Numerics and Fractals

Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions themselves are known to be the fixed points of an associated Read-Bajactarevi\'c operator. This paper establishes existence and properties of local fractal functions and discusses how they are computed. In particular, it is shown that piecewise polynomials are a special case of local fractal functions. Finally, we develop a method to compute the components of a local IFS from data or (partial differential) equations.Comment: version 2: minor updates and section 6.1 rewritten, arXiv admin note: substantial text overlap with arXiv:1309.0243. text overlap with arXiv:1309.024

Integrated spectra extraction based on signal-to-noise optimization using Integral Field Spectroscopy

We propose and explore the potential of a method to extract high signal-to-noise (S/N) integrated spectra related to physical and/or morphological regions on a 2-dimensional field using Integral Field Spectroscopy (IFS) observations by employing an optimization procedure based on either continuum (stellar) or line (nebular) emission features. The optimization method is applied to a set of IFS VLT-VIMOS observations of (U)LIRG galaxies, describing the advantages of the optimization by comparing the results with a fixed-aperture, single spectrum case, and by implementing some statistical tests. We demonstrate that the S/N of the IFS optimized integrated spectra is significantly enhanced when compared with the single aperture unprocessed case. We provide an iterative user-friendly and versatile IDL algorithm that allows the user to spatially integrate spectra following more standard procedures. This is made available to the community as part of the PINGSoft IFS software package.Comment: Accepted for publication in Astronomy & Astrophysics, 12 pages, 7 figure

Vertical structure and physical processes of the Madden-Julian oscillation: Linking hindcast fidelity to simulated diabatic heating and moistening

Many theories for the Madden-Julian oscillation (MJO) focus on diabatic processes, particularly the evolution of vertical heating and moistening. Poor MJO performance in weather and climate models is often blamed on biases in these processes and their interactions with the large-scale circulation. We introduce one of three components of a model-evaluation project, which aims to connect MJO fidelity in models to their representations of several physical processes, focusing on diabatic heating and moistening. This component consists of 20-day hindcasts, initialised daily during two MJO events in winter 2009-10. The 13 models exhibit a range of skill: several have accurate forecasts to 20 days' lead, while others perform similarly to statistical models (8-11 days). Models that maintain the observed MJO amplitude accurately predict propagation, but not vice versa. We find no link between hindcast fidelity and the precipitation-moisture relationship, in contrast to other recent studies. There is also no relationship between models' performance and the evolution of their diabatic-heating profiles with rain rate. A more robust association emerges between models' fidelity and net moistening: the highest-skill models show a clear transition from low-level moistening for light rainfall to mid-level moistening at moderate rainfall and upper-level moistening for heavy rainfall. The mid-level moistening, arising from both dynamics and physics, may be most important. Accurately representing many processes may be necessary, but not sufficient for capturing the MJO, which suggests that models fail to predict the MJO for a broad range of reasons and limits the possibility of finding a panacea

A flexible and efficient radiation scheme for the ECMWF model

This paper describes a new radiation scheme ecRad for use both in the model of the European Centre for Medium‐Range Weather Forecasts (ECMWF), and off‐line for noncommercial research. Its modular structure allows the spectral resolution, the description of cloud and aerosol optical properties, and the solver, to be changed independently. The available solvers include the Monte Carlo Independent Column Approximation (McICA), Tripleclouds, and the Speedy Algorithm for Radiative Transfer through Cloud Sides (SPARTACUS), the latter which makes ECMWF the first global model capable of representing the 3‐D radiative effects of clouds. The new implementation of the operational McICA solver produces less noise in atmospheric heating rates, and is 41% faster, which can yield indirect forecast skill improvements via calling the radiation scheme more frequently. We demonstrate how longwave scattering may be implemented for clouds but not aerosols, which is only 4% more computationally costly overall than neglecting longwave scattering and yields further modest forecast improvements. It is also shown how a sequence of radiation changes in the last few years has led to a substantial reduction in stratospheric temperature biases

Direct multiscale coupling of a transport code to gyrokinetic turbulence codes

Direct coupling between a transport solver and local, nonlinear gyrokinetic calculations using the multiscale gyrokinetic code TRINITY [M. Barnes, Ph.D. thesis, arxiv:0901.2868] is described. The coupling of the microscopic and macroscopic physics is done within the framework of multiscale gyrokinetic theory, of which we present the assumptions and key results. An assumption of scale separation in space and time allows for the simulation of turbulence in small regions of the space-time grid, which are embedded in a coarse grid on which the transport equations are implicitly evolved. This leads to a reduction in computational expense of several orders of magnitude, making first-principles simulations of the full fusion device volume over the confinement time feasible on current computing resources. Numerical results from TRINITY simulations are presented and compared with experimental data from JET and ASDEX Upgrade plasmas.Comment: 12 pages, 13 figures, invited paper for 2009 APS-DPP meeting, submitted to Phys. Plasma

Cloud impacts on photochemistry: Building a climatology of photolysis rates from the Atmospheric Tomography mission

Abstract. Measurements from actinic flux spectroradiometers on board the NASA DC-8 during the Atmospheric Tomography (ATom) mission provide an extensive set of statistics on how clouds alter photolysis rates (J values) throughout the remote Pacific and Atlantic Ocean basins. J values control tropospheric ozone and methane abundances, and thus clouds have been included for more than three decades in tropospheric chemistry modeling. ATom made four profiling circumnavigations of the troposphere capturing each of the seasons during 2016–2018. This work examines J values from the Pacific Ocean flights of the first deployment, but publishes the complete Atom-1 data set (29 July to 23 August 2016). We compare the observed J values (every 3 s along flight track) with those calculated by nine global chemistry–climate/transport models (globally gridded, hourly, for a mid-August day). To compare these disparate data sets, we build a commensurate statistical picture of the impact of clouds on J values using the ratio of J-cloudy (standard, sometimes cloudy conditions) to J-clear (artificially cleared of clouds). The range of modeled cloud effects is inconsistently large but they fall into two distinct classes: (1) models with large cloud effects showing mostly enhanced J values aloft and or diminished at the surface and (2) models with small effects having nearly clear-sky J values much of the time. The ATom-1 measurements generally favor large cloud effects but are not precise or robust enough to point out the best cloud-modeling approach. The models here have resolutions of 50–200 km and thus reduce the occurrence of clear sky when averaging over grid cells. In situ measurements also average scattered sunlight over a mixed cloud field, but only out to scales of tens of kilometers. A primary uncertainty remains in the role of clouds in chemistry, in particular, how models average over cloud fields, and how such averages can simulate measurements. NERC ACSIS LTSM projec

The ALADIN system and its canonical model configurations AROME CY41T1 and ALARO CY40T1

The ALADIN System is a numerical weather prediction (NWP) system developed by the international ALADIN consortium for operational weather forecasting and research purposes. It is based on a code that is shared with the global model IFS of the ECMWF and the ARPEGE model of Meteo-France. Today, this system can be used to provide a multitude of high-resolution limited-area model (LAM) configurations. A few configurations are thoroughly validated and prepared to be used for the operational weather forecasting in the 16 partner institutes of this consortium. These configurations are called the ALADIN canonical model configurations (CMCs). There are currently three CMCs: the ALADIN baseline CMC, the AROME CMC and the ALARO CMC. Other configurations are possible for research, such as process studies and climate simulations. The purpose of this paper is (i) to define the ALADIN System in relation to the global counterparts IFS and ARPEGE, (ii) to explain the notion of the CMCs, (iii) to document their most recent versions, and (iv) to illustrate the process of the validation and the porting of these configurations to the operational forecast suites of the partner institutes of the ALADIN consortium. This paper is restricted to the forecast model only; data assimilation techniques and postprocessing techniques are part of the ALADIN System but they are not discussed here

Shapley Supercluster Survey: Ram-Pressure Stripping vs. Tidal Interactions in the Shapley Supercluster

We present two new examples of galaxies undergoing transformation in the Shapley supercluster core. These low-mass (stellar mass from 0.4E10 to 1E10 Msun) galaxies are members of the two clusters SC-1329-313 (z=0.045) and SC-1327-312 (z=0.049). Integral-field spectroscopy complemented by imaging in ugriK bands and in Halpha narrow-band are used to disentangle the effects of tidal interaction (TI) and ram-pressure stripping (RPS). In both galaxies, SOS-61086 and SOS-90630, we observe one-sided extraplanar ionized gas extending respectively 30kpc and 41kpc in projection from their disks. The galaxies' gaseous disks are truncated and the kinematics of the stellar and gas components are decoupled, supporting the RPS scenario. The emission of the ionized gas extends in the direction of a possible companion for both galaxies suggesting a TI. The overall gas velocity field of SOS-61086 is reproduced by ad hoc N-body/hydrodynamical simulations of RPS acting almost face-on and starting about 250Myr ago, consistent with the age of the young stellar populations. A link between the observed gas stripping and the cluster-cluster interaction experienced by SC-1329-313 and A3562 is suggested. Simulations of ram pressure acting almost edge-on are able to fully reproduce the gas velocity field of SOS-90630, but cannot at the same time reproduce the extended tail of outflowing gas. This suggests that an additional disturbance from a TI is required. This study adds a piece of evidence that RPS may take place in different environments with different impacts and witnesses the possible effect of cluster-cluster merger on RPS.Comment: 27 pages, 28 figures, MNRAS accepte