Residential environments across Denmark have become both denser and greener over 20 years

Despite much attention in the literature, knowledge about the dynamics surrounding urban densification and urban greening is still in dire need for architects, urban planners and scientists that strive to design, develop, and regenerate sustainable and resilient urban environments. Here, we investigate countrywide patterns of changes in residential density and residential nature at high spatial resolution over a time period of >20 years (1995–2016), combining a dataset of address-level population data covering all of Denmark (>2 million address points) with satellite image-derived normalised difference vegetation index (NDVI) data. Our results show that many residential environments across Denmark have witnessed simultaneous densification and greening since the mid-1990s. In fact, the most common change within 500 m neighbourhoods around individual address points is of joint increases in population and NDVI (28%), followed by increasing NDVI with stable population figures (21%). In contrast, only 8% of neighbourhoods around address points have seen a decline in either population or NDVI. Results were similar in low- middle- and high-density environments, suggesting that trends were driven by climate change but also to some degree enabled by urban planning policies that seek to increase rather than decrease nature in the cities.

Urban densification, the process of infilling the urban fabric and building upwards to increase urban density, is a strategy to prevent sprawl and achieve less energy-intensive cities while accommodating a global growing urban population [1]. However, its environmental gains have often not been properly examined [2], while it is often implicitly or explicitly considered irreconcilable with urban greening [1]. Meanwhile, nature that might be developed through urban densification provides regulating ecosystem services that are important for the wellbeing of urban residents. Green infrastructure at the metropolitan scale can provide climate change mitigation through carbon sequestering [3,4]. But more importantly, ecosystem services provide climate change adaptation, where temperature regulation and flood regulation are examples of insurance capital as extreme weather events associated with global warming become increasingly common [4][5][6]. Thus, the roles of ecosystem services for simultaneous climate adaptation and mitigation will likely grow, posing challenges for regional land use policies aiming at reducing car travel and urban sprawl in the midst of urbanisation [2,4,7].
The interplay between density and nature is also related to urban residents' well-being through mechanisms operating at the local scale. Among many ways to conceive of density, we focus on density of people. This is because city living is linked to social stress processing [8], which suggests that the higher prevalence of depression and anxiety in cities compared to the countryside [9] could be explained by exposure to many people. As an antidote to social stress, nature experience can promote health by inducing in people a state of low psychophysiological stress and restored cognitive functioning [10]. Cross-sectional evidence corroborates this interplay between experiences of social stress and restorative experiences in people's everyday life [11], while longitudinal evidence shows that growing up in greener residential areas is linked to lower risks of adulthood mental illness [12].
While the above outlined relationships between specific environmental factors and well-being are well studied, there is a relative absence of studies looking at patterns over time of density and nature in combination. Such a perspective is urgently needed for relating long-term and global scale processes such as urbanisation and climate change to local residents' well-being, both in terms of how they impact on everyday urban life but also with respect to how they impact on the ability to buffer disturbances that are likely to become more frequent in the future. Some previous studies exploring anthropogenic effects on urban vegetation have focused on distance from city centre [13], income [14] or compound measures of human activity [15]. A recent study found large parts of Berlin to have undergone simultaneous residential densification and greening over the last decade [16]. Here, we complement these studies by investigating patterns of residential density and residential nature over a time period of >20 years (1995-2016) across Denmark. Denmark has a population of about 5.8 million people in an area of about 43 000 km 2 . It has a temperate climate, with most of the country located between latitudes 55 • and 57 • N and at the terminal section of the Gulf stream. The predominant landuse is agriculture, which is interspersed with built-up areas and forest (figure 1). Copenhagen, the capital, is the largest city, with some two million people living in the metropolitan area.
To measure residential nature, we use satellite image-derived data on the normalised difference vegetation index (NDVI), a simple arithmetic transformation of spectral data [17]. Satellite-image derived NDVI can capture detailed variability in greenness across urban landscapes [18], making it suitable to analyse long-term trends related to urban development. Studies looking specifically at NDVI over time in urban areas have found that it tends to decrease with rapid urbanisation [19] but can subsequently increase as spatial expansion slows down [13,20]. Changes in NDVI also relate to large-scale drivers. Warmer temperatures in the temperate zone has been found to drive regional NDVI increases in the 1990s and 2000s [21,22]. However, the correlation with temperature has seemingly decreased in recent years while the correlation with precipitation has increased [15]. Species diversity has also been suggested as a driver in the temperate zone [23].
Rather than analysing NDVI across the complete landscape, we combine it with a dataset of addresslevel population data (>2 million address points) to estimate neighbourhood-scale exposure to nature [24]. This allows nationwide co-analysis with detailed measures of residential population density. In the following, we investigate neighbourhood changes in residential density and NDVI from 1995 to 2016, first across all Danish residential environments, and then broken down into categories of low-, medium-and high-residential density.

Address-level exposure
To measure population density and exposure to greenspace, individual address points were used. This data was derived from the 2016 version of the geocoded Danish Residence Database from the register of official standard addresses (for details, see [26]). We used only records with exact coordinates (∼2 million addresses, or ∼97% of all records within the borders of Denmark), excluding some entries where the address was recorded only within a 1 × 1 km area. For each address point and for each year 1995-2016, we calculated the number of residents and amount of greenspace within circular areas of 250, 500 and 1000 m radii (hereafter called neighbourhoods, see figure 2 for illustration).

Population density
Population density estimations are based on individual residence records from the Danish Civil Registration System as documented in the Danish Residence Database [26]. This database is maintained by Centre for Integrated Register-based Research at Aarhus University (CIRRAU) and contains the exact number of individuals at each address point. Due to Danish data protection regulations, data can only be exported from the CIRRAU data environment and co-analysed with other data after it is anonymised, posing issues with neighbourhoods with very few residents. Thus, the exact number of residents within neighbourhoods on 1 January for each year was calculated in SAS software through a series of SQL statements based on distances between points, before measurements were truncated into 50 unit bins (i.e. measurements of 0-49 persons were reassigned to 25, 50-99 persons were reassigned to 75, etc). A total of 50 unit bins were used as they ensure that measurements are anonymous in the least densely populated areas, but also retain much variation between addresses as neighbourhood measurements are often in the 100s or 1000s (figure S1, which is available online at stacks.iop.org/ERL/16/014022/mmedia). Measurements in this truncated form were then exported and co-analysed with NDVI data.

NDVI
In Google Earth Engine [27], we accessed surface reflectance Tier 1 images from Landsat-5 (TM) from 1995 to 2012 [28], Landsat-7 (ETM+) from 1998 to 2018 [29] and Landsat-8 (OLI) from 2012 to 2018 [30]. These data are at 30 m spatial resolution with systematic terrain correction and atmospheric correction, including a per-pixel cloud mask produced with the Fmask algorithm [31], allowing removal of cloud and cloud shadow pixels within Google Earth Engine. Two collections of scenes were created: first, from 1 May to 31 August, and second, from 1 July to 31 July. The reason for this was to explore and disentangle trends for the majority of the growing season and the peak of it, respectively. NDVI was calculated from the near-infrared (NIR) and red (R) bands using the formula NDVI = (NIR−R)/(NIR+R). Per-pixel median values were extracted from each composite to produce annual NDVI images.
Using data from Landsat-7 (ETM+) and Landsat-8 (OLI) in time-series can entail complications as they are equipped with different sensors [32]. To calibrate these data, NDVI values for August 2015 from each satellite were extracted at 10 000 sample sites across Denmark, allowing evaluation of the effects of transforming OLI data through reduced major axis (RMA) regression as well as ordinary least squares regression (see [32]). We used the coefficients reported in Roy et al [32] and found RMA regression to better adjust the underestimated reflectance in OLI images (figure S2), and thus multiplied NDVI values from Landsat-8 with the RMA regression coefficients to harmonise data across the years.
To get rid of water areas that would bias neighbourhood NDVI calculations, a masking layer created from the Danish land-use land-cover map from the year 2011 [25] was used (for details, see supplementary information). After removing water areas, moving windows (function 'focal' in [33]) were used to calculate mean NDVI values for the three neighbourhood scales. Because of the 30 m cell size, we used quadratic matrices with radii of 255, 495 and 1005 m (17 × 17, 33 × 33 and 67 × 67 cells, respectively) where cells in corner areas were given no weight while remaining cells were given weight 1 (see figure 2 for illustration). NDVI values were joined to addresses by overlaying rasters with address points from the Danish Residence Database and assigning points with the value of the overlapping raster cell.

Calculating and mapping trends of change across Denmark
The change of the Danish population's residential environment was explored over the study period. For each address point, neighbourhood residents and NDVI within 250, 500 and 1000 m, respectively, were regressed on time in years. As predictive capacity was not an objective of the models, we used linear regression, without incorporating non-linearity or an autoregressive term. Coefficients of annual change for each variable at each address point were extracted, unless time did not predict a change in a variable (p-value > 0.05) when the coefficient was set to 0.
To explore combined changes in population and NDVI, a 3 × 3 matrix with the classes increasing, stable or decreasing for each variable was used to assign each address point a population-NDVI combination. Changes in environments of different density were explored by splitting the dataset into three roughly equally sized population density categories (<400, 400-1200, and >1200 people within 500 m) to investigate population and NDVI trends up until 2016 in the least, middle and most dense thirds of neighbourhoods separately. For May-August values and July values, respectively, median, 20th percentile and 80th percentile values were calculated in each of the categories. Linear models with median values regressed on time in years were fitted.
All results were visualised with maps of regression coefficients across Denmark, as well as histograms, bivariate density plots and time series diagrams.

Validation of NDVI trends
The trends observed in our NDVI dataset were verified by comparing it to three other satellite image datasets. The methods and results of this validation can be found in the supplementary information.

Results
As the patterns of changes within 250 and 1000 m neighbourhood sizes did not differ considerably (see table S1), the results section focuses on changes within 500 m of address points (NDVI values reported are median values from 1 May to 31 August unless otherwise stated). Within 500 m neighbourhoods, the median population has increased by 12% from 825 people in 1995-925 people in 2016 ( figure 3(a)). About 740 000 address points (35%) had stable population numbers-these occur in all types of settings, but with a low median value of 225 people, indicating that neighbourhoods with unchanging population density are mostly rural. About 870 000 address points (42%) had a significant increase, while about 475 000 (23%) had a significant decrease. The density of these environments largely overlap; the median in the increase group went from 1025 to 1275 people (+24%), while the median in the decrease group went from 1125 to 975 people (-13%). Changes in population are geographically unevenly spread across Denmark (figure 4). The largest increases have occurred in central parts of larger cities, whereas the largest decreases have mostly occurred in fringe suburban areas of larger cities. Thus, population flows in Denmark since 1995 has not been an urbanisation process in its classical meaning (see [34]), as the overall share of urban dwellers has not increased much.
NDVI fluctuates considerably from year to year, but overall there is a clear increasing trend: residential environments in Denmark has become greener (see figure 3(b) for histograms and figure 5 for a map). The mean regression coefficient times the number of years of the study period amounts to 0.028 (a 7% increase). Most of this increase occurred in the latter half of the 1990s. A total of 1.33 million address points (64%) had a significant increase, while only 44 000 (2%) had a significant decrease. The NDVI values of these groups largely overlap. 710 000 address points (34%) had stable NDVI values; these areas had on average higher values than both increasing and decreasing areas, as can be seen when comparing the green and grey areas in figure 3(b).
In terms of combined changes of population and NDVI, classified as either increasing, stable or decreasing, all combinations are represented (table 1). However, joint increases is the most common combination (roughly 580 000 address points), >100 times more common than joint decreases, the least common combination (roughly 5600 address points). Joint increases is the most common combination in the large cities but also appear in other environments, whereas increasing populations coupled with stable or decreasing NDVI is found in some areas of new development in cities, stable populations coupled with any NDVI change is found mostly in rural areas, and decreasing populations with increasing NDVI is found in fringe suburban areas of cities( figure 6).
In 1995, about 665 000 points (32%) had a neighbourhood population below 400. The median population in this category stayed stable at 75 in both 1995 and 2016, while the median NDVI increased from 0.45 to 0.51. About 675 000 points (32%) had a population from 400 to 1200. The median population in this category increased from 755 in  7(b)) but for no categories for only July (figure 7(c)),indicating that despite generally increasing NDVI there has not been an increase in peak period greenness. A visual inspection   of the trends seems to suggest a browning from 2001 to 2007 and then greening again from 2007 to 2016, especially in denser environments. The trend is smoother with less oscillations in denser environments compared with less dense, which is reflected in better linear model fits. Trends for the 20th and 80th percentiles in each category follow the medians closely. These results overall suggest that residential environments across Denmark have generally become greener, irrespective of population density and despite continued densification.

Discussion
Our main result is counter-intuitive when imagining a spatial trade-off between residential densification and residential greening. We found that residential environments down to the level of neighbourhoods surrounding individual address points across all of Denmark have generally become both denser, in terms of residential population, and greener, in terms of NDVI, since the mid-1990s. This study complements those by Persson et al [14], that revealed a greening trend in Stockholm, Jin et al [13] and Du et al [20], that revealed greening in some Chinese cities, and Wellmann et al [16], that showed how Berlin has also undergone simultaneous densification and greening. However, to our knowledge, this analysis is the first to show a nationwide consistent greening trend in densifying urban environments around individual address points where the urban residents live.

Potential reasons for densification and greening across Denmark
One of our main findings is that NDVI changes have been generally positive, regardless of neighbourhood residential density or greenness. This calls into question whether the trends revealed in this study is attributable to factors unrelated to the built environment. Denmark has like most of the world got warmer in recent decades; the temperature average between 2006-2015 was 1.2 • C higher than the 1961-1990 average [35]. The NDVI trend observed in this study resembles a large-scale greening-browning-greening pattern across the northern hemisphere during 1982-2012 [15]. Increasing NDVI >35º N in the nineties can largely be attributed to increasing temperatures [21]. Warmer weather has led to longer growing seasons in Europe [36][37][38]. However, the relative importance of temperature as a driver has decreased over the last decades while the relative importance of precipitation has increased [15]. As climate change unfolds and temperature becomes less of a limiting factor for plant growth in northern Europe, variability in precipitation will likely increase both within and across years [39]. This calls into question how urban planners and landscape architects can adapt to this development by creating green infrastructure that thrive in variable precipitation conditions and at the same time build resilience towards extreme weather events [5]. Even though NDVI change is affected by global drivers, land-use and spatial planning also matter. This might explain why Denmark's rural areas display divergent patterns (figure 5). NDVI has increased most in mainland Denmark's central and southwestern parts that consist of sandy outwash plains. These areas have been the target for policies aiming to double the area of forest [40] and restore wetlands [41]. The rest of Denmark mostly have soils of clayey tills where many rural areas do not show an NDVI increase. For example, on the island Samsø (located between (A) and (C) in figure 5), the forested areas are stable, whereas areas of NDVI decrease could reflect agriculture shifting to less green crops. Between 2011 and 2016, Samsø's total agricultural area was largely constant, but grass and potato cultivation decreased with 18% and 15%, respectively, and grain cultivation increased with 19% [42]. Similar developments may explain NDVI decreases in many rural settings throughout eastern Denmark.
Median NDVI throughout the summer has increased uniformly in the vast majority of urban areas even as residential density has also increased in many of these. However, we did not find evidence for an increased peak period greenness, suggesting that longer growing seasons accounted for most greening throughout the summer and that any areal increase or maturation of urban greenspace is small in comparison. However, trends driven by large-scale climatic variables might be complemented by urban planning policies that seek to enhance blue-green elements in already built-up environments (see for example [43]). The building volumes of Copenhagen and Aarhus underwent only modest horizontal and vertical expansion since 1987 while their populations grew [44]. The flow of people from suburban to inner-city areas could be seen as a reaction towards active planning for dispersion in the decades leading up to the nineties [45]. Moreover, Copenhagen has due to active interventions in its infrastructure witnessed a biking revolution since the nineties, with some 50% of journeys in the city now being carried out by bike [46]. This might have freed up some impervious surfaces for greening, as seems to have been the case in other greening cities [13].
In summary, even though climate change is reasonably the main driver behind greening in Denmark, the fact that Danish residential environments have also become denser might have been enabled due a shift in urban planning policy from a focus on spatial expansion to one of increasing rather than decreasing natural land in the cities. As a comparison, Berlin achieved simultaneous densification and greening by converting industrial land, brownfields or roads [16]. This provides some encouragement from the global perspective, as most large cities around the world have recently undergone spatial expansion [47] associated with detrimental urban encroachment on carbon pools, biodiversity and fertile farmlands [48,49], and might now be in a position to switch course. Yet, the added pressure on well-being for urban populations that climate change presents is not evenly shared across the world, nor across social classes within each city [50]. Also, while urban citizens of the Global South are expected to disproportionately be impacted by climate change, the greening of neighbourhoods in the Global North is in part possible because natural resources are withdrawn from distant ecosystems by way of social-ecological teleconnections [51]. This calls for integrated systems assessments on scales from the local to the global in the area of urbanisation and land-use intensification.

Limitations and further work
The processed dataset post anonymisation does not contain information on residents at individual address points, but only on the number of residents within neighbourhoods. In most single-family houses, residents per address point would be 2-5 people, but in large multi-story buildings, this might be hundreds of people. Thus, even though we can determine how residential environments themselves have changed over time, we cannot in detail answer the question how neighbourhood population density or NDVI has changed for the average resident in Denmark. We can, however, with confidence say that most residents have experienced simultaneous densification and greening of their home environment. This is because address points in neighbourhoods with larger populations as a general rule will have more people living at them, so these environments would have been 'weighted heavier' in an individualunit analysis. Future work could link these neighbourhood measurements to individuals to study health outcomes. From the point of view of advancing theory around stress reduction [52], attention restoration [53] and biophilia [54], it would be illuminating to study areas that have seen increases in both NDVI and people. The biophilia hypothesis predicts that these areas have become more conducive to well-being, while stress reduction theory and attention restoration theory predicts that there could be some breakpoint where negative impacts from stress induced by crowding outweighs the positive impacts from sensory interaction with natural features.
Our study is ecological in nature, meaning that we investigate average neighbourhood changes. The utility of this approach rests on a 'proximity argument' , i.e. that individuals are exposed to the environment in which they live. This could be refined by using personalised sensors (see [55,56]) to understand the daily trajectories of people, to move from ecological measures to individualised exposure and provide a better understanding of to what extent and under what circumstances the 'proximity argument' holds for modelling real-life exposure.

Conclusion
With space in cities being a limiting resource, scholarly discussion around urban sustainability is still often framed in a simplistic dichotomous fashion, which hampers understanding of what makes urban neighbourhoods resilient from the point of view of urban residents' well-being [11]. With increasing availability of large high-resolution spatiotemporal datasets and better methods for extracting information relevant for urban life from these datasets [44], we are better suited than ever to conduct multivariable dynamic analyses of the urban environment. Herein, we have presented a methodologically relatively simple yet high-resolution analysis of residential density and residential nature across Denmark. We not only uncovered an expected large variation between different neighbourhoods, but also to us, a surprising yet robust result: over a period of ca. 20 years the general trend across Danish neighbourhoods has been of simultaneous increasing population density and greening. Furthermore, migration within Denmark has been characterised more by population flows from suburbs/exurban areas to innercity areas, rather than between rural and urban areas. However, all kinds of residential environments in Denmark have become greener over the past decades, even those kinds where most population growth has occurred. Crucially, this is not a net result of some areas densifying and others greening but is true of neighbourhoods around individual address points.
We realise that the capacity to respond to global processes and the pressure on urban well-being that climate change presents is not evenly shared across the world, nor across social classes within each nation [50]. Yet, our results lend support to the possibility that cities in industrialised nations can become both denser and greener. Most large cities still plan for the automobile, resulting in urban encroachment on biodiversity-rich land and fertile farmlands with detrimental impacts on both local well-being and the global Earth system. However, as this is to our knowledge the first nationwide analysis at the level of individual address points, it is possible that the patterns we found can also be found elsewhere. We welcome further investigations as these results provide much needed encouragement for sustainable urbanisation around the world.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.
The script used for downloading NDVI data in Google Earth Engine can be found here: https://code.earthengine.google.com/10e03693709 ac04d84f1a333a7f9b538 All R scripts used to prepare data, calculating values around addresses, and performing regressions can be found here: https://github.com/kallesam/ dk_pop_nat The data that support the findings of this study are available upon reasonable request from the authors.

Acknowledgments
We appreciate the valuable input from Carsten Bøcker Pedersen, Ingo Fetzer and Adrian Baggström in discussions around the design and implementation of this research. K S was supported by FORMAS Grant No. 2016-01193. T-H K C was supported by a PhD scholarship from the Taiwanese Ministry of Education, and T-H K C and C S were supported by BERTHA-the Danish Big Data Centre for Environment and Health funded by the Novo Nordisk Foundation Challenge Programme (Grant No. NNF17OC0027864). K S and T-H K C designed the research with input from C S and S B; K S, T-H K C and S A prepared the data; K S and T-H K C performed the analysis; and K S, T-H K C, S A, S A B, C S and S B wrote the paper.