Local existence of quasispherical space–time initial data

We consider the system of Einstein constraint equations in the special case when the spacelike 3-manifold is assumed to satisfy the quasispherical ansatz of Bartnik. We introduce two different time slicing conditions, under each of which we may view the resulting constraint equations as a parabolic∕elliptic∕ODE system of partial differential equations. We combine recent existence results for parabolic equations in Sobolev space with an iterative method to prove local existence results for the quasispherical Einstein constraint equations under the two different time slicing conditions.The author’s research has been supported by an ARC/DETYA Indigenous Researchers Development Scheme

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

Machine Learning based Parameter Sensitivity of Regional Climate Models -- A Case Study of the WRF Model for Heat Extremes over Southeast Australia

Heatwaves and bushfires cause substantial impacts on society and ecosystems across the globe. Accurate information of heat extremes is needed to support the development of actionable mitigation and adaptation strategies. Regional climate models are commonly used to better understand the dynamics of these events. These models have very large input parameter sets, and the parameters within the physics schemes substantially influence the model's performance. However, parameter sensitivity analysis (SA) of regional models for heat extremes is largely unexplored. Here, we focus on the southeast Australian region, one of the global hotspots of heat extremes. In southeast Australia Weather Research and Forecasting (WRF) model is the widely used regional model to simulate extreme weather events across the region. Hence in this study, we focus on the sensitivity of WRF model parameters to surface meteorological variables such as temperature, relative humidity, and wind speed during two extreme heat events over southeast Australia. Due to the presence of multiple parameters and their complex relationship with output variables, a machine learning (ML) surrogate-based global sensitivity analysis method is considered for the SA. The ML surrogate-based Sobol SA is used to identify the sensitivity of 24 adjustable parameters in seven different physics schemes of the WRF model. Results show that out of these 24, only three parameters, namely the scattering tuning parameter, multiplier of saturated soil water content, and profile shape exponent in the momentum diffusivity coefficient, are important for the considered meteorological variables. These SA results are consistent for the two different extreme heat events. Further, we investigated the physical significance of sensitive parameters. This study's results will help in further optimising WRF parameters to improve model simulation

Properties of reaction fronts in a non-adiabatic two stage exothermic-endothermic competitive reaction scheme

We numerically derive the properties of reaction fronts arising in a pre-mixed one dimensional two staged non-adiabatic competitive exothermic-endothermic reaction scheme where both reaction pathways compete for the same fuel. We utilise FlexPDE and the method of lines to obtain numerical solutions for properties such as the front speed and stability over a range of parameter values such as the Lewis number and the ratios of enthalpies and activation energies. Steady and pulsating speeds are demonstrated for specific regions of the parameter space. We also show that in some circumstances there exists a chaotic regime of combustion wave propagation. References M. J. Antal and G. Varhegyi, Cellulose Pyrolysis Kinetics - The Current State of Knowledge, Industrial and Engineering Chemistry Research, 34(3):703–717, 1995 doi:10.1021/ie00042a001 R. Ball, A. C. McIntosh and J. Brindley, Thermokinetic Models for Simultaneous Reactions: a Comparative Study, Combustion Theory and Modelling, 3(3):447–468, 1999. doi:10.1088/1364-7830/3/3/302 S. K. Chan and R. Turcotte, Onset Temperatures in Hot Wire Ignition of AN-Based Emulsions, Propellants Explosives Pyrotechnics, 34(1):41–49, 2009. doi:10.1002/prep.200700288 FlexPDE$^{TM}$, PDE Solutions Inc, http://www.pdesolutions.com. V. V. Gubernov, A. Kobolov, A. Polezhaev and H. Sidhu, Period Doubling and Chaotic Transient in a Model of Chain-Branching Combustion Wave Propagation, Proceedings of the Royal Society A, 2011. doi:10.1098/rspa.2009.0668 V. V. Gubernov, J. J. Sharples, H. S. Sidhu, A. C. McIntosh and J. Brindley, Properties of Combustion Waves in the Model with Competitive Exo- and Endothermic Reactions, Journal of Mathematical Chemistry, 50(8):2130–2140, 2012. doi:10.1007/s10910-012-0021-y V. V. Gubernov, H. S. Sidhu, G. N. Mercer, The Effect of Ambient Temperature on the Propagation of Nonadiabatic Combustion Waves, Journal of Mathematical of Mathematical Chemistry, 37(2):149–162, 2005. doi:10.1007/s10910-004-1447-7 A. Hmaidi, A. C. McIntosh and J. Brindley, A Mathematical Model of Hotspot Condensed Phase Ignition in the Presence of a Competitive Endothermic Reaction, Combustion Theory and Modelling, 14(6):893–920, 2010. doi:10.1080/13647830.2010.519050 D. A. Kessler, V. N. Gamezo and E. S. Oran, Simulations of Flame Acceleration and Deflagration-to-Detonation Transitions in Methane-Air Systems, Combustion and Flame, 157(11):2063–2077, 2010. doi:10.1016/j.combustflame.2010.04.011 F. Liu, D. L. S. McElwain and C. P. Please, Simulation of Combustion Waves for Two-Stage Reactions, Proceedings of the 8th Biennial Computational Techniques and Applications Conference (CTAC97), pages 385–392, 1998. A. Makino, Fundamental Aspects of the Heterogeneous Flame in the Self-Propagating High-Temperature Synthesis (SHS) Process, Progress in Energy and Combustion Sciences, 27(1):1–74, 2001. doi:10.1016/S0360-1285(00)00004-6 A. G. Merzhanov and E. N. Rumanov, Physics of Reaction Waves, Reviews of Modern Physics, 71(4):1173–1211, 1999. doi:10.1103/RevModPhys.71.1173 C. P. Please, F. Liu and D. L. S. McElwain, Condensed Phase Combustion Travelling Waves with Sequential Exothermic or Endothermic Reactions, Combustion Theory and Modelling, 7(1):129–143, 2003. doi:10.1088/1364-7830/7/1/307 W. E. Schiesser, The numerical method of lines: Integration of Partial Differential Equations, Academic Press, Inc, 1991. J. J. Sharples, H. S. Sidhu, A. C. Mcintosh, J. Brindley and V. V. Gubernov, Analysis of Combustion Waves Arising in the Presence of a Competitive Endothermic Reaction, IMA Journal of Applied Mathematics, 77(1):18–31, 2012. doi:10.1093/imamat/hxr072 V. P. Sinditskii, V. Y. Egorshev, A. I. Levshenkov and V. V. Serushkin, Ammonium nitrate: Combustion Mechanism and the Role of Additives, Propellants Explosives Pyrotechnics, 30(4):269–280, 2005. doi:10.1002/prep.200500017 J. Subrahmanyam and M. Vijayakumar, Self-Propagating High-Temperature Synthesis, Journal of Materials Science, 27(23):6249–6273, 1992. doi:10.1007/BF00576271 R. Turcotte, S. Goldthorp, C. M. Badeen and S. K. Chan, Hot-Wire Ignition of AN-Based Emulsions, Propellants Explosives Pyrotechnics, 33(6):472–481, 2008. doi:10.1002/prep.200700276 S. Walia, R. O. Weber, K. Latham, P. Petersen, J. T. Abrahamson, M. S. Strano, and K. Kalantar-zadeh, Oscillatory Thermopower Waves Based on Bi$_2$Te$_3$ Films, Advanced Functional Materials, 21(11):2072–2079, 2011. doi:10.1002/adfm.201001979 R. O. Weber, G. N. Mercer, H. S. Sidhu and B. F. Gray, Combustion Waves for Gases ($Le=1$) and Solids ($Le\rightarrow \infty$), Proceedings of the Royal Society of London A, 453(1960):1105–1118, 1997. doi:10.1098/rspa.1997.0062 W. Y. S. Wee, J. J. Sharples, H. S. Sidhu and V. V. Gubernov, Analysis of a Two-Stage Competitive Endothermic-Exothermic Reaction Scheme, Proceedings of the 40th Australian Chemical Engineering Conference (CHEMECA 2012), submitted June 2012

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