Expectations of linear functions with respect to truncazted multinormal distributions, with applications for uncertainty analysis in environmental modelling

Uncertainty can hamper the stringency of commitments under cap and trade schemes. We assess how well intensity targets, where countries' permit allocations are indexed to future realised GDP, can cope with uncertainties in a post-Kyoto international greenhouse emissions trading scheme. We present some empirical foundations for intensity targets and derive a simple rule for the optimal degree of indexation to GDP. Using an 18-region simulation model of a 2020 global cap-and-trade treaty under multiple uncertainties and endogenous commitments, we estimate that optimal intensity targets could achieve global abatement as much as 20 per cent higher than under absolute targets, and even greater increases in welfare measures. The optimal degree of indexation to GDP would vary greatly between countries, including super-indexation in some advanced countries, and partial indexation for most developing countries. Standard intensity targets (with one-toone indexation) would also improve the overall outcome, but to a lesser degree and not in all cases. Although target indexation is no magic wand for a future global climate treaty, gains from reduced cost uncertainty might justify increased complexity, framing issues and other potential downsides of intensity targets.linear functions, truncazted multinormal distributions, uncertainty analysis, environmental modelling

Expectations of linear functions with respect to truncated multinormal distributions, with applications for uncertainty analysis in environmental modelling

This paper discusses results concerning multivariate normal distributions that are subject to truncation by a hyperplane and how such results can be applied to uncertainty analysis in the environmental sciences. We present a suite of results concerning truncated multivariate normal distributions, some of which already appear in the mathematical literature. The focus here is to make these types of results more accesible to the environmental science community and to this end we include a conceptually simple alternative derivation of an important result. We illustrate how the theory of truncated multivariate normal distributions can be employed in the environmental sciences by means of an example from the economics of climate change control

Modelling the moisture effect on the rate of spread of fire in a leaf-like fuel element

In this study, the effect of fuel moisture content (FMC) on the pyrolysis, ignition, and rate of drying processes of a leaf-like fuel element is numerically investigated. To start the ignition, an upward hot airflow is placed under the leaf-like fuel source. The dry fuel was considered as cellulose. The current study is validated against published experimental data, using the time history of fuel mass loss measurement. The effect of FMC on the mass fraction of oxygen is also investigated. The transient solver of FireFOAM, which uses the Large Eddy Simulation (LES), is used to perform the numerical simulations. The results confirm that an increase in the amount of fuel moisture content leads to a decrease in the rate of spread of the fire and an increase in the drying process time. It is also found that during both drying and pyrolysis process, different parts of a selected fuel element have different temperatures. This is mainly due to the decrease of moisture concentration near the ignition point. Results showed that at t= 6.5 s the volumetric average temperature of the solid fuel for the case with FMC 26%, is 642 K while for FMC of 34%, this temperature is 605 K

Modeling Wind Direction Distributions Using a Diagnostic Model in the Context of Probabilistic Fire Spread Prediction

With emerging research on the dynamics of extreme fire behavior, it is increasingly important for wind models, used in operational fire prediction, to accurately capture areas of complex flow across rugged terrain. Additionally, the emergence of ensemble and stochastic modeling frameworks has led to the discussion of uncertainty in fire prediction. To capture the uncertainty of modeled fire outputs, it is necessary to recast uncertain inputs in probabilistic terms. WindNinja is the diagnostic wind model currently being applied within a number of operational fire prediction frameworks across the world. For computational efficiency, allowing for real-time or faster than real-time prediction, the physical equations governing wind flow across a complex terrain are often simplified. The model has a number of well documented limitations, for instance, it is known to perform poorly on leeward slopes. First, this study is aimed at understanding these limitations in a probabilistic context, by comparing individual deterministic predictions to observed distributions of wind direction. Secondly, a novel application of the deterministic WindNinja model is presented in this study which is shown to enable prediction of wind direction distributions that capture some of the variability of complex wind flow. Recasting wind fields in terms of probability distributions enables a better understanding of variability across the landscape, and provides the probabilistic information required to capture uncertainty through ensemble or stochastic fire modeling. The comparisons detailed in this study indicate the potential for WindNinja to predict multi-modal wind direction distributions that represent complex wind behaviors, including re-circulation regions on leeward slopes. However, the limitations of using deterministic models within probabilistic frameworks are also highlighted. To enhance fire prediction and to better understand uncertainty, it is recommended that statistical approaches also be developed to complement existing physics-based deterministic wind models

Drivers of long-distance spotting during wildfires in south-eastern Australia

We analysed the influence of wildfire area, topography, fuel, surface weather and upper-level weather conditions on long-distance spotting during wildfires. The analysis was based on a large dataset of 338 observations, from aircraft-acquired optical line scans, of spotting wildfires in south-east Australia between 2002 and 2018. Source fire area (a measure of fire activity) was the most important predictor of maximum spotting distance and the number of long-distance spot fires produced (i.e. >500 m from a source fire). Weather (surface and upper-level), vegetation and topographic variables had important secondary effects. Spotting distance and number of long-distance spot fires increased strongly with increasing source fire area, particularly under strong winds and in areas containing dense forest and steep slopes. General vegetation descriptors better predicted spotting compared with bark hazard and presence variables, suggesting systems that measure and map bark spotting potential need improvement. The results from this study have important implications for the development of predictive spotting and wildfire behaviour models

Patterns of space use in sympatric marine colonial predators reveals scales of spatial partitioning

E.L.J. and D.J.F.R. were funded under Scottish Government grant MMSS001/01. D.J.F.R. was funded by the UK Department of Energy and Climate Change (DECC) as part of their Offshore Energy Strategic Environmental Assessment programme. S.S. was part-funded by the EU MYFISH project.Species distribution maps can provide important information to focus conservation efforts and enable spatial management of human activities. Two sympatric marine predators, grey seals Halichoerus grypus and harbour seals Phoca vitulina have overlapping ranges on land and at sea but contrasting population dynamics around Britain: whilst grey seals have generally increased, harbour seals have shown significant regional declines. We analysed two decades of at-sea movement data and terrestrial count data from these species to produce high resolution, broad-scale maps of distribution and associated uncertainty to inform conservation and management. Our results showed that grey seals use offshore areas connected to their haul-out sites by prominent corridors and harbour seals primarily stay within 50km of the coastline. Both species show fine-scale offshore spatial segregation off the east coast of Britain and broad-scale partitioning off western Scotland. These results illustrate that for broad-scale marine spatial planning, the conservation needs of harbour seals (primarily inshore, the exception being selected offshore usage areas) are different from those of grey seals (up to 100km offshore and corridors connecting these areas to haul-out sites). More generally, our results illustrate the importance of detailed knowledge of marine predator distributions to inform marine spatial planning; for instance, spatial prioritisation is not necessarily the most effective spatial planning strategy even when conserving species with similar taxonomy.Peer reviewe

Connections of climate change and variability to large and extreme forest fires in southeast Australia

The 2019/20 Black Summer bushfire disaster in southeast Australia was unprecedented: the extensive area of forest burnt, the radiative power of the fires, and the extraordinary number of fires that developed into extreme pyroconvective events were all unmatched in the historical record. Australia’s hottest and driest year on record, 2019, was characterised by exceptionally dry fuel loads that primed the landscape to burn when exposed to dangerous fire weather and ignition. The combination of climate variability and long-term climate trends generated the climate extremes experienced in 2019, and the compounding effects of two or more modes of climate variability in their fire-promoting phases (as occurred in 2019) has historically increased the chances of large forest fires occurring in southeast Australia. Palaeoclimate evidence also demonstrates that fire-promoting phases of tropical Pacific and Indian ocean variability are now unusually frequent compared with natural variability in preindustrial times. Indicators of forest fire danger in southeast Australia have already emerged outside of the range of historical experience, suggesting that projections made more than a decade ago that increases in climate-driven fire risk would be detectable by 2020, have indeed eventuated. The multiple climate change contributors to fire risk in southeast Australia, as well as the observed non-linear escalation of fire extent and intensity, raise the likelihood that fire events may continue to rapidly intensify in the future. Improving local and national adaptation measures while also pursuing ambitious global climate change mitigation efforts would provide the best strategy for limiting further increases in fire risk in southeast Australia

Linear and quasilinear parabolic equations in Sobolev space

AbstractWe consider linear parabolic equations of second order in a Sobolev space setting. We obtain existence and uniqueness results for such equations on a closed two-dimensional manifold, with minimal assumptions about the regularity of the coefficients of the elliptic operator. In particular, we derive a priori estimates relating the Sobolev regularity of the coefficients of the elliptic operator to that of the solution. The results obtained are used in conjunction with an iteration argument to yield existence results for quasilinear parabolic equations

Climate Change Significantly Alters Future Wildfire Mitigation Opportunities in Southeastern Australia

©2020. American Geophysical Union. All Rights Reserved. Prescribed burning is used globally to mitigate the risks of wildfires, with severe wildfires increasing in frequency in recent decades. Despite their importance in wildfire management, the nature of future changes to prescribed burn windows under global warming remains uncertain. We use a regional climate projection ensemble to provide a robust spatiotemporal quantification of statistically significant future changes in prescribed burn windows for southeastern Australia. There are significant decreases during months presently used for prescribed burning, that is, in March to May in 2060–2079 versus 1990–2009 across several temperate regions. Conversely, burn windows show widespread significant increases in June to August, that is, months when burns have rarely occurred historically, and also in spring (September–October). Overall, projected changes in temperature and fuel moisture show the most widespread and largest decreases (or increases) in the number of days within their respective ranges suitable for conducting burns. These results support wildfire risk mitigation planning