Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling

Nonlinear state-space modelling is a very powerful black-box modelling approach. However powerful, the resulting models tend to be complex, described by a large number of parameters. In many cases interpretability is preferred over complexity, making too complex models unfit or undesired. In this work, the complexity of such models is reduced by retrieving a more structured, parsimonious model from the data, without exploiting physical knowledge. Essential to the method is a translation of all multivariate nonlinear functions, typically found in nonlinear state-space models, into sets of univariate nonlinear functions. The latter is computed from a tensor decomposition. It is shown that typically an excess of degrees of freedom are used in the description of the nonlinear system whereas reduced representations can be found. The method yields highly structured state-space models where the nonlinearity is contained in as little as a single univariate function, with limited loss of performance. Results are illustrated on simulations and experiments for: the forced Duffing oscillator, the forced Van der Pol oscillator, a Bouc-Wen hysteretic system, and a Li-Ion battery model.Comment: submitted to Mechanical Systems and Signal Processin

A nonlinear model of vortex-induced forces on an oscillating cylinder in a fluid flow

A nonlinear model relating the imposed motion of a circular cylinder, submerged in a fluid flow, to the transverse force coefficient is presented. The nonlinear fluid system, featuring vortex shedding patterns, limit cycle oscillations and synchronisation, is studied both for swept sine and multisine excitation. A nonparametric nonlinear distortion analysis (FAST) is used to distinguish odd from even nonlinear behaviour. The information which is obtained from the nonlinear analysis is explicitly used in constructing a nonlinear model of the polynomial nonlinear state-space (PNLSS) type. The latter results in a reduction of the number of parameters and an increased accuracy compared to the generic modelling approach where typically no such information of the nonlinearity is used. The obtained model is able to accurately simulate time series of the transverse force coefficient over a wide range of the frequency-amplitude plane of imposed cylinder motion.Comment: Accepted for publication in Journal of Fluids and Structure

Spatio-temporal assessment of beech growth in relation to climate extremes in Slovenia – An integrated approach using remote sensing and tree-ring data

Climate change is predicted to affect tree growth due to increased frequency and intensity of extreme events such as ice storms, droughts and heatwaves. Yet, there is still a lot of uncertainty on how trees respond to an increase in frequency of extreme events. Use of both ground-based wood increment (i.e. ring width) and remotely sensed data (i.e. vegetation indices) can be used to scale-up ground measurements, where there is a link between the two, but this has only been demonstrated in a few studies. We used tree-ring data together with crown features derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) to assess the effect of extreme climate events on the growth of beech (Fagus sylvatica L.) in Slovenia. We found evidence that years with climate extremes during the growing season (drought, high temperatures) had a lower ring width index (RWI) but we could not find such evidence for the remotely sensed EVI (Enhanced Vegetation Index). However, when assessing specific events where leaf burning or wilting has been reported (e.g. August 2011) we did see large EVI anomalies. This implies that the impact of drought or heatwave events cannot be captured by EVI anomalies until physical damage on the canopy is caused. This also means that upscaling the effect of climate extremes on RWI by using EVI anomalies is not straightforward. An exception is the 2014 ice storm that caused a large decline in both RWI and EVI. Extreme climatic parameters explained just a small part of the variation in both RWI and EVI by, which could indicate an effect of other climate variables (e.g. late frost) or biotic stressors such as insect outbreaks. Furthermore, we found that RWI was lower in the year after a climate extreme occurred in the late summer. Most likely due to the gradual increase in temperature and more frequent drought we found negative trends in RWI and EVI. EVI maps could indicate where beech is sensitive to climate changes and could be used for planning mitigation interventions. Logical next steps should focus on a tree-based understanding of the short -and long-term effects of climate extremes on tree growth and survival, taking into account differential carbon allocation to the crown (EVI) and to wood-based variables. This research highlights the value of an integrated approach for upscaling tree-based knowledge to the forest level

The number of tree species on Earth

One of the most fundamental questions in ecology is how many species inhabit the Earth. However, due to massive logistical and financial challenges and taxonomic difficulties connected to the species concept definition, the global numbers of species, including those of important and well-studied life forms such as trees, still remain largely unknown. Here, based on global groundsourced data, we estimate the total tree species richness at global, continental, and biome levels. Our results indicate that there are 73,000 tree species globally, among which ∼9,000 tree species are yet to be discovered. Roughly 40% of undiscovered tree species are in South America. Moreover, almost one-third of all tree species to be discovered may be rare, with very low populations and limited spatial distribution (likely in remote tropical lowlands and mountains). These findings highlight the vulnerability of global forest biodiversity to anthropogenic changes in land use and climate, which disproportionately threaten rare species and thus, global tree richness

High aboveground carbon stock of African tropical montane forests

Tropical forests store 40-50 per cent of terrestrial vegetation carbon(1). However, spatial variations in aboveground live tree biomass carbon (AGC) stocks remain poorly understood, in particular in tropical montane forests(2). Owing to climatic and soil changes with increasing elevation(3), AGC stocks are lower in tropical montane forests compared with lowland forests(2). Here we assemble and analyse a dataset of structurally intact old-growth forests (AfriMont) spanning 44 montane sites in 12 African countries. We find that montane sites in the AfriMont plot network have a mean AGC stock of 149.4 megagrams of carbon per hectare (95% confidence interval 137.1-164.2), which is comparable to lowland forests in the African Tropical Rainforest Observation Network(4) and about 70 per cent and 32 per cent higher than averages from plot networks in montane(2,5,6) and lowland(7) forests in the Neotropics, respectively. Notably, our results are two-thirds higher than the Intergovernmental Panel on Climate Change default values for these forests in Africa(8). We find that the low stem density and high abundance of large trees of African lowland forests(4) is mirrored in the montane forests sampled. This carbon store is endangered: we estimate that 0.8 million hectares of old-growth African montane forest have been lost since 2000. We provide country-specific montane forest AGC stock estimates modelled from our plot network to help to guide forest conservation and reforestation interventions. Our findings highlight the need for conserving these biodiverse(9,10) and carbon-rich ecosystems. The aboveground carbon stock of a montane African forest network is comparable to that of a lowland African forest network and two-thirds higher than default values for these montane forests.Peer reviewe

The number of tree species on Earth.

One of the most fundamental questions in ecology is how many species inhabit the Earth. However, due to massive logistical and financial challenges and taxonomic difficulties connected to the species concept definition, the global numbers of species, including those of important and well-studied life forms such as trees, still remain largely unknown. Here, based on global ground-sourced data, we estimate the total tree species richness at global, continental, and biome levels. Our results indicate that there are ∼73,000 tree species globally, among which ∼9,000 tree species are yet to be discovered. Roughly 40% of undiscovered tree species are in South America. Moreover, almost one-third of all tree species to be discovered may be rare, with very low populations and limited spatial distribution (likely in remote tropical lowlands and mountains). These findings highlight the vulnerability of global forest biodiversity to anthropogenic changes in land use and climate, which disproportionately threaten rare species and thus, global tree richness

The number of tree species on Earth.

One of the most fundamental questions in ecology is how many species inhabit the Earth. However, due to massive logistical and financial challenges and taxonomic difficulties connected to the species concept definition, the global numbers of species, including those of important and well-studied life forms such as trees, still remain largely unknown. Here, based on global ground-sourced data, we estimate the total tree species richness at global, continental, and biome levels. Our results indicate that there are ∼73,000 tree species globally, among which ∼9,000 tree species are yet to be discovered. Roughly 40% of undiscovered tree species are in South America. Moreover, almost one-third of all tree species to be discovered may be rare, with very low populations and limited spatial distribution (likely in remote tropical lowlands and mountains). These findings highlight the vulnerability of global forest biodiversity to anthropogenic changes in land use and climate, which disproportionately threaten rare species and thus, global tree richness

Integrated global assessment of the natural forest carbon potential

Forests are a substantial terrestrial carbon sink, but anthropogenic changes in land use and climate have considerably reduced the scale of this system 1. Remote-sensing estimates to quantify carbon losses from global forests 2–5 are characterized by considerable uncertainty and we lack a comprehensive ground-sourced evaluation to benchmark these estimates. Here we combine several ground-sourced 6 and satellite-derived approaches 2,7,8 to evaluate the scale of the global forest carbon potential outside agricultural and urban lands. Despite regional variation, the predictions demonstrated remarkable consistency at a global scale, with only a 12% difference between the ground-sourced and satellite-derived estimates. At present, global forest carbon storage is markedly under the natural potential, with a total deficit of 226 Gt (model range = 151–363 Gt) in areas with low human footprint. Most (61%, 139 Gt C) of this potential is in areas with existing forests, in which ecosystem protection can allow forests to recover to maturity. The remaining 39% (87 Gt C) of potential lies in regions in which forests have been removed or fragmented. Although forests cannot be a substitute for emissions reductions, our results support the idea 2,3,9 that the conservation, restoration and sustainable management of diverse forests offer valuable contributions to meeting global climate and biodiversity targets

The global biogeography of tree leaf form and habit

Understanding what controls global leaf type variation in trees is crucial for comprehending their role in terrestrial ecosystems, including carbon, water and nutrient dynamics. Yet our understanding of the factors influencing forest leaf types remains incomplete, leaving us uncertain about the global proportions of needle-leaved, broadleaved, evergreen and deciduous trees. To address these gaps, we conducted a global, ground-sourced assessment of forest leaf-type variation by integrating forest inventory data with comprehensive leaf form (broadleaf vs needle-leaf) and habit (evergreen vs deciduous) records. We found that global variation in leaf habit is primarily driven by isothermality and soil characteristics, while leaf form is predominantly driven by temperature. Given these relationships, we estimate that 38% of global tree individuals are needle-leaved evergreen, 29% are broadleaved evergreen, 27% are broadleaved deciduous and 5% are needle-leaved deciduous. The aboveground biomass distribution among these tree types is approximately 21% (126.4 Gt), 54% (335.7 Gt), 22% (136.2 Gt) and 3% (18.7 Gt), respectively. We further project that, depending on future emissions pathways, 17–34% of forested areas will experience climate conditions by the end of the century that currently support a different forest type, highlighting the intensification of climatic stress on existing forests. By quantifying the distribution of tree leaf types and their corresponding biomass, and identifying regions where climate change will exert greatest pressure on current leaf types, our results can help improve predictions of future terrestrial ecosystem functioning and carbon cycling

The global biogeography of tree leaf form and habit

Understanding what controls global leaf type variation in trees is crucial for comprehending their role in terrestrial ecosystems, including carbon, water and nutrient dynamics. Yet our understanding of the factors influencing forest leaf types remains incomplete, leaving us uncertain about the global proportions of needle-leaved, broadleaved, evergreen and deciduous trees. To address these gaps, we conducted a global, ground-sourced assessment of forest leaf-type variation by integrating forest inventory data with comprehensive leaf form (broadleaf vs needle-leaf) and habit (evergreen vs deciduous) records. We found that global variation in leaf habit is primarily driven by isothermality and soil characteristics, while leaf form is predominantly driven by temperature. Given these relationships, we estimate that 38% of global tree individuals are needle-leaved evergreen, 29% are broadleaved evergreen, 27% are broadleaved deciduous and 5% are needle-leaved deciduous. The aboveground biomass distribution among these tree types is approximately 21% (126.4 Gt), 54% (335.7 Gt), 22% (136.2 Gt) and 3% (18.7 Gt), respectively. We further project that, depending on future emissions pathways, 17-34% of forested areas will experience climate conditions by the end of the century that currently support a different forest type, highlighting the intensification of climatic stress on existing forests. By quantifying the distribution of tree leaf types and their corresponding biomass, and identifying regions where climate change will exert greatest pressure on current leaf types, our results can help improve predictions of future terrestrial ecosystem functioning and carbon cycling