An extreme analysis for the 2010 precipitation event at the south of Saskatchewan prairie

After a prolonged drought period in the early 2000s, the Canadian prairie experienced a remarkably wet year in 2010. Five stations near the edge of the Saskatchewan boreal forest recorded historically high cumulative precipitation (from April to September). The exceptional wet year causes the public concerns on flood controls and land use management in the region. Using the Canadian National Climate Data Achieve, characteristics of six-month cumulative precipitation sums over Saskatchewan prairie are investigated by the Generalised Extreme Value (GEV) Theory. Based on the unconstrained GEV distribution, the 2010 event is outside the estimated 95% confidence intervals for the five Canadian prairie stations. On the contrary, the exceptional high 2010 cumulative perception sums for the five stations are still bounded by the estimated confidence bounds if the GEV distribution is constrained to the Gumbel distribution (i.e. setting the shape factor of the GEV distribution to be zero). These results demonstrate that the classical extreme analysis is useful for planning unprecedented extreme events in the Canadian Prairie, if the GEV distribution is constrained to the Gumbel distribution with the estimated uncertainty bounds based on the order statistics. © 2012 Global NEST Printed in Greece. All rights reserved

Surface tension in an intrinsic curvature model with fixed one-dimensional boundaries

A triangulated fixed connectivity surface model is investigated by using the Monte Carlo simulation technique. In order to have the macroscopic surface tension \tau, the vertices on the one-dimensional boundaries are fixed as the edges (=circles) of the tubular surface in the simulations. The size of the tubular surface is chosen such that the projected area becomes the regular square of area A. An intrinsic curvature energy with a microscopic bending rigidity b is included in the Hamiltonian. We found that the model undergoes a first-order transition of surface fluctuations at finite b, where the surface tension \tau discontinuously changes. The gap of \tau remains constant at the transition point in a certain range of values A/N^\prime at sufficiently large N^\prime, which is the total number of vertices excluding the fixed vertices on the boundaries. The value of \tau remains almost zero in the wrinkled phase at the transition point while \tau remains negative finite in the smooth phase in that range of A/N^\prime.Comment: 12 pages, 8 figure

Disaggregation of spatial rainfall fields for hydrological modelling

International audienceMeteorological models generate fields of precipitation and other climatological variables as spatial averages at the scale of the grid used for numerical solution. The grid-scale can be large, particularly for GCMs, and disaggregation is required, for example to generate appropriate spatial-temporal properties of rainfall for coupling with surface-boundary conditions or more general hydrological applications. A method is presented here which considers the generation of the wet areas and the simulation of rainfall intensities separately. For the first task, a nearest-neighbour Markov scheme, based upon a Bayesian technique used in image processing, is implemented so as to preserve the structural features of the observed rainfall. Essentially, the large-scale field and the previously disaggregated field are used as evidence in an iterative procedure which aims at selecting a realisation according to the joint posterior probability distribution. In the second task the morphological characteristics of the field of rainfall intensities are reproduced through a random sampling of intensities according to a beta distribution and their allocation to pixels chosen so that the higher intensities are more likely to be further from the dry areas. The components of the scheme are assessed for Arkansas-Red River basin radar rainfall (hourly averages) by disaggregating from 40 km x 40 km to 8 km x 8 km. The wet/dry scheme provides a good reproduction both of the number of correctly classified pixels and the coverage, while the intensitiy scheme generates fields with an adequate variance within the grid-squares, so that this scheme provides the hydrologist with a useful tool for the downscaling of meteorological model outputs. Keywords: Rainfall, disaggregation, General Circulation Model, Bayesian analysi

Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries

An intrinsic curvature model is investigated using the canonical Monte Carlo simulations on dynamically triangulated spherical surfaces of size upto N=4842 with two fixed-vertices separated by the distance 2L. We found a first-order transition at finite curvature coefficient \alpha, and moreover that the order of the transition remains unchanged even when L is enlarged such that the surfaces become sufficiently oblong. This is in sharp contrast to the known results of the same model on tethered surfaces, where the transition weakens to a second-order one as L is increased. The phase transition of the model in this paper separates the smooth phase from the crumpled phase. The surfaces become string-like between two point-boundaries in the crumpled phase. On the contrary, we can see a spherical lump on the oblong surfaces in the smooth phase. The string tension was calculated and was found to have a jump at the transition point. The value of \sigma is independent of L in the smooth phase, while it increases with increasing L in the crumpled phase. This behavior of \sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu, where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled phase. We should note that a possibility of a continuous transition is not completely eliminated.Comment: 15 pages with 10 figure

Analysis of aggregation and disaggregation effects for grid-based hydrological models and the development of improved precipitation disaggregation procedures for GCMs

International audienceAppropriate representation of hydrological processes within atmospheric General Circulation Models (GCMs) is important with respect to internal model dynamics (e.g. surface feedback effects on atmospheric fluxes, continental runoff production) and to simulation of terrestrial impacts of climate change. However, at the scale of a GCM grid-square, several methodological problems arise. Spatial disaggregation of grid-square average climatological parameters is required in particular to produce appropriate point intensities from average precipitation. Conversely, aggregation of land surface heterogeneity is necessary for grid-scale or catchment scale application. The performance of grid-based hydrological models is evaluated for two large (104km2) UK catchments. Simple schemes, using sub-grid average of individual land use at 40 km scale and with no calibration, perform well at the annual time-scale and, with the addition of a (calibrated) routing component, at the daily and monthly time-scale. Decoupling of hillslope and channel routing does not necessarily improve performance or identifiability. Scale dependence is investigated through application of distribution functions for rainfall and soil moisture at 100 km scale. The results depend on climate, but show interdependence of the representation of sub-grid rainfall and soil moisture distribution. Rainfall distribution is analysed directly using radar rainfall data from the UK and the Arkansas Red River, USA. Among other properties, the scale dependence of spatial coverage upon radar pixel resolution and GCM grid-scale, as well as the serial correlation of coverages are investigated. This leads to a revised methodology for GCM application, as a simple extension of current procedures. A new location-based approach using an image processing technique is then presented, to allow for the preservation of the spatial memory of the process

The spectral dimension of generic trees

We define generic ensembles of infinite trees. These are limits as $N\to\infty$ of ensembles of finite trees of fixed size $N$, defined in terms of a set of branching weights. Among these ensembles are those supported on trees with vertices of a uniformly bounded order. The associated probability measures are supported on trees with a single spine and Hausdorff dimension $d_h =2$. Our main result is that their spectral dimension is $d_s=4/3$, and that the critical exponent of the mass, defined as the exponential decay rate of the two-point function along the spine, is 1/3

Coulomb-gas formulation of SU(2) branes and chiral blocks

We construct boundary states in $SU(2)_k$ WZNW models using the bosonized Wakimoto free-field representation and study their properties. We introduce a Fock space representation of Ishibashi states which are coherent states of bosons with zero-mode momenta (boundary Coulomb-gas charges) summed over certain lattices according to Fock space resolution of $SU(2)_k$. The Virasoro invariance of the coherent states leads to families of boundary states including the B-type D-branes found by Maldacena, Moore and Seiberg, as well as the A-type corresponding to trivial current gluing conditions. We then use the Coulomb-gas technique to compute exact correlation functions of WZNW primary fields on the disk topology with A- and B-type Cardy states on the boundary. We check that the obtained chiral blocks for A-branes are solutions of the Knizhnik-Zamolodchikov equations.Comment: 14 pages, 3 figures, revtex4. Essentially the published versio

Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size

We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_\xi]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_\xi$, which corresponds to the area of the membrane coarse-grained at the mesh size $\xi$. We show that the meshwork modifies the membrane tension $\sigma$ both below and above the scale $\xi$, inducing a tension-jump $\Delta\sigma=dF_\mathrm{el}/dA_\xi$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes coupled to their cytoskeleton. Our results indicate that the cytoskeleton might be under extensional stress, which would provide a means to regulate available membrane area. We also predict an observable tension jump for membranes decorated with polymer "brushes"