Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

One-site density matrix renormalization group and alternating minimum energy algorithm

Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating direction scheme with the auxiliary (e.g. gradient) information, which substantially improves the convergence in many difficult cases. Being conceptually close, these methods have different derivation, implementation, theoretical and practical properties. We emphasize the differences, and reproduce the numerical example to compare the performance of two algorithms.Comment: Submitted to the proceedings of ENUMATH 201

Precipitable Water Comparisons Over Ghana using PPP Techniques and Reanalysis Data

Atmospheric Water vapor is an important greenhouse gas and contributes greatly in maintaining the Earth’s energy balance. This critical meteorological parameter is not being sensed by any of the 22 synoptic weather stations in Ghana. This study presents a highly precise tool for water vapor sensing based on the concept Global Navigation Satellite Systems (GNSS) meteorology and tests the computed results against global reanalysis data. Conventional approaches used to sense the atmospheric water vapor or Precipitable Water (PW) such as radiosondes, hygrometers, microwave radiometers or sun photometers are expensive and have coverage and temporal limitations. Whereas GNSS meteorological concept offers an easier, inexpensive and all-weather technique to retrieve PW or Integrated Water Vapor (IWV) from zenith tropospheric delays (ZTD) over a reference station. This study employed precise point positioning (PPP) techniques to quantify the extend of delays on the signal due to the troposphere and stratosphere where atmospheric water vapor resides. Stringent processing criteria were set using an elevation cut-off of 5 degrees, precise orbital and clock products were used as well as nominal tropospheric corrections and mapping functions implemented. The delays which are originally slanted are mapped unto the zenith direction and integrated with surface meteorological parameters to retrieve PW or IWV. The gLAB software, Canadian Spatial Reference System (CSRS) and Automatic Precise Positioning Service (APPS) online PPP services were the approaches used to compute ZTD. PW values obtained were compared with Japanese Metro Agency Reanalysis (JRA), European Centre for Medium-Range Weather Forecasts Reanalysis (ERA-interim) and National Center for Environmental Prediction (NCEP) global reanalysis data. Correlation analysis were run on the logged station data using the three approaches and global reanalysis data. The obtained results show stronger correlation between the retrieved PW values and those provided by the ERA-interim. Finally, the study results indicate that with a more densified network of GNSS base stations the retrieved PW or IWV will greatly improve numerical weather predictions in Ghana.Keywords: GNSS Signals, PPP, Integrated Water vapour, Precipitable Water, Reanalysis Model

Semi-Lagrangian methods in air pollution models

Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990) and Machenhauer et al. (2008) as possible. The focus in this study is on accuracy and local mass conservation. <br><br> The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999), second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002), third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Conserving Semi-Lagrangian (LMCSL), by Kaas (2008), and last, semi-Lagrangian cubic interpolation with a locally mass conserving monotonic filter by Kaas and Nielsen (2010). <br><br> Semi-Lagrangian (SL) interpolation is a classical method for atmospheric modeling, cascade interpolation is more efficient computationally, modified interpolation weights assure mass conservation and the locally mass conserving monotonic filter imposes monotonicity. <br><br> All schemes are tested with advection alone or with advection and chemistry together under both typical rural and urban conditions using different temporal and spatial resolution. The methods are compared with a current state-of-the-art scheme, Accurate Space Derivatives (ASD), see Frohn et al. (2002), presently used at the National Environmental Research Institute (NERI) in Denmark. To enable a consistent comparison only non-divergent flow configurations are tested. <br><br> The test cases are based either on the traditional slotted cylinder or the rotating cone, where the schemes' ability to model both steep gradients and slopes are challenged. <br><br> The tests showed that the locally mass conserving monotonic filter improved the results significantly for some of the test cases, however, not for all. It was found that the semi-Lagrangian schemes, in almost every case, were not able to outperform the current ASD scheme used in DEHM with respect to accuracy

Incorporation of pollen data in source maps is vital for pollen dispersion models

Information about distribution of pollen sources, i.e. their presence and abundance in a specific region, is important especially when atmospheric transport models are applied to forecast pollen concentrations. The goal of this study is to evaluate three pollen source maps using an atmospheric transport model and study the effect on the model results by combining these source maps with pollen data. Here we evaluate three maps for the birch taxon: (1) a map derived by combining land cover data and forest inventory; (2) a map obtained from land cover data and calibrated using model simulations and pollen observations; (3) a statistical map resulting from analysis of forest inventory and forest plot data. The maps were introduced to the Enviro-HIRLAM (Environment – High Resolution Limited Area Model) as input data to simulate birch pollen concentrations over Europe for the birch pollen season 2006. 18 model runs were performed using each of the selected maps in turn with and without calibration with observed pollen data from 2006. The model results were compared with the pollen observation data at 12 measurement sites located in Finland, Denmark and Russia.We show that calibration of the maps using pollen observations significantly improved the model performance for all three maps. The findings also indicate the large sensitivity of the model results to the source maps and agree well with other studies on birch showing that pollen or hybrid-based source maps provide the best model performance. This study highlights the importance of including pollen data in the production of source maps for pollen dispersion modelling and for exposure studies

Shape analysis on homogeneous spaces: a generalised SRVT framework

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. One computationally efficient approach to shape analysis is based on the Square Root Velocity Transform (SRVT). In this paper we propose a generalised SRVT framework for shapes on homogeneous manifolds. The method opens up for a variety of possibilities based on different choices of Lie group action and giving rise to different Riemannian metrics.Comment: 28 pages; 4 figures, 30 subfigures; notes for proceedings of the Abel Symposium 2016: "Computation and Combinatorics in Dynamics, Stochastics and Control". v3: amended the text to improve readability and clarify some points; updated and added some references; added pseudocode for the dynamic programming algorithm used. The main results remain unchange

ISOCAM observations of the rho Ophiuchi cloud: Luminosity and mass functions of the pre-main sequence embedded cluster

We present the results of the first extensive mid-infrared (IR) imaging survey of the rho Ophiuchi embedded cluster, performed with the ISOCAM camera on board the ISO satellite. The main molecular cloud L1688, as well as L1689N and L1689S, have been completely surveyed for point sources at 6.7 and 14.3 micron. A total of 425 sources are detected including 16 Class I, 123 Class II, and 77 Class III young stellar objects (YSOs). Essentially all of the mid-IR sources coincide with near-IR sources, but a large proportion of them are recognized for the first time as YSOs. Our dual-wavelength survey allows us to identify essentially all the YSOs with IR excess in the embedded cluster down to Fnu ~ 10 - 15 mJy. It more than doubles the known population of Class II YSOs and represents the most complete census to date of newly formed stars in the rho Ophiuchi central region. The stellar luminosity function of the complete sample of Class II YSOs is derived with a good accuracy down to L= 0.03 Lsun. A modeling of this lumino- sity function, using available pre-main sequence tracks and plausible star for- mation histories, allows us to derive the mass distribution of the Class II YSOs which arguably reflects the IMF of the embedded cluster. We estimate that the IMF in rho Ophiuchi is well described by a two-component power law with a low- mass index of -0.35+/-0.25, a high-mass index of -1.7 (to be compared with the Salpeter value of -1.35), and a break occurring at M = 0.55+/-0.25 Msun. This IMF is flat with no evidence for a low-mass cutoff down to at least 0.06 Msun.Comment: A&A Document Class -- version 5.01, 27 pages, 10 figures v2: typos added including few changes in source numberin

A deep optical/near-infrared catalog of Serpens

We present a deep optical/near-infrared imaging survey of the Serpens molecular cloud. This survey constitutes the complementary optical data to the Spitzer "Core To Disk" (c2d) Legacy survey in this cloud. The survey was conducted using the Wide Field Camera at the Isaac Newton Telescope. About 0.96 square degrees were imaged in the R and Z filters, covering the entire region where most of the young stellar objects identified by the c2d survey are located. 26524 point-like sources were detected in both R and Z bands down to R=24.5 mag and Z=23 mag with a signal-to-noise ratio better than 3. The 95% completeness limit of our catalog corresponds to 0.04 solar masses for members of the Serpens star forming region (age 2 Myr and distance 260 pc) in the absence of extinction. Adopting the typical extinction of the observed area (Av=7 mag), we estimate a 95% completeness level down to 0.1 solar masses. The astrometric accuracy of our catalog is 0.4 arcsec with respect to the 2MASS catalog. Our final catalog contains J2000 celestial coordinates, magnitudes in the R and Z bands calibrated to the SDSS photometric system and, where possible, JHK magnitudes from 2MASS for sources in 0.96 square degrees in the direction of Serpens. This data product has been already used within the frame of the c2d Spitzer Legacy Project analysis in Serpens to study the star/disk formation and evolution in this cloud; here we use it to obtain new indications of the disk-less population in Serpens.Comment: 7 page, 5 figure