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Ecological sampling and structural complexity profilesThe ecological sampling consists of 10 surveys, taking place in 2005 and from 2008 to 2016, and documents changes in coral colony abundance and size distributions (i.e. width, length, and height) for the three most conspicuous taxa (i.e. Acropora, Pocillopora, and Porites) within a 10 m2 transect on the outer slope23. To quantify reef structural complexity, we built a 3D model of the coral assemblages distributed along a cross-section of the reef substrate separating the 20 m water depth from the reef crest, representing a 160 m stretch along the reef slope (Fig. 1). First, we take 200 overlapping high-resolution photos (300 dpi) of 10 individual corals from each species (i.e. n = 30 coral colonies) and built 3D models using the Agisoft Metashape software24, capturing intra- and inter-species morphological variability (Fig. 1). Then, we systematically and randomly select one of the ten 3D coral models for each taxon to add to the substrate until that the sum of the planar area for each 3D coral models match with the coral cover reported for each taxon and for each year23. We randomly place coral colonies along the 160 m reef cross-section going from 20 m depth to the reef crest (Fig. 1). The individual coral 3D models are resized in width, length, and height according to ecological surveys, and, randomly rotated between − π/2 and π/2 to ensure ecological variability. Finally, we estimated structural complexity of the 3D coral assemblage model using the function rumple_index of the LidR package25 in R 4.0.026. We repeat this approach 100 times for each year, resulting in a total of 1000 reef structural complexity profiles. Our estimates are consistent with previous reef structural complexity estimates at this location27.Figure 1(a) Representation of the three different coral species (Acropora hyacinthus in red, Pocillopora cf. verrucosa in yellow, and Porites lutea in blue). (b) A representaitive Ha’apiti reef cross-section simulation (one of 1000 total simulations) on the outer slope across a water depth range of 0–20 m.Full size imageHydrodynamic and topographic measurementsMo’orea (French Polynesia) is encircled by coral reefs, 500–700 m wide with a dominant swell direction coming from the southwest. In this study, we focus on Ha’apiti, a site with a southwest orientation that is considered as a high-energy site28. We extract 30-year offshore wave data (1980–2010) from a wave hindcast8,29 (Fig. 2a). We also collect high-frequency, in situ wave data using INW PT2X Aquistar and DHI SensorONE pressure transducers (PTs), which are logged at 4 Hz30. The sensors are installed at four locations along a cross-shelf gradient (Fig. 2b,c) covering a 250 m long stretch, including sections through the fore reef, reef crest, and reef flat. Pressure records are corrected for pressure attenuation with depth31 and are split into 15-min bursts30.Figure 2(a) Histogram of the offshore wave height (m) at Ha’apiti, Mo’orea (French Polynesia) in 2016. (b) Aerial view of Ha’apiti (WorldView-3 imagery) with an outline of the wave transect and sensor location. The ecological sampling took place near the S1 location c. Topographic cross-section of the wave transect and position of the sensors on the sea bottom.Full size imageThe beach profile and the reef morphology are measured using airborne bathymetric and topo-bathymetric lidar surveys conducted in June 2015 by the Service Hydrographique & Océanographique de la Marine (SHOM). The bathymetric data are defined by the combination of bathymetric laser (for the submerged part of the beach) and topo-bathymetric laser (for the subaerial beach). The data come at 1 m resolution and are available at https://diffusion.shom.fr.Hydraulic roughness vs structural complexitySpectral attenuation analysis of the water level measurements32,33 is used to estimate the Nikuradse (hydraulic; kn) roughness34 of the coral reef surface along the beach profile sections covered by the pressure transducers. The method is described in detail in the references provided above and uses the conservation of energy equations to obtain estimates of wave energy dissipation from friction. We obtain more than 300 kn estimates for each pair of sensors, each representing a different geomorphologic section. Since the field measurements took place in 2015, the kn outputs obtained from the fore reef section concur with the reef structural complexity estimates of that year (Fig. 3). Then, we define a coefficient factor according to the geomorphologic section as ⍺back reef = kn, back reef/kn, fore reef and ⍺reef crest = kn, reef crest/kn, fore reef. We carefully delineate the sandy section from the reef sections within the cross-shelf gradient (i.e. within the reef flat, lagoon section) and apply the following procedure. First, for the reef sections, we apply the relationship between the reef structural complexity and kn (Fig. 3) to convert our reef structural complexity estimates into continuous kn profiles through Monte Carlo simulations, using the coefficient factor of each geomorphologic section (e.g., forereef, reef crest, and back reef). Second, for the sandy section, we define kn on the grounds of the mean grain size (d50 = 63 μm). Applying this workflow (Fig. 3), we obtain 100 continuous kn profiles for each year (i.e. n = 1000 kn profiles in total).Figure 3Flow chart illustrating how the kn profiles have been obtained along the cross-section at Ha’apiti. The relationship between the Structural complexity (SC) and the Nikuradse roughness (kn) measurements can be described as kn = 0.01 × SC2.98.Full size imageHydrodynamic modelNearshore wave propagation is simulated using a nonlinear wave model based on the Boussinesq Equations35. The rationale of using a Boussinesq type model instead of other types of models (e.g. SWAN) is that the former is able to describe in detail (i.e. 1 m grid resolution) several hydrodynamic parameters (e.g. nearshore nonlinear wave propagation, shoaling, refraction, dissipation due to the bottom friction and breaking and run-up) in the swash zone. The model is defined as follows:$$frac{partial U}{partial t}+frac{1}{h}frac{partial {M}_{u}}{partial x}-frac{1}{h}Ufrac{partial left(Uhright)}{partial x}+gfrac{partialupzeta }{partial x}=frac{left({d}^{2}+2partialupzeta right)}{3}frac{{partial }^{3}U}{partial {x}^{2}partial t}+{d}_{x}hfrac{{partial }^{2}U}{partial xpartial t}+frac{{partial }^{2}}{3}left(Ufrac{{partial }^{3}U}{{partial x}^{3}}-frac{partial U}{partial x}frac{{partial }^{2}U}{partial {x}^{2}}right)+dfrac{partialupzeta }{partial mathrm{x}}frac{{partial }^{2}U}{partialupzeta partial mathrm{t}}+d{d}_{x}Ufrac{{partial }^{2}U}{partial {x}^{2}}+{d}_{x}frac{partialupzeta }{partial mathrm{x}}frac{partial mathrm{U}}{partial mathrm{t}}-dfrac{{partial }^{2}}{partial mathrm{x}partial mathrm{t}}left(delta frac{partial mathrm{U}}{partial mathrm{x}}right)+E-frac{{tau }_{b}}{rho h}+B{d}^{2}left(frac{{partial }^{3}U}{partial {x}^{2}}+gfrac{{partial }^{3}upzeta }{partial {x}^{3}}+frac{{partial }^{2}left(Ufrac{partial U}{partial x}right)}{partial {x}^{2}}right)+2Bd{d}_{x}left(frac{{partial }^{2}U}{partial xpartial t}+gfrac{{partial }^{2}upzeta }{partial {mathrm{x}}^{2}}right),$$
(1)
where, U is the mean over the depth horizontal velocity, ζ is the surface elevation, d is the water depth, uo is the near bottom velocity, h = d + ζ, ({M}_{u}=left(d+zeta right){u}_{0}^{2}+delta ({c}^{2}-{u}_{0}^{2})), δ is the roller thickness determined geometrically36, E is an eddy viscosity, τb is the bed friction term and B = 1/1535.In this work the wave breaking mechanism is based on the surface roller concept36. However, in the swash zone, surface roller is not present and the eddy viscosity concept is used to describe the breaking process. The term E in Eq. (1) is written:$${mathrm{E}}_{{mathrm{b}}_{mathrm{x}}}= {mathrm{B}}_{mathrm{b}}frac{1}{mathrm{h}+upeta }{left{{{mathrm{v}}_{e}left[left(mathrm{h}+upeta right)mathrm{U}right]}_{mathrm{x}}right}}_{mathrm{x}},$$
(2)
where ({v}_{e}) is the eddy viscosity coefficient:$${mathrm{v}}_{mathrm{e}}={{ell}}^{2}left|frac{partial {mathrm{U}}}{partial {mathrm{x}}}right|,$$
(3)
where ({ell}) is the mixing length ({ell}) = 3.5 h και Βb37.The width of the swash zone is assumed to extend from the run-down point (seaward boundary) up to the run-up point (landward boundary). We start from a first estimate of the run-up R using the Stockdon formula38 and the depths below R/4 are considered as the swash zone, using Eq. (2). The final wave run-up height R which comes as output is estimated by the model.The ‘dry bed’ boundary condition is used to simulate run-up35. The numerical solution is based on the fourth-order time predictor–corrector scheme39. Therefore, the bed friction term τb is calculated such as:$${tau }_{bx}=frac{1}{2}rho {f}_{w}Uleft|Uright|,$$
(4)
where fw is the bottom friction coefficient40, which is an explicit approximation to the implicit, semi-empirical formula given by Jonsson, 196741.$${f}_{mathrm{w}}=mathrm{exp}left[{5.213left(frac{{mathrm{k}}_{mathrm{n}}}{{mathrm{alpha }}_{0}}right)}^{0.194}-5.977right],$$
(5)
where αo is the amplitude of the near-bed wave orbital motion and kn is the Nikuradse roughness height.Simulations and post processingWe use our wave propagation model to assess how different coral reef states affect the impact waves have on the coast. We run an ensemble of 10,000 simulations that covers all the possible combinations of (i) 10 bottom roughness profiles expressing the different observed coral reef states (i.e. healthy vs. not unhealthy); and (ii) 1000 percentiles of wave conditions. The wave conditions are produced as follows: (i) from the weekly values, we estimate all significant wave height (Hs) percentiles from 0.1 to 100, with a step of 0.1; (ii) the resulting 1000 Hs values are linked to the corresponding peak wave period Tp using a copula expressing the dependence of the two variables42. The output of the simulations is the nearshore Hs and 2% exceedance run-up (R2%) height for each of the 1000 conditions and 10 coral reef states. To quantify how the coral reef states are altering wave propagation during extreme events, we apply extreme value analysis to estimate the R2% for different return periods43. We then compare how the return period curves changed from the two coral reef states and we define the change in frequency of extreme R2% under unhealthy coral reefs. It is important to highlight that the tidal range is  More

When I first came to the Amazon from central Brazil in 1978, I was planning to stay just a year, but I was mesmerized by the size of the rainforest’s rivers and its biodiversity. I ended up staying longer and earned my master’s degree in aquatic biology in 1984 from the National Institute for Amazonian Research (INPA), in Manaus, Brazil. I then went to get my PhD in ecology and evolutionary biology at the University of Arizona in Tucson, and returned to Manaus in 1998 to work as an ichthyologist at INPA.I was part of the team that started INPA’s fish collection in 1978. At the time, most scientific information on Amazonian fish, including specimens, had been collected by researchers and stored at other institutions around the world. Brazilians couldn’t easily access any of it. Now, INPA has preserved and catalogued more than 600,000 fish, all of which are available to our graduate students and scientific community.
Women in science
This picture, from last June, was taken at a Manicoré River creek in northwest Brazil during a Greenpeace expedition. I’m holding a bag of small fish, collected using sieves.Since 2006, the riverside communities on the Manicoré have been advocating for a reserve to protect their land from non-sustainable practices. They asked Greenpeace to help map the area’s biodiversity to bolster their application. Greenpeace in turn invited INPA researchers for its mapping expedition. We spent 20 days collecting and registering the wide range of creatures in the Manicoré’s basins.Besides fires, the Amazon has been hit hard by deforestation and industrial activities. We registered a decline in populations of several fish species after the construction of the hydroelectric complex of Belo Monte — the second- largest in the world — in the Xingu River. These species can thrive only in the oxygenated environment of running rivers and waterfalls, which have been largely destroyed. More

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Vegetation and land-cover dataTo monitor vegetation at the global scale, we use three datasets: (1) vegetation optical depth (VOD, 0.25°, Ku-Band, daily 1987–201723) (Fig. 1A), (2) AVHRR GIMMSv3g normalized difference vegetation index (NDVI, 1/12°, bi-weekly 1981–201524) (Fig. 1B), and (3) MODIS MOD13 NDVI at 0.05° (16-day, 2000–202125). We correct for spurious values in the NDVI data (e.g., cloud contamination) using the method of Chen et al.43. We resample the VOD data using bi-weekly medians to agree with the NDVI data time sampling.For all three vegetation datasets, we remove seasonality and long-term trends using seasonal trend decomposition by Loess4,44 based on the proposed optimal parameters listed in Cleveland et al.44 (code available on Zenodo45). That is, we use a period of 24 (bi-monthly, 1 year), 47 for the trend smoother (just under 2 years) and 25 for low-pass (just over 1 year). We only use the STL residual—the de-seasoned and de-trended NDVI and VOD time series—in our analysis.To contextualize our understanding of vegetation resilience, we use MODIS MCD12Q1 land cover46 (Fig. 1C) as well as a global average aridity index based on WorldCLIM data31 (Fig. 1D). We exclude from our analysis anthropogenic and non-vegetated landscapes (e.g., permanent snow and ice, desert, urban), as well as any land covers which have changed (e.g., forest to grassland) during the period 2001–2020.Precipitation data and variability metricsTo measure precipitation at the global scale, we rely upon ERA5 data (~30 km, monthly, 1981–2021)33. We process global-scale precipitation metrics using the Google Earth Engine47 platform. We further use the sum of soil moisture from the surface down to 28 cm of depth (first two layers of the ECMWF Integrated Forecasting System soil moisture estimates) to quantify soil moisture means and inter-annual variability33.It is well-documented that vegetation resilience is responsive to the MAP of certain regions1. However, the role of precipitation variability in controlling vegetation resilience has not been well-studied. Here we examine precipitation variability in terms of both intra- and inter-annual patterns. Intra-annual precipitation variability is determined in terms of the Walsh-Lawler Seasonality index32 (Fig. 1D), calculated using monthly data from ERA533.Partly due to the fact that precipitation is non-negative, simple inter-annual variability metrics such as the standard deviation of annual precipitation sums are biased by the absolute precipitation sums; higher precipitation regions have a higher possible range of variability. To limit the influence of MAP, we hence investigate the standard deviation of annual precipitation sums normalized by the MAP, over the period 1981–2021, based on ERA5 data33 (Fig. 1F). We motivate our normalization by MAP with the strong linear relationship between MAP and MAP standard deviation (Supplementary Fig. S2). We further confirm our discovered relationships (Fig. 5) using only those regions where MAP was between the 40 and 60th percentile of MAP for a given land cover (Supplementary Figs. S11,S12). This serves as an additional check that our normalization of MAP standard deviation by MAP does not bias the inferred relationship between vegetation resilience and precipitation variability. Similarly, we generate a normalized inter-annual soil moisture variability by normalizing year-on-year soil moisture standard deviation (Supplementary Fig. S8) by long-term mean soil moisture (Supplementary Fig. S5).Empirical resilience estimationResilience is defined as the ability of a system to recover from perturbations, and can be quantified empirically by the speed of recovery to the previous state16,17. To measure resilience on the global scale, we employ a recently introduced methodology4 which we will briefly summarize in the following.We first identify sharp transitions in the vegetation time series using an 18-point (9 month) moving window to define local slopes throughout the time series48. We then identify slopes above the 99th percentile, and define connected regions as individual perturbations. The highest peak (largest instantaneous slope) within each connected region is then labeled as an individual disturbance.The employed approach does not delineate every rapid transition in a time series due to our reliance on percentiles; our dataset will be inherently biased towards the largest transitions. Furthermore, the same transitions are not guaranteed to be captured for both NDVI and VOD data in each location, as the percentiles will naturally vary between the datasets. Finally, our method will in some cases produce false positives, especially in cases where a given time series does not have any significant rapid transitions. To limit the influence of false positives on our results, we discard any perturbations where the time series does not drop significantly, and where the period before and after a given transition does not pass a two-sample Kolmogorov–Smirnov test4.Finally, using our global set of time-series transitions, we can identify each local vegetation (NDVI or VOD) minima, and use the five following years of data to fit an exponential function to the residual time series, assuming that the recovery after a perturbation to a vegetation state x0 follows approximately the equation$$x(t),approx ,{x}_{0}{e}^{rt}$$
(1)
where x(t) denotes the vegetation state at time t after the perturbation. Negative r indicates that the vegetation system will return to the original stable state at rate ∣r∣. For positive r, the initial perturbation would be amplified, suggesting a non-resilient vegetation state. Our empirical recovery rates are defined as the fitted exponent r, obtained for each detected transition in the NDVI and VOD residual time series. We finally use the coefficient of determination R2 to remove instances where the fitted exponential poorly matches the underlying data4.For the empirical estimate of the restoring rate obtained from fitting an exponential to the recovery after an abrupt negative deviation of VOD or NDVI, abrupt changes in the mean state induced by changing sensors rather than an actual vegetation shift may impact the results. However, all datasets used here are tightly cross-calibrated to eliminate mean-shifts when new instruments are introduced23,24. It is therefore unlikely that changes in the instrumentation of the various datasets unduly influence our empirical estimates of λ.Dynamical system metrics of resilienceThe lag-one autocorrelation (AC1) has previously been proposed to measure the stability of real-world dynamical systems in general, and the resilience of vegetation systems in particular1,19,20,21,49. Based on the concept of critical slowing down, the AC1 has, together with the variance, also been suggested as an early-warning indicator for forthcoming critical transitions50,51. Mathematically, the suitability of the variance and AC1 as resilience measures and early-warning indicators can be motivated as follows4,52,53. First, linearize the system around a given stable state x*:$$dbar{x}=lambda bar{x}dt+sigma dW$$
(2)
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