Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Water vapour continuum absorption in near-infrared windows derived from laboratory measurements

In most near-infrared atmospheric windows, absorption of solar radiation is dominated by the water vapor self-continuum and yet there is a paucity of measurements in these windows. We report new laboratory measurements of the self-continuum absorption at temperatures between 293 and 472 K and pressures from 0.015 to 5 atm in four near-infrared windows between 1 and 4 m (10000-2500 cm-1); the measurements are made over a wider range of wavenumber, temperatures and pressures than any previous measurements. They show that the self-continuum in these windows is typically one order of magnitude stronger than given in representations of the continuum widely used in climate and weather prediction models. These results are also not consistent with current theories attributing the self continuum within windows to the far-wings of strong spectral lines in the nearby water vapor absorption bands; we suggest that they are more consistent with water dimers being the major contributor to the continuum. The calculated global-average clear-sky atmospheric absorption of solar radiation is increased by 0.75 W/m2 (which is about 1% of the total clear-sky absorption) by using these new measurements as compared to calculations with the MT_CKD-2.5 self-continuum model.

Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

The water vapour continuum: brief history and recent developments

The water vapour continuum is characterised by absorption that varies smoothly with wavelength, from the visible to the microwave. It is present within the rotational and vibrational–rotational bands of water vapour, which consist of large numbers of narrow spectral lines, and in the many ‘windows’ between these bands. The continuum absorption in the window regions is of particular importance for the Earth’s radiation budget and for remote-sensing techniques that exploit these windows. Historically, most attention has focused on the 8–12 μm (mid-infrared) atmospheric window, where the continuum is relatively well-characterised, but there have been many fewer measurements within bands and in other window regions. In addition, the causes of the continuum remain a subject of controversy. This paper provides a brief historical overview of the development of understanding of the continuum and then reviews recent developments, with a focus on the near-infrared spectral region. Recent laboratory measurements in near-infrared windows, which reveal absorption typically an order of magnitude stronger than in widely used continuum models, are shown to have important consequences for remote-sensing techniques that use these windows for retrieving cloud properties.

A continuum model of a fishing net

A working report for the Department of Agriculture and Fisheries, Scotland, Marine Laboratory Aberdeen

Absolute high spectral resolution measurements of surface solar radiation for detection of water vapour continuum absorption

Solar-pointing Fourier transform infrared (FTIR) spectroscopy offers the capability to measure both the fine scale and broadband spectral structure of atmospheric transmission simultaneously across wide spectral regions. It is therefore suited to the study of both water vapour monomer and continuum absorption behaviours. However, in order to properly address this issue, it is necessary to radiatively calibrate the FTIR instrument response. A solar-pointing high-resolution FTIR spectrometer was deployed as part of the ‘Continuum Absorption by Visible and Infrared radiation and its Atmospheric Relevance’ (CAVIAR) consortium project. This paper describes the radiative calibration process using an ultra-high-temperature blackbody and the consideration of the related influence factors. The result is a radiatively calibrated measurement of the solar irradiation at the ground across the IR region from 2000 to 10 000 cm−1 with an uncertainty of between 3.3 and 5.9 per cent. This measurement is shown to be in good general agreement with a radiative-transfer model. The results from the CAVIAR field measurements are being used in ongoing studies of atmospheric absorbers, in particular the water vapour continuum.

Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements

For a long time, it has been believed that atmospheric absorption of radiation within wavelength regions of relatively high infrared transmittance (so-called ‘windows’) was dominated by the water vapour self-continuum, that is, spectrally smooth absorption caused by H2O−H2O pair interaction. Absorption due to the foreign continuum (i.e. caused mostly by H2O−N2 bimolecular absorption in the Earth's atmosphere) was considered to be negligible in the windows. We report new retrievals of the water vapour foreign continuum from high-resolution laboratory measurements at temperatures between 350 and 430 K in four near-infrared windows between 1.1 and 5 μm (9000–2000 cm−1). Our results indicate that the foreign continuum in these windows has a very weak temperature dependence and is typically between one and two orders of magnitude stronger than that given in representations of the continuum currently used in many climate and weather prediction models. This indicates that absorption owing to the foreign continuum may be comparable to the self-continuum under atmospheric conditions in the investigated windows. The calculated global-average clear-sky atmospheric absorption of solar radiation is increased by approximately 0.46 W m−2 (or 0.6% of the total clear-sky absorption) by using these new measurements when compared with calculations applying the widely used MTCKD (Mlawer–Tobin–Clough–Kneizys–Davies) foreign-continuum model.

Climate change and coupling of macronutrient cycles along the atmospheric, terrestrial, freshwater and estuarine continuum

This paper provides an introduction to the Special Issue on “Climate Change and Coupling of Macronutrient Cycles along the Atmospheric, Terrestrial, Freshwater and Estuarine Continuum”, dedicated to Colin Neal on his retirement. It is not intended to be a review of this vast subject, but an attempt to synthesize some of the major findings from the 22 contributions to the Special Issue in the context of what is already known. The major research challenges involved in understanding coupled macronutrient cycles in these environmental media are highlighted, and the difficulties of making credible predictions of the effects of climate change are discussed. Of particular concern is the possibility of interactions which will enhance greenhouse gas concentrations and provide positive feedback to global warming.

Near-infrared water vapour self-continuum at close to room temperature

The gaseous absorption of solar radiation within near-infrared atmospheric windows in the Earth's atmosphere is dominated by the water vapour continuum. Recent measurements by Baranov et al. (2011) [17] in 2500 cm−1 (4 μm) window and by Ptashnik et al. (2011) [18] in a few near-infrared windows revealed that the self-continuum absorption is typically an order of magnitude stronger than given by the MT_CKD continuum model prior to version 2.5. Most of these measurements, however, were made at elevated temperatures, which makes their application to atmospheric conditions difficult. Here we report new laboratory measurements of the self-continuum absorption at 289 and 318 K in the near-infrared spectral region 1300–8000 cm−1, using a multipass 30 m base cell with total optical path 612 m. Our results confirm the main conclusions of the previous measurements both within bands and in windows. Of particular note is that we present what we believe to be the first near-room temperature measurement using Fourier Transform Spectrometry of the self-continuum in the 6200 cm−1 (1.6 μm) window, which provides tentative evidence that, at such temperatures, the water vapour continuum absorption may be as strong as it is in 2.1 μm and 4 μm windows and up to 2 orders of magnitude stronger than the MT_CKD-2.5 continuum. We note that alternative methods of measuring the continuum in this window have yielded widely differing assessment of its strength, which emphasises the need for further measurements.

Invisible and visible language planning: ideological factors in the family language policy of Chinese immigrant families in Quebec

This ethnographic inquiry examines how family languages policies are planned and developed in ten Chinese immigrant families in Quebec, Canada, with regard to their children’s language and literacy education in three languages, Chinese, English, and French. The focus is on how multilingualism is perceived and valued, and how these three languages are linked to particular linguistic markets. The parental ideology that underpins the family language policy, the invisible language planning, is the central focus of analysis. The results suggest that family language policies are strongly influenced by socio-political and economical factors. In addition, the study confirms that the parents’ educational background, their immigration experiences and their cultural disposition, in this case pervaded by Confucian thinking, contribute significantly to parental expectations and aspirations and thus to the family language policies.

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.