Wildfire national carbon accounting: how natural and anthropogenic landscape fires emissions are treated in the 2020 Australian government greenhouse gas accounts report to the UNFCCC.

Greenhouse gas (GHG) accounting of emissions from land use, land-use change, and forestry necessarily involves consideration of landscape fire. This is of particular importance for Australia given that natural and human fire is a common occurrence, and many ecosystems are adapted to fire, and require periodic burning for plant regeneration and ecological health. Landscape fire takes many forms, can be started by humans or by lightning, and can be managed or uncontrolled. We briefly review the underlying logic of greenhouse gas accounting involving landscape fire in the 2020 Australian Government GHG inventory report. The treatment of wildfire that Australia chooses to enact under the internationally agreed guidelines is based on two core assumptions (a) that effects of natural and anthropogenic fire in Australian vegetation carbon stocks are transient and they return to the pre-fire level relatively quickly, and (b) that historically and geographically anomalous wildfires in forests should be excluded from national anthropogenic emission estimates because they are beyond human control. It is now widely accepted that anthropogenic climate change is contributing to increased frequency and severity of forest fires in Australia, therefore challenging assumptions about the human agency in fire-related GHG emissions and carbon balance. Currently, the national inventory focuses on forest fires; we suggest national greenhouse gas accounting needs to provide a more detailed reporting of vegetation fires including: (a) more detailed mapping of fire severity patterns; (b) more comprehensive emission factors; (c) better growth and recovery models from different vegetation types; (d) improved understanding how fires of different severities affect carbon stocks; and (e) improved analysis of the human agency behind the causes of emissions, including ignition types and fire-weather conditions. This more comprehensive accounting of carbon emissions would provide greater incentives to improve fire management practices that reduce the frequency, severity, and extent of uncontrolled landscape fires.

Tree mortality and carbon emission as a function of wildfire severity in south-eastern Australian temperate forests.

Disturbance trends over recent decades indicate that climate change is resulting in increased fire severity and extent in Australia's temperate Eucalyptus forests. As disturbance cycles become shorter and more severe, empirical measurements are required to identify potential change in forest carbon (C) stock and emissions. However, such estimates are rare in the literature. The 2019-2020 wildfires burnt through 6 to 7 million ha of mainly temperate open Eucalyptus forest in south-east Australia, with top down emission estimates ranging from 97 to 130 tonnes CO2 ha-1. Study sites that had been assessed for all aboveground C pools prior to the wildfires, were burnt in January 2020 by wildfire that varied in severity. Here we quantify the impact of high and low/moderate fire severities on tree mortality, C loss and C redistribution and assess implications for future C storage in these temperate Eucalyptus forests. Higher fire severity resulted in greater overstorey tree mortality but not understorey or loss of dead standing trees than in low/moderate severity fires. High severity fires combusted almost twice as much C from live trees (42 Mg C ha-1) as low/moderate severity fires (25 Mg C ha-1), while C loss from dead standing trees was similar among fire severity classes (average 17 Mg C ha-1). Total aboveground C lost across study sites was 42 Mg C ha-1 for high and 47 Mg C ha-1 for low/moderate severity, with an average of 45 Mg C ha-1 equivalent to 15 % (high severity) and 14 % (low/moderate severity) of AGC. Extrapolating our findings to other tall to medium open Eucalyptus forests across Victoria revealed that 37.33 ± 12.25 Tg C (mean ± s.e.) or 152 ± 50 Mg CO2 ha-1 was lost to the atmosphere from the 0.9 million ha of these productive forests, equating to about 20 % of Australia's total net annual emissions.

Pulse and Press Disturbances Have Different Effects on Transient Community Dynamics.

AbstractDisturbances are important determinants of diversity, and the combination of their aspects (e.g., disturbance intensity, frequency) can result in complex diversity patterns. Here, we leverage an important approach to classifying disturbances in terms of temporal span to understand the implications for species coexistence: pulse disturbances are acute and discrete events, while press disturbances occur continuously through time. We incorporate the resultant mortality rates into a common framework involving disturbance frequency and intensity. Press disturbances can be encoded into models in two distinct ways, and we show that the appropriateness of each depends on the type of data available. Using this framework, we compare the effects of pulse versus press disturbance on both asymptotic and transient dynamics of a two-species Lotka-Volterra competition model to understand how they engage with equalizing mechanisms of coexistence. We show that press and pulse disturbances differ in transient behavior, though their asymptotic diversity patterns are similar. Our work shows that these differences depend on how the underlying disturbance aspects interact and that the two ways of characterizing press disturbances can lead to contrasting interpretations of disturbance-diversity relationships. Our work demonstrates how theoretical modeling can strategically guide and help the interpretation of empirical work.

A globally relevant change taxonomy and evidence-based change framework for land monitoring.

A globally relevant and standardized taxonomy and framework for consistently describing land cover change based on evidence is presented, which makes use of structured land cover taxonomies and is underpinned by the Driver-Pressure-State-Impact-Response (DPSIR) framework. The Global Change Taxonomy currently lists 246 classes based on the notation 'impact (pressure)', with this encompassing the consequence of observed change and associated reason(s), and uses scale-independent terms that factor in time. Evidence for different impacts is gathered through temporal comparison (e.g., days, decades apart) of land cover classes constructed and described from Environmental Descriptors (EDs; state indicators) with pre-defined measurement units (e.g., m, %) or categories (e.g., species type). Evidence for pressures, whether abiotic, biotic or human-influenced, is similarly accumulated, but EDs often differ from those used to determine impacts. Each impact and pressure term is defined separately, allowing flexible combination into 'impact (pressure)' categories, and all are listed in an openly accessible glossary to ensure consistent use and common understanding. The taxonomy and framework are globally relevant and can reference EDs quantified on the ground, retrieved/classified remotely (from ground-based, airborne or spaceborne sensors) or predicted through modelling. By providing capacity to more consistently describe change processes-including land degradation, desertification and ecosystem restoration-the overall framework addresses a wide and diverse range of local to international needs including those relevant to policy, socioeconomics and land management. Actions in response to impacts and pressures and monitoring towards targets are also supported to assist future planning, including impact mitigation actions.

Effects of prescribed fire frequency on wildfire emissions and carbon sequestration in a fire adapted ecosystem using a comprehensive carbon model.

Prescribed fire to reduce forest fuels has been routinely applied to reduce wildfire risk in many parts of the world. It has also been proposed that prescribed fire can be used to mitigate greenhouse gas (GHG) emissions. Although prescribed fire creates emissions, if the treatment also decreases the incidence of subsequent wildfires, it is possible for the net outcome to be an emissions decline. Previous studies have suggested prescribed fire, at the frequencies required to materially impact wildfire occurrence, generally leads to net emissions increases. A focus on emissions means any change in carbon storage within the ecosystem remains unaccounted for; because living, dead, and soil carbon pools are characterized by different residence times, a re-distribution of carbon amongst these pools may either reduce or increase long-term ecosystem carbon stores. A full ecosystem carbon model has been developed to investigate the implications of prescribed fire management on total Net Ecosystem Carbon Balance (NECB), inclusive of both emissions and carbon storage. Consistent with previous work, the results suggested limited potential for reducing net GHG emissions through applying prescribed fire, with higher emissions from prescribed fire approximately offset by lower emissions and avoided carbon losses from the subsequent reduction in wildfire frequency. For example, shortening the prescribed fire interval from 25 to 10 years resulted in a NECB sequestration that was typically less than ±0.4 Mg C ha-1 yr-1, or less than approximately 0.1% of the total ecosystem carbon storage. Hence, whilst there was limited opportunity for achieving emission abatement outcomes from changing prescribed fire management, there were no significant emission penalties for doing so. These results suggest land managers should be free to adopt prescribed fire regimes to target specific management outcomes, without significantly impacting net emissions or total ecosystem carbon storage over the long term.

How disturbance history alters invasion success: biotic legacies and regime change.

Disturbance is a key factor shaping ecological communities, but little is understood about how the effects of disturbance processes accumulate over time. When disturbance regimes change, historical processes may influence future community structure, for example, by altering invasibility compared to communities with stable regimes. Here, we use an annual plant model to investigate how the history of disturbance alters invasion success. In particular, we show how two communities can have different outcomes from species introduction, solely due to past differences in disturbance regimes that generated different biotic legacies. We demonstrate that historical differences can enhance or suppress the persistence of introduced species, and that biotic legacies generated by stable disturbance history decay over time, though legacies can persist for unexpectedly long durations. This establishes a formal theoretical foundation for disturbance legacies having profound effects on communities, and highlights the value of further research on the biotic legacies of disturbance.

Mapping carbon accumulation potential from global natural forest regrowth.

To constrain global warming, we must strongly curtail greenhouse gas emissions and capture excess atmospheric carbon dioxide1,2. Regrowing natural forests is a prominent strategy for capturing additional carbon3, but accurate assessments of its potential are limited by uncertainty and variability in carbon accumulation rates2,3. To assess why and where rates differ, here we compile 13,112 georeferenced measurements of carbon accumulation. Climatic factors explain variation in rates better than land-use history, so we combine the field measurements with 66 environmental covariate layers to create a global, one-kilometre-resolution map of potential aboveground carbon accumulation rates for the first 30 years of natural forest regrowth. This map shows over 100-fold variation in rates across the globe, and indicates that default rates from the Intergovernmental Panel on Climate Change (IPCC)4,5 may underestimate aboveground carbon accumulation rates by 32 per cent on average and do not capture eight-fold variation within ecozones. Conversely, we conclude that maximum climate mitigation potential from natural forest regrowth is 11 per cent lower than previously reported3 owing to the use of overly high rates for the location of potential new forest. Although our data compilation includes more studies and sites than previous efforts, our results depend on data availability, which is concentrated in ten countries, and data quality, which varies across studies. However, the plots cover most of the environmental conditions across the areas for which we predicted carbon accumulation rates (except for northern Africa and northeast Asia). We therefore provide a robust and globally consistent tool for assessing natural forest regrowth as a climate mitigation strategy.

Roosting Site Usage, Gregarious Roosting and Behavioral Interactions During Roost-assembly of Two Lycaenidae Butterflies.

Lycaenidae is one of the larger of the world's butterfly families, based on number and diversity of species, but knowledge of roosting in this group is sparse. Zizina otis riukuensis and Zizeeria maha okinawana are two small lycaenids that are commonly found in urban settings and widely distributed across much of Asia. We conducted experiments on a university campus to determine the plant species and plant structures commonly used by these two blues when roosting. We also tested the hypothesis that gregarious roosting exists in these two blues by demonstrating the non-random distribution of roosting blues and the tight mapping of their roosts to the spatial distribution of specific plant species and/or specific plant structures, as well as by demonstrating behavioral interactions among individuals during roosting-assembly. We found that both Z. otis and Z. maha roosted primarily on flowers and fruits of Tridax procumbens and Vernonia cinerea. We also found that these blues formed conspicuous roosting aggregations with significant positive associations between the flowers and fruits of both T. procumbens and V. cinerea and the blues. Moreover, our behavioral observations showed that these blues expressed various levels of interaction during roosting gatherings. Based on these findings, we conclude that gregarious roosting exists in both Z. otis and Z. maha. To our knowledge, this paper represents one of the first demonstration of nocturnal gregarious roosting in lycaenids. This study also highlights the importance of institutional estates in providing roosting resources for butterflies in urban ecosystems.

Multiple incursion pathways for Helicoverpa armigera in Brazil show its genetic diversity spreading in a connected world.

The Old World cotton bollworm Helicoverpa armigera was first detected in Brazil with subsequent reports from Paraguay, Argentina, Bolivia, and Uruguay. This pattern suggests that the H. armigera spread across the South American continent following incursions into northern/central Brazil, however, this hypothesis has not been tested. Here we compare northern and central Brazilian H. armigera mtDNA COI haplotypes with those from southern Brazil, Uruguay, Argentina, and Paraguay. We infer spatial genetic and gene flow patterns of this dispersive pest in the agricultural landscape of South America. We show that the spatial distribution of H. armigera mtDNA haplotypes and its inferred gene flow patterns in the southwestern region of South America exhibited signatures inconsistent with a single incursion hypothesis. Simulations on spatial distribution patterns show that the detection of rare and/or the absence of dominant mtDNA haplotypes in southern H. armigera populations are inconsistent with genetic signatures observed in northern and central Brazil. Incursions of H. armigera into the New World are therefore likely to have involved independent events in northern/central Brazil, and southern Brazil/Uruguay-Argentina-Paraguay. This study demonstrates the significant biosecurity challenges facing the South American continent, and highlights alternate pathways for introductions of alien species into the New World.

Risks to carbon dynamics in semi-arid woodlands of eastern Australia under current and future climates.

Extreme disturbance events, such as wildfire and drought, have large impacts on carbon storage and sequestration of forests and woodlands globally. Here, we present a modelling approach that assesses the relative impact of disturbances on carbon storage and sequestration, and how this will alter under climate change. Our case study is semi-arid Australia where large areas of land are managed to offset over 122 million tonnes of anthropogenic carbon emissions over a 100-year period. These carbon offsets include mature vegetation that has been protected from clearing and regenerating vegetation on degraded agricultural land. We use a Bayesian Network model to combine multiple probabilistic models of the risk posed by fire, drought, grazing and recruitment failure to carbon dynamics. The model is parameterised from a review of relevant literature and additional quantitative analyses presented here. We found that the risk of vegetation becoming a net source of carbon due to a mortality event, or failing to realise maximum sequestration potential, through recruitment failure in regenerating vegetation, was primarily a function of rainfall in this semi-arid environment. However, the relative size of an emissions event varied across vegetation communities depending on plant attributes, specifically resprouting capacity. Modelled climate change effects were variable, depending on the climate change projection used. Under 'best-case' or 'most-likely' climate scenarios for 2050, similar or increased projections of mean annual precipitation, associated with a build-up of fuel, were expected to drive an increase in fire activity (a 40-160% increase), but a decrease in drought (a 20-35% decrease). Under a 'worst-case' climate scenario, fire activity was expected to decline (a 37% decrease), but drought conditions remain similar (a 5% decrease). These projected changes to the frequency of drought and fire increase the risk that vegetation used for carbon offsetting will fail to provide anticipated amounts of carbon abatement over their lifetime.

Importance of disturbance history on net primary productivity in the world's most productive forests and implications for the global carbon cycle.

Analysis of growth and biomass turnover in natural forests of Eucalyptus regnans, the world's tallest angiosperm, reveals it is also the world's most productive forest type, with fire disturbance an important mediator of net primary productivity (NPP). A comprehensive empirical database was used to calculate the averaged temporal pattern of NPP from regeneration to 250 years age. NPP peaks at 23.1 ± 3.8 (95% interquantile range) Mg C ha-1  year-1 at age 14 years, and declines gradually to about 9.2 ± 0.8 Mg C ha-1  year-1 at 130 years, with an average NPP over 250 years of 11.4 ± 1.1 Mg C ha-1  year-1 , a value similar to the most productive temperate and tropical forests around the world. We then applied the age-class distribution of E. regnans resulting from relatively recent historical fires to estimate current NPP for the forest estate. Values of NPP were 40% higher (13 Mg C ha-1  year-1 ) than if forests were assumed to be at maturity (9.2 Mg C ha-1  year-1 ). The empirically derived NPP time series for the E. regnans estate was then compared against predictions from 21 global circulation models, showing that none of them had the capacity to simulate a post-disturbance peak in NPP, as found in E. regnans. The potential importance of disturbance impacts on NPP was further tested by applying a similar approach to the temperate forests of conterminous United States and of China. Allowing for the effects of disturbance, NPP summed across both regions was on average 11% (or 194 Tg C/year) greater than if all forests were assumed to be in a mature state. The results illustrate the importance of accounting for past disturbance history and growth stage when estimating forest primary productivity, with implications for carbon balance modelling at local to global scales.

Novel 3D geometry and models of the lower regions of large trees for use in carbon accounting of primary forests.

There is high uncertainty in the contribution of land-use change to anthropogenic climate change, especially pertaining to below-ground carbon loss resulting from conversion of primary-to-secondary forest. Soil organic carbon (SOC) and coarse roots are concentrated close to tree trunks, a region usually unmeasured during soil carbon sampling. Soil carbon estimates and their variation with land-use change have not been correspondingly adjusted. Our aim was to deduce allometric equations that will allow improvement of SOC estimates and tree trunk carbon estimates, for primary forest stands that include large trees in rugged terrain. Terrestrial digital photography, photogrammetry and GIS software were used to produce 3D models of the buttresses, roots and humus mounds of large trees in primary forests dominated by Eucalyptus regnans in Tasmania. Models of 29, in situ eucalypts were made and analysed. 3D models of example eucalypt roots, logging debris, rainforest tree species, fallen trees, branches, root and trunk slices, and soil profiles were also derived. Measurements in 2D, from earlier work, of three buttress 'logs' were added to the data set. The 3D models had high spatial resolution. The modelling allowed checking and correction of field measurements. Tree anatomical detail was formulated, such as buttress shape, humus volume, root volume in the under-sampled zone and trunk hollow area. The allometric relationships developed link diameter at breast height and ground slope, to SOC and tree trunk carbon, the latter including a correction for senescence. These formulae can be applied to stand-level carbon accounting. The formulae allow the typically measured, inter-tree SOC to be corrected for not sampling near large trees. The 3D models developed are irreplaceable, being for increasingly rare, large trees, and they could be useful to other scientific endeavours.

Measurements of stem diameter: implications for individual- and stand-level errors.

Stem diameter is one of the most common measurements made to assess the growth of woody vegetation, and the commercial and environmental benefits that it provides (e.g. wood or biomass products, carbon sequestration, landscape remediation). Yet inconsistency in its measurement is a continuing source of error in estimates of stand-scale measures such as basal area, biomass, and volume. Here we assessed errors in stem diameter measurement through repeated measurements of individual trees and shrubs of varying size and form (i.e. single- and multi-stemmed) across a range of contrasting stands, from complex mixed-species plantings to commercial single-species plantations. We compared a standard diameter tape with a Stepped Diameter Gauge (SDG) for time efficiency and measurement error. Measurement errors in diameter were slightly (but significantly) influenced by size and form of the tree or shrub, and stem height at which the measurement was made. Compared to standard tape measurement, the mean systematic error with SDG measurement was only -0.17 cm, but varied between -0.10 and -0.52 cm. Similarly, random error was relatively large, with standard deviations (and percentage coefficients of variation) averaging only 0.36 cm (and 3.8%), but varying between 0.14 and 0.61 cm (and 1.9 and 7.1%). However, at the stand scale, sampling errors (i.e. how well individual trees or shrubs selected for measurement of diameter represented the true stand population in terms of the average and distribution of diameter) generally had at least a tenfold greater influence on random errors in basal area estimates than errors in diameter measurements. This supports the use of diameter measurement tools that have high efficiency, such as the SDG. Use of the SDG almost halved the time required for measurements compared to the diameter tape. Based on these findings, recommendations include the following: (i) use of a tape to maximise accuracy when developing allometric models, or when monitoring relatively small changes in permanent sample plots (e.g. National Forest Inventories), noting that care is required in irregular-shaped, large-single-stemmed individuals, and (ii) use of a SDG to maximise efficiency when using inventory methods to assess basal area, and hence biomass or wood volume, at the stand scale (i.e. in studies of impacts of management or site quality) where there are budgetary constraints, noting the importance of sufficient sample sizes to ensure that the population sampled represents the true population.

An ecoclimatic framework for evaluating the resilience of vegetation to water deficit.

The surge in global efforts to understand the causes and consequences of drought on forest ecosystems has tended to focus on specific impacts such as mortality. We propose an ecoclimatic framework that takes a broader view of the ecological relevance of water deficits, linking elements of exposure and resilience to cumulative impacts on a range of ecosystem processes. This ecoclimatic framework is underpinned by two hypotheses: (i) exposure to water deficit can be represented probabilistically and used to estimate exposure thresholds across different vegetation types or ecosystems; and (ii) the cumulative impact of a series of water deficit events is defined by attributes governing the resistance and recovery of the affected processes. We present case studies comprising Pinus edulis and Eucalyptus globulus, tree species with contrasting ecological strategies, which demonstrate how links between exposure and resilience can be examined within our proposed framework. These examples reveal how climatic thresholds can be defined along a continuum of vegetation functional responses to water deficit regimes. The strength of this framework lies in identifying climatic thresholds on vegetation function in the absence of more complete mechanistic understanding, thereby guiding the formulation, application and benchmarking of more detailed modelling.

Testing the generality of above-ground biomass allometry across plant functional types at the continent scale.

Accurate ground-based estimation of the carbon stored in terrestrial ecosystems is critical to quantifying the global carbon budget. Allometric models provide cost-effective methods for biomass prediction. But do such models vary with ecoregion or plant functional type? We compiled 15 054 measurements of individual tree or shrub biomass from across Australia to examine the generality of allometric models for above-ground biomass prediction. This provided a robust case study because Australia includes ecoregions ranging from arid shrublands to tropical rainforests, and has a rich history of biomass research, particularly in planted forests. Regardless of ecoregion, for five broad categories of plant functional type (shrubs; multistemmed trees; trees of the genus Eucalyptus and closely related genera; other trees of high wood density; and other trees of low wood density), relationships between biomass and stem diameter were generic. Simple power-law models explained 84-95% of the variation in biomass, with little improvement in model performance when other plant variables (height, bole wood density), or site characteristics (climate, age, management) were included. Predictions of stand-based biomass from allometric models of varying levels of generalization (species-specific, plant functional type) were validated using whole-plot harvest data from 17 contrasting stands (range: 9-356 Mg ha(-1) ). Losses in efficiency of prediction were <1% if generalized models were used in place of species-specific models. Furthermore, application of generalized multispecies models did not introduce significant bias in biomass prediction in 92% of the 53 species tested. Further, overall efficiency of stand-level biomass prediction was 99%, with a mean absolute prediction error of only 13%. Hence, for cost-effective prediction of biomass across a wide range of stands, we recommend use of generic allometric models based on plant functional types. Development of new species-specific models is only warranted when gains in accuracy of stand-based predictions are relatively high (e.g. high-value monocultures).

Diversity-disturbance relationships: frequency and intensity interact.

An influential ecological theory, the intermediate disturbance hypothesis (IDH), predicts that intermediate levels of disturbance will maximize species diversity. Empirical studies, however, have described a wide variety of diversity-disturbance relationships (DDRs). Using experimental populations of microbes, we show that the form of the DDR depends on an interaction between disturbance frequency and intensity. We find that diversity shows a monotonically increasing, unimodal or flat relationship with disturbance, depending on the values of the disturbance aspects considered. These results confirm recent theoretical predictions, and potentially reconcile the conflicting body of empirical evidence on DDRs.

The effect of carbon credits on savanna land management and priorities for biodiversity conservation.

Carbon finance offers the potential to change land management and conservation planning priorities. We develop a novel approach to planning for improved land management to conserve biodiversity while utilizing potential revenue from carbon biosequestration. We apply our approach in northern Australia's tropical savanna, a region of global significance for biodiversity and carbon storage, both of which are threatened by current fire and grazing regimes. Our approach aims to identify priority locations for protecting species and vegetation communities by retaining existing vegetation and managing fire and grazing regimes at a minimum cost. We explore the impact of accounting for potential carbon revenue (using a carbon price of US$14 per tonne of carbon dioxide equivalent) on priority areas for conservation and the impact of explicitly protecting carbon stocks in addition to biodiversity. Our results show that improved management can potentially raise approximately US$5 per hectare per year in carbon revenue and prevent the release of 1-2 billion tonnes of carbon dioxide equivalent over approximately 90 years. This revenue could be used to reduce the costs of improved land management by three quarters or double the number of biodiversity targets achieved and meet carbon storage targets for the same cost. These results are based on generalised cost and carbon data; more comprehensive applications will rely on fine scale, site-specific data and a supportive policy environment. Our research illustrates that the duel objective of conserving biodiversity and reducing the release of greenhouse gases offers important opportunities for cost-effective land management investments.

How frequency and intensity shape diversity-disturbance relationships.

Understanding the relationship between disturbance regimes and species diversity has been of central interest to ecologists for decades. For example, the intermediate disturbance hypothesis proposes that diversity will be highest at intermediate levels of disturbance. Although peaked (hump-shaped) diversity-disturbance relationships (DDRs) have been documented in nature, many other DDRs have been reported as well. Here, we begin to theoretically unify these diverse empirical findings by showing how a single simple model can generate several different DDRs, depending on the aspect of disturbance that is considered. Additionally, we elucidate the competition-mediated mechanism underlying our results. Our findings have the potential to reconcile apparently conflicting empirical results on the effects of disturbance on diversity.

Comment on "From plant traits to plant communities: a statistical mechanistic approach to biodiversity".

Shipley et al. (Reports, 3 November 2006, p. 812) developed a quantitative method for predicting the relative abundance of species from measured traits. We show that the method can have high explanatory power even when all trait and abundance data are randomly and independently generated, because of a mathematical dependence between the observations and predictions. We also suggest a potential solution to this problem.