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Gosling S.N.,University of Nottingham | Taylor R.G.,UCL | Arnell N.W.,University of Reading | Todd M.C.,University of Sussex
Hydrology and Earth System Sciences | Year: 2011

We present a comparative analysis of projected impacts of climate change on river runoff from two types of distributed hydrological model, a global hydrological model (GHM) and catchment-scale hydrological models (CHM). Analyses are conducted for six catchments that are global in coverage and feature strong contrasts in spatial scale as well as climatic and developmental conditions. These include the Liard (Canada), Mekong (SE Asia), Okavango (SW Africa), Rio Grande (Brazil), Xiangxi (China) and Harper's Brook (UK). A single GHM (Mac-PDM.09) is applied to all catchments whilst different CHMs are applied for each catchment. The CHMs include SLURP v. 12.2 (Liard), SLURP v. 12.7 (Mekong), Pitman (Okavango), MGB-IPH (Rio Grande), AV-SWAT-X 2005 (Xiangxi) and Cat-PDM (Harper's Brook). The CHMs typically simulate water resource impacts based on a more explicit representation of catchment water resources than that available from the GHM and the CHMs include river routing, whereas the GHM does not. Simulations of mean annual runoff, mean monthly runoff and high (Q5) and low (Q95) monthly runoff under baseline (1961-1990) and climate change scenarios are presented. We compare the simulated runoff response of each hydrological model to (1) prescribed increases in global-mean air temperature of 1.0, 2.0, 3.0, 4.0, 5.0 and 6.0 °C relative to baseline from the UKMO HadCM3 Global Climate Model (GCM) to explore response to different amounts of climate forcing, and (2) a prescribed increase in global-mean air temperature of 2.0 °C relative to baseline for seven GCMs to explore response to climate model structural uncertainty. We find that the differences in projected changes of mean annual runoff between the two types of hydrological model can be substantial for a given GCM (e.g. an absolute GHM-CHM difference in mean annual runoff percentage change for UKMO HadCM3 2 °C warming of up to 25%), and they are generally larger for indicators of high and low monthly runoff. However, they are relatively small in comparison to the range of projections across the seven GCMs. Hence, for the six catchments and seven GCMs we considered, climate model structural uncertainty is greater than the uncertainty associated with the type of hydrological model applied. Moreover, shifts in the seasonal cycle of runoff with climate change are represented similarly by both hydrological models, although for some catchments the monthly timing of high and low flows differs. This implies that for studies that seek to quantify and assess the role of climate model uncertainty on catchment-scale runoff, it may be equally as feasible to apply a GHM (Mac-PDM.09 here) as it is to apply a CHM, especially when climate modelling uncertainty across the range of available GCMs is as large as it currently is. Whilst the GHM is able to represent the broad climate change signal that is represented by the CHMs, we find however, that for some catchments there are differences between GHMs and CHMs in mean annual runoff due to differences in potential evapotranspiration estimation methods, in the representation of the seasonality of runoff, and in the magnitude of changes in extreme (Q5, Q95) monthly runoff, all of which have implications for future water management issues. © Author(s) 2011.

Hunt D.,University of London | Raivich G.,University College London | Anderson P.N.,UCL
Frontiers in Molecular Neuroscience | Year: 2012

ATF3 belongs to the ATF/CREB family of transcription factors and is often described as an adaptive response gene whose activity is usually regulated by stressful stimuli. Although expressed in a number of splice variants and generally recognized as a transcriptional repressor, ATF3 has the ability to interact with a number of other transcription factors including c-Jun to form complexes which not only repress, but can also activate various genes. ATF3 expression is modulated mainly at the transcriptional level and has markedly different effects in different types of cell. The levels of ATF3 mRNA and protein are normally very low in neurons and glia but their expression is rapidly upregulated in response to injury. ATF3 expression in neurons is closely linked to their survival and the regeneration of their axons following axotomy, and that in peripheral nerves correlates with the generation of a Schwann cell phenotype that is conducive to axonal regeneration. ATF3 is also induced by TLR ligands but acts as a negative regulator of TLR signaling, suppressing the innate immune response which is involved in immuno-surveillance and can enhance or reduce the survival of injured neurons and promote the regeneration of their axons. © 2012 Anderson.

de Maere A.,UCL
Communications in Mathematical Physics | Year: 2010

For a Coupled Map Lattice with a specific strong coupling emulating Stavskaya's probabilistic cellular automata, we prove the existence of a phase transition using a Peierls argument, and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling. This implies the exponential decay, in space and in time, of the correlation functions of the invariant measures. © 2010 Springer-Verlag.

Ajanki O.,University of Helsinki | Huveneers F.,UCL
Communications in Mathematical Physics | Year: 2011

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T1 and Tn. Let EJn be the steady-state energy current across the chain, averaged over the masses. We prove that EJn ~ (T1 - Tn)n-3/2 in the limit n → ∞, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices. © 2010 Springer-Verlag.

In the following we focus on the supernovae closest to Earth. Of course, on a considerably larger scale than 100 pc, more recent (<300,000 yr ago) explosions have occurred, such as Vela and Geminga, which may have left signatures in 14C, cosmic rays and Earth’s biosphere28, 29, 30, 31, but not in 60Fe owing to the large distances from Earth. In case of the nearby stellar moving group, we closely examined each star’s velocity, including its uncertainty, and calculated the most probable path for the group inside the Local Bubble. Since the progenitors could not be observed directly, we assume them to have followed this trajectory together with the other group members. The putative explosion sites were calculated for each star (see Fig. 1 and Extended Data Table 1). Coordinates and velocities from still-existing stars of subgroups UCL and LCC were inserted into the epicyclic equations of motion32, 33 to trace their trajectories back in time7. The cumulative distribution function can be written as where we assume the planar and vertical stellar motions to be statistically independent and therefore decoupled. Hence, the components of the distribution function are described by where x , z , u , v , and w are the observed quantities of the positional and velocity components7. Here x, y and z denote the direction towards the Galactic Centre, the Galactic rotation and the North Galactic Pole, respectively. The associated σ are the corresponding Gaussian uncertainties. The positional error of the y-component, σ , is small compared to the error of the x-component, that is, y  = y , and is therefore neglected. The conditional probability p is given by a δ distribution The index t denotes the components of stellar motion at time t calculated by the epicyclic equations32, 33. The observed uncertainties increase with distance, that is, when traced backwards in time. This results in probability clouds for each explosion time, from which a location of highest probability is extracted and assumed to be the explosion site of the perished star. Figure 1 depicts such clouds for the two most recent supernovae. The radius R of the outer Local Bubble shell at time t after the explosion of the first supernova was calculated by21 Here, N is the number of supernovae, E is the explosion energy in units of 1051 erg, n is the outer interstellar gas number density in units of cm−3, into which the shell is expanding, and t is the evolution time in units of 107 yr. For densities higher than 0.3 cm−3, the shell is not able to reach the Solar System because, in the analytical model, the first supernova had to be assumed to explode in the Local Bubble centre. The same also happens in the numerical simulation (although no restriction about the first explosion site had to be made) of the Local Bubble expansion into a homogeneous medium; hence this interstellar gas density is chosen as an upper limit. The free expansion of an individual shell, calculated in the analytical model, occurred into a low-density Local Bubble medium7, 11 of 5 × 10−3 cm−3. This phase lasts approximately 6,000 yr and covers a distance of about 25 pc, with variations depending on the ejected mass. The subsequent energy-driven expansion is calculated by an approximation due to Kahn23, taking into account the density gradient and the counter-pressure of the ambient bubble medium where the density profile of the Local Bubble medium is ρ = Ωrn with n = 9/2 (for a single supernova shell) and E is the supernova explosion energy. The time-dependent expression for Ω includes the density n of the ambient medium and the beginning of the energy-driven supernova remnant evolution. When written in the dimensionless units introduced above, equation (6) reads as To obtain the correct hierarchy of shells, it is required that the radius R of each supernova remnant obeys at all times and positions indicating that equation (7) only holds until an interior supernova shell hits the outer Local Bubble shell. The amount of ejected 60Fe was estimated using several nucleosynthesis models34, 35, 36, 37. Depending on the input (such as cross-sections, mass loss and rotation) into these models, the 60Fe yield is scattered over a wide range between 10−6M and 10−4M . The mass-dependent yields were plotted and fitted by an exponential function. Thus, for each initial mass of an exploded star a yield of the order of 10−5 was obtained (see Extended Data Table 1 and Extended Data Fig. 1). The 60Fe fluence, which is the number of 60Fe atoms per cm2 that is incorporated into the ferromanganese crust, is calculated by38 where r is the distance of the supernova explosion to the Solar System, M is the ejected 60Fe mass, A its atomic mass number, m the proton mass, and U the uptake factor. U is divided by a factor of 4 to account for the ratio of Earth’s cross-section to its surface area. The formula includes the exponential decay of 60Fe atoms with time t, where t is its half-life. The fluence is converted into 60Fe/Fe ratios by normalizing it to the amount of stable Fe in the crust of 15.27 wt% (ref. 39). Finally, only a fraction of 60Fe, the so-called uptake factor U, is eventually incorporated into the crust. An earlier proposed value of U was about 0.6% (ref. 2), but more recent analyses point to a much higher value40. In our models we have adopted the original value, which takes into account not only the uptake into the crust, but further losses during transport and the yield uncertainties. It may therefore be interpreted as the 60Fe survival fraction, and is close to the value of 0.5% (ref. 5). The numerical simulations have been performed with a modified version of the massively parallel multi-purpose astrophysical fluid code RAMSES41. It uses a second-order unsplit Godunov scheme for solving the hydrodynamical equations on an adaptive octree grid, and a Particle-Mesh solver for computing the trajectories of collisionless particles, which represent individual massive stars in our setup (see below). The computational domain is cubic with a side length of 3 kpc. In the model with the homogeneous background medium, all boundaries are treated as periodic, whereas in the model with the inhomogeneous background medium periodic and outflow boundaries are applied at the vertical and horizontal sides, respectively. The inhomogeneous background medium is self-consistently generated by exposing an initial interstellar gas distribution, derived from observations42, for 180 Myr (a timescale comparable to that required to reach a dynamical equilibrium43) to the combined effects of the Galactic gravitational field44, 45, heating by the interstellar radiation field and cooling by collisional ionization equilibrium processes (all modelled using the spectral synthesis code CLOUDY46), as well as winds of massive stars, and supernovae. Our simulations currently neglect magnetic fields, because their dynamical effects are, when compared to turbulence, presumably small on the scale of the dynamical evolution of the isolated patch of interstellar matter43, and in particular the Local Bubble. In the case of the Local Bubble, the magnetic field should be concentrated in the supershell, where it has been swept, together with the matter, by successive supernova explosions. The Local Bubble interior should thus be almost field-free. Stars in the mass range considered of 0.5 ≤ M/M ≤ 150 are assumed to form at a Galactic rate47 when the gas in a computational cell exceeds (falls below) a certain density (temperature) threshold, with the initial stellar mass spectrum obeying an IMF48. However, only candidates for Type II supernovae (10 ≤ M/M ≤ 30) are converted into actual star particles, which is certainly justified for the young moving groups, which generated the Local Bubble and Loop I. Both their (main-sequence) lifetimes and their mass loss (due to stellar wind and the supernova) are taken to be functions of their initial masses37. The stellar wind velocity is assumed to be constant and is set equal to the canonical value of 2,000 km s−1. Freshly spawned stellar particles receive in addition a random drift velocity49 of 5 km s−1, to account for the observed velocity dispersion. Owing to the high computational demands of such a complex simulation, the finest numerical grid is here somewhat coarser (2.9 pc) than in the model with the homogeneous background medium. As was tested by means of calculating filling factors and probability distribution functions, the inhomogeneous medium, however, serves as a much more realistic environment for studying the Local Bubble evolution scenario. Using a model for non-self-gravitating compressible turbulence50, we analysed the properties of turbulence in our simulated patch of the Galactic disk. We also51 found that turbulence is injected at the scales of breaking open superbubbles, and, furthermore, that the structure functions up to higher orders are nicely matched by a scaling law specifically derived for supersonic turbulence, in which shocks represent the most dissipative structures52. As noted before, 60Fe is treated as a passive scalar, which is justified by its low concentration, precluding any relevant back-reactions on the flow (for example, buoyancy). The spatiotemporal evolution of the 60Fe distribution can therefore be approximately described by an advection–diffusion equation of the form53 where Z is the 60Fe mass fraction, u is the fluid velocity, and α is the diffusivity of the contaminant (which is assumed here to be isotropic). Besides taking into account the radioactive decay of 60Fe (using its latest derived half-life9, 10), we have actively modelled only the left-hand side of this equation, which is motivated by the fact that, particularly in the interstellar medium, diffusive effects are usually restricted to the very small scale (the so-called microscale) of turbulence. However, our simulations still feature non-zero diffusion of 60Fe arising from the numerical scheme itself. Since such numerical diffusion has been demonstrated to operate in general faster and on larger scales than its physical counterpart54, the timescale of mixing in our simulations represents a lower limit to the mixing timescale resulting from physical diffusion. The RAMSES code is available for free download online (https://bitbucket.org/rteyssie/ramses). The newly written or modified routines of the code, as well as the analytical model, which was programmed in MATHEMATICA, that are required for producing the specific setup and results discussed here, are still being improved and extended, and will therefore be released in the future. 60Fe is the most suitable long-lived radionuclide for detecting recent nearby supernova explosions because (1) it is not produced by terrestrial sources, (2) its extraterrestrial influx via interstellar dust particles and micrometeorites is negligible, and (3) all primordial 60Fe has decayed since the formation of the Solar System. Here we present the distributions of two other candidate isotopes, 26Al (t  = 0.7 Myr) and 53Mn (t  = 3.7 Myr), in the ferromanganese crust. Again, we performed analytical calculations using the supernova remnant expansion model described by Kahn23, and assume that the outer boundary evolves as a superbubble shell21. Therefore, stellar explosion times and arrival times are identical to the 60Fe model. In addition, the survival fraction of 0.6% was adopted from this model. Here, to be conservative, we used the highest possible yields for 26Al and 53Mn (see Extended Data Figs 2 and 3)35, 36. Furthermore, relative supernova abundances of 60Fe/26Al are suggested55 to lie between 0.6 and 23. As a second approach, we have used the upper and lower limits of these ratios to scale the measured 60Fe signal in the 1.7–2.6-Myr-old layer of the ferromanganese crust and estimate the expected 26Al abundance, taking into account the different half-lives. In this case it is important to consider the large atmospheric production of 26Al, which arises from spallation of mainly Ar atoms by cosmic rays in Earth’s atmosphere. The deposition of 26Al onto the layers is displayed in Extended Data Fig. 4. The concentration of the radionuclide is normalized to the stable Al content of 0.6 wt% in the crust (K. Knie, private communication, November 2015). The terrestrial 26Al background, usually of the order of 26Al/27Al ≈ 10−13 at the surface56, 57, overwhelms any possible supernova signal in all scenarios considered here. Clearly, a detection of a 26Al supernova peak in the crust is challenging, since the accelerator mass spectrometry measurement uncertainties are larger than the modelled supernova signature. The 26Al estimate presented here is consistent with the 26Al value measured in the ferromanganese crust (K. Knie, private communication, November 2015) as well as with recent measurements performed in deep-sea sediments, where no supernova signal was found58. The situation is similar for 53Mn. Extraterrestrial interstellar dust particles and micrometeoritic influx may distribute 53Mn on Earth and hide a potential supernova signal (Extended Data Fig. 5). The 53Mn concentration was normalized to the stable 55Mn content of 22.67 wt% and the results are in agreement with 53Mn accelerator mass spectrometry measurements performed in the ferromanganese crust39. Again, the measurement error bars are larger than the calculated supernova signal and therefore the extraterrestrial background hampers the detection of supernova-produced 53Mn.

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