Ecology

Effects of seasonality on physiochemical properties of waterThe characteristics of the physical and chemical factors of the river are shown in Table 1. Variance analysis showed that the environmental conditions during the four seasons were significantly different (P  More

Coral collection and laboratory acclimationCorals were obtained from the nursery at Mote Marine Laboratory’s Elizabeth Moore International Center for Coral Reef Research & Restoration. Acropora cervicornis fragments (apical tips ~ 5–6 cm in length) were obtained from Mote’s in situ nursery and mounted to a plastic base with marine epoxy (Instant Ocean Holdfast). The A. cervicornis genotypes used in this study were Mote Marine Laboratory genotype numbers 7, 31, 50, 57, and 70 (n = 12 ramets from each of the 5 genets). The coral O. faveolata was obtained from Mote’s ex situ nursery as fragments (~ 3–4 cm2) attached to individual carbonate plugs. Six genotypes of O. faveolata were used in deoxygenation treatments from genotype numbers F3A, F8, F27, F61, F125, and F132 (n = 12 ramets from each of the 6 genets). The immediate environmental conditions at the ex situ coral nursery are not known in detail, however the corals were maintained in an open, flow-through system with high flow rates and continuous bubbling with air stones.Corals were transported to the wet lab facilities at the Smithsonian Marine Station (SMS) in Fort Pierce, FL and experiments were conducted between October and December 2019. Corals were acclimated to laboratory conditions for 4–6 weeks before exposure to deoxygenation treatments. During this period, corals were kept in an indoor, closed seawater system. Holding tanks contained ~ 570 L of seawater that was recirculated through a sump containing rigorous aeration (ambient air) and a heater/chiller that maintained the temperature at ~ 27 ºC (see Table S3 for all parameters). Water was pumped from the sump through a UV sterilizer (Coralife) and then back into the holding tank. Water flow and circulation was maintained by two aquarium pumps (AquaTop MaxFlow MCP-5), and yielded a full water exchange through the sump ~ 8.5 times per hour. Light was provided by LED aquarium lights (HQD) with a maximum photosynthetically active radiation (PAR) of ~ 300 µmol photon m−2 s−1. Full water changes were conducted weekly, and non-living surfaces on the coral fragments (e.g., plastic or carbonate bases) were cleaned at least once a week to reduce algal growth. Conditions within the acclimation tanks closely matched the ambient (i.e., normoxic) conditions at the collection locations and in the oxygen treatments (Table S3, Fig. S4).Field dissolved oxygen conditionsOxygen concentrations were monitored at Mote Marine Laboratory’s in situ nursery (24.56 latitude, − 81.40 longitude) at the depth of coral outplants (~ 5–6 m) to parameterize oxygen conditions used in laboratory experiments. A dissolved oxygen sensor (miniDot, PMEL) was calibrated according to manufacturer protocols and attached to the benthos adjacent to coral outplants. Dissolved oxygen and temperature were logged every ten minutes for the duration of deployment. Hourly and daily average DO concentrations are presented for one month encompassing the approximate time of coral retrievals (Fig. S4). The 6.25 mg L−1 treatment in the laboratory experiments simulates the average normoxic conditions at the site of collection (6.18 ± 0.10, SD), while the most severe deoxygenation treatment (1.00 mg L−1) simulated extreme oxygen depletion that has occurred during acute deoxygenation events on coral reefs21,22,52 (Fig. S4). The two intermediate deoxygenation treatments represented incremental increases by ~ 2 mg L−1 to capture coral responses over a full range of oxygen conditions (Fig. S4).Experimental designDeoxygenation experiments were conducted in the wet lab facilities at SMS using a mesocosm array consisting of 12 tanks (50 L, AquaLogic Systems), with each tank functioning as a closed system with fully independent temperature and oxygen control. Targeted oxygen levels for treatments were 1.00, 2.25, 4.25, and 6.25 mg L−1 DO, with three independent tank replicates for each oxygen level. Oxygen treatments are referred to by the targeted DO concentrations. Species were run in separate, sequential experiments, and genotypes within a species were co-mingled in treatment tanks with one replicate of each genotype per tank.Oxygen concentrations were maintained in each independent tank by bubbling seawater with nitrogen gas and ambient air, with gas injection controlled through a DO feedback and solenoid valves (Neptune Systems). Oxygen levels were monitored every 15 s in each tank by an OxyGuard DO probe connected to an aquarium controller (Neptune Systems, Apex Aquacontroller), which opened or closed the respective solenoid valves to add nitrogen or air in order to maintain the programmed treatment conditions. Oxygen probes were calibrated at the start of experiments, and then again after five days, following the manufacturer’s protocol.Temperature control was maintained in treatment aquaria through an independent heating/chilling loop in each tank and monitored by AquaLogic temperature probes (sensu53). The average temperature at the collection site in the month prior to collection was 29.01 ± 0.62 ℃ (SD) (Fig. S4), which represents seasonally warm temperatures of the Florida Keys54,55. To reduce the potential confounding effects of temperature on responses to deoxygenation, we acclimated corals to 27 ℃ during the holding period, and conducted experiments at ~ 27 ℃. This represents the average annual temperature at the collection site in the Florida Keys, is the temperature that O. faveolata fragments were maintained at in the ex situ nursery prior to collection (27.0 ± 0.62 ℃), and is commonly used as the ambient temperature for corals from this location54,56. Each tank contained an additional probe (Neptune Systems) that logged temperature every 10 s for the duration of the experiment. In addition to continuous monitoring of DO and temperature, discrete measurements were taken each day for DO, temperature, pH, and salinity with a handheld multi-parameter water quality meter (YSI ProDSS with optical DO sensor) (Tables 1, 2, Tables S1, S2). The YSI DO probe was calibrated at the start of every day following manufacturer protocols and used to validate DO measurements from OxyGuard probes and to adjust programmed values to maintain treatment targets when necessary.Individual tanks were supplied with a 7-color LED aquarium light (Aquaillumination, Hydra 52), programmed to simulate a diel light cycle over a 12:12 h photoperiod, and set to maximum irradiance of ~ 300 µmol photon m−2 s−1 (PAR). This maximum intensity is likely lower than what corals may experience in situ during peak midday irradiances, however, it matches the irradiance levels these corals were maintained at in the ex situ nursery (320 ± 182 SD, n = 45) and is sufficient to stimulate maximal photosynthesis without causing light stress45. Light levels were measured with a light meter (Licor, LI-1400) and an underwater spherical quantum sensor (LI-193SA) submerged at the center of each tank at the start of each experiment and again after five days. Oxygen, temperature, and light conditions were effectively maintained at or near targeted levels for the duration of each experiment (Fig. 1, Table 1), with minimal differences between replicate tanks within a treatment (Tables S1, S2). We did not simultaneously manipulate pH in treatment tanks, which resulted in differences in pH between treatments due to bubbling with nitrogen gas (Tables 1, 2).Coral conditionCorals were monitored daily during the experiments for changes in live tissue cover and photophysiology, and then destructively sampled at the end of the experiment for symbiont densities. Fragments were visually evaluated at each time point for evidence of bleaching, tissue loss, and mortality. Tissue loss was quantified as the percent of each fragment with exposed skeleton, resulting from the sloughing of tissue. Fragments were categorized as dead when all living tissue was lost.The A. cervicornis experiment ended after five days, at which point 50% of corals in the lowest DO treatment were dead or displayed partial mortality. We ended the O. faveolata experiment after 11 days, more than twice the duration of the A. cervicornis experiment (Fig. 1), at which point no observable signs of deterioration were detected in corals from any treatment (Fig. 2a).PAM fluorometryPAM fluorometry is a non-destructive method that directly measures chlorophyll fluorescence and the activity of photosystem II (PSII)57, and the quantum yield can be used as a proxy for coral stress36,58. For all PAM readings, one measurement was taken from the same position on each fragment with the probe held at a 90º angle ~ 0.5 cm from the coral surface (angle and distance were maintained with a Walz probe holder). To optimize initial fluorescence (F0) to between 300–500, the following PAM settings were used: gain = 2, damp = 2, saturation intensity = 8, saturation width = 0.8, and measuring light intensity = 10 for A. cervicornis and 6 for O. faveolata. PAM measurements were taken pre-dawn daily, at 0500–0600 h. The position on A. cervicornis fragments was shifted if tissue sloughing occurred so that measurements were taken on living tissue. After the final PAM measurements, corals were snap frozen in liquid nitrogen and stored at − 80 ºC for subsequent analyses.Symbiont densitySymbiont density analyses were conducted at the University of Florida in Gainesville, FL following standard protocols (sensu59). In brief, tissue was stripped from the coral skeleton with an air brush (Master Airbrush S68) and filtered seawater. The tissue slurry was then homogenized with a handheld electric tissue homogenizer (Tissue-Tearor) and subsampled for symbiont counts. Symbiont cells were counted with a hemocytometer, with six replicate counts per fragment. Replicate counts were averaged per fragment for all analyses.Surface area of A. cervicornis fragments was determined by wax dipping60 and the surface area of O. faveolata fragments was determined through image analysis in ImageJ. For A. cervicornis, surface area was then corrected by the percent tissue loss recorded for each fragment. Symbiont densities were normalized to fragment live tissue surface area and expressed as cells per cm−2.Statistical analysesAll analyses were conducted in R (v 4.0.2)61. The effects of fixed and random factors were evaluated with linear mixed effects models using the package lme462. Normality and homoscedasticity of variances of response variables were evaluated by visual inspection of residuals and Levene’s tests, respectively. All variables met model assumptions, and results are reported for full models that included all fixed and random effects.For maximum quantum yield and tissue loss, the factor corresponding to measurements repeated daily from the start to end of the experiment (i.e., Day 1, 2, 3, etc.) is referred to as “day”. Day, genotype, and treatment were treated as fixed factors in the analysis of maximum quantum yield and tissue loss, with individual included as a random factor to account for repeated measures, and tank as random factor to account for fragments of different genotypes within a tank (Tables 2, 3). For symbiont density, genotype and treatment were analyzed as fixed factors, and tank as a random factor (Table 4). The significance of fixed effects was evaluated with type II ANOVA tables using Satterthwaite’s method, and Tukey’s post-hoc tests were used where necessary to determine significant differences between levels of a factor using the package emmeans63. Data in main figures in which genotype was not a significant effect (i.e., all response variables) are presented as treatment averages (± SE), pooled across genotypes. More

Data for all analysed radionuclides are presented in the “Supplementary Material”. Cryoconite samples were collected on Nalli Glacier (Supplementary Fig. S1) on Sept. 25, 2017 (samples 1701–1714) and on Sept. 10, 2018 (samples 1801–1814) at 28 spots (Fig. 2, Supplementary Table S1). Gamma spectrometric analysis of samples showed the presence of anthropogenic radionuclides 137Cs, 241Am, and 207Bi. All quoted radioactivity values were recalculated for the sampling date, except those for 241Am since the concentration of the parent 241Pu isotope is unknown. However, for this isotope, the correction for decay is negligible. The activity of 137Cs reached 8093 (± 69) Bq kg−1 of dry weight, that of 241Am reached 58.3 (± 2.3) Bq kg−1 and that of 207Bi reached 6.3 (± 0.6) Bq kg−1. The natural radionuclides 210Pb and 7Be were also present in all samples. The activity of 210Pb varied in the range of 1280–9750 Bq kg−1. In addition, in the investigated samples, a significant amount of short-lived cosmogenic radionuclide 7Be was found, whose specific activity reached 2418 (± 76) Bq kg−1 (Fig. 3, Supplementary Table S2). To evaluate the contribution of atmospheric components to the total 210Pb activity, 226Ra activity was determined and found to be 17–27 Bq kg−1 (Supplementary Table S2). Based on the 210Pb/226Ra ratio, we conclude that more than 98% of 210Pb was of atmospheric provenance.Figure 2Location of sampling points on Nalli Glacier. A—137Cs activity zone  95%) of corresponding rocks and numerous outcrops likely promoted entrapment of these elements into explosion clouds, and their subsequent precipitation with radionuclides. This feature of the geological structure of the area explains the extremely high enrichment of surface waters in elements such as Zn, Pb, Sr, Ni, As, Cr, Co, Se, Te, Cd, W, Cu, Sb, and Sn; for many of them, the excess reaches 10-fold with respect to the Clrake values51. This hypothesis is supported by obvious correlations between the concentrations of Bi, Ag, Sn, Sb, Pb, Cd, W, and Cu and the activity of anthropogenic radionuclides 137Cs, 241Am and 207Bi. This relationship is obviously related to the simultaneous release of elements and radionuclides from the contaminated ice layer and their entrapment in cryoconite holes. More

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For the past five years, I’ve studied oysters — a commercially and environmentally important species in southeast England. My research is very practical: I help to solve problems by working with oyster growers (known locally as oystermen), regulators and other community members. Resulting papers are evidence of work I’ve already done.Most oysters in this area are a non-native species (Crassostrea giga). Locally, it’s well established and has been since the 1960s, but allowing it to spread to nearby estuary systems has been controversial: there are concerns that it could become an invasive species.Working with aquaculture producers, I help to guide efforts to restore the native oyster (Ostrea edulis), populations of which declined owing to overfishing, habitat destruction, pollution and disease. Crassostrea giga oysters have provided enough income for oyster growers to spend time and effort restoring the local species. We’ve done some cool things, including creating one of the largest coastal marine conservation zones in the United Kingdom — more than 284 square kilometres — and all for an unseen brown invertebrate that lacks the charisma of a dolphin.This picture is from a typical day in the field. During high tides, we go out in a boat to take sonar readings to map potential oyster habitats; at low tide, we put on waders and go out on the mud flats to look for juvenile oysters. We focus our conservation efforts on spots where juvenile oysters are already trying to get established.Amazingly, these filter feeders don’t require feeding by humans, and they clean the water as they grow. Bivalve aquaculture such as this has become a cornerstone of the ‘blue economy’ — using marine resources sustainably for economic growth while preserving ocean health. It will take more work to determine how the balance can be reached, but oysters will be part of that conversation.

Nature 600, 182 (2021)
doi: https://doi.org/10.1038/d41586-021-03573-5

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As a starting point, we compare the vulnerability of four districts in Lyon, Paris (France), Firenze (Italy) and New York (US). These cities were chosen as emblematic of different topologies, resulting from different historical urban layering. The historic center of Firenze (panel b in Fig. 1) is mainly characterized by a dense urban fabric with a medieval signature of narrow and winding streets24. In Paris (panel c), Haussman’s renovation plan at the end of the 19th century supplemented the North–South and East–West ancient crossroad by a second network of concentric large avenues25. The rectilinear grid of Manhattan, New York, originates from 181126,27 and extends along the spine of Manhattan island (panel d). Despite the significant difference in size, a similar regular pattern is found in the modern urban area of Lyon (panel a), developed in the second half of the 19th century. In the insets of Fig. 1, we report for each city a polar histogram of the orientation of the streets. Although greater variability is observable for the orientation of the streets in the urban areas of Firenze (panel b) and Paris (panel c), two main orthogonal axes are found in the spatial structure of each city.The urban networks analysed in this work were delimited in order to be large enough to include the distinctive patterns of these four cities. The edges of the areas were traced along physical boundaries (e.g., rivers, parks, railways, large avenues) which act as elements of discontinuity in the dispersion process. Where not possible, the break was forced along wide streets.We promptly computed vulnerability maps for the selected urban areas by means of the centrality metric we derived in20 and recall in the “Methods” section. The nodes with the highest centrality values (V) are the most vulnerable as they correspond to the best spreading locations in the urban fabric. The spreading potential of a node is evaluated based on the extent of the area that is contaminated when the release takes place in this same node.We report in Fig. 1 the vulnerability maps of the four urban areas for the indicative scenario of a wind blowing at an angle (phi =45^circ). In the insets of Fig. 1, the wind direction is indicated with a red arrow. Given the different orientation and structure of the street networks, (phi) is defined as a clockwise angle with respect to the main axis of the city, which is identified as the longest bar in the polar histogram of street orientation.To extend the analysis to multiple meteorological scenarios, we estimated the vulnerability of each node (seen as a spreading source) for eight different wind directions ((phi =0^circ), (45^circ), (90^circ), (135^circ), (180^circ), (225^circ), (270^circ), (315^circ)). In this way, for each city, we obtained an extended dataset of vulnerability values that we represent in a compact way by means of a cumulative distribution function, as shown in Fig. 2a. The intercept of the cdf represents the nodes with null vulnerability. These are mostly located along the physical edges of the domain where the pollutant gas is blown away by the wind without affecting other streets. Where the delimitation of the network is forced (for example on the sides of central park as regards Manhattan), the interruption of the propagation, in the vulnerability model, is also constrained. This does not result in any artificial effect when the boundary is located upwind with respect to the network (propagation carries on from the boundary towards the considered urban area). On the other hand, when the boundary is downwind, vulnerability can be there underestimated. Considering the multiple wind directions simulated and the small number of nodes belonging to these edges (1% of the total number of network nodes), this effect has been calculated negligible to the purposes of this work.According to the mean values (vertical dashed lines) of the distributions reported in Fig. 2, New York is the most vulnerable city on average, while Firenze is the most protected. The vulnerability of New York and Lyon are the most sensitive to changes in wind direction, as shown by Fig. 2.b, where a polar histogram reports the mean vulnerability for each city for the eight directions of the approaching wind. In general, the spreading potential is more effective when the wind is oblique ((phi =45^circ ,) (135^circ), (225^circ), and (315^circ)) to the main orthogonal axes of the street network, as evidenced by the higher vulnerability observed for the dark gray sectors of Fig. 2b. We also notice that vulnerability for parallel ((phi =0^circ ,) (phi =180^circ)) and perpendicular ((phi =90^circ ,) (phi =270^circ)) wind directions is quite similar. This seems counterintuitive as previous studies (e.g.,28,29) have reported that a perpendicular wind is much more unfavorable for the dispersion of pollutants in a street. In this regard, we underline that (phi) is here defined with respect to the main axis of the city, so for (phi =90^circ) not all streets will be perpendicular to the wind direction. For example, in the regular network of Manhattan we expect the number of perpendicular streets to be similar to that of parallel streets, when (phi =90^circ).Figure 1Vulnerability maps for (a) Lyon, (b) Firenze, (c) Paris, and (d) New York for a wind direction of (45^circ) with respect to the main axis of the urban fabric. The polar histograms in the insets report the distribution of street orientation, while the red arrows represent the wind direction with respect to the street network. Panels a1–d1 show the urban pattern in a rectangular area of 0.5 km(^2) (reported in panels a–d) for the cities of Lyon, Firenze, Paris, and New York, respectively. Background images made with QGIS 2.18 (https://qgis.org).Full size imageFigure 2Vulnerability distribution for different cities and wind directions. (a) Cdf of node vulnerability for the different cities under eight different wind directions. The mean vulnerability is shown as a dashed line and reported numerically together with the standard deviation (in parentheses). (b) Mean vulnerability of city networks for each wind direction. Colors blue, yellow, green and magenta correspond to the urban networks of Lyon, Firenze, Paris and New York, respectively.Full size imageThe reasons for the different resilience of cities (and their patterning) to gas propagation are embedded in the centrality metric adopted to compute urban vulnerability. The key factors for node vulnerability can then be analytically recognized in the metric definition (Eqs. 4–5 in “Methods”): the highest vulnerabilities are achieved when the set of reachable nodes ((mathcal {V})) from the source node is large, and the paths connecting the source and the reachable nodes ((d_{sr})) are short, i.e. the propagation cost ((omega)) along the paths is minimal. In other words, the spots in a city (i.e. nodes in a network) with the highest spreading potential are those from which a toxic plume can reach many other locations with significant concentration. Going beyond the vulnerability results, we aim here to decompose the aforementioned elaborate and meaningful quantities (the set of reachable nodes, the shortest paths, the propagation cost) in elementary properties of the urban area in order to link the vulnerability of a city to its tangible characteristics.We start by disassembling the propagation cost associated to each street. Given a source node, a pollutant plume will propagate along the streets downwind the node. The propagation cost of each street (Eq. 4) describes the decay of concentration that the plume undergoes when it propagates along the street. Neglecting physico-chemical transformations, this cost depends on the transport processes within the streets and is a function of two dimensionless quantities: a geometrical ratio between the length (l) and height (h) of the street canyon, and a dynamic ratio between the exchange rate of pollutants towards the atmosphere above roof level (v) and the advective velocity along the longitudinal (u) axis of the street. According to30 and31, these two velocities can be parametrized as a function of the external wind intensity, the cosine ((theta)) of the angle between the wind direction and the orientation of the street, the geometry of the street canyon (its length l, height h and width w) and the aerodynamic roughness of building walls. As detailed in the Methods, the dependence of the propagation cost on the external wind intensity disappears as both velocities u and v scale linearly with it. Assuming constant aerodynamic resistance of the surfaces, the parameters l, h, w, (theta), remain the relevant building blocks for the propagation cost along a street.We underline that the parametrizations adopted here for the transport mechanisms in a street are based on the up-to-date literature and are currently employed in operational models (see the Methods section for mode details). Any refinements to this transport model may be included in the future. In this case, the cost associated to each street may depend on additional parameters that, however, we expect to be of second-order importance to those listed above.While pollutant transport in a single street canyon (i.e. the propagation cost) has been easily broken down into its basic elements, the information enclosed in the shortest paths ((d_{sr})) and in the set of reachable nodes from the source ((mathcal {V})) is much more challenging to trace back to evident properties of the city. These quantities depend on the sequence of streets that must be traveled to connect a source node to the surrounding nodes, i.e. on the way the streets are interconnected. The information is thus primarily topological. However, we point out that the interconnectivity of the network is not frozen, but dynamic, as it is given by the reaction of the urban structure to the direction of the external wind. In fact, the links of the street network are directed according to the orientation of the approaching wind. Moreover, the connectivity between the nodes is limited by the decay of the concentration along the streets. Although a target node may be reached from the source node by means of a path across the network, the two nodes may not actually be connected by a propagation path as the pollutant concentration may vanish along the path. For these reasons, traditional descriptors of network topology cannot be applied directly to describe the topological component of the vulnerability. Instead, we have to look for tailored and simple indicators that can express the wind-driven interconnectivity of the street network and the reachability potential between the nodes.Focusing on a node as spreading source, we infer that the number of links in its downwind area gives a first estimate of the potential for a release in the node to affect many other locations in the network. To delimit this downwind area, we adopt the concept of n-hop neighborhood32,33. Two nodes are n hops apart if it is possible to reach the target node from the source node by traveling n links. We identify the downwind area of the source node as the subnetwork composed by the nodes that are reachable from the source via at most n hops along the directed links. We propose the number of links in this neighborhood (k) as a suitable measure of reachability from the node. This reachability depends upon three features: (i) the local structure of the street network, (ii) the direction of the wind, and (iii) the topological distance n. This latter parameter is intuitively correlated to the intensity of the release. More precisely, it depends on the ratio between the magnitude of the toxic release at the source and the threshold value for pollutant concentration to be significant. In this work, n is taken as constant and its value is obtained from an optimization analysis detailed in the “Methods” section (Fig. 6) .Once the (n-hop) neighborhood of a node is delimited, the number of links k is not exhaustive in giving information about the properties of the paths connecting the source to the other nodes of the neighborhood. For the same k, different structures of the neighborhood can take place (see Fig. 6b), with consequent different outcomes for the propagation process that we are breaking down to basic components. The higher the number of links outgoing each node of the neighborhood, the higher the potential concentration for the k links, as they are topologically closer to the source. This feature can be accounted for by means of a simple branching index (b) for the node neighborhood, defined in Eq. 8 as the average outdegree for the nodes belonging to the neighborhood34.The disassembling analysis presented above suggests that the spreading potential of a node, and thus its vulnerability, mainly depends on the topological parameters k and b and on the geometrical characteristics of its neighborhood, i.e. L, H, W, (Theta), where the capital letters are used to indicate the local average (over the n-hop neighborhood) for the length (l), height (h), width (w), and orientation ((theta)) of the street canyons.In adopting averaged geometrical properties, we are assuming that these characteristics are rather homogeneous in the surroundings of a node. While the height, width and length of the street canyons are actually quite uniform on a local scale, especially in European city centers, the same does not apply to the orientation of the streets. The streets of a neighborhood intersect each other at different angles (e.g., at (90^circ) in grid plans), and the intensity of the wind in the streets changes strongly with their orientation. Low wind streets act as bottlenecks in the propagation paths, thus strongly influencing the spreading dynamics. For this reason, the standard deviation of street orientation in the neighborhood ((sigma)) is expected to be an additional topological index of node vulnerability.To assess whether the identified parameters are valuable basic elements of node vulnerability, we perform a regression analysis adopting a simple (but versatile) non linear model of the form:$$begin{aligned} V_{pred}=alpha L^beta H^gamma W^delta Theta ^epsilon k^zeta b^eta (1-sigma )^lambda . end{aligned}$$
(1)
We estimate the coefficients (alpha) to (lambda) by means of a nonlinear least square technique (namely the fitnlm function in Matlab) that minimizes the sum of the squares of the residuals between the predicted vulnerability (V_{pred}) and the vulnerability V obtained from the centrality metric (Eq. 5 in “Methods”). The regression is performed considering all the scenarios presented in this study: four different urban networks and eight different wind directions. The p-values for the coefficients (alpha) to (lambda) tend to zero, indicating that the relationships between the independent variables and the observations (V) are statistically significant. Note that in Eq. (1) we adopt (1-sigma) as predictor, instead of (sigma), to avoid null entries, as (sigma) takes value in [0 1). To explain the reason for this range for (sigma), we point out that the angle between the wind direction and the street axis is defined in [(-90^circ) (90^circ)]. As a consequence, the cosine ((theta)) of the angle varies in [0 1] and the standard deviation of (theta) (i.e. (sigma)) varies in [0 1).The scatter plot in Fig. 3 compares (V_{pred}) against V. Points correspond to the nodes of the four urban networks in the eight wind scenarios. The figure suggests that 80% of the spreading capacity (V) of a spot in a city can be grasped from the basic geometrical and topological characteristics of its neighborhood. To identify the most influential parameters in the regression, we evaluate the gain in the coefficient of determination (R^2) as they are progressively included in the model (red circles in the inset). The quantities are entered in order to optimize (R^2) at each addition. Alternatively, the role of each parameter can be evaluated adopting the concept of unique contribution (triangles in the inset), i.e. the loss in the coefficient of determination induced by the exclusion of the parameter from the model35. Both analyses reveal k and (sigma) as the main indicators for the vulnerability of a node. Actually, more than 60% of the total variance (inset in Fig. 3) is explained by these two parameters, unveiling the crucial role of topology in governing the dynamics of pollutants in urban areas. The effect of the geometrical properties (L, H, W, (Theta)) of the street canyons is secondary. Among these, the contribution of the building height (H) is the most remarkable as its contribution, combined with that of the two topological parameters k and (sigma), brings the correlation to almost its maximum value.Given these results, it is enlightening to show some tangible examples of how the three simple indicators k, (sigma) and H dominate urban vulnerability. We wonder which of these properties determine the distinct vulnerability of neighboring areas belonging to the same district, and which ones differentiate the resilience of cities with a different urban history.Figure 3Correlation of node vulnerability with basic geometrical and topological parameters of the street network. Color (blue to red) is associated to point density. Left y-axis of inset: trend of the coefficient of determination (R^2) as the urban indicators are progressively included in the model. Right y-axis of inset: unique contribution of the indicators.Full size imageFigure 4a shows the spatial distribution of the key parameters k, (sigma) and H and of node vulnerability, for Manhattan and a wind direction (phi =45^circ). In panel b, high street reachability (k) is observed in the central part of Midtown, in the heart of Downtown, and near Wall Street. An homogeneous distribution in the orientation of the streets with respect to the incident wind (low values for (sigma) and thus high (1-sigma)) is especially found in Midtown (panel c). Finally, in panel d, high-buildings (H) distinguish the Financial District and East Midtown. A perfect match between the four layers is not expected as vulnerability is given by the synergistic contribution of the different parameters. However, in line with the results of the regression model shown in Fig. 3, a positive correlation is observable between the most vulnerable areas (circled areas comprising the nodes with highest V in panel a of Fig. 4) and those with the highest values for the three indicators. In these areas, high buildings inhibit the vertical exchange of pollutants between the streets and the atmosphere above, as largely discussed in literature (see e.g.36,37). This inhibition limits the concentration decay along the propagation paths and facilitates large-scale contamination. Moreover, the great number (k) of streets topologically close to the node increase the impact of the release. The effect of (sigma) is significant especially for the vulnerability of Midtown. Here, since (phi =45^circ) and the street network is regular, (theta) (the cosine of the wind-street angle) is almost the same for all the streets. Therefore, the standard deviation of (theta) ((sigma)) is low and the predictor (1-sigma) is high. Physically, this means that the external wind approaches all the streets with almost the same angle. As a consequence, the intensity of the longitudinal wind in the streets is similar (the street aspect ratio is also similar) and the propagation takes place equally along both the dominant and lateral segments of the street network38, thus favoring the spread over large areas. Although high values of H and (1-sigma) can be detected in the North-East corner of Midtown too, here the vulnerability is mitigated by a higher discontinuity in the urban pattern (low k). This feature, together with the great overlapping of red areas in panel a with those in panel b, evidences the key role of street reachability (k) in the heterogeneity of vulnerability between areas of the same urban district.Figure 4Street network of Midtown and Downtown Manhattan. Node color is associated to node vulnerability (V), and to its key indicators: street reachability (k), inhomogeneity in street orientation ((sigma)), and average height of buildings in the node neighborhood (H).Full size imageFrom these observations, we move to a broader view and investigate the structural fragility of a city as a whole. In Fig. 5a–c, we report the probability density function (pdf) of the key parameters k, (1-sigma) and H. For each city, the pdf is calculated over all the network nodes and for the different wind directions. So, each pdf is representative of eight different networks for the same urban area. In panel a, the distributions for the four cities are quite similar but the tails of the pdfs highlight that the highest values for street reachability (k) occur in the street networks of Lyon and New York. The homogeneity in street orientation with respect to the wind (panel b), expressed by (1-sigma), exhibits a bimodal distribution and a slightly higher mean for the regular street network of New York. The two peaks are associated to distinctive wind scenarios, as will be discussed below. Also in this case, the observation of the tails of the pdfs reveals that high values of the vulnerability indicator are more probable in Lyon and New York. Finally, the distribution of building height (panel c) presents the most marked difference between the considered architectures, with high-rise buildings contributing to the heavy pdf tail of Manhattan. Comparing these results with those in Fig. 2a, Manhattan’s greatest vulnerability appears to be due to the greater depth of the urban canyons (high H) and the greater homogeneity, on average, in wind-street orientation (high (1-sigma)). Conversely, the medieval structure of Firenze, with higher heterogeneity in street orientation (low (1-sigma)) and low buildings (low H), enhances street ventilation and hinders propagation over long distances. Moreover, the tails of the pdfs for k and (1-sigma) reveal the role of topology in the higher variability of vulnerability values (given by the standard deviation of the pdfs in Fig. 2) for the street networks of Lyon and Manhattan.After discussing the behavior of the single parameters, we assess the synergistic contribution of the three quantities. To this aim, we define a simple correlation index (rho =widehat{k} cdot (1-widehat{sigma }) cdot widehat{H}), where the hat denotes a min-max normalization of the parameters, i.e. the range of values of each parameter is rescaled in [0, 1]. For the urban areas of Manhattan, Lyon, Paris, and Firenze, (rho) gives 0.039, 0.017, 0.012, and 0.011, respectively. This ranking complies with the ranking inferable in Fig. 2 for the average vulnerability of the cities. This result confirms that vulnerability occurs when the three parameters are correlated, as already evidenced in Fig. 4.To make the picture even more fascinating, it is worth noting that the role of topology, shown above as key, is dynamic as it varies according to the direction of the wind impacting the urban fabric. In panels d to f of Fig. 5, the pdfs of k, (1-sigma) and H are distinguished for four wind directions ((phi =0^circ), (45^circ), (90^circ) and (135^circ)). For each angle, the statistics are calculated over the examined cities, together. Although wind orientation alters the direction of the network links, and thus the delimitation of the n-hop neighboring area of each node, street reachability (panel d) and building height (panel f) remain statistically invariant for the different wind directions, suggesting a rather isotropic structure of the urban fabric. On the other hand, the variability in street orientation with respect to the wind (panel e) presents two distinctive trends for wind directions aligned with or oblique to the main axes of the street network. To explain this behavior, we refer to the simple case of a grid-like urban plan, like Manhattan’s plan. When (phi =0^circ) or (90^circ), (theta) (the cosine of the angle between the street and the wind direction) mostly switches between 0 (for the streets aligned with the wind) and 1 (for the orthogonal streets), resulting in a high standard deviation over the neighborhood (low (1-sigma)). When (phi =45^circ) or (135^circ), instead, the incident angle (theta) mainly takes intermediate values, leading to higher values for (1-sigma). This distinctive behavior is clearly detectable in the two peaks that we have observed in panel b for the regular grid of Lyon and New York. The left peak of the bimodal distribution corresponds to the scenarios with aligned wind directions, while the right peak occurs for oblique wind directions over the city. A more irregular street pattern in Firenze and Paris adds random contributions to the way the wind approaches the street, thus altering this bimodal shape. Going back to panel e, the greater homogeneity in wind-street orientation (higher (1-sigma)) for (phi =45^circ) or (135^circ) gives insights into the higher vulnerability found for the scenarios with these wind directions in almost all cities (dark gray sectors in Fig. 2b). This result is confirmed by the correlation ((rho)) between the three rescaled parameters ((widehat{k}), (1-widehat{sigma }), (widehat{H})). The correlation (rho) is estimated separately for the different wind directions, but considering the nodes from the four urban areas together. For oblique wind directions, (rho) is about twice ((rho =0.035)) the value found for the aligned wind directions ((rho =0.018)).Figure 5Probability density function of the key parameters k, (1-sigma), H. In the first row, each curve refers to a city and includes vulnerability data from eight different wind directions. In the second row, each curve corresponds to a specific wind direction and includes vulnerability data from the four cities, together.Full size image More