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ABSTRACT The COVID-19 pandemic and the resulting economic recession negatively affected many people’s physical, social, and psychological health and has been shown to change population-level

mobility, but little attention has been given to park visitations as an indicator. Estimating the frequency of park visitations from aggregated mobility data of all the parks in Washington

State (USA), we study trends in park use one year prior to and two years during the COVID-19 pandemic. Our findings indicate that the gravity model is a robust model for the park visitation

behavior in different spatial resolutions of city level and state level and different socio-economical classes. Incorporating network structure, our detailed analysis highlights that

high-income level residents changed their recreational behavior by visiting their local parks more and a broader recreational options outside of their local census area; whereas the

low-income residents changed their visitation behavior by reducing their recreational choices. SIMILAR CONTENT BEING VIEWED BY OTHERS CHANGE OF URBAN PARK USAGE AS A RESPONSE TO THE COVID-19

GLOBAL PANDEMIC Article Open access 07 November 2023 HISTORICAL REDLINING AND PARK USE DURING THE COVID-19 PANDEMIC: EVIDENCE FROM BIG MOBILITY DATA Article 24 June 2023 EXPLORING PARK

VISITATION TRENDS DURING THE COVID-19 PANDEMIC IN HUNGARY BY USING MOBILE DEVICE LOCATION DATA Article Open access 08 July 2023 INTRODUCTION Parks and recreational systems serve as vital

connectors, linking both residents and visitors to the beauty of nature, offering opportunities for physical and mental well-being 1,2,3,4, and fostering social interaction and community

cohesion5,6,7. Having information about park visitation and usage is an important first step for policymakers to be able to address and plan for fair and equitable access to parks7

especially during significant societal disruptions such as those observed during the COVID-19 pandemic. During the COVID-19 pandemic, many people shifted to remote working and different

socio-economic classes exhibited disparities in their mobility choices as well as leisure time and affordances to access parks and recreational sites. At the population level, some evidence

indicated that park visitation increased in 20208,9,10. However several recent studies on the impact of the pandemic on park visitation have concluded different observations. A global

analysis of park visitation patterns using data collected primarily from Google’s Community Mobility Reports11 showed that park visitation has increased since February 2020, compared to

visitor numbers prior to the COVID-19 pandemic8. Other studies, such as12 showed a 14% decline in urban park visitation during the pandemic, based on a study of US urban parks using data

from SafeGraph13. In8 authors conducted a longitudinal study of Instagram posts from 100K users (1,185 green spaces) in four Asian cities and showed a 5.3% surge during the pandemic. Suse et

al.14 also used Instagram data to show that there are contrasting observations across 4 US metropolitan cities and argued more contextual information is needed to explain the differences.

Despite its importance, little attention has been given to understanding and modeling the statistical and structural patterns of park visitations and how these patterns have been changed in

regards to seeking nature and recreational opportunities during large societal phenomena such as the COVID-19 pandemic. In a broader domain of literature, human mobility has been studied in

the past decades15 from various perspectives. Existing large-scale mobility studies have applied state-of-the-art models such as the gravity model16,17,18,19, the radiation model20 and

others21,22,23 to seek understanding of city structure24,25,26,27,28, epidemics29,30,31, and visitation patterns32. In order to improve our understanding of park visitation, here we seek to

model park visitations into the underlying statistical and structural patterns of travel distance over a period of two years. To do so, we borrow tenets from mobility literature and apply

the state-of-the-art mobility model based on the Gravity Law that has successfully modeled mobility by concentrating on the spatial dependence of population flows. The gravity model has been

widely applied in the past with great success in modeling the mobility behavior of people across the city in different contexts such as transportation16,33, migration34 and most recently

smart mobility such as dock-less bicycles35,36. In this study, we analyze large-scale longitudinal park visitation data from a year prior to the COVID-19 pandemic and one year during. Our

data is based on the aggregated mobility data from mobile phones, which captures the visitation count of 3,665 parks and recreational sides of different sizes and functionalities across the

state of Washington, USA. Our analysis makes the following actionable insights for researchers and the community of practitioners: On one hand, we show that the statistics of park visitation

obey the general gravity model and are robust with variations on population-related parameters (i.e., socio-economic level of visitors), spatial-related parameters (i.e., size of the city)

and a temporal-related parameter (i.e., seasons). We also show that the gravity model exhibits different parameters pre and during pandemic for different socio-economic groups of the

population. Simply put, our results indicate that park visitation behavior for lower-income level class exhibited the least changes during the pandemic, however; this change is a function of

random variation and is not predictable. Furthermore, for the higher income level class we observe more pronounced changes in park visitation behavior during the pandemic, which can be

explained as the shorter distance visitations have increased at a greater rate. Comparing parks in different spatial city groups indicates that the visitation pattern for parks located in

large cities experiences a change opposite to the one that the visitation pattern for parks located in small cities. In larger cities, the behavioral change has focused on a reduction in

visitations to further distant parks, and in smaller towns behavior has changed towards an increase in further afield visitations. Our analysis of modeling park visitation as a network

structure shows that the in-degree distribution of parks is power-law, both pre-and during the pandemic. Moreover, we find a linear association related to both changes in visitor diversity

(in-degree of parks) and the recreational propensity of residents (out-degree of census blocks) due to the pandemic. The higher the socio-economic level of the census block, the less change

in their recreational propensity, maintaining a larger set of recreational options throughout the pandemic. Finally, from the park perspective, we observe that the larger parks exhibited a

greater positive change in the diversity of visitors, and parks that were more popular (measured as visitor density) prior to the pandemic exhibited a drop in the diversity of visitors

during the pandemic. RESULTS GRAVITY MODEL AS THE ROBUST PARK VISITATION MODEL IN WASHINGTON STATE We aim to study the park visitation behavior by the examples of parks in Washington State

and how it changes during the COVID-19 pandemic. In particular, we want to understand how the pandemic affects the behavior of different socio-economical and spatial groups in terms of park

visitation. In doing so, the first step is to find the general pattern that park visitation obeys. The gravity model in its general form asserts that the number of visits from the origin (i)

to destination (j), noted as _T__i__j_, is proportional to the number of visitors living in the origin _i_, _O__i_, the attractiveness of the destination j, _D__j_, a normalization weight

_W_, and finally, there is a decreasing function, _f_(_c_), in terms of the cost of the visit, _c_, which is dependent on the distance between i and j. The gravity model in its general form

can be formulated as Equation (1). $${T}_{ij}=W\,{O}_{i}\,{D}_{j}\,f(c)$$ (1) The gravity model is more general than other state-of-art visitation models, such as the radiation model20 and

the intervening opportunities model22 as all these models are special variants of the gravity model by choosing the proper cost function, f(c)15. Therefore, we consider park visitation obeys

the gravity model and tune the parameters of a general gravity model in a way that fits the park visitation patterns. To explore the park visitation patterns, we consider the home census

block group (CBG) of a visitor, _C__B__G__i_, as its origin, and the park it is visiting, _p__a__r__k__j_, as the destination. The home census block group for a visitor is the CBG the

visitor spends most of the nighttime hours there (see Methods). Our data is spatially aggregated, with the number of visitors originating from the _C__B__G__i_ as _O__i_. In addition, each

_p__a__r__k__j_ has _D__j_ number of total visits from origins. Since the number of visits from _C__B__G__i_ to the _p__a__r__k__j_, _T__i__j_, depends on the distance between them, we need

to calculate the distance between each pair of CBG and park. The distance between _C__B__G__i_ and _p__a__r__k__j_, _r__i__j_, is considered as the geodesic distance between the park

location and the census block location. In this problem, the gravity model can be formulated as: $${T}_{ij}=\frac{{O}_{i}}{{\sum }_{i}{O}_{i}}\times \frac{K{D}_{j}}{{r}_{ij}^{{\alpha

}^{{\prime} }}}$$ (2) with _K_ and _α_ parameters that are estimated based on the data fit. To measure the uncertainty of _α_, we compute the square root of the diagonal elements of the

covariance matrix of coefficients, known as the standard error of the coefficient, denoted by “se". We used aggregate mobile data from Washington State, USA. This data covers the visits

to 3665 parks from 220426 residential census blocks (See Methods for a full description of the dataset). We separated our data into two categories pre-pandemic and during-pandemic. The

pre-pandemic category starts from March 2019 upto but not including March 2020, and the during-pandemic category starts from March 2020 until March 2021. Additionally, the visitation data is

spatially aggregated up to the size of census block groups, therefore, we use granulating bins of equal length _δ__r__i__j_ = 0.5 km to calculate the distance (Fig. 1a). We now show that

_T__i__j_ for both above categories obeys the gravity model in the form of Equation (3), where \(\alpha =-{\alpha }^{{\prime} }\). $$\log \left(\frac{{\sum }_{i}{O}_{i}}{{O}_{i}}\times

\frac{{T}_{ij}}{{D}_{j}}\right)=\alpha \,\log ({r}_{ij})+\log(K)$$ (3) Figure 1b shows the gravity model for pre and during-pandemic data. In this plot, the slope of lines represents the

parameter _α_, and the y-intercept represents _l__o__g_(_K_) (Equation (2)). Put simply, the parameter _α_ quantifies the unlikelihood of visiting a distant park. That is the greater the _α_

is, visitation of closer parks becomes more frequent. In both categories, the park visitation obeys the gravity model accurately. Another observation is in regards to the parameter _α_

(i.e., the slope of the trend) where we can see that _α_ does not exhibit any significant change. The standard error (_s__e_) assesses the goodness of fit for _α_. However, to examine the

significance of the difference between the pre-pandemic and during-pandemic data sets, we conducted a pairwise z-test (See Methods). Throughout the rest of this article, we exclusively

report differences in _α_, indicating a preference for shorter or longer distances, only when the compared data sets show statistically significant differences, irrespective of the goodness

of the fit. To address the challenge of large overlaps in standard errors and enhance the reliability of the interpretation, a larger sample size analysis is required. In Fig. 1b, we found

that the two distributions are significantly different, as evidenced by a z-stat of 2.35 (_p_ < 0.01). This observation means that although during the pandemic park visitation has

significantly dropped (Supplementary Fig. 1), the general trend regarding the traveled distance has remained the same as a whole. As our goal is to study the behavioral changes in park

visitation due to COVID-19, we dis-aggregate our data to correspond to different seasons, socio-economic, and spatial groups and analyze if and how selecting a subset of our original data

affects the slope of gravity model (_α_). We remark that we do not investigate _K_ since it is a normalization parameter so that the sum of the visitors to _p__a__r__k__j_ from all CBGs,

∑_i__T__i__j_, is equal to _D__j_. Thus in the following sections, we will use filters based on the seasons, the socio-economical vulnerability of visitors, and the spatial scale of cities

to understand the differences between various behaviors of these groups during the pandemic. FILTERING BY SEASONAL PATTERNS As the literature on park visitation has previously shown37,38,

there is a large degree of variation in park visitation trends, both the number of visits and spatial behavior of visitors, during warmer and colder seasons. To account for seasonality in

park visitation trends, we divided our data into two temporal categories corresponding to the warm season when the average monthly temperature is higher than the average yearly temperature

(corresponding to May to October), and cold seasons with a mean monthly temperature lower than average yearly temperature (November to April). Figure 2 shows that the gravity model

accurately describes the park visitation pattern in cold and warm seasons separately. This shows that the gravity model is robust in describing the park visitation pattern after using

temporal filters. However, in comparing the two distributions during the cold season using a paired sample z-test, we observe no significant difference between pre- and during the pandemic.

Furthermore, we observe no difference in parameter _α_ pre- and during the pandemic after using the temporal filter. As previously mentioned, the magnitude of park visitation is different in

cold versus warm seasons, therefore we will keep the warm seasonal filter throughout studying the gravity model using socioeconomic and spatial filters. FILTERING BY SOCIOECONOMIC LEVEL OF

VISITORS Previous studies have already shown that the decrease in mobility due to the COVID-19 pandemic is related to the socio-economic level of individuals39,40,41,42. Besides, parks and

green spaces have been disturbed unequally between different socio-economic groups43,44. To indicate the difference in park visitation patterns of different socio-economic levels, we divided

our data into different groups based on the Social Vulnerability Index (SVI) of the origins (see Methods Section) and focused our analysis on socio-economic groups that capture the most and

least vulnerable parts of the society as commonly defined by sociologists45. The first group is the group with origins of visit from regions with SVI > 0.75, named as the most vulnerable

group, indicating the group of visitors which are the most vulnerable socio-economically speaking. The second group, which includes the group of visits originating from regions with SVI 

< 0.25 named the least vulnerable group. In order to study the effect of the COVID-19 pandemic on park visits of these groups, let us first consider the gravity model for the warm season

(shown in Supplementary Figures 2 panels c and d). In the warm seasons, we can see that both the effect of the pandemic and the differences between the most versus the least vulnerable group

become more visible, Fig. 3a. In the warm season, the parameter _α_ in the least vulnerable group increases positively (z stat = 3.05, _p_ value < 0.005), while in the most vulnerable

group, it decreases (_z_ stat = 3.48, _p_ value < 0.0005). In both cases, the two distributions were significantly different from each other (see Supplementary Figure 2). This observation

means that while using the socio-economic filter, the effect of the COVID-19 pandemic on the park visitation behavior in the warm season is greater than in the cold season. Moreover, the

effect of the pandemic on the behavior of park visitors from the most socioeconomic vulnerable group is the opposite of its effect on the behavior of the least vulnerable socio-economic

group. While during the pandemic distance starts to play a bigger role as the cost of a visit for the least vulnerable visitors, the most vulnerable visitors exhibit a less association

between distance and propensity of park visits. Fig. 3 panels b and c present these observations for two different socio-economic groups. In general, a subset of data, whose selection is not

based on a simple random sampling (or sub-sampling), does not necessarily guarantee to represent the original (or same) statistical distribution. In other words, here selecting the visit of

the most or the least vulnerable groups does not guarantee to fulfill the gravity model again. Nevertheless, in this section, we observed that the data from these sub-samplings still obey

the gravity model, albeit with different values of parameter _α_. As a plausible mechanism to justify the changes in _α_, we described a basic null model (see Methods). We considered two

different random individuals’ changes of behaviors, similar to white and pink noise, and showed how they alter _α_ in the gravity model. In summary, the addition of uncorrelated randomness

can lead to a change opposite to that observed when adding distance-correlated randomness. In studying the null model we can observe the following: Pre-Pandemic: Adding white noise to the

fitted gravity model of the middle socio-economic class, defined as those originating from census blocks with 0.25<SVI<0.75, we can reproduce the parameter \({\alpha }^{{\prime} }\) of

the pattern for the least vulnerable groups of society. Whereas to reproduce the same distribution, (i.e. same parameters), of the most vulnerable group pre-pandemic, we needed to add pink

noise to the middle class. In other words, reaching the behavior of the most vulnerable group from the behavior of the middle class requires random changes that are correlated to the

distance. During the Pandemic: We can explain the variation in park visitation between the middle class and least/most vulnerable population by the addition of pink noise. That means that

the variation between the middle class and the least/most vulnerable class in visits with longer distances is greater. The deviation of the least vulnerable group from the middle class is at

its highest during the pandemic. While the behavior of the least vulnerable group gets farther from the middle class during the pandemic, the behavior of the most vulnerable group gets

closer to the middle class during the pandemic. The variation of the most vulnerable class from the middle class is at its highest rate pre-pandemic. These observations are in agreement with

the null model’s results, demonstrating how the addition of white or pink noise influences the slope. Nevertheless, in order to conclude concretely, a cross-check analysis with individuals’

data is needed, which due to privacy regulations we had no access to. FILTERING PARKS BY SIZE OF CITIES Previous research shows that people living in larger cities commute longer distances

in their daily travels46, and thus spread of COVID-19 has been shown to increase with the size of the city47. For these reasons, we investigate the visitation pattern and its changes due to

the pandemic for parks located in different city sizes. To do so, we divide parks into two groups based on the population of the city they are located in. In defining city boundaries we used

information provided by the Bureau of the Census to map our data to cities. The first group includes parks located in the 10 most populated cities in Washington State. These ten cities,

Seattle, Spokane, Tacoma, Vancouver, Bellevue, Kent, Everett, Spokane Valley, Renton, and Kirkland, have an overall population of 49.4% of the Washington state population. We refer to this

spatial grouping as “large city groups". The second group includes parks located in the remaining Washington state cities. We refer to this group of parks as “small city groups".

In studying the behavior of these two groups of parks, we include our warm season filter. We observe that the park visitation pattern obeys the gravity model for both spatial groups. We

observe the statistical significance of differences in pre and during-pandemic distributions for large cities (z score = 3.88, _p_ value < 0.0001). However, we do not observe this

difference in small cities. Figure 4a shows that the COVID-19 pandemic had no impact on the parameter _α_ of the gravity model (_α_ remains approximately −0.6 for large cities and −0.5 for

small cities). This difference in the _α_ parameters between different types of cities means that for parks in large cities, the pandemic has led to a sharper decline in the number of

visitors, and more significantly so with the increasing distance from parks. The number of visitors to parks in small cities decreases slower compared to larger cities. Fig. 4b, c illustrate

the probability density function for a randomly selected park in a small city (b) and a large city (c). we can see that the COVID-19 pandemic has affected park visitation in both small and

large cities more significantly. Thus far we have shown that the visitation patterns differ by size of the city and by season. One way of studying what deviation from the visitation pattern

in small cities develops the pattern that we see in large cities is to add noise to the visitation patterns in small cities. In the pre-pandemic period, we built the large cities’ pattern by

adding pink noise to the pattern for small cities (Fig. 3 in Supplementary Material). However, in the case of patterns during the pandemic, we added pink noise with higher intensity to the

pattern for small cities to rebuild the pattern for large cities (see Fig. 3 in Supplementary Material). Referring to the null model hypothesis (see Methods), this can be interpreted that

during the pandemic, the deviation of pattern for large cities from the small cities decreases more with the distance. This shows that the pandemic causes short-distance transportation to

differ more while comparing park visitation in small vs large cities. However, as mentioned above a cross-check with individual traces is needed. VISITATION NETWORK The results presented so

far have focused on the population-level analysis of park visitation data. We have shown that the gravity model holds for park visitation and moreover, it reveals characteristics related to

recreational patterns before and during the pandemic. As the gravity model is primarily based on the distance between the home location of the visitors and parks, changes in its parameters

are also a way to quantify the impact of traveled distance on visitation patterns of different groups of people during the pandemic. However, an alternative way of examining the impact of

the pandemic on recreational visits is to study the visitation patterns independent of the traveled distance and rather focus on the structural patterns pre and during the pandemic. In other

words, we seek to understand whether the visits have any predefined structure or happen at random. To answer this question, we adapt network analysis, which represents the visits’

structure, to understand and quantify the difference in the visitation network. Network analysis has been heavily employed in understanding the diversity of regions and in relation to

socio-economic status. Eagle et al.48 found a strong correlation between the number of each individual’s relationships and the economic development of their community. Chang et al.49 have

modeled the spread of the COVID-19 virus using fine-grained dynamic mobility networks. They showed that racial and socio-economic disadvantaged groups visit more crowded places and were not

able to reduce their mobility as sharply due to the pandemic, thus they suffered from a higher infection rate. From a policy-making perspective, network analysis can help provide information

about the resource allocation of parks and recreational areas. For example, the extent to which a park serves the local residents of the immediate area versus attracting people from all

across the region is a consideration in resource planning, from creating more cycling routes and facilities at a park to planning for alternative public transportation stops and routes.

Furthermore, knowing about the visit propensity of people to travel outside of their residential neighborhood can also indicate the need for addressing equity to park access across the

population. For instance, Seattle Park and Recreation state their mission on increasing equity in access to parks and distributing resources such that it “takes into account past history and

current position, so that future outcomes are fairly distributed”7. In this section, we model our data as a visitation network as detailed next. INFERRING VISITATION NETWORK In the field of

network science, the concepts of “in-degree" and “out-degree" hold pivotal significance in elucidating network dynamics. These fundamental metrics serve to measure the

quantification of efflux or the extent to which an entity disseminates connections/interactions to other entities within the network (i.e., out-degree) and the extent to which an entity is

the recipient of connections or interactions from other entities within the network (i.e., in-degree). Thus park visitation network based on the movement of visitors from CBGs to parks can

be presented as a directed bipartite network in the form _G_ = (_U_, _V_, _E_), where: _U_ = {_u_1, _u_2, …, _u__n_} represents _n_ CBGs, _V_ = {_v_1, _v_2, …, _v__m_} represents _m_ parks,

E ⊆ {(_u__i_, _v__j_)∣_u__i_ ∈ _U_ and _v__j_ ∈ _V_}. We used the same SafeGraph data to build the park visitation network but we removed seasonal and socio-economic filters. In doing so, we

connect the _C__B__G__i_ to _p__a__r__k__j_ only if _T__i__j_ ≥ 2 (see Methods). In making the visitation networks, park visitation has been considered from March 2019 till March 2020, a

year before the start of the pandemic (pre-pandemic network), and again from March 2020 until March 2021, a year after the start of the pandemic (during the pandemic network). Each CBG is

labeled with an SVI of the residential area, the number of residing devices, and its area in square kilometers. Each park is labeled with an SVI related to its location, the total number of

visitors, and its area in square kilometers. Figure 5a illustrates the schematic presentation of park visitation as a bipartite network in which each CBG is connected to multiple parks with

unweighted edges. Each link between the _C__B__G__i_ and _p__a__r__k__j_ means that there are at least two visitors who live in _C__B__G__i_ and visited _p__a__r__k__j_. Thus the network

analysis focuses on two sides: first, the CBGs’ out-degree (Fig. 5b) which presents the recreational propensity of the CBG residents going to parks. Secondly, the parks’ in-degree (Fig. 5c),

which presents the diversity of park visitors originating from different census blocks. As presented in the heatmaps both diversity and recreational propensity have decreased during the

COVID-9 pandemic. Regarding the propensity (Fig. 5b), we can see that some areas (such as Haller Lake and Downtown) exhibit a sharp decline in the magnitude of visits to parks outside of

their local area (out-degree edges). As we show next this decline in CBG degree is higher for low-income and highly populated areas in the city. We also observe a great reduction in the

diversity of the visitors (incoming edges) to the parks (Fig. 5c). As our analysis will show parks with higher demand face a greater degree of park degree changes. Some of these changes

could also be due to other major factors besides the pandemic. For example, the closure of the West Seattle Bridge during 2021–2022 is known to have reduced accessibility to Alki Beach (Fig.

 5c), and Woodland Park closure due to homeless encampment. QUANTIFYING NETWORK PROPERTIES Let’s continue with a quantitative analysis of this bipartite network. We first show the Cumulative

distribution function (CDF) of the CBG’s out-degree and also the park’s in-degree (Fig. 6) and then the changes in the park’s in-degree (Fig. 7). Initially, we look at Fig. 6, the

out-degree (panel a) and in-degree (panel b) distributions of the park visitation network, which are heavy-tailed distributions. We observe that out-degree distribution can be described

neither with normal nor scale-free distributions. Nevertheless, by having renormalization factors, the power-law distributions fit the in-degree distributions as shown in Fig. 6b, but the

parameters of the fitted curve, _γ_ and _x__m__i__n_, change due to the pandemic. To identify the most suitable descriptive law for these distributions, additional studies are required.

Moreover, in order to see how park degrees relatively changed, we plotted the change in the degree of parks versus the degree of the park in the pre-pandemic network for all the parks in

Washington State (Fig. 7a) and four large cities in Washington state separately (Fig. 7b). Fig. 7 shows that the degree of parks changes linearly with their degree in the pre-pandemic

situation with a negative slope. This means that parks with visitors from a wider range of CBGs experience a bigger decrease in the number of CBGs that visit them. Since the pandemic causes

a decrease in the CBG degree (Fig. 6a), therefore it’s reflected in propensity, as well (Fig. 5 maps this decrease for Seattle CBGs). NETWORK CORRELATION ANALYSIS Given the park visitation

network, now we want to know whether diversity of parks and propensity of CBGs depend on socio-economic status and geometric scale. This question can be answered by measuring the linear

correlation between degrees in the visitation network and SVI, Area (park or CBG), and number density (visitors/ residents). The main observations of this analysis are the following: First

examining propensity (Table 1), we observe a strong statistically significant correlation between the CBG degree and SVI. That is the higher the social vulnerability of an area, the

residents of that area exhibit a lower propensity in park visitation, both pre (_ρ_ = − 0.93) and during the pandemic (_ρ_ = − 0.90). Therefore, residents of the least vulnerable areas

(i.e., low SVI) visit a broader range of parks compared to the most vulnerable areas (i.e., high SVI). However, there is a high positive correlation between the change in the CBG degree and

SVI (_ρ_ = 0.87). This shows that if the SVI is higher (more vulnerable), then the change in the degree due to the pandemic is also higher. Therefore, the pandemic has a higher effect on the

propensity of the most vulnerable CBGs compared to the least vulnerable ones. We also observe that the population density (as measured by devices per area) for different census areas

exhibits a negative correlation with the change in park propensity (_ρ_ = − 0.70). Simply put, residents in the denser areas (such as the Downtown area in Fig. 5b consisting of apartment

blocks) reduced their choices of recreational visits. We remark that this observation could be specific to characteristics of urban design and lifestyle in the United States and more

specifically to Washington state where socioeconomic status and population density are intertwined. Second examining diversity (Table 2), indicates contrasting observations regarding the

SVI. That is parks in richer areas of Washington State did not exhibit a significant difference in their visitors’ diversity. However, we observe that parks located in higher-density areas

have a higher diversity during the pandemic (_ρ_ = 0.94). Moreover, the change caused by the COVID-19 pandemic in the degree of larger parks (area) is higher compared to smaller ones (_ρ_ = 

0.79). This shows that the increase in diversity of larger parks is higher due to the pandemic. Our results show that the park area does not have a strong correlation with the degree of the

park pre and during the pandemic, the change in diversity is highly correlated with the park area. We also show that the CBG degree is highly correlated with SVI both pre and during the

pandemic. This also results in a correlation between the change in CBG degree and the SVI. CONCLUSIONS In summary, we have analyzed the park visits of Washington State pre and during the

pandemic from two perspectives: on one side, we showed that visits obey scale-free laws, namely, the gravity model and this pattern is robust, even though the slopes change due to different

factors. On the other side, we inferred a network of visits, measured some network properties, and showed how the propensity and diversity of the visits were changed and which factors could

play a role in it. We also showed that the in-degree and the out-degree of recreational visits from neighborhoods are heavy-tailed distributions. To identify the most suitable descriptive

law for these distributions, additional studies are required. Overall, our results shine a light on practical implications for policymakers and park managers on one hand and raise some

theoretical questions on the other hand. Putting all the reported observations together, our analysis highlights the following practical implications: due to the pandemic the higher-income

level residents changed their behavior by visiting more local parks and broader recreational options outside of their local census area; whereas the low-income residents changed their

visitation behavior greatly by reducing their recreational choices outside of their local area and their traveled distance did not follow a predictable pattern. These behavior changes might

be due to the lack of access to specific facilities in parks or the closure of parks in the most vulnerable areas. It could also resonate with the greater work-life balance imposed by the

pandemic for only a certain group of the population (i.e., economically resilient). A practical implication of this result is that policymakers can potentially plan alternative recreational

activities in areas with low socioeconomic levels. Neighborhood programs such as meet-ups, outdoor clubs, etc. that take steps to prevent transmission of the virus but target specifically

low-income residents to be more active could help bring equitable recreational access. We also observed that the recreational behavior in small versus large cities is different, and thus the

scale of the city is also another factor that should be accounted for in decision-making. We believe, having access to a more detailed and richer dataset could help to understand the

underlying causes of the behavioral shifts we observed in this study. For instance, rich content from social media posts along with qualitative surveys of the park visitors could help us

understand more about their decisions of selecting a particular recreational site over other alternatives. Finally, having access to large-scale fine-grain (non-aggregated) mobility data

could help us to portray a more accurate picture of recreational choices. We believe in much the same way that technology companies, scientists, and local authorities worked together to

create infrastructure for tracking and tracing the spread of the COVID-19 virus, a unified effort that addresses privacy concerns upfront could be mounted to enable advanced modeling of the

recreational choices at the individual level. Our work has various theoretical implications and prospects for the research community: first and foremost our study shows that even by only

sub-sampling the urban mobility data, namely visits to parks, the gravity model was still well fulfilled. Furthermore, additional sub-sampling, namely three different filters of seasonality,

socio-economic, and spatial ones showed that the gravity model is robust while only the slope differs for different filters and also pre and during pandemics. In closing this work creates

opportunities to focus future studies on the following: i) confirming the universality of the gravity model when applied to recreational patterns of other cities and countries from different

ranges of GDP and cultures. ii) analyzing under which conditions sub-sampling can keep the original scaling law. iii) investigating how to infer the original general law by knowing the

sub-sampled statistical law, for instance by knowing the slope of gravity model for a given filtered data. iv) how to improve null models in order to understand the underlying mechanisms of

observed changes. Finally, our analysis revealed that the degree of parks in the visitation network follows a power-law distribution while the park visits obey the gravity model. Knowing

these two perspectives, a research question arises as to whether ensemble models generate synthetic park visitation traces. In the same vein, we believe future work will include applying

advances of graph-based neural networks50 to enhance the gravity model as a non-linear model similar to recent efforts by51 to generate synthetic traces. Such models can be then adjusted for

socio-economic variations using the fairness regularizer layer in their architecture to force the model to tune for different socio-economic levels during the training process52. METHODS

DATA In this study, we used three different types of data described as follows: SAFEGRAPH MOBILITY DATA SafeGraph is a commercial company that provides Point of Interest (POI) and

Location-Based Services (LBS) data in the U.S, Canada, and the United Kingdom13 The dataset is an aggregated dataset of anonymized location data from numerous mobile applications. SafeGraph

captures the movement of people between POIs that have been marked as parks and green spaces in the SafeGraph Core Places API. Unlike location-based social networks, which require active

participation on the part of the user to upload and share images, SafeGraph collects its data from users who have installed one of the many affiliated mobile applications on their devices.

Users’ locations are recorded even while they are not actively using an application. It is therefore nonparticipatory and platform-independent. For these reasons, SafeGraph is less sensitive

to biases that would result from changes in the popularity of the use of certain applications over time49,53,54. Furthermore, the validity and viability of SafeGraph data as a proxy of cite

visitation in US national parks has been reported recently by55. To preserve the privacy of users, SafeGraph data is provided in monthly and spatial aggregates, presenting the number of

visitors and their visit characteristics, such as the aggregated total number of visitors who originated from each census block group (CBG). CBGs are geographical units that typically

contain a population of between 600 and 3000 people. This rich aggregated information allows us to analyze changes in visitation patterns and visitor characteristics independent and

de-coupled from online behavior. Figure 8b shows the correlation of population with the number of devices SafeGraph has collected data from for each state. We can see that sampling from the

population is correlated with the population in each state with Pearson’s r equal to 0.97. We collected all the data associated with Parks and Green Natural areas of Washington state under a

research license provided by SafeGraph. We used SafeGraph weekly pattern data from November 2018 till February 2021 for 3665 parks in Washington state and 220426 census block groups (U.S.).

The population of devices in each CBG _i_, _O__i_, is given as number_devices_residing in this data. SafeGraph defines the home of visitors as the CBG that the visitor has spent most of

their time during nighttime hours (between 6 pm and 7 am) in a 6-week period. The number of visitors for each park j, _D__j_, is given by raw_visit_counts, and the number of visitors from

CBG _i_ to the park j, _T__i__j_ is given by the visitor_home_cbgs in SafeGraph weekly pattern data. Note that SafeGraph reports the _T__i__j_ between an origin and a destination, if the

_T__i__j_ at least is equal to two, and if 2 ≤ _T__i__j_ < 4, SafeGraph reports _T__i__j_ as four. We applied the following steps in processing Safegraph data for the Gravity model. i) we

aggregated distances between origins and destinations using _δ__r_ = 500 meter bins. ii) In filtering the seasonal and yearly patterns using monthly patterns, we only kept parks whose data

was available for each month in a desired season/year. SOCIAL VULNERABILITY INDEX DATA The Social Vulnerability Index (SVI) developed by the Centers for Disease Control and Prevention is a

metric that captures the resilience of each community at the census tract level. This index combines 15 U.S. census variables grouped into four themes: socioeconomic status, household

composition, race/ethnicity/language, and housing/transportation, in order to rank census tracts by their relative vulnerability to hazardous events. Each of these themes has its own

percentile ranking where greater percentile values represent greater vulnerability. In this study, we used the first theme that corresponds to _socioeconomic_ status to understand the shift

in visitors’ socio-economic background pre and during the pandemic. Fig. 8a shows the distribution of different socio-economic groups in the Washington population and in the sample from

SafeGraph. As shown in this bar plot, the distribution in the Washington population is the same as the distribution in the SafeGraph sampling. CENSUS DATA We obtained US population data from

the 2019 American Community Survey (ACS) product of the U.S. Census Bureau, provided by SafeGraph’s Open Census Data. We computed a CBG’s population density by dividing the 2019 population

estimate by the land area of the CBG as reported by CBG geographic data of SafeGraph’s Open Census Data. SafeGraph “uses the cartographic boundary files, which define simplified shapes of

geographic entities designed for plotting, provided by the U.S. census." REPORTING Z-TEST STATISTICS To examine the difference between two distributions we employed a parametric test,

z-test, to determine if the means of two distributions differ. The z-test is a parametric statistical test used when the sample size is sufficiently large (greater than 30). In our case, we

applied the paired sample z-test to compare the points in the gravity model of the pre-pandemic and during-pandemic distributions. NULL HYPOTHESIS (_H_ 0) The null hypothesis posits that

there is no significant difference between the means of the two distributions. PROCEDURE To test the null hypothesis: * 1. We calculated the mean (\(\bar{x}\)) and standard deviation (_σ_)

of the data for both groups. * 2. We computed the z-score using the formula: $$z=\frac{{\bar{x}}_{1}-{\bar{x}}_{2}}{\sqrt{\frac{{s}_{1}^{2}}{{n}_{1}}+\frac{{s}_{2}^{2}}{{n}_{2}}}}$$ where

\({\bar{x}}_{1}\) and \({\bar{x}}_{2}\) are the means, _s_1 and _s_2 are the standard deviations, and _n_1 and _n_2 are the sample sizes of pre and during-pandemic groups, respectively. * 3.

We then checked the z-score against the critical value for the chosen significance level to determine statistical significance. We set the significance level at _α_ = 0.05 for all

statistical tests. WHITE AND PINK NOISE (NULL MODEL) In order to understand better the changes of slops in the gravity model, let’s go one step further with a simple null model. Thus we

assume that the individuals’ change behaviors have been random and see how the slop would change, as shown in Fig. 9. Simulating a fixed gravity model with _a_ ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 

1.0} (corresponding to the parameter \({\alpha }^{{\prime} }\) in empirical data), we add two types of noises to the flow, _T__i__j_ in the model: namely white and pink. Firstly we consider

white noise with the simplest representation of it. The term “white” refers to independent and identically distributed random variables that are added to our model as follows: $$\Delta

{T}_{ij}={\sigma }_{noise}\times rand\{0,1\}$$ (4) where _σ__n__o__i__s__e_ is the noise level. Secondly, we assume even though the change of behaviors has been random but was correlated to

the distance. Thus we can consider bigger fluctuations for shorter distances which obey a power-law function. We refer to this noise as “pink” noise. The noise is produced as follows:

$$\Delta {T}_{ij}={\sigma }_{noise}\times \frac{rand\{0,1\}}{{r}_{ij}+1}$$ (5) where _σ__n__o__i__s__e_ is the noise level and _r__i__j_ id the distance between CBG and a park. Figure 9

shows that regardless of the initial slope, white noise (panel a) decreases _a_, while pink noise (panel b) increases the slope. Also the smaller the _a_ is or the bigger the noise level,

_σ__n__o__i__s__e_, is, the bigger the change of the slop would be. We remark that our focus here is not on explaining why these scaling patterns are observed, as reference18 has already

reviewed “the main theoretical models in the literature aimed at explaining the origin and emergence of urban scaling.” Instead, our investigation delves into possible statistical scenarios

behind these changes. Therefore, we proposed the simple null model involving the addition of noise (both correlated, pink noise, and uncorrelated, white noise, to the distance) for

comparison with the empirical data. To gain a deeper understanding of the underlying processes that generate data consistent with the observed patterns, as well as the changes that occur

prior to and during a pandemic, one can take a further step by utilizing null models similar to the ones presented in reference19. Furthermore, this work involves a comparison of different

models in urban scaling laws, including gravity models. A similar approach can be a topic for further studies as well. To seek further elaboration on how and why the changes occurred, a

cross-check analysis with individuals’ data is needed. Unfortunately, due to privacy regulations, we have no access to such data. Moreover, one can employ a similar approach and directly add

noise to a specifically empirical data set, using it as the baseline, aiming to determine the type and level of noise that could replicate a similar trend in the targeted data set. Through

this exploration of noise, statistically, we can interpret that changes might have occurred randomly and could be correlated (pink) or uncorrelated (white) with distance. REPORTING SUMMARY

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article. DATA AVAILABILITY Aggregated mobile phone data that was used in this

study are freely available to researchers, non-profit organizations, and governments through the SafeGraph COVID-19 Data Consortium (https://www.safegraph.com/covid-19-data-consortium). CODE

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Environ. Manage._ 317, 115410 (2022). Article  PubMed  Google Scholar  Download references ACKNOWLEDGEMENTS F.G. would like to thank Eduardo Goldani Altmann for his valuable comment

regarding the statistical laws and models. M. T. acknowledges the support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany´s Excellence Strategy –

EXC-2068 – 390729961 (Excellence Cluster Physics of Life). The publication of this work was made possible by generous support from the US National Science Foundation (NSF) award IIS-2304213

and the University of Washington Bothell Faculty Publication and Production Award Application. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Physics, Sharif University of

Technology, Tehran, Iran Zahra Ghadiri & Fakhteh Ghanbarnejad * Computing and Software Systems, University of Washington, Bothell, WA, USA Afra Mashhadi * Chair for Network Dynamics,

Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technical University of Dresden, 01062, Dresden, Germany Marc Timme & Fakhteh Ghanbarnejad Authors

* Zahra Ghadiri View author publications You can also search for this author inPubMed Google Scholar * Afra Mashhadi View author publications You can also search for this author inPubMed 

Google Scholar * Marc Timme View author publications You can also search for this author inPubMed Google Scholar * Fakhteh Ghanbarnejad View author publications You can also search for this

author inPubMed Google Scholar CONTRIBUTIONS A.M. and F.G. conceived and designed the research. A.M. acquired the Safegraph dataset and applied preprocessing. Z.G. carried out numerical

experiments and analysis of the processed dataset. Z.G., A.M., and F.G. summarized the results. Z.G., A.M., M.T., and F.G. contributed to the writing of the manuscript. F.G. and A.M.

substantially revised the article during its review and shepherding process. CORRESPONDING AUTHOR Correspondence to Fakhteh Ghanbarnejad. ETHICS DECLARATIONS COMPETING INTERESTS The authors

declare no competing interests. PEER REVIEW PEER REVIEW INFORMATION _Communications Physics_ thanks Jorge P Rodriguez and the other, anonymous, reviewer(s) for their contribution to the peer

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