Aircraft observations and model simulations of concentration and particle size distribution in the Eyjafjallajökull volcanic ash cloud

The Eyjafjallajökull volcano in Iceland emitted a cloud of ash into the atmosphere during April and May 2010. Over the UK the ash cloud was observed by the FAAM BAe-146 Atmospheric Research Aircraft which was equipped with in-situ probes measuring the concentration of volcanic ash carried by particles of varying sizes. The UK Met Office Numerical Atmospheric-dispersion Modelling Environment (NAME) has been used to simulate the evolution of the ash cloud emitted by the Eyjafjallajökull volcano during the period 4–18 May 2010. In the NAME simulations the processes controlling the evolution of the concentration and particle size distribution include sedimentation and deposition of particles, horizontal dispersion and vertical wind shear. For travel times between 24 and 72 h, a 1/t relationship describes the evolution of the concentration at the centre of the ash cloud and the particle size distribution remains fairly constant. Although NAME does not represent the effects of microphysical processes, it can capture the observed decrease in concentration with travel time in this period. This suggests that, for this eruption, microphysical processes play a small role in determining the evolution of the distal ash cloud. Quantitative comparison with observations shows that NAME can simulate the observed column-integrated mass if around 4% of the total emitted mass is assumed to be transported as far as the UK by small particles (< 30 μm diameter). NAME can also simulate the observed particle size distribution if a distal particle size distribution that contains a large fraction of < 10 μm diameter particles is used, consistent with the idea that phraetomagmatic volcanoes, such as Eyjafjallajökull, emit very fine particles.

Computer simulations of pyroclastic flows from dome collapse

We present a method of simulating both the avalanche and surge components of pyroclastic flows generated by lava collapsing from a growing Pelean dome. This is used to successfully model the pyroclastic flows generated on 12 May 1996 by the Soufriere Hills volcano, Montserrat. In simulating the avalanche component we use a simple 3-fold parameterisation of flow acceleration for which we choose values using an inverse method. The surge component is simulated by a 1D hydraulic balance of sedimentation of clasts and entrainment of air away from the avalanche source. We show how multiple simulations based on uncertainty of the starting conditions and parameters, specifically location and size (mass flux), could be used to map hazard zones.

Multiple stationary solutions of an irradiated slab

A mathematical model describing the heat budget of an irradiated medium is introduced. The one-dimensional form of the equations and boundary conditions are presented and analysed. Heat transport at one face of the slab occurs by absorption (and reflection) of an incoming beam of short-wave radiation with a fraction of this radiation penetrating into the body of the slab, a diffusive heat flux in the slab and a prescribed incoming heat flux term. The other face of the slab is immersed in its own melt and is considered to be a free surface. Here, temperature continuity is prescribed and evolution of the surface is determined by a Stefan condition. These boundary conditions are flexible enough to describe a range of situations such as a laser shining on an opaque medium, or the natural environment of polar sea ice or lake ice. A two-stream radiation model is used which replaces the simple Beer’s law of radiation attenuation frequently used for semi-infinite domains. The stationary solutions of the governing equations are sought and it is found that there exists two possible stationary solutions for a given set of boundary conditions and a range of parameter choices. It is found that the existence of two stationary solutions is a direct result of the model of radiation absorption, due to its effect on the albedo of the medium. A linear stability analysis and numerical calculations indicate that where two stationary solutions exist, the solution corresponding to a larger thickness is always stable and the solution corresponding to a smaller thickness is unstable. Numerical simulations reveal that when there are two solutions, if the slab is thinner than the smaller stationary thickness it will melt completely, whereas if the slab is thicker than the smaller stationary thickness it will evolve toward the larger stationary thickness. These results indicate that other mechanisms (e.g. wave-induced agglomeration of crystals) are necessary to grow a slab from zero initial thickness in the parameter regime that yields two stationary solutions.

A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer

Monte Carlo field-theoretic simulations (MCFTS) are performed on melts of symmetric diblock copolymer for invariant polymerization indexes extending down to experimentally relevant values of N̅ ∼ 10^4. The simulations are performed with a fluctuating composition field, W_−(r), and a pressure field, W_+(r), that follows the saddle-point approximation. Our study focuses on the disordered-state structure function, S(k), and the order−disorder transition (ODT). Although shortwavelength fluctuations cause an ultraviolet (UV) divergence in three dimensions, this is readily compensated for with the use of an effective Flory−Huggins interaction parameter, χ_e. The resulting S(k) matches the predictions of renormalized one-loop (ROL) calculations over the full range of χ_eN and N̅ examined in our study, and agrees well with Fredrickson−Helfand (F−H) theory near the ODT. Consistent with the F−H theory, the ODT is discontinuous for finite N̅ and the shift in (χ_eN)_ODT follows the predicted N̅^−1/3 scaling over our range of N̅.

Evaluation of coupled ocean-atmosphere simulations of northern hemisphere extratropical climates in the mid-Holocene

We have used the BIOME4 biogeography–biochemistry model and comparison with palaeovegetation data to evaluate the response of six ocean–atmosphere general circulation models to mid-Holocene changes in orbital forcing in the mid- to high-latitudes of the northern hemisphere. All the models produce: (a) a northward shift of the northern limit of boreal forest, in response to simulated summer warming in high-latitudes. The northward shift is markedly asymmetric, with larger shifts in Eurasia than in North America; (b) an expansion of xerophytic vegetation in mid-continental North America and Eurasia, in response to increased temperatures during the growing season; (c) a northward expansion of temperate forests in eastern North America, in response to simulated winter warming. The northward shift of the northern limit of boreal forest and the northward expansion of temperate forests in North America are supported by palaeovegetation data. The expansion of xerophytic vegetation in mid-continental North America is consistent with palaeodata, although the extent may be over-estimated. The simulated expansion of xerophytic vegetation in Eurasia is not supported by the data. Analysis of an asynchronous coupling of one model to an equilibrium-vegetation model suggests vegetation feedback exacerbates this mid-continental drying and produces conditions more unlike the observations. Not all features of the simulations are robust: some models produce winter warming over Europe while others produce winter cooling. As a result, some models show a northward shift of temperate forests (consistent with, though less marked than, the expansion shown by data) and others produce a reduction in temperate forests. Elucidation of the cause of such differences is a focus of the current phase of the Palaeoclimate Modelling Intercomparison Project.

Simulations of the impact of orbital forcing and ocean on the Asian summer monsoon during the Holocene

The importance of orbital forcing and ocean impact on the Asian summer monsoon in the Holocene is investigated by comparing simulations with a fully coupled ocean–atmosphere general circulation model (FOAM) and with the atmospheric component of this model (FSSTAM) forced with prescribed modern sea-surface temperatures (SSTs). The results show: (1) the ocean amplifies the orbitally-induced increase in African monsoon precipitation, makes somewhat increase in southern India and damps the increase over the southeastern China. (2) The ocean could change the spatial distribution and local intensity of the orbitally-induced latitudinal atmospheric oscillation over the southeastern China and the subtropical western Pacific Ocean. (3) The orbital forcing mostly enhances the Asian summer precipitation in the FOAM and FSSTAM simulations. However, the ocean reduces the orbitally-induced summer precipitation and postpones the time of summer monsoon onset over the Asian monsoon region. (4) The orbital forcing considerably enhances the intensity of upper divergence, which is amplified by ocean further, over the eastern hemisphere. But the divergence is weaker in the FOAM simulations than in the FSSTAM simulations when the orbital forcing is fixed. (5) The orbital forcing can enhance the amplitude of precipitation variability over the subtropical Africa, the southeastern China and northwestern China, inversely, reduce it over central India and North China in the FOAM and FSSTAM simulations. The ocean obviously reduces the amplitude of precipitation variability over most of the Asian monsoon regions in the fixed orbital forcing simulations. (6) The areas characterized by increased summer precipitation in the long-term mean are mostly characterized by increased amplitude of short-term variability, whereas regions characterized by decreased precipitation are primarily characterized by decreased amplitude of short-term variability. However, the influences of orbital forcing or dynamical ocean on regional climate depend on the model.

Results of PMIP2 coupled simulations of the mid-Holocene and Last Glacial Maximum, Part 2: feedbacks with emphasis on the location of the ITCZ and mid- and high latitudes heat budget

A set of coupled ocean-atmosphere(-vegetation) simulations using state of the art climate models is now available for the Last Glacial Maximum (LGM) and the Mid-Holocene (MH) through the second phase of the Paleoclimate Modeling Intercomparison Project (PMIP2). Here we quantify the latitudinal shift of the location of the Intertropical Convergence Zone (ITCZ) in the tropical regions during boreal summer and the change in precipitation in the northern part of the ITCZ. For both periods the shift is more pronounced over the continents and East Asia. The maritime continent is the region where the largest spread is found between models. We also clearly establish that the larger the increase in the meridional temperature gradient in the tropical Atlantic during summer at the MH, the larger the change in precipitation over West Africa. The vegetation feedback is however not as large as found in previous studies, probably due to model differences in the control simulation. Finally, we show that the feedback from snow and sea-ice at mid and high latitudes contributes for half of the cooling in the Northern Hemisphere for the LGM, with the remaining being achieved by the reduced CO2 and water vapour in the atmosphere. For the MH the snow and albedo feedbacks strengthen the spring cooling and enhance the boreal summer warming, whereas water vapour reinforces the late summer warming. These feedbacks are modest in the Southern Hemisphere. For the LGM most of the surface cooling is due to CO2 and water vapour.

Results of PMIP2 coupled simulations of the mid-Holocene and Last Glacial Maximum, Part 1: experiments and large-scale features

A set of coupled ocean-atmosphere simulations using state of the art climate models is now available for the Last Glacial Maximum and the Mid-Holocene through the second phase of the Paleoclimate Modeling Intercomparison Project (PMIP2). This study presents the large-scale features of the simulated climates and compares the new model results to those of the atmospheric models from the first phase of the PMIP, for which sea surface temperature was prescribed or computed using simple slab ocean formulations. We consider the large-scale features of the climate change, pointing out some of the major differences between the different sets of experiments. We show in particular that systematic differences between PMIP1 and PMIP2 simulations are due to the interactive ocean, such as the amplification of the African monsoon at the Mid-Holocene or the change in precipitation in mid-latitudes at the LGM. Also the PMIP2 simulations are in general in better agreement with data than PMIP1 simulations.

Climate and CO2 controls on global vegetation distribution at the last glacial maximum: analysis based on palaeovegetation data, biome modelling and palaeoclimate simulations.

The global vegetation response to climate and atmospheric CO2 changes between the last glacial maximum and recent times is examined using an equilibrium vegetation model (BIOME4), driven by output from 17 climate simulations from the Palaeoclimate Modelling Intercomparison Project. Features common to all of the simulations include expansion of treeless vegetation in high northern latitudes; southward displacement and fragmentation of boreal and temperate forests; and expansion of drought-tolerant biomes in the tropics. These features are broadly consistent with pollen-based reconstructions of vegetation distribution at the last glacial maximum. Glacial vegetation in high latitudes reflects cold and dry conditions due to the low CO2 concentration and the presence of large continental ice sheets. The extent of drought-tolerant vegetation in tropical and subtropical latitudes reflects a generally drier low-latitude climate. Comparisons of the observations with BIOME4 simulations, with and without consideration of the direct physiological effect of CO2 concentration on C3 photosynthesis, suggest an important additional role of low CO2 concentration in restricting the extent of forests, especially in the tropics. Global forest cover was overestimated by all models when climate change alone was used to drive BIOME4, and estimated more accurately when physiological effects of CO2 concentration were included. This result suggests that both CO2 effects and climate effects were important in determining glacial-interglacial changes in vegetation. More realistic simulations of glacial vegetation and climate will need to take into account the feedback effects of these structural and physiological changes on the climate.