A model of melt pond evolution on sea ice

A one-dimensional, thermodynamic, and radiative model of a melt pond on sea ice is presented that explicitly treats the melt pond as an extra phase. A two-stream radiation model, which allows albedo to be determined from bulk optical properties, and a parameterization of the summertime evolution of optical properties, is used. Heat transport within the sea ice is described using an equation describing heat transport in a mushy layer of a binary alloy (salt water). The model is tested by comparison of numerical simulations with SHEBA data and previous modeling. The presence of melt ponds on the sea ice surface is demonstrated to have a significant effect on the heat and mass balance. Sensitivity tests indicate that the maximum melt pond depth is highly sensitive to optical parameters and drainage. INDEX TERMS: 4207 Oceanography: General: Arctic and Antarctic oceanography; 4255 Oceanography: General: Numerical modeling; 4299 Oceanography: General: General or miscellaneous; KEYWORDS: sea ice, melt pond, albedo, Arctic Ocean, radiation model, thermodynamic

Non-steady state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Fast identification algorithms for Gaussian process model

A class identification algorithms is introduced for Gaussian process(GP)models.The fundamental approach is to propose a new kernel function which leads to a covariance matrix with low rank,a property that is consequently exploited for computational efficiency for both model parameter estimation and model predictions.The objective of either maximizing the marginal likelihood or the Kullback–Leibler (K–L) divergence between the estimated output probability density function(pdf)and the true pdf has been used as respective cost functions.For each cost function,an efficient coordinate descent algorithm is proposed to estimate the kernel parameters using a one dimensional derivative free search, and noise variance using a fast gradient descent algorithm. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Analysis of incoherent scatter radar data from non-thermal F-region plasma

A procedure is presented for fitting incoherent scatter radar data from non-thermal F-region ionospheric plasma, using theoretical spectra previously predicted. It is found that values of the shape distortion factor D∗, associated with deviations of the ion velocity distribution from a Maxwellian distribution, and ion temperatures can be deduced (the results being independent of the path of iteration) if the angle between the line-of-sight and the geomagnetic field is larger than about 15–20°. The procedure can be used with one or both of two sets of assumptions. These concern the validity of the adopted model for the line-of-sight ion velocity distribution in the one case or for the full three-dimensional ion velocity distribution function in the other. The distribution function employed was developed to describe the line-of-sight velocity distribution for large aspect angles, but both experimental data and Monte Carlo simulations indicate that the form of the field-perpendicular distribution can also describe the distribution at more general aspect angles. The assumption of this form for the line-of-sight velocity distribution at a general aspect angle enables rigorous derivation of values of the one-dimensional, line-of-sight ion temperature. With some additional assumptions (principally that the field-parallel distribution is always Maxwellian and there is a simple relationship between the ion temperature anisotropy and the distortion of the field-perpendicular distribution from a Maxwellian), fits to data for large aspect angles enable determination of line-of-sight temperatures at all aspect angles and hence, of the average ion temperature and the ion temperature anisotropy. For small aspect angles, the analysis is restricted to the determination of the line-of-sight ion temperature because the theoretical spectrum is insensitive to non-thermal effects when the plasma is viewed along directions almost parallel to the magnetic field. This limitation is expected to apply to any realistic model of the ion velocity distribution function and its consequences are discussed. Fit strategies which allow for mixed ion composition are also considered. Examples of fits to data from various EISCAT observing programmes are presented.

On the determination of ion temperature in the auroral F-region ionosphere

Assessment is made of the effect of the assumed form for the ion velocity distribution function on estimates of three-dimensional ion temperature from one-dimensional observations. Incoherent scatter observations by the EISCAT radar at a variety of aspect angles are used to demonstrate features of ion temperature determination and to study the ion velocity distribution function. One form of the distribution function which has recently been widely used In the interpretation of EISCAT measurements, is found to be consistent with the data presented here, in that no deviation from a Maxwellian can be detected for observations along the magnetic field line and that the ion temperature and its anisotropy are accurately predicted. It is shown that theoretical predictions of the anisotropy by Monte Carlo computations are very accurate, the observed value being greater by only a few percent. It is also demonstrated for the case studied that errors of up to 93% are introduced into the ion temperature estimate if the anisotropy is neglected. Observations at an aspect angle of 54.7°, which are not subject to this error, have a much smaller uncertainty (less than 1%) due to the adopted form of the distribution of line-of-sight velocity.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Joint multiple dictionary learning for tensor sparse coding

Traditional dictionary learning algorithms are used for finding a sparse representation on high dimensional data by transforming samples into a one-dimensional (1D) vector. This 1D model loses the inherent spatial structure property of data. An alternative solution is to employ Tensor Decomposition for dictionary learning on their original structural form —a tensor— by learning multiple dictionaries along each mode and the corresponding sparse representation in respect to the Kronecker product of these dictionaries. To learn tensor dictionaries along each mode, all the existing methods update each dictionary iteratively in an alternating manner. Because atoms from each mode dictionary jointly make contributions to the sparsity of tensor, existing works ignore atoms correlations between different mode dictionaries by treating each mode dictionary independently. In this paper, we propose a joint multiple dictionary learning method for tensor sparse coding, which explores atom correlations for sparse representation and updates multiple atoms from each mode dictionary simultaneously. In this algorithm, the Frequent-Pattern Tree (FP-tree) mining algorithm is employed to exploit frequent atom patterns in the sparse representation. Inspired by the idea of K-SVD, we develop a new dictionary update method that jointly updates elements in each pattern. Experimental results demonstrate our method outperforms other tensor based dictionary learning algorithms.

Recent lake-level and outflow variations at Lake Viljandi, Estonia: validation of a coupled lake-catchment modelling scheme for climate change studies

Changes in the depth of Lake Viljandi between 1940 and 1990 were simulated using a lake water and energy-balance model driven by standard monthly weather data. Catchment runoff was simulated using a one-dimensional hydrological model, with a two-layer soil, a single-layer snowpack, a simple representation of vegetation cover and similarly modest input requirements. Outflow was modelled as a function of lake level. The simulated record of lake level and outflow matched observations of lake-level variations (r = 0.78) and streamflow (r = 0.87) well. The ability of the model to capture both intra- and inter-annual variations in the behaviour of a specific lake, despite the relatively simple input requirements, makes it extremely suitable for investigations of the impacts of climate change on lake water balance.

Simulation of long-term thermal characteristics of three Estonian lakes

A one-dimensional surface energy-balance lake model, coupled to a thermodynamic model of lake ice, is used to simulate variations in the temperature of and evaporation from three Estonian lakes: Karujärv, Viljandi and Kirjaku. The model is driven by daily climate data, derived by cubic-spline interpolation from monthly mean data, and was run for periods of 8 years (Kirjaku) up to 30 years (Viljandi). Simulated surface water temperature is in good agreement with observations: mean differences between simulated and observed temperatures are from −0.8°C to +0.1°C. The simulated duration of snow and ice cover is comparable with observed. However, the model generally underpredicts ice thickness and overpredicts snow depth. Sensitivity analyses suggest that the model results are robust across a wide range (0.1–2.0 m−1) of lake extinction coefficient: surface temperature differs by less than 0.5°C between extreme values of the extinction coefficient. The model results are more sensitive to snow and ice albedos. However, changing the snow (0.2–0.9) and ice (0.15–0.55) albedos within realistic ranges does not improve the simulations of snow depth and ice thickness. The underestimation of ice thickness is correlated with the overestimation of snow cover, since a thick snow layer insulates the ice and limits ice formation. The overestimation of snow cover results from the assumption that all the simulated winter precipitation occurs as snow, a direct consequence of using daily climate data derived by interpolation from mean monthly data.

Polymorphism and optical properties in [NH4][InSe2]

The solvothermal synthesis and characterization of two indium selenides with stoichiometry [NH4][InSe2] is described. Yellow [NH4][InSe2] (1), which exhibits a layered structure, was initially prepared in an aqueous solution of trans-1,4-diaminocyclohexane, and subsequently using a concentrated ammonia solution. A red polymorph of one-dimensional character, [NH4][InSe2] (2), was obtained using 3,5-dimethylpyridine as solvent. [NH4][InSe2] (1) crystallizes in the non-centrosymmetric space group Cc (a=11.5147(6), b=11.3242(6), c=15.9969(9) Å and β=100.354(3)°). The structural motif of the layers is the In4Se10 adamantane unit, composed of four corner-linked InSe4 tetrahedra. These units are linked by their corners, forming [InSe2]− layers which are stacked back to back along the c-direction, and interspaced by [NH4]+cations. The one-dimensional polymorph, (2), crystallizes in the tetragonal space group, I4/mcm (a=8.2519(16), c=6.9059 (14) Å). This structure contains infinite chains of edge-sharing InSe4 tetrahedra separated by [NH4]+ cations.

A systematic method of parameterisation estimation using data assimilation

In numerical weather prediction, parameterisations are used to simulate missing physics in the model. These can be due to a lack of scientific understanding or a lack of computing power available to address all the known physical processes. Parameterisations are sources of large uncertainty in a model as parameter values used in these parameterisations cannot be measured directly and hence are often not well known; and the parameterisations themselves are also approximations of the processes present in the true atmosphere. Whilst there are many efficient and effective methods for combined state/parameter estimation in data assimilation (DA), such as state augmentation, these are not effective at estimating the structure of parameterisations. A new method of parameterisation estimation is proposed that uses sequential DA methods to estimate errors in the numerical models at each space-time point for each model equation. These errors are then fitted to pre-determined functional forms of missing physics or parameterisations that are based upon prior information. We applied the method to a one-dimensional advection model with additive model error, and it is shown that the method can accurately estimate parameterisations, with consistent error estimates. Furthermore, it is shown how the method depends on the quality of the DA results. The results indicate that this new method is a powerful tool in systematic model improvement.

Modeling study of the aspect ratio influence on urban canopy energy fluxes with a modified wall-canyon energy budget scheme

The influence of the aspect ratio (building height/street canyon width) and the mean building height of cities on local energy fluxes and temperatures is studied by means of an Urban Canopy Model (UCM) coupled with a one-dimensional second-order turbulence closure model. The UCM presented is similar to the Town Energy Balance (TEB) model in most of its features but differs in a few important aspects. In particular, the street canyon walls are treated separately which leads to a different budget of radiation within the street canyon walls. The UCM has been calibrated using observations of incoming global and diffuse solar radiation, incoming long-wave radiation and air temperature at a site in So Paulo, Brazil. Sensitivity studies with various aspect ratios have been performed to assess their impact on urban temperatures and energy fluxes at the top of the canopy layer. In these simulations, it is assumed that the anthropogenic heat flux and latent heat fluxes are negligible. Results show that the simulated net radiation and sensible heat fluxes at the top of the canopy decrease and the stored heat increases as the aspect ratio increases. The simulated air temperature follows the behavior of the sensible heat flux. (C) 2010 Elsevier Ltd. All rights reserved.

A numerical investigation of the atmosphere-ocean thermal contrast over the coastal upwelling region of Cabo Frio, Brazil

An one-dimensional atmospheric second order closure model, coupled to an oceanic mixed layer model, is used to investigate the short term variation of the atmospheric and oceanic boundary layers in the coastal upwelling area of Cabo Frio, Brazil (23 degrees S, 42 degrees 08`W). The numerical simulations were carried out to evaluate the impact caused by the thermal contrast between atmosphere and ocean on the vertical extent and other properties of both atmospheric and oceanic boundary layers. The numerical simulations were designed taking as reference the observations carried out during the passage of a cold front that disrupted the upwelling regime in Cabo Frio in July of 1992. The simulations indicated that in 10 hours the mechanical mixing, sustained by a constant background flow of 10 in s(-1), increases the atmospheric boundary layer in 214 in when the atmosphere is initially 2 K warmer than the ocean (positive thermal contrast observed during upwelling regime). For an atmosphere initially -2 K colder than the ocean (negative thermal contrast observed during passage of the cold front), the incipient thermal convection intensifies the mechanical mixing increasing the vertical extent of the atmospheric boundary layer in 360 in. The vertical evolution of the atmospheric boundary layer is consistent with the observations carried out in Cabo Frio during upwelling condition. When the upwelling is disrupted, the discrepancy between the simulated and observed atmospheric boundary layer heights in Cabo Frio during July of 1992 increases considerably. During the period of 10 hours, the simulated oceanic mixed layer deepens 2 in and 5.4 in for positive and negative thermal contrasts of 2 K and -2 K, respectively. In the latter case, the larger vertical extent of the oceanic mixed layer is due to the presence of thermal convection in the atmospheric boundary layer, which in turn is associated to the absence of upwelling caused by the passage of cold fronts in Cabo Frio.

A METHOD FOR THE STUDY OF ACCRETION DISK EMISSION IN CATACLYSMIC VARIABLES. I. THE MODEL

We have developed a spectrum synthesis method for modeling the ultraviolet (UV) emission from the accretion disk from cataclysmic variables (CVs). The disk is separated into concentric rings, with an internal structure from the Wade & Hubeny disk-atmosphere models. For each ring, a wind atmosphere is calculated in the comoving frame with a vertical velocity structure obtained from a solution of the Euler equation. Using simple assumptions, regarding rotation and the wind streamlines, these one-dimensional models are combined into a single 2.5-dimensional model for which we compute synthetic spectra. We find that the resulting line and continuum behavior as a function of the orbital inclination is consistent with the observations, and verify that the accretion rate affects the wind temperature, leading to corresponding trends in the intensity of UV lines. In general, we also find that the primary mass has a strong effect on the P Cygni absorption profiles, the synthetic emission line profiles are strongly sensitive to the wind temperature structure, and an increase in the mass-loss rate enhances the resonance line intensities. Synthetic spectra were compared with UV data for two high orbital inclination nova-like CVs-RW Tri and V347 Pup. We needed to include disk regions with arbitrary enhanced mass loss to reproduce reasonably well widths and line profiles. This fact and a lack of flux in some high ionization lines may be the signature of the presence of density-enhanced regions in the wind, or alternatively, may result from inadequacies in some of our simplifying assumptions.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.