Philippa Kaur

Wild animals construct various types of structures that are adaptive to their life and reproduction. For example, termites that inhabit the African savanna use soil to construct a huge mound that reaches 10 m in height; they produce hollows and holes in these mounds to allow air ventilation, thereby keeping the internal temperature constant1. In addition, prairie dogs inhabiting the North American prairie dig vertically and horizontally extending burrows in the ground that they use for shelter and rearing offspring; these burrows have multiple entrances, some of which are chimney-shaped to improve ventilation efficiency2. In the field of biomimetics, researchers apply the principles of animal-created structures in applications useful to humans3.The white-spotted pufferfish Torquigener albomaculosus (Pisces: Tetraodontidae) is a relatively small species that grows to ~10 cm in total total length (Fig. 1). Male T. albomaculosus individuals construct an intricate geometric circular structure, known as the “mystery circle,” with a diameter of 2 m in the sand of the seabed;4 the discovery of these structures has fascinated researchers and the general public worldwide. The male pufferfish digs the sand on the seabed with its fins and body while swimming straight ahead toward the centre from different directions, and a circular structure composed of radially aligned peaks and valleys was constructed. Finally, the male creates a maze-like pattern by flapping its anal fin on the bottom of the central zone4. Thus, the male completes the circular structure by himself. Furthermore, we discovered that the earliest stage of the mystery circle is composed of dozens of irregular depressions, which might function as landmarks for the formation of the radial patterns5. By accumulating observations of pufferfish behaviour, we were able to conduct a computer simulation including the swimming trajectory of the pufferfish extracted from video images wherein they constructed the circular structure. This simulation revealed that an elaborate circular geometric pattern is inevitably formed if the pufferfish repeats the digging behavior on the seabed using simple rules6. We also observed the reproductive behaviour of the pufferfish and found that they consistently breed in a semilunar cycle from spring to summer. Each male constructs a mystery circle and spawns with multiple females on the nest, and the male cares for the eggs alone until they hatch. Some of the elements of the circular structure, i.e., its size, symmetry, ornaments, and maze-like pattern, might be important factors in terms of female mate choice4,7.Fig. 1The white-spotted pufferfish Torquigener albomaculosus. Lateral view of a male (a), and male digging behaviour on the seabed while rolling up fine sand particles (b).Full size imageAlthough data on the reproductive ecology and circle-construction behaviour of these pufferfish have been collected, many questions remain. Our interdisciplinary research currently has two themes: (i) theoretical studies on the logic of 3D-structure formation of the circular structure and (ii) ethological studies on the relationship between female mate choice and the features of the structure. To advance these studies, it is essential to collect quantitative data on the circular structure. Thus, we reconstructed 3D models of six completed mystery circles using a “structure from motion” (SfM) algorithm (Fig. 2).Fig. 2“Mystery circle” constructed by a white-spotted pufferfish (Torquigener albomaculosus). 3D model displayed on a computer (a), one of the video frames used to reconstruct the 3D model (b), and a Styrofoam model output in full size created using a 3D printer and the 3D data (c) for a specific mystery circle 20160615_K13.Full size imageOn the other hand, the mystery circle constructed by the pufferfish may have potential applications in biomimetics similar to the structures constructed by termites and prairie dogs. To support the importance of its structural characteristics, it has been observed that the water passing through the valley upstream always gathers in the center of the structure, regardless of the direction of water flow4. Furthermore, particle size analysis of the sand forming the mystery circle has revealed that it has the function of extracting fine-grained sand particles from the valleys arranged radially to the outside and directing them to the center (Kawase, in prep.). The field of computational fluid dynamics, which makes full use of fluid dynamics technology, engineering knowledge, and computers, will logically clarify the characteristics of the 3D structure of the mystery circle we have reconstructed here. Shameem et al. reconstructed a 3D model of a mystery circle to explore the flow features with 2D computational fluid dynamic simulations8. Since our model has already been quantified as 3D data, computational fluid analysis can be immediately performed using this data, and the structural features of the mystery circle are expected to be applied in a wide range of fields, such as architecture and engineering, via biomimetics. More

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Constant contacts modelWe assume the affected population is composed of two risk-groups, a fraction p of the population is composed of risk-takers (RT) and the remaining fraction (1-p) are risk-evaders (RE). We differentiate the RT and RE subpopulations by assuming the RE population face a reduced likelihood of infection due to adopting precautionary behaviors. On the other hand, we assume RT do not follow public health recommendations, thus facing a higher risk of infection, relative to the RE population. Political or ideological reasons, economic stress, the lack of reasonable alternatives, epidemic politicization or the lack of trust in public health authorities are some of the documented factors that potentially lead the population to risk the dangers of COVID-19 infection44, 45.Previous mathematical models consider complex within-host disease dynamics46 or the impact of exogenous factors on the COVID-19 transmission dynamics47. In this study, we focus on incorporating individual heterogeneous adaptive behavioral responses, based on group-specific infection risk perceptions. Our model of disease progression assumes that individuals in each behavioral group may show the following health status: Susceptible (S), infectious Exposed (E), Infectious symptomatic (I), infectious Asymptomatic (A), and Recovered (R). We consider a pre-symptomatic infectious health status (E), following evidence suggesting that exposed individuals exhibit a period of viral shedding38, 48,49,50,51. RT susceptible individuals ((S_1)) can get infected by making contacts with either: symptomatic ones (I) with a baseline per-contact likelihood of disease transmission (beta), exposed individuals ((E_1) and (E_2)) with reduced per-contact likelihood of infection (rho beta) , or asymptomatic individuals ((A_1) and (A_2)) with reduced per-contact likelihood of infection (alpha beta). Similarly RE susceptible individuals ((S_2)) may get infected by making contacts with symptomatic, exposed or asymptomatic individuals at respective likelihoods, (epsilon beta), (rho epsilon beta), and (alpha epsilon beta), where (0 More

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Land coverUrban landscapes are characterized by small clusters of patches, forming land mosaics that are distinct from natural landscapes. An accurate estimation of climate forcing requires a land cover dataset at high resolutions that does not omit small urban patches. In this study, the RF estimates are based on 500-m and 1-km land cover datasets. This fine resolution is necessary to preserve spatial details of small urban patches while avoiding the large underestimation of urban land areas at coarse resolution (e.g., ~19% underestimation at 10 km compared to that at 1 km)3. We used 500-m resolution MODIS Land Cover product (MCD12Q1v006) for historical land cover changes. For future urban land cover distributions, we used the global urban land expansion products simulated under the SSPs for 2030–2100 (i.e., Chen-2020)4. The simulation performance was tested using historical urban expansion from 2000 to 2015 based on Global Human Settlement Layer51, where the agreement between simulated and observed urban land was evaluated using the Figure of Merit (FoM) indicator52 that has showed similar or better values than those reported in other existing land simulation applications4. The high-resolution Chen-2020 also shows very high spatial consistency with the prominent coarse resolution global urban land projection LUH2 that is recommended in CMIP64. Considering different scenarios is also necessary to account for the uncertainties of future socioeconomic and environmental conditions, so we included simulated urban lands under three scenarios (Supplementary Table 1): Sustainability -SSP1, Middle of the Road – SSP2, and Fossil-fueled Development – SSP553. Within each SSP scenario, the product provides a likelihood map of each grid becoming urban, based on 100 urbanization simulations. We used the likelihood map to account for spatial uncertainties of urban expansion by deriving 90% confidence intervals of projected urban land demand within a SSP scenario. We used the MODIS IGBP Land Cover classes (Supplementary Table 2) and resampled the original 500-m resolution MODIS products in 2018 to 1-km resolution to match the future simulations when it was used as a baseline year. To isolate the independent effect of urbanization (vs other types of land uses) in future estimates, land covers that are not converted to urban are assumed to have the same cover types as in 2018 (i.e., the baseline year). Though there are other global land cover products for current periods, we choose the MODIS IGBP land cover products because the albedo look-up maps (LUMs) were based on IGBP land cover types (see Albedo Look-Up Maps).To further evaluate the uncertainties caused by different projections of future urbanization, we also included the other two SSPs from Chen-2020, and another two 1-km resolution urban land cover products projected for the future for the purpose of comparison. The other two products include four projections of SRES scenarios (i.e., A1, B1, A1B, and B2) (i.e., Li-2017 mentioned above)3 and one without scenario description but assumed historical development would continue (i.e., Zhou-2019 mentioned above)2. These projections of future urban land expansion were calibrated with different historical urban land products and can be regarded as independent.Albedo look-up maps (LUMs)Albedo Look-Up Maps (LUMs)31 were derived from the intersection of MODIS land cover54 and surface albedo55 products, which are used to determine the albedo values for each IGBP land cover type by month and by location. Monthly means of white-sky (i.e., diffuse surface illumination condition) and black sky (i.e., direct surface illumination condition) during 2001–2011 were processed for snow-free and snow-covered periods for each of the 17 IGBP land cover classes at spatial resolutions of 0.05°−1°31. The LUMs have been verified by comparing the reconstructed albedo using the LUMs with the original MODIS albedo, which shows very similar values31. We used the LUMs at a resolution of 1° due to the significantly fewer missing values, to assure the spatial continuity of albedo changes at a global scale while keeping the matches with the 1° resolution of radiation data and RF kernels. The underlying assumption is that albedo of the same land cover type varies insignificantly within a 1° grid.Snow and radiation productSnow cover can significantly change the albedo of land regardless of cover types (Supplementary Fig. 4). In this study, we tally monthly albedo using snow-free and snow-covered categories in estimating RF. Past and present snow-free and snow-covered conditions were derived from level 3 MODIS/Terra Snow Cover (MOD10CM.006)56 at 0.05° spatial resolution and resampled to a 1° spatial resolution. Monthly means of 2001–2005 vs 2015–2019 were used for 2001 and 2018 respectively. For future periods, ensemble mean snow cover for each year and month, projected under the CMIP5 framework for three Representative Concentration Pathway (RCP) scenarios (i.e., RCP2.6, RCP4.5, and RCP8.5) were used (for more details see Supplementary Note 2B). By comparing the model outputs with MODIS observations for a recent decade (2006–2015), we found that the multi-model mean snow cover was systematically biased compared to MODIS observations. Consequently, we calibrated the ensemble mean projections by subtracting the biases for the grids. In each 10th year of the future (e.g., 2030, 2040, etc.), the decadal monthly mean snow cover (e.g., 2026–2035 for 2030, and 2036–2045 for 2040, etc.) was used for the year.We used the long-term monthly averages (1981–2010) of diffuse and direct incoming surface solar radiation reanalysis Gaussian grid product from National Centers for Environmental Prediction (NCEP)57. Visible and near infrared beam downward radiation and diffuse downward radiation from NCEP were used to compute the white-sky and black-sky fractions. As for snow cover, ensemble mean shortwave radiation at surface (SWSF) and at top-of-atmosphere (SWTOA) projected from CMIP5 models (Supplementary Note 3C) for RCP2.6, RCP4.5, and RCP8.5 were collected for empirically computing future albedo kernels (see section 3.4 below).Radiative kernelsRadiative kernels were used to compute top-of-atmosphere RF due to small perturbations of temperature, water vapor, and albedo. We used the latest state-of-the-art albedo kernels calculated with CESM v1.1.258 to compute RF in 2018 relative to 2001. In brief, the albedo kernel is the change in top-of-atmosphere radiative flux for a 0.01 change in surface albedo. The CESM1.1.2 kernels are separated into clear- and all-sky illumination conditions. We used the all-sky kernels because we include both black-sky and white-sky albedos. For future periods, because there are no available radiative kernels produced from general circulation models, we approximated the future kernels using an empirical parameterization following Bright et al.59:$${K}_{m}left(iright)={{SW}}^{{SF}}(i)times {sqrt}left(frac{{{SW}}^{{SF}}(i)}{{{SW}}^{{TOA}}(i)}right)/(-100)$$
(1)
where m is the month, i is the location, and SWSF and SWTOA are the surface and top-of-atmosphere shortwave radiation; dividing by −100 is for matching the CESM1.1.2 kernel definition of a 0.01 change in surface albedo.Estimation of albedo change and RFWe analyzed the RF in 2018 due to albedo changes caused by urbanization since 2001 (2018–2001), and in the future from 2030 to 2100 at decadal intervals (i.e., 2030, 2040, 2050, …, and 2100) since 2018 under three illustrative scenarios: SSP1-2.6, SSP2-4.5, and SSP5-8.5, which combine SSP-based urbanization projections and RCP-based climate projections. The three illustrative scenarios were selected following the scenario designation of the latest IPCC report50 and represent low greenhouse gas (GHG) emissions with CO2 emissions declining to net zero around or after 2050, intermediate GHG emissions with CO2 emissions remaining around current levels until the mid-century, and very high CO2 emissions that roughly double from current levels by 2050, respectively. We selected 2018 as the baseline year to divide the past from the future because 2018 was the latest year with available MODIS land cover products at the time of this study. We used ArcGIS 10.6 to produce spatial maps of all variables, including area of each land cover type within a 1° × 1°-grid, snow cover, albedo, radiation, and kernels, and R 3.6.1 to compute the RF.We focused only on albedo changes induced by urbanization, including the conversions from all other 16 IGBP land cover types to urban land. The changes of albedo for each grid (x, y) of a month (m) were obtained by computing the difference between albedo of that grid in the baseline year (t = t0) and in a later year (t = t1) with urban expansion:$${triangle alpha }_{m,t1-t0}(x,y)={alpha }_{m,t=t1}(x,y)-{alpha }_{m,t=t0}(x,y)$$
(2)
where αm, t = t1 (x, y) and αm, t = t0) (x, y) is the albedo for each grid (x,y) of a month (m) at the base year and later year respectively; the grid-scale albedo is computed as the weighted sum of albedo by land cover types with the weighing factor corresponding to areal percentage of a land cover within the grid. The albedo for each land cover type of a grid was then obtained by applying the albedo LUMs that provide spatially continuous black-sky, white-sky, snow-covered, and snow-free albedo maps for a given month for each land cover. Firstly, monthly mean albedo is computed as:$${alpha }_{m,t}(x,y)=mathop{sum }limits_{l=1}^{17}mathop{sum }limits_{s=0}^{1}mathop{sum }limits_{r=0}^{1}{{f}_{l,t}(x,y){f}_{s,m,t}(x,y)f}_{r,m,t}(x,y)left({alpha }_{l,s,r,m}(x,y)right)$$
(3)
where m is the month, t is the year, l is the land cover type, fl is the proportion of a cover type within the grid, fs,m,t is the fraction for snow-covered (s = 0) and snow-free (s = 1) conditions of the time (m, t), fr,m,t (x, y) is the fraction for white-sky (r = 0) or black-sky (r = 1) conditions of the time, and αl,s,r,m (x, y) is the albedo for land cover type l in month m that is extracted from the albedo LUMs corresponding to snow condition (s) and radiation condition (r). The annual mean albedo change is reported as the mean of monthly albedo change:$${triangle alpha }_{t1-t0}(x,y)=frac{1}{12}mathop{sum }limits_{m=1}^{m=12}({alpha }_{m,t=t1}(x,y)-{alpha }_{m,t=t0}(x,y))$$
(4)
The conversion of other land covers to urban land can contribute differently to the global RF, as the total area that is converted into urban land is different among non-urban land covers and the albedo differences between urban land and non-urban land cover types vary. To estimate the proportional contributions of different land conversions, we first decomposed the total albedo of each grid into the proportion of each land cover type:$${alpha }_{l,m,t}(x,y)={f}_{l,m,t}(x,y)mathop{sum }limits_{s=0}^{1}mathop{sum }limits_{r=0}^{1}{f}_{s,m,t}(x,y){f}_{r,m,t}(x,y)left({alpha }_{l,s,r,m}(x,y)right)$$
(5)
The global RF due to albedo change caused by conversion from each non-urban land cover type (l ≠ 13) to urban land (l = 13) (see Supplementary Table 2 land cover labels) was calculated as:$${{RF}}_{triangle alpha ,l(lne 13),{global}}=frac{1}{{A}_{{Earth}}}mathop{sum }limits_{i=1}^{n}mathop{sum }limits_{m=1}^{12}{({alpha }_{13,m,t=t1}left(iright)-{alpha }_{l,m,t=t0}left(iright))Delta p}_{lto 13}left(iright){Area}left(iright){K}_{m}(i)$$
(6)
where i refers to a grid, n is the total number of pixels on global lands, AEarth is the global surface area (5.1  ×  108 km2), α13,m,t = t1) (i) is the albedo of urban land in month m in the later year with urban expansion, αl,m,t = t0 (i) is the albedo of a targeted non-urban land cover type in the base year t0, Δpl→13 is the percentage of the non-urban land cover type that is converted to urban land in the year t1 compared to year t0, Area(i) is the area of the pixel, and Km (i) is the radiative kernel at the grid.The global RF due to urbanization-induced albedo changes was then calculated as:$${{RF}}_{triangle alpha ,{global}}=mathop{sum }limits_{l=1}^{17}{{RF}}_{triangle alpha ,l,{global}}(l,ne, 13)$$
(7)
GWP: CO2-equivalentWe followed GWP calculations by explicitly accounting for the lifetime and dynamic behavior of CO2 to convert RF to CO2 equivalent60,61:$${GWP}[{kg},{of},{{CO}}_{2}-{eq}]=frac{{int }_{t=0}^{{TH}}{{RF}}_{triangle alpha ,{global}}(t)}{{k}_{{CO}_2}{int }_{t=0}^{{TH}}{y}_{{{CO}}_{2}}(t)}$$
(8)
where kCO2 is radiative efficiency of CO2 in the atmosphere (W/m2/kg) at a constant background concentration of 389 ppmv, which is taken as 1.76  ×  1015 W/m2/kg62, and RF∆α,global is the global RF caused by albedo changes (W/m2). ({y}_{{{CO}}_{2}}) is the impulse-response function (IRF) for CO2 that ranges from 1 at the time of the emission pulse (t = 0) to 0.41 after 100 years, and here it is set to a mean value of 0.52 over 100 years60. The time horizon (TH) of our GWP calculations was fixed at 100 years following IPCC standards and previous studies60,63,64.Global mean surface air temperature changeWe estimated the 100-year global mean surface temperature change for the estimated RF by adopting an equilibrium climate sensitivity (ECS), defined as the global mean surface air temperature increase that follows a doubling of pre-industrial atmospheric carbon dioxide (RF = 3.7 W/m2). Given a value of RF induced by a forcing agent, the temperature change is estimated as RF/3.7 × ECS. To consider the uncertainties of ECS, we adopted a mean value of 3 °C and a very likely (90% confidence interval) range of 2–5 °C following IPCC AR650. Without knowing the exact distribution shape of ECS and future albedo-change-induced RF, we created a log-normal distribution (Supplementary Note 4) to approximate their asymmetric distribution through numerical simulation. We then conducted Monte Carlo simulations that draw 5000 random samples from each distribution to jointly estimate the uncertainties of global mean surface air temperature changes. We report the mean and 90% interval ranges of the change in temperature. More

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