Perturbation growth at the convective scale for CSIP IOP18

The Met Office Unified Model is run for a case observed during Intensive Observation Period 18 (IOP18) of the Convective Storms Initiation Project (CSIP). The aims are to identify the physical processes that lead to perturbation growth at the convective scale in response to model-state perturbations and to determine their sensitivity to the character of the perturbations. The case is strongly upper-level forced but with detailed mesoscale/convective-scale evolution that is dependent on smaller-scale processes. Potential temperature is perturbed within the boundary layer. The effects on perturbation growth of both the amplitude and typical scalelength of the perturbations are investigated and perturbations are applied either sequentially (every 30 min throughout the simulation) or at specific times. The direct effects (within one timestep) of the perturbations are to generate propagating Lamb and acoustic waves and produce generally small changes in cloud parameters and convective instability. In exceptional cases a perturbation at a specific gridpoint leads to switching of the diagnosed boundary-layer type or discontinuous changes in convective instability, through the generation or removal of a lid. The indirect effects (during the entire simulation) are changes in the intensity and location of precipitation and in the cloud size distribution. Qualitatively different behaviour is found for strong (1K amplitude) and weak (0.01K amplitude) perturbations, with faster growth after sunrise found only for the weaker perturbations. However, the overall perturbation growth (as measured by the root-mean-square error of accumulated precipitation) reaches similar values at saturation, regardless of the perturbation characterisation.

The use of earth observation techniques to improve catchment-scale pollution predictions

Remote sensing can potentially provide information useful in improving pollution transport modelling in agricultural catchments. Realisation of this potential will depend on the availability of the raw data, development of information extraction techniques, and the impact of the assimilation of the derived information into models. High spatial resolution hyperspectral imagery of a farm near Hereford, UK is analysed. A technique is described to automatically identify the soil and vegetation endmembers within a field, enabling vegetation fractional cover estimation. The aerially-acquired laser altimetry is used to produce digital elevation models of the site. At the subfield scale the hypothesis that higher resolution topography will make a substantial difference to contaminant transport is tested using the AGricultural Non-Point Source (AGNPS) model. Slope aspect and direction information are extracted from the topography at different resolutions to study the effects on soil erosion, deposition, runoff and nutrient losses. Field-scale models are often used to model drainage water, nitrate and runoff/sediment loss, but the demanding input data requirements make scaling up to catchment level difficult. By determining the input range of spatial variables gathered from EO data, and comparing the response of models to the range of variation measured, the critical model inputs can be identified. Response surfaces to variation in these inputs constrain uncertainty in model predictions and are presented. Although optical earth observation analysis can provide fractional vegetation cover, cloud cover and semi-random weather patterns can hinder data acquisition in Northern Europe. A Spring and Autumn cloud cover analysis is carried out over seven UK sites close to agricultural districts, using historic satellite image metadata, climate modelling and historic ground weather observations. Results are assessed in terms of probability of acquisition probability and implications for future earth observation missions. (C) 2003 Elsevier Ltd. All rights reserved.

Causes of the apparent scale independence of fractal indices associated with forest fragmentation in Bolivia

In a recent investigation, Landsat TM and ETM+ data were used to simulate different resolutions of remotely-sensed images (from 30 to 1100 m) and to analyze the effect of resolution on a range of landscape metrics associated with spatial patterns of forest fragmentation in Chapare, Bolivia since the mid-1980s. Whereas most metrics were found to be highly dependent on pixel size, several fractal metrics (DLFD, MPFD, and AWMPFD) were apparently independent of image resolution, in contradiction with a sizeable body of literature indicating that fractal dimensions of natural objects depend strongly on image characteristics. The present re-analysis of the Chapare images, using two alternative algorithms routinely used for the evaluation of fractal dimensions, shows that the values of the box-counting and information fractal dimensions are systematically larger, sometimes by as much as 85%, than the "fractal" indices DLFD, MPFD, and AWMFD for the same images. In addition, the geometrical fractal features of the forest and non-forest patches in the Chapare region strongly depend on the resolution of images used in the analysis. The largest dependency on resolution occurs for the box-counting fractal dimension in the case of the non-forest patches in 1993, where the difference between the 30 and I 100 m-resolution images corresponds to 24% of the full theoretical range (1.0 to 2.0) of the mass fractal dimension. The observation that the indices DLFD, MPFD, and AWMPFD, unlike the classical fractal dimensions, appear relatively unaffected by resolution in the case of the Chapare images seems due essentially to the fact that these indices are based on a heuristic, "non-geometric" approach to fractals. Because of their lack of a foundation in fractal geometry, nothing guarantees that these indices will be resolution-independent in general. (C) 2006 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

A comparative study of Java and C performance in two large-scale parallel applications

In the 1990s the Message Passing Interface Forum defined MPI bindings for Fortran, C, and C++. With the success of MPI these relatively conservative languages have continued to dominate in the parallel computing community. There are compelling arguments in favour of more modern languages like Java. These include portability, better runtime error checking, modularity, and multi-threading. But these arguments have not converted many HPC programmers, perhaps due to the scarcity of full-scale scientific Java codes, and the lack of evidence for performance competitive with C or Fortran. This paper tries to redress this situation by porting two scientific applications to Java. Both of these applications are parallelized using our thread-safe Java messaging system—MPJ Express. The first application is the Gadget-2 code, which is a massively parallel structure formation code for cosmological simulations. The second application uses the finite-domain time-difference method for simulations in the area of computational electromagnetics. We evaluate and compare the performance of the Java and C versions of these two scientific applications, and demonstrate that the Java codes can achieve performance comparable with legacy applications written in conventional HPC languages. Copyright © 2009 John Wiley & Sons, Ltd.

On a non-autonomous difference equation

Abu-Saris and DeVault proposed two open problems about the difference equation x(n+1) = a(n)x(n)/x(n-1), n = 0, 1, 2,..., where a(n) not equal 0 for n = 0, 1, 2..., x(-1) not equal 0, x(0) not equal 0. In this paper we provide solutions to the two open problems. (c) 2004 Elsevier Inc. All rights reserved.

Flux difference splitting for inviscid, real gases with non-equilibrium chemistry

A flux-difference splitting method is presented for the inviscid terms of the compressible flow equations for chemical non-equilibrium gases

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Estimating the direct aerosol radiative perturbation: impact of ocean surface representation and aerosol non-sphericity

Atmospheric aerosols are now actively studied, in particular because of their radiative and climate impacts. Estimations of the direct aerosol radiative perturbation, caused by extinction of incident solar radiation, usually rely on radiative transfer codes and involve simplifying hypotheses. This paper addresses two approximations which are widely used for the sake of simplicity and limiting the computational cost of the calculations. Firstly, it is shown that using a Lambertian albedo instead of the more rigorous bidirectional reflectance distribution function (BRDF) to model the ocean surface radiative properties leads to large relative errors in the instantaneous aerosol radiative perturbation. When averaging over the day, these errors cancel out to acceptable levels of less than 3% (except in the northern hemisphere winter). The other scope of this study is to address aerosol non-sphericity effects. Comparing an experimental phase function with an equivalent Mie-calculated phase function, we found acceptable relative errors if the aerosol radiative perturbation calculated for a given optical thickness is daily averaged. However, retrieval of the optical thickness of non-spherical aerosols assuming spherical particles can lead to significant errors. This is due to significant differences between the spherical and non-spherical phase functions. Discrepancies in aerosol radiative perturbation between the spherical and non-spherical cases are sometimes reduced and sometimes enhanced if the aerosol optical thickness for the spherical case is adjusted to fit the simulated radiance of the non-spherical case.

Impact of the modal aerosol scheme GLOMAP-mode on aerosol forcing in the Hadley Centre Global Environmental Model

The Hadley Centre Global Environmental Model (HadGEM) includes two aerosol schemes: the Coupled Large-scale Aerosol Simulator for Studies in Climate (CLASSIC), and the new Global Model of Aerosol Processes (GLOMAP-mode). GLOMAP-mode is a modal aerosol microphysics scheme that simulates not only aerosol mass but also aerosol number, represents internally-mixed particles, and includes aerosol microphysical processes such as nucleation. In this study, both schemes provide hindcast simulations of natural and anthropogenic aerosol species for the period 2000–2006. HadGEM simulations of the aerosol optical depth using GLOMAP-mode compare better than CLASSIC against a data-assimilated aerosol re-analysis and aerosol ground-based observations. Because of differences in wet deposition rates, GLOMAP-mode sulphate aerosol residence time is two days longer than CLASSIC sulphate aerosols, whereas black carbon residence time is much shorter. As a result, CLASSIC underestimates aerosol optical depths in continental regions of the Northern Hemisphere and likely overestimates absorption in remote regions. Aerosol direct and first indirect radiative forcings are computed from simulations of aerosols with emissions for the year 1850 and 2000. In 1850, GLOMAP-mode predicts lower aerosol optical depths and higher cloud droplet number concentrations than CLASSIC. Consequently, simulated clouds are much less susceptible to natural and anthropogenic aerosol changes when the microphysical scheme is used. In particular, the response of cloud condensation nuclei to an increase in dimethyl sulphide emissions becomes a factor of four smaller. The combined effect of different 1850 baselines, residence times, and abilities to affect cloud droplet number, leads to substantial differences in the aerosol forcings simulated by the two schemes. GLOMAP-mode finds a presentday direct aerosol forcing of −0.49Wm−2 on a global average, 72% stronger than the corresponding forcing from CLASSIC. This difference is compensated by changes in first indirect aerosol forcing: the forcing of −1.17Wm−2 obtained with GLOMAP-mode is 20% weaker than with CLASSIC. Results suggest that mass-based schemes such as CLASSIC lack the necessary sophistication to provide realistic input to aerosol-cloud interaction schemes. Furthermore, the importance of the 1850 baseline highlights how model skill in predicting present-day aerosol does not guarantee reliable forcing estimates. Those findings suggest that the more complex representation of aerosol processes in microphysical schemes improves the fidelity of simulated aerosol forcings.

Representation of model error in a convective-scale ensemble prediction system

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office’s 24- member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model’s parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits “jumpiness” in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.