basic notion underlying this assumption is that factors such as transport costs and travel times determine the spatial interaction of two places, which decreases with increasing distance (Rich 1980). This effect is called 'distance-decay' and is often represented with a negative exponential function (Skov-Petersen 2001, Iacono et al 2008.
In addition to the distance-decay effect, we accounted for the contribution of local characteristics to the attractiveness of a location. Accordingly, we calculated a population potential v for each grid cell i and time step t that represents the attractiveness of any given location: where l i is the proportion of cell i available for human settlement 7 , P is the population of cell j or i at time t, β is a parameter reflecting the strength of the distancedecay effect, d ij is the distance between cells i and j, and A i is a factor reflecting the local attractiveness of cell i. The number of neighboring cell indices N i is determined by the gravity window within which the distance-decay effect applies. We calculated v i (t) separately for urban and rural populations, based on unique urban and rural β parameters for coastal and inland locations 8 , and distinct gravity windows for the two geographical regions (see next section for further detail). We then spatially distributed the national-level population of t+1 to each grid cell proportional to v i (t).

Calibration
The model was calibrated to historical changes in population patterns; therefore, spatial population data for at least two time steps were required. We used the global human settlement layer (Florczyk et  Following Jones and O'Neill (2016), we calibrated the model separately to urban versus rural changes in population patterns. Therefore, we defined the urban population per grid cell using the GHS-based settlement model (GHS-SMOD) , Pesaresi et al 2019. To harmonize the total urban population per country based on GHS-SMOD with the UN World Urbanization Prospects' (WUP) urbanization level for each country (United Nations, Department of Economic and Social Affairs, Population Division 2019), we added (deducted) population from densely populated neighboring grid cells to (from) the urban population in a series of three steps until the urban population numbers matched those of the WUP (SM4).
We established the distance parameter β for urban and rural locations by minimizing the sum of the squared errors produced by the model at the grid cell level for each ten-year calibration period, following Jones and O'Neill (2016). As not all countries were equally suitable for this procedure due to differences in the currency and spatial detail of the census and administrative unit data underlying GHS-POP (Center for International Earth Science Information Network-CIESIN-Columbia University 2017), we selected one country per geographical region (i.e. Spain, Tunisia) as representative of the migration processes in the region. We tested different gravity windows for each region, assuming that (a) daily trip distances in the Mediterranean are shorter than the 100 km window used by Jones and O'Neill 9 , and (b) daily trip distances are shorter in the southern and eastern Mediterranean compared to the northern Mediterranean, using the lower motorization rate as a proxy for trip distances (Eurostat 2019) due to a lack of consistent region-wide data. We found a gravity window of 20 km for the northern and 10 km for the southern and eastern parts of the region to best reflect the distance-decay effect. Finally, we averaged the established urban and rural β parameters across the two calibration periods and modified them to be able to account for differences in population development patterns in coastal versus inland locations (SM5).
In a next step, we calculated the local attractiveness factor A i in urban and rural locations for each country and grid cell by eliminating the grid-cell error ε i produced when accounting for the distancedecay effect only. Therefore, we ran equation (1) for the calibration period, applying the established coastal rural (CR), inland rural (IR), coastal urban (CU), and inland urban (IU) β parameters in the respective settlement type (i.e. CR, IR, CU, IU). As A i attained extremely high (low) values in some cells, we applied a two-step post-processing approach. First, to remove outliers, we used the middle 50% (so-called interquartile range) of the A i distribution per country. Second, we scaled A i to values ranging from −100 to 100, while retaining the original distribution of A i per country. Using this approach, we avoided overfitting the model to the historical changes in population patterns observed during the calibration period.

Validation
We validated the model by projecting the 2010 population based on the calibration period 1990-2000. Figure 1 presents scatter plots of the modeled versus the observed population for the total population, for urban populations, and for rural populations (see SM6 for corresponding Q-Q plots). The plots illustrate better model performance for urban populations compared to rural populations, with the best performance achieved when combining urban and rural populations (panel a), as reflected in R 2 and the root mean squared error. These findings agree with the findings of Jones and O'Neill (2013). A map presenting the error per grid cell relative to the observed population per cell (=relative absolute error (RAE)) for the entire Mediterranean region can be found in SM6.
We calculated further error metrics for the region to evaluate model performance in rural (CR, IR) and urban (CU, IU) locations as well as the entire Mediterranean region (supplementary table 3). In the entire Mediterranean region, the model produced a mean absolute error of 6.6, and a weighted mean absolute percentage error (WMAPE) (weighted by the population) of 14.7%, which compared well with the original version of the model that produced a WMAPE of 11.6% at the US level (Jones and O'Neill 2013). These error metrics also illustrated better model performance in urban versus rural locations (WMAPE of 18.3% versus 34.4%) as well as in coastal versus inland locations (WMAPE of 30.9% in CR versus 35.7% in IR; 18% in CU versus 18.5% in IU).

Population projections
To produce downscaled population projections with CONCLUDE that are consistent with the SSPs, we used the national-level population (Kc and Lutz 2017) and urbanization (Jiang and O'Neill 2017) projections provided in the SSP database (International Institute for Applied Systems Analysis 2018) as boundary conditions. These projections differentiate developments in high-fertility, rich OECD lowfertility, and other low-fertility countries, and include assumptions on fertility, mortality, education levels, and international migration (Kc and Lutz 2017). To reflect the future spatial development patterns per SSP, we modified the calibrated β parameters for each SSP by interpreting the qualitative assumptions described in the global SSP narratives O'Neill 2017, O'Neill et al 2017) and the Mediterranean coastal SSP narratives (Reimann et al 2018), and by conducting a sensitivity analysis (SM7). Additionally, we applied SSP-specific population density thresholds per grid cell based on the observed maximum population density of 2015, and accounted for future changes in habitability under the SSPs by adjusting the spatial mask l i . Finally, we produced population projections in ten-year time steps from 2020 to 2100 and for each SSP by modeling urban and rural populations separately based on the respective coastal and inland β parameters. We further redefined some rural and urban population cells after each time step based on population density and contiguity (following Jones and O'Neill 2016) before combining them to obtain the total population.

Results
The spatial population projection datasets produced for each SSP and ten year time step are publicly available at Reimann et al 2021 The following sections first describe the spatial population patterns per SSP and then provide a more detailed description of the urban as well as coastal population patterns in the two geographical regions. Figure 2 presents a selected set of the population projections, including the baseline distribution (2010) along with each SSP in 2100. These spatial population patterns reflect the national-level population (Kc and Lutz 2017) and urbanization projections (Jiang and O'Neill 2017) (SM8) as well as the qualitative assumptions regarding spatial development patterns described in each SSP . In SSP1, countries experience rapid urbanization, with urbanization levels of around 95% (2100) across the entire region. Effective management combined with population decline in the second half of the century results in high-density, compact urban settlements. In SSP2, urbanization is less rapid, with higher urbanization levels in the northern parts of the region (ca. 93%) compared to the South and East (roughly 85%). Population growth is mixed across countries and spatial development is slightly more concentrated than observed in historical patterns, leading to urban sprawl in countries with high urbanization levels and a growing population (e.g. France, Israel). SSP3 is characterized by low urbanization rates, with urbanization levels of roughly 84% in the northern Mediterranean and 65% in the southern and eastern Mediterranean. Population declines in almost all northern countries and increases rapidly in southern and eastern countries, resulting in sprawling development in the South and East. In SSP4, urbanization increases rapidly, with urbanization levels of around 93% across the region. Population decreases in most countries, notable exceptions being France and countries of the Middle East, where high urban sprawl can be observed until 2100. SSP5 is characterized by urbanization levels similar to those in SSP1, combined with rapid population growth in northern countries and the Middle East, which leads to considerable urban sprawl, particularly in northern parts of the region.

Urban population density
The population development patterns described in section 3.1 are further illustrated in figure 3 which presents urban population densities per SSP and geographical region. In the baseline year (2010), urban population density is about four times higher in southern and eastern Mediterranean countries than in countries of the Mediterranean North (figure 3(a)); this difference is projected to increase until 2100 under all SSPs, with the largest difference in SSP3, where urban settlements are projected to be eight times more densely populated in the South and East. In northern countries, urban population density increases in SSP1 and decreases in all other SSPs in 2100, compared to the baseline. The highest urban population density (1600 people km −2 ) is projected in SSP1 and the lowest density of roughly 700 people km −2 in SSP5. These results reflect the continuation of high urban sprawl (except in SSP1), in combination with population decline in the second half of the century in SSPs 1-4. In the South and East, urban population density increases in SSPs 1-3 and decreases in SSPs 4 and 5 until 2100, compared to 2010. The highest urban population density of over 8000 people km −2 is projected in SSP3, the scenario with the highest expected population growth in these countries; the lowest density of ca. 4150 people km −2 is projected under SSP4. Figure 3(b) presents the development of urban population densities in the course of the century, differentiating between coastal and inland locations. In both geographical regions, density is higher in coastal locations compared to inland locations under all SSPs and time steps except the base year. In the Mediterranean North, urban population density in coastal locations first increases in SSPs 1-4, before it decreases in the second half of the century; in inland locations, density decreases in the course of the century in all SSPs except SSP1 where it first increases and starts to decrease in 2080. In the South and East, urban population density increases in coastal and inland locations under SSPs 1-3, with a rapid increase in coastal locations, which levels off in SSP1 from 2080 onwards. Under SSPs 4 and 5, urban population density experiences some increase in coastal locations until 2070 and remains on a similar level in inland locations in the course of the century.

Coastal population
Comparing the population in coastal locations across SSPs and geographical regions (figure 4), we observe, similar to urban population density, a population three orders of magnitude higher in coastal locations in southern and eastern countries compared to the Mediterranean North in 2010 ( figure 4(a)). This difference is projected to increase until 2100 under all SSPs except SSP5 where coastal population increases considerably in the northern Mediterranean as well, resulting in the highest coastal population (15.2 million) in 2100. Further, the number of people in coastal locations in the North increases slightly in SSP1 and SSP2 and decreases in SSPs 3 and 4 compared to the baseline, with the lowest number of roughly 6.5 million people in coastal locations under SSP3. In the South and East, we observe the

Discussion
Our spatially downscaled population projections account for important migration processes within countries (i.e. rural-urban and inland-coastal) as well as for plausible future spatial development patterns (i.e. urban sprawl). As such they constitute improved representations of future population distributions and are useful for a wide range of IAV assessments. The spatial resolution (30 arc seconds) is suitable for capturing these development trends and patterns while avoiding a misleading impression of certainty as future socioeconomic developments are highly uncertain (Preston et al 2011, Sherbinin et al 2019. Therefore, we anticipate that the developed projections are particularly meaningful for assessments at continental to regional scales, for example for analyzing exposure to extreme heat, water scarcity, and flooding (coastal, fluvial, pluvial). In such assessments, it is important to consider different SSPs in order to represent the range of uncertainty in future exposure. The insights of these assessments can support decision-making by identifying hotspots of future exposure where adaptation is urgently needed. Therefore, decisions can be made that are robust under a wide range of plausible futures (Moss et al 2010, Walker et al 2013, Haasnoot et al 2020. However, to inform local-scale decisions such as the implementation of specific adaptation measures, more refined modeling approaches are needed that allow for integrating local characteristics based on more refined scenario assumptions (e.g. Reimann et al 2021) and more detailed input data to further downscale the developed population projections (e.g.

Merkens and Vafeidis 2018).
Our results suggest higher future climate change exposure in southern and eastern Mediterranean countries compared to northern Mediterranean countries due to consistently higher urban densities and coastal population under all SSPs. However, exposure would differ markedly across SSPs, depending on the socioeconomic challenges for adaptation that result from differences in the effectiveness of policies and institutions, economic growth, and technological change among others .
Assuming that an increase in urban population density increases the urban heat island (UHI) effect, therefore leading to higher urban heat stress, which will exacerbate due to climate change (Chapman et al 2017, Koomen and Diogo 2017, Vanos et al 2020, heat exposure would be highest under SSP3 in the South and East and SSP1 in the North. As SSP1 is characterized by sustainable development with well-managed, compact urban areas and low adaptation challenges, it would result in potentially lower exposure than SSP3 (assuming all else equal), as SSP3 is characterized by high adaptation challenges due to slow economic growth, low technological development, and weak policies and institutions. Similarly, coastal exposure would be highest in the South and East under SSP3, with a large share of the coastal population living in rural settlements, where coastal protection is expected to be rarely pursued as costs often exceed benefits . In the North, coastal exposure would be highest under SSP5 and SSP1, which are both characterized by low adaptation challenges. Due to high urban sprawl in SSP5, we expect coastal adaptation to be more challenging than in SSP1. Furthermore, as SSP5 experiences rapid economic growth, residual risk would be high, leading to high damages in case of adaptation failure during coastal flooding. While we are aware that the future lies somewhere between (or even beyond) the five SSPs , our results suggest that future spatial population patterns will contribute to higher exposure in the southern and eastern Mediterranean, which may exacerbate already existing disparities between the two geographical regions (MedECC 2020).
To be able to further contextualize these results, the population projections can be enriched by additional demographic and socioeconomic variables important for IAV research, such as age, sex, race, education, poverty, and income.  (Murakami and Yamagata 2019). Furthermore, our projections do not account for the potential impacts of climate change on migration, which is expected to increase once impacts such as flooding, heat stress, and droughts become more severe (Black et al 2011, McLeman 2019. To account for this effect, plausible future changes in climatic conditions based on the Representative Concentration Pathways (RCPs) (Van Vuuren et al 2011) can be integrated into the model to produce projections that account for climate change-induced migration, a first example being the work of Rigaud et al (2018). Such integrated assessments can additionally explore potential feedbacks between climate change, adaptation strategies, and migration patterns, which are expected to influence future impacts substantially (Aerts et al 2018). An aspect that we have not included in this study is the influence of shocks such as conflict, economic crises, or pandemics (e.g. COVID-19) on socioeconomic development as shocks are, by definition, not captured in the plausible 10 descriptions of the SSPs. However, as we explore a large range of uncertainty by projecting spatial population patterns under the five SSPs, we assume that the effects of most shocks are covered by this uncertainty range, as pointed out by O'Neill et al (2020).
To evaluate the performance of the model in producing spatial population projections, we compared our results to those of previous work that accounted either for inland-coastal migration (Merkens et al 2016, Reimann et al 2018 or for urban sprawl (Jones andO'Neill 2016, downscaled by Gao 2017). As two studies do not provide projections that distinguish between urban and rural populations, we focus on the coastal population. We find that the population numbers projected in coastal locations in 2100 for each SSP are similar across the four studies, but also show marked differences (figure 5). Similar to Jones and O'Neill, we project the highest coastal population of 108 million in SSP3 and the lowest population of 51 million in SSP4. However, we project a 13%-25% higher coastal population than Jones and O'Neill under all SSPs except SSP3 where our projected population is 0.9% lower. These patterns reflect the higher attractiveness of coastal locations implemented in our approach, as established during model calibration (SM5). In SSP3, this effect is superimposed by rapid population decline in northern Mediterranean countries in SSP3 (section 3.1), which leads to a higher decline in coastal population in our approach compared to Jones and O'Neill as population decline takes place relative to attractiveness (i.e. more attractive locations experience higher decline). This potential model limitation needs further analysis which is currently inhibited by a lack of empirical evidence regarding the spatial patterns during phases of population decline (Grübler et al 2007, Jones andO'Neill 2013).
In contrast to our approach, the coastal approach of Merkens et al and Reimann et al projects the lowest coastal population of 41/35 million in SSP1, based on the assumption that the implementation of regulatory policies leads to sustainable and effective management of coastal areas, thereby reducing their attractiveness. The number of coastal inhabitants is about 30%-40% lower compared to our approach. This difference reflects one limitation of the gravity approach, which models aggregate population trends primarily based on the distance-decay effect (section 2.1) and does not account for the effects of policy on a location's attractiveness. Future work can integrate such effects into the model as an additional model layer similar to the spatial mask (l i ), in which the population potential in effectively managed locations could be set to 0. Further, SSP5 is the only scenario where the coastal approach results in roughly the same or a slightly higher number of coastal inhabitants (5%) as it assumes coastal locations to be very attractive, while not accounting for the sprawling development that we assume under SSP5.
Of the four approaches, our approach spans the narrowest uncertainty range across the SSPs with regard to the population projected in coastal locations in 2100 (i.e. 56.5 million versus 61.1-64 million), which suggests that accounting for several processes that drive spatial population patterns can reduce the range of uncertainty. As our approach results in the highest number of coastal inhabitants under almost all SSPs, we expect these results to be particularly meaningful from a risk-management perspective as strategies for reducing risk can be developed based on 'worst-case' conditions (Hinkel et al 2015). Comparison of the spatial population patterns projected under the four approaches further supports that our approach produces plausible results (supplementary figure 9). However, it also illustrates the limited comparability of the four modeling approaches due to different input data used, which result in distinct spatial population patterns.
When using our population projections, the following additional limitations need to be considered. First, we calibrated the model to a relatively short period of twenty years due to a lack of long-term gridded population data. This period was characterized by population growth in most Mediterranean countries. As we expect to see declining population numbers in the second half of the century under almost all SSPs, the observed changes in population patterns are not necessarily indicative of future patterns. Second, since we were not able to calibrate the β parameters for each country individually, the calibrated parameters may not reflect the spatial development patterns in all countries of the respective geographical region to the same degree. Similarly, we had to post-process the calibrated parameters to reflect differences in development patterns in coastal versus inland locations as our calibration procedure did not produce plausible parameters for these locations. We assume the reason for this being the small strip of land defined as coastal compared to its inland counterpart, which may impede finding the optimal β parameter (section 2.2; SM5). Third, we would like to point out that the redefinition of grid cells into urban and rural populations after each projection time step (section 2.4) can follow a different algorithm than the one used in this study, one example being the 'degree of urbanization' .
More broadly, gravity-based models have several limitations that merit further discussion. First, the underlying assumption that densely populated locations are more attractive for human settlement than less densely populated locations results in higher population growth in large cities compared to smaller cities, although small-and medium-sized cities are expected to experience higher population growth in the next decades (Birkmann et al 2016, United Nations, Department of Economic and Social Affairs, Population Division 2019, Gao and O'Neill 2020). To account for this phenomenon, the population potential can be calculated conditional to the city size (i.e. the total number of people residing in an urban agglomeration), which could be implemented in the model in follow-up work. However, by applying the local attractiveness factor A i and a population density threshold per grid cell (SM7), our approach produces more diverse spatial patterns than a basic gravity approach. Second, as population potential is calculated based on observed settlement patterns, these patterns consolidate in the future, and new settlements can only emerge under very specific conditions. While this limitation may result in implausible spatial population patterns in less developed countries that are expected to experience rapid population growth until 2100, we expect it to be negligible in the Mediterranean region as population is expected to decline in the second half of the century in most countries and SSPs; in those countries that will experience rapid growth (e.g. the MENA (Middle East and North Africa) region under SSP3) land available for human settlement is limited (supplementary figure 2); Mediterranean settlement patterns have developed since antiquity (Cazenave 2014), thereby giving reason to believe that new settlements are less likely to emerge.
Despite its limitations, CONCLUDE produces plausible distributions of future population patterns for each SSP, which can be updated once new knowledge and data become available. The model allows for integrating additional model layers (e.g. a policy layer) as a weight on the population potential (v i ), and can be extended to explore climate changeinduced migration, for example by correlating the local attractiveness factor A i to changes in environmental conditions with the help of spatial regression models (Rigaud et al 2018). Due to its modest data requirements, we expect the model to be particularly relevant for producing consistent projections in datascarce regions like the Mediterranean region, where detailed region-wide data are often lacking (Lange et al 2020). As we rely on freely available global input data, the model can easily be extended to other continents, regions, or the global scale, given that sufficient computing resources are available.

Conclusion
This paper presents SSP-based gridded population projections that account for rural-urban and coastal-inland migration processes as well as for spatial changes in settlement patterns (i.e. urban sprawl), which have been produced with CON-CLUDE, an extended gravity-based model specifically developed for this study. We apply the model to the Mediterranean region, accounting for distinct characteristics in northern versus southern and eastern Mediterranean countries. Our projections have a spatial resolution of 30 arc seconds, a temporal resolution of ten-year time steps (2020-2100), and are consistent with the five SSPs, both in terms of qualitative narrative assumptions as well as national-level population projections. These projections explore the range of uncertainty regarding plausible future spatial population patterns in the 21st century and are useful for a wide range of IAV assessments. The model can be extended to account for the effects of climate change or spatial policies on a location's attractiveness for human settlement. As the model has modest data requirements and is calibrated to freely available global input data, it can be extended to other continental and/or global scales.
Future work can further refine the modeling approach by addressing its limitations such as separately calibrating the model to coastal versus inland locations; selecting a larger set of countries for the β calibration; and calibrating the model separately to phases of population growth and decline. Such refinements can also include the use of higher-resolution input data to be able to produce meaningful results at regional to national scale. Suitable datasets may be WorldPop (Tatem 2017) or a higher-resolution version of GHS-POP , which are available at spatial resolutions of 3 arc seconds and 9 arc seconds, respectively. Further, a systematic assessment of the model's sensitivity to different population input data, urban versus rural population classification algorithms, and the choice of β parameters would provide useful insights for model users. Moreover, the model can be extended for integrated assessments to explore feedbacks between climate change impacts, adaptation strategies, and migration processes. For such assessments, different SSPs, RCPs, and Shared Policy Assumptions (SPAs)  can be combined, as envisaged as part of the SSP-RCP-SPA scenario framework . Additionally, future research can explore the potential of the model for producing spatial projections of other key variables in IAV research. Last, we would like to encourage use of the developed population projections in Mediterranean IAV assessments.

Data availability statement
The data that support the findings of this study are openly available at Reimann et al 2021. These data include gridded population projections for each SSP and ten-year time step (2010-2100). The model scripts (R Core Team 2020) are available from the corresponding author upon reasonable request.