Viscous overstability and eccentricity evolution in three-dimensional gaseous discs

We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent, and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes.     

A comparison of local simulations and reduced models of MRI-induced turbulence

We run mean-field shearing-box numerical simulations with a temperature-dependent resistivity and compare them to a reduced dynamical model. Our simulations reveal the co-existence of two quasi-steady states, a 'quiet' state and an 'active' turbulent state, confirming the predictions of the reduced model. The initial conditions determine on which state the simulation ultimately settles. The active state is strongly influenced by the geometry of the computational box and the thermal properties of the gas. Cubic domains support permanent channel flows, bar-shaped domains exhibit eruptive behaviour, and horizontal slabs give rise to infrequent channels. Meanwhile, longer cooling time-scales lead to higher saturation amplitudes.     

Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling

In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes.     

Hydrodynamical simulations of viscous overstability in Saturn’s rings

We perform axisymmetric hydrodynamical simulations that describe the nonlinear outcome of the viscous overstability in dense planetary rings. These simulations are particularly relevant for Cassini observations of fine-scale structure in Saturn’s A and B-ring, which take the form of periodic microstructure on the 0.1 km scale, and irregular larger-scale variations on 1-10 km. Nonlinear wavetrains dominate all the simulations, and we associate them with the observed periodic microstructure. The waves can undergo small chaotic fluctuations in their phase and amplitude, and may be punctuated by more formidable ‘wave defects’ distributed on longer scales. It is unclear, however, whether the defects are connected to the irregular larger-scale variations observed by Cassini. The long-term behaviour of the simulations is dominated by the imposed boundary conditions, and more generally by the limitations of the local model we use: the shearing box. When periodic boundary conditions are imposed, the system eventually settles on a uniform travelling wave of a predictable wavelength, while reflecting boundaries, and boundaries with buffer zones, maintain a disordered saturated state. The simulations omit self-gravity, though we examine its influence in future work.     

Computing cross-isotherm volume transports from ocean temperature observations and surface heat fluxes,with application to the Barents Sea inflow

A method for determining the cross-isotherm ocean transport from surface heat flux and ocean temperature data is derived. By computing the volume flux through the isotherm that extend from 19°E, 74°N to the eastern part of the Kola Peninsula, the flow through the western entrance of the Barents Sea south of 74°N is estimated. Using three different surface heat flux datasets, the inflow is found to range from 2.9 to 4.5 Sv in winter (October–March) and from 0.4 to 1.4 Sv in summer (April–September; 1 Sv=10⁶ m³ s⁻¹). The seasonal variations are stronger than indicated by results from direct current measurements, probably because the seasonal cycle of the surface heat fluxes is overestimated along the considered isotherm. The annual mean inflow ranges from 1.9 to 2.2 Sv during a cold period (1986–1988), and from 2.4 to 3.0 Sv during a warm period (1990–1992), close to reported observations.     

Estimation of the Spatial Variation in Evapotranspiration based on Landsat TM and NOAA Satellite Imagery

Søgaard, Henrik: Estimation of the Spatial Variation in Evapotranspiration based on Landsat TM and NOAA Satellite Imagery. Geografisk Tidsskrift 92: 80–85. Copenhagen 1992.

During the last decade, the use of satellite imagery for monitoring water and energy budgets has gained increasing interest. Based on ground reference data collected above a barley field located near Viborg in Jutland, the so-called simplified relationship between net radiation, temperature, and evapotranspiration was examined. It was found that the difference between evapotranspiration and net radiation depends on both the temperature difference between the surface and the air, and the surface roughness. The derived relationship was applied for monitoring evapotranspiration on the basis of surface temperature measured by the NOAA- satellites. This paper will present this study and examine the resolution problem caused by the field size being less in area than the 1 km by 1 km covered by a single NOAA picture element. For a selected day in July, this was done by comparing the NOAA data with Landsat TM-data which has a 120 m resolution in the thermal band.     

The coronal source of the slow solar wind

Periods of very low solar wind velocity at 1 AU, during the interval from 1977 to 1983, are identified and mapped back to the coronal source surface at 2.5 R . In total 25 such low-velocity events were found. Inferred source locations were characterized with respect to their position relative to the coronal neutral line. The study showed that in 17 out of 25 cases the slow solar wind originated across a coronal neutral line. In the remaining cases the source was either along the neutral line or insides a warp. A prediction of the IMF polarity to be expected at Earth, from the computed coronal magnetic field, was also done. It failed clearly only in four cases out of 25 events. In three cases the prediction was uncertain because of missing data. Possible explanations of why the potential model sometimes predicts a wrong polarity are discussed.