A continuum model of melt pond evolution on Arctic sea ice

[1] During the Northern Hemisphere summer, absorbed solar radiation melts snow and the upper surface of Arctic sea ice to generate meltwater that accumulates in ponds. The melt ponds reduce the albedo of the sea ice cover during the melting season, with a significant impact on the heat and mass budget of the sea ice and the upper ocean. We have developed a model, designed to be suitable for inclusion into a global circulation model (GCM), which simulates the formation and evolution of the melt pond cover. In order to be compatible with existing GCM sea ice models, our melt pond model builds upon the existing theory of the evolution of the sea ice thickness distribution. Since this theory does not describe the topography of the ice cover, which is crucial to determining the location, extent, and depth of individual ponds, we have needed to introduce some assumptions. We describe our model, present calculations and a sensitivity analysis, and discuss our results.

Continuum sea ice rheology determined from subcontinuum mechanics

[1] A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

An exploration of the equivalent weights particle filter

Particle filters are fully non-linear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high-dimensional geophysical applications the number of particles required by the sequential importance resampling (SIR) particle filter in order to capture the high probability region of the posterior, is too large to make them usable. However particle filters can be formulated using proposal densities, which gives greater freedom in how particles are sampled and allows for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function. This gives rise to the possibility of non-linear data assimilation in large dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model.

Global radiative and climate effect of the water vapour continuum at visible and near-infrared wavelengths

Recent laboratory measurements show that absorption by the water vapour continuum in near-infrared windows may be about an order of magnitude higher than assumed in many radiation codes. The radiative impact of the continuum at visible and near-infrared wavelengths is examined for the present day and for a possible future warmer climate (with a global-mean total column water increase of 33%). The calculations use a continuum model frequently used in climate models (‘CKD’) and a continuum model where absorption is enhanced at wavelengths greater than 1 µm based on recent measurements (‘CAVIAR’). The continuum predominantly changes the partitioning between solar radiation absorbed by the surface and the atmosphere; changes in top-of-atmosphere net irradiances are smaller. The global-mean clear-sky atmospheric absorption is enhanced by 1.5 W m−2 (about 2%) and 2.8 W m−2 (about 3.5%) for CKD and CAVIAR respectively, relative to a hypothetical no-continuum case, with all-sky enhancements about 80% of these values. The continuum is, in relative terms, more important for radiation budget changes between the present day and a possible future climate. Relative to the no-continuum case, the increase in global-mean clear-sky absorption is 8% higher using CKD and almost 20% higher using CAVIAR; all-sky enhancements are about half these values. The effect of the continuum is estimated for the solar component of the water vapour feedback, the reduction in downward surface irradiance and precipitation change in a warmer world. For CKD and CAVIAR respectively, and relative to the no-continuum case, the solar component of the water vapour feedback is enhanced by about 4 and 9%, the change in clear-sky downward surface irradiance is 7 and 18% more negative, and the global-mean precipitation response decreases by 1 and 4%. There is a continued need for improved continuum measurements, especially at atmospheric temperatures and at wavelengths below 2 µm.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

The water vapour continuum in near-infrared windows – current understanding and prospects for its inclusion in spectroscopic databases

Spectroscopic catalogues, such as GEISA and HITRAN, do not yet include information on the water vapour continuum that pervades visible, infrared and microwave spectral regions. This is partly because, in some spectral regions, there are rather few laboratory measurements in conditions close to those in the Earth’s atmosphere; hence understanding of the characteristics of the continuum absorption is still emerging. This is particularly so in the near-infrared and visible, where there has been renewed interest and activity in recent years. In this paper we present a critical review focusing on recent laboratory measurements in two near-infrared window regions (centred on 4700 and 6300 cm−1) and include reference to the window centred on 2600 cm−1 where more measurements have been reported. The rather few available measurements, have used Fourier transform spectroscopy (FTS), cavity ring down spectroscopy, optical-feedback – cavity enhanced laser spectroscopy and, in very narrow regions, calorimetric interferometry. These systems have different advantages and disadvantages. Fourier Transform Spectroscopy can measure the continuum across both these and neighbouring windows; by contrast, the cavity laser techniques are limited to fewer wavenumbers, but have a much higher inherent sensitivity. The available results present a diverse view of the characteristics of continuum absorption, with differences in continuum strength exceeding a factor of 10 in the cores of these windows. In individual windows, the temperature dependence of the water vapour self-continuum differs significantly in the few sets of measurements that allow an analysis. The available data also indicate that the temperature dependence differs significantly between different near-infrared windows. These pioneering measurements provide an impetus for further measurements. Improvements and/or extensions in existing techniques would aid progress to a full characterisation of the continuum – as an example, we report pilot measurements of the water vapour self-continuum using a supercontinuum laser source coupled to an FTS. Such improvements, as well as additional measurements and analyses in other laboratories, would enable the inclusion of the water vapour continuum in future spectroscopic databases, and therefore allow for a more reliable forward modelling of the radiative properties of the atmosphere. It would also allow a more confident assessment of different theoretical descriptions of the underlying cause or causes of continuum absorption.

THE COMPTON-THICK SEYFERT 2 NUCLEUS OF NGC 3281: TORUS CONSTRAINTS FROM THE 9.7 mu m SILICATE ABSORPTION

We present mid-infrared (mid-IR) spectra of the Compton-thick Seyfert 2 galaxy NGC 3281, obtained with the Thermal-Region Camera Spectrograph at the Gemini-South telescope. The spectra present a very deep silicate absorption at 9.7 mu m, and [S IV] 10.5 mu m and [Ne II] 12.7 mu m ionic lines, but no evidence of polycyclic aromatic hydrocarbon emission. We find that the nuclear optical extinction is in the range 24 mag <= A(V) <= 83 mag. A temperature T = 300 K was found for the blackbody dust continuum component of the unresolved 65 pc nucleus and the region at 130 pc SE, while the region at 130 pc NW reveals a colder temperature (200 K). We describe the nuclear spectrum of NGC 3281 using a clumpy torus model that suggests that the nucleus of this galaxy hosts a dusty toroidal structure. According to this model, the ratio between the inner and outer radius of the torus in NGC 3281 is R(0)/R(d) = 20, with 14 clouds in the equatorial radius with optical depth of tau(V) = 40 mag. We would be looking in the direction of the torus equatorial radius (i = 60 degrees), which has outer radius of R(0) similar to 11 pc. The column density is N(H) approximate to 1.2 x 10(24) cm(-2) and the iron K alpha equivalent width (approximate to 0.5-1.2 keV) is used to check the torus geometry. Our findings indicate that the X-ray absorbing column density, which classifies NGC 3281 as a Compton-thick source, may also be responsible for the absorption at 9.7 mu m providing strong evidence that the silicate dust responsible for this absorption can be located in the active galactic nucleus torus.

Conversion coefficients from air kerma to personal dose equivalent in mammography

In this work, the scattered X-ray beams produced by a mammography unit with a Mo/Mo, Mo/Rh and W/Rh anode/filter combinations were applied in the evaluation of the Hp(10, 0) and mean conversion coefficients from air kerma to the personal dose equivalent ((C) over barH(p(10,0 degrees))). The higher values of H(p)(10,0 degrees) are related to the Mo/Rh combination whereas the lower ones are for the W/Rh target/filter. (C) over barH(p(10,0 degrees)) values are in the range 0.19-0.54 Sv/Gy, where the higher values comprise the W/Rh combination. (C) 2009 Elsevier Ltd. All rights reserved.

Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010

Solvent effects on the electronic absorption spectrum of camphor using continuum, discrete or explicit approaches

We address the effect of solvation on the lowest electronic excitation energy of camphor. The solvents considered represent a large variation in-solvent polarity. We consider three conceptually different ways of accounting for the solvent using either an implicit, a discrete or an explicit solvation model. The solvatochromic shifts in polar solvents are found to be in good agreement with the experimental data for all three solvent models. However, both the implicit and discrete solvation models are less successful in predicting solvatochromic shifts for solvents of low polarity. The results presented suggest the importance of using explicit solvent molecules in the case of nonpolar solvents. (C) 2009 Elsevier B.V. All rights reserved.

Performance of GEANT4 in dosimetry applications: Calculation of X-ray spectra and kerma-to-dose equivalent conversion coefficients

In order to validate the Geant4 toolkit for dosimetry applications, simulations were performed to calculate conversion coefficients h(10, alpha) from air kerma free-in-air to personal dose equivalent Hp(10, a). The simulations consisted of two parts: the production of X-rays with radiation qualities of narrow and wide spectra, and the interaction of radiation with ICRU tissue-equivalent and ISO water slab phantoms. The half-value layers of the X-ray spectra obtained by simulation were compared with experimental results. Mean energy, spectral resolution, half-value layers and conversion coefficients were compared with ISO reference values. The good agreement between results from simulation and reference data shows that the Geant4 is suitable for dosimetry applications which involve photons with energies in the range of ten to a few hundreds of keV. (C) 2008 Elsevier Ltd. All rights reserved.

Equivalent Circuits and Nanoplasmonics

We show how a circuit analysis, used widely in electrical engineering, finds application to problems of light wave injection and transport in subwavelength structures in the optical frequency range. Lumped circuit and transmission-line analysis may prove helpful in the design of plasmonic devices with standard, functional properties.